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Title: Ancient and modern engineering and the Isthmian canal
Author: William Hubert Burr
Release date: April 19, 2025 [eBook #75910]
Language: English
Original publication: New York: J. Wiley & Sons, 1903
Credits: Peter Becker and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)
*** START OF THE PROJECT GUTENBERG EBOOK ANCIENT AND MODERN ENGINEERING AND THE ISTHMIAN CANAL ***
Transcriber’s Notes:
Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
Equal signs “=” before and after a word or phrase indicate =bold=
in the original text.
Small capitals have been converted to SOLID capitals.
Illustrations have been moved so they do not break up paragraphs.
Deprecated spellings have been preserved.
Typographical and punctuation errors have been silently corrected.
ANCIENT
AND
MODERN ENGINEERING
AND
THE ISTHMIAN CANAL.
BY
WILLIAM H. BURR, C.E.,
_Professor of Civil-Engineering in Columbia University;
Member of the American Society of Civil Engineers and of
the Institution of Civil Engineers of Great Britain._
_FIRST EDITION._
FIRST THOUSAND.
NEW YORK:
JOHN WILEY & SONS.
LONDON: CHAPMAN & HALL, LIMITED.
1903.
Copyright, 1902,
BY
WILLIAM H. BURR
ROBERT DRUMMOND, PRINTER, NEW YORK.
INTRODUCTION.
This book is the outcome of a course of six lectures delivered at the
Cooper Union in the city of New York in February and March, 1902,
under the auspices of Columbia University. It seemed desirable by the
President of the University that the subject-matter of the lectures
should be prepared for ultimate publication. The six Parts of the
book, therefore, comprise the substance of the six lectures, suitably
expanded for the purposes of publication.
It may be interesting to state that the half-tone illustrations
have, with scarcely an exception, been prepared from photographs of
the actual subjects illustrated. All such illustrations in Parts V
and VI devoted to the Nicaragua and Panama Canal routes are made
from photographs at the various locations by members of the force of
the Isthmian Canal Commission; they are, therefore, absolutely true
representations of the actual localities to which they apply.
For other illustrations the author wishes to express his indebtedness
to Messrs. G. P. Putnam’s Sons, Messrs. Turneaure and Russell, John
Wiley & Sons, The Morrison-Jewell Filtration Company, Mr. H. M. Sperry,
Signal Engineer, _The Engineering News_, _The Railroad Gazette_, The
American Society of Civil Engineers, The Standard Switch and Signal
Company, The Baldwin Locomotive Works, the American Locomotive Works,
Mr. Clemens Herschel, and the International Pump Company, and to
others from whom the author has received courtesies which he deeply
appreciates.
The classification or division of the matter of the text, and the table
of contents, have been made so complete, with a view to convenience
even of the desultory reader in seeking any particular subject or
paragraph, that no index has been prepared, as it is believed that the
table of contents, as arranged, practically supplies the information
ordinarily given by a comprehensive index.
Complete and detailed treatments of the purely technical matters
covered by Part II will be found in the author’s “Elasticity and
Resistance of Materials” and in his “Stresses in Bridge and Roof
Trusses, Arched Ribs and Suspension Bridges.”
W. H. B.
COLUMBIA UNIVERSITY,
October 24, 1902.
CONTENTS.
PART I.
_ANCIENT CIVIL-ENGINEERING WORKS._
CHAPTER I.
ART. PAGE
1. Introductory 1
2. Hydraulic Works of Chaldea and Egypt 2
3. Structural Works in Chaldea and Egypt 4
4. Ancient Maritime Commerce 7
5. The Change of the Nile Channel at Memphis 8
6. The Pyramids 8
7. Obelisks, Labyrinths, and Temples 12
8. Nile Irrigation 13
9. Prehistoric Bridge-building 14
10. Ancient Brick-making 15
11. Ancient Arches 16
CHAPTER II.
12. The Beginnings of Engineering Works of Record 19
13. The Appian Way and other Roman Roads 20
14. Natural Advantages of Rome in Structural Stones 22
15. Pozzuolana Hydraulic Cement 24
16. Roman Bricks and Masonry 25
17. Roman Building Laws 27
18. Old Roman Walls 27
19. The Servian Wall 28
20. Old Roman Sewers 29
21. Early Roman Bridges 31
22. Bridge of Alcantara 35
23. Military Bridges of the Romans 35
24. The Roman Arch 36
CHAPTER III.
25. The Roman Water-supply 37
26. The Roman Aqueducts 38
27. Anio Vetus 39
28. Tepula 40
29. Virgo 40
30. Alsietina 40
31. Claudia 41
32. Anio Novus 42
33. Lengths and Dates of Aqueducts 42
34. Intakes and Settling-basins 43
35. Delivery-tanks 44
36. Leakage and Lining of Aqueducts 44
37. Grade of Aqueduct Channels 45
38. Qualities of Roman Waters 46
39. Combined Aqueducts 46
40. Property Rights in Roman Waters 46
41. Ajutages and Unit of Measurement 47
42. The Stealing of Water 49
43. Aqueduct Alignment and Design of Siphons 49
CHAPTER IV.
44. Antiquity of Masonry Aqueducts 52
45. Pont du Gard 52
46. Aqueducts at Segovia, Metz, and other Places 53
47. Tunnels 54
48. Ostia, the Harbor of Rome 56
49. Harbors of Claudius and Trajan 58
CHAPTER V.
50. Ancient Engineering Science 60
51. Ancient Views of the Physical Properties of Materials 61
52. Roman Civil Engineers Searching for Water 62
53. Locating and Designing Conduits 63
54. Siphons 64
55. Healthful Sites for Cities 65
56. Foundations of Structures 65
57. Pozzuolana and Sand 66
58. Lime Mortar 66
59. Roman Bricks according to Vitruvius 66
60. Roman Timber 67
61. The Rules of Vitruvius for Harbors 67
62. The Thrusts of Arches and Earth;
Retaining-walls and Pavements 68
63. The Professional Spirit of Vitruvius 68
64. Mechanical Appliances of the Ancients 69
65. Unlimited Forces and Time 69
PART II.
_BRIDGES._
CHAPTER VI.
66. Introductory 70
67. First Cast-iron Arch 70
68. Early Timber Bridges in America 71
69. Town Lattice Bridge 72
70. Howe Truss 74
71. Pratt Truss 76
72. Squire Whipple’s Work 77
73. Character of Work of Early Builders 77
CHAPTER VII.
74. Modern Bridge Theory 78
75. The Stresses in Beams 79
76. Vertical and Horizontal Shearing Stresses 80
77. Law of Variation of Stresses of Tension and Compression 82
78. Fundamental Formulæ of Theory of Beams 83
79. Practical Applications 85
80. Deflection 86
81. Bending Moments and Shears with Single Load 87
82. Bending Moments and Shears with any System of Loads 89
83. Bending Moments and Shears with Uniform Loads 92
84. Greatest Shear for Uniform Moving Load 94
85. Bending Moments and Shears for Cantilever Beams 96
86. Greatest Bending Moment with any System of Loading 97
87. Applications to Rolled Beams 99
CHAPTER VIII.
88. The Truss Element or Triangle of Bracing 100
89. Simple Trusses 101
90. The Pratt Truss Type 102
91. The Howe Truss Type 105
92. The Simple Triangular Truss 106
93. Through- and Deck-Bridges 108
94. Multiple Systems of Triangulation 108
95. Influence of Mill and Shop Capacity on Length of Span 109
96. Trusses with Broken or Inclined Chords 109
97. Position of any Moving Load for Greatest Webb Stress 110
98. Application of Criterions for both Chord and Web Stresses 111
99. Influence Lines 112
100. Influence Lines for Moments both for Beams and Trusses 113
101. Influence Lines for Shears both for Beams and Trusses 115
102. Application of Influence-line Method to Trusses 118
CHAPTER IX.
103. Lateral Wind Pressure on Trusses 122
104. Upper and Lower Lateral Bracing 124
105. Bridge Plans and Shopwork 125
106. Erection of Bridges 126
107. Statically Determinate Trusses 126
108. Continuous Beams and Trusses—Theorem of Three Moments 128
109. Application to Draw- or Swing-bridges 130
110. Special Method for Deflection of Trusses 130
111. Application of Method for Deflection of Triangular Frame 133
112. Application of Method for Deflection to Truss 134
113. Method of Least Work 137
114. Application of Method of Least Work to General Problem 138
115. Application of Method of Least Work to Trussed Beam 139
116. Removal of Indetermination by Methods of Least Work
and Deflection 141
CHAPTER X.
117. The Arched Rib, of both Steel and Masonry 142
118. Arched Rib with Ends Fixed 144
119. Arched Rib with Ends Jointed 144
120. Arched Rib with Crown and Ends Jointed 145
121. Relative Stiffness of Arched Ribs 145
122. General Conditions of Analysis of Arched Ribs 146
CHAPTER XI.
123. Beams of Combined Steel and Concrete 149
CHAPTER XII.
124. The Masonry Arch 154
125. Old and New Theories of the Arch 155
126. Stress Conditions in the Arch-ring 158
127. Applications to an Actual Arch 158
128. Intensities of Pressure in the Arch-ring 162
129. Permissible Working Pressures 163
130. Largest Arch Spans 163
CHAPTER XIII.
131. Cantilever and Stiffened Suspension Bridges 166
132. Cantilever Bridges 166
133. Stiffened Suspension Bridges 168
134. The Stiffening Truss 170
135. Location and Arrangement of Stiffening Trusses 171
136. Division of Load between Cables and Stiffening Truss 173
137. Stresses in Cables and Moments and Shears in Trusses 174
138. Thermal Stresses and Moments in Stiffened
Suspension Bridges 175
139. Formation of the Cables 176
140. Economical Limits of Spans 177
PART III.
_WATER-WORKS FOR CITIES AND TOWNS._
CHAPTER XIV.
141. Introductory 179
142. First Steam-pumps 180
143. Water-supply of Paris and London 181
144. Early Water-pipes 181
145. Earliest Water-supplies in the United States 182
146. Quality and Uses of Public Water-supply 182
147. Amount of Public Water-supply 183
148. Increase of Daily Consumption and the Division
of that Consumption 183
149. Waste of Public Water 186
150. Analysis of Reasonable Daily Supply per Head of Population 188
151. Actual Daily Consumption in Cities of the United States 189
152. Actual Daily Consumption in Foreign Cities 191
153. Variations in Rate of Daily Consumption 192
154. Supply of Fire-streams 193
CHAPTER XV.
155. Waste of Water, Particularly in the City of New York 196
156. Division of Daily Consumption in the City of New York 197
157. Daily Domestic Consumption 198
158. Incurable and Curable Wastes 199
159. Needless and Incurable Waste in City of New York 200
160. Increase in Population 200
161. Sources of Public Water-supplies 202
162. Rain-gauges and their Records 204
163. Elements of Annual and Monthly Rainfall 204
164. Hourly or Less Rates of Rainfall 207
165. Extent of Heavy Rain-storms 207
166. Provision for Low Rainfall Years 208
167. Available Portion of Rainfall or Run-off of Watersheds 209
168. Run-off of Sudbury Watershed 211
169. Run-off of Croton Watershed 211
170. Evaporation from Reservoirs 213
171. Evaporation from the Earth’s Surface 215
CHAPTER XVI.
172. Application of Fitzgerald’s Results to the Croton Watershed 216
173. The Capacity of the Croton Watershed 217
174. Necessary Storage for New York Supply to Compensate
for Deficiency 218
175. No Exact Rule for Storage Capacity 220
176. The Color of Water 221
177. Stripping Reservoir Sites 222
178. Average Depth of Reservoirs should be as
Great as Practicable 224
179. Overturn of Contents of Reservoirs Due to
Seasonal Changes of Temperature 224
180. The Construction of Reservoirs 225
181. Gate-houses, and Pipe-lines in Embankments 229
182. High Masonry Dams 230
CHAPTER XVII.
183. Gravity Supplies 234
184. Masonry Conduits 234
185. Metal Conduits 236
186. General Formula for Discharge of Conduits—Chezy’s Formula 237
187. Kutter’s Formula 239
188. Hydraulic Gradient 241
189. Flow of Water in Large Masonry Conduits 244
190. Flow of Water through Large Closed Pipes 245
191. Change of Hydraulic Gradient by Changing Diameter of Pip 250
192. Control of Flow by Gates at Upper End of Pipe-line 251
193. Flow in Old and New Cast-iron Pipes—Tubercles 251
194. Timber-stave Pipes 253
CHAPTER XVIII.
195. Pumping and Pumps 254
196. Resistances of Pumps and Main—Dynamic Head 258
197. Duty of Pumping-engines 260
198. Data to be Observed in Pumping-engine Tests 261
199. Basis of Computations for Duty 262
200. Heat-units and Ash in 100 Pounds of Coal,
and Amount of Work Equivalent to a Heat-unit 262
201. Three Methods of Estimating Duty 265
202. Trial Test and Duty of Allis Pumping-engine 265
203. Conditions Affecting Duty of Pumping-engines 266
204. Speeds and Duties of Modern Pumping-engines 266
CHAPTER XIX.
205. Distributing-reservoirs and their Capacities 267
206. System of Distributing Mains and Pipes 268
207. Diameters of and Velocities in Distributing Mains and Pipes 269
208. Required Pressures in Mains and Pipes 270
209. Fire-hydrants 270
210. Elements of Distributing Systems 270
CHAPTER XX.
211. Sanitary Improvement of Public Water-supplies 276
212. Improvement by Sedimentation 277
213. Sedimentation Aided by Chemicals 279
214. Amount of Solid Matter Removed by Sedimentation 279
215. Two Methods of Operating Sedimentation-basins 279
216. Sizes and Construction of Settling-basins 280
217. Two Methods of Filtration 281
218. Conditions Necessary for Reduction of Organic Matter 282
219. Slow Filtration through Sand—Intermittent Filtration 283
220. Removal of Bacteria in the Filter 286
221. Preliminary Treatment—Sizes of Sand Grains 286
222. Most Effective Sizes of Sand Grains 288
223. Air and Water Capacities 288
224. Bacterial Efficiency and Purification—Hygienic Efficiency 290
225. Bacterial Activity near Top of Filter 290
226. Rate of Filtration 291
227. Effective Head on Filter 291
228. Constant Rate of Filtration Necessary 292
229. Scraping of Filters 293
230. Introduction of Water to Intermittent Filters 294
231. Effect of Low Temperature 294
232. Choice of Intermittent or Continuous Filtration 294
233. Size and Arrangement of Slow Sand Filters 295
234. Design of Filter-beds 296
235. Covered Filters 299
236. Clear-water Drain-pipes of Filters 299
237. Arrangement of the Sand at Lawrence and Albany 300
238. Velocity of Flow through Sand 302
239. Frequency of Scraping and Amount Filtered between Scrapings 303
240. Cleaning the Clogged Sand 303
241. Controlling or Regulating Apparatus 305
242. Cost of Slow Sand Filters 307
243. Cost of Operation of Albany Filter 308
244. Operation and Cost of Operation of Lawrence Filter 309
245. Sanitary Results of Operation of Lawrence
and Albany Filters 310
246. Rapid Filtration with Coagulants 311
247. Operation of Coagulants 312
248. Principal Parts of Mechanical Filter-plant—Coagulation
and Subsidence 313
249. Amount of Coagulant—Advantageous Effect of Alum
on Organic Matter 314
250. High Heads and Rates for Rapid Filtration 315
251. Types and General Arrangement of Mechanical Filters 316
252. Cost of Mechanical Filters 318
253. Relative Features of Slow and Rapid Filtration 318
PART IV.
_SOME FEATURES OF RAILROAD ENGINEERING._
CHAPTER XXI.
254. Introductory 320
255. Train Resistances 322
256. Grades 322
257. Curves 324
258. Resistance of Curves and Compensation in Grades 324
259. Transition Curves 325
260. Road-bed, including Ties 327
261. Mountain Locations of Railroad Lines 328
262. The Georgetown Loop 331
263. Tunnel-loop Location, Rhætian Railways, Switzerland 331
CHAPTER XXII.
264. Railroad Signalling 335
265. The Pilot Guard 335
266. The Train-Staff 335
267. First Basis of Railroad Signalling 336
268. Code of American Railway Association 337
268_a_. The Block 338
269. Three Classes of Railroad Signals 338
270. The Banner Signal 338
271. The Semaphore 340
272. Colors for Signalling 340
273. Indications of the Semaphore 341
274. General Character of Block System 342
275. Block Systems in Use 343
276. Locations of Signals 344
277. Home, Distant, and Advance Signals 344
278. Typical Working of Auto-controlled Manual System 345
279. General Results 348
280. Distant Signals 349
281. Function of Advance Signals 349
282. Signalling at a Single-track Crossing 350
283. Signalling at a Double-track Crossing 352
284. Signalling for Double-track Junction and Cross-over 352
285. General Observations 353
286. Interlocking-machines 354
287. Methods of Applying Power in Systems of Signalling 357
288. Train-staff Signalling 358
CHAPTER XXIII.
289. Evolution of the Locomotive 363
290. Increase of Locomotive Weight and Rate
of Combustion of Fuel 365
291. Principal Parts of a Modern Locomotive 366
292. The Wootten Fire-box and Boiler 367
293. Locomotives with Wootten Boilers 370
294. Recent Improvements in Locomotive Design 372
295. Compound Locomotives with Tandem Cylinders 373
296. Evaporative Efficiency of Different Rates of Combustion 375
296_a_. Tractive Force of a Locomotive 376
297. Central Atlantic Type of Locomotive 378
298. Consolidation Engine, N. Y. C. & H. R. R. R. 379
299. P., B. & L. E. Consolidation Engine 380
300. L. S. & M. S. Fast Passenger Engine 381
301. Northern Pacific Tandem Compound Locomotive 382
302. Union Pacific Vauclain Compound Locomotive 384
303. Southern Pacific Mogul with Vanderbilt Boiler 384
304. The “Soo” Decapod Locomotive 385
305. The A., T. & S. F. Decapod, the Heaviest Locomotive
yet Built 386
306. Comparison of Some of the Heaviest Locomotives in Use 389
PART V.
_THE NICARAGUA ROUTE FOR A SHIP-CANAL._
307. Feasibility of Nicaragua Route 390
308. Discovery of Lake Nicaragua 390
309. Early Maritime Commerce with Lake Nicaragua 391
310. Early Examination of Nicaragua Route 392
311. English Invasion of Nicaragua 392
312. Atlantic and Pacific Ship-canal Company 392
313. Survey and Project of Col. O. W. Childs 393
314. The Project of the Maritime Canal Company 393
315. The Work of the Ludlow and Nicaragua Canal Commissions 394
316. The Route of the Isthmian Canal Commission 395
317. Standard Dimensions of Canal Prism 396
318. The San Juan Delta 397
319. The San Carlos and Serapiqui Rivers 398
320. The Rapids and Castillo Viejo 399
321. The Upper San Juan 399
322. The Rainfall from Greytown to the Lake 399
323. Lake-surface Elevation and Slope of the River 400
324. Discharges of the San Juan, San Carlos, Serapiqui 401
325. Navigation on the San Juan 401
326. The Canal Line through the Lake and Across the West Side 402
327. Character of the Country West of the Lake 403
328. Granada to Managua, thence to Corinto 404
329. General Features of the Route 404
330. Artificial Harbor at Greytown 405
331. Artificial Harbor at Brito 407
332. From Greytown Harbor to Lock No. 2 408
333. From Lock No. 2 to the Lake 409
334. Fort San Carlos to Brito 410
335. Examinations by Borings 411
336. Classification and Estimate of Quantities 412
337. Classification and Unit Prices 413
338. Curvature of the Route 413
339. The Conchuda Dam and Wasteway 414
340. Regulation of the Lake Level 417
341. Evaporation and Lockage 418
342. The Required Slope of the Canalized River Surface 419
343. All Surplus Water to be Discharged over the Conchuda Dam 419
344. Control of the Surface Elevation of the Lake 420
345. Greatest Velocities in Canalized River 425
346. Wasteways or Overflows 427
347. Temporary Harbors and Service Railroad 427
348. Itemized Statement of Length and Cost 427
PART VI.
_THE PANAMA ROUTE FOR A SHIP-CANAL._
349. The First Panama Transit Line 429
350. Harbor of Porto Bello Established in 1597 429
351. First Traffic along the Chagres River, and
the Importance of the Isthmian Commerce 431
352. First Survey for Isthmian Canal Ordered in 1520 431
353. Old Panama Sacked by Morgan and the Present City Founded 431
354. The Beginnings of the French Enterprise 432
355. The Wyse Concession and the International Congress of 1870 432
356. The Plan without Locks of the Old Panama Canal Company 433
357. The Control of the Floods in the Chagres 434
358. Estimate of Time and Cost—Appointment of Liquidators 435
359. The “Commission d’Etude” 435
360. Extensions of Time for Completion 436
361. Organization of the New Panama Canal Company, 1894 437
362. Priority of the Panama Railroad Concession 437
363. Resumption of Work by the New Company—The Engineering
Commission and the Comité Technique 438
364. Plan of the New Company 439
365. Alternative Plan of the New Panama Canal Company 440
366. The Isthmian Canal Commission and its Work 441
367. The Route of the Isthmian Canal Commission that of
the New Panama Canal Company 441
368. Plan for a Sea-level Canal 443
369. Colon Harbor and Canal Entrance 443
370. Panama Harbor and Entrance to Canal 444
371. The Route from Colon to Bohio 445
372. The Bohio Dam 446
373. Variation in Surface Elevation of Lake 448
374. The Extent of Lake Bohio and the Canal Line in It 448
375. The Floods of the Chagres 449
376. The Gigante Spillway or Waste-weir 450
377. Storage in Lake Bohio for Driest Dry Season 451
378. Lake Bohio as a Flood Controller 452
379. Effect of Highest Floods on Current in Channel
in Lake Bohio 453
380. Alhajuela Reservoir not Needed at Opening of Canal 453
381. Locks on Panama Route 454
382. The Bohio Locks 454
383. The Pedro Miguel and Miraflores Locks 454
384. Guard-gates near Obispo 455
385. Character and Stability of the Culebra Cut 455
386. Length and Curvature 456
387. Small Diversion-channels 457
388. Principal Items of Work to be Performed 457
389. Lengths of Sections and Elements of Total Cost 458
390. The Twenty Per Cent Allowances for Exigencies 459
391. Value of Plant, Property, and Rights on the Isthmus 460
392. Offer of New Panama Coal Company to Sell for $40,000,000 461
393. Annual Costs of Operation and Maintenance 462
394. Volcanoes and Earthquakes 463
395. Hygienic Conditions on the Two Routes 464
396. Time of Passage Through the Canal 465
397. Time for Completion on the Two Routes 466
398. Industrial and Commercial Value of the Canal 469
399. Comparison of Routes 471
PART I.
_ANCIENT CIVIL-ENGINEERING WORKS._
CHAPTER I.
=1. Introductory.=—It is a common impression even among civil engineers
that their profession is of modern origin, and it is frequently called
the youngest of the professions. That impression is erroneous from
every point of view. Many engineering works of magnitude and of great
importance to the people whom they served were executed in the very
dawn of history, and they have been followed by many other works of at
least equal magnitude and under circumstances scarcely less noteworthy,
of which we have either remains or records. During the lapse of the
arts and of almost every process of civilization throughout the
darkness of the Middle Ages there was little if any progress made
in the art of the engineer, and what little was done was executed
almost entirely under the name of architecture. With the revival of
intellectual activity and with the development of science the value
of its practical application to the growing nations of the civilized
world caused the modern profession of civil-engineering to take
definite shape and to be known by the name which it now carries, but
which was not known to ancient peoples. Unfortunately the beginnings
of engineering cannot be traced; there is no historical record running
back far enough to render account of the earliest engineering works
whose ruins remain as enduring evidence of what was then accomplished.
It is probably correct to state that the material progress of any
people has always been concurrent with the development of the
art of civil-engineering, and, hence, that the practice of civil
engineering began among the people who made the earliest progress in
civilization, to whom “the art of directing the Great Sources of Power
in Nature for the use and convenience of man” became an early and
imperative necessity. Indeed that conclusion is confirmed by the most
ancient ruins of what may be termed public works that archæological
investigations have revealed to us, among which are those to be found
in the Chaldean region, in India, and in Egypt. Obviously, anything
like a detailed account of the structural and other works of such
ancient character must be lacking, as some of them were built before
even the beginnings of history. Our only data, therefore, are the
remains of such works, and unfortunately they have too frequently been
subject to the destructive operations of both man and nature.
=2. Hydraulic Works of Chaldea and Egypt.=—It is absolutely certain
that the populous centres of prehistoric times could not have existed
nor have been served with those means of communication imperatively
necessary to their welfare without the practice of the art of
engineering, under whatever name they may have applied to it. It is
known beyond any doubt that the anciently populous and prosperous
country at the head of the Persian Gulf and watered by the Euphrates
and the Tigris was irrigated and served by a most complete system
of canals, and the same observation can be made in reference to the
valley of the Nile. It is not possible at this period of that country’s
history to determine to what extent irrigation was practised or how
extensively the former country was served by water transportation
conducted along artificial channels; but hydraulic works, including
dams and sluices with other regulating appliances designed to bring
waters from the rivers on to the land, were certainly among the
earliest executed for the benefit of the communities inhabiting those
regions. The remains of those works, spread over a large territory
in the vicinity of ancient Babylon, Nippur, and other centres of
population, show beyond the slightest doubt that there existed a
network of water communication throughout what was in those days
a country rich in agricultural products and which supported the
operations of a most prosperous commerce. These canals were of ample
dimensions to float boats of no mean size, although much smaller than
those occupied in our larger systems of canal transportation. They
were many miles in length, frequently interlacing among themselves
and intersecting both the Tigris and the Euphrates. The remains of
these canals, some of them still containing water, show that they must
originally have been filled to depths varying from five or six to
fifteen or twenty feet, and that their widths may have been twenty-five
or thirty feet or more. Another curious feature is their occasional
arrangement in twos and threes alongside of each other with embankments
only between. The entire Euphrates-Tigris valley from the head of the
Persian Gulf at least to modern Baghdad (i.e., Babylonia) and possibly
to ancient Nineveh was served by these artificial waterways. Later,
when Alexander the Great made one of his victorious expeditions through
the Assyrian country, he found in the Tigris obstructions to the
passage of his ships down-stream in the shape of masonry dams. This was
between 356 and 322 B.C. These substantial dams were built across the
river for the purpose of intakes to irrigating-canals for the benefit
of the adjacent country. These canals, like those of Egypt, were fitted
with all the necessary regulating-devices of sluices or gates, both
of a crude character, but evidently sufficiently effective for their
purpose.
[Illustration]
It is known that there were in those early days interchanges of large
amounts and varieties of commodities, and it is almost if not quite
certain that the countries tributary to the Persian Gulf not only
produced sufficient grain for their own needs, but also carried on
considerable commerce with the Asiatic coast. We have no means of
ascertaining either the volume or the precise character of the traffic,
but there is little or no doubt of its existence. It is established
also that the waters of the Red Sea and the Nile were connected by a
canal about 1450 B.C. Recent investigations about Nippur and other
sites of ancient cities in that region confirm other indications that
the practice of some branches of hydraulic engineering had received
material development from possibly two to four thousand years before
the Christian era.
=3. Structural Works in Chaldea and Egypt.=—The ruins of ancient
buildings which have been unearthed by excavations in the same vicinity
show with the same degree of certainty that the art of constructing
buildings of considerable dimensions had also made material progress
at the same time, and in many cases must have involved engineering
considerations of a decided character both as to structural materials
and to foundations. Bricks were manufactured and used. Stones were
quarried and dressed for building purposes and applied so as to
produce structural results of considerable excellence. Even the arch
was probably used to some extent in that locality in those early
days, but stone and timber beams were constantly employed. In the
prehistoric masonry constructions of both the Egyptians and Chaldeans
and probably other prehistoric peoples, lime or cement mortar was not
employed, but came into use at a subsequent period when the properties
of lime and cement as cementing materials began to be recognized. The
first cementing material probably used in Egypt was a sticky clay, or
possibly a calcareous clay or earth. The same material was also used
in the valley of the Euphrates, but in the latter country there are
springs of bitumen, where that material exudes from the earth in large
quantities. The use of this asphaltic cement at times possibly involved
that of sand or gravel in some of the early constructions. Later,
lime mortar and possibly a weak hydraulic cement came to be employed,
although there is little if any evidence of the latter material.
Iron was manufactured and used at least in small quantities, and for
some structural purposes, even though in a crude manner. Bituminous
or other asphaltic material was found as a natural product at various
points, and its value for certain structural purposes was well known;
it was used both for waterproofing and for cement. It is practically
certain that the construction of engineering works whose interesting
ruins still remain involved a considerable number of affiliated
engineering operations of which no evidence has yet been found, and of
the employment of tools and appliances of which we have no record. So
far as these works were of a public character they were constructed
by the aid of a very different labor system from that now existing.
The kings or ruling potentates of those early times were clothed with
the most arbitrary authority, sometimes exercised wisely in the best
interests of their people, but at other times the ruling motive was
selfishness actuated by the most intense egotism and brutal tyranny.
Hence all public works were executed practically as royal enterprises
and chiefly by forced labor, perhaps generally without compensation
except mere sustenance. Under such conditions it was possible to
construct works on a scale out of all proportion to national usefulness
and without structural economy. When it is remembered that these
conditions existed without even the shadow of engineering science, it
is obvious that structural economy or the adaptation of well-considered
means to an end will not be found to characterize engineering
operations of prehistoric times. Nevertheless there are evidences of
good judgment and reasonable engineering design found in connection
with some of these works, particularly with those of an hydraulic
character. Water was lifted or pumped by spiral or screw machines and
by water-wheels, and it is not improbable that other appliances of
power served the purposes of many industrial and crude manufacturing
operations which it is now impossible for us to determine.
[Illustration: FIG. 1.—Home Built on Piles in the Land of Punt.]
It is an interesting fact that while many ancient works were
exceedingly massive, like the pyramids, the largest of those of which
the ruins have been preserved seldom seem to show little or any
evidence of serious settlement. Whether the ancients had unusually
sound ideas as to the design of foundation works, or whether those only
have come down to us that were founded directly upon rock, we have
scarcely any means of deciding. Nor can we determine at this time what
special recourses were available for foundation work on soft ground.
Probably one of the earliest recognized instances, if not the earliest,
of the building of structures on piles is that given by Sir George
Rawlinson, when he states that a fleet of merchant vessels sent down
the northeast African coast by the Egyptian queen Hatasu, probably 1700
B.C. or 1600 B.C., found a people whose huts were supported on piles in
order to raise them above the marshy ground and possibly for additional
safety. A representation (Fig. 1) of one of these native homes on piles
is found among Egyptian hieroglyphics of the period of Queen Hatasu.
=4. Ancient Maritime Commerce.=—It is well known that both the Chaldean
region and the Nile valley and delta, at least from Ethiopia to the
Mediterranean Sea, were densely populated during the period of two to
four or five thousand years before the Christian era. By means of the
irrigation works to which reference has already been made both lands
became highly productive, and it is also well known that those peoples
carried on a considerable commerce with other countries, as did the
Phœnicians also, at least between the innumerable wars which seemed
to be the main business of states in those days. These commercial
operations required not only the construction of fleets of what seem
to us small vessels for such purposes, but also harbor-works at least
suitable to the vessels then in use. The marine activity of the
Phœnicians is undoubted, and there is strong reason to believe that
there was also similar activity between Babylonian ports and those east
of them along the shores of the Indian Ocean, perhaps even as far as
ancient Cathay, and possibly also to the eastern coast of Africa.
Investigations in the early history of Egypt have shown that a
Phœnician fleet, constructed at some Egyptian port on the Red Sea,
undoubtedly made the complete circuit of Africa and returned to Egypt
through the Mediterranean Sea the third year after setting out, over
2100 years (about 600 B.C.) before the historic fleet of the Portuguese
explorer Vasco da Gama sailed the same circuit in the opposite
direction. It is therefore probable, in view of these facts, that at
least simple harbor-works of sufficient efficiency for those early days
found place in the public works of the ancient kingdoms bordering upon
the Mediterranean and Red seas and the Persian Gulf.
=5. The Change of the Nile Channel at Memphis.=—Although such obscure
accounts as can be gathered in connection with the founding of the
city of Memphis are so shadowy as to be largely legendary, it has been
established beyond much if any doubt that prior to its building the
reigning Egyptian monarch determined to change the course of the Nile
so as to make it flow on the easterly side of the valley instead of the
westerly. This was for the purpose of securing ample space for his city
on the west of the river, and, also, that the latter might furnish a
defence towards the east, from which direction invading enemies usually
approached. He accordingly formed an immense dam or dike across the
Nile as it then existed, and compelled it to change its course near
the foot of the Libyan Hills on the west and seek a new channel nearer
the easterly side of the valley. This must have been an engineering
work of almost appalling magnitude in those early times, yet even with
the crude means and limited resources of that early period, possibly,
if not probably, at least 5000 B.C., the work was successfully
accomplished.
=6. The Pyramids.=—Among the most prominent ancient structural works
are the pyramids of Egypt, those royal tombs of which so much has been
written. These are found chiefly in the immediate vicinity of Memphis
on the Nile. There are sixty or seventy of them in all, the first of
which was built by the Egyptian king Khufu and is known as the “Great
Pyramid” or the “First Pyramid of Ghizeh.” They have been called “the
most prodigious of all human constructions.” Their ages are uncertain,
but they probably date from about 4000 B.C. to about 2500 B.C. These
are antedated, however, by two Egyptian pyramidal constructions of
still more ancient character whose ages cannot be determined, one at
Meydoum and the other at Saccarah.
[Illustration: A Corner of the Great Pyramid.
(Copyright by S. S. McClure Co., 1902. Courtesy of _McClure’s
Magazine_.)]
[Illustration: FIG. 2.—Section of the Great Pyramid.]
[Illustration: FIG. 3.]
The pyramids at Memphis are constructed of limestone and granite, the
latter being the prominent material and used entirely for certain
portions of the pyramids where the stone would be subjected to severe
duty. The great mass of most of the pyramids consists of roughly hewn
or squared blocks with little of any material properly considered
mortar. The interior portions, especially of the later pyramids, were
sometimes partially composed of chips, rough stones, mud bricks, or
even mud, cellular retaining-walls being used in the latter cases for
the main structural features. In all pyramids, however, the outer or
exposed surfaces and the walls and roofs of all interior chambers were
finished with finely jointed large stones, perhaps usually polished.
The Great Pyramid has a square base, which was originally 764 feet on a
side, with a height of apex above the surface of the ground of over 480
feet. This great mass of masonry contains about 3,500,000 cubic yards
and weighs nearly 7,000,000 tons. The area of its base is 13.4 acres.
The Greek historian Herodotus states that its construction required the
labor of 100,000 men for twenty years. An enormous quantity of granite
was required to be transported about 500 miles down the Nile from the
quarries at Syene. Some of the blocks at the base are 30 feet long with
a cross-section of 5 feet by 4 or 5 feet. The bulk of the entire mass
is of comparatively small stones, although so squared and dressed as
to fit closely together. Familiar descriptions of this work have told
us that the small passages leading from the exterior to the sepulchral
chambers are placed nearly in a vertical plane through the apex. The
highest or king’s chamber, as it is called, measures 34 feet by 17
feet and is 19 feet high, and in it is placed the sarcophagus of King
Khufu. It is composed entirely of granite most exactly cut and fitted
and beautifully polished. The construction of the roof is remarkable,
as it is composed of nine great blocks “each nearly 19 feet long and 4
feet wide, which are laid side by side upon the walls so as to form a
complete ceiling.” There is a singular feature of construction of this
ceiling designed to remove all pressure from it and consisting of five
alternate open spaces and blocks of granite placed in vertical series,
the highest open space being roofed over with inclined granite slabs
leaning or strutted against each other like the letter V inverted.
This arrangement relieves the ceiling of the sepulchral chamber from
all pressure; indeed only the inclined highest set of granite blocks
or slabs carry any load besides their own weight. There are two small
ventilating- or air-shafts running in about equally inclined directions
upward from the king’s chamber to the north and south faces of the
pyramid. These air-shafts are square and vary between 6 and 9 inches on
a side. The age of this pyramid is probably not far from 5000 years.
[Illustration: Entrance to the Great Pyramid.]
The second pyramid is not much inferior in size to the Great Pyramid,
its base being a square of about 707 feet on a side, and its height
about 454 feet. The remaining pyramids are much inferior in size,
diminishing to comparatively small dimensions, and of materials much
inferior to those used in the earlier and larger pyramids.
=7. Obelisks, Labyrinths, and Temples.=—Among other constructions of
the Egyptians which may be called engineering in character, as well
as architectural, are the obelisks, the “Labyrinth” so called, on the
shore of Lake Mœris, and the magnificent temples at the ancient capital
Thebes, which are the most remarkable architectural creations probably
that the world has ever known. These latter were not completed by one
king, as was each of the pyramids. They were sometimes despoiled and
largely wrecked by invading hosts from Assyria, and then reconstructed
in following periods by successive Egyptian kings and again added
to by still subsequent monarchs, whose reigns were characterized
by statesmanship, success in war, and prosperity in the country.
Their construction conclusively indicates laborious operations and
transportation of great blocks of stone characteristic of engineering
development of the highest order for the days in which they took place.
The dates of these constructions are by no means well defined, but they
extend over the period running from probably about 2500 B.C. to about
400 B.C., with the summit of excellence about midway between.
Another class of ancient structures which can receive but a passing
notice, although it deserves more, is the elaborate rock tombs of some
of the old Egyptian monarchs in the rocks of the Libyan Hills. They
were very extensive constructions and contained numerous successions
of “passages, chambers, corridors, staircases, and pillared halls,
each further removed from the entrance than the last, and all covered
with an infinite number of brilliant paintings.” These tombs really
constituted rock tunnels with complicated ramifications which must have
added much to the difficulty of the work and required the exercise of
engineering skill and resources of a high order.
[Illustration]
=8. Nile Irrigation.=—The value of the waters of the Nile for
irrigation and fertilization were fully appreciated by the ancient
Egyptians. They also apparently realized the national value of some
means of equalizing the overflow, although the annual régimen of
the Nile was unusually uniform. There were, however, periods of
great depression throughout the whole Nile valley consequent upon
the phenomenal failure of overflow to the normal extent. One of the
earliest monarchs who was actuated by a fine public spirit undertook to
solve the problem of providing against such depressions by diverting
a portion of the flood-waters of the Nile into an enormous reservoir,
so that during seasons of insufficient inundation the reservoir-waters
could be drawn upon for the purpose of irrigation. This monarch is
known as the good Amenemhat, although the Greeks call him Mœris. In
the Nile valley, less than a hundred miles above Memphis, on the
left side or to the west of the river, there is a gap in the Libyan
Hills leading to an immense depression, the lower parts of which are
much below the level of the water in the Nile. This topographical
depression, perhaps 50 miles in length by 30 in breadth, with an area
between 600 and 700 square miles, now contains two bodies of water or
lakes, one known as the Birket Keroun and the other as Lake Mœris.
The vicinity of this depression is called the Fayoum. A narrow rocky
gorge connects it with the west branch of the Nile, known as Bahr el
Yousuf, and it is probable that during extreme high water in the Nile
there was a natural overflow into the Fayoum. The good Amenemhat, with
the judgment of an engineer, or guided by advisers who possessed that
judgment, appreciated the potential value of this natural depression
as a possible reservoir for the surplus Nile waters and excavated a
channel, possibly a natural channel enlarged, of suitable depth from it
to the Bahr el Yousuf. As a consequence he secured a storage-reservoir
of enormous capacity and which proved of inestimable value to the
lowlands along the Nile in times of shortage in the river-floods.
Investigators have differed much in their conclusions as to the extent
of this reservoir. Some have maintained that only the lower depressions
of the Fayoum were filled for reservoir purposes, while others, like
Mr. Cope Whitehouse, believe that the entire depression of the Fayoum
was utilized with the exception of a few very high points, and that
the depth of water might have been as much as 300 feet in some places.
In the latter case the circuit of the lake would have been from 300 to
500 miles. Whatever may have been the size of the lake, however, its
construction and use with its regulating-works was a piece of hydraulic
engineering of the highest type, and it indicates an extraordinary
development of that class of operations for the period in which it was
executed. The exact date of this construction cannot be determined, but
it may have been as early as 2000 B.C., or perhaps earlier.
=9. Prehistoric Bridge-building.=—The development of the art of
bridge-building seems to have lagged somewhat in the prehistoric
period. The use of rafts and boats prevented the need of bridges for
crossing streams from being pressing. It is not improbable that some
small and crude pile or other timber structures of short spans were
employed, but no remains of this class of construction have been found.
Large quantities of timber and much of an excellent quality were used
in the construction of buildings. That much is known, but there is
practically no evidence leading to the belief that timber bridges of
any magnitude were used by prehistoric people. It is highly probable
that single-timber-beam crossings of small streams were used, but that
must be considered the limit of ancient bridging until other evidence
than that now available is found.
=10. Ancient Brick-making.=—It has already been seen that stone as a
building material has been used since the most ancient periods, and the
use of brick goes back almost as far. Fortunately it was frequently
a custom of the ancient brick-makers to stamp proprietary marks upon
their bricks, and we know by these marks that bricks were made in the
Chaldean regions certainly from 3000 to 4000 years before the Christian
era. In Egypt also the manufacture of brick dates back nearly or quite
as far. Some of these Chaldean bricks, as well as those in other parts
of the ancient world, were of poor quality, readily destroyed by water
or even a heavy storm of rain when driving upon them. Other bricks,
however, were manufactured of good quality of material and by such
methods as to produce results which compare favorably with our modern
building-bricks. The ruins of cities, at least in Assyria and Chaldea,
show that enormous buildings, many of them palaces of kings, were
constructed largely of these bricks, although they were elaborately
decorated with other material. The walls were heavy, indeed so massive
that many of the ruin-mounds are frequently formed almost entirely
of the disintegrated brick of poorer quality. These old builders not
only executed their work on a large scale, but did not hesitate to
pile up practically an artificial mountain of earth, or other suitable
material, on which to construct a palace or temple. The danger of
water to these native bricks was so well known and recognized that
elaborate and very excellent systems of subsurface drains or sewers
were frequently constructed to carry off the storm-water as fast as it
fell.
=11. Ancient Arches.=—In the practice of these building operations it
became necessary to form many openings and to construct roofs for the
sewers or drains, and the arch, both true and false, came to be used in
the Euphrates valley, in that of the Nile, and in other portions of the
ancient world. Pointed sewer-arches of brick have been found in what
is supposed to be the palace of Nimrod on the Tigris River, possibly
of the date about 1300 B.C. Excavations at Nippur have revealed a
mud-brick pointed arch supposed to date back to possibly 4000 B.C.
Also semicircular voussoir arches have been discovered at the ruins
of Khorsabad near Nineveh with spans of 12 to 15 feet. These arches
are supposed to belong to the reign of Sargon, an Assyrian king who
flourished about 705 to 722 B.C. Again, the ancient so-called treasury
of Atreus at Mycenæ in Greece, although a dome, exhibits an excellent
example of the method of forming the false arch, the date of the
construction being probably about 1000 B.C. The main portion of this
structure consists of a pointed dome, the diameter of the base being 48
feet and the interior central height 49 feet. A central section shows a
beehive shape, as in Fig. 6.
[Illustration: VAULTED DRAIN, KHORSABAD FIG. 4.]
[Illustration: VAULTED DRAINS, KHORSABAD. FIG. 5.]
The exterior approach is between two walls 20 feet apart, the
intermediate entrance to the dome or main chamber being a passage
9 feet 6 inches wide at the bottom and 7 feet 10 inches at the top
and about 19 feet high. At right angles to the entrance there is a
chamber 27 feet by 20 feet cut into the adjacent rock, entered through
a doorway about 4 feet 6 inches wide and 9 feet 6 inches high. Both
the main entrance to the dome and the doorway to the adjacent chamber
are covered or roofed with large flat lintel-stones, over which
are the triangular relieving (false) arches, so common in ancient
construction, by which the lintels are relieved of load, the triangular
openings being closed by single, great upright flat stones. There are a
considerable number of these in Greece. The stone used is a “hard and
beautiful breccia” from the neighboring hills and Mount Eubora near
by. The courses of stone are about two feet thick and closely fitted
without cement.
[Illustration: FIG. 6.—Plan and Section of the Treasury of Atreus at
Mycenæ.]
1. Plan of the Treasury of Atreus: _A_, rock-cut chamber, probably a
tomb; _B_, doorway; _C_, approach.
2. Section of the above: _B_, doorway; _C_, approach filled up with
earth; _D_, slope of the ground; _E_, wall on north side of approach;
_F_, lintel stone, weight 133 tons; _G_, door to rock-cut chamber.
The great majority, or perhaps all, of the Assyrian true arches, so
far discovered, are formed of wedge-shaped bricks, most of them being
semicircular, although some are pointed, the span being not over
about 15 feet. The most of the arches found at Nineveh and Babylon
belong to a period reaching possibly from 1300 to 800 B.C., but some
of the Egyptian arches are still older. Egyptians, Assyrians, Greeks,
and other ancient people used false arches formed by projecting each
horizontal course of stones or bricks over that below it on either side
of an opening. The repetition of this procedure at last brings both
sides of the opening together at the top of the arch, and they are
surmounted at that point with a single flat stone, brick, or tile. It
has been supposed by some that these false arches, whose sides may be
formed either straight or curved, exhibit the oldest form of the arch,
and that the true arch with its ring or rings of wedge-shaped voussoirs
was a subsequent development. It is possible that this is true, but
the complete proof certainly is lacking. In Egypt and Chaldea both
styles of arches were used concurrently, and it is probably impossible
to determine which preceded the other. Again, some engineers have
contended that two flat slabs of stone leaning against each other,
each inclined like the rafters of a roof, was the original form of the
arch, as found in the pyramids of Egypt; but it is probable that the
true arch was used in Chaldea prior to the time of the pyramids. Indeed
crude arches of brick have been found at Thebes in Egypt dating back
possibly to 2500 B.C., or still earlier. Aside from that, however,
such an arrangement of two stones is not an arch at all, either true
or false. The arrangement is simply a combination of two beams. A
condition of stress characteristic of that in the true arch is lacking.
The ancient character of the engineering works whose ruins are found
in Chaldea and Assyria is shown by the simple facts that Babylon was
destroyed about the year 690 B.C. and Nineveh about the year 606 B.C.
CHAPTER II.
=12. The Beginnings of Engineering Works of Record.=—In a later
period of the world’s history we reach a stage in the development of
engineering works of which we have both records and remains in such
well-defined shape that the characteristics of the profession may
be realized in a definite manner. This is particularly true of the
civil-engineering works of the Romans. In their sturdy and unyielding
character, with their limitless energy and resolution, the conditions
requisite for the execution of engineering works of great magnitude are
found. An effeminate or generally æsthetic nation like the Greeks would
furnish but indifferent opportunity for the inception and development
of great engineering works, but the resolute and vigorous Roman nation
offered precisely the conditions needed. They appreciated among other
things the absolute necessity of the freest possible communication
with the countries which they conquered and made part of their own
empire. They recognized water transportation as the most economical
and effective, and used it wherever possible. They also realized the
advantages of roads of the highest degree of solidity and excellence.
No other roads have ever been constructed so direct, so solid, and so
admirably adapted to their purposes as those built by the Romans. They
virtually ignored all obstacles and built their highways in the most
direct line practicable, making deep cuts and fills with apparently
little regard for those features which we consider obstacles of
sufficient magnitude to be avoided. They regarded this system of land
communication so highly that they made it radiate from the Golden
Mile-stone in the Roman Forum. The point from which radiated these
roads was therefore in the very centre of Roman life and authority,
and it fitly indicated the importance which the Roman government gave
to the system of communication that bound together with the strongest
bonds all parts of the republic and of the empire.
The design and construction of these roads must have been a matter to
which their constructors gave the most careful attention and study.
They were works involving principles deduced from the most careful
thought and extended experience. There were incorporated in them
the most effective materials of construction then known, and it was
evidently the purpose of their constructors that they should possess
indefinite endurance. The existence of some of them at the present
time, with no other attention given to them than required for ordinary
maintenance, demonstrates that the confidence of the builders was not
misplaced.
[Illustration: Street Fountain and Watering-trough in Pompeii. Called
the Fountain of Plenty, from the figure with Horn of Plenty on the
perforated upright post.]
=13. The Appian Way and other Roman Roads.=—Probably the oldest and
most celebrated of these old Roman roads is the Appian Way. It was the
most substantially built, and the breadth of roadway varied from 14
to 18 feet exclusive of the footwalks. Statius called it the Queen of
Roads. It was begun by Appius Claudius Cæcus, 312 years before the
Christian era. He carried its construction from the Roman gate called
Porta Capena to Capua, but it was not entirely completed till about the
year 30 B.C. Its total length was three hundred and fifty miles, and
it formed a perfect highway from Rome to Brundisium, an important port
on what may be called the southeastern point of Italy. It was built in
such an enduring manner that it appears to have been in perfect repair
as late as 500 to 565 A.D.
The plan of construction of these roads was so varied as to suit
local conditions, but only as required by sound engineering judgment.
They wisely employed local materials wherever possible, but did not
hesitate to transport proper material from distant points wherever
necessary. This seemed to be one of their fundamental principles of
road construction. In this respect the old Romans exhibited more
engineering and business wisdom than some of the American states in
the beginnings of improved road construction in this country. An
examination of the remains of some Roman roads now existing appears to
indicate that in earth the bottom of the requisite excavation was first
suitably compacted, apparently by ramming, although rollers may have
been used. On this compacted subgrade were laid two or three courses
of flat stones on their beds and generally in mortar. The second layer
placed on the preceding was rubble masonry of small stones or of coarse
concrete. On the latter was placed the third layer of finer concrete.
The fourth or surface course, consisting of close and nicely jointed
polygonal blocks, was then put in place, and formed an excellent
unyielding pavement. This resulted in a most substantial roadway,
sometimes exceeding 3 feet in total thickness. It is difficult to
conceive of a more substantial and enduring type of road construction.
The two lower layers were omitted when the road was constructed in
rock. Obviously the finer concrete constituting the second layer from
the top surface was a binder between the pavement surface and the
foundation of the roadway structure.
The paved part of a great road was usually about 16 feet in width,
and raised stone causeways or walls separated it from an unpaved way
on each side having half the width of the main or paved portion. This
seemed to be the type of the great or main Roman roads. Other highways
of less important character were constructed of inferior materials,
earth or clay sometimes being used instead of mortar; but in such cases
greater crowning was employed, and the road was more elevated, possibly
for better drainage. Then, as now, adequate drainage was considered one
of the first features of good road design. City streets were paved with
the nicely jointed polygonal blocks to which reference has already been
made, while the footways were paved with rectangular slabs much like
our modern sidewalks.
[Illustration: EXAMPLE OF EARLY BASALT ROAD.
BY THE TEMPLE OF SATURN ON THE CLIVUS CAPITOLINUS.
FIG. 7.]
The smooth polygonal pavements of the old Romans put to the keenest
shame the barbarous cobblestone street surfaces with which the people
of American cities have been and are still so tortured.
The beneficial influence of these old Roman highways has extended down
even to the present time in France, where some of them were built.
The unnecessarily elaborate construction has not been followed, but
the recognition of the public benefits of excellent roads has been
maintained. The lower course of the foundation-stones apparently began
to be set on edge toward the latter part of the eighteenth century, the
French engineer Tresaguet having adopted that practice in 1764. At the
same time he reduced the thickness of the upper layers. His methods
were but modifications of the old Roman system, and they prevailed in
France until the influence of the English engineers Macadam and Telford
began to be felt.
=14. Natural Advantages of Rome in Structural Stones.=—Although the
ancient Romans were born engineers, possessing the mental qualities and
sturdy character requisite for the analytic treatment and execution of
engineering problems, it is doubtful whether they would have attained
to such an advanced position in structural matters had not the city of
Rome been so favorably located.
The geological character of the great Roman plain and the Roman hills
certainly contributed most materially to the early development of
some of the most prominent of the Roman engineering works. The plain
surrounding the city of Rome is composed largely of alluvial and sandy
deposits, or of the emissions of neighboring volcanoes, of which the
Alban Hills form a group. While these and other volcanic hills in the
vicinity are, and have been for a long period, quiescent, they were
formerly in a very active state. The scoriæ, or matter emitted in
volcanic eruptions, is found there in all possible degrees of coherence
or solidity, from pulverulent masses to hard rock. The characteristic
Roman material called tufa is a mixture of volcanic ash and sand, loose
and friable, as dropped from the eruptions in large quantities or again
compressed into masses with all degrees of hardness. The hard varieties
of yellow or brown tufa form building material much used, although a
considerable percentage of it would not be considered fit building
material for structures of even moderate height at the present time.
The most of it weathers easily, but forms a fairly good building-stone
when protected by a coating of plaster or stucco.
Another class of building-stones found at or in the vicinity of Rome
is the so-called “peperino,” consisting chiefly of two varieties of
conglomerate of ash, gravel, broken pieces of lava, and pieces of
limestone, some possessing good weathering qualities, while others
do not. Ancient quarries of these stones exist whence millions of
cubic yards have been removed, and are still being worked. The better
varieties of “peperino” possess good resisting qualities, and were much
used in those portions of masonry construction where high resistance
was needed, as in the ring-stones of arches, heavily loaded points of
foundations, and other similar situations.
Some of the prehistoric masonry remains of the Romans show that their
earliest constructors appreciated intelligently the qualities of this
stone for portions of works where the duty was most severe.
Lava from the extinct volcanoes of the Alban Hills called “silex” was
used for paving roads and for making concrete. It was hard and of gray
color. At times considerable quantities of this stone were employed.
A species of pure limestone called “travertine,” of a creamy white
color, was quarried at Tibur or Tivoli, and began to be used about
the second century B.C. Vitruvius speaks of its having good weathering
qualities, but naturally it is easily calcined. Its structure is
crystalline, and it is strong in consequence of that quality only when
it is laid on its bed.
=15. Pozzuolana Hydraulic Cement.=—The most valuable of all building
materials of old Rome was the “pozzuolana,” as it furnished the basis
of a strong, enduring, and economic concrete, and permitted almost
an indefinite development of masonry construction. Had there not
been at Rome the materials ready at hand to be manufactured into an
excellent cementing product, it is highly probable that neither the
structural advance nor the commercial supremacy of the Roman people
could have been attained. It is at least certain that the majority
of the great masonry works constructed by the Romans could not have
been built without the hydraulic cementing material produced with so
little difficulty and in such large quantities from the volcanic earth
called pozzuolana. The name is believed to have its origin from the
large masses of this material at Pozzuoli near Naples. Great beds are
also found at and near Rome. The earliest date of its use cannot be
determined, but it has given that strong and durable character to Roman
concrete which has enabled Roman masonry to stand throughout centuries,
to the admiration of engineers.
It is a volcanic ash, generally pulverulent, of a reddish color, but
differs somewhat in appearance and texture according to the locality
from which it is taken. It consists chiefly of silicate of alumina, but
contains a little oxide of iron, alkali, and possibly other components.
The Romans therefore pulverized the pozzuolana and mixed it with lime
to make hydraulic cement. This in turn was mixed with sand and gravel
and broken stone to form mortar and concrete, and that process is
carried on to this day. The concrete was hand-mixed, and treated about
as it is at present. After having been well mixed the Romans frequently
deposited it in layers of 6 to 9 or 10 inches thick, and subjected
it to ramming. In connection with this matter of mortar and concrete
production, Vitruvius observes that pit-sand is preferable to either
sea or river sand.
=16. Roman Bricks and Masonry.=—The Romans produced bricks both by
sun-baking and by burning, although there are now remaining apparently
no specimens of the former in Rome. Bricks were used very largely for
facing purposes, such as a veneer for concrete work. The failure to
recognize this fact has led some investigators and writers into error.
As matter of fact bricks were used as a covering for concrete work, the
latter performing all the structural functions.
The old Roman aqueducts were frequently lined with concrete, made of a
mixture of pozzuolana, lime, and crushed (pounded) bricks or potsherds.
The same material was also used for floors under the fine mortar in
which the mosaics were imbedded.
Marble came into use in Rome about 100 B.C., from Luna, near modern
Carrara, Mt. Hymettus, and Mt. Pentelicus, near Athens and the Isle of
Paros, nearly all being for sculpture purposes. Colored and structural
marbles were brought from quarries in various parts of Italy, Greece,
Phrygia, Egypt, near Thebes (oriental alabaster or “onyx”), Arabia, and
near Damascus.
From the latter part of the first century B.C. the hard building-stones
like granites and basalts were brought to Rome in large quantities.
Most of the granites came from Philæ on the Nile. The basalts came both
from Lacedæmonia and Egypt. Both emery (from the island of Naxos in the
Ægean Sea) and diamond-dust drills were used in quarrying or working
these stones. Ships among the largest, if not the largest, of those
days, were built to transport obelisks and other large monoliths.
The quality of ancient Roman mortar varies considerably as it is now
found. That of the first and second centuries is remarkably hard, and
made with red pozzuolana. In the third century it began to be inferior
in quality, brown pozzuolana sometimes being used. The reason for this
difference in quality cannot be confidently assigned. The deterioration
noted in the third century work may be due to the introduction of bad
materials, or to the wrong manipulation of material intrinsically good,
or it is not unlikely the deterioration is due to a combination of
these two influences. The use of mortar indicates a class of early
construction; it is found in the Servian wall on the Aventine, of date
700 B.C., or possibly earlier.
[Illustration: Dovetail Wooden Tenon. Wooden Dowel. FIG. 8.]
Under the empire (27 B.C. to A.D. 475) large blocks of tufa, limestone
(travertine), or marble were set with very close joints, with either
no mortar or, if any, as thin as paper; end, top, and bottom clamps of
iron were used to bond such stones together. It was also customary, in
laying such large, nicely finished blocks of stone without mortar, to
use double dovetailed wooden ties, or, as in the case of columns, a
continuous central dowel of wood, as shown in the figures.
The joints were frequently so close as to give the impression that the
stones might have been fitted by grinding together. In rectangular
dimension stonework (ashlar) great care was taken, as at present, to
secure a good bond by the use of judiciously proportioned headers and
stretchers. Foundation courses were made thicker than the body of
the superincumbent wall, apparently to distribute foundation weights
precisely as done at present. Weaker stone was used in thicker portions
of walls, and strong stone in thinner portions. Also at points of
concentrated loading, piers or columns of strong stone are found built
into the bodies of walls of softer or weaker stone. Quarry chips,
broken lava, broken bricks, or other suitable refuse fragments were
used for concrete in the interest of economy, the broken material
always being so chosen as to possess a sharp surface to which the
cement would attach itself in the strongest possible bond.
At the quarries where the stones were cut the latter were marked
apparently to identify their places in the complete structure, or
for other purposes. The remains of the quarries themselves as seen
at present are remarkable both for their enormous extent and for the
system on which the quarrying was conducted. It appears that the
systems employed were admirably adapted to the character of the stone
worked, and that the quarrying operations were executed as efficiently
and with as sound engineering judgment as those employed in great
modern quarries.
=17. Roman Building Laws.=—So much depended upon the excellence of the
building in Rome, and upon the materials and methods employed, that
building laws or municipal regulations were enacted in the ancient
city, prescribing kind and quality of material, thickness of walls,
maximum height of buildings, minimum width of streets, and many other
provisions quite similar to those enacted in our modern cities. The
differences appear to arise from the different local conditions to
be dealt with, rather than from any failure on the part of the old
Romans to reach an adequate conception of the general plans suitable
for the masses of buildings in a great city. Prior to the great fire
A.D. 64 in Nero’s reign, an act prescribing fire-proof exterior
coverings of buildings was under consideration, and subsequently to
that conflagration it was enacted into law. Many of the city roads or
streets were paved with closely fitting irregular polygonal blocks of
basalt, laid on concrete foundations, and with limestone (travertine)
curbs and gutters, producing an effect not unlike our modern streets.
=18. Old Roman Walls.=—In no class of works did the ancient Romans show
greater engineering skill or development than in the massive masonry
structures that were built not only in and about the city of Rome, but
also in distant provinces under Roman jurisdiction. Among the home
structures various walls, constituting strong defences against the
attacks of enemies, stand in particular prominence. Some of these great
structures had their origin prior even to historic times. The so-called
“Wall of Romulus,” around the famous Roma Quadrata of the Palentine,
is among the latter. It is supposed by many that this wall formed the
primitive circuit of the legendary city of Romulus. That, however, is
an archæological and not an engineering question, and, whatever its
correct answer may be, the wall itself is a great engineering work;
it demonstrates that the early Romans, whatever may have been their
origin, had attained no little skill in quarrying and in the building
of dry masonry, no mortar being used in this ancient wall. Portions
of it 40 feet high and 10 feet thick at bottom, built against a rocky
hill, are still standing. The courses are 22 to 24 inches thick, and
they are laid as alternate headers and stretchers; the lengths of the
blocks being 3 to 5 feet, and the width from 19 to 22 inches. The ends
of the blocks are carefully worked and true, as are the vertical joints
in much of the wall, although some of the latter, on the other hand,
are left as much as 2 inches open.
Civil engineers, who are familiar with the difficulties frequently
experienced in laying up dry walls of considerable height, as evidenced
by many instances of failure probably within the knowledge of every
experienced engineer, will realize that this great dry masonry
structure must have been put in place by men of no little engineering
capacity. The rock is soft tufa, and marks on the blocks indicate that
chisels from ¼ to ¾ inch in width were used, as well as sharp-pointed
picks. In all cases the faces of the blocks were left undressed, i.e.,
in modern terms they were “quarry-faced.”
=19. The Servian Wall.=—Later in the history of Rome the great Servian
Wall, built chiefly by Servius Tullius to enclose the seven hills
of Rome, occupies a most prominent position as an engineering work.
Part of the wall, all of which belongs to the regal period (753 to
509 B.C.), is supposed to be earlier than Servius, and may have been
planned and executed by Tarquinius Priscus. A part only of the stones
of this wall were laid in cement mortar, and concrete was used, to
some extent at least, in its foundation and backing. The presence of
cement mortar in this structure differentiates it radically from the
wall of Romulus. Probably the discovery of pozzuolana cement, and
the fabrication of mortar and concrete from it, had been made in the
intervening period between the two constructions. Tufa, usually the
softer varieties but of varying degrees of hardness, was mostly used
in this wall, and the blocks were placed, as in the previous instance,
as alternate headers and stretchers in courses about two feet thick.
Portions of the wall 45 feet high and about 12 feet thick have been
uncovered. At points it was pierced with arched openings of 11 feet 5
inches span, possibly as embrasures for catapults or other engines of
war. The upper parts of these openings are circular arches with the
usual wedge-like ring-stones. The voussoirs were cut from peperino
stone. This wall, like that of Romulus, was constructed as a military
work of defence, and at some points it was built up from the bottom
of a wide foss 30 feet deep. At such places it was counterforted or
buttressed, a portion of wall 11 feet 6 inches long being found between
two counterforts, each of the latter being 9 feet wide and projecting 7
feet 9 inches out from the wall.
[Illustration: FIG. 9.—Part of Servian Wall on Aventine.]
[Illustration: FIG. 10.—Wall and Agger of Servius.]
=20. Old Roman Sewers.=—It is demonstrable by the writings of Vitruvius
and others that the old Romans, or at any rate the better educated of
them, possessed a correct general idea of some portions of the science
of Sanitary Engineering, so far as anything of the nature of science
could then be known. Their sanitary views were certainly abreast of
the scientific knowledge of that early day. The existence of the
“cloacæ,” or great sewers, of the ancient city of Rome showed that
its people, or at least its rulers, not only appreciated the value
of draining and sewering their city, but also that they knew how to
secure the construction of efficient and enduring sewers or drains. It
has been stated, and it is probably true, that this system of cloacæ,
or sewers, was so complete that every street of the ancient city was
drained through its members into the Tiber. They were undoubtedly the
result of a gradual growth in sewer construction and did not spring
at once into existence, but they date back certainly to the beginning
of the period of the kings (753 B.C.). The famous Cloaca Maxima, as
great as any sewer in the system, and certainly the most noted, is
still in use, much of it being in good order. The mouth of the latter
where it discharges into the Tiber is 11 feet wide and 12 feet high,
constituting a large arch opening with three rings of voussoirs of
peperino stone. Many other sewers of this system are also built with
arch tops of the same stone, with neatly cut and closely fitting
voussoirs. We do not find, unfortunately, any detailed accounts of the
procedures involved in the design of these sewers, yet it is altogether
probable that the old Roman civil engineers formed the cross-sections,
grades, and other physical features of their sewer system by rational
processes, although they would doubtless appear crude and elementary at
the present time. It would not be strange if they made many failures in
the course of their structural experiences, but they certainly left in
the old Roman sewers examples of enduring work of its kind.
Some portions of this ancient sewer system are built with tops that are
not true arches, and it is not impossible that they antedate the regal
period. These tops are false arches formed of horizontal courses of
tufa or peperino, each projecting over that below until the two sides
thus formed meet at the top. The outline of the crowns of such sewers
may therefore be triangular, curved, or polygonal; they were usually
triangular. Smaller drains forming feeders to the larger members of
the system were formed with tops composed of two flat stones laid with
equal inclination to a vertical line so as to lean against each other
at their upper edges and over the axis of the sewer. This method of
forming the tops of the drains by two inclined flat stones was a crude
but effective way of accomplishing the desired purpose.
The main members of this great sewer system seem to have followed the
meandering courses of small rivers or streams, constituting the natural
drainage-courses of the site of the city. The Cloaca Maxima has an
exceedingly crooked course and it, along with others, was probably
first formed by walling up the sides of a stream and subsequently
closing in the top. Modern engineers know that such an alignment for
a sewer is viciously bad, and while this complicated system of drains
is admirably constructed in many ways for its date, it cannot be
considered a perfect piece of engineering work in the light of present
engineering knowledge. It is probable that the walling in of the sides
of the original streams began to be done in Rome at least as early as
the advent of the Tarquins, possibly as early as 800 B.C. or earlier.
We know little about the original outfalls or points of discharge into
the Tiber, except that, as previously stated, these points were made
through the massive quay-walls constructed during the period of the
kings along both shores of the Tiber, probably largely for defence as
originally built. The discharge of the old Roman sewers through the
face of this quay-wall and into the river is precisely the manner in
which the sewers of New York City in many places are discharged into
the North, East, and Harlem rivers.
The Cloaca Maxima is not the only great ancient sewer thus far
discovered. There are at least two others equal to it, and some of the
single stones with which they are built contain as much as 45 cubic
feet each. These cloacæ were not mere sewers; indeed they were more
drains than sewers, for they carried off flood-waters and the natural
drainage as well as the sewerage. They were therefore combined sewers
and drains closely akin to the sewers of our “combined” systems. The
openings into them were made along the streets of Rome and in public
buildings or some other public places. There is no evidence that
they were ventilated except through these openings, and from each
noxious gases were constantly rising to be taken into the lungs of
the passers-by. It is a rather curious as well as important fact that
so far as excavations have been made there is practically no evidence
that a private residence in Rome was connected with the sewers. The
“latrines” were generally located adjacent to the Roman kitchens and
discharged into the cloacæ.
=21. Early Roman Bridges.=—The early Romans were excellent
bridge-builders as well as constructors in other lines of engineering
work. Although the ancient city was first located on the left bank of
the Tiber, apparently it was but a comparatively short time before
the need of means for readily crossing from bank to bank was felt.
The capacity of the Roman engineers was equal to the demands of the
occasion, and it is now known that seven or eight ancient bridges
connected the two shores of the river Tiber. The oldest bridge is that
known as Pons Sublicius. No iron was used in its construction, as
bronze was the chief metal employed in that early day. The structure
was probably all of timber except possibly the abutments and the piers.
A French engineer, Colonel Emy, has exhibited in his “Traité de l’Art
de la Charpenterie” a plan of this structure restored as an all-timber
bridge with pile foundations. Lanciani, on the other hand, believes
that the abutments and piers must have been of masonry. The masonry
structures, however, known to exist at a later day may have been parts
of the work of rebuilding after the two destructions by floods. The
date of its construction is not known, but tradition places it in
the time of Ancus Marcius. This may or may not be correct. A flood
destroyed the bridge in 23 B.C., and again in the time of Antoninus
Pius, but on both occasions it was rebuilt. The structure has long
since disappeared. The piers only remained for a number of centuries,
and the last traces of them were removed in 1877 in order to clear the
bed of the river.
Fig. 11 shows Colonel Emy’s restoration of the plan for the pile bridge
which Julius Cæsar built across the Rhine in ten days for military
purposes. This plan may or may not include accurate features of the
structure, but it is certain that such a timber bridge was built, and
well preserved pieces of the piles have been taken from under water
at the site little the worse for wear after two thousand years of
submersion.
The censor Ælius Scaurus built a masonry arch across the Tiber about
a mile and a half from Rome in the year 100 B.C. This bridge is now
known as the Ponte Molle, and some parts of the original structure are
supposed to be included in it, having been retained in the repeated
alterations. The arches vary in span from 51 to 79 feet, and the width
of the structure is a little less than 29 feet.
In or about the year 104 A.D. the emperor Trajan constructed what
is supposed to be a wooden arch bridge with masonry piers across the
Danube just below the rapids of the Iron Gate.
[Illustration: Cross-section at Pier.]
[Illustration: Plan at Pier.
FIG. 11.—Bridge thrown across the Rhine by Julius Cæsar.]
A _bas relief_ on the Trajan Column at Rome exhibits the timber arches,
but fails to give the span lengths, which have been the subject of much
controversy, some supposing them to have been as much as 170 feet.
The ancient Pons Fabricius, now known as Ponte Quattiro Capi, still
exists, and it is the only one which remains intact after an expiration
of nearly two thousand years. It has three arches, the fourth being
concealed by the modern embankment at one end; a small arch pierces the
pier between the other two arches. This structure is divided into two
parts by the island of Æsculapius. It is known that a wooden bridge
must have joined that island with the left bank of the Tiber as early
as 192 B.C., and a similar structure on the other side of the island
is supposed to have completed the structure. While Lucius Fabricius
was Commissioner of Roads in the year 62 B.C. he reconstructed the
first-named portion into a masonry structure of arches. An engraved
inscription below the parapets shows that the work was duly and
satisfactorily completed, and further that it was the custom to require
the constructors or builders of bridges to guarantee their work for the
period of forty years. Possession of the last deposit, made in advance
as a guarantee of the satisfactory fulfilment of the contract, could
not be regained until the forty-first year after completion.
[Illustration: FIG. 12.—Trajan’s Bridge.]
The Pons Cestius is a bridge since known as the Pons Gratianus and
Ponte di S. Bartolomeo. Its first construction is supposed to have been
completed in or about 46 B.C., and it was rebuilt for the first time in
A.D. 365. A third restoration took place in the eleventh century. The
modern reconstruction in 1886-89 was so complete that only the middle
arch remains as an ancient portion of the structure. The island divides
the bridge into two parts, the Ship of Æsculapius lying between the
two, but it is not known when or by whom the island was turned into
that form.
Another old Roman bridge, of which but a small portion is now standing,
is Pons Æmilius, the piers of which were founded in 181 B.C., but the
arches were added and the bridge completed only in 143 B.C. It was
badly placed, so that the current of the river in times of high water
exerted a heavy pressure upon the piers, and in consequence it was at
least four times carried away by floods, the first time in the year
A.D. 280.
The discovery of what appears to be a row of three or four ruins of
piers nearly 340 feet up-stream from the Ponte Sisto seems to indicate
that a bridge was once located at that point, although little or
nothing is known of it as a bridge structure. Some suppose it to be the
bridge of Agrippa.
The most historical of all the old Roman bridges is that which was
called Pons Ælius, now known as Ponte S. Angelo, built by Hadrian A.D.
136. Before the reconstruction of the bridge in 1892 six masonry
arches were visible, and the discovery of two more since that date
makes a total of eight, of which it is supposed that only three were
needed in a dry season. The pavement of the approach to this bridge as
it existed in 1892 was the ancient roadway surface. Its condition at
that time was an evidence of the substantial character of the old Roman
pavement.
Below the latter bridge remains of another can be seen at low water. It
is supposed that this structure was the work of Nero, although its name
is not known.
The modern Ponte Sisto is a reconstruction of the old Pons
Valentinianus or bridge of Valentinian I. The latter was an old Roman
bridge, and it was regarded as one of the most impressive of all the
structures crossing the river. It was rebuilt in A.D. 366-67.
The most of these bridges were built of masonry and are of the usual
substantial type characteristic of the early Romans. They were
ornamented by masonry features in the main portions and by ornate
balustrades along either side of the roadway and sidewalks. The roadway
pavements were of the usual irregular polygonal old Roman type, the
sidewalk surfaces being composed of the large slabs or stones commonly
used in the early days of Rome for that purpose.
=22. Bridge of Alcantara.=—Among the old Roman bridges should be
mentioned that constructed at Alcantara in Spain, supposedly by Trajan,
about A.D. 105. It is 670 feet long and its greatest height is 210
feet. One of its spans is partially destroyed. The structure is built
of blocks of stone without cementing material. In this case the number
of arches is even, there being six in all, the central two having
larger spans than those which flank them. It is a bridge of no little
impressiveness and beauty and is a most successful design.
=23. Military Bridges of the Romans.=—In the old Roman military
expeditions the art of constructing temporary timber structures along
lines of communication was well known and practised with a high degree
of ability. Just what system of construction was employed cannot be
determined, but piles were constantly used. At least some of these
timber military bridges, and possibly all, were constructed with
comparatively short spans, the trusses being composed of such braces
and beams as might be put in place between bents of piles. As already
observed, some of the sticks of these bridges have been found in the
beds of German rivers, and at other places, perfectly preserved after
an immersion of about two thousand years. These instances furnish
conclusive evidence of the enduring qualities of timber always
saturated with water.
=24. The Roman Arch.=—The Romans developed the semicircular arch to a
high degree of excellence, and used it most extensively in many sewers,
roads, and aqueducts. While the aqueduct spans were usually made with
a length of about 18 or 20 feet, they built arches with span lengths
as much as 120 feet or more, comparing favorably with our modern
arch-bridge work. They seldom used any other curve for their arches
than the circular, and when they built bridges an odd number of spans
was usually employed, with the central opening the largest, possibly in
obedience to the well-known esthetic law that an odd number of openings
is more agreeable to the eye than an even number. Apparently they were
apprehensive of the safety of the piers from which their arches sprang,
and it was not an uncommon rule to make the thickness of the piers one
third of the clear span. Nearly one fourth of the entire length of the
structure would thus be occupied by the pier thicknesses. Although
the use of mortar, both lime and cement, early came into use with the
Romans, they usually laid up the ring-stones of their arches dry, i.e.,
with out the interposition of mortar joints.
CHAPTER III.
=25. The Roman Water-supply.=—There is no stronger evidence of
engineering development in ancient Rome, nor of the advanced state of
civilization which characterized its people, than its famous system of
water-supply, which was remarkable both for the volume of water daily
supplied to the city and for the extensive aqueducts, many of whose
ruins still stand, as impressive monuments of the vast public works
completed by the Romans. These ruins, and those of many other works,
would of themselves assure us of the elaborate system of supply, but
fortunately there has been preserved a most admirable description of
it, the laws regulating consumption, the manner of administering the
water department of the government of the ancient city, and much other
collateral information of a most interesting character. In the work
entitled, in English, “The Two Books on the Water-supply of the City
of Rome,” by (Sextus) Julius Frontinus, an eminent old Roman citizen,
who, besides having filled the office of water commissioner[1] of
the city, was governor of Britain and three times consul, as well as
having enjoyed the dignity of being augur. He may properly be called
a Roman engineer, although he evidently was a man of many public
affairs, and so esteemed by the emperors who ruled during his time
that he accompanied them in various wars as a military man of high
rank. He wrote seven books at least, viz., “A Treatise on Surveying,”
“Art of War,” “Strategematics,” “Essays on Farming,” “Treatise on
Boundaries, Roads, etc.,” “A Work on Roman Colonies,” and his account
of the water-works of Rome, entitled “De Aquis.” It is the latter
book in which engineers are particularly interested. The translation
of this book from the original Latin is made from what is termed the
“Montecassino Manuscript,” an account of which with the translation is
given by Mr. Clemens Herschel in his entertaining work, “Frontinus, and
the Water-supply of the City of Rome.”
[1] The first permanent water commissioner in Rome was M. Agrippa,
son-in-law of Cæsar Augustus, who took office B.C. 34. He was one of
the greatest Roman engineers and constructors, if indeed he was not the
first in rank.
As near as can be determined Frontinus lived from about A.D. 35 to
A.D. 103 or 104. Judging from the offices which Frontinus held and
the honors which he enjoyed throughout his life, it would appear that
he was a patrician; he was certainly a man of excellent executive
capacity, of intellectual vigor and refined taste, and a conscientious
public servant. The water-supply of the city was held by the Romans
to be one of the most important of all its public works, and its
administration during the life of Frontinus was entrusted to what
we should call a water commissioner, appointed by the emperor. It
was considered to be an office of dignity and honor, and the proper
discharge of its responsibilities was a public duty which required a
high order of talent, as well as great integrity of character.
=26. The Roman Aqueducts.=—Frontinus states that from the foundation
of the city of Rome until 313 B.C., i.e., for a period of 441 years,
the only water-supply was that drawn either from the river Tiber or
from wells or springs. The veneration of the Romans for springs is a
well-known feature of their religious tenets. They were preserved with
the greatest care, and hedged about with careful safeguards against
irreverent treatment or polluting conditions. Apparently after this
date the people of Rome began to feel the need of a public water-supply
adequate to meet the requirements of a great city. At any rate, in
the year 313 B.C. the first aqueduct, called the Appia, for bringing
public water into the city of Rome was attempted by Censors Appius
Claudius, Crassus, and C. Plautius, the former having constructed the
aqueduct, and the latter having found the springs. Appius must have
been an engineer of no mean capacity, for it was he who constructed
the first portion of the Appian Way. The origin of this water-supply
is some springs about 10 miles from Rome, and they may now be seen at
the bottom of stone quarries in the valley of the Anio River. This
aqueduct, Aqua Appia, is mostly an underground waterway, only about
300 feet of it being carried on masonry arches. At the point where
it enters the city it was over 50 feet below the surface; its clear
cross-section is given as 2½ feet wide by 5 feet high. The elevation of
its water surface in Rome was probably under 60 feet above sea-level.
[Illustration: Claudia, of dimension stone, and Anio Novus, of brick
and concrete, on top of it.]
=27. Anio Vetus.=—The next aqueduct built for the water-supply of Rome
was called Anio Vetus. It was built 272-269 B.C., and is about 43 miles
long; it took its water from the river Anio. About 1100 feet of its
length was carried above ground on an artificial structure. It also
was a low-level aqueduct, the elevation at which it delivered water
at Rome being about 150 feet above sea-level. It was built of heavy
blocks of masonry, laid in cement, and the cross-section of its channel
was about 3.7 feet wide by 8 feet high. In the year 144 B.C. the Roman
senate made an appropriation equal to about $400,000 of our money to
repair the two aqueducts already constructed, and to construct a new
one called Aqua Marcia, to deliver water to the city at an elevation
of about 195 feet above sea-level. This aqueduct was finished 140
B.C.; it is nearly 58 miles long, and carried water of most excellent
quality through a channel which, at the head of the aqueduct, was
5⅞ feet wide by 8³/₁₀ feet high, but farther down the structure was
reduced to 3 feet wide by 5⁷/₁₀ feet high. The excellent water of these
springs is used for the present supply of Rome, and is brought in the
Aqua Pia, built in 1869, as a reconstruction of the old Aqua Marcia.
This aqueduct, like its two predecessors, is built of dimension stone,
18 inches by 18 inches by 42 inches, or larger, laid in cement; but
concrete and brick were used in the later aqueducts, with the exception
of Claudia.
=28. Tepula.=—The aqueduct called Aqua Tepula, about 11 miles in
length, and completed 125 B.C., was constructed to bring into the
city of Rome a slightly warm water from the volcanic springs situated
on the hill called Monte Albani (Alban Hills) southeast of Rome. The
temperature of these springs is about 63° Fahr. In the year B.C. 33
Agrippa caused the water from some springs high up the same valley to
be brought in over the aqueduct Aqua Julia, 14 miles long. This latter
water was considerably colder than that of the Tepula Springs. The two
waters were united before reaching Rome and allowed to flow together
far enough to be thoroughly mixed. They were then divided and carried
into Rome in two conduits. The volume of water carried in the Aqua
Julia was about three times that taken from the Tepula Springs, the
cross-section of the latter being only 2.7 feet wide by 3.3 feet high,
while that of Julia was 2.3 feet by 4.6 feet. The water from Aqua Julia
entered Rome at an elevation of about 212 feet above sea-level, and
that from Aqua Tepula about 11 feet lower.
=29. Virgo.=—The sixth aqueduct in chronological order was called
Virgo, and it was completed 19 B.C. It takes water from springs about 8
miles from Rome and only about 80 feet above sea-level, but the length
of the aqueduct is about 13 miles. The delivery of water in the city by
this aqueduct is about 67 feet above that level. The cross-section of
this channel is about 1.6 feet wide and 6.6 feet high.
=30. Alsietina.=—The preceding aqueducts are all located on the left or
easterly bank of the Tiber, but one early structure was located on the
right bank of the Tiber to supply what was called the Trans-Tiberine
section of the city, and it was known as Aqua Alsietina. The emperor
Augustus had this aqueduct constructed during his reign, and it was
finished in the year A.D. 10. Its source is a small lake of the same
name with itself, about 20 miles from Rome. The elevation of this lake
is about 680 feet above sea-level, while the water was delivered at
an elevation of about 55 feet above the same level. The water carried
by this aqueduct was of such a poor quality that Frontinus could not
“conceive why such a wise prince as Augustus should have brought to
Rome such a discreditable and unwholesome water as the Alsietina,
unless it was for the use of Naumachia.” The latter was a small
artificial lake or pond in which sham naval fights were conducted.
[Illustration:
Sand and Pebble Catch-tanks near Tivoli. Dimension-stone aqueducts of
Marcia at either end of the tank built of small stone; _opus incretum_.
The arches are chambers of the tanks.]
=31. Claudia.=—The eighth aqueduct described by Frontinus is the Aqua
Claudia, built of dimension stone, which he calls a magnificent work
on account of the large volume of water which it supplied, its good
quality, and the impressive character of considerable portions of the
aqueduct itself, between 9 and 10 miles being carried on arches. It was
built in 38-52 A.D. and is forty-three miles long. The sources of its
supply are found in the valley of the Anio, and consequently it belongs
to the system on the left bank of the Tiber. The cross-section of its
channel was about 3.3 feet wide by 6.6 feet high. It was a work greatly
admired by the Roman people, as is evidenced by the praise “given to
it by Roman authors who wrote at that time.” It delivered water at the
Palatine 185 feet above sea-level. According to Pliny, the combined
cost of it and the Aqua Anio Novus was 55,500,000 sestertii, or nearly
$3,000,000. This aqueduct probably belongs to the highest type of Roman
hydraulic engineering. It follows closely the location of the Aqua
Marcia, although its alignment now includes a cut-off tunnel about 3
miles long, the latter having been constructed about thirty-six years
after the aqueduct was opened. Mr. Clemens Herschel observes that the
total sum expended for these two aqueducts makes a cost of about $6 per
lineal foot for the two. The arches of this aqueduct and those of the
Anio Novus have clear spans of 18 to 20 feet, with a thickness at the
crown of about 3 feet.
=32. Anio Novus.=—The ninth aqueduct described by Frontinus is called
Anio Novus. It was also constructed in the years A.D. 38-52. This
aqueduct has a length of about 54 miles and takes its supply from
artificial reservoirs constructed by Nero at his country-seat in the
valley of the Anio near modern Subiaco. This structure is built of
brick masonry lined with concrete. That portion of the Aqua Claudia
which is located on the Campagna carries for 7 miles the Anio Novus,
and it forms the long line of aqueduct ruins near Roma Vecchia. The
upper surface of the arch-ring at the crown forms the bottom of the
channel of the aqueduct. The cross-section of the channel of the Anio
Novus was 3.3 feet wide by 9 feet high. The elevation of the water in
this, as in the Claudia, when it reached the Palatine was about 185
feet above sea-level. The Anio Novus in some respects would seem to be
a scarcely less notable work than the Claudia. About 8 miles of its
length is carried on arches, some of them reaching a height of about
105 feet from the ground.
=33. Lengths and Dates of Aqueducts.=—These nine aqueducts constituted
all those described by Frontinus, as no others were completed prior to
his time. Five others were, however, subsequently completed between
the years 109 A.D. and 306 A.D., but enough has already been shown in
connection with the older structures to show the character of the
water-supply of ancient Rome.
The following tabular statement is a part of that given by Mr. F. W.
Blackford in “The Journal of the Association of Engineering Societies,”
December, 1896. It shows the dates and lengths of the ancient aqueducts
of Rome between the years 312 B.C. and 226 A.D., with the length of
the arch portions. The list includes those built up to the end of the
Empire. It will be observed that the total length of the aqueducts
is 346 miles, and that of the arch portions 44 miles. The figures
vary a little from those given by Lanciani and others, but they are
essentially accurate.
+------------+--------+----------+----------+
| | | Total |Length of |
| Name. | Date. |Length in |Arches in |
| | B.C. | Miles. | Miles. |
+------------+--------+----------+----------+
|Appia | 312 | 11 | Little |
|Vetus | 272-264| 43 | ” |
|Marcia | 145 | 61 | 12 |
|Tepula | 126 | 13 | Little |
|Julia | 34 | 15 | 6 |
|Virgo | 21 | 14 | Little |
| | | | |
| | A.D. | | |
|Alsietina | 10 | 22 | Little |
|Augusta | 10 | 6 | ” |
|Claudia | 50 | 46 | 10 |
|Anio Novus | 52 | 58 | 9 |
|Triana | 109 | 42 | Little |
|Alexandrina | 226 | 15 | 7 |
| +--------+----------+----------+
| Totals | 346 | 44 |
+------------+--------+----------+----------+
=34. Intakes and Settling-basins.=—The preceding brief descriptions
of the old Roman aqueducts give but a superficial idea of the real
features of those great works and of the system of water-supply of
which they were such essential portions. Enough has been shown,
however, to demonstrate conclusively that the engineers and
constructors of old Rome were men who, on the one hand, possessed a
high order of engineering talent and, on the other, ability to put in
place great structures whose proportions and physical characteristics
have commanded the admiration of engineers and others from the time
of their completion to the present day. If a detailed statement were
to be made in regard to the water-supply of ancient Rome, it would
appear that much care was taken to insure wholesome and potable water.
At the intakes of a number of the aqueducts, reservoirs or basins
were constructed in which the waters were first received and which
acted as settling-basins, so that as much sedimentation as possible
might take place. Similar basins (picinæ) were also constructed at
different points along the aqueducts for the same purpose and for
such other purposes as the preservation of the water in a portion
of the aqueduct in case another portion had to be repaired or met
with an accident which for the time being might put it out of use.
These basins were usually constructed of a number of apartments, the
water flowing from one to the other, very much as sewage in some
sewage-disposal works flows at the present time through a series of
settling-basins. The object of these picinæ was the clearing of the
water by sedimentation. Indeed there was in some cases a use of salt in
the water to aid in clarifying it. This is an early type of the modern
process of clarifying water by chemical precipitation, not the best of
potable water practice, but one that is sometimes permissible.
=35. Delivery-tanks.=—The aqueducts brought the water to castellæ
or delivery-tanks, i.e., small reservoirs, both inside the city and
outside of it, and from these users were obliged by law to take
their supplies; that is, for baths, for fountains, for public uses,
for irrigation, and for private uses. When Frontinus wrote his “De
Aquis” a little less than three tenths of all the water brought to
Rome by the aqueducts was used outside of the city. The remainder was
distributed in the city from 247 delivery-tanks or small reservoirs,
about one sixth of it being consumed by 39 ornamental fountains and 591
water-basins.
=36. Leakage and Lining of Aqueducts.=—These aqueducts were by no
means water-tight. Indeed they were subject to serious leakage, and
Frontinus shows that forces of laborers were constantly employed in
maintaining and repairing them. As has been stated, the older aqueducts
were built of dimension stones, while the later were constructed of
concrete or bricks and concrete. The channels of these aqueducts, as
well as reservoirs and other similar structures, were made as nearly
water-tight as possible by lining them with a concrete in which
pottery, broken into fine fragments, was mixed with mortar.
[Illustration: Claudia and Anio Novus near Porta Furba. Repairs in
brickwork and in a composite of concrete and brickwork.]
=37. Grade of Aqueduct Channels.=—The fall of the water surface in
these aqueducts cannot be exactly determined. The levelling-instruments
used by the Romans were simple and, as we should regard them, crude,
although they served fairly well the purposes to which they were
applied. They were not sufficiently accurate to determine closely the
slope or grade of the water surface in the aqueduct channels. The
deposition of the lime from the water along the water surface on the
sides of the channels in many cases would enable that slope to be
determined at the present time, but sufficiently careful examinations
have not yet been made for that purpose. Lanciani states that the
slopes in the Aqua Anio Vetus vary from about one in one thousand to
four in one thousand. An examination of the incrustation on the sides
of the Aqua Marcia near its intake makes it appear that the slope of
the surface was about .06 foot per 100 feet, which would produce a
velocity, according to the formula of Darcy, of about 3.3 feet per
second. In some aqueducts built in Roman provinces it would appear that
slopes have been found ranging from one in six hundred to one in three
thousand.
=38. Qualities of Roman Waters.=—The chief characteristic in most of
the old Roman waters was their extreme hardness. They range from 11°
to 48° of hardness, the latter belonging to the water of the Anio,
while the potable waters in this country scarcely reach 5°. The old
Romans recognized these characteristics of their waters and, as has
been intimated, used the best of them for table purposes, while the
less wholesome were employed for fountains, flushing sewers, and other
purposes not affected by undesirable qualities. The water from Claudia,
for instance, was used for the imperial table. The water from the Aqua
Marcia was also of excellent quality, while that brought in by the Aqua
Alsietina was probably not used for potable purposes at all.
=39. Combined Aqueducts.=—In several cases a number of aqueduct
channels were carried in one aqueduct. A marked instance of this kind
was that of Julia, Tepula, and Marcia, all being carried in vertical
series in one structure. Numerous instances of this sort occurred.
=40. Property Rights in Roman Waters.=—In reading the two books of
Frontinus one will be impressed by the property values which the old
Romans created in water rights. The laws of Rome were exceedingly
explicit as to the rights of water-users and as to the manner in which
water should be taken from the aqueducts and from the pipes leading
from the reservoirs in and about the city. The proper methods for
taking the water and using it were carefully set forth, and penalties
were prescribed for violations of the laws pertaining to the use of
water. There were many abuses in old Rome in the administration of
the public water-supply, and one of the most troublesome duties which
Frontinus had to perform lay in reforming those abuses and preventing
the stealing of water. The unit of use of water (a “quinaria,” whose
value is not now determinable) was the volume which would flow from
an orifice .907 inch in diameter and having an area of about .63 of
a square inch. Mr. Herschel shows that in consequence of the failure
of the Romans to understand the laws of the discharge of water under
varying heads, the quinaria may have ranged from .0143 cubic foot to
.0044 cubic foot per second or between even wider limits.
=41. Ajutages and Unit of Measurement.=—Frontinus describes twenty-five
ajutages of different diameter, officially approved in connection with
the Roman system of public water-supply; but only fifteen of these were
actually used in his day. All of these were circular in form, although
two others had been used prior to that time. They varied in diameter
from .907 to 8.964 English inches and were originally made of lead, but
that soft metal lent itself too easily to the efforts of unscrupulous
water-users to enlarge them by thinning the metal. In his time they
were made of bronze, which was a hard metal and could not be tampered
with so as to enlarge its cross-section. The discharge through the
smallest of these ajutages was the quinaria, the unit in the scale of
water rights. The largest of the above ajutages had a capacity of a
little over 97 quinariæ.
This unit (the quinaria) was based wholly on superficial area, and had
no relation whatever to the head over the orifice or to the velocity
corresponding to that head. Although Frontinus refers in several cases
to the fact that the deeper the ajutage is placed below the water
surface the greater will be the discharge through it, also to the fact
that a channel or pipe of a given area of cross-section will pass
more water when the latter flows through it with a high velocity, he
and other Roman engineers seem to have failed completely to connect
the idea of volume of discharge to the product of area of section by
velocity. In the Roman mind of his day, and for perhaps several hundred
years after that, the area of the cross-section of the prism of water
in motion was the only measure of the volume of discharge. This seems
actually preposterous at the present time, and yet, as observed by Mr.
Herschel, possibly a majority of people now living have no clearer idea
of the volume of water flowing in either a closed or open channel.
Existing statutes even respecting water rights bear out this statement,
improbable as it may at first sight appear. This early Roman view of
the discharge is, however, in some respects inexplicable, for Hero of
Alexandria wrote, probably in the period 100-50 B.C., that the section
of flow only was not sufficient to determine the quantity of water
furnished by a spring. He proceeded to set forth that it was also
necessary to know the velocity of the current, and further explained
that by forming a reservoir into which a stream would discharge for an
hour the flow or discharge of that stream for the same length of time
would be equal to the volume of water received by the reservoir. His
ideas as to the discharge of a stream of water were apparently as clear
as those of a hydraulic engineer of the present time. Indeed the method
which he outlines is one which is now used wherever practicable.
It has been a question with some whether Frontinus and other Roman
engineers were acquainted with the fact that a flaring or outward
ajutage would increase the flow or discharge through the orifice.
The evidence seems insufficient to establish completely that degree
of knowledge on their part. At the same time, in the CXII chapter of
Frontinus’ book on the “Water-supply of the City of Rome,” he states
that in some cases pipes of greater diameter than that of the orifice
were improperly attached to legal ajutages. He then states: “As a
consequence the water, not being held together for the lawful distance,
and being on the contrary forced through the short restricted distance,
easily filled the adjoining larger pipe.” He was convinced that the
use of a pipe with increased diameter under such circumstances would
give the user of the water a larger supply than that to which he was
entitled, and he was certainly right in at least most cases.
The actual unit orifice through which the unit volume of water called
the quinaria was discharged was usually of bronze stamped by a proper
official, thus making its use legal for a given amount of water. The
Roman engineers understood that such an orifice should be inserted
accurately at right angles to the side of the vessel or orifice, and
that was the only legal way to make the insertion. Furthermore, the law
required that there should be no change in the diameter of the pipe
within 50 feet of the orifice. It was well known that a flaring pipe
of increased diameter applied immediately at the orifice would largely
increase the discharge, and unscrupulous people resorted to that means
for increasing the amount of water to be obtained for a given price.
=42. The Stealing of Water.=—It appears also that Frontinus experienced
much trouble from clandestine abstraction of water from reservoirs and
water-pipes. The administration of the water commissioner’s office
had been exceedingly corrupt prior to his induction into office, and
some of his most troublesome official work arose from his efforts to
detect water-thieves, and to guard the supply system from being tapped
irregularly or illegally. We occasionally hear of similar instances of
water-stealing at the present time, which shows that human nature has
not altogether changed since the time of Frontinus.
=43. Aqueduct Alignment and Design of Siphons.=—The alignment of some
of the Roman aqueducts followed closely the contours of the hills
around the heads of valleys, while others took a more direct line
across the valleys on suitable structures, frequently series of arches.
Judging from our own point of view it may not be clear at first sight
why such extensive masonry constructions were used when the aqueduct
could have been kept in excavation by following more closely the
topography of the country. There is little doubt that the Romans knew
perfectly well what they were about. Indeed it is definitely stated in
some of the old Roman writings that the structures were built across
valleys for the specific purpose of saving distance which, in most
instances at least, meant saving in cost.
These masonry structures, it must be remembered, were built of material
immediately at hand. Furthermore, these aqueducts were generally only
made of sufficient width for the purpose of carrying water-channels.
They were not wide structures. In some cases they were not more than
8 feet or 9 feet wide for a height of nearly 100 feet. The cost of
construction was thus largely reduced below that of wide structures.
[Illustration: Old Roman Lead and Terra-cotta Pipe.]
The Romans were perfectly familiar with the construction of inverted
siphons. As a matter of fact Vitruvius, in Chapter VII of his Eighth
book, describes in detail how they should be designed. His specific
descriptions relate to lead pipes, but it is clear from what he states
at other points that he considered earthenware pipes equally available.
He sets forth how the pipes should be carried down one slope, along
the bottom of the valley, and up the other slope, the lowest portion
being called the “venter.” He realized the necessity of guarding all
elbows in the pipe by using a single piece of stone as a detail for the
elbow, a hole being cut in it in each direction in which the adjoining
sections of pipe should be inserted, the sections of lead pipe being
10 feet long, and even goes so far as to describe the stand-pipes that
should be inserted for the purpose of allowing air to escape. Vitruvius
also advises that the water should not only be admitted to inverted
siphons in a gradual manner, but that ashes should be thrown into the
water when the siphon is first used in order that they may settle into
the joints or open places so as to close any existing leaks. Lead pipe
siphons, 12 to 18 inches in diameter, with 1 inch thickness of metal
under 200 feet head, built in ancient times, have been found at Lyons
in France. Also a drain-pipe siphon with masonry reinforcement was
built at Alatri in Italy 125 B.C. to carry water under a head of
about 340 feet. There are other notable instances of inverted siphons
constructed and used during the ancient Roman period, some of them
being of lead pipe imbedded in concrete.
CHAPTER IV.
=44. Antiquity of Masonry Aqueducts.=—Masonry aqueducts, either solid
or with open arches, were not first constructed by the city of Rome;
their origin was much farther back in antiquity than that. The Greeks
at least used them before the Roman engineers, and it is not unlikely
that the latter drew their original ideas from the former, if indeed
they were not instructed by them. Nor during the times of the Romans
was the construction of aqueducts confined to Rome. Wherever Roman
colonies were created it would appear that vast sums were expended in
the construction of aqueducts for the purpose of suitably supplying
cities with water. Such constructions are found at many points in
Spain, France, and other countries which were in ancient times Roman
colonies. It is probable that there are not less than one hundred, and
perhaps many more, of such structures in existence at the present time.
=45. Pont du Gard.=—Among the more prominent aqueducts constructed
during the old Roman period and outside of Italy were the Pont du Gard
at Nismes in the south of France, and those at Segovia and Tarragona in
Spain. The Pont du Gard has three tiers of arches with a single channel
at the top. The greatest height above the river Gardon is about 180
feet, and the length of the structure along the second tier of arches
is 885 feet. The arches in the lowest tier are 51 feet, 63 feet, and
80.5 feet in span, while the arches in the highest tier are uniformly
15 feet 9 inches in span. The thickness of the masonry at the top of
the structure from face to face is 11 feet 9 inches, and 20 feet 9
inches at the lower tier of arches, the thickness at the intermediate
tier being 15 feet.
The largest arch has a depth of keystone of 5 feet 3 inches, while the
other arches of the lower tier have a depth of keystone of 5 feet. The
depth of the ring-stones of the small upper arches is 2 feet 7 inches.
This structure forms a sort of composite construction, the lower arches
constituting four separate arch-rings placed side by side, making a
total thickness of 20 feet 9 inches. The intermediate arches consist
of three similar series of narrow arches placed side by side, but the
masonry of the upper tier is continuous throughout from face to face.
The three and four parallel series of arches of the middle and lowest
tiers are in no way bonded or connected with each other. There is no
cementing material in any of the arch-rings, but cement mortar was used
in rubble masonry or concrete around the channel through which the
water flowed above the upper tier of small arches. This structure is
supposed to have been built between the years 31 B.C. and 14 A.D.
=46. Aqueducts at Segovia, Metz, and Other Places.=—The Segovia
aqueduct was built by the emperor Trajan about A.D. 100-115. It is
built without mortar, and has 109 arches, but 30 are modern, being
reproductions of the old. It has a length of over 2400 feet, and in
places its height is about 100 feet. The old Tarragona aqueduct is
built with two series of arches, 25 being in the upper series and 11
in the lower. It is 876 feet long and has a maximum height of over 80
feet. At Mayence there are ruins of an aqueduct about 16,000 feet long.
In Dacia, Africa, and Greece there are other similar ruins. Near Metz
are the remains of a large old Roman aqueduct. It consisted of a single
row of arches, and had no features of particular prominence. This
latter observation, however, could not be made of one of the bridges in
the aqueduct at Antioch. Although the masonry and design of this latter
structure were crude, its greatest height is 200 feet, and its length
700 feet. The lower portion of this structure was a solid wall with the
exception of two openings, the arches extending in a single row along
its upper portion. On the island of Mytilene are the ruins of another
old aqueduct about 500 feet long, with a maximum height of about 80 feet.
The building of these remarkable aqueducts was practised at least
down to the later periods of the Roman empire, that of Pyrgos, near
Constantinople,—built not earlier than the tenth century,—being an
excellent example. It consists of two branches at right angles to each
other. The greater branch is 670 feet long, and its greatest height
106 feet. There are three tiers of arches, the two upper being of
semicircular and the lower of Gothic outline. The number in each tier
for a given height is the same, but with an increasing length of span
in rising from the lowest to the highest tier. Thus the highest tier of
piers is the lightest, relieving the top of the structure of weight.
The lowest row of piers is reinforced by counterforts or buttresses.
At the top of the structure the width or thickness is 11 feet, but the
thickness increases uniformly to 21 feet at the bottom. The smaller
branch of the aqueduct is 300 feet long, and was built with twelve
semicircular arches.
=47. Tunnels.=—The construction of tunnels, especially in connection
with the building of aqueducts, constituting a branch of engineering
procedure, was frequently practised by the ancient nations. Large
tunnel-works were executed many times by the ancient Greeks and Romans.
It would seem that the Greeks were the instructors of the Romans in
this line of engineering operations. As early as B.C. 625 we are told
that the Greek engineer Eupalinus constructed a tunnel 8 feet broad, 8
feet high, and 4200 feet long, through which was built a channel for
carrying water to the city of Athens.
Sixty-five years later a similar work was constructed for the same
Grecian city. Indeed it appears that tunnels were constructed in the
time of the earliest history of aqueducts built to supply ancient Greek
and Roman cities with water.
It is certain that at the beginning of the Christian era tunnelling
processes were well known among the Romans. Vitruvius writes, in
speaking of the construction of aqueducts, in Chapter VII of the Eighth
Book: “If hills intervene between the city wall and spring head,
tunnels underground must be made, preserving the fall above assigned;
if the ground cut through be sandstone or stone, the channel may be cut
therein; but if the soil be earth or gravel, side walls must be built,
and an arch turned over, and through this the water may be conducted.
The distance between the shafts over the tunnelled part is to be 120
feet.”
The Romans pierced rock in their tunnel-work, not only by chiselling,
but sometimes by building fire against the rock so as to heat it as
hot as possible. The heated rock was then drenched with cold water, so
that it might be cracked and disintegrated to as great an extent as
practicable. According to Pliny vinegar was used instead of water in
some cases, under the impression that it was more efficacious.
[Illustration: Roman water-pipe made of bored-out blocks of stone.]
One of the methods mentioned by Vitruvius is plainly “the cut and
cover” procedure of the present day. In Duruy’s history of Rome a
tunnel over three miles long is mentioned on a line of an aqueduct at
Antibes in France, as well as another constructed to drain Lake Fucinus
in Italy, about A.D. 50. It is there stated that the latter required
eleven years’ labor of 30,000 men to build a rock tunnel with a section
of 86 to 96 square feet 18,000 feet long.
Lanciani, in his “Ancient Rome,” states that about A.D. 152 a Roman
engineer (Nonius Datus) began the construction of a tunnel in Algeria,
and after having carefully laid out the axis of the tunnel across the
ridge “by surveying, and taking the levels of the mountains,” left the
progress of the work in the hands of the contractor and his workmen.
After the rather long absence from such a work of four years he was
called back by the Roman governor to ascertain why the two opposite
sections of the tunnel, as constructed, would not meet, and to take
the requisite measures for the completion of the work through which
water was to be conducted to Saldæ in a suitable channel. He explains
that there should have been no difficulty, and that the failure of the
two headings to meet was due to the negligence of the contractor and
his assistant, whom he states “had committed blunder upon blunder,”
although he writes, “As always happens in these cases, the fault was
attributed to the engineer.” He solved the problem by connecting the
two approximately parallel tunnels by a transverse tunnel, so that
water was finally brought to the city of Saldæ.
The art of tunnel construction has been one of the most widely
practised branches of Civil-Engineering from the times of the ancient
Assyrians, Egyptians, Greeks, Romans, and other ancient nations down to
the present.
=48. Ostia, the Harbor of Rome.=—The capacity of the ancient Romans
to build harbor-works is shown by what they did at Ostia, which was
then at the mouth of the Tiber, but is now not less than four miles
inland from the present shore line. At the Ostia mouth of the river the
present annual average advance seaward is not less than 30 feet, and at
the Fiumicino mouth about one third of that amount.
[Illustration: FIG. 13.—Plan of Ostia and Porto.]
The ancient port of Ostia is supposed to have been founded during the
reign of the fourth king Ancus Marcius, but it attained its period
of greatest importance during the reign of Claudius and Trajanus. At
that time the fertile portions of the Campania had been so largely
taken up by the country-places of the wealthy Romans that it was no
longer possible for the peasantry to cultivate sufficient ground to
yield the grain required by the home market of the Romans. Large
fleets were consequently engaged in the foreign grain-trade of Rome.
The wheat and other grain required in great quantities was grown
mostly in Egypt, although Carthage and other countries supplied large
amounts. The great fleets occupied in this trade made ancient Ostia
their Roman port. At the present time it has no inhabitants, but is a
group of complete ruins, with its streets of tombs, baths, palaces,
and temples, deeply covered with the accumulations of many centuries.
Enough excavations have been made along the shores of the Tiber at
this point to show that the river was bordered with continuous and
substantial masonry quays, flanked on the land side by successions of
great warehouses, obviously designed to receive grain, wine, oil, and
other products of the time. The entrance to this harbor was difficult,
as the mouth of the river was shallow, with bars apparently obstructing
its approach. There were no jetties, or other seaward works for the
protection of vessels desiring to make the harbor. It is stated that
during one storm nearly or quite two hundred vessels were destroyed
while they were actually in the harbor.
=49. Harbors of Claudius and Trajan.=—The difficulty in entering the
mouth of the Tiber prompted the emperor Claudius to construct another
harbor to accommodate the vast commerce then centring at the port of
Rome. Instead of increasing the capacity of Ostia and opening the mouth
of the river by deepening it, he constructed a new harbor on what was
then the seashore, a short distance from Ostia, and connected it with
the Tiber by a canal, the extension of which by the natural forces of
the river has become the Fiumicino, the only present navigable entrance
to the river. This harbor was enclosed by two walls stretching out
from the shore, and converging on the sea side to a suitable opening
left for the entrance of ships. The superficial area of this harbor
was about 175 acres, but it became insufficient during the time of
Trajan. He then proceeded to excavate inland a hexagonal harbor with
a superficial area of about 100 acres, which was connected both with
the harbor of Claudius and the canal connecting the latter with the
Tiber. These harbor-works were elaborate in their fittings for the
accommodation of ships, and were built most substantially of masonry.
They showed that at least in some branches of harbor-work the old
Romans were as good engineers as in the construction of aqueducts,
bridges, and other internal public works. The harbors at ancient
Ostia, including those of Claudius and Trajan, were not the only works
of their class constructed by the Romans, but they are sufficient to
show as great advancement in harbor and dock work as in other lines of
engineering.
These harbors were practically defenceless and exposed to the
incursions of pirates, which came to be frequently and successfully
made in the days of the declining power of Rome. It was therefore
rather early in the Christian era that these attacks discouraged, and
ultimately drove away, first, the maritime business of the Romans and,
subsequently, all the inhabitants of these ports, leaving the pillaged
remnants of the vast harbor-works, warehouses, palaces, temples, and
other buildings in the ruined condition in which they are now found.
CHAPTER V.
=50. Ancient Engineering Science.=—The state of what may be called the
philosophy or science of engineering construction in ancient Rome is
admirably illustrated by the work on Architecture by Marcus Vitruvius
Pollio, who is ordinarily known as Vitruvius, and who wrote probably a
little more than two thousand years ago. He calls himself an architect,
and his work is a classic in that profession of which he claims to be
a member. Although much of his work was purely architectural, a great
portion of it, on the other hand, was not architecture as we now know
it, but civil-engineering in the best sense of the term. It must be
remembered, therefore, that what is here written applies to that large
portion of his work which is purely civil-engineering.
It will be seen that although he understood really little or nothing
about the science of civil-engineering as we now comprehend it, he
perceived many of the general and fundamental principles of the best
practice of that profession and frequently applied them in a manner
which would do credit to a modern civil engineer. He not only laid
down axioms to govern the design of civil-engineering structures and
machinery for the transmission of power, but he also set forth many
considerations bearing upon public and private health and the practice
of sanitary engineering in a way that was highly creditable to the
state of scientific knowledge in his day. Speaking of the general
qualifications of an architect, remembering that that word as he
understood it includes the civil engineer, he states: “An architect
should be ingenious, and apt in the acquisition of knowledge; ... he
should be a good writer, a skilful draughtsman, versed in geometry and
optics, expert at figures, acquainted with history, informed on the
principles of natural and moral philosophy, somewhat of a musician,
not ignorant of the sciences both of law and physics, nor of the
motions, laws, and relations to each other of the heavenly bodies.”
Again he adds: “Moral philosophy will teach the architect to be above
meanness in his dealings and to avoid arrogance; it will make him just,
compliant, and faithful to his employer; and, what is of the highest
importance, it will prevent avarice gaining an ascendency over him; for
he should not be occupied with the thoughts of filling his coffers, nor
with the desire of grasping everything in the shape of gain, but by
the gravity of his manners and a good character should be careful to
preserve his dignity.”
These quaint statements of the desirable qualities of a professional
man are worthy to be considered rules of good professional living at
this time fully as much as they were in the days of old Rome. His
esteem for his profession was evidently high, but not higher than the
value which every civil engineer should put upon his professional
life. The need of a general education for a civil engineer is greater
now even than in his day, although musical accomplishments need not
be considered as essential in modern engineering practice. That
qualification, it is interesting to observe in passing, was inserted by
Vitruvius in order to illustrate the wide range of engineering practice
in those days when the architect-engineer was called upon, among other
things, to construct catapults and other engines of war, in which
a nice adjustment of gut ropes was determined by the musical tones
emitted under the desired tension.
=51. Ancient Views of the Physical Properties of Materials.=—When it
is remembered that the chemical constitution of materials used in
engineering was absolutely unknown, that no quantitative determination
of physical qualities had been made, and that the first correct
conception of engineering science had yet to be acquired, it is
a matter of wonder that there had been attained the engineering
development evidenced both by ancient writings like those of Vitruvius
and great engineering works like those of Rome, in the Babylonian Plain
and in Egypt. In discussing the problem of water-supply, he mentions
that certain learned ancients, “physiologists and philosophers,
maintained that there are four elements—air, fire, water, and earth—and
that their mixture, according to the difference of the species,
formed a natural mode of different qualities. We must recollect that
not only from these elements are all things generated, but that they
can neither be nourished nor grow without their assistance.” This
view of the construction of material things was not conducive to a
clear comprehension of those physical laws which lie at the foundation
of engineering science, and it is absolutely essential that these
elementary considerations be kept constantly in view in considering the
engineering attainments of the Romans and other ancient peoples.
=52. Roman Civil Engineers Searching for Water.=—In ancient times, as
at present, it was very important in many cases to know where to look
for water, and how to make what might promise to be a successful search
for it. Vitruvius states that the sources of water for a supply may
easily be found “if the springs are open and flowing above ground.” If
the sources are not so evident, but are more obscure, he recommends
that “before sunrise one must lie down prostrate in the spot where he
seeks to find it, and, with his chin placed on the ground and fixed,
look around the place; for, the chin being fixed, the eye cannot range
upwards further than it ought and is confined to the level of the
place. Then where the vapors are seen curling together and rising into
the air, there dig, because those appearances are not discovered in dry
places.” This method of discovering water-supply would be considered
by modern engineers at least somewhat awkward as well as damp and
disagreeable in the early morning hours. It is not more fantastic,
however, or less philosophical than the use of the divining-rod, which
has been practised in modern times as well as ancient, and is used even
in some country districts at the present time.
Vitruvius does not forget that the local features, including both
those of soil and of an artificial character, may affect the quality
of the water and possibly make it dangerous. He, therefore, sets forth
general directions by which good potable water may be found and that
of a dangerous nature avoided. The necessity of distinguishing between
good and bad water was as present to his mind and to the minds of the
old Roman engineers as to civil engineers of the present day, but the
means for making a successful discrimination were crude and obviously
faulty, and very often unsuccessful. He set forth, what is well known,
that rain-water when collected from an uncontaminated atmosphere is
most wholesome, but proceeds to give reasons which would not now be
considered in the highest degree scientific.
In Chapter V of his Eighth Book there are described some “means of
judging water” so quaint and amusing that they may now well be quoted
even though no civil engineer would be bold enough to cite them in
modern hydraulic practice. He says: “If it be of an open and running
stream, before we lay it on, the shape of the limbs of the inhabitants
of the neighborhood should be looked to and considered. If they are
strongly formed, of fresh color, with sound legs and without blear
eyes, the supply is of good quality.” At another point he comes rather
closely to our modern requirements which look to the exclusion of
minute and elementary vegetable growths, when he says: “Moreover, if
the water itself, when in the spring, is limpid and transparent, and
the places over which it runs do not generate moss, nor reeds, nor
other filth be near it, everything about it having a clean appearance,
it will be manifest by these signs that such water is light and
exceedingly wholesome.”
=53. Locating and Designing Conduits.=—In treating of the manner
of conducting water in pipes or other conduits, he adverts to the
necessity of accurate levelling and the instruments that were used for
that purpose. The three instruments which he mentions as being used are
called the dioptra, the level (_libra aquaria_), and the chorobates,
the latter consisting of a rod about 20 feet in length, having two
legs at its extremities of equal length and at right angles to it.
Cross-pieces were fastened between the rod and the legs with vertical
lines accurately marked on them. These vertical lines were placed in
a truly vertical position by means of plumb-lines so that the top of
the rod was perfectly level, and the work could thus be made level in
reference to it.
In Rome the water was generally conducted either by means of open
channels, usually built in masonry for the purpose, or in lead pipes,
or in “earthen tubes.” Vitruvius states that the open channels should
be as solid as possible, and have a fall of not less than one half a
foot in 100 feet. The open channels were covered with an arch top, so
that the sun might be kept from striking the water. After bringing the
water to the city it was divided into three parts. One was for the
supply of pools and fountains, another for the supply of baths, and
a third for the supply of private houses. A charge was made for the
use of water for the pools, fountains, and baths, and in this way a
yearly revenue was obtained. A further charge was also made for the
water used in private houses, the revenue from which was applied for
the maintenance of the aqueduct which supplied the water. The treatment
to be given to the different soils, rocks, and other materials through
which the conduit was built which brought the supply to Rome is duly
set forth by Vitruvius, and he describes the conditions under which
tunnels were constructed. He also described the methods of classifying
the lead pipes through which water was conducted from the reservoirs
to the various points in the city after stating that they must be made
in lengths of not less than 10 feet. The sheets of lead employed in
the manufacture of the pipes he describes as ranging in width from 5
inches to 100 inches. The diameter of the pipe would obviously equal
very closely the width of the sheet divided by the ratio between the
circumference and the diameter of the corresponding circle.
=54. Siphons.=—He speaks of passing valleys in the construction of the
conduits by means of what we now call siphons, and prescribes a method
for relieving it of the accumulated air. In speaking of earthen tubes
or pipes he says that they are to be provided not less than 2 inches
thick and “tongued at one end so that they may fit into one another,”
the joints being coated with quicklime and oil. He further observes
that water conducted through earthen pipes is more wholesome than that
through lead, and that water conveyed in lead must be injurious because
from it white lead is obtained, which is said to be injurious to the
human system. Indeed the effects of lead-poisoning were recognized in
those early days, and its avoidance was attempted. In the digging of
wells he wisely states that “the utmost ingenuity and discrimination”
must be used in the examination of the conditions under which wells
were to be dug. He also appreciated the advantage of sedimentation,
for he advises that reservoirs be made in compartments so that, as the
water flows from one to another, sedimentation may take place and the
water be made more wholesome.
=55. Healthful Sites for Cities.=—In the location of cities, as well as
of private residences, Vitruvius lays down the general principle that
the greatest care should be taken to select sites which are healthy
and subject only to clean and sanitary surroundings. Marshy places and
those subject to fogs, especially those “charged with the exhalations
of the fenny animals,” are to be avoided. Apparently this reference to
“fenny animals” may have beneath it the fundamental idea of bacteria,
but that is not certain. The main point of all these directions for
the securing of sanitary conditions of living is that, so far as his
technical knowledge permitted him to go, he insists on the same class
of wholesome conditions that would be prescribed by a modern sanitary
engineer.
=56. Foundations of Structures.=—Similarly in Chapter V of his
First Book, on “Foundations of Walls and Towers,” Vitruvius shows a
realization of the principal conditions needful and requisite for
the suitable founding of heavy buildings. After a sanitary site for
a city is determined and one that can be put in communication with
other people “by good roads, and river or sea navigation for the
transportation of merchandise,” he proceeds to state that “foundations
should be carried down to solid bottom, if such can be found, and
that they should be built thereon of such thickness as may be
necessary for the proper support of that part of the wall standing
above the natural level of the ground. They should be of the soundest
workmanship, and materials of greater thickness than the walls above.”
Again, in speaking of the foundations supporting columns, he states:
“The intervals between the foundations brought up under the columns
should be either rammed down hard, or arched, so as to prevent the
foundation-piers from swerving. If solid ground cannot be come to,
and the ground be loose or marshy, the place must be excavated,
cleared, and either alder, olive, or oak piles, previously charred,
must be driven with a machine as close to each other as possible
and the intervals between the piles filled with ashes. The heaviest
foundations may be laid on such a base.” It is thus seen that pile
foundations were used by the Romans, and that the piles were driven
with a machine. It would be difficult to give sounder general rules of
practice even after more than two thousand years’ additional experience.
=57. Pozzuolana and Sand.=—Of all the materials which were useful to
the Romans in their various classes of construction, including the
foundations of roads, “pozzuolana” must have been the most useful,
and that which contributed more to the development of successful
construction in Rome than any other single agent. Vitruvius speaks
of it frequently and gives rules not only for the use of it in the
production of mortar and concrete, but also lays down at considerable
length the treatment which should be given to lime in order to produce
the best results. It was common, according to his statements, to use
two measures of “pozzuolana” with one of lime in order to obtain
a suitable cementing material. This mixture was used in varying
proportions with sand and gravel or broken stone to produce concrete.
He describes the various grades of sands to be found about Rome and the
manner of using them. The statement is made that sand should be free of
earth and that the best of it was such as to yield a “grating sound”
when “rubbed between the fingers.” This is certainly a good engineering
test of sand. He prefers pit-sand to either river- or sea-sand; indeed
throughout all his directions regarding this particular class of
construction his rules might be used at the present time with perfect
propriety.
=58. Lime Mortar.=—The old Romans had also discovered the advisability
of allowing lime to stand for a considerable period of time after
slaking. This insured the slaking of all those small portions which
were possibly a little hydraulic and therefore slaked very slowly. He
prescribes as a good proportion two parts of sand to one of lime, and
also mentions the proportion of three to one. He attempts to explain
the setting, as we term it, of lime, but his explanation in obscure
terms, involving qualities of the elements of fire and air, is not very
satisfactory.
=59. Roman Bricks according to Vitruvius.=—As is well known, the
Romans were good brick-makers, and they were well aware that bricks
made from “ductile and cohesive” “red or white chalky” earth were far
preferable to those made of more gravelly or sandy clay. The Roman
bricks were both sun-dried and kiln-burned.
=60. Roman Timber.=—Timber was a material much used by the Romans, and
the greater part of that which they used probably was grown in Italy,
although considerable quantities were imported from other localities.
Vitruvius writes in considerable detail concerning the selection of
timber while standing, as well as in reference to its treatment before
being used in structures. Like every material used by the old Romans
in construction, the various kinds and qualities of timber received
careful study from them, and they were by no means novices in the art
of producing the best results from those kinds of timber with which
they were familiar.
=61. The Rules of Vitruvius for Harbors.=—In Chapter XII of his Fifth
Book Vitruvius lays down certain general rules for the selection and
formation of harbors, and it is known that the Romans were familiar
with elaborate and effective harbor construction, as is shown by
that at Ostia. He appreciates that a natural harbor is one which has
“rocks or long promontories jutting out, which from the shape of the
place form curves or angles,” and that in such places “nothing more
is necessary than to construct portices and arsenals around them, or
passages to the markets.” He then proceeds to state that if such a
natural formation is not to be found, and that if “on one side there
is a more proper shore than on the other, by means of building or of
heaps of stones, a projection is run out, and in this the enclosures of
harbors are formed.” He then proceeds to explain how “pozzuolana” and
lime, in the proportion of two of the former to one of the latter, are
used in subaqueous construction. He also prescribed a mode of building
a masonry wall up from the bottom of an excavation made within what we
should call a coffer-dam, formed, among other things, “of oaken piles
tied together with chain pieces.” The Romans knew well how to select
harbors and how to construct in an effective manner the artificial
works connected with them, although it appears that the effects of
tidal and river currents in estuaries were neither well understood in
themselves nor in their transporting power of the solid material which
those currents eroded.
=62. The Thrusts of Arches and Earth; Retaining-walls and
Pavements.=—Although the Romans possessed little or no knowledge
of analytical mechanics they attained to some good qualitative
mechanical conceptions. Among other things they understood fairly
well the general character of the thrust of an arch and the tendency
of the earth to overthrow a retaining-wall. They knew that a massive
abutment was needed to receive safely the thrust of an arch, and they
counterforted or buttressed retaining-walls in order to hold them
firmly in place. They also realized the danger of wet earth pressing
against a retaining-wall, and even made a series of offsets or teeth
on the inside of the wall on which the earth rested in order to aid in
holding the wall in place. Vitruvius recommends as a safeguard against
the pressure of earth wet by winter rains that “the thickness of the
wall must be proportioned to the weight of earth against it,” and that
counterforts or buttresses be employed “at a distance from each other
equal to the height of the foundations, and of the same width as the
foundations,” the projections at the bottom being equal in thickness to
that of the wall, and diminishing toward the top.
He gives in considerable detail instructions for the forming of
pavements and stucco work, so many examples of which are still existing
in Rome. These rules are in many respects precisely the same as would
govern the construction of similar work at the present time. There are
also described in a general way the methods of producing white and
red lead, as pigments of paints, and a considerable number of other
pigments of different colors.
=63. The Professional Spirit of Vitruvius.=—It is evident, from many
passages in the writings of this Roman architect-engineer, that the
ways of the professional men in old Rome were not always such as led to
his peace of mind. Vitruvius utters bitter complaints which show that
he did not consider purely professional knowledge and service to be
adequately recognized or appreciated by his countrymen. He writes that
in the city of Ephesus an ancient law provided that if the cost of a
given work completed under the plans and specifications of an architect
did not exceed the estimate, he was commended “with decrees and
honors,” but if the cost exceeded the estimate with 25 per cent added
thereto, he “was required to pay that excess out of his own pocket.”
Then he exclaims, “Would to God that such a law existed among the Roman
people, not only in respect to their public but also to their private
buildings, for then the unskilful could not commit their depredations
with impunity, and those who were the most skilful in the intricacies
of the art would follow the profession!”
=64. Mechanical Appliances of the Ancients.=—It is well known that the
ancients possessed at least some simple types of machines, for the
reason that they raised many great stones to a considerable height in
completed works after having transported them great distances from the
quarries whence they were taken. Undoubtedly these machines were of a
simple and crude character and were made effective largely by the power
of great numbers of men. We are not acquainted with all the details
of these machines, although the general types are fairly well known.
The elementary machines, including the lever, the inclined plane, the
pulley, and the screw, which is only an application of the inclined
plane, were all used not only by the Romans, but probably by every
civilized ancient nation. Vitruvius describes a considerable number of
these machines, and from his descriptions it is clear that they had
wide application in the structural works of the Romans. The block and
fall, as we term the pulley at the present time, was a common machine
in the plant of a Roman constructor, as were also various modifications
and applications of the lever, the roller, and the inclined plane.
=65. Unlimited Forces and Time.=—It is neither surprising nor very
remarkable that with the use of these simple machines, aided by a
practically unlimited number of men, the necessary raising or other
movement of heavy weights was accomplished by the Romans and other
ancient peoples. It is to be borne in mind that the element of time was
of far less consequence in those days than at present, and that the
rate of progress made in the construction of most if not all ancient
engineering works was what we should consider intolerably slow.
PART II.
_BRIDGES._
CHAPTER VI.
=66. Introductory.=—Although the bridge structures of to-day serve the
same general purposes as those served by the most ancient structures,
they are very different engineering products. It is not long, in
comparison with the historic and prehistoric periods during which
bridges have been built, since the science of mechanics has been
sufficiently developed to make bridge design a rational procedure; and
it is scarcely more than a century since the principles of mechanics
were first applied to the design of bridge structures in such a way as
to determine even approximately the amount of stress produced in any
member by the imposed load. Naturally the first efforts made toward a
truly rational bridge design were in fact simple and crude and only
loosely approximate in their results. Probably the first analytic
treatment of bridges was given to the design of arches in masonry and
then in cast-iron. As the action of forces in structures became better
known through the development of mechanical science, the applications
of the latter became less crude and approximate and the approach to the
refined accuracy of the present day was begun.
=67. First Cast-iron Arch.=—These older structures, nearly all of them
arches or more or less related to the arch, first appeared in cast-iron
in the latter part of the eighteenth century, when nothing like an
accurate analysis of forces developed by the application of a given
load was known. The first cast-iron arch was erected over the Severn
in England near Coalbrookdale in the year 1779. This bridge had a
span of 100 feet, and the under surface of the arch or soffit at the
crown was 45 feet above the points at the abutment from which the arch
sprang, or, as civil engineers put it, the arch had a span of 100 feet
and a rise or versine of 45 feet. Other cast-iron arches were built in
England soon after.
=68. Early Timber Bridges in America.=—Timber bridges have been built
since the earliest historic periods and even earlier, but the widest
and boldest applications of timber to bridge structures have been made
in this country, beginning near the end of the eighteenth century and
running to the middle of the nineteenth century, when timber began to
be displaced by iron. Timber bridges and those of combined iron and
timber are built to some extent even at the present day, but the most
extended work of this class is to be found in the period just named.
In 1660 what was called the “Great Bridge” was built across the
Charles River near Boston, and was a structure on piles. Other similar
structures followed, but the first long-span timber bridge, where
genuine bridge trussing or framing was used, appears to have been
completed in 1792, when Colonel William P. Riddle constructed the
Amoskeag Bridge across the Merrimac River at Manchester, N. H., in
six spans of a little over 92 feet from centre to centre of piers.
From that time timber bridges, mostly on the combined arch and truss
principle, were built, many of them examples of remarkably excellent
engineering structures for their day. Among these the most prominent
were the Bellows Falls Bridge, in two spans of 184 feet each from
centre to centre of piers, over the Connecticut River, built in 1785-92
by Colonel Enoch Hale; the Essex-Merrimac Bridge over the Merrimac
River, three miles above Newburyport, Mass., built by Timothy Palmer
in 1792, consisting actually of two bridges with Deer Island between
them, the principal feature of each being a kind of arched truss of 160
feet span on one side of the island and 113 feet span on the other;
the Piscataqua Bridge, seven miles above Portsmouth, N. H., in which
a “stupendous arch of 244 feet cord is allowed to be a masterly piece
of architecture, planned and built by the ingenious Timothy Palmer of
Newburyport, Mass.,” in 1794; the so-called “Permanent Bridge” over
the Schuylkill River at Philadelphia, built in 1804-06 in two arches
of 150 feet and one of 195 feet, all in the clear, after the design
of Timothy Palmer; the Waterford Bridge over the Hudson River, built
in 1804 by Theodore Burr, in four combined arch and truss spans, one
of 154 feet, one of 161 feet, one of 176 feet, and the fourth of 180
feet, all in the clear; the Trenton Bridge, built in 1804-06 over
the Delaware River at Trenton, N. J., by Theodore Burr, in five arch
spans of the bowstring type, ranging from 161 feet to 203 feet in the
clear; a remarkable kind of wooden suspension bridge built by Theodore
Burr in 1808 across the Mohawk River at Schenectady, N. Y., in spans
ranging in length from 157 feet to 190 feet; the Susquehanna Bridge at
Harrisburg, Pa., built by Theodore Burr in 1812-16 in twelve spans of
about 210 feet each; the so-called Colossus Bridge, built in 1812 by
Lewis Wernwag over the Schuylkill River at Fairmount, Pa., with a clear
span of 340 feet 3¾ inches; the New Hope Bridge, built in 1814 over the
Delaware River, in six 175 feet combined arch and truss spans, and a
considerable number of others built by the same engineer.
Some of these wooden bridges, like those at Easton, Pa., and at
Waterford, N. Y., remained in use for over ninety years with only
ordinary repairs and with nearly all of the timber in good condition.
In such cases the arches and trusses have been housed and covered
with boards, so as to make what has been commonly called a covered
bridge. The curious timber suspension bridge built by Theodore Burr
at Schenectady was used twenty years as originally built, but its
excessive deflection under loads made it necessary to build up a pier
under the middle of each span so as to support the bridge structure
at those points. These bridges were all constructed to carry highway
traffic, but timber bridges to carry railroad traffic were subsequently
built on similar plans, except that Burr’s plan of wooden suspension
bridge at Schenectady was never repeated.
[Illustration: MOHAWK BRIDGE AT SCHENECTADY N.Y.
Built by Theodore Burr.
FIG. 1.]
[Illustration: PATENT BRIDGE “COLOSSUS”
Across the River Schuylkill at Philadelphia.
Single Arch 340 feet 3¾ inches.
Built by Lewis Wernwag.
FIG. 2.]
=69. Town Lattice Bridge.=—A later type of timber bridge which was
most extensively used in this country was invented by Ithiel Town in
January, 1820, which was known as the Town lattice bridge. This timber
bridge was among those used for railroad structures. As shown by the
plan it was composed of a close timber lattice, heavy plank being used
as the lattice members, and they were all joined by wooden pins at
their intersections. This type of timber structure was comparatively
common not longer ago than twenty-five years, and probably some
structures of its kind are still in use. The close latticework with its
many pinned intersections made a very safe and strong frame-work, and
it enjoyed deserved popularity. It was the forerunner in timber of the
modern all-riveted iron and steel lattice truss. It is of sufficient
significance to state, in connection with the Town lattice, that its
inventor claimed that his trusses could be made of wrought or cast-iron
as well as timber. In many cases timber arches were combined with them.
[Illustration: FIG. 3.]
=70. Howe Truss.=—The next distinct advance made in the development
of bridge construction in the United States was made by brevet
Lieutenant-Colonel Long of the Corps of Engineers, U.S.A., in 1830-39,
and by William Howe, who patented the bridge known as the Howe
truss, although the structure more lately known under that name is a
modification of Howe’s original truss. Long’s truss was entirely of
timber, including the keys, pins, or treenails required, and it was
frequently built in combination with the wooden arch. The truss was
considerably used, but it was not sufficiently popular to remain in
use.
[Illustration: Howe Truss-Bridge.]
[Illustration: FIG. 4.]
The Howe truss was not an all-wooden bridge. The top and bottom
horizontal members, known as “chords,” the inclined braces between
them and the vertical end braces, all connecting the two chords, were
of timber, and they were bolted at all intersections; but the vertical
braces were of round iron with screw ends. These rods extended through
both chords and received nuts at both ends pressing on cast-iron
washers through which the rods extended. These wrought-iron round rods
were in groups at each panel-point, numbering as many as existing
stresses required. The ends of the timber braces abutted against
cast-iron joint-boxes. The railroad floor was carried on heavy timber
ties running entirely across the bridge and resting upon the lower
chord members. It was a structure simple in character, easily framed,
and of materials readily secured. It was also easily erected and could
quickly be constructed for any reasonable length of span. It possessed
so many merits that it became widely adopted and is used in modified
form at the present day, particularly on lines where the first cost
of construction must be kept as low as possible. The large amount of
timber in it and the simple character of its wrought-iron or steel
members greatly reduces its first cost.
=71. Pratt Truss.=—In 1844 the two Pratts, Thomas W. and Caleb,
patented the truss, largely of timber, which has since been perpetuated
in form by probably the largest number of iron and steel spans ever
constructed on a single type. The original Pratt trusses had timber
upper and lower chords, but the vertical braces were also made of
timber instead of iron, while the inclined braces were of round
wrought-iron with screw ends, the reverse of the web arrangement in the
Howe type. This truss had the great advantage of making the longest
braces (of iron) resist tension only, while the shorter vertical braces
resist compression. As a partially timber bridge it could not compete
with the Howe truss, because it contained materially more iron and
consequently was more costly. This structure practically closed the
period of development of timber bridges.
=72. Squire Whipple’s Work.=—What amounted to a new epoch in the
development of bridge construction in this country practically began
in 1840 when Squire Whipple built his first bowstring truss with
wrought-iron tension and cast-iron compression members. While the
Pratts and Howe had begun to employ to some extent the analysis of
stresses in the design of their bridge members, the era of exact bridge
analysis began with Squire Whipple. He subjected his bridge designs to
the exacting requirements of a rational analysis, and to him belongs
the honor of placing the design of bridges upon the firm foundation of
a systematic mathematical analysis.
=73. Character of Work of Early Builders.=—The names of Palmer, Burr,
and Wernwag were connected with an era of admirable engineering works,
but, with bridge analysis practically unknown, and with the simplest
and crudest materials at their disposal, their resources were largely
constituted of an intuitive engineering judgment of high quality and
remarkable force in the execution of their designs never excelled in
American engineering. They occasionally made failures, it is true,
but it is not recorded that they ever made the same error twice, and
the works which they constructed form a series of precedents which
have made themselves felt in the entire development of American
bridge-building.
CHAPTER VII.
=74. Modern Bridge Theory.=—The evolution of bridge design having
reached that point where necessity of accurate analysis began to make
itself felt, it is necessary to recognize some of the fundamental
theoretical considerations which lie at the base of modern bridge
theory, and which involve to a considerable extent that branch of
engineering science known as the elasticity or strength of the
materials used in engineering construction.
The entire group of modern bridge structures may be divided into simple
beams or girders, trusses, arches, suspension bridges, and arched ribs,
each class being adapted to carry either highway or railway traffic.
That class of structure known as beams or girders is characterized by
very few features. There are solid beams like those of timber, with
square or rectangular cross-sections, and the so-called flanged girders
which are constituted of two horizontal pieces, one at the top and the
other at the bottom, connected by a vertical plate running the entire
length of the beam. The fundamental theory is identically the same for
both and is known as the “common theory of flexure,” i.e., the theory
of beams carrying loads.
If an ordinary scantling or piece of timber of square or rectangular
cross-section, like a plank or a timber joist, so commonly used for
floors, be supported at each end, it is a matter of common observation
that it will sustain an amount of load depending upon the dimensions
of the stick and length of span. When such a bar or piece is loaded
certain forces or stresses, as they are called, are brought into action
in its interior. The word “stress” is used simply to indicate a force
that exists in the interior of any piece of material. It is a force and
nothing else. It is treated and analyzed in every way precisely as a
force. If the stresses or forces set up by the loading in the interior
of the bar become greater than the material can resist, it begins to
break, and the breaking of that portion of the timber in which the
stresses or forces are greatest constitutes its failure. The load which
produces this failure in a beam is called the breaking load of the
beam. In engineering practice all beams are so designed or proportioned
that the greatest load placed on them shall be only a safe percentage
of the breaking load; the safe load usually being found between ⅓ and ⅙
of the breaking load. In most buildings the safe or working load, as it
is called, is probably about ¼ of the breaking load.
[Illustration: FIG. 5.]
[Illustration: FIG. 6.]
[Illustration: FIG. 7.]
=75. The Stresses in Beams.=—The proper design of beams or girders to
carry prescribed loads is based upon the stresses which are developed
or brought into action by them. It can easily be observed that if a
beam supported at each end be composed of a number of thin planks or
boards placed one upon the other, it will carry very little load. Each
plank or board acts independently of the others and a very small load
will cause a sag, as shown in Fig. 6. If there be taken, on the other
hand, a beam made of a single stick of timber of the same width and
depth as the number of planks shown in Fig. 6, so as to secure the
solid beam shown in Fig. 7, it is a further common observation that
this latter beam may carry many times the load which the laminated
beam, shown in Fig. 6, sustains. The thin planks or boards readily
slide over each other, so that the ends present the serrated form
shown in Fig. 6. The preventing of this sliding is the sole cause of
the greatly increased stiffness of the solid beam shown in Fig. 7, for
there is thus developed along the imaginary horizontal sections in the
solid beam of Fig. 7 what are called shearing forces or stresses; and
since they exist on horizontal sections or planes running throughout
the entire length of the beam, they are called horizontal shears.
At each end of the beam shown in Fig. 7 there will be an upward or
supporting force exerted by the abutments on which the ends of the beam
rest. Those upward or supporting forces are shown at _R_ and _R′_ and
are called reactions, because the abutments, so to speak, react against
the ends of the beam when the latter is loaded. These reactions depend
for their value on the amount and the location of the loading which the
beam carries. Obviously these upward forces or reactions tend to cut or
shear off the ends of the beam immediately above them, and if the loads
were sufficiently large and the beam kept from bending, the reactions
would actually shear off those ends, just as punches or shears in
a machine-shop actually shear off the metal when the rivet-hole is
punched, or when a plate is cut by shearing into two parts. The beam,
however, bends or sags before shearing apart actually takes place.
[Illustration: FIG. 8.]
[Illustration: FIG. 9.]
=76. Vertical and Horizontal Shearing Stresses.=—If it be supposed
that the length of the beam is divided into a great number of parts by
imaginary vertical lines, like those shown in Fig. 8, then vertical
shearing forces will be developed in those vertical planes and
sometimes, though not often, they are enough to cause failure. It is
not an uncommon thing, on the other hand, in timber to have actual
shearing failure take place along a horizontal plane through the centre
of the beam. Indeed this is recognized frequently as the principal
method of failure in very short spans. When this horizontal shearing
failure takes place, the upper and lower parts of the beam slide over
each other and act precisely like the group of planks shown in Fig. 6.
If, then, the loaded beam be divided by vertical and horizontal planes
into the small rectangular portions shown in Figs. 8 and 9, on each
such vertical and horizontal imaginary plane there will be respectively
vertical and horizontal shearing forces, which are shown by arrows in
Fig. 9. It will be noticed in that figure that in each corner of the
rectangle the two shearing forces act either toward or from each other;
in no case do the two adjacent shearing forces act around the rectangle
in the same direction. This is a condition of shearing stresses
peculiar to the bent beam. It can be demonstrated by theory and is
confirmed by experiment. There is a further peculiarity about these
shearing forces which act in pairs either toward or from the same angle
in any rectangle, and it is that the two stresses adjacent to each
other have precisely the same value per square inch (or any square unit
that may be used) of the surface on which they act. These stresses per
square inch vary, however, either along the length of the beam or as
the centre line of any normal cross-section is departed from. They are
greatest along the centre line or central horizontal plane represented
by _AB_, and they are zero at the top and bottom surfaces of the beam.
Inasmuch as the horizontal shear along the plane _AʹBʹ_ is less than
that along _AB_ in Fig. 9, a part of the latter has been taken up by
the horizontal fibres of the beam lying between the two planes. In
other words, the horizontal layer of fibres at _AʹBʹ_ is subjected to a
greater stress or force along its length than at _AB_. The same general
observation can be made in reference to any horizontal layer of fibres
that is farther away from the centre than another. Hence the farther
any fibre is from the centre the greater will be the stress or force
to which it is subjected in the direction of its length. It results,
then, that the horizontal layers of fibres which are farthest from the
centre line of the beam, i.e., those at the exterior surfaces, will be
subjected to the greatest force or stress, and that is precisely what
exists in a loaded beam whatever the material may be.
=77. Law of Variation of Stresses of Tension and Compression.=—Since
a horizontal beam supported at each end is deflected or bent downward
when loaded, it will take a curved form like that shown in either Fig.
7 or Fig. 10; but this deflection can only take place by the shortening
of the top of the beam and the lengthening of its bottom. This shows
that the upper part of the beam is compressed throughout its entire
length, while the lower part is stretched. In engineering language,
it is stated that the upper part of the beam is thus subjected to
compression and the lower part to tension. The horizontal layers
or fibres receive their tension and compression from the vertical
and horizontal shearing forces in the manner already explained. If
the conditions of loading of the bent beam should be subjected to
mathematical analysis, it would be found that throughout the originally
horizontal plane _AB_, Fig. 7, passing through the centre of each
section there would be no stress of either tension or compression,
although the horizontal shearing stress there would be a maximum.
Further, as this central plane is departed from the stress of tension
or compression per square inch in any vertical section would be found
to increase directly as the distance from it. This is a very simple
law, but one of the greatest importance in the design of all beams
and girders, whatever may be the form or size of cross-section. It
is a law, which applies equally to the solid timber beam and to the
flanged steel girder, whether that girder be rolled in the mill or
built up of plates and angles or other sections in the shop. It is a
fundamental law of what is called the common theory of flexure, and
is the very foundation of all beam and girder design. The horizontal
plane represented by the line _AB_ in Fig. 8, along which there is
neither tension nor compression, is called the “neutral plane,” and its
intersection with any normal cross-section of the beam is called the
“neutral axis” of that section. Mathematical analysis shows that the
neutral plane passes through the centres of gravity of all the normal
sections of the beam and, hence, that the neutral axis passes through
the passes through the centre of gravity of the section to which it
belongs.
=78. Fundamental Formulæ of Theory of Beams.=—The fundamental formulæ
of the theory of loaded beams may be quite simply written. Fig. 10
exhibits in a much exaggerated manner a bent beam supporting any
system of loads _W₁_, _W₂_, _W₃_, etc., while Fig. 11 shows a normal
cross-section of the same beam. In Fig. 10 _AB_ is the neutral line,
and in Fig. 11 _CD_ is the neutral axis passing through the centre of
gravity, _c.g._, of the section.
[Illustration: FIG. 10.]
[Illustration: FIG. 11.]
If _a_ is the amount of force or stress on a square inch (or other
square unit), i.e., the intensity of stress, at the distance of unity
from the neutral axis _CD_ of the section, then, by the fundamental
law already stated, the amount acting on another square inch at any
other distance _z_ from the neutral axis will be _az_. This quantity
is called the “intensity of stress” (tension or compression) at the
distance _z_ from the neutral axis. Evidently it has its greatest
values in the extreme fibres of the section, i.e., _ad_ and _ad_₁. At
the neutral axis _az_ becomes equal to zero. _FG_ in Fig. 11 represents
the same line as _FG_ in Fig. 10. If the line _FH_ in Fig. 11 be laid
down equal to _ad_ and at right angles to _FG_, and if _O_ represent
the centre of gravity, _c.g._, of the section, then let the straight
line _LH_ be drawn. Any line drawn parallel to _FH_ from _FG_ to _LH_
will represent the intensity of stress in the corresponding part of the
beam’s cross-section. Obviously, as these lines are drawn in opposite
directions from _FG_, those above _O_ will indicate stress of one kind,
and those below that point stress of another kind, i.e., if that above
be tension, that below will be compression. It can be demonstrated by a
simple process that the total tension on one side of the neutral axis
is just equal to the total compression on the other side, and from that
condition it follows that the neutral axis must pass through the centre
of gravity or centroid of the section.
Returning to the left-hand portion of Fig. 11, let _dA_ represent a
very small portion of the cross-section; then will _az. dA_ be the
amount of stress acting on it. The moment of this stress or force about
the neutral axis will be
_azdA·z = az²·dA_.
If this expression be applied to every small portion of the entire
section, the aggregate or total sum of the small moments so found will
be the moment of all the stresses in the section about the neutral
axis. That moment will have the value
_M_ = ⌠_az²·dA_ = _a_⌠_z²·dA_ = _aI_. (1)
⌡ ⌡
In equation (1) the symbol ∫ means that the sum of all the small
quantities to the right of it is taken, and _I_ stands for that sum
which, in the science of mechanics, is called the moment of inertia of
the cross-section about its neutral axis. The value of the quantity
_I_ may easily be computed for all forms of section. Numerical values
belonging to all the usual forms employed in engineering practice
are found in extended tables in the handbooks of the large iron and
steel companies of the country, so that its use ordinarily involves no
computations of its value.
Equation (1) may readily be changed into two other forms for
convenient practical use. In Fig. 10 _mn_ is supposed to be a very
short portion of the centre line of the beam represented by _dl_.
Before the beam is bent the section _FG_ is supposed to have the
position _MN_ parallel to _PQ_. Also let _u_ be the small amount of
stretching or compression (shortening) of a unit’s length of fibre at
unit’s distance from the centre line _AB_ of the beam, then will _udl_
and _uzdl_ be the short lines parallel to _GN_ in the triangle _GmN_
shown in the figure. The point _C_ is the centre of curvature of the
line _mn_, and _Cn = Cm_ is the radius. The two triangles _Cnm_ and
_mNG_ are therefore similar, hence
_udl_ _mn_ _dl_ I
------- = ---- = ----- ∴ u = ---. (2)
I ρ ρ ρ
If the quantity called the coefficient or modulus of elasticity be
represented by _E_, then, by the fundamental law of the theory of
elasticity in solid bodies,
_a = Eu_. (3)
As has already been shown, the greatest stresses (intensities) in the
section are +_ad_ (tension) and -_ad_₁ (compression). If _K_ represent
that greatest intensity of stress, then
_K_
_K = ad_, and _a_ = ----. (4)
_d_
If the value of _a_ from equation (4) be substituted in equation (1),
_KI_
_M_ = -----. (5)
_d_
=79. Practical Applications.=—Equation (5) is a formula constantly
used in engineering practice. All quantities in the second member are
known in any given case. _K_ is prescribed in the specifications,
and is known as the “working resistance” in the design of beams and
girders. For rolled steel beams in buildings it is frequently taken at
16,000 pounds, i.e., 16,000 pounds per square inch, about one fourth
the breaking strength of the steel. In railroad-bridge work it may be
found between 10,000 and 12,000 pounds, or approximately one fifth of
the breaking strength of the steel. The quantities _I_ and _d_ depend
upon the form and dimensions of the cross-section, and are either known
or may be determined. The quotient _I ÷ d_ is now known as the “section
modulus,” and its numerical values for all forms of rolled beams can
be found in published tables. The use of equation (5) is therefore in
the highest degree convenient and practicable.
=80. Deflection.=—It is frequently necessary, both in the design of
beams and framed bridges, to ascertain how much the given loading will
cause the beam or truss to sag, or, in engineering language, to deflect
below the position occupied when unloaded. The deflection is determined
by the sagging in the vertical plane of the neutral line below its
position when the structure carries no load. In Fig. 10 the curved line
_AB_ is the neutral line of the beam when supporting loads. If the
loads should be removed, the line _AB_ would return to a horizontal
position. The line drawn horizontally through _A_ and indicated by _x_
is the position of the centre line of the beam before being bent. The
vertical distance _w_ below this horizontal line shows the amount by
which the point at the end of the line _x_ is dropped in consequence of
the flexure of the beam. The vertical distance _w_ is therefore called
the deflection. Evidently the deflection varies with the amount of
loading and with the distance from the end of the beam. The curved line
_AB_ in one special case only is a circle. The general character of
that curve is determined by the loading and the length of span.
In order that the deflection may be properly considered it is necessary
that the relation between _x_ and _w_ shall be established for all
conditions of loading and length of span. If the value of _u_ from
equation (2) be placed in equation (3), there will result
_E_
_a_ = ---. (6)
ρ
If the value of _a_ from equation (6) be substituted in the last member
of equation (1), there will at once result
_EI_
_M_ = ----. (7)
ρ
It is established by a very simple process in differential calculus that
_I d²w_
---- = ------. (8)
ρ dx²
Hence, substituting from equation (8) in equation (7),
_d²w_
_M = EI_ -----. (9)
_dx²_
Equation (9) may be used by means of some very simple operations in
integral calculus to determine the value of _w_ in terms of _x_ and the
loads on the beam when the value of the bending moment _M_ is known,
and the procedures for determining that quantity will presently be
given.
Using the processes of the calculus, the two following equations will
immediately be found:
_dw_ 1
----- = ---- ⌠ _Mdx_; (10)
_dx EI_ ⌡
1
_w = ----- ⌠⌠ Mdx²_ (11)
_EI_ ⌡⌡
As already explained, numerical values for both _E_ and _I_ may be
taken at once from tables already prepared for all materials and for
all shapes of beams ordinarily employed in structural work, so that
equation (11) enables the deflection or sag of the bent beam to be
computed in any case. The expression _dw/dx_ is the tangent of the
angle made by the neutral line of a bent beam with a horizontal line at
any given point, and it is a quantity that it is sometimes necessary to
determine. _dw_ and _dx_ are indefinitely short vertical and horizontal
lines respectively, as shown immediately to the left of _B_ in Fig. 10.
Equation (11) is not used in structural work nearly as much as equation
(5), but both of them are of practical value and involve only simple
operations in their use.
=81. Bending Moments and Shears with Single Load.=—The second members
of equations (5) and (9) exhibit values of the moments of the internal
forces or stresses in any normal cross-section of a bent beam about the
neutral axis of the section, while the values of _M_ must be expressed
in terms of the external forces or loading. Inasmuch as the latter
moment develops just the internal moment, it is obvious that the two
must be equal. In order to write the value of the external moment in
terms of any loading, it is probably the simplest procedure to consider
a beam carrying a single load. In Fig. 12, _AB_ is such a beam, and
_W_ is a load which may be placed anywhere in the span, whose length
is _l_. The distances of the load from the abutments are represented
by _x_₁ and _x_₂. The reactions or supporting forces exerted under
the ends of the beam at the abutments are shown by _R_ and _R′_. The
reactions, determined by the simple law of the lever, are
_x₂ x₁_
_R = W_ ---- and _Rʹ = W_ ---- (12)
_l l_
The greatest bending moment in the beam will occur at the point of
application of the load, and its value will be
_x₁x₂_
_M₁ = Rx₁ = W_ ------- = -_Rʹx₂_. (13)
_l_
[Illustration:
_Wx₁x₂_
_M₁ = Rx₁ = -Rʹx₂_ = -------
_l_
FIG. 12.]
The bending moments at the end of the beam are obviously zero, and
the second and fourth members of equation (13) show that the moment
increases directly as the distance from either end. Hence in the
lower portion of Fig. 12, at _D_, immediately under the load _W_, the
line _DC_ is laid off at any convenient scale to represent the moment
_M_₁. The straight lines _AC_ and _CB_ are then drawn. Any vertical
intercept, as _FH_ or _KL_, between _AB_ and either _AC_ or _CB_ will
represent the bending moment at the corresponding point in the beam.
The simple triangular diagram _ACB_ therefore represents the complete
condition of bending of the beam under the single load _W_ placed at
any point in the span.
The beam _AB_ is supposed for the moment to have no weight.
Consequently the only force acting upon the portion of the beam _AO_
is the reaction _R_, and, similarly, _Rʹ_ is the only force acting
upon the portion _OB_. Obviously so far as the simple action of these
two forces or reactions is concerned, the tendency of each is to cause
vertical slices of the beam, so to speak, to slide over each other. In
other words, in engineering language, the portion _AO_ of the beam is
subjected to the shear _S = R_, while _OB_ is subjected to the shear
_Sʹ = -Rʹ_. The cross-sectional area of the beam must be sufficient to
resist the shear _S_ or _Sʹ_. The upper part of Fig. 13 shaded with
broken vertical lines indicates this condition of shear. It is evident
from this simple case that the total vertical shears at the ends of any
beam will be the reactions or supporting forces exerted at those ends,
and that each will remain constant for the adjoining portion of the
beam.
The third member of equation (13) shows that the greatest bending
moment _M_₁ in the beam varies as the product _x_₁_x_₂ of the segments
of the span. That product will have its greatest value when _x_₁ =
_x_₂. Hence _a simple beam loaded by a single weight will be subjected
to the greatest possible bending moment when the weight is placed at
the middle of the span, at which point also that moment will be found_.
=82. Bending Moments and Shears with any System of Loads.=—The general
case of a simple beam loaded with any system of weights whatever may
be represented in Fig. 13, in which the beam of Fig. 12 is supposed to
carry three loads, _w_₁, _w_₂, _w_₃. The spacing of the loads is as
shown. The reactions or supporting forces _Rʹ_ are determined precisely
as in Fig. 12, each reaction in this case being the resultant of three
loads instead of one. Applying the law of the lever as before, the
reaction _R_ will have the value
_d d + c d + c + b_
_R = W₃--- + W₂------- + W₁-----------_. (14)
_l l l_
A similar value may be written for _Rʹ_, but it is probably simpler,
after having found one reaction, to write
_R′ = W₁ + W₂ + W₃ - R_. (15)
As the beam is supposed to have no weight, no load will act upon the
beam between the given weights. The bending moments at the points of
application of the three weights or loads will be
_M₁_ = _Ra_, }
_M₂_ = _R_(_a + b_) - _W₁b_, } (16)
_M₃_ = _R_(_a + b + c_) - _W₁_(_b + c_) - W₂c_.}
After substituting the value of _R_ from equation (14) in equations
(16) the values of the latter are at once known.
[Illustration: FIG. 13.]
The bending produced by each weight will also be represented precisely
like that in Fig. 12. The triangle _ANB_ represents the bending
produced by _W_₁; _AOB_ the bending produced by _W_₂; and _APB_ the
bending produced by _W_₃. The resultant bending effect produced by the
three loads or weights acting simultaneously is simply the summation
of the three effects each due to a single load. Hence _DC_ is erected
vertically through the point of application of _W_₁, so as to equal
_DN_ added to the two vertical intercepts between _AB_ and _AP_, and
_AB_ and _AO_. Similarly, _HF_ is equal to _HO_ added to the intercepts
between _AB_ and _AP_, and _AB_ and _BN_. Finally, _KL_ is equal to
_PL_ added to the other two intercepts, one between _AB_ and _BN_,
and the other between _AB_ and _BO_. Straight lines then are drawn
through _A_, _C_, _F_, _K_, and _B_. Any vertical intercept between
_AB_ and _ACFKB_ will represent the bending moment in the beam at the
corresponding point. Obviously any number of loads of any magnitude, or
a uniform load, may be treated in precisely the same way.
An important practical rule can readily be deduced from the equations
(16), each one of which may be regarded as a general equation of
moments. If the system of three, or any other number of loads, be moved
a small distance Δ_x_, while they all remain separated by the same
distances as before, the bending moment _M_ will be changed by the
amount shown in equation (16_a_):
_ΔM = RΔx - W₁Δx - W₂Δx -_ etc. (16_a_)
If the notation of the differential calculus be used by writing the
letter _d_ instead of Δ, and if both members of equation (16_a_) be
then divided by _dx_, equation (16_b_) will result:
_ΔM dM_
--- = ---- = _R - W₁ - W₂_ - etc. = shear. (16_b_)
_Δx dx_
The second member of this equation shows the sum of all the external
forces acting on one portion of the beam, that portion being limited
by the section about which the moment _M_ acts. That sum of all the
external forces, as given by the second member of equation (16_b_),
is evidently the total transverse shear at the section considered.
Equation (16_b_) then shows, in the language of the differential
calculus, that the first derivative of _M_ in respect to _x_ is
equal to the total transverse shear. It is further established in
the differential calculus that whenever a function, such as _M_, the
bending moment, is a maximum or a minimum, the first derivative is
equal to zero. The application of this principle to equation (16_b_)
shows that the bending moment in any beam or truss has its greatest
value wherever the shear is zero. Hence, in order to determine at what
section the bending moment has its greatest value in any loaded beam
carrying a given system of loads, it is only necessary to sum up all
the forces or loads, including the reaction _R_, on that beam from one
end to the point where that sum or shear is zero; at this latter point
the greatest moment sought will be found. This is a very simple method
of determining the section at which the greatest moment in the beam
exists.
The preceding formulæ and diagrams may be extended to include any
number of loads, and they are constantly used in engineering practice,
not only for beams and girders in buildings, but also for bridges
carrying railroad trains. Whatever may be the number of loads,
the expressions for the bending moments at the various points of
application of those loads are to be written precisely as indicated in
equations (16). When the number of loads becomes great the number of
terms in the equations correspondingly increase, but in reality they
are just as simple as those for a smaller number of loads.
The diagram for the vertical shear in this beam is the lower part of
Fig. 13. As in the case of Fig. 12 the shear at _A_ is the reaction
_R_, as it is _Rʹ_ at the other end of the beam. The shear in the
portion _AD_ of the beam has the value _R_, but in passing the point
_D_ to the right the weight _W₁_ represented by _OT_ must be subtracted
from _R_, so that the shear over the section _b_ of the span is _R_ -
_W₁_ or _QV_ in the diagram. Similarly, in passing the point _H_ toward
the right, both _W₂_ and _W₁_ must be subtracted from _R_, giving the
negative shear (the previous shear being taken positive) _VW_. The
negative shear _VW_ remains constant throughout the distance _c_, but
is increased by _W₃_ at the point _L_, so that throughout the distance
_d_ the shear _Sʹ_ = _-Rʹ_. These shear values are all shown in the
lower portion of Fig. 13 by the vertical shaded lines. Obviously it is
a matter of indifference whether the shear above the straight line _GJ_
is made positive or negative; it is only necessary to recognize that
the signs are different.
In the case of heavy beams, either built or rolled, as in railroad
structures, it is of the greatest importance to determine both the
bending moments and the shears, as represented in the preceding
equations and diagrams, and to provide sufficient metal to resist them.
The case of Fig. 13 is perfectly general for moments and shears, and
the methods developed are applicable to any amount or any system of
loading whatever.
=83. Bending Moments and Shears with Uniform Loads.=—Fig. 14 represents
what is really a special case of Fig. 13, in which the loading is
uniform for each unit of length of the beam throughout the whole span
_l_. Inasmuch as the load is uniformly distributed, it is evident that
the reaction at each end of the beam will be one half the total load, or
_wl_
_R = R_ʹ = ----. (17)
2
[Illustration: FIG. 14.]
The general expression for the bending moment at any point _G_ in the
span, and located at the distance _x_ from the end _A_, will take the
form
_x w_
_M_ = _Rx_ - _wx_.--- = --- _x_(l-_x_). (18)
2 2
This equation, giving the value of _M_, is the equation of a parabola
with the vertex over the middle of the span. The bending moment at the
latter point will be found by placing _x = l/2_ in equation (18), which
will give
_wl²_
_M_ = -----. (19)
8
Hence, in Fig. 14, if the vertical line _DC_ be erected at _D_, so as
to represent the value of _M_ in equation (19) to a convenient scale,
the parabola _ACB_ may be at once drawn. Any vertical intercept, as
_GF_ between _AB_ and the curve _AFCB_, will represent by the same
scale the bending moment in the beam at the point indicated by the
intercept. Equation (19), giving the greatest external bending moment
in a simple beam due to a uniform load, is constantly employed in
structural work, and shows that that moment is equal to the total load
multiplied by one eighth of the span.
It has already been shown, in connection with Fig. 12, that when a
single centre weight rests on a beam the centre bending moment is
equal to that weight multiplied by one fourth the span. If the total
uniform load in the one case is equal to the single load in the other,
these equations show that the single centre load will produce just
double the bending moment due to the same load uniformly distributed
over the span. Wherever it is feasible, therefore, the load should be
distributed rather than concentrated at the centre of the span.
That portion of Fig. 14 shaded with vertical lines shows the shear
existing in the beam. Evidently the shear at each end is equal to the
reaction, or one half the total load on the span. The expression for
the shear at any point, as _G_, distant _x_ from _A_ will be
( _l_ )
_S = R_ - _wx_ = _w_( ---- - _x_). (20)
( 2 )
If _x = l/2_ in equation (20), _S_ becomes equal to zero. In other
words, there is no shear at the centre of the span of a beam uniformly
loaded. Hence, if at each end of the span a vertical line _AK_ or _BL_
be laid off downward, and if straight lines _KD_ and _DL_ be drawn,
any vertical intercept, as _GH_, between these lines and _AB_ will
represent the shear at the corresponding point. Equation (20) also
shows that the shear _S_ at any point is equal to the load resting on
the beam between the centre _D_ and that point. Although this case of
uniform loading is a special one it finds wide application in practical
operations.
=84. Greatest Shear for Uniform Moving Load.=—The preceding loads have
been treated as if they were occupying fixed positions on the beams
considered. This is not always the case. Many of the most important
problems in connection with the loading of beams and bridges arise
under the supposition that the load is movable, like that of a passing
railroad train. One of the simplest of these problems, although of much
importance, consists in finding the location of a uniform moving load,
like that of a train of cars, which will produce the greatest shear at
a given point of a simple beam, such as that represented in Fig. 15, in
which a moving load is supposed to pass continuously over the span from
the left-hand end _A_. It is required to determine what position of
this uniform load will produce the greatest shear at the section _C_.
[Illustration: FIG. 15.]
Let the moving load extend from _A_ to any point _D_ to the right of
_C_. The two reactions _R_ and _Rʹ_ may be found by the methods already
indicated. Let _W_ represent the uniform load resting on the portion
_CD_ of the span. The shear _S′_ existing at _C_ will be
_Sʹ = Rʹ - W_. (21)
Let _R‴_ be that part of _Rʹ_ which is due to _W_, and _Rʺ_ that part
due to the load on _AC_. Evidently _R‴_ is less than _W_; then
_Sʹ = Rʺ + R‴ - W_. (22)
Since the negative quantity _W_ is greater than the positive quantity
_R‴_, _S′_ will have its greatest value when both _W_ and _R‴_ are
zero. Hence the greatest shear at the point _C_ will exist when
_Sʹ = Rʺ_. (23)
Obviously the loading must extend at least from _A_ to _C_ in order
that _Rʺ_ may have its maximum value. Hence _the greatest shear at any
section will exist when the uniform load extends from the end of the
span to that section, whatever may be the density of the load_.
If the segment of the span covered by the moving load is greater than
one half the span, the maximum shear is called the _main shear_; but
if that segment is less than one half the span, the maximum shear is
called the _counter-shear_. The reason for these two names will be
apparent later in the discussion of bridge-trusses.
This rule for determining the maximum shear at any section of a beam is
equally applicable to bridge-trusses under certain conditions, and has
an important bearing upon the determination of the greatest stresses in
some of the members of bridge-frames, although it has less importance
now than it had in the earlier days of bridge-building.
=85. Bending Moments and Shears for Cantilever Beams.=—The case of a
loaded overhanging beam or cantilever bracket, as shown in Fig. 16, is
sometimes found. In that figure a single weight _W_ is supposed to be
applied at the end, while a uniform load _w_ per unit of length extends
over its length _l_. The bending moment at any point _C_ distant _x_
from the end will obviously be
_wx²_
_M = Wx_ + -----. (24)
2
[Illustration: FIG. 16.]
The greatest value of the bending moment will be found by placing _x_
equal to _l_ in equation (24), and it will have the value
_wl²_
_M₁ = Wl_ + -----. (25)
2
The shear at any point and at the end _A_ respectively will be
_S = W + wx_ and _S₁ = W + wl_. (26)
The shear due to _W_ is equal to itself and is constant throughout the
whole length of the beam.
The second term of the second member of equation (24) is the equation
of a parabola with its vertex at _B_, Fig. 16. Hence if _AF_ be laid
off equal to (_wl_²)/2, and if the parabola _FHB_ be drawn, any
vertical intercept, as _HK_, between that curve and _AB_ will represent
the bending moment at the corresponding point. On the other hand, the
first term of the second member of equation (24) shows that the bending
moment due to _W_ varies directly as the distance from _B_. Hence if
_AG_ be laid off vertically downward from _A_ equal to _Wl_ to any
convenient scale, then any intercept, as _KL_, between _AB_ and _BG_
will represent the bending moment due to _W_ at the corresponding point
of the beam.
=86. Greatest Bending Moment with any System of Loading.=—One of the
most important positions of loading to be established either for
simple beams or for bridge-trusses is that at which any given system
of loading whatever is to be placed on any span so as to produce the
maximum bending moment at any prescribed point in that span. In order
to make the case perfectly general a system of arbitrary loads, like
that shown in Fig. 17, is assumed and the system is supposed to be a
moving one.
[Illustration: FIG. 17.]
The separate loads are placed at fixed distances apart, indicated by
the letters _a_, _b_, _c_, _d_, etc., _W_₁ being supposed to be at
the head of the train, while _W_ is the last load having a variable
distance _x_ between it and the end of the span. In Fig. 17 this system
of moving loads or train is supposed to pass over the span _l_ from
right to left. The problem is to determine the position of the loading,
so that the bending moment at the section _C_ of the beam or truss
will be a maximum, the section _C_ being at the distance _lʹ_ from the
left-hand end of the span. The complete analysis of this problem is
comparatively simple and may readily be found, but it is not necessary
for the accomplishment of the present purpose to give it here. In order
to exhibit the formula which expresses the desired condition, let _W_ₙʹ
be that weight which is really placed at _C_, but which is assumed to
be an indefinitely short distance to the left of that point, for a
reason which will presently be explained. The equation of condition or
criterion sought will then be the following:
_lʹ W₁ + W₂ + ... + Wₙʹ_
----- = ------------------------. (27)
_l W₁ + W₂ + W₃ + ... + Wₙ_
If the loads are so placed as to fulfil the condition expressed in
equation (27), the bending moment at section _C_ will be a maximum. If
the variation in the train weights is very great, it is possible that
there may be more than one position of the train which will satisfy
that equation. It is necessary, therefore, frequently to try different
positions of the loading by that criterion and then ascertain which
of the resulting maximum moments is the greatest. It is not usually
necessary to make more than one or two such trials. The application of
the equation is therefore simple and involves but little labor.
It will usually happen that _W_ₙʹ in equation (27) is not to be taken
as the whole of that weight, but only so much of it as may be necessary
to satisfy the equation. This is simply assuming that any weight,
_W_, may be considered as made up of two separate weights placed
indefinitely near to each other, which is permissible.
After having found the position of loading which satisfies equation
(27), the resulting maximum bending moment will take the following form:
_lʹ_
_M₁_ = ----- [_W₁a_ + (_W₁+ W₂_)_b_ + ... + (_W₁ + W₂ + ... + Wₙ_)_x_]
_l_
- _W₁a_ - (_W₁ + W₂_)_b_ - ... - (_W₁ + W₂ + ... + W₍ₙʹ₋₁₎_)(?). (28)
In this equation _x_ corresponds to the position of loading for maximum
bending, while the sign (?) represents the distance between the
concentrations _W_₍ₙʹ₋₁₎ and _W_ₙʹ. This equation has a very formidable
appearance, but its composition is simple and it is constantly used in
making computations for the design of railroad bridges. The loads _W_₁,
_W_₂, _W_₃, etc., represent the actual weights on the driving-axles and
other axles of locomotives, tenders, and cars, and the spacings _a_,
_b_, _c_, etc., are the actual spacings found between those axles. In
other words, these quantities are the actual weights and dimensions of
the different portions of moving railroad trains.
The computations indicated by equation (28) are not made anew in every
instance. Concentrated weights of typical locomotives, tenders, and
cars are prescribed by different railroad companies for their different
classes of trains, ranging from the heaviest freight traffic to the
lightest passenger train. A tabulation is then made from equation
(28) for each such typical train, and it is used as frequently as is
necessary to design a bridge to carry the prescribed traffic. The
tabulations thus made are never changed for a given or prescribed
loading.
=87. Applications to Rolled Beams.=—It is to be remembered that these
last observations do not limit the use of equations (27) and (28) to
railroad-bridge trusses only; they are equally applicable to solid and
rolled beams and are frequently used in connection with their design.
Great quantities of these beams and various rolled steel shapes are
used in the construction of large modern city buildings, as well as in
railroad and highway bridge structures. The steel frames of the great
office buildings, so many of which are seen in New York and Chicago as
well as in other cities, which carry the entire weight of the building,
are formed wholly of these steel shapes. The so-called handbooks
published by steel-producing companies exhibit the various shapes
rolled in each mill. These books also give in tabular statements many
numerical values of the moment of inertia, the section modulus, and
other elements of all these sections, so that the formulæ which have
been established in the preceding pages may be applied in practical
work with great convenience and little labor. Tables are also given
showing the sizes of rolled beams required to sustain the loads named
in them. Such tables are formed for practical use, so that, knowing
the distance apart of the beams, their span, and the load per square
foot which they carry, the required size of beam may be selected
without even computation. Such labor-saving tables are quite common
at the present time, and they reduce greatly the labor of numerical
computations.
CHAPTER VIII.
=88. The Truss Element or Triangle of Bracing.=—A number of the
preceding formulæ find their applications to bridge-trusses, as well
as to beams; hence it is necessary to give attention at least to some
simple forms of those trusses.
[Illustration: FIG. 18.]
[Illustration: FIG. 18_a_.]
The skeleton of every bridge-truss properly designed to carry its load
is an assemblage of triangles. In other words, the truss element, i.e.,
the simplest possible truss, is the triangular frame, such as is shown
in skeleton in Figs. 18 and 18_a_. These simple triangular frames are
sometimes called the King-post Truss. The action of such a triangular
frame in carrying a vertical load is extremely simple. In Fig. 18 let
the weight _W_ be suspended from the apex _C_ of the triangle. The
line _CF_ represents that weight, and if the latter be resolved into
its two components parallel to the two upper members of the triangular
frame, the two component forces _CG_ and _CD_ will result. If from _D_
and _G_ the horizontal lines _DH_ and _GO_ be drawn, those two lines
will represent the horizontal components of the forces or stresses in
the two bars _CA_ and _CB_. The force _HD_ will act to the left at the
point _A_, and the force _CG_ will act to the right at _B_, and as
these two forces are equal and opposite to each other, equilibrium will
result. Either of the horizontal forces will represent the magnitude
of the tension in _AB_. Both _AC_ and _CB_ will be in compression,
the former being compressed by the force _CD_, and the latter by the
force _CG_. The manner of drawing a parallelogram of forces makes the
triangle _COG_ similar to _CNB_, and _CHD_ similar to _CNA_; hence
_HW_ divided by _CH_ will be equal to _AN_ divided by _NB_. But _HW_
is the vertical component of the stress in _CB_, while _CH_ is the
vertical component of the stress in _AC_, the latter being represented
by the reaction _R_ and the former by the reaction _R′_. It is seen,
therefore, that the weight _W_ is carried by the frame to the two
abutment supports _A_ and _B_, precisely as if it were a solid beam. In
other words, the important principle is established that when weights
rest upon a simple truss supported at each end they will produce
reactions at the ends in accordance with the principle of the lever,
precisely as in the case of a solid beam. In engineering parlance it
is stated that the weight _W_ is divided according to the principle of
the lever, and that each portion travels to its proper abutment through
the members of the triangular frame. If the two inclined members of the
triangular frame are equally inclined to a vertical, the case of Fig.
18_a_ results, in which one half of the weight goes to each abutment.
The triangular frame, with equally inclined sides, shown in Fig. 18_a_,
is evidently the simplest form of roof-truss, constituting two equally
inclined members with a horizontal tie.
=89. Simple Trusses.=—The simplest forms of trussing used for bridge
purposes are those shown in Figs. 19, 20, and 21. There are many other
forms which are exhibited in complete treatises on bridge structures,
but these three are as simple as any, and they have been far more used
than any other types. The horizontal members _af_ and _AB_ are called
the “chords,” the former being the upper chord and the latter the lower
chord. The vertical and inclined members connecting the two chords are
called the web members or braces. When a bridge is loaded, either by
its own weight only, or by its own weight added to that of a moving
train of cars, the upper chord will evidently be in compression, while
the lower chord is in tension. A portion, which may be called a half,
of the web members will be in tension and the other portion, or half,
will be in compression.
The function of the upper and lower chords is to take up or resist
the horizontal tension and compression which correspond to the direct
stresses of tension and compression existing in the longitudinal
fibres of a loaded solid or flanged beam. The metal designed to take
these so-called direct stresses is concentrated in the chords of
trusses, whereas it is distributed throughout the entire section of a
beam, whether that beam be solid or flanged. The function of the web
members of a truss is to resist the transverse or vertical shear which
is represented by the algebraic sum of the reactions and loads. The
total section of a solid beam resists these vertical shears, while
the web only of a flanged beam is estimated to perform that duty. The
horizontal shears, which have already been recognized as existing along
the horizontal planes in a bent beam, are resisted by the inclined
web members of a truss, the horizontal stress components being the
horizontal shears, whereas the vertical shears are resisted by the
vertical web members of a truss. If the web members are all inclined,
as shown in Fig. 21, each web member resists both horizontal and
vertical shear. It is thus seen that the members of a truss perform
precisely the same duties as the various portions of either solid or
flanged beams. Inasmuch as the chords of bridge-trusses resist the
direct or horizontal stresses of tension and compression produced
by the bending in the truss, it is obvious that the greatest chord
stresses will be found at the centre of the span, and that they will
be the smallest at the ends of the span. In the web members, on the
contrary, since the vertical shear is the greatest at the ends of the
span and equal to the reactions at those points, decreasing towards
the centre precisely as in solid beams, the greatest web stresses
will be found at the ends of the span and the least near the centre.
It is obvious that the areas of cross-sections of either chords or
web members must be proportioned to the stresses which they carry.
Hence the distribution of stresses just described tends to a uniform
distribution of the truss weights over the span.
=90. The Pratt Truss Type.=—In the discussion of these three simple
types of trusses, the simplest possible loading of a perfectly uniform
train will be assumed. The portions into which the trusses are divided
by the vertical or inclined bracing are called panels. In Fig. 19, for
instance, the points 1, 2, 3, 4, 5, and 6 of the lower chord and _a_,
_b_, _c_, _d_, _e_, and _f_ of the upper chord are called panel-points.
The distance between each consecutive two of these points is called a
panel length. The uniform train-load which is to be assumed will be
represented by the weight _W_ at each panel-point. This is called the
“moving load” or “live load.” The own weight of the structure is called
the “dead load” or the “fixed load.” The dead load per upper-chord
panel will be taken as _Wʹ_, and _W_₁ for the lower chord. The loads to
be used will, therefore, be as follows:
Panel moving load = _W_;
Upper-chord panel dead load = _Wʹ_;
Lower ” ” ” ” = _W_₁.
There will also be used the length of panel and depth of truss as
follows:
Panel length = _p_;
Depth of truss = _d_.
In these simple trusses with horizontal upper and lower chords the
stress in any inclined web members is equal to the shear multiplied by
the secant of the inclination of the members to a vertical line. Also,
at each panel-point every inclined web member, in passing from the end
to the centre of the span, adds to either chord stress at that point
an amount represented by the horizontal component of the stress which
it carries; or, what is the same thing, an amount equal to the shear
at the panel in question multiplied by the tangent of its angle of
inclination to a vertical line.
It has already been shown in discussing solid beams that the greatest
shear at any section will be found when the uniform moving load covers
one of the segments of the span. This principle holds equally true for
trusses carrying uniform panel-loads like those under consideration. In
determining the stresses in these trusses, therefore, the inclined web
members will take their greatest stresses when the moving train or load
extends from the farthest end of the span up to the foot of the member
in question. In this connection it is to be observed also that any two
web members meeting in the chord which does not carry the moving load
take their greatest stresses for the same position of the latter. The
so-called “counter web members” take no stresses from the dead load.
Inasmuch as every load placed upon a truss will produce compression in
the upper chord and tension in the lower, the greatest chord stresses
will obviously exist when the moving load covers the entire span,
and that condition of loading is to be used for the stresses in the
following cases.
Bearing these general observations in mind, the ordinary simple method
of truss analysis yields the tabulated statement of stresses given
below for the three types selected for consideration. The first case to
be treated is that of Fig. 19, which represents the Pratt truss type.
The moving load is supposed to pass across the bridge from right to
left. The plus sign indicates tension and the minus sign compression.
[Illustration: FIG. 19.]
_Stress in c₁_ = + (¹/₇ + ²/₇) _W_ sec a = ³/₇ _W_ sec _a_.
_Stress in T₄_ = + (¹/₇ + ²/₇ + ³/₇) _W_ sec a = ⁶/₇ _W_ sec _a_;
” ” _T₃_ = + [(¹/₇ + ²/₇ + ³/₇ + ⁴/₇) _W_ + _Wʹ_ + _W₁_] sec _a_
= (¹⁰/₇ _W_ + _Wʹ_ + _W₁_) sec _a_;
” ” _T₂_ = + [(¹/₇ + ²/₇ + ³/₇ + ⁴/₇ + ⁵/₇) _W_ + _2wʹ_ + _2w₁_] sec _a_
= (¹⁵/₇ W + 2wʹ + 2w₁) sec _a_;
” ” _T₁_ = + (_W_ + _W₁_).
_Stress in P₃_ = -(⁶/₇ _W_ + _Wʹ_);
” ” _P₂_ = -(¹⁰/₇ _W_ + 2_Wʹ_ + _W₁_);
” ” _P₁_ = -3(_W_ + _Wʹ_ + _W₁_) sec _a_.
_Stress in L₁_ =_Stress in L₂_ = + 3(_W_ + _Wʹ_ + _W₁_) tan _a_;
” ” _L₃_ = ” ” _L₂_ + 2(_W_ + _Wʹ_ + _W₁_)tan _a_
+ + 5(_W_ + _Wʹ_ + _W₁_) tan _a_;
” ” _L₄_ = ” ” _L₃_ + (_W_ + _Wʹ_ + _W₁_) tan _a_
+ 6(_W_ + _Wʹ_ + _W₁_) tan _a_.
_Stress in U₁_ = _-Stress in L₃_ = -5(_W_ + _Wʹ_ + _W₁_) tan α;
” ” _U₂_ = - ” ” _L₄_ = -6(_W_ + _Wʹ_ + _W₁_) tan α;
” ” _U₃_ = ” ” _U₂_ = -6(_W_ + _Wʹ_ + _W₁_) tan α.
It is easy to check any of the chord stresses by the method of moments.
As an example, let moments first be taken about the panel-point 5
in the lower chord, and then about the panel-point _c_ in the upper
chord. The following expressions for the chord members _U₁_ and _L₄_
will be found, and it will be noticed that they are identical with
the stresses for the same members given in the preceding tabulation,
the counter-members, shown in broken lines, being omitted from
consideration as they are not needed.
_R.2p_ - (_W + Wʹ + W₁_)_p_
_Stress in U₁_ = ------------------------------
_d_
_p_
= 5(_W + Wʹ + W₁_) ---- = 5(_W + Wʹ + W₁_) tan α. (29)
_d_
_R.3p_ - 2(_W + Wʹ + W₁_) . 1½_p_
_Stress in L₄_ = ----------------------------------
_d_
= 6(_W + Wʹ + W₁_) tan α. (30)
[Illustration: FIG. 20.]
=91. The Howe Truss Type.=—The truss shown in Fig. 20 is the skeleton
of the Howe truss, to which reference has already been made. The
inclined web members are all in compression, while the vertical web
members are all in tension. In the Howe truss all compression members
are composed of timber. It has the disadvantage of subjecting the
longest web members to compression. It thus makes the truss, if built
all in iron or steel, heavier and more expensive than the trusses of
the Pratt type. As in the preceding case, the moving train or load is
supposed to pass across the bridge from _B_ to _A_. Also, as before,
the + sign indicates tension and the - sign compression. The greatest
stresses, given in the tabulated statement below, can be computed or
checked by the method of moments in this case, precisely as in the
preceding.
_Stress in c₁_ = -(¹/₇ + ²/₇) _W_ sec _a_ = -³/₇ _W_ sec _a_.
_Stress in P₄_ = -(¹/₇ + ²/₇ + ³/₇) _W_ sec _a_ = -⁶/₇ _W_ sec _a_;
” ” P₃_ = -(_¹⁰/₇ W + Wʹ + W₁_) sec _a_;
” ” P₂_ = -(_¹⁵/₇ W + 2Wʹ + 2W₁_) sec _a_;
” ” P₁_ = -3(_W + Wʹ + W₁_) sec _a_.
_Stress in T₃_ = + (_¹⁰/₇ W + W₁_) sec _a_;
” ” T₂_ = + (_¹⁵/₇ W + Wʹ + 2W₁_) sec _a_;
” ” T₁_ = + (_3W + 2Wʹ + 3W₁_) sec _a_.
_Stress in L₁_ = + 3(_W + Wʹ +W₁_) tan _a_;
” ” L₂_ = + 3(_W + Wʹ + W₁_) tan _a_+2(_W + Wʹ + W₁_) tan _a_
= + 5(_W + Wʹ + W₁_) tan _a_;
” ” L₃_ = + 5(_W + Wʹ + W₁_) tan _a_+(_W + Wʹ + W₁_) tan _a_
= + 6(_W + Wʹ + W₁_) tan _a_;
” ” L₄_ = _Stress in L₃._
_Stress in U₁_ = _- Stress in L₁_
” ” U₂_ = _- ” ” L₂_;
” ” U₃_ = _- ” ” L₃_.
It will be noticed in the cases of Figs. 19 and 20 that upper and lower
chord panels in the same lozenge or oblique panel have identically
the same stresses, but with opposite signs. For instance, in Fig. 20
the stress in _U₂_ is equal in amount to that in _L₂_; and the same
observation can be made in reference to the stresses in _U₂_ and _L₄_
of Fig. 19. This must necessarily always be the case in trusses having
vertical web members.
In making computations for these forms of trusses it is very essential
to observe where the first counter-member, as _c₁_, must be used. These
counter-members may be omitted if the proper main web members near the
centre of the span are designed to take both tension and compression.
=92. The Simple Triangular Truss.=—The truss shown in Fig. 21, in which
all the web members have equal inclination to a vertical line, is
sometimes called the Warren Truss, although that term has also been
applied specially to this type of truss so proportioned as to make the
depth just equal to the panel length. As before, the moving train is
supposed to pass over the bridge from _B_ toward _A_, while the + sign
represents tension and the - sign compression. The greatest stresses
are the following.
[Illustration: FIG. 21.]
{ -(_⁶/₇W + ½Wʹ_) sec _a_, or
_Stress in P₄_ = { +(_⁶/₇W - ½W′_) sec _a_;
” ” P₃_ = { -(_¹⁰/₇W + 1½W′ + W₁_) sec _a_, or
{ +(_³/₇ W - 1½Wʹ - W₁_) sec _a_;
” ” P₂_ = -(_¹⁵/₇ W + 2½Wʹ + 2W₁_) sec _a_;
” ” P₁_ = -(_3W + 3½ Wʹ + 3W₁_) sec _a_.
{ +(_¹⁰/₇W + ½Wʹ + W₁_) sec _a_, or
_Stress in T₃_ = { -(_³/₇W - ½Wʹ - W₁_) sec _a_;
” ” T₂_ = +(_¹⁵/₇W + 1½W′ + 2W₁_) sec _a_;
” ” T₁_ = +(_3W + 2½Wʹ + 3W₁_) sec _a_.
_Stress in L₁_ = + 3(_W + Wʹ + W₁_) tan _a + ½W′_ tan _a_;
” ” L₂_ = _Stress in L₁_ + (_5W + 5Wʹ + 5W₁_) tan _a_
= + 8(_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_;
” ” L₃_ = _Stress in L₂_ + 3(_W + Wʹ + W₁_) tan _a_
= + 11 (_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_;
” ” L₄_ = _Stress in L₃_ + (_W + Wʹ + W₁_) tan _a_
= + 12 (_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_.
_Stress in U₁_ = -6(_W + Wʹ + W₁_) tan _a_;
” ” U₂_ = -6(_W + Wʹ + W₁_)tan _a_ - 4(_W + Wʹ + W₁_) tan _a_
= -10(_W + Wʹ + W₁_) tan _a_;
” ” U₃_ = -10(_W+ Wʹ+ W₁_) tan _a_ - 2(_W + Wʹ + W₁_) tan _a_
= -12(_W + Wʹ + W₁_) tan _a_.
The chord stresses may be checked or found by the method of moments,
precisely as in the case of Fig. 19. If, for instance, it is desired
to determine the stresses in the upper chord member _U₂_, moments must
be taken about the lower-chord panel-point 5, and about the upper-chord
panel-point _d_ for the lower-chord stress in _L₄_. Taking moments
about those points, results given in equations (31) and (32) will at
once follow, which it will be observed are identical with the values
previously found for the same members.
(_3W + 3½ W′ + 3W₁_)._2p_ - 2_W′p_ - (_W + W₁_)_p_
_Stress in U₂_ = - -------------------------------------------------
_d_
= -10(_W + W′ + W₁_) tan _a_. (31)
(_3W + 3½ W′ + 3W₁_)._3½ p_ - 3(_W + W₁_)._1½p - 3W′.2p_
_Stress in L₄_ = + -------------------------------------------------------
_d_
= + 12(_W + W₁ + W′_) tan _a_ + ½_W′_ tan _a_. (32)
=93. Through- and Deck-Bridges.=—These simple trusses have all been
taken as belonging to the “through” type, i.e., the moving load passes
along their lower chords. It is quite common to have the moving load
pass along the upper chords, in which cases the bridges are said to be
“deck” structures. The general methods of computation are precisely
the same whether the trusses be deck or through. It is only necessary
carefully to observe that the application of the methods of analysis
depends upon the position of each panel-load as it passes across the
structure.
[Illustration: Fig. 22.]
=94. Multiple Systems of Triangulation.=—Figs. 19, 20, and 21 exhibit
what are called single systems of triangulation or single systems
of bracing, but in each of those types the system of web members
may be double or triple; in other words, they may be manifold.
There have been many bridges built in which two or more systems
of bracing are employed. Fig. 22 represents a truss with a double
system of triangulation, known at one time as the Whipple truss.
Fig. 23, again, exhibits a quadruple system of triangulation with all
inclined web members. The method of computation for such manifold
systems is precisely the same as for a single system, each system in
the compound truss being treated as carrying those loads only which
rest at its panel-points. This procedure is not quite accurate. The
complete consideration of an exact method of computation would take
the treatment into a region of rather complicated analysis beyond the
purposes of these lectures, but its outlines will be set forth on a
later page. The exact method of treatment of two or more web systems
involves the elastic properties of the material of which the trusses
are composed. In the best modern bridge practice engineers prefer to
design trusses of all lengths with single web systems, although the
panels are frequently subdivided to avoid stringers and floor-beams of
too great weight.
[Illustration: Fig. 23.]
=95. Influence of Mill and Shop Capacity on Length of Span.=—In
the early years of iron and steel bridge-building the sizes of
individual members were limited by the shop capacity for handling
and manufacturing, and by the relatively small dimensions of bars of
various shapes, and of plates which could be produced by rolling-mills.
As both mill and shop processes have advanced and their capacities
increased, corresponding progress has been made in bridge design. Civil
engineers have availed themselves of those advances, so that at the
present time single system trusses with depths as great as 85 feet or
more and spans of over 550 feet are not considered specially remarkable.
=96. Trusses with Broken or Inclined Chords.=—As the lengths of spans
have increased certain substantial advantages have been gained in
design by no longer making the upper chords horizontal in the case of
long through-spans, or indeed in the cases of through-spans of moderate
length. The greatest bending moments and the greatest chord stresses
have been shown to exist at the centre of the span, while the greatest
web stresses are found near the ends. Trusses may be lightened in view
of those considerations by making their depths less at the ends than at
the centre. This not only decreases the sectional areas of the heaviest
web members near the ends of the truss, but also shortens them. It
adds somewhat to the sectional area of the end upper-chord members,
but the resultant effect is a decrease in total weight of material and
increased stability against wind pressure by the decreased height and
less exposure near the ends. It has therefore come to be the ruling
practice at the present time to make through-trusses with inclined
upper chords for practically all spans from about 200 feet upward. A
skeleton diagram of such a truss is given in Fig. 24.
[Illustration: Fig. 24.]
=97. Position of any Moving Load for Greatest Web Stress.=—In the
preceding treatment of bridge-trusses with parallel and horizontal
chords a moving or live load has been taken as a series of uniform
weights concentrated at the panel-points. This simple procedure
was formerly generally used, and at the present time it is
occasionally employed, but it is now almost universal practice to
assume for railroad bridges a moving load consisting of a series of
concentrations, which represent both in amount and distribution the
weights on the axles of an actual railroad train. If a bridge is
supposed to be traversed by such a train, it becomes necessary to
determine a method for ascertaining the positions of the train causing
the greatest stresses in the various members of the bridge-truss. The
mathematical demonstration of the formulæ determining those positions
of loading need not be given here, but it can be found in almost any
standard work on bridges.
In order to show concisely the results of such a demonstration let it
be desired to find the position of a moving load which will give the
greatest stress to any web member, as _S_ in Fig. 24. Let the point of
intersection of _GK_ and _DC_ be found in the point _O_, then let _CK_
be extended, and on its extension let the perpendicular _h_ be dropped
from _O_. The distance of the point _O_ from _A_, the end of the span,
is _i_, while _m_ is the distance _AD_. Using the same notation which
has been employed in the discussion of beams, together with that shown
in Fig. 24, equation (33) expresses the condition to be fulfilled by
the train-loads in order that _S_ shall have its greatest stress. The
first parenthesis in the second member of that equation represents the
load between the panel _p_ and the left end of the span, while the
second parenthesis represents the load in panel _p_ itself.
_l_
_W₁ + W₂ + ... + Wₙ_ = - ----(_W₁ + W₂_ + etc.)
_i_
_l_(_m + i_)
+ (_W₃ + W₄_ + etc.) --------------- (33)
_pi_.
It will be noticed in equation (33) that the quantity _m_ shows in
what panel the inclined web member whose greatest stress is desired
is located, and it is important to observe that panel carefully. If,
for instance, the vertical member _KD_ were in question, the point _O_
would be located at the intersection of the panel _NK_ and the lower
chord of the bridge. In other words, the point _O_ must be at the
intersection of the two chord members belonging to the same panel in
which the web member is located.
=98. Application of Criterions for both Chord and Web Stresses.=—The
criterion, equation (33), belongs to web members only. If it is desired
to find the position of moving load which will give the greatest chord
stresses in any panel, equation (27), already established for beams,
is to be used precisely as it stands, the quantity _l′_ representing
the distance from one end of the span to the panel-point about which
moments are taken.
If the desired positions of the moving load for greatest stresses have
been found by equations (27) and (33), those stresses themselves are
readily found by taking moments about panel-points for chord members
and about the intersection-points _O_, Fig. 24, for web members.
These operations are simple in character and are performed with
great facility. Tabulations and diagrams are made for given systems
of loading by which these computations are much shortened and which
enable the numerical work of any special case to be performed quickly
and with little liability to error. These tabulations and diagrams and
other shortening processes may be found set forth in detail in many
publications and works on bridge structures. They constitute a part of
the office outfit of civil engineers engaged in structural work.
The criterion, equation (27), for the greatest bending moments in a
bridge is applicable to any truss whatever, whether the chords are
parallel or inclined, but it is not so with equation (33). If the
chords of the trusses are parallel, the quantity _i_ in equation (33)
becomes infinitely great, and the equation takes the following form:
_l_
_W₁ + W₂ + ... + Wₙ_ = ---- (_W₃ + W₄_ + etc.) (34)
_p_
Ordinarily the span _l_ divided by the panel length _p_ is equal to the
number of panels in the span. Hence equation (34) shows, in the case
of parallel or horizontal chords, that when the moving load is placed
for the greatest web stress in any panel, the total load on the bridge
is equal to the load in that panel multiplied by the total number of
panels.
=99. Influence Lines.=—A graphical method, known as that of “influence
lines,” is used for determining the greatest shears and bending moments
caused by a train of concentrated weights passing along a beam or
bridge-truss. Obviously it must express in essence that which has
already been shown by the formulæ which determine positions of moving
loads for the greatest shears and bending moments. In reality it is the
application of graphical methods which have become so popular to the
determination of the greatest stresses in beams and bridges.
=100. Influence Lines for Moments both for Beams and Trusses.=—It is
convenient to construct these influence lines for an arbitrary load
which may be considered a unit load; the effect of any other load will
then be in proportion to its magnitude. The results determined from
influence lines drawn for a load which may be considered a unit can,
therefore, be made available for other loads by multiplying the former
by the ratio between any desired load and that for which the influence
lines are found.
[Illustration: FIG. 25.—Bending Moment in a Simple Beam.]
_AB_ in Fig. 25 represents a beam simply supported at each end, so
that any load _g_ resting upon it will be divided between the points
of support, according to the law of the lever. Let it be desired to
determine the bending moment at the section _X_ produced by the load
_g_ in all of its positions as it passes across the span from _A_ to
_B_. Two expressions for the bending moment must be written, one for
the load _g_ at any point in _AX_, and the other for the load at any
point in _BX_. The expression for the first bending moment is
_z_
_M = g_ ----(_l-x_), (_a_)
_l_
and that for the latter
_l-z_
_M′ = g_ ---- _x_. (_b_)
_l_
As shown in the figure, _z_ and _x_, the latter locating the section at
which the bending moments are to be found, are measured to the right
from _A_. Equation (_a_) shows that if the quantity _g_(l-_x_) be laid
off, by any convenient scale, as _BK_ at right angles to _AB_, _XC_
will represent the moment _M_ by the same scale when _x = z_ or when
_z_ has any value between 0 and _x_. Similarly will _AD_ be laid off
at right angles to _AB_ by the same scale as before, to represent _gx_.
Then when _x = z_ the expression for _M′_ will have the same value _XC_
as before. Hence if the lines _AC_ and _CB_ be drawn as parts of _AK_
and _DB_, any vertical intercept between _AB_ and _ACB_ will represent
the bending at _X_ produced by the load _g_ when placed at the point
from which the intercept is drawn. The lines _AC_ and _CB_ are the
influence lines for the bending moments produced by the load _g_ in its
passage across the span _AB_. It is to be observed that the influence
lines are continuous only when the positions of the moving load are
consecutive. In case those positions are not consecutive the influence
lines are polygonal in form.
If there are a number of loads _g_ resting on the span at the same
time, the total bending moments produced at _X_ will be found by taking
the sum of all the vertical intercepts between _AB_ and _ACB_, drawn at
the various points where those loads rest. The influence lines drawn
for a single load, therefore, may be at once used for any number of
loads.
The load _g_ is considered as a unit load. If the vertical intercepts
representing the bending moments by the scale used are themselves
represented by _y_, and if _W_ represent any load whatever, the general
expression for the bending moment at _X_, produced by any system of
loads, will be
_l_
---- ∑_Wy._ (_c_)
_g_
If this expression be written as a series, the general value of the
bending moment will be the following:
_l_
_M_ = --- (_W₁y₁ + W₂y₂ + W₃y₃_ + etc.). (_d_)
_g_
The effect of a moving train upon the bending moment at any given
section is thus easily made apparent by means of influence lines. It is
obvious that there will be as many influence lines to be drawn as there
are sections to be considered. In the case of a truss-bridge there will
be such a section at every panel-point.
A slight modification of the preceding results is to be made when the
loads are applied to the beam or truss at panel-points only.
In Fig. 25 let 1, 2, 3, 4, 5, 6, and 7 be panel-points at which loads
are applied, and let the load _g_ be located at the distance _z′_ to
the right of panel-point 5, also let the panel length be _p_. The
reactions at 5 and 6 will then be
_p-z′_ _z′_
_R₅ = g_ -------- and _R₆ = g_ ------.
_p_ _p_
The reactions at _A_ will then be
_l-z_
_R = g_ ------.
_l_
Hence the moment at any section _X_ in the panel in question will be
[ _l-x z′_]
_M = Rx-R₅_{_z_′-(_z-x_)} = _g_[ ---- _z_-(_z-z′ + p-x_)---]. (_e_)
[ _l p_ ]
Remembering that _z-z′_ is a constant quantity, it is at once clear
that the preceding expression is the equation of a straight line,
with _M_ and _z_ or _z′_ the variables. If _z′ = 0_, equation (_e_)
becomes identical with equation (_a_), while if _z′ = p_, it becomes
identical with equation (_b_). Hence the influence line for the panel
in which the load is placed, as 5-6, is the straight line _KL_. It is
manifest that when the load _g_ is in any other panel than that in
which the section _X_ is located, the effect of the two reactions at
the extremities of that panel will be precisely the same at the section
as the weight itself acting along its own line of action. Hence the
two portions _AK_ and _BL_ of the influence line are to be constructed
as if the load were applied directly to the beam or truss, and in the
manner already shown. The complete influence line will then be _AKLB_,
and it shows that the existence of the panel slightly reduces the
bending at any section within its limits. The panel 5-6, as treated,
is that of a beam in which the bending moment will, in general, vary
from point to point. If _AB_ were a truss, however, _X_ would always be
taken at a panel-point, and no intercept between panel-points, as 5 and
6, would be considered.
=101. Influence Lines for Shears both for Beams and Trusses.=—The
influence lines for shears in a simple beam, supported at each end,
can be drawn in the manner shown in Fig. 25_a_. In that figure _AB_
represents a non-continuous beam with span _l_ supported from _A_. The
reaction at _A_ will be
_l-z_
_R_ = ----- _g_.
_l_
[Illustration: FIG. 25_a_.—Shear in a Simple Beam.]
Let _X_ be the section at which the shear for various positions of _g_
is to be found. When _g_ is placed at any point between _A_ and _X_ the
shear _S_ at the latter point will be
_z_
_S_ = _R_ = _g_ = -_g_ ----; (_f_)
_l_
but when the load is placed between _B_ and _X_ the shear becomes
_z_
_S_′ = _R_ = _g-g_ ----. (_h_)
_l_
Obviously these two values of the shear are equations of two parallel
straight lines, that represented by equation (_f_) passing through
_A_, and that represented by equation (_h_) passing through _B_, the
constant vertical distance between them being _g_. Hence let _BF_ be
laid off negatively downward and _AG_ positively upward, each being
equal to _g_ by any convenient scale. The ordinates drawn from the
various positions 1, 2, 3 ... 6 of _g_ on _AB_ to _AD_ and _BC_ will
be the shears at _X_ produced by the load _g_ at any point of the
span, and determined by equations (_f_) and (_h_). The influence line,
therefore, for the section _X_ will be the broken line _ADCB_. When
_g_ is at _X_ the sign of the shear changes, since the latter passes
through a zero value.
If a train of weights _W₁_, _W₂_, _W₃_, etc., passes across the span,
the total shear at _X_ will be found by taking the sum of the vertical
intercepts between _AB_ and _ADCB_, drawn at the positions occupied by
the various single weights of the train. If those single weights are
expressed in terms of the unit load _g_, the shear _S_ will have the
value
1
_S_ = ---- ∑ _Wy_;
_g_
_y_ being the general value of the intercept between _AB_ and the
influence line. The latter shows that the greatest negative shear at
_X_ will exist when the greatest possible amount of loading is placed
on _AX_ only, while the greatest positive shear at the same section
will exist when _BX_ only is loaded. If _BX_ is the smaller segment of
span, the latter shear is called the “counter-shear,” and the former
the “main shear.”
If the loads are applied at panel-points of the span only, the
treatment is the same in general character as that employed for bending
moments. In Fig. 25_a_ let 4 and 5 be the panel-points between which
the load _g_ is found, and let the panel length be _p_. Also, let _z′_
be the distance of the weight _g_ from panel-point 4. The reactions at
_A_ and 4 will then be
_l - z p - z′_
_R_ = ------_g_ and _R₄_ = ----------- _g_.
_l p_
The shear at the section _X_ for any position of the weight _g_ will
then be
(_z′ z_)
_S_ = _R - R₄_ = _g_(--- - ---). (_k_)
(_p l_)
As this is the equation of a straight line, with _S_ and _z_ or _z′_
for the coordinates, the influence line for the panel in which the
section _X_ is located will be the straight line represented by _KL_ in
Fig. 25_a_.
If _z′_ is placed equal to 0 and _p_ successively, then will equation
(_k_) become identical with equations (_f_) and (_h_) in succession.
The shears at points 4 and 5 will therefore take the same values as if
the loads were applied directly to the beam. For the reasons stated in
connection with the consideration of bending moments, loads in other
panels than that containing the section for which the influence line
is drawn will have the same effect on that section as if they were
applied directly to the beam or truss. Hence _AKLB_ is the complete
influence line for this case.
It is evident that there must be as many influence lines drawn as there
are sections to be discussed. Also, if _g_ is taken as some convenient
unit, i.e., 1000 or 10,000 pounds, it is clear that the labors of
computation will be much reduced.
=102. Application of Influence-line Method to Trusses.=—In considering
both the bending moments and shears when the loads are applied at
panel-points, it has been assumed, as would be the case in an ordinary
beam, that the bending moments as well as the shears may vary in the
panel; but this latter condition does not hold in a bridge-truss.
Neither bending moment nor shear varies in any one panel. Yet the
influence lines for moments and shears are to be drawn precisely as
shown in Figs. 25 and 25_a_. The section _X_ will always be found at
a panel-point, and no intercept drawn within the limits of the panel
adjacent to that section carrying the load _g_ is to be used. This
method will be illustrated by the aid of Fig. 25_b_.
The employment of influence lines may be illustrated by determining
the moment and shear in a single section of the truss shown in Fig.
24, which is reproduced in Fig. 25_c_, when carrying the moving load
exhibited in Fig. 25_b_, although its use may be much extended beyond
this simple procedure.
The moving load shown in Fig. 25_b_ is that of a railroad train
consisting of a uniform train-load of 4000 pounds per linear foot
drawn by two locomotives with the wheel concentrations shown; it is
a train-load frequently used in the design of the heaviest class of
railroad structures. If the criterion of equation (27) be applied to
this moving load, passing along the truss shown in Fig. 25_c_, from
left to right, it will be found that the greatest bending moment is
produced at the section _Q_ when the second driving-axle of the second
locomotive is placed at the truss section in question, as shown in Fig.
25_c_.
The unit load to be used in connection with the influence lines will be
taken at 10,000 pounds. Remembering that the panel lengths are each 30
feet, it will be seen that the panel-point _Q_ is 150 feet from _A_.
Hence the product _gx_ will be 1,500,000 foot-pounds. Similarly the
product _g_(l - _x_) will be 900,000 foot-pounds. Laying off the first
of these quantities, as _AD_, at a scale of 1,000,000 foot-pounds per
linear inch, and the second quantity, as _BK_, by the same scale, the
influence line _ACB_ can at once be completed. Vertical lines are next
to be drawn through the positions of the various weights, including
one through the centre of the uniform train-load 110 feet in length
resting on the truss. The vertical line through the centre of the
uniform train-load is shown at _O_. By carefully scaling the vertical
intercepts between _AB_ and _ACB_, and remembering that each of the
loads on the truss must be divided by 10,000, the following tabulated
statement will be obtained, the sum of the intercepts for each set
of equal weights being added into one item, and all the items of
intercepts being multiplied by 1,000,000:
.195 × 110 × .4 × 1,000,000 = 8,580,000 foot-pounds.
1.78 × 2.6 × ” = 4,628,000 ” ”
2.14 × 4 × ” = 8,560,000 ” ”
.485 × 2 × ” = 970,000 ” ”
1.525 × 2.6 × ” = 3,965,000 ” ”
.9 × 4 × ” = 3,600,000 ” ”
.12 × 2 × ” = 240,000 ” ”
----------
2⟌30,543,000 ” ”
----------
Moment for one truss = 15,271,500 ” ”
The lever-arm of _ef_, i.e., the normal distance from _Q_ to _ef_, is
39.7 feet. Hence the stress in _ef_ is
15,271,500
----------- = 384,700 pounds.
39.7
All the chord stresses can obviously be found in the same manner.
In order to place the same moving load so as to produce the greatest
shear at the same section _Q_, the criterion of equation (33) must be
employed. The dimensions of the truss shown in connection with Fig. 29
give the following data to be used in that equation: _i_ = 210 feet,
_m_ = 60 feet, and _p_ = 30 feet.
_l_(_m + i_) _l_
Hence ------------ = 10²/₇, --- = 1¹/₇.
_pi i_
[Illustration: FIG. 25_b_.]
[Illustration: FIG. 25_c_.]
[Illustration: FIG. 25_d_.]
Introducing these quantities into equation (33), and remembering
that the train moves on to the bridge from _A_, it would be found
that the second axle of the first locomotive must be placed at the
section _Q_, as shown in Fig. 25_d_, which exhibits the lower-chord
panel-points numbered from 1 to 7. The conventional unit load _g_
will be taken in this case at 20,000 pounds. It is represented as
_AG_ and _BF_ (Fig. 25_d_), laid off at a scale of 10,000 pounds per
inch. _K_ is immediately under panel-point 5 and _L_ is immediately
above panel-point 6, hence the broken line _AKLB_ is the influence
line desired. The vertical lines are then drawn from each train
concentration in its proper position, all as shown, including the
vertical line through the centre of the 54 feet of uniform train-load
on the left. The summation of all the vertical intercepts between _AB_
and the influence line _AKL_, having regard to the scale and to the
ratio between the various loads and the unit load _g_, will give the
following tabular statement:
.22 × 54 × .2 × 10,000 = 23,760 pounds.
2.2 × 1.3 × ” = 28,600 ”
3.02 × 2 × ” = 60,400 ”
.9 × 1 × ” = 9,000 ”
4.06 × 1.3 × ” = 53,780 ”
4.53 × 2 × ” = 90,060 ”
.5 × 1 × ” = 5,000 ”
--------
2⟌ 270,600 ”
--------
Shear for one truss = 135,300 ”
These simple operations illustrate the main principles of the method of
influence lines from which numerous and useful extensions may be made.
CHAPTER IX.
=103. Lateral Wind Pressure on Trusses.=—The duties of a bridge
structure are not confined entirely to the supporting of vertical
loads. There are some horizontal or lateral loads of considerable
magnitude which must be resisted; these are the wind loads resulting
from wind pressure against both structure and moving train. In order
to determine the magnitudes of these loads it is assumed in the first
place that the direction of the wind is practically or exactly at
right angles to the planes of the trusses and the sides of the cars.
This assumption is essentially correct. There is probably nothing
else so variable as both the direction and pressure of the wind.
These variations are not so apparent in the exposure of our bodies
to the wind, for the reason that we cannot readily appreciate even
considerable changes either in direction or pressure. As a matter of
fact suitable measuring apparatus shows that there is nothing steady
or continued in connection with the wind unless it be its incessant
variability. Its direction may be either horizontal or inclined, or
even vertical, while within a few seconds its pressure may vary between
wide limits. Under such circumstances the wind is as likely to blow
directly against both bridge and train as in any other direction, and
inasmuch as such a condition would subject the structure to its most
severe duty against lateral forces, it is only safe and proper that
the assumption should be made. The open work of bridge-trusses enables
the wind to exert practically its full pressure against both trusses
of a single-track bridge, or against even three trusses if they are
used for a double-track structure. Hence it is customary to take the
exposed surface of bridge-trusses as the total projected area on a
plane throughout the bridge axis of both trusses if there are two, or
of three trusses if there are three. Inasmuch as the floor of a bridge
from its lowest point to the top of the rails or other highest point
of the floor is practically closed against the passage of the wind,
all that surface between the lowest point and the top of the rail or
highest floor-member is considered area on which wind pressure may act.
Many experimental observations show that on large surfaces, greater
perhaps than 400 or 500 square feet in area, the pressure of the wind
seldom exceeds 20 or 25 pounds per square foot, while it may reach 80
or 90 pounds, or possibly more on small surfaces of from 2 to 40 or 50
square feet in area. This distinction between small and large exposed
areas in the treatment of wind pressures is fundamental and should
never be neglected.
This whole subject of wind pressures has not yet been brought into
a completely definite or well-defined condition through lack of
sufficient experimental observations, but in order to be at least
reasonably safe civil engineers frequently, and perhaps usually,
assume a wind pressure acting simultaneously on both bridge and train
at 30 pounds per square foot of exposed surface and 50 pounds per
square foot of the total exposed surface of a bridge structure which
carries no moving load. This distinction arises chiefly from the fact
that a wind pressure of 30 pounds per square foot on the side of many
railroad trains, particularly light ones, will overturn them, and it
would be useless to use a larger pressure for a loaded structure. There
have been wind pressures in this country so great as to blow unloaded
bridges off their piers; indeed in one case a locomotive was overturned
which must have resisted a wind pressure on its exposed surface of not
less than 90 pounds and possibly more than 100 pounds per square foot.
The consideration of wind pressure is of the greatest importance in
connection with the high trusses of long spans, as well as in long
suspension and cantilever bridges, and in the design of high viaducts,
all of which structures receive lateral wind pressures of great
magnitude.
Some engineers, instead of deducing the lateral wind loads from the
area of the projected truss surfaces, specify a certain amount for
each linear foot of span, as in ”The General Specifications for Steel
Railroad Bridges and Viaducts” by Mr. Theodore Cooper it is prescribed
that a lateral force of 150 pounds for each foot of span shall be taken
along the upper chords of through-bridges and the lower chords of
deck-bridges for all spans up to 300 feet in length; and that for the
same spans a lateral force of 450 pounds for each foot of span shall
be taken for the lower chords of through-spans and the upper chords of
deck-spans, 300 pounds of this to be treated as a moving load and as
acting on a train of cars at a line 8⁵/₁₀ feet above the base of rail.
When the span exceeds 300 feet in length each of the above amounts
of load per linear foot is to be increased by 10 pounds for each
additional 30 feet of span.
Special wind-loadings and conditions under which they are to be used
are also prescribed for viaducts.
These wind loads are resisted in the bridges on which they act by a
truss formed between each two upper chords for the upper portion of the
bridge, and between each two lower chords for the lower portion of the
structure.
[Illustration: FIG. 26.]
=104. Upper and Lower Lateral Bracing.=—Fig. 26 shows what are called
the upper and lower lateral bracing for such trusses as are shown in
the preceding figures. The wind is supposed to act in the direction
shown by the arrow. _DERA_ and _KLBC_ are the two portals at the ends
of the structure, braced so as to resist the lateral wind pressures.
It will be observed that the systems of bracing between the chords
make an ordinary truss, but in a horizontal plane, except in the
case of inclined chords like that of Fig. 24. In the latter case the
lateral trusses are obviously not in horizontal planes, but they may
be considered in computations precisely as if they were. These lateral
trusses are then treated with their horizontal panel wind loads just
as the vertical trusses are treated for their corresponding vertical
loads, and the resulting stresses are employed in designing web and
chord members precisely as in vertical trusses. The wind stresses in
the chords, in some cases, are to be added to those due to vertical
loading, and in some cases subtracted. In other words, the resultant
stresses are recognized and the chord members are so designed as
properly to resist them. At the present time it is the tendency
in the best structural work to make all the web members of these
lateral trusses of such section that they can resist both tension
and compression, as this contributes to the general stiffness of the
structure. On account of the great variability of the wind pressures
and the liability of the blows of greatest intensity to vary suddenly,
some engineers regard all the wind load on structure or train as a
moving load and make their computations accordingly. It is an excellent
practice and is probably at least as close an approximation to actual
wind effects as the assumption of a uniform wind pressure on a
structure.
Both the lateral and transverse wind bracing of railroad bridges have
other essential duties to perform than the resistance of lateral wind
pressures. Rapidly moving railroad trains produce a swaying effect on
a bridge, in consequence of unavoidable unevenness of tracks, lack of
balance of locomotive driving-wheels, and other similar influences.
These must be resisted wholly by the lateral and transverse bracing,
and these results constitute an important part of the duties of that
bracing. These peculiar demands, in connection with the lateral
stability of bridges, make it the more desirable that the lateral and
transverse bracing should be as stiff as practicable.
=105. Bridge Plans and Shopwork.=—After the computations for a bridge
design are completed in a civil engineer’s office they are placed in
the drawing-room, where the most detailed and exact plans of every
piece which enters the bridge are made. The numerical computations
connected with this part of bridge construction are of a laborious
nature and must be made with absolute accuracy, otherwise it would be
quite impossible to put the bridge together in the field. The various
quantities of bars, plates, angles, and other shapes required are then
ordered from the rolling-mill by means of these plans or drawings. On
receipt of the material at the shop the shopwork of manufacture is
begun, and it involves a great variety of operations. The bridge-shop
is filled with tools and engines of the heaviest description. Punches,
lathes, planers, riveters, forges, boring and other machines of the
largest dimensions are all brought to bear in the manufacture of the
completed bridge.
=106. Erection of Bridges.=—When the shop operations are completed
the bridge members are shipped to the site where the bridge is to be
erected or put in place for final use. A timber staging, frequently
of the heaviest timbers for large spans, called false works, is first
erected in a temporary but very substantial manner. The top of this
false work, or timber staging, is of such height that it will receive
the steelwork of the bridge at exactly the right elevation. The bridge
members are then brought onto the staging and each put in place and
joined with pins and rivets. If the shopwork has not been done with
mathematical accuracy, the bridge will not go together. On the accuracy
of the shopwork, therefore, depends the possibility of properly fitting
and joining the structure in its final position. The operations of the
shop are so nicely disposed and so accurately performed that it is not
an exaggeration to state that the serious misfit of a bridge member
in American engineering practice at the present time is practically
impossible. This leads to rapid erection so that the steelwork of a
pin-connected railroad bridge 500 feet long can be put in place on the
timber staging, or false works, and made safe in less than four days,
although such a feat would have been considered impossible twenty years
ago.
[Illustration: FIG. 27.]
=107. Statically Determinate Trusses.=—The bridge structures which
have been treated require but the simplest analysis, based only on
statical equations of equilibrium of forces acting in one plane, i.e.,
the plane of the truss. It is known from the science of mechanics that
the number of those equations is at most but three for any system of
forces or loads, viz., two equations of forces and one of moments. This
may be simply illustrated by the system of forces _F₁_, _F₂_, etc., in
Fig. 27. Let each force be resolved into its vertical and horizontal
components _V_ and _H_. Also let _l₁_, _l₂_, etc. (not shown in the
figure), be the normals or lever-arms dropped from any point _A_ on the
lines of action of the forces _F₁_, _F₂_, etc., so that the moments of
the forces about that point will be _F₁l₁_, _F₂l₂_, etc. The conditions
of purely statical equilibrium are expressed by the three general
equations
_H₁ + H₂_ + etc. = _F₁_ cos _a₁_ + _F₂_ cos _a₂_ + etc. = 0; (35)
_V₁ + V₂_ + etc. = _F₁_ sin _a₁_ + _F₂_ sin _a₂_ + etc. = 0; (36)
_Fl = F₁l₁ + F₂l₂_ + etc. = 0. (37)
If all the forces except three are known, obviously those three can
be found by the three preceding equations; but if more than three are
unknown, those three equations are not sufficient to find them. Other
equations must be available or the unknown forces cannot be found. In
modern methods of stress determinations those other needed equations
express known elastic relations or values, such as deflections or the
work performed in stressing the different members of structures under
loads. A few fundamental equations of these methods will be given.
In Figs. 19, 20, and 21 let the truss be cut or divided by the
imaginary sections _QS_. Each section cuts but three members, and as
the loads and reactions are known, the stresses in the cut members
will yield but three unknown forces, which may be found by the three
equations of equilibrium (35), (36), (37). If more than three members
are cut, however, as in the section _TV_ of Figs. 22 and 23, making
more than three unknown equations to be found, other equations than
the three of statical equilibrium must be available. Hence the general
principle that _if it is possible to cut not more than three members
by a section through the truss, it is statically determinate_, but _if
it is not possible to cut less than four or more, the stresses are
statically indeterminate_.
At each joint in the truss the stresses in the members meeting there
constitute, with the external forces or loads acting at the same point,
a system in equilibrium represented by the two equations (35) and (36).
If there are _m_ such joints in the entire structure, there will be
2_m_ such equations by which the same number of unknown quantities
may be found. Since equilibrium exists at every joint in the truss,
the entire truss will be in equilibrium, and that is equivalent to
the equilibrium of all the external forces acting on it. This latter
condition is expressed by the three equations (35), (36), and (37),
and they are essentially included in the number 2_m_. Hence there
will remain but 2_m_ - 3 equations available for the determination of
unknown stresses or external forces.
If, therefore, all the external forces (loads and reactions) are
known, the 2_m_ - 3 equations of static equilibrium can be applied
to the determination of stresses in the bars of the truss or other
structure. It follows, therefore, that the greatest number of bars that
a statically determinate truss can have is
_n_ = 2_m_ - 3. (38)
In Fig. 19 there are twelve joints and twenty-one members, omitting
counter web members and the verticals _ab_ and _fl_, which are,
statically speaking, either superfluous or not really bars of the
truss. Hence
_m_ = 12 and 2_m_ - 3 = 21. (39)
Again, in Fig. 21 there are fifteen joints. Hence
_m_ = 15, 2_m_ - 3 = 27,
and there are twenty-seven bars or members of the truss. The number of
joints and bars in actual, statically determinate trusses, therefore,
confirm the results.
=108. Continuous Beams and Trusses—Theorem of Three Moments.=—These
considerations find direct application to what are known as ”continuous
beams,” i.e., beams (or trusses) which reach continuously over two or
more spans, as shown in Fig. 28.
[Illustration: FIG. 28.]
The beam shown is continuous over three spans, but a beam or truss may
be continuous over any number of spans. In general the ends of the beam
or girder may be fixed or held at the ends _A_ and _D_, so that bending
moments _M_ and _M₃_ at the same points may have value. The bending
moments at the other points of support are represented by _M₁_, _M₂_,
etc. The points of support may or may not be at the same elevation, but
they are usually assumed to be so in engineering practice. Finally,
it is ordinarily assumed that the continuous structure is straight
before being loaded, and that in that condition it simply touches the
points of support. Whether the preceding assumptions are made or not,
a perfectly general equation can be written expressing the relation
between the bending moments over each set of three consecutive points
of support, as _M_, _M₁_, and _M₂_, or _M₁_, M₂, and M₃. Such an
equation expresses what is called the ”Theorem of Three Moments.” It is
not necessary to give the most general form of this theorem, as that
which is ordinarily used embodies the simplifying assumptions already
described. This simplified form of the ”Theorem of Three Moments”
applied to the case of Fig. 28 will yield the following two equations:
1 ₁
_Ml₁ + 2M₁_(_l₁ + l₂_) + _M₂l₂_ + ---- ∑ _W_(_l₁² - z²_)_z_
_l₁_
1 ₂
+ ----- ∑ _W_(_l₂² - z²__)z_ = 0. (40)
_l₂_
1 ₂
_M₁l₂ + 2M₂_(_l₂ + l₃_) + _M₃l₃_ + ------ ∑ _W_(_l₂² - z²_)
_l₂_
1 ₃
+ ---- ∑ _W_(_l₃² - z²_)_z_ = 0. (41)
_l₃_
The figure over the sign of summation shows the span to which the
summation belongs. If there is but one weight or load _W_ in each span,
the sign of summation is to be omitted. In an ordinary bridge structure
or beam the ends are simply supported and _M = M₃ = 0_. In any case if
the number of supports be _n_, there will be _n_ - 2 equations like the
preceding.
If the end moments _M_ and _M₃_ are not zero, they will be determinable
by the local conditions in each instance. In any event, therefore, they
will be known, and there will be but _n_ - 2 unknown moments to be
found by the same number of equations. When the moments are known the
reactions follow from simple formulæ.
=109. Application to Draw- or Swing-bridges.=—In general the
reactions or supporting forces of the beams and trusses of ordinary
civil-engineering practice are vertical, and all their points
of application are known. Hence there are but two equations of
equilibrium, equations (36) and (37), for external forces. These two
equations for the external forces and the _n_ - 2 equations derived
from the theorem of three moments are therefore always sufficient to
determine the _n_ reactions. After the reactions are known all the
stresses in the bars or members of the trusses can at once be found.
The preceding equations and methods as described are constantly
employed in the design and construction of swing- or drawbridges.
=110. Special Method for Deflection of Trusses.=—The method of finding
the elastic deflections produced by the bending of solid beams has
already been shown, but it is frequently necessary to determine the
elastic deflections of bridge-trusses or other jointed or so-called
articulate frames or structures. It is not practicable to use the
same formulæ for the latter class of structures as for the former.
The elastic deflection of a bridge- or roof-truss depends upon the
stretching or compressions of its various members in consequence of the
tensile or compressive forces to which they are subjected. Any method
by which the deflection is found, therefore, must involve these elastic
changes of length. There are a number of methods which give the desired
expressions, but probably the simplest as well as the most elegant
procedure is that which reaches the desired expression through the
consideration of the work performed in the truss members in producing
their elastic lengthenings and shortenings.
The general features of this method can readily be shown by reference
to Fig. 29. It may be supposed that it is desired to find the
deflection of any point, as _J_, of the lower chord produced both by
the dead and live load which it carries. It is known from what has
preceded that every member of the upper chord will be shortened and
that every member of the lower chord will be lengthened; and also that
generally the vertical web members will be shortened and the inclined
web members lengthened. If there can be obtained an expression giving
that part of the deflection of _J_ which is due to the change of
length of any one member of the truss independently of the others,
then that expression may be applied to every other member in the
entire truss, and by taking the sum of all those effects the desired
deflection will at once result. While this expression will be found for
some one particular truss member, it will be of such a general form
that it may be used for any truss member whatever; it will be written
for the upper-chord member _BC_ in Fig. 29.
[Illustration: FIG. 29.]
The general problem is to determine the deflection of the point _J_
when the bridge carries both dead and moving load over the entire span,
as shown in Fig. 29. The general plan of procedure is first to find
the stresses due to this combined load in every member of the truss,
so that the corresponding lengthening or shortening is at once shown.
The effect of this lengthening and shortening for any single member
_BC_ in producing deflection at _J_ is then determined; the sum of all
such effects for every member of the truss is next taken, and that sum
is the deflection sought. In this case the vertical deflection will be
found, because that is the deflection generally desired in connection
with bridge structures, but precisely the same method and essentially
the same formulæ are used to find the deflection in any direction
whatever. The following notation will be employed:
Let _w_ = deflection in inches at any panel-point or joint
of the truss;
” _P_ = any arbitrary load or weight supposed to be hung at
the point where the deflection is desired and
acting as if gradually applied. This may be taken
as unity;
” _Z_ = stress produced in any member of truss by _P_;
” _S_ = stress produced in any member of truss by the combined
dead and moving loads;
Let _l_ = length in inches of any member of the truss in which
_Z_ or _S_ is found;
” _A_ = area of cross-section of same member in square inches;
” _E_ = coefficient of elasticity.
_S_ or _Z_ may be either tension or compression, and the formulæ will
be so expressed that tension will be made positive and compression
negative.
The change of length of the chord member _BC_ produced by a stress
gradually increasing from zero to _S_ is
_S_
----_l_.
_AE_
If it be supposed that _BC_ is a spring of such stiffness that it will
be compressed by the gradual application of _Z_ exactly as much as
the shortening of the actual member by the stress _S_, the deflection
of the point 4 with the weight _P_ hung from it, and due to that
compression alone, will be precisely the same as that due to the actual
shortening of _BC_ by the combined dead and moving loads.
It is known by one of the elementary principles of mechanics that,
since _P_ acts along the direction of the vertical deflection _w_, the
work performed by the weight _P_ over that deflection is equal to the
work performed by _Z_ over the change of length _l_. Hence
_l l Sl_
--- _Pw_ = --- _Z_ ----, or
2 2 _AE_
_Z Sl_
_w_ = --- ----. (42)
_P AE_
The quantity _Z÷P_ is the stress produced in the member by a unit load
applied at the joint or point where the deflection is desired. Again,
_S÷A_ is the stress per unit of area, i.e., intensity of stress, in the
member considered by the actual dead and moving loads. For brevity let
these be written
_Z S_
--- = _z_ and --- = _s_;
_P A_
then
_zsl_
_w_ = ------. (43)
_E_
If the influence of every member of the truss is similarly expressed,
the value of the total deflection produced by the dead and moving loads
will be
_zsl_
_w_ = ∑ ------. (44)
_E_
The sign of summation ∑ indicates that the summation is to extend over
all the web and chord members of the truss.
=111. Application of Method for Deflection to Triangular Frame.=—Before
applying those equations to the case of Fig. 29 it is best to consider
a simpler case, i.e., that of the triangular frame shown in Fig. 18.
The reactions are
_l₂ l₁_
_R_ = --- _W_ and _Rʹ_ = --- _W_. (45)
_l l_
The stresses in the various members are:
_l₁_
In _CB_, _S_ = ---- _W_ sec α.
_l_
_l₂_
” _CA_, _S_ = ---- _W_ sec β.
_l_
_l₂ l₁_
” _AB_, _S_ = --- _W_ tan β = --- _W_ tan α.
_l l_
Also: _CB = h_ sec α; area of section = _A₁_.
_CA = h_ sec β; ” ” ” = _A₂_.
_AB = l_; ” ” ” = _A₃_.
In this instance it is simplest to take _P = W_. Equation (44) then
gives
( _l₁² h_ sec³ α _l₂² h_ sec³ _β_
_w_ = (----- ---------- + ----- -------------
( _l² A₁ l² A₂_
_l₂² l_ tan² _β_ ) _W_
+ ---- ------------) ------. (46)
_l² A₃_ ) _E_
Let it be supposed that
_l_ = 25 feet = 300 inches;
_h_ = 8 feet 4 inches = 100 inches;
_l₂_ = 16 feet 8 inches = 200 inches and _l₁_ = 100 inches;
tan β = 1; sec β = 1.414;
sec α = 2.24;
_W_ = 10,000 pounds.
If the bars are all supposed to be of yellow-pine timber, there may be
taken
_E_ = 1,000,000 pounds;
_A₁_ = 10″ × 12″ = 120 square inches;
_A₂_ = 10″ × 10″ = 100 square inches;
_A₃_ = 10″ × 12″ = 120 square inches.
The insertion of these quantities in equation (46) gives the deflection
_w_ = .01042 + .01253 + .01111 = 0.034. (47)
Equation (47) is so written as to show the portion of the deflection
due to each member of the frame.
In applying either equation (43) or equation (44) care must be taken
to give each stress and its corresponding strain (lengthening or
shortening) the proper sign. As the formulæ have been written and
used, a tensile stress and its resulting stretch must each be written
positive, while a compressive stress must be written negative. This
holds true for both the stresses _Z_ and _S_ (or _z_ and _s_). The
magnitude of the assumed load _P_ is a matter of indifference, since
the stress _Z_ will always be proportional to it and the ratio _P ÷ Z_
will therefore be constant. _P_ is frequently taken as unity; or, as in
the case just given, it may have any value that the conditions of the
problem make most convenient.
=112. Application of Method for Deflection to Truss.=—In making
application of the deflection formulæ to any steel railroad truss
similar to that shown in Fig. 29, it will first be necessary to
determine the stresses in all its members due to the dead and moving
loads, since the deflection under the moving load is sought. These
loads will be considered uniform, and that is sufficiently accurate for
any railroad bridge. The moving train-load will be taken as covering
the entire span, assumed, for a single-track railroad, 240 feet in
length between centres of end pins. There are eight panels of 30
feet each, and the depth of truss at centre is 40 feet. Other truss
dimensions are as shown in Fig. 29. The dead loads, or own weight, are
taken at 400 pounds per linear foot of span for the rails and other
pieces that constitute the track; at 400 pounds per linear foot for
the steel floor-beams and stringers, and 1600 pounds per linear foot
for the weight of trusses and bracing. The moving train-load will be
taken at 4000 pounds per linear foot. This will make the panel-loads
for each truss as follows:
Lower-chord dead load, 30 × 800 = 24,000 pounds per panel.
Lower-chord moving load, 30 × 2000 = 60,000 ” ” ”
------
Total load on lower chord = 84,000 ” ” ”
Upper-chord dead load, 30 × 400 = 12,000 ” ” ”
The structure is a “through” bridge, hence all moving loads rest on the
lower chord.
[Illustration: FIG. 30.]
The stresses in the truss members due to the combined uniform dead and
moving load are best found by the graphical method. One diagram only is
needed to determine all the stresses, and it is shown in Fig. 30. This
diagram is drawn accurately to scale, and the stresses measured from it
are shown in the table on page 136.
The stresses in all the truss members due to the unit load hung at
_J_ are readily found by the single diagram shown in Fig. 31, also
carefully drawn to scale. These stresses measured from the diagram
are given in the table as indicated by the column _z_; they are also
represented in equation (44) by the letter _z_. The quantity _s_ in
equation (44) is the intensity of the stress (pounds per square inch of
cross-section of member) produced by the combined dead and moving loads
in each member. As shown, these stresses are least in the web members
near the centre of the span, and greatest in the chord members. The
lengths in inches of the truss members are shown in the proper column
of the table. It will be observed that all counter web members are
omitted, as they are not needed for the uniform load. The coefficient
of elasticity (_E_) is taken at 28,000,000 pounds. The quantities
represented by the second member of equation (44) are computed from
these data, and they appear in the last column of the table, the sum
of which gives the desired deflection in inches. The elements of the
table show how much of the deflection is due to the chords and to the
web members, and they show that disregarding the latter would lead to a
considerable error.
+-------+----------+---------+--------+-----+---------+
| | _S_ | _s_ | _z_ | _l_ | _w_ |
+-------+----------+---------+--------+-----+---------+
| _L₁_ | +373,300 | +12,000 | +.555 | 360 | +.08563 |
| _L₂_ | +373,300 | +12,000 | +.555 | 360 | +.08563 |
| _L₃_ | +480,000 | +12,000 | +.833 | 360 | +.1284 |
| _L₄_ | +540,000 | +12,000 | +1.125 | 360 | +.1736 |
| _P₁_ | -502,300 | -9,000 | -.748 | 472 | +.1132 |
| _U₁_ | -501,000 | -9,500 | -.870 | 376 | +.1108 |
| _U₂_ | -544,800 | -10,000 | -1.135 | 363 | +.1472 |
| _U₃_ | -576,000 | -10,000 | -1.50 | 360 | +.1928 |
| _T₁_ | +84,000 | +9,000 | 0 | 324 | -- |
| _T₂_ | +143,500 | +10,000 | +.3738| 472 | +.0629 |
| _P₂_ | -12,000 | -1,000 | -.250 | 432 | +.00386 |
| _T₃_ | +93,720 | +7,400 | +.456 | 562 | +.0677 |
| _P₃_ | +12,000 | +1,000 | -.35 | 480 | -.0060 |
| _T₄_ | +60,000 | +4,800 | +.625 | 600 | +.0643 |
| _P₄_ | -12,000 | -1,000 | 0 | 480 | -- |
+-------+----------+---------+--------+-----+---------+
Deflection for ½ truss members = 1.2300 inches.
Deflection at _J_ = 2 × 1.2300 = 2.4600 inches.
[Illustration: FIG. 31.]
As the deflection is usually desired in inches, the lengths of members
must be taken in the same unit.
=113. Method of Least Work.=—The so-called theorem or principle of
“Least Work” is closely related to the subject of elastic deflections
just considered in its availability for furnishing equations of
condition in addition to those of a purely statical character in cases
where indetermination would result without them. This principle of
least work is expressed in the simple statement that when any structure
supports external loading the work performed in producing elastic
deformation of all the members will be the least possible. Although
this principle may not be susceptible of a complete and general
demonstration, it may be shown to hold true in many cases if not all.
The hypothesis is most reasonable and furnishes elegant solutions in
many useful problems.
The application of this principle requires the determination of
expressions for the work performed in the elastic lengthening and
shortening of pieces subjected either to tension or compression, and
for the work performed in the elastic bending of beams carrying loads
at right angles to their axes. Both of these expressions can be very
simply found.
Let it be supposed that a piece of material whose length is _L_ and the
area of whose cross-section is _A_ is either stretched or compressed by
the weight or load _S_ applied so as to increase gradually from zero to
its full value. The elastic change of length will be _SL/AE_, _E_ being
the coefficient of elasticity. The average force acting will be ½_S_,
hence the work performed in producing the strain will be
1 _S²L_
--- -----. (48)
2 _AE_
It will generally be best, although not necessary, to take _L_ in
inches. The expression (48) applies either to tension or compression
precisely as it stands.
To obtain the expression for the work performed by the stresses in a
beam bent by loads acting at right angles to its axis, a differential
length (_dL_) of the beam is considered at any normal section in
which the bending moment is _M_, the total length being _L_. Let _I_
be the moment of inertia of the normal section, _A_, about an axis
passing through the centre of gravity of the latter, and let _k_ be the
intensity of stress (usually the stress per square inch) at any point
distant _d_ from the axis about which _I_ is taken. The elastic change
produced in the indefinitely short length _dL_ when the intensity _k_
exists is (_k/E_)_dL_. If _dA_ is an indefinitely small portion of
the normal section, the average force or stress, either of tension or
compression, acting through the small elastic change of length just
given, can be written by the aid of equation (5) as
_Md_
½_k.dA_ = ----- ._dA._ (49)
2_I_
Hence the work performed in any normal section of the member, for which
_M_ remains unchanged, will be, since ∫_k.dA.d_ = _M_,
⌠ _M M²_
⌡ ------ _kd.dA.dL_ = ----- _dL._ (50)
2_IE_ 2_IE_
The work performed throughout the entire piece will then be
⌠ _M²_
⌡ ------ _dL._ (51)
2_IE_
Each of the expressions (48) and (51) belongs to a single piece or
member of the structure. The total work performed in all the pieces
subjected either to direct stress or to bending, and which, according
to the principle of least work, must be a minimum, is found by taking
the summation of the two preceding expressions:
1 ⎲ _S²L_ 1 ⎲ ⌠ _M²_
_e_ = ----⎳ ------ + ----- ⎳ ⌡ ----- _dL_ = minimum. (52)
2_E_ _A_ 2_E_ _I_
In making an application of equation (52) it is to be remembered that
_S_ is the direct stress of tension or compression in any member, and
that _M_ is the general value of the bending moment in any bent member
expressed in terms of the length _L_.
=114. Application of Method of Least Work to General Problem.=—The
problem which generally presents itself in the use of equation (52)
is the finding of an equation which expresses the condition that the
work expended in producing elastic deformation shall be a minimum, some
particular stress in the structure or some external load or force being
the variable. If _t_ represent that variable, then the desired equation
of condition will be found simply by placing the first differential
coefficient of _e_ in equation (52) equal to zero:
_de_ 1 (⎲ _S dS_ ⎲ ⌠ _M dM_ )
----- = ----(⎳ --- --- _dL_ + ⎳ ⌡ ---- --- _dL_) = 0. (53)
_dt_ _E_( _A dt_ _I dt_ )
The solution of equation (53) will give a value of _t_ which will make
the work performed as expressed in equation (52) a minimum. This method
is not a difficult one to employ in such cases as those of drawbridges
and stiffened suspension bridges. In the latter case particularly it is
of great practical value.
=115. Application of Method of Least Work to Trussed Beam.=—The method
of least work may be illustrated by the application of the preceding
equations to the simple truss shown in Fig. 32. The pieces _BC_ and
_GD_ are supposed to be of yellow-pine timber, the former 10 inches by
14 inches (vertical) in section and the latter 8 inches by 10 inches,
while each of the pieces _BD_ and _DC_ are two 1⅝-inch round steel
bars. The coefficient of elasticity _E_ will be taken at 1,000,000
pounds for the timber and 28,000,000 for the steel. The length of _BC_
is 360 inches; _GD_ 96 inches; _BD_ = 96 × 2.13 = 204.5 inches.
tan α = 1.875 and sec α = 2.13.
The weight _W_ resting at _G_ is 20,000 pounds. A part of this weight
is carried by _BC_ as a simple timber beam, while the remainder of the
load will be carried on the triangular frame _BCD_ acting as a truss,
the elastic deflection of the latter throwing a part of the load on
_BC_ acting as a beam. According to the principle of least work the
division of the load will be such as to make the work performed in
straining the different members of the system a minimum.
That part of _W_ which rests on _BC_ as a simple beam may be
represented by _W₁_, while _W₂_ represents the remaining portion
carried by the triangular frame. As _G_ is at the centre of the span,
the beam reaction at either _B_ or _C_ is ½_W₁_. Hence the general
value of the bending moment in either half of the beam at any distance
_x_ from either _B_ or _C_ is
_M_ = ½_W₁x._ Hence _M²dL_ = ¼_W₁²x²dx_.
As there is but one member acting as a beam, whose moment of inertia
_I_ is constant, the second term of the second member of equation (52)
becomes, by the aid of the preceding equation,
1 1 ¹/₂ 1 _W₁²l³_
----- ⌠ _M²dL_ = ---- ⌠ _¼W₁²x²dx_ = ---- --------. (54)
2_EI_ ⌡ _EI_ ⌡₀ _EI_ 96
[Illustration: FIG. 32.]
The numerical elements of the expression for the work done in the
members of the triangular frame are:
Member. Stress. Length. Area of Section.
_BC_ ½_W₂_ tan _α_ 360 inches = _l_ 140 square inches
_DC_ ½_W₂_ sec _α_ 204.5 ” 4.14 ” ”
_DG_ _W₂_ 96 ” 80 ” ”
10 × 14³ 27440
_I_ = -------- = ------- = 2286.7.
12 12
The substitution of those quantities in the first term of the second
member of equation (52) will give
1 ⎲ _S²L_ 1 ( _W₂²_ tan² _α_.360 _W₂²_.96 )
-----⎳ ----- = ---------- (------------------ + ----------)
2_E A_ 2,000,000 ( 4 × 140 80 )
2 _W₂²_ sec² _α_ .204.5
+ ----------- --------------------- = .000,003,73 _W₂²_.
56,000,000 4 × 4.14
The substitution of numerical quantities in equation (54) gives
1 _W₁²l³_
---- -------- = .000,213_W₁²_.
_EI_ 96
Or, since _W - W₂ = W₁_,
_e_ = .000,003,73_W₂²_ + .000,213(_W - W₂)²_. (55)
Hence
_de_
---- = .000,007,46_W₂_ - .000,426(_W - W₂_) = 0. (56)
_dW₂_
The solution of this equation gives
_W₂_ = .893_W_ = 19,660 pounds.
_W₁_ = 340 ”
It is interesting to observe that the first term of the second member
of equation (56) is the deflection of the point of application of _W₂_
as a point in the frame, while the second term is the deflection of
the point of application of _W₁_ considered as a point of the beam.
In other words, the condition resulting from the application of the
principle of least work is equivalent to making the elastic deflections
by _W₁_ and _W₂_ equal. Indeed equation (53) expresses the equivalence
of deflections whenever the features of the problem are such as to
involve concurrent deflections of two different parts of the structure.
=116. Removal of Indetermination by Methods of Least Work and
Deflection.=—The indetermination existing in connection with the
computations for such trusses as those shown in Fig. 22 and Fig.
23 can be removed by finding equations of condition by the aid of
the method of least work or of deflections. It is evident that the
component systems of bracing of which such trusses are composed must
all deflect equally. Hence expressions may be found for the deflections
of those component trusses, each under its own load. Since these
deflections must be equal, equations of condition at once result. A
sufficient number of such equations, taken with those required by
statical equilibrium, can be found to solve completely the problem.
Such methods, however, are laborious, and the ordinary assumption of
each system carrying wholly the loads resting at its panel-points is
sufficiently near for all ordinary purposes.
The method of least work can be very conveniently used for the solution
of a great number of simple problems, like that which requires the
determination of the four reactions under the four legs of a table,
carrying a single weight or a number of weights, and many others of the
same character.
CHAPTER X.
=117. The Arched Rib, of both Steel and Masonry.=—During the past ten
or fifteen years the type of bridge structure called the arched rib has
come into much use, and its merits insure for it a wider application in
the future. It partakes somewhat of the nature of both truss and arch;
or it may be considered a curved beam or girder. The ordinary beam
or truss when placed in a horizontal position and loaded vertically
yields only vertical reactions. Under the same conditions, however, the
arched rib will produce both vertical and horizontal reactions, and the
latter must either be resisted by abutments of sufficient mass, or by a
tie-rod, usually horizontal, connecting the springing points of the rib.
The arched rib may be built solid, as was done in the early days of
bridge-building in this country when engineers like Palmer, Burr, and
Wernwag introduced timber arches in combination with their wooden
trusses, or as a curved plate girder, one of the most prominent
examples of which is the Washington Bridge across the Harlem River
in the city of New York; or, again, as a braced frame or curved
truss, like the 800 feet arched rib carrying the roadway traffic and
trolley cars across the Niagara gorge, or like those used in such
great railroad train-sheds as the Grand Central Station, New York,
the Pennsylvania stations at Jersey City and Philadelphia, and the
Philadelphia and Reading station in Philadelphia. Those are all
admirable examples of steel arched ribs, and they are built to sustain
not only vertical loads but, in the case of station roofs, the normal
or horizontal wind pressures.
Within a few years, less than ten, another type of arched rib has
been brought into use and promises to be one of the most beautiful as
well as the most substantial applications of this type of structure;
that is, the arched rib of combined steel and concrete. Many examples
of this type of structure already exist both in this country and in
Europe, probably the most prominent of which in this country is that at
Topeka, Kansas, across the Kansas River.
[Illustration: =FIG. 33.=]
[Illustration: =FIG. 34.=]
[Illustration: =FIG. 35.=]
The characteristic feature of this type of structure, so far as the
stresses developed in it are concerned, is the thrust throughout its
length, more or less nearly parallel to its axis, which is combined
with the bending moments and shears similar to those found in
ordinary bridge-trusses. This thrust is the arch characteristic and
differentiates it in a measure from the ordinary bridge-truss, while
the bending moments and shears to which it is subjected differentiate
it, on the other hand, from the pure arch type or a series of blocks
in which thrust only exists. The thrust, bending moments, and shears
in arched ribs are all affected by certain principal features of
design. Those features are either fixedness of the ends of the ribs
or the presence of pin-joints at those ends or at the crown. Fig. 33
represents an arched rib with its ends _D_ and _F_ supposed to be
rigidly fixed in masonry or by other effective means.
=118. Arched Rib with Ends Fixed.=—The railroad steel arched bridge at
St. Louis, built by Captain Eads between 1868 and 1874, is a structure
of this character. The three spans (two each 537 feet 3 inches and one
552 feet 6 inches in length from centre to centre of piers) consist of
ribs the main members of which are composed of chrome steel. It was a
structure of unprecedented span when it was built, and constituted one
of the boldest pieces of engineering in its day. The chords of the ribs
are tubes made of steel staves, and their ends are rigidly anchored
to the masonry piers on which they rest. It is exceedingly difficult,
indeed impossible, to fix rigidly the ends of such a structure,
and observations in this particular instance have shown that the
extremities of the ribs are not truly fixed, for the piers themselves
yield a little, giving elastic motion under some conditions of loading.
=119. Arched Rib with Ends Jointed.=—The rib shown in Fig. 34 is
different from the preceding in that pin-joints are supplied at each
end, so that the rib may experience elastic distortion or strain by
small rotations about the pins at _A_ and _B_. In the computations for
such a design it is assumed that the ends of the rib may freely change
their inclination at those points. As a matter of fact the friction
is so great, even if no corrosion exists, as to prevent motion, but
the presence of the pins makes no bending moment possible at the end
joints, and the failure to move freely probably produces no serious
effect upon the stresses in the ribs. The presence of these pin-joints
simplifies the computations of stresses and renders them better
defined, so that there is less doubt as to the actual condition of
stress under a given load than in the type shown in Fig. 33 with ends
fixed more or less stiffly. In Fig. 34, if the horizontal force _H_
exerted by the ends of the rib against the points of support is known,
the remaining stresses in the structure can readily be computed; but
neither in Fig. 34 nor in Fig. 33 are statical equations sufficient for
the determination of stresses. Equations of condition, depending upon
the elastic properties of the material, are required before solutions
of the problems arising can be made.
=120. Arched Rib with Crown and Ends Jointed.=—The rib shown in Fig.
35 possesses one characteristic radically different from any found in
the ribs of Figs. 33 and 34, in that it is three-jointed, one pin-joint
being at the crown and one at each end. So far as the conditions of
stress are concerned, this is the simplest rib of all. Since there is a
pin-joint at the crown as well as at the ends, the bending moments must
be zero at each of those three points whatever may be the condition of
loading. The point of application of the force or thrust at the crown,
therefore, is always known, as well as the points of application at the
ends of the joints. As will presently be seen, this condition makes
equations of statical equilibrium sufficient for the determination of
all stresses in the rib, and no equations depending upon the elastic
properties of the material are required. The stresses in this class of
ribs, therefore, are more easily determined than in the other two, and
they are better defined. These qualities have insured for it a somewhat
more popular position than either of the other two classes. The ribs
of the great train-sheds of the Pennsylvania and Reading railroads in
Jersey City and in Philadelphia belong to this class, while those of
the Grand Central Station at New York City belong to the class shown
in Fig. 34, as does the arched rib across the Niagara gorge, to which
reference has already been made.
=121. Relative Stiffness of Arch Ribs.=—Obviously the three-hinged
ribs are less stiff than the two-hinged ribs or those with fixed
ends. This is a matter of less consequence for station roofs than for
structures carrying railroad loads. The joints of the two-hinged rib
being at the ends of the structure, there is but little difference in
stiffness between that class of ribs and those with ends fixed. Indeed
the difference is so slight, and the uncertainty as to the degree of
fixedness of the fixed ends of the rib is so great, that the latter
type of rib possesses no real advantage over that with hinged ends.
=122. General Conditions of Analysis of Arched Ribs.=—In each of the
three types of arched ribs shown in Figs. 33, 34, and 35 it is supposed
that all external forces act in the vertical planes which contain the
centre lines of the various members of the rib. There are, therefore,
the three conditions of statical equilibrium expressed by the three
equations (35), (36), and (37). In practically all cases, except those
of arched ribs employed in roof construction, all the external loads
are vertical. In such cases the equations of statical equilibrium of
the entire structure may be reduced to two only, viz., equations (36)
and (37). These features of the problems connected with the design
of arched ribs will always make necessary, except in the case of the
three-hinged rib (Fig. 35), equations of condition depending upon the
elastic properties of the structure.
The rib represented by Fig. 33 is supposed to have its ends so fixed
that the inclinations of the centre line at _F_ and _D_ will never
change whatever may be the loading or the variation of temperature.
This requires the application at each of those points of a couple whose
moment varies in value, but which is always equal and opposite to the
bending moment at the same point produced by the loads imposed on the
rib. It is also to be observed that the loads resting upon the rib are
not divided between the points of support _F_ and _D_ in accordance
with the law of the lever, since the conditions of fixedness at the
ends are equivalent to continuity. There are then to be found, as
acting external to the rib, the two vertical reactions and the two
moments at _F_ and _D_, as well as the horizontal thrust exerted at
the ends of the structure, which is sometimes resisted by the tie-rod,
making five unknown quantities. Inasmuch as all external loading is
supposed to be vertical, equations (36) and (37) are the only statical
equations available, and three others, depending upon the elastic
properties of the structure, must be supplied in order to obtain the
total of five equations of condition to determine the five unknown
quantities. Inasmuch as the end inclinations remain unchanged, the
total extension or compression of the material at any given constant
distance from the axis of the rib taken between the two end sections
_F_ and _D_ must be equal to zero. Similarly, whatever may be the
amount or condition of loading, the vertical and horizontal deflections
of either of the ends _F_ or _D_ in relation to the other must be zero,
since no relative motion between these two points can take place. It
is not necessary in these lectures to give the demonstration of the
equations which express the three preceding elastic conditions, but if
_M_ is the general value of the bending moment for any point of the
rib, and if _x_ and _y_ are the horizontal and vertical coordinates of
the centre line of the rib, taking the central point of the section at
either _F_ or _D_ as an origin, those equations, taken in the order in
which the elastic conditions have been named, will be the following,
in which _n_ represents a short length of rib within which the bending
moment _M_ is supposed to remain unchanged.
F F F
⎲ ⎲ ⎲
⎳ _nM_ = 0; ⎳ _nMx_ = 0; ⎳ _nMy_ = 0. (57)
D D D
The second and third of these equations express the condition that
the vertical and horizontal deflections respectively of the two ends
in reference to each other shall be zero. The conditions expressed by
equation (57) are constantly used in engineering practice to determine
the bending moments and stresses which exist in the arched rib with
fixed ends. The graphical method is ordinarily used for that purpose,
as its employment is a comparatively simple procedure for a rib whose
curvature is any whatever.
If the rib has hinged joints at the ends, as in Fig. 34, obviously
there can be no bending moment at either of those two points, and hence
the two equations of condition which were required in connection with
Fig. 33 to determine them will not be needed. There is, therefore,
no restriction as to the angle of inclination of the centre line of
the rib at those two points. Again, it is obvious that either end _A_
or _B_ may have vertical movement, i.e., deflection in reference to
the other, without affecting the condition of stress in any member of
the rib; but it is equally obvious that neither _A_ nor _B_ can be
moved horizontally, i.e., deflected in reference to the other, without
producing bending in the rib and developing stresses in the various
members. The unknown quantities in this case are, therefore, only the
horizontal thrust _H_ exerted at the two springing points _A_ and
_B_, and the two vertical reactions, making a total of three unknown
quantities, equations for two of which will be given by equations
(36) and (37). The other equation required is the third expression in
equation (57), expressing the condition that the horizontal deflection
of either of the points _A_ or _B_ in respect to the other is zero,
since the span _AB_ is supposed to remain unchanged. By the application
of the graphical method to this case, as to the preceding, the
employment of equations (36), (37), and (58) will afford an easy and
quick determination of the three unknown quantities, whatever may be
the curvature of the rib.
A
⎲
⎳ _nMy_ = 0. (58)
B
If the reactions and horizontal thrust _H_ are found, stresses in every
member may readily be computed and the complete design made.
If the arch is three-hinged, as in Fig. 35, the condition that the
bending moment must be zero at the crown _C_ under all conditions of
loading gives a third statical equation independent of the elastic
properties of the structure which, in connection with equations (36)
and (37), give three equations of condition sufficient to determine the
two vertical reactions and the horizontal thrust _H_. In this case, as
has already been stated, no elastic equations of condition are required.
The determination of the end reactions, bending moments, and horizontal
thrust _H_, in these various cases, is all that is necessary in order
to compute with ease and immediately the stresses in every member of
the rib. These computations are obviously the final numerical work
required for the complete design of the structure. These procedures are
always followed, and in precisely the manner indicated, in the design
of arched ribs by civil engineers, whether the rib be articulated,
i.e., with open bracing, or with a solid plate web, like those of the
Washington Bridge across the Harlem River.
CHAPTER XI.
=123. Beams of Combined Steel and Concrete.=[2]—A reference has already
been made to a class of beams and arches recently come into use and now
quite widely employed, composed of steel and concrete, the former being
completely surrounded by and imbedded in the latter. These composite
beams are very extensively used in the floors of fire-proof buildings
as well as for other purposes. Arches of combined concrete and steel
were probably first built in Germany and but a comparatively few years
ago. During the past ten years they have been largely introduced into
this country, and many such structures have not only been designed but
built. The most prominent design of arches of combined concrete and
steel are those of the proposed memorial bridge across the Potomac
River at Washington, for which a first prize was awarded as the result
of a national competition in the early part of 1900. So far as the
bending or flexure of these composite beams and arches is concerned,
the theory is identically the same for both, the formulæ for each of
which are given below. In order to express these formulæ the following
notation will be needed:
[2] For a complete and detailed statement of this whole subject,
including design work, reference should be made to the author’s
“Elasticity and Resistance of Materials.”
[Illustration: MEMORIAL BRIDGE ACROSS THE POTOMAC
AT WASHINGTON D.C.
WM. H. BURR, Civil Engineer.
E. P. CASEY, Associated Architect.
PLAN NO. 2.
Plan Awarded First Prize in National Competition.
River spans 192 feet clear. Total length of structure 3615 feet.]
[Illustration:
WM. H. BURR, Civil Engineer.
E. P. CASEY, Associated Architect.
PLAN NO. 1.
The Towers of this Plan were Recommended by Board of Award to be
Substituted for Those in Plan No. 2.
River spans 283 feet clear. Total length of structure 3437 feet.]
_P_ is the thrust along the arch determined by the methods explained in
the consideration of arched ribs.
_l_ is the distance of the line of the thrust _P_ from the axis of the
arched rib.
_E₁_ and _E₂_ are coefficients of elasticity for the two materials.
_A₁_ and _A₂_ are areas of normal section of the two materials.
_I₁_ and _I₂_ are moments of inertia of _A₁_ and _A₂_ about the neutral
axes of the composite beam or arch sections.
_k₁_ and _k₂_ are intensities of bending stress in the extreme fibres
of the two materials.
_h₁_ and _h₂_ are total depths of the two materials.
_d₁_ and _d₂_ are distances from the neutral axes to farthest fibres of
the two materials; distances to other extreme fibres would be (_h₁-d₁_)
and (_h₂-d₂_).
_W₁_ and _W₂_ are loads, either distributed or concentrated, carried by
the two portions.
_W = W₁ + W₂_ is total load on the beam or arch.
_q₁ = W₁/W_ and _q₂ = W₂/W_; ∴ _q₁ + q₂_ = 1; _e = E₂/E₁_.
The application of the theory of flexure to the case of a beam or arch
of two different materials, steel and concrete in this case, will give
the following results:
_M = Pl_; hence _M₁ = q₁Pl_ and _M₂ = q₂Pl_. (59)
_W₁ E₁I₁_
_q₁_ = --- = ----------- (60)
_W E₁I₁ + E₂I₂_
_W₂ E₂I₂_
_q₂_ = --- = ------------ (61)
_W E₁I₁ + E₂I₂_
_p Md_
_k₁_ = ---------- + --------- (62)
_A₁ + eA₂ I₁ + eI₂_
( _P Md_ )
_k₂_ = _e_(---------- + ------------) (63)
( _A₁ + eA₂ I₁ + eI₂_ )
These formulæ exhibit some of the main features of the analysis which
must be used in designing either beams or arches of combined steel and
concrete. In the use of these equations care must be taken to give the
proper sign to the bending moment _M_. They obviously apply to the
combination of any two materials, although at the present time the only
two used in such composite structures are steel and concrete. If the
subscript 1 belongs to the concrete portion, and the subscript 2 to the
steel portion, there may be taken _E₁_ = 1,500,000 to 3,000,000 and
_E₂_ = 30,000,000. Hence _e_ = 20 to 10.
The purpose of introducing the steel into the concrete is to make
available in the composite structure the high tensile resistance
of that metal. A very small steel cross-section is sufficient to
satisfactorily accomplish that purpose. The percentage of the total
composite section represented by the steel will vary somewhat with the
dimensions of the structure and the mode of using the material; it will
usually range from 0.75 per cent to 1.5 per cent of the total section.
The large mass of concrete in which the steel should be completely
imbedded serves not only to afford a large portion of the compressive
resistance required in both arches and beams, but also to preserve the
steel effectively from corrosion. Many experiments have shown that it
requires but a small per cent of steel section to give great tensile
resistance to the composite mass.
CHAPTER XII.
=124. The Masonry Arch.=—The masonry arch is so old that its origin
is lost in antiquity, but its complete theory has been developed with
that of other bridge structures only within the latest period. It is
only possible here to give some of the main features of that theory and
a few of the fundamental ideas on which it is based. It is customary
among engineers to regard the masonry arch as an assemblage of blocks
finely cut to accurate dimensions, so that the assumption of either a
uniform or uniformly varying pressure in the surface of contact between
any two may be at least sufficiently near the truth for all practical
purposes. Although care is taken to make joints between ring-stones
or voussoirs completely cemented or filled with a rich cement mortar,
it is usually the implicit assumption that such joints do not resist
tension. As a matter of fact many arch joints are capable of resisting
considerable tension, but, in consequence of settlement or shrinkage,
cracks in them that may be almost or quite imperceptible frequently
prevent complete continuity. It is, therefore, considered judicious to
determine the stability of the ordinary masonry arch on the assumption
that the joints do not resist tension.
In these observations it is not intended to convey the impression that
no analysts treat the ordinary arch as a continuous elastic masonry
mass, like the composite arches of steel and concrete. Although much
may be said in favor of such treatment for all arches, it is believed
that prolonged experience with arch structures makes it advisable to
neglect any small capacity of resistance to tension which an ordinary
cut-stone masonry joint may possess, in the interests of reasonable
security.
The ring-stones or voussoirs of an arch are usually cut to form
circular or elliptic curves, or to lines which do not differ sensibly
from those curves. The arch-ring may make a complete semicircle, as
in the old Roman arches, or a segment of a semicircle; or the stones
may be arranged to make a pointed arch, like the Gothic; or, again,
a complete semiellipse may be formed, or possibly a segment of that
curve. When a complete semiellipse or complete semicircle is formed,
the arches are said to be full-centred, and in those cases they spring
from a horizontal joint at each end. On the other hand, segmental
arches spring from inclined joints at each end called skew-backs.
=125. Old and New Theories of the Arch.=—In the older theories of the
arch, considered as a series of blocks simply abutting against each
other, the resultant loading on each block was assumed to be vertical.
In the modern theories, on the other hand, the resultant loading on any
block is taken precisely as it is, either vertical or inclined, as the
case may be. Many arches are loaded with earth over their arch-rings.
This earth loading produces a horizontal pressure against each of the
stones, as well as a vertical loading due to its own weight. In such
cases it is necessary to recognize this horizontal or lateral pressure
of the earth, as it is called, as a part of the arch loading.
It is known from the theory of earth pressure that the amount of that
pressure per square foot or any other square unit may vary between
rather wide limits, the upper of which is called the abutting power
of earth, and the latter the conjugate pressure due to its own weight
only. If _w_ is the weight per cubic unit of earth and _x_ the depth
considered, and if φ be the angle of repose of the earth, the abutting
power per square unit will have the value:
1 + sin φ
_p_ = _wx_ ---------. (64)
1 - sin φ
while the horizontal or conjugate pressure due to the weight of earth
only will be:
1 - sin φ
_pʹ_ = _wx_ ---------. (65)
1 + sin φ
The use of these formulæ will be illustrated by actual arch
computations.
[Illustration: FIG. 36.]
[Illustration: FIG. 37.]
Fig. 36 is supposed to show a set of ring-stones for an arch of any
curvature whatever. The joints _LM_ and _ON_ represent the skew-backs
or springing joints, while _R_ and _R₁_ represent the supporting
forces or reactions with centres of action at _aʹ_ and _a₁_. The ring
is divided into blocks or pieces by the joints at _a_, _b_, _c_, _d_,
and _e_, the resultant loading or force on each block being given by
the lines with arrow-heads and numbered 1, 2, 3, 4, 5, 6, and 7. Fig.
37 represents a force polygon constructed in the ordinary manner by
laying off carefully to scale the two reactions _R_ and _R₁_, together
with the loads or forces numbered 1 to 7, inclusive. By constructing
the so-called polygonal frame in the ring-stones of Fig. 36 in the
usual manner with its lines or sides parallel to the radiating lines in
Fig. 37, as shown by the broken lines, the points _a_, _b_, _c_, etc.,
are found where the resultant forces cut each joint. The line drawn
through those points thus determined is called the line of resistance
of the arch. Obviously, if that line of resistance be determined, the
complete stability or instability of the arch, as the case may be, will
be established. Furthermore, the complete determination of the force
polygon in Fig. 37, and the corresponding polygonal frame drawn in the
arch-ring, constitute all the computations involved in the design of an
arch.
The thrust _T₀_ at the crown, shown both in Fig. 36 and Fig. 37, is
frequently horizontal, although not necessarily so; its value is shown
by Fig. 37. In the older arch theories a principle was enunciated
called the “principle of least resistance.” The thrust _T₀_ is a
fundamental and so-called passive force. That is, its magnitude depends
not only upon its position, but also largely upon the magnitude of
the active forces which represent the loading on the arch-ring. Under
the principle of least resistance it was laid down as a fundamental
proposition, in making arch computations, that this passive force
_T₀_ must be the least possible consistent with the stability of the
structure. While this provisional proposition answered its purpose
well enough, there are other clearer methods of procedure which are
thoroughly rational and involve the employment of no extraneous
considerations other than those attached to the determination of
statical equilibrium.
A scrutiny of the conditions existing in Fig. 36 will show that if the
external forces or loadings on the individual blocks of the ring are
given, four quantities are to be determined, viz., the two reactions
_R_ and _R₁_ and their lines of action. Inasmuch as no elastic
features of the structure are to be considered, there are available
for the determination of these four quantities the three equations of
equilibrium, equations (35), (36), and (37), which are not sufficient
for the purpose. If one line of action, such as that of _R_, be located
by assuming its point of application _aʹ_, the three equations just
named will be sufficient for the determination of the remaining three
equations; and that is precisely the method employed. It is tentative,
but perfectly practicable. If, instead of assuming one of the points
of application of the reactions, we assume both of those points and
construct a trial polygonal frame, it will be necessary to use but two
of the three equations of statical equilibrium. For that purpose there
are employed equations (35) and (36), but in a graphical manner, which
will presently be illustrated.
=126. Stress Conditions in the Arch-ring.=—Before proceeding to the
construction of an actual line of resistance, a little consideration
must be given to the stress conditions in the arch-ring. As the joints
are considered capable of resisting no tension, the dimensions of the
arch-ring must be finally so proportioned that pressure only will exist
in each and every joint. If each centre of pressure, as _a_, _b_, etc.,
in Fig. 36, is found in the middle third of the joint, it is known from
a very simple demonstration in mechanics that no tension will ever
exist in that joint, although the pressure may be zero at one extremity
and a maximum at the other. This is the condition usually imposed in
designing an arch-ring to carry given dead or live loads. It is usually
specified that “the line of resistance of the ring must lie in the
middle third.” It must be borne in mind, however, that the stability
of the ring is perfectly consistent with the location of the line of
resistance outside of the limits of the middle third, provided it is
not so far outside as to induce crushing of the ring-stones. Whenever
that crushing begins the arch is in serious danger and complete failure
is likely to result.
=127. Applications to an Actual Arch.=—These principles will be applied
to the arch-ring shown in Fig. 38, in which the clear span _TU_ is
90 feet. The radius _CO_ of the soffit (as the under surface of the
arch is called) is 50 feet, the ring being circular and segmental. The
uniform thickness of the ring shown at the various joints is assumed
at 4 feet as a trial value. The loading above the ring to the level of
the line _EʹO_ is assumed to be dry earth weighing, when well rammed
in place, 100 pounds per cubic foot. The depth of this earth filling
at the crown _n_ of the arch is taken at 4 feet. The ring-stones are
assumed to be of granite or best quality of limestone, weighing 160
pounds per cubic foot. The thickness or width of arch-ring of one foot
is assumed, as each foot in width is like every other foot, and the
loads are taken for that width of ring. The rectangle _EJJʹEʹ_ is
supposed to represent a moving load covering one half of the span and
averaging 500 pounds per linear foot; in other words, averaging 500
pounds per square foot of upper surface projected in the line _EʹO_.
The total length of the arch-ring, measured on the soffit, is about
113 feet, and it is divided into ten equal portions for the purpose of
convenient computation. The radial joints so located are as shown at
_de_, _fg_, _hk_. From the points where these joints cut the extrados
(as the upper surface of the arch-ring is called) vertical broken lines
are erected, as shown in Fig. 38.
[Illustration: FIG. 38.]
The horizontal line drawn to the left from _f_ gives the vertical
projection of that part of the extrados between _d_ and _f_, and the
horizontal earth pressure on _df_ will be precisely the same in amount
as that on the vertical projection of _df_, as just found. In the same
manner the horizontal earth pressure on that part of the extrados
between any two adjacent joints may be found. The mid-depths of these
vertical projections below the line _E′O_ are to be carefully measured
by scale and then used for the values of _x_ in equations (64) and
(65), which now become equations (66) and (67), as the angle of repose
φ is taken to correspond to a slope of earth surface of 1 vertical on
1½ horizontal.
_p = 3.51wx._ (66)
_pʹ = 0.285wx._ (67)
The horizontal earth pressures thus found are as follows:
_h₁_ = { 101,500 pounds; _h₃_ = { 30,625 pounds;
{ 8,700 ” { 2,625 ”
_h₂_ = { 59,500 ” _h₄_ = { 9,800 ”
{ 5,100 ” { 840 ”
These quantities _h₁_, etc., are found by multiplying the two
intensities _p_ and _p′_ by the vertical projections of the surface
on which they act. The larger values are found by equation (66) and
represent the abutting power of the earth, while the smaller values
are found by equation (67), and represent the horizontal or conjugate
pressure of the earth due to its own weight only. The actual horizontal
earth pressure against the arch-ring may lie anywhere between these
limits.
The weights of the moving load, earth, and ring-stones between each
pair of vertical lines and radial joints shown in Fig. 38 are next to
be determined, and they are as follows:
_W₁_ = 27,300 pounds; _W₆_ = 12,300 pounds;
_W₂_ = 27,900 ” _W₇_ = 15,550 ”
_W₃_ = 24,500 ” _W₈_ = 19,500 ”
_W₄_ = 21,300 ” _W₉_ = 19,400 ”
_W₅_ = 18,300 ” _W₁₀_ = 24,300 ”
The centres of gravity of these various vertical forces are shown in
Fig. 38 at the points _W₁_, _W₂_, etc. The triangles of forces shown
in that figure and composed, each one, of a vertical and horizontal
force as described, are laid down in actual position on the arch-ring,
as shown. All data are thus secured for completing the force polygon
and polygonal frame or line of resistance. It will be assumed that
the reactions _R_ and _R′_ cut the springing joints at _c_ and _a_,
respectively, one third of the width of the joint from the soffit,
and it will further be assumed that _b_, the mid-point of the joint
at the crown, is also in the line of resistance. The assumption of
the location of these three points is made for the reason, as is well
known, that with a given system of forces a polygonal frame may be
found which will pass through any three points in the ring.
[Illustration: FIG. 39.]
The force polygon _B_, 1, 2, 3, ..., 10, _A_, Fig. 39, is then drawn
with the loadings on each ring segment found as already explained.
The horizontal forces are taken as represented by the smaller values
of _h₁_, _h₂_, _h₃_, _h₄_. Other force polygons with larger values of
these horizontal forces were tried and not found satisfactory. Having
constructed the force polygon and assumed the trial pole _Pʹ_, the
radial lines are drawn from it as shown in Fig. 39. The polygonal
frame shown in broken lines in Fig. 38 results from this trial pole.
The frame practically passes through _b_ and _c_, but leaves the ring,
passing outside of it, above the joint _VU_. The point _q_ in this
frame is vertically above _a_. The “three-point” method of finding the
frame that will pass through _a_, _b_, and _c_ was then employed. The
line _A6_, Fig. 39, was drawn; then _P′D_ was drawn parallel to _qb_,
Fig. 38 (not shown); after which _PD_ was drawn parallel to _ab_,
until it intercepted the horizontal line _PQ_, the line _PʹQ_ having
previously been drawn parallel to _qc_ (not shown). The final pole
_P_ was thus found. The polygonal frame shown in full lines in the
arch-ring was then drawn with sides parallel to the lines radiating
from _P_, all in accordance with the usual methods for such graphic
analysis. That polygonal frame lies within the middle third of the
arch-ring, although at three points it touches the limit of the middle
third. The arch, therefore, is stable.
This construction shows that, with the actual loading of the ring, a
line of resistance can be found lying within the middle third; its
stability under the conditions assumed is, therefore, demonstrated.
It does not follow that the line of resistance as determined must
necessarily exist, since there may be others located still more
favorably for stability. This indetermination results from the fact
already observed that the equations of statical equilibrium are not
sufficient in number to determine the four unknown quantities (the
two horizontal and the two vertical reactions); but the process of
demonstrating the stability of the arch-ring is simple and sufficient
for all ordinary purposes. The line of resistance found, if not the
true one, is so near to it that no sensible waste of material is
involved in employing it. This indetermination has prompted some
engineers and other analysts to consider all arch-rings as elastic,
thus obtaining other equations of condition. While such a procedure may
be permissible, it is scarcely necessary, and perhaps not advisable, in
view of the fact that many joints of cut-stone arches become slightly
open by very small cracks, resulting possibly from unequal settlement,
quite harmless in themselves, having practically no effect upon the
stability of the structure.
=128. Intensities of Pressure in the Arch-ring.=—It still remains to
ascertain whether the actual pressures of masonry in the arch-ring are
too high or not. The greatest single force shown in the force polygon
in Fig. 39 is the reaction _R_, having a value by scale of 122,000
pounds, under the left end of the arch, and it is supposed to act at
the limit of the middle third of the joint. Hence the average pressure
on that joint will be
122,000 × 2
----------- = 61,000 pounds per square foot.
4
This value may be taken as satisfactory for granite or the best quality
of limestone.
Again, it is necessary in bridges, as in some other structures, to
determine whether there is any liability of stones to slip on each
other. In order that motion shall take place the resultant forces
acting on the surface of a stone joint must have an inclination to
that surface less than a value which is not well determined and which
depends upon the condition of the surface of the stone; it certainly
must be less than 70°. The inclination of every resultant force in Fig.
38 to the surface on which it acts is considerably greater than that
value and, hence, the stability of friction is certainly secured.
=129. Permissible Working Pressures.=—The working values of pressures
permissible on cut-stone and brick or other masonry must be inferred
from the results of the actual tests of such classes of masonry in
connection with the results of experience with structures in which the
actual pressures existing are known. It is safe to state that with
such classes of material as are used in the best grade of engineering
structures these pressures will generally be found not to exceed the
following limits:
Concrete, 20,000 to 40,000 pounds per square foot.
Cement rubble, same values.
Hard-burned brick, cement mortar joints, 30,000 to 50,000 pounds per
square foot.
Limestone ashlar, 40,000 to 60,000 pounds per square foot.
Granite ashlar, 50,000 to 70,000 pounds per square foot.
The masonry arch is at the same time the most graceful and the most
substantial and durable of all bridge structures, and it is deservedly
coming to be more and more used in modern bridge practice. One of the
greatest railroad corporations in the United States has, for a number
of years, been substituting, wherever practicable, masonry arches for
the iron and steel structures replaced. The high degree of excellence
already developed in this country in the manufacture of the best grades
of hydraulic cement at reasonable prices, and the abundance of cut
stone, has brought this type of structure within the limits of a sound
economy where cost but a few years ago would have excluded it. It is
obviously limited in use to spans that are not very great but yet
considerably longer than any hitherto constructed.
[Illustration]
[Illustration: FIG. 40.—Elevation of Luxemburg Bridge and Sections of
Main Span.]
=130. Largest Arch Spans.=—The longest arch span yet built has been but
recently completed in Germany at the city of Luxemburg. This bridge has
a span of 275.5 feet and a rise of 101.8 feet. It is rather peculiarly
built in two parallel parts separated 19.5 feet in the clear, the space
between being spanned by slabs or beams of combined concrete and steel.
The arch-ring is 4.75 feet thick at the crown and 7.18 feet thick at a
point 53.14 feet vertically below the crown where it joins the spandrel
masonry. The roadway is about 52.5 feet wide and 144.5 feet above the
water in the Petrusse River, which it spans.
[Illustration: Cabin John Bridge, near Washington, D. C.]
The longest arch in this country is known as the Cabin John Bridge of
220 feet span and 57.5 feet rise. It is a segmental arch and is located
a short distance from the city of Washington, carrying the aqueduct for
the water-supply of that city. These lengths of span may be exceeded in
good ordinary masonry construction, but the high degree of strength and
comparative lightness which characterize the combination of steel and
concrete will enable bridges to be built in considerably greater spans
than any yet contemplated in cut-stone masonry.
CHAPTER XIII.
=131. Cantilever and Stiffened Suspension Bridges.=—There are two other
types of bridges of later development which have, in recent years,
become prominent by remarkable examples of both completed structure
and design; they are known as the cantilever and stiffened suspension
bridges. Both are adapted to long spans, although the latter may be
applied to much longer spans than the former. A cantilever structure,
with a main span of 1800 feet between centres of piers, is now in
process of construction across the St. Lawrence River at Quebec, while
the well-known Forth Bridge across the Firth of Forth in Scotland has
a main span of 1710 feet. The longest stiffened suspension bridge yet
constructed is the New York and Brooklyn Bridge, with a river span
of about 1595.5 feet between centres of towers, but the stiffened
suspension system has been shown by actual design to be applicable to
spans of more than 3200 feet, with material now commercially produced.
[Illustration: FIG. 41.]
[Illustration: FIG. 42.—Monongahela Bridge—Pittsburgh, Carnegie &
Western Railroad (Wabash), at Pittsburgh.]
=132. Cantilever Bridges.=—Figs. 41 and 42 exhibit in skeleton outline
two prominent cantilever designs for structures in this country.
That shown in Fig. 41 was intended for a bridge across the Hudson
River between Sixtieth and Seventieth streets, New York City. The
main central opening has a span of 1800 feet, and a length of 2000
feet between centres of towers. Fig. 42 shows the Monongahela River
cantilever bridge,[3] now being built at Pittsburgh, Penn. Both figures
exhibit the prominent features of the cantilever system. The main parts
are the towers, at each end of the centre span, which are 534.5 feet
high in the North River Bridge and 135 feet high in the Monongahela
River structure, and the central main or river span with its simple
non-continuous truss hung from the ends of the cantilever brackets or
arms which flank it on both sides. These cantilever arms are simply
projecting trusses continuous with the shore- or anchor-arms. They
rest on the piers at either end of the main span, as a lever rests
on its fulcrum. This arrangement requires the shore extremities or
the anchor-arms to be anchored down by a heavy weight formed by the
masonry piers at those points. Recapitulating and starting from the two
shore ends of the structure, there are the anchor-spans, continuous
at the towers, with the cantilever arms projecting outward toward the
centre of the main opening and supporting at their ends the suspended
truss, which is a simple, non-continuous one. It is thus evident that
the cantilever bridge is a structure composed of continuous trusses
with points of contraflexure permanently fixed at the ends of the
suspended span. The greatest bending moments are at the towers, and
the great depth at that point is given for the purpose of affording
adequate resistance to those moments by the members of the structure.
The following statement shows some elements of the more prominent
cantilever bridges of this country and of the Forth Bridge:
[3] This bridge was designed by and is being constructed under the
direction of Messrs. Boller and Hodge, Consulting Engineers, New York
City.
Length of Cantilever
Name. Opening, Centre to Total Length.
Centre of Towers.
Pittsburgh 812 feet. 1504 feet.
Red Rock (Colo.) 660 ” 990 ”
Memphis (Tenn.) 790.48 ” 2378.2 ”
Forth 1710 ” 5330 ”
The arrangement of web members of cantilever structures is designed to
be such as will transfer the loads from the points of application to
the points of support in the shortest and most direct paths. Both Figs.
41 and 42 show these general results accomplished by an advantageous
arrangement of web members.
It is interesting to note that the first cantilever bridge designed
and built in this country was constructed in 1871. This structure was
designed and erected by the late C. Shaler Smith, a prominent civil
engineer of his day.
=133. Stiffened Suspension Bridges.=—The stiffened suspension bridge is
a structure radically different in its main features and its mode of
transferring load to points of support from any heretofore considered,
except arched ribs. When a load is supported by a beam or truss, the
stresses, either in the web members of the truss or in the solid web
of the beams, travel up and down those members in zigzag directions
with a relatively large amount of metal required for that kind of
transference. That metal is represented by the weight of the web
members of the truss and of the solid web of the beam. Again, there are
two sets of truss members—the chords or flanges, one of which sustains
tension and the other an equal amount of compression. The greater part
of this metal must be so placed and used that the working intensities
of stress are comparatively small. This is particularly the case in
compression members of both chords and webs which constitute the
greater portion of the weight of the truss. All compression members
are known as long columns which sustain not only direct compression
but bending, and the amount of stress or load which they carry per
square inch is relatively small, decreasing as the length increases.
For all these reasons the amount of metal required for both beams and
trusses is comparatively large. In suspension bridges, however, the
conditions requiring the employment of a relatively large amount of
metal with relatively small unit stresses are absent. The main members
of a suspension bridge are the cables and the stiffening trusses, the
latter being light in reference to the length of span. The cables are
subjected to tension only, which is the most economical of all methods
of using metal. A member in tension tends to straighten itself, so
that it is never subjected to bending by the load which it carries.
The opposite condition exists with compression members. Again, grades
of steel possessing the highest ultimate resistance may be used in the
manufacture of cables. It is well known that wire is the strongest form
in which either wrought-iron or steel can be manufactured. While the
ultimate tensile resistance of ordinary structural steel will seldom
rise above 70,000 pounds per square inch, steel wire, suitable to be
used in suspension-bridge cables, may be depended upon, at the present
time, to give an ultimate resistance of at least 180,000 pounds per
square inch. The elastic limit of ordinary structural steel is but
little above half its ultimate resistance, while the elastic limit
of the steel used in suspension-bridge cables is probably not less
than three fourths of its ultimate resistance. It is seen, therefore,
that the high resistance of steel wire makes the steel cable of the
suspension bridge a remarkably economical application of metal to
structural purposes.
The latest example of stiffened suspension-bridge is the new East River
Bridge reaching across the East River from Broadway in Brooklyn to
Delancey Street, New York City, now being built, with a main span of
1600 feet between centres of towers. The entire length of the metal
structure is 7200 feet, and the elevation of the centres of cable at
the tops of the towers is 333 feet above mean high water.
Fig. 43 shows a view of this bridge. Its three principal divisions are
the cables, the stiffening trusses, and the towers. The latter afford
suitable points of support for the cables, which not only extend over
the river span, but are carried back to points on the land where they
are securely attached to a heavy mass of anchorage masonry. These
anchorages must be sufficiently heavy to prevent any load which may
come upon the bridge from moving them by the pull of the cables. It is
usual to make these masses so great that they are capable of resisting
from two to two and a half times the pull of the cables.
[Illustration: FIG. 43.—New East River Bridge.]
=134. The Stiffening Truss.=—The function of the stiffening trusses
is peculiar and imperatively essential to the proper action of the
whole system. If they are absent and a weight should be placed upon
the cable at any point, a deep sag at that point would result. If a
moving load should attempt to pass along a roadway supported by a cable
only, the latter would be greatly distorted, and it would be impossible
to use such a structure for ordinary traffic. Some means must then
be employed by which the cable shall maintain essentially the same
shape and position, whatever may be the amount of loading. It can be
readily shown that if any perfectly flexible suspension-bridge cable
carries a load of uniform intensity over the span from one tower to
the other, the curve of the cable will be a parabola, with its vertex
at the lowest point. Furthermore, it can also be shown that if any
portion of the span be subjected to a uniform load, the corresponding
portion of the cable will also assume a parabolic curve. It is assumed
in all ordinary suspension-bridge design that the total weight of the
structure, including the cables and the suspension-rods which connect
the stiffening trusses to the cable, is uniformly distributed over
the span, and that assumption is essentially correct. So far as the
weight of the structure is concerned, therefore, the curve of the cable
will always be parabolic. It only remains, therefore, to devise such
stiffening trusses as will cause any moving load passing on or over
the bridge to be carried uniformly to the cables throughout the entire
span. This condition means that if any moving load whatever covers any
portion of the span, the corresponding pull of the suspension-rods on
the cables must be uniform from one tower to the other, and that result
can be practically accomplished by the proper design of stiffening
trusses; it is the complete function of those trusses to perform just
that duty.
=135. Location and Arrangement of Stiffening Trusses.=—It has been,
and is at the present time to a considerable extent, an open question
as to the best location and arrangement of the stiffening trusses. The
more common method in structures built is that illustrated by the New
York and Brooklyn and the new East River bridges. Those stiffening
trusses are uniform in depth, extending from one tower to the other, or
into the land spans, and connected with the cables by suspension-rods
running from the latter down to the lower chords of the trusses. It is
obvious that the floor along which the moving load is carried must have
considerable transverse stiffness, and hence it may appear advisable
to place the stiffening trusses so that the floor may be carried by
them. On the other hand, some civil engineers maintain that it is a
better distribution of stiffening metal to place it where the cables
themselves may form members of the stiffening trusses, with a view to
greater economy of material.
Figs. 44, 45, and 46 illustrate some of the principal proposed methods
of constructing stiffening trusses in direct connection with the
cables. The structure shown in Fig. 44 illustrates the skeleton design
of the Point Bridge at Pittsburgh. The curved member is a parabolic
cable composed of eye-bars. This parabolic cable carries the entire
weight of the structure and moving load when uniformly distributed. If
a single weight rests at the centre, the two straight members of the
upper chord may be assumed to carry it. If a single weight rests at any
other point of the span, it will be distributed by the bracing between
the straight and curved members of the stiffening truss. Obviously the
most unbalanced loading will occur when one half of the span is covered
with moving load. In that case the bowstring stiffening truss in either
half of Fig. 44 will make the required distribution and prevent the
parabolic tension member from changing its form.
[Illustration: FIG. 44.]
[Illustration: FIG. 45.]
[Illustration: FIG. 46.]
The type of bracing shown in Fig. 45 possesses some advantages of
a peculiar nature. Each curved lower chord of the stiffening truss
corresponds to the position of the perfectly flexible cable with
the moving load covering that half of the span which belongs to the
greatest sag of the cable. The two parabolic cables thus cross each
other in a symmetrical manner at the centre of the span. If the moving
load covers the entire span, the line of resistance or centre line of
imaginary cable will be the parabola, shown by the broken line midway
along each crescent stiffening truss. The diagonal bracing placed
between the cables is so distributed and applied as to maintain the
positions of cables under all conditions of loading.
The mode of constructing the stiffening truss between two cables, shown
in Fig. 46, is that adopted by Mr. G. Lindenthal in his design for a
proposed stiffened suspension bridge across the Hudson River with a
span of about 3000 feet. The two cables are parabolic in curvature and
may be either concentric or parallel. This system of stiffening bracing
possesses some advantages of uniformity and is well placed to secure
efficient results. The same system has been used in suspension bridges
of short span by Mr. Lindenthal at both St. Louis and Pittsburgh. The
stiffening bracing produces practically a continuous stiffening truss
from one tower to the other, whereas the systems shown in Figs. 44 and
45 involve practically a joint at the centre of the span.
In all these three types of vertical stiffness the floor is designed
to meet only the exigencies of local loading, being connected with the
stiffening truss above by suspension bars or rods, preferably of stiff
section.
When stiffening trusses are placed along the line of the floor, as in
the case of the two East River bridges, to which reference has already
been made, those trusses need not necessarily be of uniform depth, and
they may be continuous from tower to tower or jointed at the centre,
like those of the New York and Brooklyn suspension bridge. This centre
joint detracts a little from the stiffness of the structure, but in a
proper design this is not serious.
=136. Division of Load between Cables and Stiffening Truss.=—In a case
where continuous stiffening trusses are employed it is obvious that
they may carry some portion of the moving load as ordinary trusses.
The portion so carried will be that which is required to make the
deflection of the stiffening truss equal to that of the cable added
to the stretch of the suspension-rods. In the old theory of the
stiffening truss constructed along the floor of the bridge this effect
was ignored, and the computations for the stresses in those trusses
were made by the aid of equations of statical equilibrium only. That
assumption, that the cable carried the entire load, was necessary
to remove the ambiguity which would otherwise exist. In modern
suspension-bridge design those trusses may be assumed continuous from
tower to tower with their ends anchored at the towers, or they may be
designed to be carried continuously through portions of the land spans
and held at their extremities by struts reaching down to anchorages,
so that those ends may never rise nor fall, but move horizontally if
required. If there are no pin-joints in the trusses at the centre
and ends of the main span, equations of statical equilibrium are not
sufficient to enable the reactions under the trusses and the horizontal
component of cable tension to be found.
One of the best methods of procedure for such cases is that of
least work, in which the horizontal component of cable tension is
so found that the total work performed in the elastic deflection of
the stiffening trusses, suspension-rods, cables, and towers is a
minimum. After having found this horizontal component of the cable
tension and the reactions under the stiffening trusses, the stresses
in all the members of the entire structure can be at once determined.
It is obvious that the stiffening truss and the cables must deflect
together. It is equally evident that the deeper the stiffening trusses
are the more load will be required to deflect them to any given
amount, and hence that the deeper they are the more load they will
carry independently of the cable. It is desirable to throw as much of
the duty of carrying loads upon the cables as possible. It therefore
follows that the stiffening trusses should be made as shallow as the
proper discharge of their stiffening duties will permit.
=137. Stresses in Cables and Moments and Shears in Trusses.=—The
necessary limits of this discussion will not permit even the simplest
analyses to be given. It is evident, however, that the greatest
cable stresses will exist at the tops of the towers, and that if the
horizontal component of cable tension be found by any proper method,
the stress at any other point will be equal to that horizontal
component multiplied by the secant of cable inclination to a horizontal
line, it being supposed that the suspenders are found in a vertical
plane.
If the stiffening trusses are jointed at the centre of the main span,
as well as at the ends, the simple equations of statical equilibrium
are sufficient in number to make all computations, for the reason that
the centre pin-joint gives the additional condition that, whatever
may be the amount or distribution of loading, the centre moment must
be zero. If _l_ is the length of main or centre span and _p_ the
moving load per linear foot of span, and if the stiffening trusses run
from tower to tower, the following equations will give their greatest
moments and shears both by the old and new theory of the stiffening
truss.
_p_ = load per lin. ft., _l_ = length of span in ft.,
Old theory. New theory.
Max. moment _M_ = 0.01856_pl_² _M_ = 0.01652_pl_²}no centre
Max. shear _S_ = ⅛_pl_ _S_ = ⅛_pl_ } hinge.
With centre hinge _M_ = 0.01883_pl_² and _S_ = ⅛_pl_
The details of the theory of stiffening trusses for suspension
bridges have been well developed during the past few years and are
fully exhibited in modern engineering literature. The long spans
requiring stiffened suspension bridges are usually found over navigable
streams, and hence those bridges must be placed at comparatively
high elevations. This is illustrated by the clear height of 135 feet
required under the East River suspension-bridge structures already
completed and in progress. Furthermore, the heights of towers above
the lowest points of the cables usually run from one eighth to one
twelfth of the span. These features expose the entire structure to
comparatively high wind pressures, which must be carefully provided
against. This is done by the requisite lateral bracing between the
stiffening trusses and by what is called the cradling of the cables.
The latter expression simply means that the cables as they are built
are swung out of a vertical plane and toward the axis of the structure,
being held in that position by suitable details. The cables on opposite
sides of the bridge are thus moved in toward each other so as to
produce increased stability against lateral movement. Occasionally
horizontal cables are stretched between the towers in parabolic curves
in order to resist horizontal pressures, just as the main cables carry
vertical loads. This matter of stability against lateral wind pressures
requires and receives the same degree of careful consideration in
design as that accorded to the effects of vertical loading. The same
general observation applies also to the design of the towers.
=138. Thermal Stresses and Moments in Stiffened Suspension
Bridges.=—All material used in engineering structures expands and
contracts with rising and falling temperatures to such an extent
that the resulting motions must be provided for in structures of
considerable magnitude. In ordinary truss-bridges one end is supported
upon rollers, so that as the span changes its length the truss ends
move the required amount upon the rollers. In the case of stiffened
suspension bridges, however, the ends of the cables at the anchorages
are rigidly fixed, so that any adjustment required by change of
temperature must be consistent with the change of length of cable
between the anchorages. The backstays, which are those portions of
the cables extending from the anchorages to the tops of the towers,
expand and contract precisely as do the portions of the cable between
the tops of the towers. As the cables lengthen, therefore, the sag or
rise at the centre of the main span will be due to the change in the
entire length of cable from anchorage to anchorage. In order to meet
this condition it is usual to support the cables at the tops of the
towers on seats called saddles which rest upon rollers, so as to afford
any motion that may be required. Designs have been made in which the
cables are fixed to the tops of steel towers. In such cases changes
of temperature would subject the towers to considerable bending which
would be provided for in the design.
The rise and fall at the centres of long spans of stiffened suspension
bridges is considerable; indeed, for a variation of 120° Fahr. the
centre of the New York and Brooklyn Bridge changes its elevation by
4.6 feet if the saddles are free to move, as intended. In the case of
a stiffened suspension bridge designed to cross the North River at New
York City with a main span of 3200 feet a variation of 120° Fahr. in
temperature would produce a change of elevation of the centre of the
span of 6.36 feet. Such thermal motions in the structure obviously will
produce stresses of considerable magnitude in various parts of the
stiffening trusses, all of which are invariably recognized and provided
for in good design.
=139. Formation of the Cables.=—At the present time suspension-bridge
cables are made by grouping together in one cylindrical mass a large
number of so-called strands or individual small cables, each composed
of a large number of parallel wires about one sixth of an inch in
diameter. The four cables of the New York and Brooklyn Bridge are each
composed of 19 strands, each of the latter containing 332 parallel
wires, making a total of 6308 wires, the cables themselves being
15½ inches in diameter. The wire is No. 7 gauge, i.e., 0.18 inch in
diameter. In the new East River Bridge each of the four cables is 18¼
inches in diameter and contains 37 strands, each strand being composed
of 208 wires all laid parallel to each other, or a total of 7696 wires.
The size of the wire is No. 6 (Roebling) gauge, i.e., 0.192 inch in
diameter. These strands are formed by laying wire by wire, each in
its proper place. The strands are then bound together into a single
cable, around which is tightly wound a sheathing or casing of smaller
wire, 0.134 inch in diameter for the New York and Brooklyn Bridge. The
tightness of this binding wire insures the unity of the whole cable,
each wire having been placed in its original position so as to take a
tension equal to that of each of the other wires. The suspension-rods
are usually of wire cables and are attached by suitable details to the
lower chords of the stiffening truss, also by specially designed clamps
to the cable. The stiffening trusses are usually built with all riveted
joints, so as to secure the greatest possible stiffness from end to
end. The stiffened suspension bridge has been shown by experience, as
well as by theory, to be well adapted to carry railroad traffic over
long spans.
=140. Economical Limits of Spans.=—In the past, suspension bridges
have, in a number of cases, been built for comparatively short spans,
but it is well recognized among engineers that their economical use
must be found for spans of comparatively great length. While definite
lower limits cannot now be assigned to such spans, it is probable that
with present materials of construction and with available shop and
mill capacities the ordinary truss-bridge may be economically used up
to spans approximately 700 to 800 feet, and that above that limit the
cantilever system is economically applicable to lengths of span not yet
determined but probably between 1600 and 2000 feet. The special field
of economical employment of the long-span stiffened suspension bridge
will be found at the upper limit of the cantilever system. So far as
present investigations indicate, the stiffened suspension type of
structure may be employed to advantage from about 1800 feet up to the
maximum practicable length of span not yet assignable, but perhaps in
the vicinity of 4000 feet. Obviously such limits are approximate only
and may be pushed upward by further improvements in the production of
material and in the enlargement of both shop and mill capacity.
PART III.
_WATER-WORKS FOR CITIES AND TOWNS._
CHAPTER XIV.
=141. Introductory.=—A preceding lecture in this course has shown to
what an advanced state the public supply of water to large cities was
developed in ancient times. The old Romans, Greeks, Egyptians, and
other ancient peoples evidently possessed an adequate appreciation of
the value of efficient systems of public water-supply. Very curiously
that appreciation diminished so greatly as almost to disappear
during the middle ages. The demoralization of public spirit and the
decrease of national power which followed the fall of Rome induced, in
their turn, among other things, a neglect of the works of the great
water system of Rome, entailing their partial destruction. The same
retrogression in civilization seemed to affect other ancient nations
as well, until probably the lowest state of the use of public waters
and the construction of public water systems was reached somewhere
between A.D. 1000 and A.D. 1300 or 1400. Without reasonable doubt the
terrible epidemics or plagues of the middle ages can be charged to the
absence of suitable water-supplies and affiliated consequences. During
that middle period of the absence of scientific knowledge and any
apparent desire to acquire it, sanitary works and consequently sanitary
conditions of life were absolutely neglected. No progress whatever was
made toward reaching those conditions so imperative in large centres of
population for the well-being of the community. Grossly polluted waters
were constantly used for public and private supplies, and no efforts
whatever were made among the masses toward the suitable disposition
of refuse matters or, in a word, to attain to sanitary conditions of
living.
A few important works were completed, particularly in Spain, but
nothing indicative of general relief from the depths of ignorance and
sanitary demoralization to which the greater portion of the civilized
world had sunk at that time. The city of Paris took all its water from
the Seine, except that which was supplied by a small aqueduct built in
1183. So small was the supply, aside from the water obtained from the
river, that in 1550 it is estimated that the former amounted to about
one quart only per head of population per day. The situation in London
was equally bad, for it was only in the first half of the thirteenth
century that spring-water was brought to the city by means of lead
pipes and masonry conduits. Public water-works began to be constructed
in Germany on a small scale in the early part of the fifteenth century.
Obviously no pumps were available in those early days of water-supply,
so that the small systems which have been mentioned were of the
gravity class; that is, the water flowed naturally in open or closed
channels from its sources to the points of consumption. Pumps of a
simple and crude type first began to be used at a point on the old
London Bridge in 1582, and in Hanover in 1527. Subsequently to those
dates other pumps were set up on London Bridge, and installations
of the same class of machinery were made in Paris in 1608, usually
operated by water-power in some simple manner, as by the force of the
water-currents. In 1624 the Paris supply received a reinforcement of
200,000 gallons per day by the completion of the aqueduct Arcueil. The
New River Company was incorporated in 1619 for the partial supply of
the city of London, and it began to lay its pipes at that time. As its
name indicates, it took its supply from New River, and the inception of
its business is believed to mark the first application of the principle
of supplying each house with water. This company is still in existence
and furnishes a considerable portion of the present London supply.
=142. First Steam-pumps.=—The application of steam to the creation or
development of power by Watt, near the end of the eighteenth century,
stimulated greatly the construction of water-works, as it offered a
very convenient and economical system of pumping. It seems probable
that the first steam-pumps were used in London in 1761. Twenty years
later a steam-pump was erected in Paris, while another was installed in
1783. The second steam-pump in London was probably constructed in 1787.
In all these earlier instances of the use of steam-pumps river supplies
were naturally used.
=143. Water-supply of Paris and London.=—After the early employment of
steam pumping-machinery demonstrated its great efficiency for public
water-supplies, the extension of the latter became more rapid, and
since 1800 the supplies of the two great cities of London and Paris
have been greatly increased. As late as 1890 the Paris supply amounted
to about 65 gallons per head of population, one fourth of which was
used as potable, being drawn from springs, while three fourths, drawn
from rivers, was used for street-cleaning or other public purposes.
This supply, however, was found inadequate and was re-enforced in 1892
by an addition of 30,000,000 gallons per day of potable water brought
to the city by an aqueduct 63 miles long. Another addition of about
15,000,000 gallons has been provided more recently.
Rather curiously the water-supply of London is afforded by eight
private companies, one of which is the old New River Company already
mentioned. These companies, with one exception, draw their supply
mainly from the rivers Thames and Lea, all such water being filtered.
The remaining company draws its water from deep wells driven into the
chalk. The total population supplied amounts to about 5,500,000, the
rate of supply being thus less than 45 gallons per head per day.
=144. Early Water-pipes.=—Inasmuch as the use of cast-iron for pipes
was only begun about the year 1800, other materials were used prior
to that date. As is well known, the pipes used in ancient water-works
were either of lead or earthenware. In the eighteenth century wooden
pipes made of logs with their centres bored out were used, sometimes
6 or 7 inches in diameter. As many lines of these log pipes were used
as needed to conduct a single line of supply. In the earlier portion
of the nineteenth century such log pipes, usually of pine or spruce,
were used by the old Manhattan Company for the supply of New York
City. A section of such a wooden pipe, with a bore of about 2½ inches
is preserved in the museum of the Department of Civil-Engineering of
Columbia University. Large quantities of such pipes were formerly used.
=145. Earliest Water-supplies in the United States.=—The earliest
system of public water-supply in this country was completed for the
city of Boston in 1652. This was a gravity system. It is believed
that the first pumping-machinery for such a supply was set up for the
town of Bethlehem, Pa., and put in operation in 1754. Subsequently
water-supplies were completed for Providence, R. I., 1772, and for
Morristown, N. J., in 1791; the latter has maintained a continuous
existence since that date. The first use of steam pumping-machinery in
this country was in Philadelphia in 1800. This machinery, curiously
enough, was largely of wood, including some portions of the boiler; it
was necessarily very crude and would perform with 100 pounds of coal
only about one twenty-fifth or one thirtieth of what may be expected
from first-class pumping-machinery at the present time. Other cities
and towns soon began to follow the lead of these earlier municipalities
in the construction of public water-supplies, but the principal
development in this class of public works has taken place since about
1850.
It is estimated that the total population supplied in 1880 was about
12,000,000, which rose to about 23,000,000 in 1890, and it is probably
not less than 50,000,000 at the present time.
=146. Quality and Uses of Public Water-supply.=—Advances in the public
supplies in this country have been made rather in the line of quantity
than quality. Insufficient attention has been given both to the
quality of the original supply and to the character of the reservoirs
in which it is gathered until within possibly the past decade. A few
cities like Boston have scrutinized with care both the quality of the
water and the character of the bottom and banks of reservoirs, and
have spared neither means nor expense to acquire a high degree of
excellence in their potable water. The same observations can be applied
to a few other large cities, but to a few only. The realization of
the dependence of public health upon the character of water-supply,
however, has been rapidly extending, and it will doubtless be but a
short time before the care exercised in collecting and preparing water
for public use will be as great in this country as in Europe, where few
large cities omit the filtration of public waters.
The distribution of water supplied for public use is not limited to
domestic purposes, although that class of consumption controls public
health so far as it is affected by the consumption of water. The
applications of water to such public purposes as street-cleaning and
the extinguishing of fires are of the greatest importance and must
receive most careful consideration. Again, the so-called system of
water-carriage in the disposal of domestic and manufacturing wastes,
constituting the field of sewage-disposal, depends wholly upon the
efficiency of the water-supply.
=147. Amount of Public Water-supply.=—The first question confronting
an engineer in the design of public water-supply is the amount which
should be provided, usually stated on the basis of an estimated
quantity per head of population. This is not in all cases completely
rational, but it is by far the best basis available. If the
water-supply is designed for a small city or town previously supplied
by wells or other individual sources, the first year’s consumption
will be low per head of population for the reason that many people
will retain their own sources instead of taking a share of the public
supply. As time elapses that portion of population decreases quite
rapidly in numbers, and in a comparatively few years practically the
whole population will use the public supply. In communities, therefore,
where public systems have long existed and it is desired either to
add to the old supply or to install new ones, the only safe basis of
estimate is the entire population.
=148. Increase of Daily Consumption and the Division of that
Consumption.=—The amount of water required per head of population might
naturally be assumed identical with the past consumption, but that
would frequently be incorrect. It is one of the most prominent features
of the history of public water-supplies in this country that the
consumption per head of population has increased with great rapidity
from the early years of the installation of the different systems,
for reasons both legitimate and illegitimate. The daily average
consumption of water from the Cochituate Works of the Boston supply
increased from 42 gallons per head of population in 1850 to 107 gallons
in 1893, and in the Mystic Works of the same supply the increase was
from 27 gallons in 1865 to 89 gallons in 1894. Again, the daily average
consumption in Chicago rose from 43 gallons per head per day in 1860
to 147 gallons in 1893, while in Philadelphia during the same period
the increase was from 36 gallons per head per day to 150 gallons. In
Cambridge, Mass., the increase in daily average consumption per head
of population was from 44 gallons in 1870 to 70 gallons in 1894. These
instances are sufficient to show that, under existing conditions, the
daily consumption was increased at a rapid rate in the cities named,
and they have been selected as fairly representative of the whole
field. Civil engineers have made extended studies in connection with
this question in a great number of cities, for it bears upon one of the
most important lines of public works. It is absolutely essential to
the health and business prosperity of every city that the water-supply
should be abundant, safe, and adapted to the industrial and commercial
pursuits of its population. It is imperative, therefore, that the
division of the daily supply should be carefully analyzed. For this
purpose the water-supply of a city may be, and frequently is, divided
into four parts:
(1) That used for domestic purposes;
(2) That used for commercial and industrial purposes;
(3) That used for public purposes;
(4) That part of the supply which is wasted.
1. That portion of the supply consumed for domestic purposes includes
not only the water used in private residences, but in those branches
of consumption which may be considered of a household character found
in hotels, clubs, stores, markets, laundries, and stables, or for
any other residential service. As might be expected, this branch of
consumption varies largely from one city to another. The results
of one of the most interesting and suggestive studies ever made in
connection with this subject are given by Mr. Dexter Brackett, M. Am.
Soc. C. E., in the Transactions of the American Society of Civil
Engineers for 1895. In Boston the purely domestic consumption varied
in different houses and apartments from 59 gallons per head per day
in costly apartments down to 16.6 gallons per head per day in the
poorest class of apartment. In Brookline, one of the finest suburbs of
Boston, the quantity was 44.3 gallons per day. In some other cities
of Massachusetts, as Newton, Fall River, and Worcester, this class of
consumption varied from 6.6 gallons to 26.5 gallons per day, the latter
quantity being found at Newton in some of the best residences, and the
former at houses also in Newton having but one faucet each. In Yonkers,
N. Y., where the system was metered, the amount was 21.4 gallons per
head of population per day, while in portions of London, England, it
varied from 18.6 to 25.5 gallons per head per day. The average of these
figures gives a result of 18.2 gallons per head per day, which, in
round numbers, may be put at 20 gallons.
2. It is obvious that the rate of consumption for commercial and
industrial purposes in any city must vary far more than that for
domestic purposes, for the reason that some cities may be essentially
residential in character while others may be essentially manufacturing.
At the same time, it is to be remembered that many manufacturing
establishments may have their own water-supply. The city of Fall River,
Mass., is eminently a manufacturing city, yet Mr. Brackett found that
the manufacturing demand on the public water-supply amounted to 2
gallons only per inhabitant per day, as the manufacturers draw the
most of their supply from the river, but that where the manufacturers
depend upon the public supply for all their water the amount rises to
a value between 20 and 30 gallons per inhabitant. In Boston in 1892
the water consumed for all manufacturing and industrial purposes,
including railroads, gas-works, elevators, breweries, etc., amounted
to 9.24 gallons per head of population per day, while in Yonkers in
1897 the total consumption for commercial purposes was 27.4 gallons per
head per day. In the city of New York, as nearly as can be estimated,
the consumption for commercial purposes is probably not far from 25
gallons per inhabitant per day. Reviewing all these results, it may
be stated that the water consumption for commercial and industrial
purposes will generally range from 10 to 30 gallons per inhabitant per
day.
3. The consumption of water for public purposes is a smaller amount
than either of the two preceding. It covers such uses as public
buildings, schools, street-sprinkling, sewer-flushing, fountains,
fires, and other miscellaneous objects, more or less similar to those
just named. The total use of this character was 3.75 gallons per
inhabitant per day for Boston in 1892, and 5.57 gallons per inhabitant
per day for Fall River in 1899. A few other cities give the following
results: Minneapolis in 1897, 5 gallons; Indianapolis, 3 gallons;
Rochester, N. Y., 3 gallons; Newton, Mass., 4 gallons; Madison, Wis.,
10 gallons. In Paris it is estimated that not far from 2.5 gallons per
head of population per day are used. It is probable, therefore, that an
amount of 5 gallons per day per inhabitant will cover this particular
line of consumption.
4. A substantial portion of the water-supply of every city fails to
serve any useful purpose, for the reason that it runs to waste either
by intention or by neglect. The sources of this waste are defective
plumbing, including leaky faucets and cocks; deliberate omission to
close faucets and cocks, constituting wilful waste; defective or broken
mains, including leaky joints; and waste to prevent freezing.
=149. Waste of Public Water.=—All these wastes except the last are
inexcusable. There is no difficulty in detecting defective plumbing,
and its existence is generally known to the householder; but if the
wasted water is not measured and paid for, it is far too frequently
considered more economical to continue the waste than to pay for
the plumber’s services. In a multitude of cases cocks are left open
indefinitely for all sorts of insignificant reasons; in closets,
under the erroneous impression that the continuous running of the
stream will materially aid in a more effective cleansing of soil-
and sewer-pipes, failing completely to appreciate that a far more
powerful stream is required for that purpose; sometimes in sinks, for
refrigerating purposes, and in many other inexcusably wrong ways.
These sources of wilful waste lead to large losses and constitute
one of the most unsatisfactory phases of administration of a public
water system. Such losses result in a vicious waste of public money.
The amount of water flowing from leaky joints and from leaks in pipes
and mains is necessarily indeterminate because it escapes without
evidence at the surface except in rare cases. In every instance where
examinations have been made and a careful record kept of the amount
of water supplied to a city, it has been found that the aggregate of
the measured amounts consumed fail nearly to equal the total supply.
There are probable errors both in the measurement of the quantities
supplied and in the quantities consumed, but the large discrepancy
cannot be accounted for in this manner. In many cases consumed water
has even been carefully measured by meters, as at Yonkers, New York,
Newton, Milton, and Fall River, Mass., Madison, Wis., and at other
places, but yet the discrepancy appears to be nearly as wide as ever.
Again, in 1893 observations were carefully made on the consumption of
the water received by the Mystic supply of the Boston system at _all_
hours of the twenty-four. Obviously between 1 and 4 A.M. the useful
consumption should be nearly nothing, but, on the contrary, it was
found to be nearly 60 per cent of the average hourly consumption for
the entire twenty-four hours. The waste at Buffalo, N. Y., in 1894 was
estimated at 70 per cent of the total supply. Similar observations
in other places have given practically the same results. It has also
been found that, in a number of instances, where old watercourses have
been completely obliterated by considerable depths of filling required
by the adopted grades of city streets and lots, and excavations for
buildings have subsequently been opened practically the full volume of
the former streams are flowing along the original but filled channel.
This result has been observed under a practically impervious paved
city surface. It is difficult to imagine the source of such a supply
except from defective pipe systems or sewers. A flow of a least 100,000
gallons per day from a broken pipe which found its way into a sewer has
also been discovered without surface evidence. These and many other
results of experience conclusively demonstrate that much water flows
to waste unobserved from leaky joints and defective or broken pipes.
Inasmuch as cast-iron water-pipes are produced in lengths which net 12
feet as laid, there will be at least 440 joints per mile. Furthermore,
as leaky joints and broken pipes are as likely to occur at one place
as another, it seems reasonable to estimate leakage through them as
proportionate to the length of the pipe-line in a system; and that
conventional law is frequently assumed. New pipe-lines have sometimes
shown a leakage of 500 to 1200 gallons per mile of line per day. Civil
engineers have sometimes specified the maximum permissible leakage of
a new pipe-line at 60 to 80 gallons per mile of line per day for each
inch in diameter of pipe, thus permitting 600 to 800 gallons to escape
from a 10-inch pipe. In 1888 the late Mr. Chas. B. Brush reported a
leakage of about 6400 gallons per mile per day from a practically new
24-inch cast-iron main, 11 miles long, of the Hackensack Water Company,
the pressure being 110 pounds per square inch. Tests of water-pipes in
German and Dutch cities have been reported as showing less waste than
300 gallons per mile per day, but such low results, unless for very low
pressures and short lines, may reasonably be doubted. Obviously losses
of this character will probably increase with the age of the pipe. By
a very ingenious procedure based upon his own experience, Mr. Emil
Kuichling of Rochester, N. Y., reaches the conclusion that a reasonable
allowance for the waste from leaky joints and defective pipes is 2500
to 3000 gallons per mile of cast-iron pipe-line per day. If, as is
frequently the case, the population per mile of pipe ranges from 300 to
1000, the preceding allowance amounts to 3 to 10 gallons per head of
population per day. The loss or waste due to running cocks or faucets
to prevent freezing cannot be estimated with sufficient accuracy to
receive a definite valuation, but it must be considered an element of
the total item of waste.
=150. Analysis of Reasonable Daily Supply per Head of Population.=—It
has repeatedly been found that the losses or wastes set forth in the
preceding statements amount apparently to quantities varying from 30 to
50 per cent of the total supply; or, to put it a little differently,
the water unaccounted for in even the best systems now constructed
apparently may reach one third to one half of the total supply. This
is an exceedingly wasteful and unbusinesslike showing. It is probable
that the statement is, to some extent at least, an exaggeration. It
is practically certain that either the amount supplied or the amounts
consumed, or both, are never measured with the greatest accuracy, and
that the errors are such as generally swell the apparent quantity
wasted. After making judicious use of the data thus afforded by
experience, it is probable that the following tabular statement given
by Messrs. Turneaure and Russell represents limits within which should
be found the daily average supply of water in a well-constructed and
well-administered system.
+---------------------------+--------------------------------+
| | Gallons per Head per Day. |
| Use. +----------+----------+----------+
| | Minimum. | Average. | Maximum. |
+---------------------------+----------+----------+----------+
| Domestic | 15 | 25 | 40 |
| Industrial and commercial | 5 | 20 | 35 |
| Public | 3 | 5 | 10 |
| Waste | 15 | 25 | 30 |
+---------------------------+----------+----------+----------+
| Total | 38 | 75 | 115 |
+---------------------------+----------+----------+----------+
The values given in the preceding table are reasonable and sufficient
to supply the legitimate needs of any community, but, as will be shown
in the succeeding table, there are cities in this country whose average
consumption is more than twice the maximum rate given above.
=151. Actual Daily Consumption in Cities of the United States.=—The
following table exhibits the average daily consumption of water
throughout the entire year for the cities given, as determined for the
years indicated in the table.
The city of Buffalo shows a daily consumption of 271 gallons per
inhabitant, and Allegheny, Pa., 247 gallons per inhabitant. There are a
considerable number showing an average daily consumption per inhabitant
of 160 gallons or more. All such high averages exhibit extravagant use
of water, or otherwise inefficient administration of the water-supply.
The reduction of such high rates of consumption is one of the most
difficult problems confronting the administration of public works. The
use of the meter has proved most efficient in preventing wastes or
other extravagant consumption, as in that case every consumer pays a
prescribed rate for the amount which he takes.
TABLE I.
-------------------+-----------+----------+-------+-----------
| | | |Consumption
| | | Per | per
|Population.|Population|Cent of| Inhabitant
| | per Tap. | Taps | Daily,
| | |Metered| Gallons.
-------------------+-----------+----------+-------+-----------
| 1890. | 1890. | 1890. | 1890.
-------------------+-----------+----------+-------+-----------
New York | 1,515,301 | 13.9 | 20.2 | 79
Chicago | 1,099,850 | 7.1 | 2.5 | 140
Philadelphia | 1,046,964 | 6.1 | 0.3 | 132
Brooklyn | 838,547 | 8.7 | 2.5 | 72
St. Louis | 451,770 | 11.8 | 8.2 | 72
Boston | 448,477 | 6.6 | 5.0 | 80
Cincinnati | 305,891 | 8.5 | 4.1 | 112
San Francisco | 298,997 | 9.9 | 41.4 | 61
Cleveland | 270,055 | 8.7 | 5.8 | 103
Buffalo | 255,664 | 6.3 | 0.2 | 186
New Orleans | 242,039 | 54.0 | 0.4 | 37
Washington | 230,392 | 6.5 | 0.3 | 158
Montreal | 216,000 | 5.3 | 1.7 | 67
Detroit | 205,876 | 5.1 | 2.1 | 161
Milwaukee | 204,468 | 11.1 | 31.9 | 110
Toronto | 181,000 | 4.0 | 4.1 | 100
Minneapolis | 164,738 | 16.5 | 6.3 | 75
Louisville | 161,129 | 11.9 | 5.9 | 74
Rochester | 133,896 | 5.4 | 11.4 | 66
St. Paul | 133,156 | 12.7 | 4.2 | 60
Providence | 132,146 | 9.4 | 62.4 | 48
Indianapolis | 105,436 | 35.6 | 7.6 | 71
Allegheny | 105,287 | 7.0 | 0 | 238
Columbus | 88,150 | 11.5 | 6.4 | 78
Worcester | 84,655 | 8.9 | 89.4 | 59
Toledo | 81,434 | 18.6 | 9.4 | 72
Lowell | 77,696 | 9.2 | 22.9 | 66
Nashville | 76,168 | 14.9 | 0.8 | 146
Fall River | 74,398 | 14.9 | 74.6 | 29
Atlanta | 65,533 | 20.0 | 89.6 | 36
Memphis | 64,495 | 11.9 | 3.7 | 124
Quebec | 63,000 | 10.4 | 0 | 160
Dayton, O. | 61,220 | 20.0 | 3.8 | 47
Camden, N. J. | 58,313 | . . . | . . . | 131
Des Moines, Ia. | 50,093 | 20.0 | 60.0 | 55
Ottawa, Ont. | 44,000 | 4.2 | 0 | 130
Yonkers, N. Y. | 32,033 | 12.0 | 82.4 | 68
Newton, Mass. | 24,379 | 5.5 | 67.4 | 40
Madison, Wis. | 13,426 | 11.0 | 31.0 | 40
Albany, N. Y. | 98,000 | . . . | 0.4 | 162
New Bedford, Mass. | 55,000 | . . . | . . . | 99
Springfield, Mass. | 49,299 | . . . | . . . | 87
Holyoke, Mass. | 40,000 | . . . | . . . | 77
-------------------+-----------+----------+-------+-----------
-------------------+-------+-----------+-----------
| |Consumption|Consumption
| Per | per | per
|Cent of| Inhabitant| Inhabitant
| Taps | Daily, | Daily,
|Metered| Gallons. |Gallons.
-------------------+-------+-----------+-----------
| 1895. | 1895. | 1900.
-------------------+-------+-----------+-----------
New York | 27.0 | 100 | 115
Chicago | 2.8 | 139 | 190
Philadelphia | 0.74 | 162 | 229
Brooklyn | 1.9 | 89 | . . .
St. Louis | 7.4 | 98 | 111
Boston | 5.2 | 100 | 143
Cincinnati | 6.5 | 35 | 121
San Francisco | 28.0 | 63 | 73
Cleveland | 4.5 | 142 | 175
Buffalo | 0.85 | 271 | 262
New Orleans | . . . | 35 | 48
Washington | 1.5 | 200 | 174
Montreal | 1.6 | 83 | . . .
Detroit | 8.2 | 152 | 156
Milwaukee | 51.0 | 101 | 84
Toronto | 3.7 | 100 |
Minneapolis | 16.0 | 88 | 93
Louisville | 6.6 | 97 | . . .
Rochester | 18.0 | 71 | 83
St. Paul | 1.7 | 60 | 51
Providence | 74.0 | 57 | 54
Indianapolis | 7.1 | 74 | 79
Allegheny | 7.1 | 247 | . . .
Columbus | 9.3 | 127 | 183
Worcester | 90.0 | 66 | 67
Toledo | 35.0 | 70 | 59
Lowell | 33.0 | 82 | 83
Nashville | 24.0 | 139 | 140
Fall River | 82.0 | 35 | 35
Atlanta | 99.0 | 42 | 61
Memphis | 4.6 | 100 | 98
Quebec | 0 | 170 | . . .
Dayton, O. | 24.0 | 50 | 62
Camden, N. J. | 0 | 200 | 185
Des Moines, Ia. | 42.6 | 43 | 48
Ottawa, Ont. | 0 | 0 | . . .
Yonkers, N. Y. | 99.8 | 100 | 76
Newton, Mass. | 77.3 | 65 | 62
Madison, Wis. | 61.0 | 52 | 44
Albany, N. Y. | 12.3 | . . . | 192
New Bedford, Mass. | 15.4 | . . . | 101
Springfield, Mass. | 31.9 | . . . | 88
Holyoke, Mass. | 5.82 | . . . | [4]103
-------------------+-------+-----------+------------
[4] Estimated.
=152. Actual Daily Consumption in Foreign Cities.=—It has been for
a long time a well recognized fact that the daily use of water in
American municipalities is far greater per inhabitant than in European
cities. It is difficult to explain the marked difference, but it is
probably due in large part to the more extravagant general habits of
the American people. Examinations in a number of cases have shown that
the actual domestic use of water, at least in some of the American
cities, is not very different from that found in corresponding foreign
cities. Table II exhibits the consumption of water in European cities,
as compiled from various sources and given by Turneaure and Russell.
TABLE II.
---------------------------------------+-------------+-----------
| |Consumption
| Estimated | per Capita
City. | Population. | Daily,
| | Gallons.
---------------------------------------+-------------+-----------
England, 1896-97:[5] | |
London | 5,700,000 | 42
Manchester | 849,093 | 40
Liverpool | 790,000 | 34
Birmingham | 680,140 | 28
Bradford | 436,260 | 31
Leeds | 420,000 | 43
Sheffield | 415,000 | 21
Nottingham | 272,781 | 24
Brighton | 165,000 | 43
Plymouth | 98,575 | 59
Germany, 1890 (Lueger): | |
Berlin | 1,427,200 | 18
Breslau | 330,000 | 20
Cologne | 281,700 | 34
Dresden | 276,500 | 21
Düsseldorf | 144,600 | 25
Stuttgart | 139,800 | 26
Dortmund | 89,700 | 78
Wiesbaden | 62,000 | 20
France, 1892 (Bechmann): | |
Paris | 2,500,000 | 53
Marseilles | 406,919 | 202
Lyons | 401,930 | 31
Bordeaux | 252,654 | 58
Toulouse | 148,220 | 26
Nantes | 125,000 | 13
Rouen | 107,000 | 32
Brest | 70,778 | 3
Grenoble | 60,855 | 264
Other countries, 1892-96 (Bechmann): | |
Naples | 481,500 | 53
Rome | 437,419 | 264
Florence | 192,000 | 21
Venice | 130,000 | 11
Zurich | 80,000 | 60
Geneva | 70,000 | 61
Amsterdam | 515,000 | 20
Rotterdam | 240,000 | 53
Brussels | 489,500 | 20
Vienna | 1,365,000 | 20
St. Petersburg | 960,000 | 40
Bombay | 810,000 | 61
Sidney | 423,600 | 38
Buenos Ayres | 680,000 | 34
---------------------------------------+-------------+-----------
[5] Compiled, except the figures for London, by Hazen. _Engineering
News_, 1899, XLI. p. 111.
These foreign averages, with three exceptions, represent reasonable
quantities of water used, and they have been confirmed as reasonable by
many special investigations made in this country.
=153. Variations in Rate of Daily Consumption.=—The preceding
observations are all based upon an average total consumption found by
dividing the total annual consumption by the number of days in the
year. This is obviously sufficient in a determination of the total
supply needed, but it is not sufficient in those matters which involve
a rate of supply during the different hours of the day, or the amount
of the supply for the summer months as compared with those of the
winter. As a general rule the greatest supply will be required during
the hot summer months when lawn- and street-sprinkling is most active.
It appears from observations made in a considerable number of the
large cities of the United States that the maximum monthly average
consumption may run from about 110 to nearly 140 per cent of the
monthly average throughout the year. As an approximate value only, it
may be assumed for ordinary purposes that the maximum monthly demand
will be 125 per cent of the average.
The daily rate taken throughout the year is considerably more variable
than the monthly. There are days in some portions of the year when
consumption by hotels and industrial activities is at a minimum. On the
other hand, there are other days when those activities are at a maximum
and the total draft will be correspondingly high. Experience has
shown that the maximum total draft may vary from about 115 to nearly
200 per cent of the average. It is permissible, therefore, to take
approximately for general purposes the maximum total daily consumption
as 150 per cent of the average. Manifestly any total consumption will
have an hourly rate which may vary greatly from the early morning
hours, when the draft should be almost nothing, to the forenoon hours
on certain days of the week, when the draft is a maximum. These
variations have frequently been investigated, and it has been shown
that the maximum rate per hour of a maximum day may sometimes rise
higher than 300 per cent of the average hourly rate for the year. These
considerations obviously attain their greatest importance in connection
with the capacity of the plant, either power or gravity, from which the
city directly draws its supply. The hourly capacity of the pumps or
steam-plant furnishing the supply need not necessarily be equal to the
maximum, since storage-reservoirs may be and usually are used; but the
capacity of the pipe system leading from such storage-reservoirs must
be equal to the maximum hourly rate required.
=154. Supply of Fire-streams.=—The draft on a water-supply for
fire-extinguishing purposes may have an important influence upon
the hourly rate of consumption. These observations are particularly
pertinent in connection with the water-supply of small cities where the
draft of fire-engines may be considered a large percentage of the total
hourly consumption. It is obviously impossible to assign precisely the
number of fire-streams which may be required simultaneously in a city
having a given population, but experiences of a considerable number of
civil engineers furnish reasonable bases on which such estimates may be
made. Table III exhibits such estimates as made by the civil engineers
indicated. It is given by Mr. Emil Kuichling in the Transactions of the
American Society of Civil Engineers for December, 1897. Probably no
more reasonable estimate can be now presented.
TABLE III.
TABLE EXHIBITING ESTIMATED NUMBER OF FIRE-STREAMS REQUIRED
SIMULTANEOUSLY IN AMERICAN CITIES OF VARIOUS MAGNITUDES.
---------------+-------------------------------------------------
| Number of Fire-streams Required Simultaneously.
Population of +-----------+-----------+-----------+-------------
Community. | 1 | 2 | 3 | 4
| Freeman. | Shedd. | Fanning. | Kuichling.
---------------+-----------+-----------+-----------+-------------
1,000 | 2 to 3 | .. | .. | 3
4,000 | .. | .. | 7 | 6
5,000 | 4 to 8 | 5 | .. | 6
10,000 | 6 to 12 | 7 | 10 | 9
20,000 | 8 to 15 | 10 | .. | 12
40,000 | 12 to 18 | 14 | .. | 18
50,000 | .. | .. | 14 | 20
60,000 | 15 to 22 | 17 | .. | 22
100,000 | 20 to 30 | 22 | 18 | 23
150,000 | .. | .. | 25 | 34
180,000 | .. | 30 | .. | 38
200,000 | 30 to 50 | .. | .. | 40
250,000 | .. | .. | .. | 44
300,000 | .. | .. | .. | 48
---------------+-----------+-----------+-----------+-------------
The discharge of each fire-stream will of course vary with its diameter
and the pressure at the fire-engine, but as an average it is reasonable
to assume that each stream will discharge 250 gallons per minute. The
quantity of water required, therefore, to supply the estimated number
of streams given in Table III is found by simply multiplying the number
of those streams by 250, to ascertain the total number of gallons
consumed per minute. If _x_ is the number of thousand inhabitants in
any city, and if _y_ represents the required number of streams, then
Mr. Kuichling deduces the following formulæ for _y_ by the use of the
preceding tables, i.e., these formulæ express the results given in the
preceding table as nearly as simple forms of formulæ permit.
___
{ _y_ min. = 1.7√_x_ + 0.033_x_,}
{ }
For Freeman’s data: { _x_ } (1)
{ _y_ max. = --- + 10. }
{ 5 }
____ ___
For Shedd’s data: _y_ = √5_x_ = 2.24 √_x_. (2)
_x_
For Fanning’s data: _y_ = --- + 9. (3)
10
___
For the author’s data: _y_ = 2.8 √_x_. (4)
While for the average ordinary consumption of water, expressed in
gallons per head and day, _q_, Mr. Coffin’s formula, as given in his
paper previously cited, may be taken
_q_ = 40_x_⁰˙¹⁴. (5)
By combining equation (5) with equation (4), remembering that the
maximum rate of consumption is usually about 1.5 times the average,
the total draft in gallons per minute upon the discharging system at
the time of a conflagration will become as follows:
___ 3 40 × 1000
_Q_ = 250(2.8 √_x_) + ---- ---------- _x_¹˙¹⁴
2 1440
( ___ _x_¹˙¹⁴)
= 250(2.8√_x_ + --------) (6)
( 6 )
This maximum rate of consumption during a conflagration does not affect
the total supply of a large city like New York, Boston, or Chicago, but
it may become of relatively great importance in a small city or town.
In a large city this draft may and frequently does tax the capacity of
a small district of the discharging system. In designing such systems,
therefore, even for large cities, it is necessary to insure all
districts against a small local supply when a large one may pressingly
be needed.
CHAPTER XV.
=155. Waste of Water, Particularly in the City of New York.=—The
quantity of water involved in designing a water-supply for cities and
towns is much larger than that which is actually needed. The experience
of civil engineers in many cities, both in this country and in Europe,
shows conclusively that the portion of water actually wasted or running
away without serving any purpose will usually run from 30 to 50 per
cent of the total amount brought to the distributing system. In the
city of New York there is strong reason to believe that the wastage
is not less than two thirds of the total quantity supplied. It is
frequently assumed that both the quantities supplied and the quantities
uselessly wasted in New York are larger than in other places. As a
matter of fact those quantities are actually smaller than in some other
large cities. While the supply per inhabitant in New York City is much
larger than should be required, the use of water by its citizens is not
extravagant when gauged by the criterion of use in other large cities.
This question was most carefully and exhaustively investigated in 1899
and the early part of 1900 by Mr. John R. Freeman of Boston, acting for
the comptroller of the city of New York.
The usual wastes of a water-supply system may be distributed under six
principal heads. First, leaky house-plumbing; second, and “possibly
first in order of magnitude,” leaky service-pipes connecting the
house pipe system with street-mains; third, leaving water-cocks open
unnecessarily; fourth, leaky joints in street-mains or pipes; fifth,
possibly pervious beds and banks of distributing-reservoirs; sixth,
stealing or “unlawful diversion” of water through surreptitious
connections.
The sixth item is probably an extremely small one in New York, although
instances of that kind of waste have been found. It is an old wastage
known as far back in time as the ancient Roman water-supply. The second
and third items probably constitute the bulk of the wastage in this
city.
=156. Division of Daily Consumption in the City of New York.=—In the
course of his search for the various sources of consumption, Mr.
Freeman concluded from his examinations and from the use of the various
means placed at his command for measuring the daily consumption between
December 2nd and December 5th, 1899, and December 8th and December
15th, 1899, that the average daily consumption could be divided as
follows:
Gallons per Inhabitant
per Day.
Probable average amount really used 40
Assumed incurable waste 10}
Curable waste, probably 65} 75
----
Daily uniform rate of delivery by
Croton Aqueduct 115
In his investigations Mr. Freeman had the elevation of water in the
Central Park reservoir carefully observed every six minutes throughout
the twenty-four hours. At the same time the uniform flow through the
new Croton Aqueduct was known as accurately as the flow through such
a conduit can be gauged at the present time. Knowing, therefore, the
concurrent variation of volume in the Central Park reservoir supplied
by the new Croton Aqueduct and the rate of flow in that aqueduct, the
consumption of water per twenty-four hours would be known with the same
degree of accuracy with which the flow in the aqueduct is measured. It
was found by these means that the actual consumption between the hours
of 2 and 4 A.M. was at the rate of 94 gallons per inhabitant per day,
although the actual use at that time was as near zero as it is possible
to approach during the whole twenty-four hours. Nearly all of that rate
of consumption represents waste.
Summing up the whole matter in the light of his investigations, Mr.
Freeman made the following as his nearest estimate to the actual
consumption of the daily supply of water of New York City:
Gallons per
Inhabitant
ACTUAL USE: per Day.
Domestic (average) 12 - 20
Manufacturing and commercial 20 - 30
City buildings, etc. 2 - 4
Fires, street flushing and sprinkling 0.4 - 0.7
-----------
Total 34 - 55
INCURABLE WASTE (probabilities):
Leaks in mains 1 - 2
Leaks in old and abandoned service-pipes 1 - 2
Poor plumbing, all taps metered and closely inspected 2 - 3
Careless and wilful wastes 1 - 2
Under-registry of meters 1 - 1
-------
Total incurable waste and under-registry 6 -10
========
Minimum use and waste 40 -65
NEEDLESS WASTE:
Leaks in street-mains (a guess) 15- 10
Leaks in service-pipes between houses and street-mains 15- 10
(a guess)
Defective plumbing (a guess) 25- 15
Careless and wilful opening of cocks (a guess) 17- 14
To prevent freezing in winter and for cooling in summer 3 - 1
--------
Total needless waste 75- 50
========
Total consumption 115-115
=157. Daily Domestic Consumption.=—The quantity assigned in the
preceding statement to domestic use is confirmed by the abundant
experience in other cities where services are carefully metered, as in
Fall River, Lawrence, and Worcester, Mass., and in Woonsocket, R. I.,
where measurements by meters show that the domestic consumption has
varied from 11.2 to 16.3 gallons per inhabitant per day. Furthermore,
annual reports of the former Department of Public Works and the
present Department of Water-supply for the City of New York show that
during the years 1890 to 1898 such meters as have been used in the
territory supplied by the Croton and the Bronx aqueducts indicate a
daily consumption varying from 13.8 to 24.2 gallons per inhabitant
per day. The same character of confirmatory evidence can be applied
to the quantities assigned to manufacturing and commercial uses, city
buildings and fires, street flushing and sprinkling.
=158. Incurable and Curable Wastes.=—The items composing incurable
waste, unfortunately, cannot be so definitely treated. It is perfectly
well known, however, among civil engineers, that a large amount of
leakage takes place from corporation cocks, which are those inserted
in the street-mains to form the connection between the latter and the
house service-pipes. Again, many of these service-pipes are abandoned
and insufficiently closed, or not closed at all, leaving constantly
running streams whose continuous subsurface discharges escape detection
and frequently find their way into sewers. Water-pipes which have been
laid many years frequently become so deeply corroded as to afford
many leaks and sometimes cracks. Doubtless there are many portions of
a great distributing system, like that in New York City, which need
replacing and afford many large leaks, but undiscoverable from the
surface. Many lead joints of street-mains also become leaky with age,
while others are leaky when first laid in spite of inspection during
construction. Just how much these items of waste would aggregate it
is impossible accurately to state, but from careful observations made
in other places 5 to 10 gallons per day per head of population seems
reasonable. A three-year-old cast-iron fire-protection pipe 5.57 miles
long and mainly 16 inches in diameter, under an average pressure of 114
pounds per square inch, was tested in Providence in 1900 and showed a
leakage at lead joints only of 446 gallons per mile per twenty-four
hours, which was equivalent to .22 gallon per foot of lead joint per
twenty-four hours. Further tests in 1900 of seven lines of new pipe
laid by the Metropolitan Board of Boston, and tested under pressures
varying from 50 to 150 pounds per square inch by Mr. F. P. Stearns,
chief engineer, and Mr. Dexter Brackett, engineer of Distribution
Department, and having an aggregate length of 51.4 miles with diameters
ranging from 16 to 48 inches, gave an average leakage per lineal foot
of pipe in gallons per twenty-four hours ranging from .6 to 3.7 gallons
(average 2.47 gallons), equivalent to an average leakage of 3 gallons
per twenty-four hours per lineal foot of lead joint. The possible rates
of leakage from street-mains are to be applied to a total length of
pipe-lines of 833 miles for the boroughs of Manhattan and the Bronx.
The borough of Brooklyn has somewhat over 600 miles of street-mains,
but they are not to be considered in connection with the Croton and
Bronx water-supply.
All these considerations either confirm or make reasonable the
estimates of the various items of actual use and waste set forth by Mr.
Freeman.
=159. Needless and Incurable Waste in City of New York.=—Concisely
summing up his conclusions, it may be stated that in the year 1899 the
average consumption per inhabitant of the boroughs of Manhattan and the
Bronx was 115 gallons; of these 115 gallons the needless average waste
may be 65 gallons, while the incurable or necessary waste may probably
be taken at 10 gallons per inhabitant per day. It is further probable
that the total underground leakage in New York City is to be placed
somewhere between 20 to 35 gallons per inhabitant per day.
=160. Increase in Population.=—The total volume of daily supply to
any community is determined by the population; but the population is
as a whole constantly increasing. It becomes necessary, therefore, to
estimate the capacity of a water-supply system in view of the future
population of the city to be supplied. No definite rule can be set
as to the future period for which the capacity of any desired system
is to be estimated. It may be stated that no shorter period of time
than probably ten years should be considered, indeed it is frequently
prudent to provide for a period of not less than twenty years, and it
may sometimes be necessary or advisable to consider a possible source
of supply for even fifty years. Provision must be made not only for the
present population, but for the increase during those periods of time,
or at least for the possible development that may be needed.
The increase in population of cities will obviously vary for different
locations with the character of the occupations followed and with
the development of such important factors of industrial life as
railroad connections, facilities for marine commerce, the capacity for
development of the surrounding country, and other influences which aid
in the increase of commerce and industrial activity and the growth
of population. It has been observed, as a matter of experience, that
large cities generally reach a point where their subsequent increase of
population is represented by a practically constant percentage, the
value of that percentage depending upon local considerations. In 1893,
when it was desired to estimate the future population of London for as
much as forty years, it was found that the increase for the ten years
from 1881 to 1891 was 18.2 per cent, with an average of about 20 per
cent for several previous decades. It could, therefore, be reasonably
estimated for the city of London that its population at the end of any
ten-year period would be 18.2 per cent greater than its population
at the beginning of that period. In Appendix 1 of the report of the
Massachusetts State Board of Health upon the Metropolitan water-supply
for the city of Boston made in 1895, the increases for the two ten-year
periods 1870-1880 and 1880-1890 were 6 per cent and 9.6 per cent
respectively for the city proper, but for the population within a
ten-mile radius from the centre of the city they were 28.7 per cent
and 33.7 per cent respectively. The corresponding percentages for the
cities of New York, Philadelphia, and Chicago for the same periods are
as shown in the following tabular statement:
------------+-----------------------------+------------------------
| Population. |Percentages of Increase.
------------+---------+---------+---------+---------+--------------
| 1870. | 1880. | 1890. |1870-80. | 1880-90.
------------+---------+---------+---------+---------+--------------
New York |1,626,119|2,131,051|2,821,802| 31 | 32
Philadelphia| 726,247| 921,458|1,162,577| 27 | 26
Chicago | 310,996| 550,618|1,075,158| 77 | 95[6]
------------+---------+---------+---------+---------+--------------
[6] Includes added territory.
Obviously every estimate of this kind must be made upon the merits
of the case under consideration. The probable increase of population
for any particular city is sometimes estimated by considering the
circumstances of growth of some other city of practically the
same size, and if possible with the same commercial industries or
residential environment, or making suitable allowances for variations
in these respects. Since it is imperative to secure as accurate
estimates as practicable, both methods or other suitable methods should
be employed, in order that the results may be confirmed or modified by
comparison. In every case the supply system should be designed to meet
reasonable estimated requirements for the longest practicable future
period, preferably not less than twenty years.
=161. Sources of Public Water-supplies.=—One of the most important
features of a proposed water-supply is its source, since not only
the potable qualities are largely affected by it, but frequently
the amount also. The two general classes into which potable waters
are divided in respect to their sources are surface-waters and
ground-waters. Surface-waters include rain-water collected as it falls,
water from rivers or smaller streams, and water from natural lakes;
they are collected in reservoirs and lakes or impounding reservoirs.
Ground-waters are those collected from springs, from ordinary or
shallow wells, from deep or artesian wells, and from horizontal
galleries, like those sometimes constructed near and parallel to
subsurface streams or in subsurface bodies of water, affording
opportunity for filtration from the latter through sand or other open
materials to them.
The quality of water will obviously be affected by the kind of material
through which it percolates or flows. Surface-waters, flowing over
the surface of the ground or percolating but a short distance below
the surface, naturally have contact with vegetable matter, unless
they are collected in a country where the soil is sandy and where the
vegetation is scarce. If such waters flow through swamps or over beds
of peat or other similar vegetable mould or soil, they may become so
impregnated with organic matter or so deeply colored by it that they
are not available for potable purposes. Ground-waters, on the other
hand, possess the advantage of having flowed through comparatively
great depths of sand or other earthy material essentially free of
organic matter. They may, however, in some locations, carry prejudicial
amounts of objectionable salts in solution, rendering them unfit for
use. As a rule, ground-waters are apt to be of better quality than
surface-waters, but they do not generally stand storage in reservoirs
as well as surface potable waters. It is advisable to store them in
covered reservoirs from which the light is excluded, rather than in
open reservoirs. They are sometimes impregnated with salts of iron to
such an extent as to make it necessary to resort to suitable processes
for their removal, and they are also occasionally found so hard as to
require the employment of methods of softening them.
Both sources of supply are much used in the United States. Table IV
shows the percentages of the various classes of supplies as found in
this country during the year 1897; the total number of supplies having
been at that time nearly 4000.
TABLE IV.
WATER-SUPPLIES OF THE UNITED STATES.
Source. Per Cent of Total.
{Rivers 25
Surface-waters: {Lakes 7
{Impounding reservoirs 6
{Combinations .5
----- 38.5
{Shallow wells 26
{Artesian wells 10
Ground-waters: {Spring 15
{Galleries and tunnels 1
{Combinations 2
----- 54
Surface- and {Rivers and ground-waters 6
ground-waters: {Lakes and ground-waters 1
{Impounding reservoirs and ground-waters .5
---- 7.5
-------
Total 100.0
It will be observed that a little more than one half of the supplies
are from ground-waters. The practice in connection with European public
water-supplies is different in that a considerably larger percentage of
the total is taken from ground-waters.
The original source of essentially all the water available for public
water-supplies is the rainfall. It becomes of the greatest necessity,
therefore, to secure all possible information regarding rainfall
wherever it may be necessary to construct a public water-supply. Civil
engineers and other observers have for many years maintained continuous
records of rainfall observations at various points throughout the
country, but it is within only a comparatively short time that the
number of those points has been large. Through the extension of the
work of the Weather Bureau, points of rainfall observation are now
scattered quite generally throughout all States of the Union. The
oldest observations are naturally found in connection with stations
located in the Eastern States, where the rainfall is more uniformly
distributed than in many other portions of the country. Obviously
rainfall records become of the greatest importance in those localities
like the semiarid regions of the far West where long periods of no rain
occur.
=162. Rain-gauges and their Records.=—The instrument used for the
collection of rain in order to determine the amount falling in a given
time is the rain-gauge, which may be fitted with such appliances as to
give a continuous record of the rate of rainfall. It has been found
that the location of the rain-gauge has a very important influence
upon the amount of rain which it collects. It should be placed where
wind currents around high structures in its vicinity cannot affect its
record. The top of a large flat-roofed building is a good location in
a city, although the elevation above the surface of the ground, as is
well known, affects the quantity of water collected by the gauge. The
collection will be greater at a low elevation than at a high one, in
consequence of the greater wind currents at the higher point, it being
well known that less rain will be collected where there is the most
wind, other things being equal.
[Illustration: Ordinary Rain-gauge.]
=163. Elements of Annual and Monthly Rainfall.=—In consequence of
the great variations in the rate of rainfall, not only for different
portions of the country, but at different times during the same
storm, it becomes necessary to determine various quantities such as
the maximum, minimum, and mean annual rainfall, the actual monthly
rainfall for different months of the year, and the maximum and minimum
monthly rainfall for as long a period as possible. The minimum monthly
rainfall and the minimum annual rainfall are of special importance in
connection with public water-supply and water-power questions, since
those minima will, in connection with the area of a given watershed,
determine the greatest amount of water which can be made available for
use. In entering upon the consideration of such questions, therefore,
civil engineers must inform themselves with the greatest detail as
to the characteristics of the monthly and the annual rainfall of the
locality in which their works are to be located.
[Illustration: MONTHLY VARIATIONS IN RAINFALL.
FIG. 1.]
TABLE V.
GENERAL RAINFALL STATISTICS FOR THE UNITED STATES.
----------------------------+---------+---------+---------
| | Per Cent|
| | of | Per Cent
| Mean | Summer | Driest
Station. | Yearly | and | Year to
|Rainfall.| Autumn | Mean
| | Rain to| Year.
| | Mean |
| | Yearly. |
----------------------------+---------+---------+---------
North Atlantic: | | |
Boston | 45.4 | 50 | 60
New York | 44.7 | 52 | 62
Philadelphia | 42.3 | 52 | 70
Washington | 42.9 | 51 | 69
South Atlantic: | | |
Wilmington | 53.7 | 61 | 75
Charleston | 49.1 | 61 | 48
Augusta | 48.0 | 50 | 81
Jacksonville | 54.1 | 65 | 74
Key West | 38.2 | 70 | 54
Gulf and Lower Mississippi: | | |
Montgomery | 52.5 | 42 | 76
Mobile | 62.6 | 51 | 68
New Orleans | 60.3 | 52 | 64
Galveston | 47.7 | 58 | 50
Nashville | 50.2 | 46 | 67
Ohio Valley: | | |
Pittsburg | 36.6 | 53 | 70
Cincinnati | 42.1 | 50 | 60
Indianapolis | 42.2 | 51 | 59
Cairo | 42.6 | 47 | 62
Louisville | 47.2 | 48 | 74
Lake Region: | | |
Detroit | 32.5 | 56 | 65
Cleveland | 36.6 | 54 | 71
Duluth | 30.7 | 63 | 65
Upper Mississippi Valley: | | |
St. Louis | 40.8 | 52 | 55
Chicago | 34.0 | 54 | 66
Milwaukee | 31.0 | 55 | 66
Madison | 33.2 | 58 | 39
The Plains: | | |
Omaha | 31.4 | 63 | 57
North Platte | 18.1 | 61 | 56
Denver | 14.3 | 48 | 59
Cheyenne | 12.7 | 55 | 39
The Plateau: | | |
Tucson | 11.7 | 65 | 44
Santa Fé | 14.6 | 69 | 53
Salt Lake City | 18.8 | 39 | 55
Walla Walla | 15.4 | 38 | 46
Pacific Coast: | | |
Astoria | 77.0 | 33 | 64
Portland | 46.2 | 31 | 67
Sacramento | 19.9 | 16 | 42
San Francisco | 23.4 | 17 | 51
Los Angeles | 17.2 | 15 | 33
San Diego | 9.7 | 18 | 30
----------------------------+---------+---------+---------
| | |
| | |
| Per Cent| Per Cent| Number
Station. | Two | Three | of
| Driest | Driest | Years’
| Years. | Years. | Record.
| | |
| | |
----------------------------+---------+---------+---------
North Atlantic: | | |
Boston | 70 | 80 | 79
New York | 77 | 80 | 61
Philadelphia | 75 | 80 | 72
Washington | 71 | 74 | 45
South Atlantic: | | |
Wilmington | 80 | 81 | 26
Charleston | 55 | 62 | 89
Augusta | 88 | 87 | 27
Jacksonville | 77 | 83 | 27
Key West | 61 | 73 | 49
Gulf and Lower Mississippi: | | |
Montgomery | 80 | 83 | 24
Mobile | 75 | 78 | 26
New Orleans | 75 | 77 | 26
Galveston | 65 | 72 | 26
Nashville | 73 | 83 | 32
Ohio Valley: | | |
Pittsburg | 78 | 85 | 54
Cincinnati | 72 | 71 | 62
Indianapolis | 76 | 82 | 27
Cairo | 75 | 81 | 25
Louisville | 81 | 85 | 25
Lake Region: | | |
Detroit | 72 | 79 | 46
Cleveland | 74 | 81 | 41
Duluth | 81 | 88 | 26
Upper Mississippi Valley: | | |
St. Louis | 65 | 75 | 60
Chicago | 80 | 86 | 30
Milwaukee | 74 | 73 | 53
Madison | 58 | 68 | 28
The Plains: | | |
Omaha | 63 | 70 | 27
North Platte | 67 | 72 | 22
Denver | 71 | 77 | 27
Cheyenne | 62 | 75 | 27
The Plateau: | | |
Tucson | 79 | 80 | 19
Santa Fé | 63 | 66 | 37
Salt Lake City | 64 | 74 | 29
Walla Walla | 81 | 86 | 27
Pacific Coast: | | |
Astoria | 68 | 77 | 34
Portland | 76 | 79 | 27
Sacramento | 67 | 84 | 47
San Francisco | 73 | 78 | 47
Los Angeles | 48 | 59 | 24
San Diego | 54 | 61 | 47
----------------------------+---------+---------+---------
The diagram Fig. 1 and Table V are constructed from data given in
the bulletins of the Weather Bureau and exhibit some of the general
features of the rainfall for different points throughout this country.
The heavy lines of the diagram show the average monthly precipitation
at the points indicated, for periods of a considerable number of
years, as shown in the table. It will be observed that the rainfall is
comparatively uniform in the North Atlantic States but quite variable
on the Pacific coast, as well as in the Mississippi and Missouri
valleys and west of those valleys.
=164. Hourly or Less Rates of Rainfall.=—Although not often of great
importance in connection with public water-supply systems, it is
sometimes necessary to possess data regarding maximum hourly (or less)
rates of precipitation in connection with sewer or drainage work.
The earlier records give exaggerated reports of maximum rates of
rainfall, although that rate varies rapidly with the time. Throughout
a rain-storm the rate of precipitation is constantly varying and
the maximum rate seldom if ever extends over a period equal to a
half-hour; usually it lasts but a few minutes only. In this country
an average rate of 1 inch per hour, extending throughout one hour,
is phenomenal, although that rare amount is sometimes exceeded. A
maximum rate of about 4 inches per hour, lasting 15 to 30 minutes, is,
roughly speaking, about as high as any precipitation of which we have
reliable records. The waste ways or other provisions for the discharge
of surplus or flood-waters of the Metropolitan Water-supply of Boston
are designed to afford relief for a total precipitation of 6 inches
in twenty-four hours. It is safe to state that an excess of that
accommodation will probably never be required.
=165. Extent of Heavy Rain-storms.=—In all engineering questions
necessitating the consideration of these great rain-storms it is
necessary to remember that their extent is frequently much greater
than the areas of watersheds usually contemplated in connection with
water-supply work. The late Mr. James B. Francis found in the great
storm of October, 1869, which had its maximum intensity in Connecticut,
that the area over which 6 inches or more of rain fell exceeded 24,000
square miles, and that the area over which a depth of 10 inches or more
fell was 519 miles. Again, in the New England storm of February, 1886,
6 inches or more of rain fell over an area of at least 3000 square
miles. Storm records show that as much as 8 or 10 inches in depth have
fallen over areas ranging from 1800 to 500 square miles, respectively,
in a single storm.
=166. Provision for Low Rainfall Years.=—The capacity of any public
water-supply must evidently be sufficient to meet not only the general
exigencies of the year of lowest rainfall, but also the conditions
resulting from the driest periods of that year. It is customary among
civil engineers to consider months as the smaller units of a dry year.
It is necessary, therefore, to examine not only the annual rainfalls
but the monthly rates of precipitation during critical years, i.e.,
usually during dry years.
It is impossible to determine absolutely the year of least rainfall
which may be expected, but evidently the longer the period over which
observations have extended the nearer that end will be attained. It
is sometimes assumed that the lowest annual rainfall likely to be
expected in a long period of years is 80 per cent of the average annual
rainfall for the same period. Or, it is sometimes assumed that the
average rainfall for the lowest two or three consecutive years will be
80 per cent of the average for the entire period, and that the year
of minimum rainfall may be expected to yield two thirds of the annual
average precipitation. Such features will necessarily vary with the
location of the district considered. Conclusions which may be true for
the New England or northern Atlantic States probably will not hold for
the south Atlantic and Gulf States. Data for such conclusions must
be obtained from the rainfall of the locality considered. Table VI
exhibits the comparative monthly rainfall which J. T. Fanning suggests
may be used approximately for the average Atlantic coast districts.
TABLE VI.
+-----------+-----------+------------+-----------+
| | Mean | | Probable |
| | Monthly | Respective | Depth in |
| | Rainfall, | Ratios. | Inches of |
| | Inches. | | Actual |
| | | | Rainfall. |
+-----------+-----------+------------+-----------+
| January | 4 × 1.65 = 6.6 |
| February | 4 × 1.50 = 6.0 |
| March | 4 × 1.65 = 6.6 |
| April | 4 × 1.45 = 5.8 |
| May | 4 × .85 = 3.4 |
| June | 4 × .75 = 3.0 |
| July | 4 × .35 = 1.4 |
| August | 4 × .25 = 1.0 |
| September | 4 × .30 = 1.2 |
| October | 4 × .45 = 1.8 |
| November | 4 × 1.20 = 4.8 |
| December | 4 × 1.60 = 6.4 |
+-----------+------------------------------------+
If the average monthly rainfall throughout the year were one inch, the
values of the ratios would show the actual monthly precipitation. In
general the table would be used by dividing the total yearly rainfall
by 12, and then multiplying that monthly average by the proper ratio
taken from the table opposite the month required. Such tables should
only be used for approximate purposes and when actual rainfall records
are not available for the district considered.
=167. Available Portion of Rainfall or Run-off of Watersheds.=—If the
public water-supply is to be drawn from a stream where the desired
rainfall records exist, it is necessary to know what portion of the
rainfall, either in the driest or in other years, may be available.
This is one of the departments of the hydraulics of streams for which
much data yet remain to be secured. The watersheds or areas drained
by some streams, like the Sudbury River of the Boston, and the Croton
of the New York water-supply, have, however, been studied with
sufficient care to give reliable data. The amount of water flowing in
a stream from any watershed for a given period, as a year, is called
the annual “run-off” of the watershed, and it is usually expressed
as a certain percentage of the total rainfall on the area drained.
For certain purposes it is sometimes more convenient to express the
run-off from the watershed as the number of cubic feet of water per
second per square mile of area. Table VII, taken from Turneaure and
Russell, exhibits run-off data for a considerable number of streams in
connection with both average and minimum rainfalls.
TABLE VII.
STATISTICS OF THE FLOW OF STREAMS.
-----------------+---------+-------+----------------+-----------------
| Area | | Average Yearly.|Year of Minimum
Stream. | Drained,| | | Flow.
| Square | Years.+-----+-----+----+-----+------+----
| Miles. | |Rain,|Flow,|Per |Rain,|Flow,|Per
| | |Inch.|Inch.|Cent|Inch.|Inch.|Cent
-----------------+---------+-------+-----+-----+----+-----+-----+----
Sudbury | 75.2 |1875-97|45.77|22.22|48.6|32.78|11.19|34.1
Cochituate | 18.87|1863-96|47.08|20.33|43.2|31.20| 9.76|31.3
Mystic | 26.9 |1878-96|43.79|19.96|45.6|31.22| 9.32|29.8
Connecticut |10,234 |1871-85|44.69|25.25|56.5|40.02|18.25|45.6
Croton | 338 |1870-94|48.38|24.57|50.8|38.52|14.54|37.8
Upper Hudson | 4,500 |1888-96|39.70|23.36|59.0|33.49|17.46|52.2
Genesee | 1,060 |1894-96|39.82|12.95|32.5|31.00| 6.67|21.5
Passaic | 822 |1877-93|47.08|25.44|54.0|35.64|15.23|42.7
Upper Mississippi| 3,265 |1885-99|26.57|4.90 |18.4|22.86| 1.62| 7.1
=================+=========+=======+=====+=====+====+=====+=====+====
| | | Average for |Average for June
| Area | |December to May.| to November.
Stream. | Drained,| | |
| Square | Years.+-----+-----+----+-----+-----+----
| Miles. | |Rain,|Flow,|Per |Rain,|Flow,| Per
| | |Inch.|Inch.|Cent|Inch.|Inch.|Cent
-----------------+---------+-------+-----+-----+----+-----+-----+----
Sudbury | 75.2 |1875-97|22.98|17.52|76.0|22.61| 4.70|20.8
Cochituate | 18.87|1863-96|22.97|14.87|64.7|24.10| 5.46|22.7
Mystic | 26.9 |1878-96|22.11|15.12|68.4|21.66| 4.84|22.4
Connecticut |10,234 |1871-85|20.13|17.95|89.1|24.56| 7.30|29.7
Croton | 338 |1870-94|23.39|17.81|76.1|24.99| 6.76|27.0
Upper Hudson | 4,500 |1888-96|18.20|16.23|89.0|21.50| 7.13|33.0
Genesee | 1,060 |1894-96|19.58|10.20|52.2|20.24| 2.75|13.6
Passaic | 822 |1877-93|22.47|18.22|81.1|24.39| 7.19|29.5
-----------------+---------+-------+-----+-----+----+-----+-----+----
The information to be drawn from this table is sufficient to give clear
and general relations between the recorded precipitation and run-off.
The percentage of run-off is seen to vary quite widely, but as a rule
it is materially less for the year of minimum flow than for the average
year. That feature of the table is an expression of the general law,
other things being equal, that the smaller the precipitation the less
will be the percentage of run-off. A number of influences act to
produce that result. During a year of great precipitation the earth is
more nearly saturated the greater part of the time, and hence when rain
falls less of it will percolate into the ground and more of it will run
off. Again, if the ground is absolutely dry, a certain amount of rain
would have to fall before any run-off would take place. The area and
shape of a watershed will also affect to some extent the flow of the
stream which drains it. A larger run-off would reasonably be expected
from a long narrow watershed than from one more nearly circular in
outline. The greater the massing of the watershed, so to speak, the
more opportunity there is for the water to be held by the ground and
the less would be the run-off.
TABLE VIII.
AVERAGE YIELD OF SUDBURY WATERSHED, 1875-1899, INCLUSIVE,
VARIOUSLY EXPRESSED.
(Area of watershed, 75.2 square miles.)
---------+--------------------+-------------------------------
| Per Square Mile. | Rainfall.
Month. +--------------------+----------+----------+---------
|Cubic Feet |Million |Collected,|Per Cent | Total,
|per Second.|Gallons |Inches. |Collected.| Inches.
| |per Day.| | |
---------+-----------+--------+----------+----------+---------
January | 1.937| 1.252| 2.233| 51.6| 4.33
February | 2.904| 1.877| 3.050| 71.7| 4.26
March | 4.489| 2.901| 5.175| 117.4| 4.41
April | 3.124| 2.019| 3.485| 107.5| 3.24
May | 1.680| 1.086| 1.936| 58.1| 3.33
June | .735| .475| .821| 28.0| 2.93
July | .305| .197| .352| 9.3| 3.77
August | .478| .309| .551| 13.3| 4.16
September| .376| .243| .419| 13.0| 3.23
October | .829| .536| .956| 21.9| 4.37
November | 1.474| .953| 1.645| 39.0| 4.22
December | 1.612| 1.042| 1.859| 51.9| 3.58
+-----------+--------+----------+----------+--------
Year | 1.655| 1.070| 22.482| 49.1| 45.83
---------+-----------+--------+----------+----------+--------
=168. Run-off of Sudbury Watershed.=—Table VIII has been given by
Mr. Charles W. Sherman, as representing the average yield of the
Sudbury watershed for the period 1875 to 1899, inclusive, expressed in
several different ways. The average rainfall was 45.83 inches, and the
percentage which represents the run-off is 49.1 per cent of the total.
The average monthly run-off varies from .305 cubic foot (for July) to
4.489 cubic feet (for March) per second per square mile. As a general
rule it may be stated that the average run-off from the drainage areas
of New England streams amounts very closely to 1,000,000 gallons per
square mile per day. The area of the Sudbury watershed is 75.2 square
miles, with 6.5 per cent of that total area occupied by the surface of
lakes or reservoirs. As will presently be seen, the amount of exposed
water surface in any watershed has an appreciable influence upon its
run-off.
=169. Run-off of Croton Watershed.=—The total area of the Croton
watershed, from which New York City draws its supply, i.e., the area
up-stream from the new Croton Dam, is 360.4 square miles, of which 16.1
square miles, or 4.47 per cent, of its total area is water surface. Mr.
John R. Freeman found in the investigations covered by his report to
the comptroller of the city of New York in 1900 that the average annual
rainfall on that area for the thirty-two years beginning 1868 and
ending 1899 was 48.07 inches, and that the average run-off for the same
period was 47.7 per cent of the total average rainfall, equivalent to a
depth of 22.93 inches.
[Illustration: Aqueducts near Jerome Park Reservoir, New York City.]
Table IX gives the main elements of the rainfall and run-off for the
Croton watershed during the thirty-two year period, for the averages
just given.
TABLE IX.
RAINFALL ON CROTON WATERSHED IN TOTAL INCHES—1868-1898.
NATURAL FLOW OF CROTON RIVER AT OLD CROTON DAM,
IN EQUIVALENT INCHES.
PERCENTAGE OF RUN-OFF TO RAINFALL FOR EACH YEAR.
-----------+---------+---------+-----------
Year. | Total | Total |
|Rainfall.| Run-off.| Per Cent.
-----------+---------+---------+-----------
1868 | 50.33 | 33.33 | 66.22
1869 | 48.36 | 23.61 | 48.82
1870 | 44.63 | 19.20 | 43.02
1871 | 48.94 | 19.46 | 39.76
1872 | 40.74 | 16.92 | 41.53
1873 | 43.87 | 25.02 | 57.03
1874 | 42.37 | 25.10 | 59.24
1875 | 43.66 | 24.77 | 56.73
1876 | 40.68 | 21.09 | 51.84
1877 | 48.23 | 20.22 | 41.92
1878 | 55.70 | 27.17 | 48.78
1879 | 47.04 | 19.65 | 41.77
1880 | 36.92 | 12.63 | 34.21
1881 | 46.69 | 19.25 | 41.23
1882 | 52.35 | 24.28 | 46.38
1883 | 42.70 | 13.33 | 31.22
1884 | 51.28 | 24.08 | 46.96
1885 | 43.67 | 17.71 | 40.55
1886 | 47.74 | 20.10 | 42.10
1887 | 57.29 | 26.61 | 46.45
1888 | 60.69 | 35.27 | 58.12
1889 | 55.70 | 31.39 | 56.36
1890 | 54.05 | 25.95 | 48.01
1891 | 47.20 | 23.48 | 49.75
1892 | 44.28 | 17.68 | 39.93
1893 | 54.87 | 29.05 | 52.94
1894 | 47.33 | 20.56 | 43.44
1895 | 40.58 | 15.95 | 39.31
1896 | 45.85 | 23.26 | 50.73
1897 | 53.12 | 25.59 | 48.17
1898 | 57.40 | 29.72 | 51.77
1899 | 44.67 | 22.28 | 49.88
Average for| 48.07 | 22.93 | 47.70
32 years. | | |
-----------+---------+---------+-----------
The table shows that the least annual rainfall was 36.92 inches for
1880, and that the run-off represented a depth of 12.63 inches only, or
34.21 per cent of the total annual precipitation. As a rule the same
feature of a low percentage of run-off will be found belonging to the
years of low rainfall, although there are many irregularities in the
results. On the other hand, the high percentages of run-off are for the
years 1868, 1888, and 1889, and they will generally be found belonging
to years of relatively great precipitation. A low percentage of run-off
will also be lower if the year to which it belongs follows a dry year
or a dry cycle of two or three years. Similarly the high percentages
of run-off will, as a rule, be higher if they follow years of high
precipitation; that is, if they belong to a cycle of relatively great
rainfall.
=170. Evaporation from Reservoirs.=—If it is contemplated to build
reservoirs on a watershed the capacity of which is being estimated
on the basis of either the driest year or the driest two- or three
year cycle, it is necessary to make a deduction from the rainfall
for the evaporation which will take place from the surface of the
proposed reservoir. In order that that deduction may be made as a
proper allowance for added water surface in a drainage area, it is
necessary that the amount of evaporation be determined for the district
considered. The rate of evaporation is dependent upon the area of water
surface, upon the wind, and upon the temperature both of the water and
air above it. Numerous evaporation observations have been made both in
this and other countries, and extensive evaporation tables have been
prepared by the Weather Bureau, from which a reasonable estimate of the
monthly evaporation for all months in the year may be made for almost
any point in the United States. Particularly available observations
have been made by Mr. Desmond Fitzgerald of Boston on the Chestnut
Hill reservoirs of the Boston Water-supply, and by Mr. Emil Kuichling,
engineer of the Rochester Water-works, on the Mount Hope reservoir of
the Rochester supply. Table X exhibits the results of the observations
of both these civil engineers.
[Illustration: Aqueduct Division Wall of Jerome Park Reservoir, New
York City.]
As would be anticipated, the period from May to September, both
inclusive, shows by far the greatest evaporation of the whole year,
while December, January, and February are the months of least
evaporation. The total annual evaporation at Boston was 39.2 inches and
34.54 inches at Rochester.
TABLE X.
MEAN MONTHLY EVAPORATIONS.
----------------+-------------------------+-------------------------
| |
| Chestnut Hill Reservoir,| Mount Hope Reservoir,
Month. | Boston, Mass. | Rochester, N. Y.
| |
----------------+------------+------------+------------+------------
| | Per Cent | | Per Cent
|Evaporation,| of Yearly |Evaporation,| of Yearly
| Inches. |Evaporation.| Inches. |Evaporation.
----------------+------------+------------+------------+------------
January | 0.96 | 2.4 | 0.52 | 1.5
February | 1.05 | 2.7 | 0.54 | 1.6
March | 1.70 | 4.3 | 1.33 | 3.9
April | 2.97 | 7.6 | 2.62 | 7.6
May | 4.46 | 11.4 | 3.93 | 11.4
June | 5.54 | 14.2 | 4.94 | 14.3
July | 5.98 | 15.2 | 5.47 | 15.8
August | 5.50 | 14.0 | 5.30 | 15.4
September | 4.12 | 10.4 | 4.15 | 12.0
October | 3.16 | 8.1 | 3.16 | 9.1
November | 2.25 | 5.7 | 1.45 | 4.2
December | 1.51 | 3.9 | 1.13 | 3.2
+------------+------------+------------+------------
Total for year | 39.20 | | 34.54 |
+------------+------------+------------+------------
Mean temperature| 48°.6 | 47°.8
----------------+-------------------------+-------------------------
A reference to data of the Weather Bureau will show that annual
evaporation as high as 100 inches, or even more, may be expected on
the plateaux of Arizona and New Mexico. Other portions of the arid
country in the western part of the United States will indicate annual
evaporations running anywhere from 50 to 90 inches per year, while on
the north Pacific coast it will fall as low as 18 to 40 inches.
=171. Evaporation from the Earth’s Surface.=—Data are lacking for
anything like a reasonably accurate estimate of evaporation from the
earth’s surface. It is well known that the loss of water from that
source is considerable in soils like those of swamps, particularly
when exposed to the warm sun, but no reliable estimate can be obtained
for the exact amount. Nor is this necessary for the usual water-supply
problems, since it is included in the difference between the total
rainfall of any district and the observed run-off in the streams.
Indeed evaporation from reservoirs is similarly included for reservoirs
existing when the run-off observations are made.
CHAPTER XVI.
=172. Application of Fitzgerald’s Results to the Croton Watershed.=—The
evaporation data determined by Messrs. Fitzgerald and Kuichling are
sufficient for all ordinary purposes in the North Atlantic States. In
the discussion of the capacity of the Croton watershed Mr. Fitzgerald’s
results will be taken, as the conditions of the Croton watershed in
respect to temperature and atmosphere are affected by the proximity to
the ocean, and other features of the case make it more nearly like the
Metropolitan drainage area near Boston than the more elevated inland
district near Rochester.
If the monthly amounts of evaporation be taken from the preceding
table, and if it further be observed that a volume of water 1
square mile in area and 1 inch thick contains 17,377,536 gallons,
the following table (Table XI) of amounts of evaporation from the
reservoirs in the Croton watershed, including the new Croton Lake, will
result, since the total area of water surface of all these reservoirs
is 16.1 square miles.
TABLE XI.
Jan. 0.96 × 16.1 × 17,377,536 = 268,600,000 gallons.
Feb. 1.05 × ” × ” = 293,800,000 ”
Mar. 1.70 × ” × ” = 475,700,000 ”
April 2.97 × ” × ” = 831,000,000 ”
May 4.46 × ” × ” = 1,247,900,000 ”
June 5.54 × ” × ” = 1,550,100,000 ”
July 5.98 × ” × ” = 1,673,200,000 ”
Aug. 5.50 × ” × ” = 1,538,900,000 ”
Sept. 4.12 × ” × ” = 1,152,800,000 ”
Oct. 3.16 × ” × ” = 884,200,000 ”
Nov. 2.25 × ” × ” = 629,600,000 ”
Dec. 1.51 × ” × ” = 422,500,000 ”
----- --------------
39.20 Total = 10,968,300,000 ”
It will be seen from this table that the total annual evaporation from
all the reservoir surfaces of the Croton watershed, as it will exist
when the new Croton Lake is completed, will be nearly 11,000,000,000
gallons, enough to supply the boroughs of Bronx and Manhattan at the
present rate of consumption for about forty days.
=173. The Capacity of the Croton Watershed.=—The use of the preceding
figures and numbers can be well illustrated by considering the capacity
of the Croton watershed in its relations to the present water needs of
the boroughs of Bronx and Manhattan which that watershed is designed
to supply. The total area of the Croton watershed is 360.4 square
miles, of which 16.1 square miles, as has already been observed, is
water surface. As a matter of fact the run-off observations from that
watershed have been maintained or computed for the thirty-two-year
period from 1868 to 1899, inclusive, covering the evaporation from the
reservoirs and lake surfaces as they have existed during that period.
The later observations, therefore, include the effects of evaporation
from the more lately constructed reservoirs, but none of these data
cover evaporation from the entire surface of the new Croton Lake, whose
excess over that of the old reservoir is nearly one third of the total
water surface of the entire shed. As a margin of safety and for the
purpose of simplification, separate allowance will be made for the
evaporation from all the reservoir and lake surfaces of the entire
watershed as it will exist on the completion of the new Croton Lake, as
a deduction from the run-off. The preceding table (Table XI) exhibits
those deductions for evaporation as they will be made in the next table.
In Table IX the year 1880 yields the lowest run-off of the entire
thirty-two-year period. The total precipitation was 36.92 inches, and
only 34.21 per cent of it was available as run-off. The first column in
Table XII gives the amount of monthly rainfall for the entire year, the
sum of which aggregates 36.92 inches. Each of these monthly quantities
multiplied by .3421 will give the amount of rainfall available for
run-off, and the latter quantity multiplied by the number of square
miles in the watershed (360.4) will show the total depth of available
water concentrated upon a single square mile. If the latter quantity be
multiplied by 17,378,000, the total number of gallons available for the
entire month will result, from which must be subtracted the evaporation
for the same month. Carrying out these operations for each month in the
year, the monthly available quantities for water-supply will be found,
as shown in the last column.
TABLE XII.
(Jan. 3.43 × .3421 = 1.173) × 360.4 × 17,378,000 - 268,600,000 = 7,077,700,000
(Feb. 3.40 × ” = 1.163) × ” × ” - 293,800,000 = 6,989,900,000
(Mar. 3.90 × ” = 1.334) × ” × ” - 475,700,000 = 7,879,000,000
(April 3.57 × ” = 1.221) × ” × ” - 831,000,000 = 6,816,000,000
(May 1.04 × ” = .356) × ” × ” - 1,247,900,000 = 982,000,000
(June 1.40 × ” = .479) × ” × ” - 1,550,100,000 = 1,449,800,000
(July 5.86 × ” = 2.005) × ” × ” - 1,673,200,000 = 10,890,000,000
(Aug. 4.16 × ” = 1.423) × ” × ” - 1,538,900,000 = 7,373,100,000
(Sept. 2.42 × ” = .828) × ” × ” - 1,152,800,000 = 4,032,900,000
(Oct. 2.83 × ” = .968) × ” × ” - 884,200,000 = 5,178,500,000
(Nov. 2.32 × ” = .794) × ” × ” - 629,600,000 = 4,343,100,000
(Dec. 2.59 × ” = .886) × ” × ” - 422,500,000 = 5,126,300,000
-----
36.92
The sum of the twelve monthly available quantities will give the total
number of gallons per year applicable to meeting the water demands of
the boroughs of Bronx and Manhattan.
=174. Necessary Storage for New York Supply to Compensate for
Deficiency.=—At the present time the average daily consumption per
inhabitant of those two boroughs is 115 gallons, and if the total
population be taken at 2,200,000, the total daily consumption will
be 2,200,000 × 115 = 253,000,000 gallons. If the latter quantity be
multiplied by 30.5, the latter being taken as the average number of
days in the month throughout the year, the average monthly draft of
water for the two boroughs in question will be 7,716,500,000 gallons.
The subtraction of the latter quantity from the monthly results in the
preceding table will exhibit a deficiency which must be met by storage
or a surplus available for storage. Table XIII exhibits the twelve
monthly differences of that character.
TABLE XIII.
7,077,700,000 — 7,716,500,000 = - 638,800,000
6,989,900,000 — ” = - 726,600,000
7,879,000,000 — ” = + 162,500,000
6,816,000,000 — ” = - 900,500,000
982,000,000 — ” = - 6,734,500,000
1,449,800,000 — ” = - 6,266,700,000
10,890,000,000 — ” = +3,173,500,000
7,373,100,000 — ” = - 343,400,000
4,032,900,000 — ” = - 3,683,600,000
5,178,500,000 — ” = - 2,538,000,000
4,343,100,000 — ” = - 3,373,400,000
5,126,300,000 — ” = - 2,590,200,000
--------------- ---------------
-27,795,700,000 +3,336,000,000
+ 3,336,000,000
---------------
-24,459,700,000
It is seen from this table that the total monthly deficiencies
aggregate 27,795,700,000 gallons and that there are only two months in
which the run-off exceeds the consumption, the surplus for those two
months being only 3,336,000,000 gallons. The total deficiency for the
year is therefore 24,459,700,000 gallons. Dividing the latter quantity
by the average daily draft of 253,000,000 gallons, there will result
a period of 97 days, or more than one quarter of a year, during which
the minimum annual rainfall would fail to supply any water to the city
at all. These results show that in case of a low rainfall year, like
that of 1880, the precipitation upon the Croton watershed would supply
sufficient water for the boroughs of Bronx and Manhattan at the present
rate of consumption for three fourths of the year only. A distressingly
serious water famine would result unless the year were begun by
sufficient available storage in the reservoirs of the basin at least
equal to 24,459,700,000 gallons. Should such a low rainfall year or
one nearly approaching it be one of a two- or three-year low rainfall
cycle, such a reserve storage would be impossible and the resulting
conditions would be most serious for the city. If an average year, for
which the total rainfall would be about 48 inches preceded such a year
of low rainfall, the conditions would be less serious. The figures
would stand as follows:
Total run-off =
17,377,536 × 360.4 × 22.93 - 17,377,536 × 16.1 × 39.2
= 132,640,000,000 gallons.
Total annual consumption = 92,345,000,000 ”
---------------
Available for storage = 40,295,000,000 ”
Deficiency = 24,459,700,000 ”
---------------
Surplus = 15,835,300,000 ”
The average year would, therefore, yield enough run-off water if stored
to more than make up the deficiency of the least rainfall year by
nearly 16,000,000,000 gallons. In order to secure the desired volume it
would therefore be necessary to have storage capacity at least equal
to 24,459,700,000 gallons; indeed, in order to meet all the exigencies
of a public water-supply it would be necessary to have far more than
that amount. As a matter of fact there are in the Croton watershed
seven artificial reservoirs with a total storage capacity of nearly
41,000,000,000 gallons, besides a number of small ponds in addition
to the new Croton Lake which with water surface at the masonry crest
of the dam has a total additional storage capacity of 23,700,000,000
gallons. The storage capacity of the new Croton Lake may be increased
by the use of flash-boards 4 feet high placed along its crest, so
that with its water surface at grade 200 its total capacity will be
increased to 26,500,000,000 gallons. After the new Croton reservoir is
in use the total storage capacity of all the reservoirs and ponds in
the Croton watershed will be raised to 70,245,000,000 gallons, which
can be further augmented by the Jerome Park reservoir when completed by
an amount equal to 1,900,000,000 gallons. This is equivalent, at the
present rate of consumption, to a storage supply for 285 days for the
boroughs of Manhattan and the Bronx.
=175. No Exact Rule for Storage Capacity.=—This question of the
amount of storage capacity to be provided in connection with public
water-supplies is one which cannot be reduced to an exact rule.
Obviously if the continuous flow afforded from any source is always
greater per day than any draft that can ever be made upon it, no
storage-reservoirs at all would be needed, although they might be
necessary for the purpose of sedimentation. On the other hand, as in
the case of New York City, if the demand upon the supply has reached
its capacity or exceeded it for low rainfall years, it may be necessary
to provide storage capacity sufficient to collect all the run-off of
the watershed. The civil engineer must from his experience and from the
data before him determine what capacity between those limits is to be
secured. When the question of volume or capacity of storage is settled
the mode of distribution of that volume or capacity in reservoirs is
to be determined, and that affects to some extent the potability of
the water. If there is a large area of shallow storage, the vegetable
matter of the soil may affect the water in a number of ways. Again, it
is advisable in this connection to consider certain reservoir effects
as to color and contained organic matter in general.
=176. The Color of Water.=—The potability[7] of water collected from
any watershed is materially affected by its color. Although iron
may produce a brownish tinge, by far the greater amount of color
is produced by dissolved vegetable matter. Repeated examinations
of colored water have shown that discoloration is in many cases at
least a measure of the vegetable matter contained in it. While this
may not indicate that the water is materially unwholesome, it shows
conclusively the existence of conditions which are usually productive
of minute lower forms of vegetation from which both bad taste and odors
are likely to arise.
[7] What is generally known as the “Michigan standard of the purity
of drinking-water,” as specified by the Michigan State Laboratory of
Hygiene, is here given:
“1. The total residue should not exceed 500 parts per
million.
“2. The inorganic residue may constitute the total residue.
“3. The smaller amount of organic residue the better the
water.
“4. The amount of earthy bases should not exceed 200 parts
per million.
“5. The amount of sodium chloride should not exceed 20 parts
per million (i.e., ‘chlorine’ 12.1 parts per million).
“6. The amount of sulphates should not exceed 100 parts per
million.
“7. The organic matter in 1,000,000 parts of the water
should not reduce more than 8 parts of potassium
permanganate (i.e., ‘required oxygen’ 2.2 parts per
million).
“8. The amount of free ammonia should not exceed 0.05 part
per million.
“9. The amount of albuminoid ammonia should not exceed 0.15
part per million.
“10. The amount of nitric acid should not exceed 3.5 parts
per million (i.e., ‘N as nitrate’ .9 part per million).
“11. The best water contains no nitrous acid, and any water
which contains this substance in quantity sufficient
to be estimated should not be regarded as a safe
drinking-water.
“12. The water must contain no toxicogenic germs as
demonstrated by tests upon animals.
“The water must be clear and transparent, free from smell, and without
either alkaline or acid taste, and not above 5 French standard of
hardness.”
This standard is too high to be attained ordinarily in natural waters.
There are two periods in the year of maximum intensity of color, one
occurring in June and the other in November. The former is due to the
abundant drainage of peaty or other excessively vegetable soils from
the spring rains. After June the sun bleaches the water to a material
extent until the autumn, when the dying vegetation imparts more or less
coloring to the water falling upon it. This last agency produces its
maximum effect in the month of November.
There are various arbitrary scales employed by which colors may be
measured and discolored waters compared. Among others, dilute solutions
of platinum and cobalt are used, in which the relative proportions of
those substances are varied so as to resemble closely the colors of the
water. The amount of platinum used is a measure of the color, one unit
of which corresponds to one part of the metal in 10,000 parts of water.
Again, the depth at which a platinum wire 1 mm. (.039 inch) in diameter
and 1 inch long can be seen in the water is also taken as a measure
of the color, the amount of the latter being inversely as the depth.
This method has found extended and satisfactory use in connection with
the Metropolitan Water-supply of Boston, the Cochituate water having a
degree of color represented by .25 to .30, while the Sudbury water has
somewhat more than twice as much. The Cochituate water is practically
colorless.
The origin of the color of water is chiefly the swamps which drain into
the water-supply, or the vegetation remaining upon a new reservoir site
when the surface soil has not been removed before the filling of the
reservoir. The drainage of swamps should not, as a rule, be permitted
to flow into a public water-supply, as it is naturally heavily charged
with vegetable matter and is correspondingly discolored. This matter,
like many others connected with the sanitation of potable public
waters, has been most carefully investigated by the State Board of
Health of Massachusetts in connection with the Boston water-supply.
Its work has shown the strong advisability of diverting the drainage
of large swamps from a public supply as carrying too much vegetable
matter even when highly diluted by clear water conforming to desirable
sanitary standards.
=177. Stripping Reservoir Sites.=—The question of stripping or cleaning
reservoir sites of soil is also one which has been carefully studied
by the Massachusetts State Board of Health. As a consequence large
amounts of money have been expended by the city of Boston in stripping
the soil from reservoir sites to the average depth in some cases of 9
inches for wooded land and 12½ inches for meadow land. This was done
in the case of the Nashua River reservoir having a superficial area of
6.56 square miles at a cost of nearly $2,910,000, or about $700 per
acre. It has been found that the beneficial effect of this stripping
is fully secured if the black loam in which vegetation flourishes is
removed.
[Illustration: Wachusetts Reservoir, showing Stripping of Soil.]
This stripping of soil is indicative of the great care taken to secure
a high quality of water for the city of Boston, but it is not done in
the Croton watershed of the New York supply. It cannot be doubted that
the quality of the Croton supply would have been sensibly enhanced by
a similar treatment of its reservoir sites. Mr. F. B. Stearns, chief
engineer of the Metropolitan Water-supply of Boston, states that in
some cases the effects of filling reservoirs without removing the
soil and vegetable matter have “continued for twenty years or more
without apparent diminution.” On the other hand, water discolored by
vegetable matter becomes bleached to some extent at least by standing
in reservoirs whose sites have been stripped of soil.
=178. Average Depth of Reservoirs should be as Great as Practicable.=—In
the selection of reservoir locations those are preferable where the
average depths will be greatest and where shallow margins are reduced
to a minimum. It may sometimes be necessary to excavate marginal
portions which would otherwise be shallow with a full reservoir.
There should be as little water as possible of a less low-water
depth than 10 or 12 feet, otherwise there may be a tendency to
aquatic vegetable growth. The following table exhibits the areas,
average depths, capacity, and other features of a number of prominent
storage-reservoirs.
COMPARATIVE TABLE OF AREAS, DEPTHS, AND CAPACITIES OF STORAGE
RESERVOIRS WITH HEIGHTS AND LENGTHS OF DAMS.
LEGEND:
(A) = Area Square Miles.
(B) = Average Depth, Feet.
(C) = Length of Dam, Feet.
(D) = Capacity, Million Gallons.
------------------------------+-----+---+--------------+-----+-------
| | |Maximum Height| |
| | | of Dam. | |
Name and Location | | +-------+------+ |
of Reservoir. | (A) |(B)| Above | Above| (C) | (D)
| | |Ground.| Rock.| |
------------------------------+-----+---+-------+------+-----+-------
Swift River, Mass |36.96| 53| 144 | ... |2,470|406,000
Nashua River, Mass | 6.56| 46| 129 | 158 |1,250| 63,068
Nira, near Poona, India | 7.25| 27| 100 | ... |3,000| 41,143
Tansa, Bombay, India | 5.50| 33| 127 | 131 |8,770| 37,500
Khadakvasla, Poona, India | 5.50| 32| 100 | 107 |5,080| 36,737
New Croton, N. Y. | ....| ..| 157 | 225 |1,270| 32,000
Elan and Claerwen, Birmingham,| | | | | |
Eng., water-works | | | | | |
(total for six reservoirs) | 2.34| 43|98-128 | ... |4,460| 20,838
All Boston water-works | | | | | |
reservoirs combined | 5.82| 14|14-65 | ... |.....| 15,867
Vyrnwy, Liverpool, Eng. | 1.75| ..| 84 | 129 |1,350| 14,560
Ware River, Mass. | 1.62| 33| 71 | ... | 785| 11,190
Sodom, N. Y. | ....| ..| 72 | 89 | 500| 9,500
Reservoir No. 5, Boston | | | | | |
water-works | 1.91| 19| 65 | 70 |1,865| 7,438
Titicus, N. Y. | ....| ..| 105 | 115 |.....| 7,000
Hobbs Brook, Cambridge | | | | | |
water-works | 1.00| 12| 23 | ... |.....| 2,500
Cochituate, Boston water-works| 1.35| 8| .. | ... |.....| 2,160
Reservoir No. 6, Boston | | | | | |
water-works | 0.29| 25| 52 | ... |1,500| 1,500
------------------------------+-----+---+-------+------+-----+-------
=179. Overturn of Contents of Reservoirs Due to Seasonal Changes of
Temperature.=—It will be noticed that the average depth is less
than about 20 feet in few cases only. If the water is deep, its mean
temperature throughout the year will be lower than if shallow. During
the warmer portion of the year the upper layers of the water are
obviously of a higher temperature than the lower portions, since the
latter receive much less immediate effect from the sun’s rays. As the
upper portions of the water are of higher temperature, they are also
lighter and hence remain at or near the top. For the same reason the
water at the bottom of the reservoir remains there throughout the warm
season and until the cool weather of the autumn begins. The top layers
of water then continue to fall in temperature until it is lower than
that of the water at the bottom, when the surface-water becomes the
heaviest and sinks. It displaces subsurface water lighter than itself,
the latter coming to the surface to be cooled in turn.
This operation produces a complete overturning of the entire reservoir
volume as the late autumn or early winter approaches. It thus brings to
the surface-water which has been lying at the bottom of the reservoir
all summer in contact with what vegetable matter may have been there.
The depleted oxygen of the bottom water is thus replenished with a
corresponding betterment of condition. It is the great sanitary effort
of nature to improve the quality of stored water entrusted to its care,
and it continues until the surface is cooled to a temperature perhaps
lower than that of the greatest density of water.
Another great turn-over in the water of a lake or reservoir covered
with ice during the winter occurs in the spring. When the ice melts,
the resulting water rises a little in temperature until it reaches
possibly its greatest density at 39°.2 Fahr., and then sinks,
displacing subsurface water. This goes on until all the ice is melted
and until all water cooled by it, near the surface, below 39°.2 Fahr.
has been raised to that temperature. The period of summer stagnation
then follows.
=180. The Construction of Reservoirs.=—The natural topography and
sometimes the geology of the locality determines the location of the
reservoir. The first requirement obviously is tightness. If for any
reason whatever, such as leaky banks or bottom, porous subsurface
material, or for any other defect, the water cannot be retained in
the reservoir, it is useless. Some very perplexing questions in this
connection have arisen. Indeed reservoirs have been completed only
to be found incapable of holding their contents. Such results are
evidently not creditable to the engineers who are responsible for them,
and they should be avoided.
[Illustration: YARROW RESERVOIR, LIVERPOOL WATER-SUPPLY]
[Illustration: SAN LEANDRO DAM, SAN FRANCISCO WATER-WORKS]
[Illustration: TITICUS DAM, NEW YORK WATER-SUPPLY]
In order that the bottom of the reservoir may be water-tight it must
be so well supported by firm underlying material that it will not be
injured by the weight of water above it, which in artificial reservoirs
may reach 30 to 100 feet or more in depth. The subsurface material at
the site of any proposed structure of this character must, therefore,
be carefully examined so as to avoid all porous material, crevasses in
rocks, or other open places where water might escape. Objectionable
material may frequently be removed and replaced with that which is
more suitable, and rock crevices and other open places may sometimes
be filled with concrete and made satisfactory. Whatever may be the
conditions existing, the finished bottom of the reservoir should be
placed only on well-compacted, firm, unyielding material.
The character of the reservoir bottom will depend somewhat upon the
cost of suitable material of which to construct it. If a bottom of
natural earth cannot be used, a pavement of stone, brick, or concrete
may be employed from 8 inches to a foot or a foot and a half in
thickness. The reservoir banks must be placed upon carefully prepared
foundations, sometimes with masonry core-walls. They are frequently
composed of clayey and gravelly material mixed in proper proportions
and called puddle, although that term is more generally applied to a
mixture of clay and gravel designed to form a truly impervious wall
in the centre of the reservoir embankment. Some engineers require the
core-wall, as it is called, to be constructed of masonry, with the
earth or gravelly material carried up each side of this wall in layers
6 to 9 inches thick, well moistened and each layer thoroughly rolled
with a grooved roller, or treated in some equivalent manner in order
that the whole mass may not be in strata but essentially continuous
and as nearly impervious as possible. The masonry core-wall should be
founded on bed-rock or its equivalent. Its thickness will depend upon
the height of the embankment. If the latter is not more than 20 or 25
feet high, the core-wall need not be more than 4 to 6 feet thick, but
if the embankment reaches a height of 75 feet or even 100 feet, it must
be made 15 to 20 feet thick, or possibly more, at the base. Its top
should be not less than 4 or 6 feet thick, imbedded in the earth and
carried well above the highest surface of water in the reservoir.
The thickness of the clay puddle-wall employed as the central core
of the reservoir embankment is usually made much thicker than that
of masonry. As a rough rule it may be made twice as thick as the
masonry core at the deepest point and not less than about 6 feet at
the top. The thickness of the puddle core is sometimes varied to meet
the requirements of the natural material in which it is embedded at
different depths.
Frequently, when embankments are under about 20 feet high, the
core-walls may be omitted, excavation having been made at the base of
the embankment down to rock or other impervious material, and if the
entire bank is carried up with well-selected and puddled material.
The interior slopes of reservoir embankments are usually covered with
roughly dressed stone pavement 12 to 18 inches thick, laid upon a
broken stone foundation 8 to 12 inches thick, for a protection against
the wash of waves, the pavement in any case being placed upon the bank
slope after having been thoroughly and firmly compacted. The sloping
and bottom pavements, of whatever material they may be composed, should
be made continuous with each other so as to offer no escape for the
water. In some cases where it has been found difficult to make the
interior surfaces of reservoirs water-tight, asphalt or other similar
water-tight layers have been used with excellent results.
The care necessary to be exercised in the construction of storage or
other reservoirs when earth dams or embankments are used can better be
appreciated when it is realized that almost all such banks, even when
properly provided with masonry or clay-puddle core-walls, are saturated
with water, even on the down-stream side, at least throughout their
lower portions. A board of engineers appointed by the commissioners
of the Croton Aqueduct in the summer of 1901 made a large number
of examinations in the earth embankments in the Croton watershed,
and found that with scarcely an exception those embankments were
saturated throughout the lower portions of their masses, although in
every case a masonry core-wall had been built. The results of those
investigations showed that the water had percolated through the earth
portion of the embankments and even through the core-walls, which had
been carried down to bed-rock. This induced saturation, more or less,
of the material on the down-stream slopes of the embankments. When
material is thus filled with water, unless it is suitably selected, it
is apt to become soft and unstable, so that any superincumbent weight
resting upon it might produce failure. The fact that such embankments
may become saturated with water fixes limits to their heights, since
the surface of saturation in the interior of the bank has generally
a flatter slope than that of the exterior surface. The height of the
embankment therefore should be such that the exterior slope cannot cut
into the saturated material at its foot, at least to any great extent.
From what precedes it is evident that the height of an earth embankment
will depend largely upon the slope of the exterior surface. This slope
is made 1 vertical to 2, 2½, or 3 horizontal. The more gradual slope
is sometimes preferable. It is advisable also to introduce terraces
and to encourage the growth of sod so as to protect the surface from
wash. The inner paved slope may be as steep as 1 vertical to 1½ or 2
horizontal.
[Illustration: BOG BROOK DAM NO. 1.—RESERVOIR 1.]
[Illustration: TITICUS DAM.—RESERVOIR M.]
[Illustration: AMAWALK DAM.—RESERVOIR A.
Earth Dams in Croton Watershed, showing Slopes of Saturation.]
=181. Gate-houses, and Pipe-lines in Embankments.=—It is necessary
to construct the requisite pipe-lines and conduits leading from the
storage-reservoirs to the points of consumption, and sometimes such
lines bring the water to the reservoir. Wherever such pipes-line or
conduits either enter or leave a reservoir gates and valves must be
provided so as properly to control the admission and outflow of the
water. These gate-houses, as they are called, because they contain
the gates or valves and such other appurtenances or details as
are requisite for operation and maintenance, are usually built of
substantial masonry. They are the special outward features of every
reservoir construction, and their architecture should be characteristic
and suitable to the functions which they perform. Where the pipes are
carried through embankments it is necessary to use special precautions
to prevent the water from flowing along their exterior surfaces.
Many reservoirs have been constructed under defective design in this
respect, and their embankments have failed. Frequently small masonry
walls are built around the pipes and imbedded in the bank, so as to
form stops for any initial streams of water that might find their way
along the pipe. In short, every care and resource known to the civil
engineer must be employed in reservoir construction to make its bottom
and its banks proof against leakage and to secure permanence and
stability in every feature.
=182. High Masonry Dams.=—The greatest depths of water impounded in
reservoirs are found usually where it is necessary to construct a high
dam across the course of a river, as at the new Croton dam. In such
cases it is not uncommon to require a dam over 75 to 100 feet high
above the original bed of the river, which is usually constructed of
masonry with foundations carried down to bed-rock in order to secure
suitable stability and prevent flow or leakage beneath the structure.
It is necessary to secure that result not only along the foundation-bed
of the dam, but around its ends, and special care is taken in those
portions of the work.
The new Croton dam is the highest masonry structure of its class yet
built. The crest of its masonry overflow-weir is 149 feet above the
original river-bed, with the extreme top of the masonry work of the
remaining portion of the dam carried 14 feet higher. A depth of earth
and rock excavation of 131 feet below the river-bed was necessary
in order to secure a suitable foundation on bed-rock. The total
maximum height, therefore, of the new Croton dam, from the lowest
foundation-point to the extreme top, is 294 feet, and the depth of
water at the up-stream face of the dam will be 136 feet when the
overflow is just beginning, or 140 feet if 4 feet additional head be
secured by the use of flash-boards. In the prosecution of this class
of work it is necessary not only to reach bed-rock, but to remove all
soft portions of it down to sound hard material, to clean out all
crevices and fissures of sensible size, refilling them with hydraulic
cement mortar or concrete, and to shape the exposed rock surfaces so
as to make them at least approximately normal to the resultant loads
upon them, to secure a complete and as nearly as possible water-tight
bond with the superimposed masonry. If any streams or other small
watercourses should be encountered, they must either be stopped or
led off where they will not affect the work, or, as is sometimes
done, the water issuing from them may be carried safely through the
masonry mass in small pipes. The object is to keep as much water out
of the foundation-bed as possible, so as to eliminate upward pressure
underneath the dam caused by the head of water in the subsequently full
reservoir. It is a question how much dependence can be placed upon the
exclusion of water from the foundation-bed. In the best class of work
undoubtedly the bond can be good enough to exclude more or less water,
but it is probably only safe and prudent so to design the dam as to be
stable even though water be not fully excluded.
[Illustration: Cross-section of New Croton Dam.]
The stability of the masonry dam must be secured both for the reservoir
full and empty. With a full reservoir the horizontal pressure of water
on the up-stream face tends to overturn the dam down-stream. When the
water is entirely withdrawn the pressure under the up-stream edge of
the foundation becomes much greater, so that safety and stability
under both extreme conditions must be assured. There are a number of
systems of computation to which engineers resort in order to secure a
design which shall certainly be stable under all conditions. That which
is commonly employed in this country is based upon two fundamental
propositions, under one of which the pressure at any point in the
entire masonry mass must not exceed a certain safe amount per square
foot, while the other is of a more technical character, requiring that
the centre of pressure shall, in every horizontal plane of the dam,
approach nowhere nearer than one third the horizontal thickness of
the masonry to one edge of it. A further condition is also prescribed
which prevents any portion of the dam from slipping or sliding over
that below it. As a matter of fact when the first two conditions are
assured the third is usually fulfilled concurrently. Obviously there
will be great advantage accruing to a dam if the entire mass of masonry
is essentially monolithic. In order that that may be the case either
concrete or rubble is usually employed for the great mass of the
masonry structure, the exterior surfaces frequently being composed of a
shell of cut-stone, so as to provide a neat and tasteful finish. This
exterior skin or layer of cut masonry need not average more than 1½ to
2½ feet thick.
The pressures prescribed for safety in the construction of masonry dams
vary from about 16,000 to 28,000 or 30,000 pounds per square foot.
Sometimes, as in the masonry dams found in the Croton watershed, limits
of 16,000 to 20,000 pounds per square foot are prescribed for the upper
portions of the dams and a gradually increasing pressure up to 30,000
pounds per square foot in passing downward to the foundation-bed. There
are reasons of a purely technical character why the prescribed safe
working pressure must be taken less on the down-stream or front side of
the dam than on the up-stream or rear face.
The section of a masonry dam designed under the conditions outlined
will secure stability through the weight of the structure alone, hence
it is called a gravity section. In some cases the rock bed and sides
of a ravine in which the stream must be dammed will permit a curved
structure to be built, the curvature being so placed as to be convex
up-stream or against the water pressure. In such a case the dam really
becomes a horizontal arch and, if the curvature is sufficiently sharp,
it may be designed as an arch horizontally pressed. The cross-section
then has much less thickness (and hence less area) than if designed
on a straight line so as to produce a gravity section. A number of
such dams have been built, and one very remarkable example of its kind
is the Bear Valley dam in California; it was built as a part of the
irrigation system.
[Illustration: Foundation Masonry of New Croton Dam.]
CHAPTER XVII.
=183. Gravity Supplies.=—When investigation has shown that a sufficient
quantity of water may be obtained for a required public supply from any
of the sources to which reference has been made, and that a sufficient
storage capacity may be provided to meet the exigencies of low rainfall
years, it will be evident if the water can be delivered to the points
of consumption by gravity, or whether pumping must be employed, or
recourse be made to both agencies.
If the elevation of the source of supply is sufficiently great to
permit the water to flow by gravity either to storage-reservoirs or to
service-reservoirs and thence to the points of consumption, a proper
pipe-line or conduit must be designed to afford a suitable channel. If
the topography permits, a conduit may be laid which does not run full,
but which has sufficient grade or slope to induce the water to flow in
it as if it were an open channel. This is the character of such great
closed masonry channels as the new and old Croton aqueducts of the
New York water-supply and the Sudbury and Wachusetts aqueducts of the
Boston supply. These conduits are of brick masonry backed with concrete
carried sometimes on embankments and sometimes through rock tunnels.
When they act like open channels a very small slope is employed, 0.7 of
a foot per mile being a ruling gradient for the new Croton aqueduct,
and 1 foot per mile for the Sudbury. Where these conduits cross
depressions and follow approximately the surface, or where they pass
under rivers, their construction must be changed so that they will not
only run full, but under greater or less pressure, as the case may be.
=184. Masonry Conduits.=—In general the conduits employed to bring
water from the watersheds to reservoirs at or near places of
consumption may be divided into two classes, masonry and metal,
although timber-stave pipes of large diameter are much used in the
western portion of the country. The masonry conduits obviously cannot
be permitted to run full, meaning under pressure, for the reason that
masonry is not adapted to resist the tension which would be created
under the head or pressure of water induced in the full pipe. They
must rather be so employed as to permit the water to flow with its
upper surface exposed to the atmosphere, although masonry conduits are
always closed at the top. In other words, they must be permitted to
run partially full, the natural grade or slope of the water surface
in them inducing the necessary velocity of flow or current. Evidently
the velocity in such masonry conduits is comparatively small, seldom
exceeding about 3 feet per second. The new and old Croton aqueducts,
the Sudbury and Wachusetts aqueducts of the Metropolitan Water-supply
of Boston, are excellent types of such conveyors of water. They are
sometimes of circular shape, but more frequently of the horseshoe
outline for the sides and top, with an inverted arch at the bottom for
the purpose of some concentration of flow when a small amount of water
is being discharged and for structural reasons.
The interiors of these conduits are either constructed of brick or
they may be of concrete or other masonry affording smooth surfaces.
In the latest construction Portland-cement concrete or that concrete
reinforced with light rods of iron or steel is much used. Bricks, if
employed, should be of good quality and laid accurately to the outline
desired with about ¼-inch joints, so as to offer as smooth a surface as
possible for the water to flow over. In special cases the interiors of
these conduits may be finished with a smooth coating of Portland-cement
mortar. If conduits are supported on embankments, great care must be
exercised in constructing their foundation supports, since any sensible
settlement would be likely to form cracks through which much water
might easily escape. When carried through tunnels they are frequently
made circular in outline. They must occasionally be cleaned, especially
in view of the fact that low orders of vegetable growths appear on
their sides and so obstruct the free flow of water.
=185. Metal Conduits.=—Metal conduits have been much used within the
past fifteen or twenty years. Among the most prominent of these are
the Hemlock Lake aqueduct of the Rochester Water-works, and that of
the East Jersey Water Company through which the water-supply of the
city of Newark, N. J., flows. When these metal conduits or pipes equal
24 to 30 or more inches in diameter they are usually made of steel
plates, the latter being of such thickness as is required to resist
the pressure acting within them. The riveted sections of these pipes
may be of cylindrical shape, each alternate section being sufficiently
small in diameter just to enter the other alternate sections of little
larger diameter, the interior diameter of the larger sections obviously
being equal to the interior diameter of the smaller sections plus twice
the thickness of the plate. Each section may also be slightly conical
in shape, the larger ends having a diameter just large enough to pass
sufficiently over the smaller end of the next section to form a joint.
Large cast-iron pipes are also sometimes used to form these metal
conduits up to an interior diameter of 48 inches. The selection of the
type of conduit within the limits of diameter adapted to both metals is
usually made a matter of economy. The interior of the cast-iron pipe is
smoother than that of the riveted steel, although this is not a serious
matter in deciding upon the type of pipe to be used.
Steel-plate conduits have been manufactured and used up to a diameter
of 9 feet. In this case the pipe was used in connection with
water-power purposes and with a length of 153 feet only, the plates
being ½ inch thick. The steel-plate conduits of the East Jersey Water
Company’s pipes are as follows:
Diameter. Thickness. Length.
48 inches ¼ inch }
48 ” ⁵/₁₆ ” } 21 miles.
48 ” ⅜ ” }
36 ” ¼ ” 5 ”
The diameters and lengths of the metal pipes or conduits of the Hemlock
Lake conduit of the Rochester Water-works are as follows:
36-inch wrought-iron pipe 9.60 miles.
24 ” ” ” 2.96 ”
24 ” cast-iron pipe 15.82 ”
-----
Total 28.39 ”
All metal conduits or pipes are carefully coated with a suitable
asphalt or tar preparation or varnish applied hot and sometimes baked
before being put in place. This is for the purpose of protecting the
metal against corrosion. Cast-iron pipes have been used longer and
much more extensively than wrought-iron or steel, but an experience
extending over thirty to forty years has shown that the latter class of
pipes possesses satisfactory durability and may be used to advantage
whenever economical considerations may be served.
=186. General Formula for Discharge of Conduits—Chezy’s Formula.=—It
is imperative in designing aqueducts of either masonry or metal to
determine their discharging capacity, which in general will depend
largely upon the slope of channel or head of water and the resistance
offered by the bed or interior of the pipe to the flow of water. The
resistance of liquid friction is so much more than all others in this
class of water-conveyors that it is usually the only one considered.
There is a certain formula much used by civil engineers for this
purpose; it is known as Chezy’s formula, for the reason that it was
first established by the French engineer Antoine Chezy about the year
1775, although it is an open question whether the beginnings of the
formula were not made twenty or more years prior to that date. Its
demonstration involves the general consideration of the resistance
which a liquid meets in flowing over any surface, such as that of the
interior of a pipe or conduit, or the bed and banks of a stream.
The force of liquid friction is found to be proportional to the
heaviness of the liquid (i.e., to the weight of a cubic unit, such as
a cubic foot), to the area of wetted surface over which the liquid
flows, and nearly to the square of the velocity with which the liquid
moves. Hence if _lʹ_ is the length of channel, _p_ the wetted portion
of the perimeter of the cross-section, _w_ the weight of a cubic unit
of the liquid, and _v_ the velocity, the total force of liquid friction
for the length _l′_ of channel will be _F = ζwpl′v²_, ζ being the
coefficient of liquid friction. The path of the force _F_ for a unit of
time is _v_, and the work _W_ which it performs in that unit of time is
equal to the weight _wal′_ falling through the height _h′_, _a_ being
the area of the cross-section of the stream.
[Illustration: FIG. 2.]
Hence _W_ = ζ_wplʹv².v_ = _wal′h′._ (7)
_a_ _____________________ ____
ζ_v²v_ = ---- _hʹ_, _v_ = √(1/ζ) (_a/p_) (_h′/v_) = _c_√_rs_. (8)
_p_
In this equation
_____ _a_
_c_ = √(1/ζ); _r_ = ---- = hydraulic mean radius;
_p_
_hʹ_
_s_ = ----- = sine of inclination of stream’s bed.
_v_
As the motion of the water is assumed to be uniform, the head lost by
friction for the total length of channel _l_ is the total fall _h_, and
by equation (8), since
_h′ h_
--- = _s_ = ---,
_v l_
_v² l_
_h_ = ---- ---------. (9)
_c²_ (_a/p_)
If, as in the case of the ordinary cast-iron water-pipes of a public
supply system, the cross-section _a_ is circular,
_a_ (π_d²_/4) _d_
--- = --------- = ---,
_p_ π_d_ 4
and
4.2_g l v² l v²_
_h_ = ----- --- ------ = _f_ --- -----, (10)
_c² d_ 2_g d_ 2_g_
in which _f_ = 8_g_ ÷ _c²_.
The quantity _f_ is sometimes called the “friction factor.” For smooth,
new pipes from 4 feet down to 3 inches in diameter its value may be
taken from .015 to .03. An approximate mean value may be taken at .02.
The last member of equation (8) is Chezy’s formula, and it is one of
the most used expressions in hydraulic engineering. Some values for
the coefficient _c_ will presently be given. The quantity _r_ found
by dividing the area of the cross-section of the stream by the wetted
portion of its perimeter is called the “hydraulic mean radius,” or
simply the “mean radius.” The other quantity, _s_, appearing in the
formula is, as shown by the figure, the sine of the inclination of the
bed of the stream.
In order to determine the discharge of any pipe, conduit, or open
channel carrying a known depth of water, it is only necessary to
compute _r_ and _s_ from known data and select such a value of the
coefficient _c_ as may best fit the circumstances of the particular
case in question. The substitution of those quantities in Chezy’s
formula, i.e., equation (8), will give the mean velocity _v_ of the
water which, when multiplied by the area of cross-section of the
stream, will give the discharge of the latter per second of time. It
is customary to compute _r_ in feet. The coefficient _c_ is always
determined so as to give velocity in feet per second of time. Hence if
the area of the cross-section of the stream, _a_, is taken in square
feet, as is ordinarily the case, the discharge _av_ will be in cubic
feet per second.
[Illustration: Progress View of Construction of New Croton Dam.]
=187. Kutter’s Formula.=—The coefficient _c_ in Chezy’s formula is
not a constant quantity, but it varies with the mean radius _r_, with
the sine of inclination _s_, and with the character of the bottom and
sides of the open channel, i.e., with the roughness of the interior
surface of the closed pipe. Many efforts have been made and much labor
expended in order to find an expression for this coefficient which may
accurately fit various streams and pipes. These efforts have met with
only a moderate degree of success. The form of expression for _c_ which
is used most among engineers is that known as Kutter’s formula, as it
was established by the Swiss engineer W. R. Kutter. This formula is as
follows:
( 1.811 .00281)
___ ( ------ + 41.65 + ------)
√_r_ ( _n s_ )
_c_ = ---- (------------------------)
_n_ ( ___ )
( √_r_ .00281 )
( ----- + 41.65 + ------ )
( _n s_ )
The quantity _n_ in this formula is called the “coefficient of
roughness,” since its value depends upon the character of the surface
over which the water flows. It has the following set of values for the
surfaces indicated:
_n_ = 0.009 for well-planed timber;
_n_ = 0.010 for neat cement;
_n_ = 0.011 for cement with one third sand;
_n_ = 0.012 for unplaned timber;
_n_ = 0.013 for ashlar and brickwork;
_n_ = 0.015 for unclean surfaces in sewers and conduits;
_n_ = 0.017 for rubble masonry;
_n_ = 0.020 for canals in very firm gravel;
_n_ = 0.025 for canals and rivers free from stones and weeds;
_n_ = 0.030 for canals and rivers with some stones and weeds;
_n_ = 0.035 for canals and rivers in bad order.
=188. Hydraulic Gradient.=—Before illustrating the use of Chezy’s
formula in connection with masonry and metal conduits, of which mention
has already been made, it is best to define another quantity constantly
used in connection with closed iron or steel pipes. This quantity is
called the “hydraulic gradient.” If a closed iron or steel pipe is
running full of water and under pressure and if small vertical tubes
be inserted in the top of the pipe with their lower ends bent so as
to be at right angles to its axis, the water will rise to heights in
the tubes depending upon the pressures of water in the pipe or conduit
at the points of insertion. Such tubes with the water columns in them
are called piezometers. They are constantly used in connection with
water-pipes in order to show the pressures at the points where they are
inserted. A number of such pipes being inserted along an iron pipe or
conduit, a line may be imagined to be drawn through the upper surfaces
of the columns of water, and that line is called the “hydraulic
gradient.” It represents the upper surface of water in an open channel
discharging with the same velocity existing in the closed pipe.
In case Chezy’s formula is used to determine the velocity of discharge
in a closed pipe running under pressure, the sine of inclination _s_
must be that of the hydraulic gradient and not the sine of inclination
of the axis of the closed pipe. In the determination of this quantity
_s_ by the use of piezometer tubes, if a straight pipe remains of
constant section between any two points, it is only necessary to insert
the tubes at those points and observe the difference in levels of the
water columns in them. That difference of levels or elevations will
represent the height which is to be divided by the length of pipe or
conduit between the same two points in order to determine the sine _s_.
[Illustration: Progress View of Construction of New Croton Dam.]
The hydraulic gradient plays a very important part in the construction
of a long pipe-line or conduit. If any part of the pipe should rise
above the hydraulic gradient, the discharge would no longer be full
below that point. It is necessary, therefore, always to lay the pipe or
the closed conduit so that all parts of it shall be below the hydraulic
gradient. Caution is obviously necessary to lay a pipe carrying water
deep enough below the surface of the ground in cold climates to protect
the water against freezing. At the same time if the pipe-line is a long
one it must follow the surface of the ground approximately in order to
save expensive cutting. There will, therefore, generally be summits
in pipe-lines, and inasmuch as all potable water carries some air
dissolved in it, that air is liable to accumulate at the high points or
summits. If that accumulation goes on long enough, it will seriously
trench upon the carrying capacity of the pipe and decrease its flow. It
is therefore necessary to provide at summits what are called blow-off
cocks to let the air escape. At the low points of the pipe-line, on the
contrary, the solid matter, such as sand and dirt, carried by the water
is liable to accumulate, and it is customary to arrange blow-offs also
at such points, so as to enable some of the water to escape and carry
with it the sand and dirt.
[Illustration: IN LOOSE EARTH.]
[Illustration: IN ROCK.
Weston Aqueduct. Sections of Aqueduct and Embankment.]
[Illustration: SECTION OF EMBANKMENT.]
[Illustration: ON EMBANKMENT.
Weston Aqueduct. Sections of Aqueduct and Embankment. Gradient, 1 in
5000.]
=189. Flow of Water in Large Masonry Conduits.=—In order to apply
Chezy’s formula first to the flow of the masonry aqueducts of the New
York and Boston water-supplies, it is necessary to have the outlines of
those conduits so that the wetted perimeter and hence the mean radius
may be determined for any depth of water in them.
[Illustration: OUTLINES OF AQUADUCTS.
FIG. 3.]
The figure shows the desired cross-sections drawn carefully to scale.
Table XIV has been computed and arranged from data taken from various
official sources so as to show the depth, mean velocity, discharge per
second and per twenty-four hours, and the coefficient used in Chezy’s
formula, together with the coefficient of roughness _n_ in Kutter’s
formula for the conduits shown in the figure.
This table exhibits in a concise and clear manner the use of Chezy’s
formula in this class of hydraulic work.
TABLE XIV.
LEGEND:
(A) = Depth, in Feet.
(B) = Hydraulic Radius _r_, Feet.
(C) = Coefficient _c_.
(D) = Mean Velocity, Feet.
--------------------------+----+-----+--------+-------+------
| | | Grade | |
Aqueducts. | (A)| (B) | _s_. | (C) | (D)
--------------------------+----+-----+--------+-------+------
† New Croton (1899) |8.42|3.974|.0001326| 153.3 | 3.52
† ” ” (after two | | | | |
years’ use) | .. |2.338| ” | 131.3 | 2.312
‡ ” ” | .. |1 | ” | 119.3 | 1.374
‡ ” ” | .. |1.5 | ” | 126.3 | 1.781
‡ ” ” | .. |2 | ” | 129.8 | 2.114
‡ ” ” | .. |2.5 | ” | 132 | 2.404
‡ ” ” | .. |3 | ” | 133.4 | 2.661
‡ ” ” | .. |3.5 | ” | 134 | 2.887
‡ ” ” | .. |4 | ” | 134.4 | 3.095
Old Croton (1899) clean |6 |2.338| .. | 133.4 | 2.958
” ” ordinary | | | | |
condition; | | | | |
not clean |6 |2.338| .. | 123.2 | ..
” ” not clean |7.33|2.368| .. | 118.2 | ..
Dorchester Bay tunnel | .. |1.875| .. | 119 |
” ” | .. |2.338| .. | 125.0 | ..
Wachusetts, new; probably | | | | |
clean (approx.) | .. | .. | .. | 144.9 |
Sudbury, clean | .. | .5 |.000189 | 116.9 | 1.14
” ” | .. |1.0 | ” | 127.0 | 1.74
” ” | .. |1.5 | ” | 133.3 | 2.24
” ” | .. |2.0 | ” | 137.8 | 2.68
” ” | .. |2.5 | ” | 140.4 | 3.04
--------------------------+----+-----+--------+-------+------
--------------------------+----------------------+--------
| Discharge. |
--------------------------+----------------------+
|Cubic Feet| Gallons | _n_ in
Aqueducts. | per | per |Kutter’s
| Second. | 24 Hours. |Formula.
--------------------------+----------+-----------+--------
† New Croton (1899) | 371.6 |240,200,000|
† ” ” (after two | | |
years’ use) | .. | .. | .0133
‡ ” ” | | |
‡ ” ” | | |
‡ ” ” | | |
‡ ” ” | | |
‡ ” ” | | |
‡ ” ” | | |
‡ ” ” | | |
Old Croton (1899) clean | 122.8 | 79,400,000| .0133
” ” ordinary | | |
condition; | | |
not clean | .. | 73,300,000|
” ” not clean | .. | 85,600,000|
Dorchester Bay tunnel | | |
” ” | .. | .. | .014
Wachusetts, new; probably | | |
clean (approx.) | | |
Sudbury, clean | | |
” ” | | |
” ” | | |
” ” | | |
” ” | | |
--------------------------+----------+-----------+--------
† From report by J. R. Freeman to B. S. Coler, 1899.
‡ From report of New York Aqueduct Commission.
=190. Flow of Water through Large Closed Pipes.=—The masonry conduits
to which consideration has been given in the preceding paragraphs
carry water precisely as in an open canal, but the closed conduits or
pipes of steel plates and cast-iron, like the Hemlock Lake conduit at
Rochester and the East Jersey conduit of the Newark Water-works, are of
an entirely different type, as they carry water under pressure. Hence
the slope or sine of inclination _s_ belongs to the hydraulic gradient
rather than to the grade of the pipe itself. Where the pipe-line is a
long one its average grade frequently does not differ much from the
hydraulic gradient, but the latter quantity must always be used. As
in the case of the masonry conduits, the coefficient _c_ in Chezy’s
formula will vary considerably with the degree of roughness of the
interior surface of the pipe, with the slope _s_, and with the mean
radius _r_. An important distinction must be made between riveted steel
pipes and those of cast-iron, for the reason that the rivet-heads
on the inside of the former exert an appreciable influence upon the
coefficient _c_. The rivet-heads add to the roughness or unevenness of
the interior of the pipe. Table XV gives the elements of the flow or
discharge in the two pipe-lines which have been taken as types, as
determined by actual measurements; it also exhibits similar elements
for timber-stave pipes, to which reference will be made later.
[Illustration: CROTON AQUEDUCT
IN EARTH.]
As would be expected, the velocity of flow in these pipes may be and
generally is considerably higher than the velocity of movement in
masonry channels. Both Tables XV and XVI give considerable range of
coefficients computed and arranged from authoritative sources, and
the coefficients _c_ for Chezy’s formula represent the best hydraulic
practice in connection with such works at the present time. In using
the formula for any special case, great care must be taken to select
a value for _c_ which has been established for conditions as closely
as possible to those in question. This is essential in order that the
results of estimated discharges may not be disappointing, as they
sometimes have been where that condition so necessary to accuracy has
not been fulfilled.
TABLE XV.
VALUES OF COEFFICIENT _c_.
LEGEND:
(A) = Hydraulic Radius _r_.
(B) = Hydraulic Gradient.
(C) = Mean Velocity.
------------------------------+-----------------+-----+-------+------
| | | |
Pipe-line. | Diameter. | | |
| | (A) | (B) | (C)
------------------------------+-----------------+-----+-------+------
Hemlock Lake |36″ wrought-iron | 9″ |.000411| 1.532
” ” |24″ wr’t and cast| 6″ |.00239 | 3.448
Rush Lake to Mt. Hope |24″ cast-iron | 6″ |.00255 | 3.448
------------------------------+-----------------+-----+-------+------
Sudbury aqueduct |48″ ” ” | 12″ | | 3.738
” ” |48″ ” ” | 12″ | | 4.965
” ” |48″ ” ” | 12″ | | 6.195
” ” |48″ ” ” | 12″ | | 3.738
” ” |48″ ” ” | 12″ | | 4.965
” ” |48″ ” ” | 12″ | | 6.195
------------------------------+-----------------+-----+-------+------
East Jersey Water Co. |48″ steel riveted| 12″ |.002 | 4.62
| pipe | | |
Timber-stave pipe, Ogden, Utah|72″.5 | | | .5
” ” ” ” ” |72″.5 | | | 1.0
” ” ” ” ” |72″.5 | | | 1.5
” ” ” ” ” |72″.5 | | | 2.0
” ” ” ” ” |72″.5 | | | 2.5
” ” ” ” ” |72″.5 | | | 3.0
” ” ” ” ” |72″.5 | | | 3.5
” ” ” ” ” |72″.5 | | | 4.0
------------------------------+-----------------+-----+-------+------
LEGEND:
(A) = Coefficient _c_.
(B) = Cubic Feet per Second.
(C) = Gallons per 24 Hours.
------------------------------+-------+--------+---------+---------
| | Discharge. |
Pipe-line. | +--------+---------+
| (A) | (B) | (C) | Remarks.
------------------------------+-------+--------+---------+---------
Hemlock Lake | 87.3 |10.83124|7,000,000|
” ” | 99.7 |10.83124|7,000,000| 1892.
Rush Lake to Mt. Hope | 96.5 |10.83124|7,000,000+---------
Sudbury aqueduct |140.14 | | |
” ” |142.11 | | | Pipe new
” ” |144.09 | | | 1880.
| | | +---------
| | | | After
| | | | cleaning,
” ” |139.94†| | | 1894-95.
” ” |141.74†| | | Before
” ” |143.16†| | | cleaning,
| | | |_c_ = 108
| | | +---------
East Jersey Water Co. |103.3 | 58.02 |7,500,000| 1891.
Timber-stave pipe, Ogden, Utah| 72 | | | 1897.
” ” ” | 96 | | |
” ” ” |109 | | |
” ” ” |115 | | |
” ” ” |119 | | |
” ” ” |122 | | |
” ” ” |124 | | |
” ” ” |126 | | |
------------------------------+-------+--------+---------+---------
† These values correspond to the formula _c_ = 131.88_v_⁰˙⁰⁴⁵.
TABLE XVI.
___
VALUES OF _c_ IN _v_ = _c_√_rs_.
--------------+------------+-----+-----+-----+-----+-----+-----
| No. | 1 | 2 | 3 | 4 | 5 | 6
--------------+------------+-----+-----|-----+-----+-----+-----
| | | 4 | | | |
| Age | New |Years| New | New | New | New
--------------+------------+-----+-----+-----+-----+-----+-----
Velocity, | Diam. | | | | | |
Feet/sec. | Inches | 36 | 36 | 38 | 38 | 42 | 42
--------------+------------+-----+-----+-----+-----+-----+-----
0.5 | | | | | | |
1 | | 86 | | | | | 96
1.48 | | | | | | |
1.5 | | 90.6| | | | |103
2.0 | | 95.2| | | | |107.9
2.44 | | | | | |115.9|
2.5 | | 99.4| | | | |111
3 | |103.3| | | | |112.6
3.23 | | | |114 | | |
3.27 | | | |116.6| | |
3.32 |_c_ in _v_ =| | | | | |
3.5 | ___ |107 | | | | |113
3.52 | _c√rs_. | | | | | |
3.9 | | | | |109.2| |
3.96 | | | | | | |
4 | |110.6| | | | | 112.8
4.5 | |114 | | | | | 111.8
4.93 | | |106.3| | | |
5 | |117.2| | | | | 110.8
5.5 | |120.4| | | | | 110.2
6 | |123.6| | | | | 110
12.6 | | | | | | |
--------------+------------+-----+-----+-----+-----+-----+------
Kutter’s _n_ =| | | | | | |
coefficient | | .014| .013| .013| .013| .013| .013
of roughness | | | | | | |
--------------+------------+-----+-----+-----+-----+-----+----+-----
| No. | 7 | 8 | 9 | 10 | 11 |12 | 13
--------------+------------+-----+-----+-----+-----+-----+----+-----
| | | | 4 | 4 | | | 5
| Age | New | New |Years|Years| New | New|Years
--------------+------------+-----+-----+-----+-----+-----+----+-----
Velocity, | Diam. | | | | | | |
Feet per sec. | Inches | 42 | 48 | 48 | 48 | 48 | 72 | 103
--------------+------------+-----+-----+-----+-----+-----+----+-----
0.5 | | | | | | |110 |126.5
1 | |101 |101.2| 78 | 97.2| 97.1|110 |116.6
1.48 | | | | | | | |
1.5 | |102.8|105.4| 84.6|100.8| 98.7|111 |112.7
2.0 | |104.3|108.8| 89.6|103.3|100.3|110 |110.3
2.44 | | | | | | | |
2.5 | |105.5|111.2| 92.4|104.9|101.6|108 |108.8
3 | |106.4|111.8| 93 |105.3|102.2|108 |107.7
3.23 | | | | | | | |
3.27 | | | | | | | |
3.32 |_c_ in _v_ =| | | | | | |
3.5 | ___ |107.2|113.4| 93.2|104.8|103.6|110 |106.9
3.52 | _c√rs_. | | | | | | |
3.9 | | | | | | | |
3.96 | | | | | | | |
4 | |107.8|113.2| 94 |104 |104.2|111 |106.2
4.5 | |108.2|112.4| 94.2|103.7|104.7| |105.6
4.93 | | | | | | | |
5 | |108.4|112 | 94.4|103.7|105.1| |
5.5 | |108.5|111.7| 94.7|103.7|105.2| |
6 | |108.5|111.6| 94.9|103.7|105.2| |
12.6 | | | | | | | |
--------------+------------+-----+-----+-----+-----+-----+----+-----
Kutter’s _n_ =| | | | | | | |
coefficient | | .013| .013| .016| .014| .014|.014| .015
of roughness | | | | | | | |
--------------+------------+-----+-----+-----+-----+-----+----+-----
Exp. Nos. 1-2. Clemens Herschel, 1802. East Jersey Conduit,
cylindrical joints.
Nos. 3-4. E. Kuichling, 1895. New Rochester conduit,
cylindrical joints.
No. 5. I. W. Smith, 1896. Portland, Oregon, water-works.
Nos. 6-7. Clemens Herschel, 1896. East Jersey conduit,
taper joints.
No. 8. Clemens Herschel, 1892. East Jersey conduit,
cylindrical joints.
Nos. 9-10. Clemens Herschel, 1896. East Jersey conduit,
cylindrical joints.
No. 11. Clemens Herschel, 1896. East Jersey conduit,
taper joints.
No. 12. Marx, Wing, Hoskins, 1897. Pioneer El. Power Co.,
Ogden, Utah.
No. 13. Clemens Herschel, 1887. Holyoke, Mass.,
testing flume.
[Illustration: CROTON AQUEDUCT
IN ROCK.]
=191. Change of Hydraulic Gradient by Changing Diameter of Pipe.=—It
has already been seen, in the case of closed pipes or conduits, that
the hydraulic gradient with slope _s_ governs the velocity of flow, and
also that all parts of the pipe-line must be kept below that gradient.
It is sometimes desirable, in order to meet conditions either of
topography or of flow, to raise or lower the hydraulic gradient over
the whole or some portion of the pipe-line. This can easily be done
to any needed extent by varying the diameter of the pipe. An increase
in diameter will in general decrease the velocity of the water and
increase its pressure, thus increasing correspondingly the height of
the columns of water in the piezometer tubes. As the top surface of the
latter determines the hydraulic gradient, it is seen that increasing
the diameter of a portion of the pipe-line will correspondingly
raise the gradient over the same portion. Thus by a proper relative
variation of diameters the hydraulic gradient of a given pipe-line may
readily be controlled within sufficient limits to meet any ordinary
requirements of this character.
=192. Control of Flow by Gates at Upper End of Pipe-line.=—Obviously,
if the pressure in the pipe-line is diminished, less thickness of metal
will be required to resist it, and a corresponding degree of economy
may be reached by a decrease in the quantity of metal. In the 21 miles
of 48-inch steel-plate pipe of the East Jersey Water Company there is
a fall of 340 feet; if, therefore, the flow through that pipe were
regulated by a gate or gates at its lower end, the lower portion of the
line would be subjected to great intensity of pressure. If, however,
the flow through the pipe is controlled by a gate or gates at its
upper end, enough water only may be admitted to enable it to flow full
with the velocity due to the hydraulic gradient. By such a procedure
the pressure upon the pipe over and above that which is necessary to
produce the gradient is avoided. This condition is not only judicious
in the reduction of the amount of metal required, but also in reducing
both the leakage and the tendency to further leakage, which is largely
increased by high pressures. This feature of control of pressure in a
long pipe-line with considerable fall is always worthy of most careful
consideration.
=193. Flow in Old and New Cast-iron Pipes—Tubercles.=—The velocity of
flow through cast-iron mains or conduits or through the cast-iron pipes
of a distribution system of public water-supply depends largely upon
the condition of the interior surface of the pipes as affected by age.
All cast-iron pipes before being shipped from the foundry where they
are manufactured are immersed in a hot bath of suitable coal-tar pitch
composition in order to protect them from corrosion. After having been
in use a few years this coating on the interior of the pipes is worn
off in spots and corrosion at once begins. The iron oxide produced
under these circumstances forms projections, or tubercles as they are
called, of greatly exaggerated volume and out of all proportion to
the actual weight of oxide of iron. When the pipes are emptied these
tubercles are readily removed by scraping, but before their removal
they greatly obstruct the flow of water through the pipes. Indeed this
obstruction is so great that the discharging capacity of cast-iron
mains must be treated in view of its depreciation from this source.
Table XVII exhibits the value of the coefficient _c_ to be used in
Chezy’s formula for all cast-iron pipes having been in use for the
periods shown.
TABLE XVII.
TABLE OF VALUES OF _f_ AND _c_.
LEGEND:
(A) = Diameter, Inches.
(B) = Hydraulic Radius _r_, Inches.
(C) = Velocity, Feet per Second.
(D) = Coefficient _c_.
(E) = Coefficient _f_.
---------+-------------------------+-----+----+-----+-----+------
| | | | | |
Authority.| Pipe-line. | | | | |
| | (A) |(B) | (C) | (D) | (E)
| | | | | |
---------+-------------------------+-----+----+-----+-----+------
Darcy |New Pipe | 3.22| .8 | 0.29| 78.5| .0418
| | | |10.71|100.0| .0257
---------+-------------------------+-----+----+-----+-----+------
Darcy |Old cast-iron pipe lined | 9.63|2.41| 1.00| 72.5| .0489
| with deposit | | |12.42| 74.0| .0468
---------+-------------------------+-----+----+-----+-----+------
Darcy |Pipe above cleaned | 9.63|2.41| 0.91| 90.0| .0316
| | | |14.75| 98.0| .0269
---------+-------------------------+-----+----+-----+-----+------
Brush |Cast-iron pipe tar-coated|20 |5 | 2.00|114.0| .0197
| and in service 5 years. | | | 3.00|110.0| .0214
---------+-------------------------+-----+----+-----+-----+------
Darrach |Cast-iron pipe in service|20 |5 | 2.71| 67.5| .0568
| 11 years | | | 5.11| 83.0| .0376
---------+-------------------------+-----+----+-----+-----+------
Darrach |Cast-iron pipe in service|36 |9 | 1.58| 60.0| .0716
| 7 years | | | 2.37| 66.0| .0586
---------+-------------------------+-----+----+-----+-----+------
Obviously it is not possible to clean the smaller pipes of a
distribution system, but large cast-iron conduits may be emptied at
suitable periods and have their interior surfaces cleaned of tubercles
or other accumulations. At the same time, if necessary, a new coal-tar
coating can be applied.
Table XVIII exhibits the values of the coefficient _c_ to be used in
Chezy’s formula for new and clean coated cast-iron pipes. It represents
the results of actual hydraulic experience and is taken from Hamilton
Smith’s “Hydraulics.” A comparison between this table and that which
precedes will show how serious the effect of tubercles may be on the
discharging capacity of a cast-iron pipe.
____
In using Chezy’s formula, _v_ = _c_√_rs_,
in connection with either Table XVII or XVIII, the slope or sine of
inclination _s_ of the hydraulic gradient may be readily computed
by equation (10), which gives the head lost by friction in a closed
circular pipe as
_l v²_
_h_ = _f_ - --- ----.
_d_ 2_g_
It is only necessary in a straight pipe or one nearly straight to
compute the quantity
_h f v²_
_s_ = --- = --- ------.
_l d_ 2_g_
TABLE XVIII.
____
VALUES OF _c_ IN FORMULA: _v_ = _c__√_rs_.
--------+------+-------+-------+-------+-------+-------+-------
Velocity| Diameters in Feet (_d_ = 4_r_).
_v_, |
Feet per|------+-------+-------+-------+-------+-------+-------
Second.| .05 | .1 | 1 | 1.5 | 2 | 2.5 | 3
--------+------+-------+-------+-------+-------+-------+-------
1 | | 80.0 | 96.1 | 102.8 | 108.8 | 112.7 | 116.7
2 | 77.8 | 88.9 | 104.0 | 110.9 | 116.2 | 120.3 | 123.8
3 | 82.4 | 93.7 | 108.7 | 115.6 | 120.8 | 124.8 | 128.3
4 | 85.6 | 97.0 | 112.0 | 118.9 | 124.0 | 128.1 | 131.5
5 | 87.6 | 99.3 | 114.4 | 121.3 | 126.5 | 130.6 | 134.1
6 | 89.1 | 101.0 | 116.3 | 123.2 | 128.6 | 132.6 | 136.3
7 | 90.0 | 102.4 | 118.0 | 125.0 | 130.4 | 134.6 | 138.2
8 | 90.0 | 103.3 | 119.3 | 126.4 | 132.0 | 136.3 | 140.0
9 | 90.7 | 104.0 | 120.4 | 127.7 | 133.3 | 137.7 | 141.6
10 | 90.8 | 104.5 | 121.4 | 128.8 | 134.5 | 139.0 | 142.9
11 | 90.9 | 104.7 | 122.0 | 129.7 | 135.6 | 140.2 | 144.2
12 | 91.0 | 104.8 | 122.5 | 130.4 | 136.4 | 141.1 | 145.2
13 | 91.0 | 105.0 | 122.9 | 131.0 | 137.1 | 141.9 | 146.1
14 | 91.0 | 105.0 | 123.2 | 131.5 | 137.6 | 142.5 | 146.7
15 | 91.0 | 105.0 | 123.6 | 131.8 | 138.0 | 142.9 | 147.2
20(?)| | | 123.9 | 132.9 | | |
--------+------+-------+-------+-------+-------+-------+-------
Velocity| Diameters in Feet (_d = 4r_).
_v_, |
Feet per+------+-------+-------+-------+-------+-------
Second.| 3.5 | 4 | 5 | 6 | 7 | 8
--------+------+-------+-------+-------+-------+-------
1 |120.2 | 123.0 | 127.8 | 131.8 | 134.8 | 137.5
2 |127.0 | 129.9 | 134.3 | 138.0 | 141.0 | 143.3
3 |131.4 | 134.2 | 138.6 | 142.3 | 145.4 | 147.6
4 |134.6 | 137.4 | 141.9 | 145.5 | 148.6 | 151.0
5 |137.1 | 140.0 | 144.7 | 148.1 | 151.2 | 153.6
6 |139.4 | 142.3 | 146.9 | 150.5 | 153.5 |
7 |141.5 | 144.5 | 149.0 | 152.7 | |
8 |143.3 | 146.3 | 151.0 | 154.9 | |
9 |145.0 | 148.1 | 152.8 | 156.7 | |
10 |146.4 | 149.7 | 154.6 | | |
11 |147.7 | 151.0 | | | |
12 |148.8 | 152.3 | | | |
13 |149.8 | 153.2 | | | |
14 |150.5 | 154.0 | | | |
15 |151.1 | 154.6 | | | |
20(?)| | | | | |
--------+------+-------+-------+-------+-------+-------
=194. Timber-stave Pipes.=—In the western part of the country long
conduits or pipe-lines are frequently constructed of timber called
redwood. Staves of suitable thickness, sometimes 1¾ inches, are
accurately shaped and finished with smooth surfaces so as to form large
pipes of any desired diameter. These staves are held rigidly in place
with steel bands drawn tight with nuts on screw ends, so as to close
tightly the joints between them. Such wooden conduits are rapidly and
cheaply built and are very durable. They have the further advantage
of requiring no interior coating, as the timber surface remains
indefinitely unaffected by the water flowing over it. The latter part
of Table XV shows coefficients for Chezy’s formula which may be used
for such a class of timber conduits. As the interior surfaces of such
closed conduits are always very smooth, the coefficients are seen to
be relatively large, and such pipes are, therefore, well adapted to
maintain unimpaired discharging capacity for great lengths of time.
CHAPTER XVIII.
=195. Pumping and Pumps.=—When it is impossible to secure water at
sufficient elevation to be delivered to the points of consumption by
gravity, it is necessary to resort to pumping in order to raise it
to the desired level. Indeed it is sometimes necessary to resort to
pumping in connection with a gravity supply in order to deliver water
to the higher parts of the distribution system, the lower points being
supplied by gravity. This combination of gravity supply with pumping
is not unusual. That part of New York north of Thirty-fourth Street
between Lexington and Fifth avenues, north of Thirty-fifth Street
between Fifth and Sixth avenues, north of Fifty-first Street between
Sixth and Ninth avenues, north of Fifty-fifth Street between Ninth and
Tenth avenues, north of Fifty-eighth Street between Tenth and Eleventh
avenues, and north of Seventy-second Street between Eleventh Avenue
and the North River, with elevation of 60 feet or more above mean high
tide-water, is supplied from the high-service reservoir near High
Bridge, the water being elevated to it from the Croton supply by the
pumping-station at the westerly end of the bridge. The elevation of the
water surface in the High Bridge reservoir is 208 feet, and that of the
large reservoir in Central Park 115 feet, above mean high tide-water.
Some specially high points on the northern part of Manhattan Island are
supplied from the High Bridge tower, whose water surface is 316 feet
above mean high tide.
[Illustration]
[Illustration: Skeleton Pumps.]
The pumps employed for the purpose of elevating water to
distributing-reservoirs are among the finest pieces of machinery built
by engineers at the present time. They are usually actuated by steam
as a motive power, the steam being supplied from suitable boilers or
batteries of boilers in which coal is generally used as fuel. The
modern pumping-engine is in reality a combination of three classes of
machinery, the boilers, the steam-engines, and the pumps. There are
various types of boilers as well as of engines and pumps, all, when
judiciously designed and arranged, well adapted to the pumping-engine
process. The pumps are generally what are called displacement
pumps; that is, the water in the pump-cylinder is displaced by the
reciprocating motion of a piston or plunger. These pumps may be either
double-acting or single-acting; in the former case, as the piston or
plunger moves in one direction it forces the water ahead of it into
the main or pipe leading up to the reservoir into which the water is
to be delivered, while the water rising from the pump-well follows back
of the piston or plunger to the end of its stroke. When the motion
is reversed the latter water is forced on its way upward through the
main, while the water rises from the pump-well into the other end of
the water-cylinder. In the case of single-acting pumps water is drawn
up into the water-cylinder from the pump-well during one stroke and
forced up through the main during the next stroke, one operation only
being performed at one time. The pump-well is a well or tank, usually
of masonry, into which the water runs by gravity and from which the
pump raises it to the reservoir. For the purposes of accessibility and
convenience in repairing, the pump is always placed at an elevation
above the water in the pump-well, the pressure of the atmosphere on the
water in the well forcing the latter up into the pump-cylinder as the
piston recedes in its stroke. The height of a column of water 1 square
inch in section representing the pressure of the atmosphere per square
inch is about 34 feet, but a pump-cylinder should not be placed more
than about 18 feet above the surface of the water in the pump-well in
order that the water may rise readily as it follows the stroke of the
plunger.
In the operation of the ordinary pump the direction of the water as it
flows into and out of the pump-cylinder must necessarily be reversed,
and this is true also with the type of pump called the differential
plunger-pump, which is really a single-acting pump designed so as to
act in driving the water into the main like a double-acting pump,
i.e., both motions of the plunger force water through the main, but
only one draws water from the pump-well into the pump-cylinder. Valves
may be so arranged in the pump-piston as to make the progress of the
water through the pump continuous in one direction and so avoid the
irregularities and shocks which necessarily arise to some extent from a
reversal of the motion of the water.
The steam is used in the steam-cylinders of a pumping-engine precisely
as in every other type of steam-engine. At the present time compound
or triple-expansion engines are generally used, among the well-known
types being the Worthington duplex direct-acting pump without crank or
fly-wheel, the Gaskill crank and fly-wheel pumping-engine, the Allis
and the Leavitt pumping-engines, both of the latter employing the crank
and fly-wheel and both may be used as single- or double-acting pumps,
usually as the latter. The characteristic feature of the well-known
Worthington pumping-engine is the movement of the valves of each of the
two engines by the other for the purpose of securing a quiet seating of
the valves and smooth working.
One of the most important details of the pumping-engine is the
system of valves in the water-cylinder, and much ingenuity has been
successfully expended in the design of proper valve systems. These
pump-valves must, among other things, meet the following requirements
as efficiently as possible: they must close promptly and tightly, so
that no water may pass through them to create slip or leakage; they
should have a small lift, so as to allow prompt closing, and large
waterways, to permit a free flow through them with little resistance;
they must also be easily operated, so as to require little power,
and, like all details of machinery, they should be simple and easily
accessible for repairing when necessary.
As steam is always used expansively, its force impelling the plunger
will have a constant value during the early portion of the stroke
only, and a much less value, due to the expansion of the steam, at
and near the end of the stroke, while the head of water against which
the pump operates is practically constant. There is, therefore, an
excess of effort during the first part of the stroke and a deficiency
during the latter part. Unless there should be some means of taking
up or cushioning this difference, the operation of the pump would be
irregular during the stroke and productive of water-hammer or blows to
the engine. Two means are employed to remove this undesirable effect,
i.e., the fly-wheel and the air-chamber, or both. In the one case the
excess of work performed by the steam in the early part of the stroke
is stored up as energy in the accelerated motion of the fly-wheel and
given out by the latter near the end of the stroke, thus producing the
desired equalization. The air-chamber is a large reservoir containing
air, attached to and freely communicating with the force-main or pipe
near its connection with the pumps. In this case the excess of work
performed at the beginning of the stroke is used in compressing the
air in the air-chamber, sufficient water entering to accomplish that
purpose. This compressed air acts as a cushion, expanding again at the
end of the stroke and reinforcing the decreasing effort of the steam.
=196. Resistances of Pumps and Main—Dynamic Head.=—Obviously the
water flowing through the pipes, pump-cylinders, and pump-valves
will experience some resistance, and it is one purpose in good
pumping-engine design to make the progress of the water through the
pump so direct and free as to reduce these losses to a minimum.
Similarly the large pipe or main, called the force-main, leading
from the pump up to the reservoir into which the water is delivered,
sometimes several thousand feet long, will afford a resistance of
friction to the water flowing through it. The head which measures
this frictional loss is given by equation (10) on page 239. All these
resistances will increase rapidly with the velocity with which the
water flows through the pipes and other passages, as do all hydraulic
losses. It is obviously advisable, therefore, to make this velocity
as low as practicable without unduly increasing the diameter of the
force-main. This velocity seldom exceeds about 3 feet per second.
[Illustration: Allis Pump.]
[Illustration: Section of Allis Pumping-Engine.]
The static head against which the pumping-engine operates is the
vertical height or elevation between the water surfaces in the
pump-well and the reservoir. The head which represents the resistances
of the passages through the pump and force-main, when added to the sum
of the static head and the head due to the velocity in the force-main,
gives what is called the dynamic head; it represents the total head
against which the pump acts. If _h_ represents the static head, _hʹ_
the head due to all the resistances, and _h″_ the head due to the
velocity in the force-main, then the dynamic head will be
_l v² v² v²_
_H_ = _h + hʹ + h″_ = _h_ + _f_ --- ---- + _n_---- + ----,
_d_ 2_g_ 2_g_ 2_g_
in which _f_ has a value of about .015 and _n_ is a coefficient which
when multiplied by the velocity head will represent the loss of head
incurred by the water in passing through the pump-cylinder and valves.
The latter quantity is variable in value; but it is seldom more than a
few feet.
=197. Duty of Pumping-engines.=—It is thus seen that the collective
machines and force-main forming the pumping system afford opportunity
for a number of serious losses of energy found chiefly in the boiler,
the engine, and the pump. The excellence of a pumping-plant, including
the boilers, may obviously be measured by the amount of useful work
performed by a standard quantity, as 100 pounds of coal. Sixty or more
years ago, in the days of the old Cornish pumping-engine, the standard
of excellence or “duty” was the number of foot-pounds of work, i.e.,
the number of pounds lifted one foot high, performed by one bushel of
coal. As early as 1843 the Cornish pumping-engine reached a duty, per
bushel of coal, of 107,500,000 foot-pounds. These pumping-engines were
single-acting, the steam raising a weight the descent of which forced
the water up the delivery-pipe.
At a later date and until about ten years ago the usual standard or
criterion applied to pumping-engines for city water-works was the
amount of work performed in lifting water for each 100 pounds of
coal consumed; this result was also called the “duty” of the engine.
In order to determine the duty of a pumping-engine it was thus only
necessary to observe carefully for a given period of time, i.e.,
twenty-four hours or some other arbitrary period, the amount of coal
consumed, the condition of the furnace-fires at the beginning and end
of the test being as nearly the same as possible, and measure at the
same time the total amount of water discharged into the reservoir.
The total weight of water raised multiplied by the total number of
feet of elevation from the water surface in the pump-well to that in
the reservoir would give the total number of foot-pounds of useful
work performed. This quantity divided by the number of hundred pounds
of coal consumed would then give what is called the “duty” of the
pumping-engine.
=198. Data to be Observed in Pumping-engine Tests.=—Obviously it is
necessary to observe a considerable number of data with care. No
pump works with absolute perfection. A little water will run back
through the valves before they are seated, and there will be a little
leakage either through the valves or through the packing around the
piston or plunger, or both sources of leakage may exist. That leakage
and back-flow represent the amount of slip or water which escapes
to the back of the plunger after having been in front of it. In
well-constructed machinery this slip or leakage is now very small and
may be but a small fraction of one per cent. Inasmuch as the amount
of work performed by the steam will be the same whether this slip
or leakage exists or not, the latter is now frequently ignored in
estimating the duty of pumping-engines, the displacement of the piston
or plunger itself being taken as the volume of water pumped at each
stroke.
Again, in discussing the efficiency of the steam portion of the
machinery the amount of partial vacuum maintained in the vacuum-pump,
which is used to move the water of the condensed steam, is affected
by atmospheric pressure, as is the work which is performed. Hence
in complete engine tests it is necessary to observe the height of
the barometer during the test. It is also necessary to observe the
temperature of feed-water supplied to the boiler, and to use accurate
appliances for ascertaining with the greatest exactness practicable
the weight of dry steam used in the steam-cylinders and the amount of
water which it carries. It is not necessary for the present purpose
to discuss with minuteness these details, but it is evident from the
preceding observations that the complete test of a pumping-engine
involves the accurate observation of many data and their careful use in
computations. The determination of the duty alone is but a simple part
of those computations, and the duty is all that is now in question.
=199. Basis of Computations for Duty.=—It was formerly necessary in
giving the duty of a pumping-engine to state whether the 100 pounds of
coal was actually coal as shovelled into the furnace, or whether it was
that coal less the weight of ash remaining after combustion. It was
also necessary to specify the quality of coal used, because the heating
capacity of different coals may vary materially. For these different
reasons the statement of the duty of a pumping-engine in terms of a
given weight of coal consumed involved considerable uncertainty, hence
in 1891 a committee of the American Society of Mechanical Engineers,
appointed for the purpose, took into consideration the best method
of determining and stating the duty of a pumping-engine. The report
of that committee may be found in vol. XII of the Transactions of
that Society. The committee recommended that in a duty test 1,000,000
heat-units (called British Thermal Units or, as abbreviated, frequently
B.T.U.) should be substituted for 100 pounds of coal. In other words,
that the following should be the expression for the duty:
foot-pounds of work done
Duty = ----------------------------------- × 1,000,000.
total number of heat-units consumed
For some grades of coal in which 1,000,000 heat-units would be
available for every 100 pounds the numerical value of the duty
expressed in the new terms would be unchanged, but for other grades of
coal the new expression of the duty might be considerably different.
=200. Heat-units and Ash in 100 Pounds of Coal, and Amount of Work
Equivalent to a Heat-unit.=—The following table exhibits results
determined by Mr. George H. Barrus (Trans. A. S. M. E., vol. XIV. page
816), giving an approximate idea of the total number of heat-units
which are made available by the combustion of 100 pounds of coal of the
kinds indicated:
Semibitumintous:
George’s Creek Cumberland, Percentage of Ash.
1,287,400 to 1,421,700 6.1 to 8.6
Pocahontas,
1,360,800 to 1,460,300 3.2 to 6.2
New River,
1,385,800 to 1,392,200 3.5 to 5.7
Bituminous:
Youghiogheny, Pa., lump,
1,294,100 5.9
Youghiogheny, Pa., slack,
1,166,400 10.2
Frontenac, Kan.,
1,050,600 17.7
Cape Breton Caledonia,
1,242,000 8.7
Anthracite:
1,152,100 to 1,318,900 9.1 to 10.5
[Illustration: Worthington Pump.]
Each unit or B.T.U. represents the amount of heat required to raise
one pound of water at 32° Fahr. 1° Fahr., and it is equal to 778
foot-pounds of work. In other words, 778 foot-pounds of work is said
to be the mechanical equivalent of one heat-unit. The amount of work,
therefore, which one pound of dry steam is capable of performing at
any given pressure and at the corresponding temperature may readily
be found by multiplying the number of available heat-units which it
contains, and which may be readily computed if not already known, by
778, or as in a pumping-engine duty trial, knowing by observation the
number of pounds of steam at a given pressure and temperature supplied
through the steam-cylinders, the number of heat-units supplied in
that steam is at once known or may easily be computed. Then observing
or computing the total weight of water raised by the pumping-engine,
as well as the total head (the dynamic head) against which the
pumping-engine has worked, the total number of foot-pounds of work
performed can be at once deduced. This latter quantity divided by the
number of million heat-units will give the desired duty.
[Illustration: Section of Worthington Pump.]
=201. Three Methods of Estimating Duty.=—At the present time it is
frequently, and perhaps usually, customary to give the duty in terms
of 100 pounds of coal consumed, as well as in terms of 1,000,000
heat-units. Frequently, also, the duty is expressed in terms of 1000
pounds of dry steam containing about 1,000,000 heat-units. As has
sometimes been written, the duty unit is 100 for coal, 1000 for steam,
and 1,000,000 for heat-units.
=202. Trial Test and Duty of Allis Pumping-engine.=—The following data
are taken from a duty test of an Allis pumping-engine at Hackensack,
N. J., in 1899 by Prof. James E. Denton. This pumping-engine was built
to give a duty not less than 145,000,000 foot-pounds for each “1000
pounds of dry steam consumed by the engine, assuming the weight of
water delivered to be that of the number of cubic feet displaced by the
plungers on their inward stroke, i.e., to be 145,000,000 foot-pounds
at a steam pressure of 175 pounds gauge.” The capacity of the engine
was to be 12,000,000 gallons per twenty-four hours at a piston speed
not exceeding 217 feet per minute. The engine was of the vertical
triple-expansion type with cylinders 25.5 inches, 47 inches, and 73
inches in diameter with a stroke of 42¹/₁₆ inches, the single-acting
plunger being 25.524 inches in diameter. The following data and figures
illustrate the manner of computing the duty:
DUTY PER 1000 POUNDS OF DRY STEAM BY PLUNGER DISPLACEMENT.
1. Circumference of plungers, _Cl_ 80.1875 ins.
2. Length of stroke, 7 42.0625 ins.
3. Number of plungers (single-acting) 3
4. Aggregate displacement of plunger per revolution =
3_C²l_
------ = _d_ 64,4557.1 cu. ins.
4π
5. Revolutions during 24 hours, _N_ 43,337
6. Weight of one cubic foot of water, _w_ 62.42 lbs.
7. Total head pumped against, _H_ 266.61 ft.
8. Total feed-water per 24 hours, _W_ 160,354 lbs.
9. Duty per 1000 lbs. of feed-water =
_d × w H × N_ × 1000
------ × -------------
1728 _W_
266.61 × 43,337 × 1000
= 2,331,976 × ---------------------- = 168,027,200 ft.-lbs.
160,354
10. Percentage of moisture in steam at
engine-throttle valve 0.3 per cent.
168,027,200
11. Duty per 1000 lbs. of dry steam, ----------- = 168,532,800
0.997 ft.-lbs.
DUTY PER MILLION HEAT-UNITS.
12. Average steam pressure at throttle above atmosphere. 173 lbs.
13. Average feed-water temperature. 78°.5 Fahr.
14. Total heat in one pound of steam containing
0.3 per cent. of moisture above 32° Fahr. 1,194.2 B. T. U.
15. Heat per lb. of feed-water above 32° Fahr. 46.5 ”
-------
16. Heat supplied per lb. of feed-water
above 32° Fahr. 1,147.7 ”
17. Duty per lb. of feed-water. 168,027.2 ft.-lbs.
18. Duty per million B. T. U. 146,403,614 ”
=203. Conditions Affecting Duty of Pumping-engines.=—Manifestly the
duty of a pumping-engine by whatever standard it may be measured will
vary with the conditions under which it is made. A new engine running
under the favoring circumstances of a short-time test may be expected
to give a higher duty than when running under the ordinary conditions
of usage one month after another. Hence it can scarcely be expected
that the monthly performance, and much less the yearly performance, of
an engine will show as high results as when tested for a day or two or
for less time.
=204. Speeds and Duties of Modern Pumping-engines.=—The following table
gives the piston or plunger speeds of a number of the best modern
pumping-engines, and the corresponding duties, with the standards by
which those duties are measured.
LEGEND:
(A) = Piston Speed in Feet per Minute.
(B) = Duty in Foot-pounds.
-------------------------------+------+-----------+-----------------
Engine. | (A) | (B) | Expressed in
-------------------------------+------+-----------+-----------------
Ridgewood Station, Brooklyn, | | |
Worthington engine |164.0 |137,953,585| 1000 lbs. of
| | | dry steam
14th St. pumping-station, | | |
Chicago; built by Lake Erie | | |
Engine Works |210.54|133,445,000| Million B.T.U.
Allis engine at Hackensack, | | |
N. J. |210.65|146,403,416| ” ”
Snow pump at Indianapolis |214.6 |150,100,000| ” ”
Leavitt pump at Chestnut Hill | |144,499,032| ” ”
Nordberg at Wildwood |256.0 |162,132,517| ” ”
Allis at Chestnut Hill, tested | | |
May 1, 1900 |192.5 |157,002,500| Million B.T.U.
Allis at St. Louis, tested | | |
February 26, 1900 |197.16|158,077,324| ” ”
Barr at Waltham, Mass. |194.28|128,865,000| 1000 lbs. of
| | | dry steam
Allis at St. Paul, Minn. |189.0 |144,463,000| ” ” ”
Lake Erie Engine Works at | | |
Buffalo |207.7 |135,403,745| Million B.T.U.
These results show that material advances have been made in
pumping-engine designs within a comparatively few years.
CHAPTER XIX.
=205. Distributing-reservoirs and their Capacities.=—The water of a
public supply seldom runs from the storage-reservoir directly into
the distributing system or is pumped directly into it, although such
practices may in some cases be permissible for small towns or cities.
Generally distributing-reservoirs are provided either in or immediately
adjacent to the distributing system of pipes, meaning the water-pipes
large and small which are laid through the streets of a city or town,
and the service-pipes leading from the latter directly to the consumers.
The capacity ordinarily given to these distributing-reservoirs is not
controlled by any rigid rule, but depends upon the local circumstances
of each case. If they are of masonry and covered with masonry arches,
as required for the reception of some filtered waters, they are made as
small as practicable on account of their costs. If, on the contrary,
they are open and formed of suitably constructed embankments, like the
distributing-reservoirs of New York City in Central Park and at High
Bridge, they are and should be of much greater capacity. The storage
volume of the High Bridge reservoir amounts to 11,000,000 gallons,
while that of the Central Park reservoir is 1,000,000,000 gallons.
Again, the capacity of the old receiving-basin in Central Park is
200,000,000 gallons. These reservoirs act also as equalizers against
the varying draft on the system during the different portions of the
day and furnish all desired storage for the demands of fire-streams,
which, while it lasts, may be a demand at a high rate. It may be
approximately stated under ordinary circumstances that the capacity of
distributing-reservoirs for a given system should equal from two or
three to eight or ten days supply. It is advantageous to approach the
upper of those limits when practicable. The volume of water retained in
these reservoirs acts in some cases as a needed storage, while repairs
of pumping-machinery or other exigencies may temporarily stop the flow
into them. The larger their capacity the more effectively will such
exigencies be met.
=206. System of Distributing Mains and Pipes.=—Gate-houses must be
placed at the distributing-reservoirs within which are found and
operated the requisite gates controlling the supply into the reservoir
and the outflow from it into the distributing system. The latter
begins at the distributing-reservoir where there may be one or two
or more large mains, usually of cast-iron. These mains conduct the
water into the branching system of pipes which forms a network over
the entire city or town. A few lines of large pipes are laid so as
to divide the total area to be supplied into convenient portions
served by pipes of smaller diameter leading from the larger, so that
practically every street shall carry its line or lines of piping from
which every resident or user may draw the desired supply. Obviously,
as a rule, the further the beginning of the distributing system is
departed from in following out the ramifications of the various lines
the smaller will the diameter of pipe become. The smallest cast-iron
pipe of a distributing system is seldom less than 3 inches, and
sometimes not less than 4 or 6 inches. There should be no dead ends
in any distributing system. By a dead end is meant the end of a line
of pipes, which is closed so that no water circulates through it.
Whenever a branch pipe ceases it should be extended so as to connect
with some other pipe in the system in order to induce circulation. The
entire distributing system should therefore, in its extreme as well
as central portions, constitute an interlaced system and not a series
of closed ends. This is essential for the purity and potability of
the water-supply. A circulation in all parts of the entire system is
essential and it should be everywhere secured.
The diagram shows a portion of the distributing system of the city of
New York. It will be noticed that there is a complete connection of
the outlying portions, so as to make the interlacing and corresponding
circulation as complete and active as possible.
[Illustration: FIG. 4.—New York City Distributing System.]
=207. Diameters of and Velocities in Distributing Mains and Pipes.=—In
laying out a distributing system it will not be possible to base the
diameters at different points on close computations for velocity or
discharges based upon considerations of friction or other resistances,
as the conditions under which the pipes are found are too complicated
to make such a method workable. Approximate estimates may be made as
to the number of consumers to be supplied at a given section of a main
pipe, and consequently what the diameter should be to pass the required
daily supply so that the velocity may not exceed certain maximum limits
known to be advisable. Such estimates may be made at a considerable
number of what may be termed critical points of the system, and the
diameters may be ascertained in that manner with sufficient accuracy.
In this field of hydraulics a sound engineering judgment, based upon
experience, is a very important element, as it is in a great many other
engineering operations.
It will follow from these considerations that as a rule the larger
diameters of pipe in a given distributing system will belong to the
greater lengths, and it will be found that the velocities of water in
the various parts of a system will seldom exceed the following limits,
which, although stated with some precision, are to be regarded only as
approximate:
For 4-inch pipe 23 feet per second.
” 6 ” ” 23 ” ” ”
” 8 ” ” 17 ” ” ”
” 11 ” ” 12 ” ” ”
” 12 ” ” 12 ” ” ”
” 16 ” ” 9 ” ” ”
” 20 ” ” 8 ” ” ”
” 24 ” ” 7 ” ” ”
” 30 ” ” 7 ” ” ”
” 36 ” ” 7 ” ” ”
” 48 ” ” 7 ” ” ”
” 60 ” ” 7 ” ” ”
=208. Required Pressures in Mains and Pipes.=—In designing distributing
systems it is very essential so to apportion the pipes as to secure
the requisite pressure at the various street services. Like many other
features of a water-supply system no exact rules can be given, but it
may be stated that at the street-level a pressure of at least 20 to 30
pounds should be found in resident districts, and from 30 to 35 or 40
pounds in business districts. The character and height of buildings
affect these pressures to a large extent. Old pipe systems usually
have many weak points, and while pressures requisite to carry water
to the top of three- or four-story buildings are needed, any great
excess above that would be apt to cause breaks and result in serious
leakages. If the distributing system is one in which the pressure for
fire-streams is to be found at the hydrants, then greater pressures
than those named must be provided. In such cases the pressures in pipes
at the hydrants should range from 60 to 100 pounds.
=209. Fire-hydrants.=—Fire-hydrants must be placed usually at street
corners, if the blocks are not too long, and so distributed as to
control with facility the entire district in which they are found.
Unless fire-engines are used to create their own pressure, the lower
the pressure at the hydrant the nearer together the hydrants must be
placed. It is obvious, however, that when the pressure of the system
is depended upon for fire-streams it is desirable to have the pressure
comparatively high, so far as the hydrants are concerned, as under
those conditions they may be placed farther apart and a less number
will be required.
=210. Elements of Distributing Systems.=—The following table gives
a number of statistics, exhibiting the elements of the distributing
system of a considerable number of cities, including some pumping and
meter data pertinent to the costs of pumping on the one hand and the
extension of the use of meters on the other.
It contains information of no little practical value in connection
with the administration of the distributing systems and the
consumption of water in it. This table has been compiled by Mr.
Chas. W. Sherman of the New England Water-works Association, and
was published in the proceedings of that association for September,
1901. The service-pipes, varying from ½ to 10 inches in diameter,
are of cast-iron, wrought-iron, lead, galvanized iron, tin-lined,
rubber-lined, cement-lined, enamelled and tarred, the practice varying
widely not only from one city to another, but in the same city.
TABLE XIX
LEGEND:
(A) = Kind of Pipe.
(B) = Size of Pipe. Ins
(C) = Total Length in Use, Miles.
(D) = Cost of Repairs per Mile.
(E) = Total Number of Hydrants in Use.
---------------------------+--------+-----+------+------+----------
Name of City or Town. | (A) | (B) | (C) | (D) | (E)
---------------------------+--------+-----+------+------+----------
Albany, N. Y. | | | 129.7| | 808
---------------------------+--------+-----+------+------+----------
Atlantic City, N. J. | C.I. | 4-20| 47.6| | 519
| | | | | 808
---------------------------+--------+-----+------+------+----------
Boston, Mass. | C.I. | 2-48| 713.4| 27.09| 7606
---------------------------+--------+-----+------+------+----------
| C.L. | | | |
Burlington, Vt. | C.I. | 4-30| 38.0| 4.61| 213
| W.I. | | | |
---------------------------+--------+-----+------+------+----------
Cambridge, Mass. | | | | | 968
| | | | |
---------------------------+--------+-----+------+------+----------
Chelsea, Mass. | C.I. | 6-16| 37.8| | 253
| | | | |
---------------------------+--------+-----+------+------+----------
| C.I. | | | |
Concord, N. H. | C.L. | 4-30| 60.2| | 267
---------------------------+--------+-----+------+------+----------
Fall River, Mass. | C.I. | 6-24| 87.3| | 954
| | | | |
---------------------------+--------+-----+------+------+----------
Fitchburg, Mass. | C.I. | 2-20| 66.6| | 499
---------------------------+--------+-----+------+------+----------
| C.I. | | | |
Holyoke, Mass. | W.I. | ½-30| 81.6| 5.14| 860
---------------------------+--------+-----+------+------+----------
Lowell, Mass. | | | 127.8| | 1098
| | | | |
---------------------------+--------+-----+------+------+----------
| W.I. | | | |
Lynn, Mass. | C.L. | 2-20| 129.4| | 952
| C.I. | | | |
---------------------------+--------+-----+------+------+----------
Madison, Wis. | C.I. | 4-16| 34.3| | 169
| | | | |
| | | | |
---------------------------+--------+-----+------+------+----------
| C.L. | | | |
Manchester, N. H. | C.I. | 4-20| 96.9| | 743
---------------------------+--------+-----+------+------+----------
Owned by | C.I. | 6-60| 69.8| |
Metropolitan | C.L. | | | |
Water-works +--------+-----+------+------+----------
| C.I. | | | |
Tot. Sup. by | C.L. | 4-60|1360.3| | 11913
| Kal. | | | |
---------------------------+--------+-----+------+------+----------
| C.I. | | | |
Minneapolis, Minn. | Steel.|1¼-50| 269.2| | 3172
---------------------------+--------+-----+------+------+----------
New Bedford, Mass. | C.I. | 4-36| 92.7| 24.00| 738
---------------------------+--------+-----+------+------+----------
| W.I. | | | |
New London, Conn. | C.L. | 4-24| 50.5| 18.71| 258
| C.I. | | | |
---------------------------+--------+-----+------+------+----------
Newton, Mass. | C.I. | 4-20| 136.6| 6.43| 935
---------------------------+--------+-----+------+------+----------
Providence, R. I. | C.I. | 6-36| 324.6| 0.56| 1886
---------------------------+--------+-----+------+------+----------
” H.P. Fire System | C.I. |12-24| 5.6| | 92
---------------------------+--------+-----+------+------+----------
| W.I. | | | |
Quincy, Mass. | C.I. | 1-36| 144.7| 5.50| 955†
| C.L. | | | |
---------------------------+--------+-----+------+------+----------
| C.I. | | | |
Springfield, Mass. | Kal. | 2-20| 84.1| | 539
---------------------------+--------+-----+------+------+----------
Woonsocket, R. I. | C.I. | 4-20| 45.8| 3.57| 548
---------------------------+--------+-----+------+------+----------
Yonkers, N. Y. | | | 74.1| | 771
---------------------------+--------+-----+------+------+----------
Worcester, Mass. | | 2-40| 173.5| | 1763
| | | | |
---------------------------+--------+-----+------+------+----------
† Public hydrants only.
TABLE XIX. (continued)
LEGEND:
(F) = Total Number of Gates in Use.
(G) = Range of Pressure on Mains at Centre, Pounds.
(H) = Size of Service-pipe in Inches.
(I) = Total Number of Service-taps in Use.
(J) = Total Number of Meters in Use.
(K) = Total Pumpage for the Year in Gallons.
(L) = Average Static Head against which Pumps Work, Feet.
----+--------------+------+-------+--------+-----------------+------
(F)| (G) | (H) | (I) | (J) | (K) | (L)
----+--------------+------+-------+--------+-----------------+------
803| | | | 2030 | |
----+--------------+------+-------+--------+-----------------+------
| | ½-4 | 4,249| 3298 | 955,726,046 | 81.7
| | | | | 148,662,947 | 119.5
----+--------------+------+-------+--------+-----------------+------
8910| 40-90 | ½-8 | 87,525| 4516 | |
----+--------------+------+-------+--------+-----------------+------
| | | | | |
618| 70-85 | ½-6 | 3,350| 2311 | 312,896,525 | 289
| | | | | |
----+--------------+------+-------+--------+-----------------+------
| | | 14,207| 860 | 2,651,277,240 |
399| 48-50 | ⅝-2 | 6,146| 104 | |
----+--------------+------+-------+--------+-----------------+------
757| | | 3,340| 1010 | 142,772,165 |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
940| 80 | ½-2 | 6,943| 6,544 | 1,388,776,336 | 186.2
----+--------------+------+-------+--------+-----------------+------
| 75 L.S. | | | | |
554| 155 H.S. | ¾-8 | 4,432| 2,427 | |
----+--------------+------+-------+--------+-----------------+------
734| 80-100 | ⅝-4 | 3,610| 210 | |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
1188| | | 10,634| 5,586 | 2,042,066,140 | 156.1
| | | | | |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
| | | | | 378,782,675 |
966| 45-60 | ¾-4 | 13,504| 2,571 | 1,330,784,875 |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
234| | | 2,758| 2,586 | 306,637,454 | 223.8
| | | | | |
----+--------------+------+-------+--------+-----------------+-----
| | | | | |
| | | | | |
910| | ½-6 | 5,513| 3,667 | |
| | | | | |
| | | | | |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
268| | |134,496| 10,385 |15,027,410,000(a)|
| | | | | 9,431,140,000(b)|
| | | | | 2,015,130,000(c)|
----+--------------+------+-------+--------+-----------------+------
2195| | ⅝-1 | 20,064| 5,030 | 6,863,135,200 |
----+--------------+------+-------+--------+-----------------+------
| | | | | |
1065| 28-64 | ½-10| 9,280| 1,429 | 2,307,429,372 | 167.2
| | | | | |
----+--------------+------+-------+--------+-----------------+------
318| 40-48 | ½-4 | 3,088| 229 | |
----+--------------+------+-------+--------+-----------------+------
801| 84 | ½-6 | 7,087| 6,001 | 762,876,073 | 234
----+--------------+------+-------+--------+-----------------+------
3399| 64-73 | ½-10| 21,566| 17,813 | 3,833,243,445 | 171.6
| | | | | 34,401,038 | 172.4
----+--------------+------+-------+--------+-----------------+------
31| 114 | | | | 578,940,480 | 111.2
----+--------------+------+-------+--------+-----------------+------
1889| 30-35 H.S. | 1-6 | 9,764| 3,122 | |
| 100-120 L.S.†| | | | |
----+--------------+------+-------+--------+-----------------+------
1001| 78-85 | ⅝-3 | 4,330| 122 | |
| | | | | |
----+--------------+------+-------+--------+-----------------+------
456| 50-120 | ⅝-6 | 2,193| 1,889 | 340,849,628 | 237.6
----+--------------+------+-------+--------+-----------------+------
498| | ¼-8 | 4,968| 4,852 | 1,323,696,099 |
----+--------------+------+-------+--------+-----------------+------
| 70 L.S. | | | | |
2432| 150 H.S.† | | 13,292| 12,529 | |
† Public hydrants only.
C.L. = cement-lined.
(_a_) = Chestnut Hill high service.
(_b_) = Chestnut Hill low service.
(_c_) = Spot Pond Pumping-station.
TABLE XIX. (continued)
LEGEND:
(M) = Average Dynamic Head against which Pumps Work, Feet.
(N) = Duty in Foot-pounds per 100 Pounds of Coal. No Deductions.
----------------------------+--------+-------+-------+------------
| | | |
| | | |
Name of City or Town. |Kind of |Size of| (M) | (N)
| Pipe. | Pipe. | |
| | | |
----------------------------+--------+-------+-------+------------
Albany, N. Y. | .. | .. | .. | ..
----------------------------+--------+-------+-------+------------
Atlantic City, N. J. | C.I. | 4-20 | 123.3| 36,501,217
| | | 119.5| 15,518,455
----------------------------+--------+-------+-------+------------
Boston, Mass. | C.I. | 2-48 | .. | ..
----------------------------+--------+-------+-------+------------
| C.L. | | |
Burlington, Vt. | C.I. | 4-30 | 316 | ..
| W.I. | | |
----------------------------+--------+-------+-------+------------
Cambridge, Mass. | .. | .. | .. | ..
Chelsea, Mass. | C.I. | 6-16 | .. | ..
----------------------------+--------+-------+-------+------------
Concord, N. H. | C.I. | | |
| C.L. | 4-30 | .. | ..
----------------------------+--------+-------+-------+------------
Fall River, Mass. | C.I. | 6-24 | .. | ..
Fitchburg, Mass. | C.I. | 2-20 | .. | ..
----------------------------+--------+-------+-------+------------
Holyoke, Mass. | C.I. | ½-30 | .. | ..
| W.I. | | |
----------------------------+--------+-------+-------+------------
Lowell, Mass. | .. | .. | 163.9| 93,489,048
----------------------------+--------+-------+-------+------------
| W.I. | | |
Lynn, Mass. | C.L. | 2-20 | 167 | 88,780,036
| C.I. | | 167 | 87,265,319
Madison, Wis. | C.I. | 4-16 | 242.4| 47,530,839
----------------------------+--------+-------+-------+------------
Manchester, N. H. | C.L. | 4-20 | .. | ..
| C.I. | | |
----------------------------+--------+-------+-------+------------
| C.I. | 6-60 | 96.5| 121,800,000
Owned by | C.L. | | |
Metropolitan +--------+-------+-------+------------
Water-works | C.I. | 4-60 | 51.8| 109,380,000
Tot. Sup. by | C.L. | | 125.6| 80,400,000
| Kal. | | |
----------------------------+--------+-------+-------+------------
| C.I. | | |
Minneapolis, Minn. | Steel.| 1½-50 | .. | 68,016,609
----------------------------+--------+-------+-------+------------
New Bedford, Mass. | C.I. | 4-36 | 192 | 130,336,508
----------------------------+--------+-------+-------+------------
| W.I. | | |
New London, Conn. | C.L. | 4-24 | .. | ..
| C.I. | | |
----------------------------+--------+-------+-------+------------
Newton, Mass. | C.I. | 4-20 | 254 | 72,500,000
----------------------------+--------+-------+-------+------------
| | | 176.9| 101,301,600
Providence, R. I. | C.I. | 6-36 | 177.7| 60,329,100
| | | 124.7| 68,533,300
” H.P. Fire System | C.I. |12-24 | .. | ..
----------------------------+--------+-------+-------+------------
Quincy, Mass. | C.I. | | |
| Kal. | 2-20 | .. | ..
----------------------------+--------+-------+-------+------------
| W.I. | | |
Springfield, Mass. | C.I. | 1-36 | .. | ..
| C.L. | | |
----------------------------+--------+-------+-------+------------
Woonsocket, R. I. | C.I. | 4-20 | 239.5| 51,024,641
Yonkers, N. Y. | .. | .. | .. | ..
Worcester, Mass. | .. | 2-40 | .. | ..
----------------------------+--------+-------+-------+------------
TABLE XIX. (continued)
LEGEND:
(O) = Cost per Million Gallons raised 1 Foot High.
Pumping-station Expenses.
(P) = Cost per Million Gallons raised 1 Foot High.
Figured on Total Maintenance.
(R) = Rate of Interest Per Cent.
------+-------------+-------------+----------+-------------+--------
| | Net Cost of | Bonded | Value of |
(O) | (P) | Works | Debt | Sinking | (R)
| | to Date. | at Date. |Fund at Date.|
------+-------------+-------------+----------+-------------+--------
.. | $0.264 | $916,723.59| $892,000| $100,407.01| 4½-5
------+-------------+-------------+----------+-------------+--------
.. | .. |23,054,387.81|11,960,272|10,144,647.08| 3½-6
| | | | |
------+-------------+-------------+----------+-------------+--------
0.08 | 0.366 | 468,039.73| 248,000| 64,076.40| 3½-4
------+-------------+-------------+----------+-------------+--------
.. | .. | 5,670,229.52| 3,302,100| 604,326.58|
| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 483,335.52| 300,000| 50,921|
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 857,440.98| 650,000| |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 1,937,862.93| 1,920,000| 581,647.78| 5.1
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 452,091.09| 648,000| 195,908.91|
------+-------------+-------------+----------+-------------+--------
.. | .. | 1,244,742.23| 300,000| 37,403.46| 4
------+-------------+-------------+----------+-------------+--------
0.0399| .. | .. | 1,274,700| 287,226.20|
| | | | |
------+-------------+-------------+----------+-------------+--------
0.042 | 0.51 | 2,472,821.85| 1,800,300| 524,027.50| 3½-5
------+-------------+-------------+----------+-------------+--------
0.159 | .. | 337,630.13| | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 1,513.012.79| 900,000| 159,466.83| 4-6
| | | | |
------+-------------+-------------+----------+-------------+--------
0.0314| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
| | | | |
| | | | |
0.032 | | | | |
| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
0.043 | | | | |
------+-------------+-------------+----------+-------------+--------
0.033 | | | | |
------+-------------+-------------+----------+-------------+--------
0.0259| 0.2867| 1,820,107.73| 558,000| 148,793.77|av. 4.44
| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 706,978.44| 410,000| .. | 3.5-4
------+-------------+-------------+----------+-------------+--------
0.05 | 0.59 | 2,034,808.07| 2,075,000| 849,115.40| av. 4.7
| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. |L.S. = 0.0259| 6,470,093.35| 5,920,000| 713,431.62| av. 3.7
------+-------------+-------------+----------+-------------+--------
.. |H.S. = 0.1134| | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | .. | 720,500| .. | 4
| | | | |
| | | | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 2,128,559.56| 1,500,000| 461,861.90| av. 5.9
------+-------------+-------------+----------+-------------+--------
0.061 | 0.37 | 390,841.78| | |
------+-------------+-------------+----------+-------------+--------
.. | .. | 1,577,105.15| 1,475,000| 310,700 | 3.5-7
------+-------------+-------------+----------+-------------+---------
CHAPTER XX.
=211. Sanitary Improvement of Public Water-supplies.=—In the preceding
consideration of a public water-supply it has been virtually assumed
that the water will reach consumers in the proper sanitary condition;
but this is not always the case. With great increase of population
and corresponding increase of manufacturing and other industries
there arise many sources of contamination, so that pure spring- or
river-water for public supplies becomes less available and at the
present time in this country it is rarely to be had.
The legal responsibility of parties who allow sewage, manufacturing
wastes, or other contaminating matter to flow into streams is already
clearly recognized, and many cities and towns are required to dispose
of their sewage and other wastes in such manner as to avoid polluting
streams of water flowing past sewer outfalls or manufacturing
establishments; but even these restraints are not sufficient. If a
stream has once been polluted it can scarcely be considered safe as
a supply for potable water for public or private purposes. There are
certain diseases whose bacilli are water-borne and which are conveyed
by drinking-water containing them; prominent among such diseases are
typhoid fever and cholera. Experience has many times shown that these
bacilli or disease germs may find their way from isolated country
houses as well as from the sewage of cities into water that would
otherwise be potable. Besides such considerations as these it is
equally well known from engineering experience that many waters of
otherwise fair quality carry the remains of organic matter in one shape
or another which operate prejudicially to the physical condition of
those who drink such water. It is therefore becoming more and more
the conviction of civil engineers and sanitarians that there are
few sources of potable water so free from some degree of pollution
that the supplies drawn from them do not require treatment in order
to put them into good condition for drinking. It is not intended in
this observation to state that there are no streams or springs from
which natural waters may not be immediately used for domestic purposes
without improving them by artificial means, but it may be stated even
at the present time that no water of a public water-supply should
be used without treatment, unless the most thorough bacteriological
examinations show that its sanitary condition is eminently satisfactory.
It is the common experience of many public water-supplies in this
country that during certain seasons of the year, extending through the
summer and autumn months, certain low forms of vegetation flourish,
causing sometimes discoloration and always offensive tastes and odors.
While such waters are usually not dangerous, they certainly are not
desirable and may cause the human system to become receptive in respect
to pathogenic bacilli. The tendency at the present time, therefore,
is to consider the improvement of any water-supply that may be
contemplated for any city or town.
=212. Improvement by Sedimentation.=—The two broad methods of improving
the water of a public supply at the present time are sedimentation and
filtration, the latter generally through clean sand, although sometimes
other fine granular material or porous mass is used. The operation of
sedimentation is carried on when water is allowed to stand absolutely
at rest or to move through a series of basins with such small velocity
that the greater portion of the solid material held in suspension is
given an opportunity to settle to the bottom. All water which is taken
from natural sources, whether surface or underground, carries some
solid matter. Some waters, like spring-water or from an underground
supply, are so clear as to be very nearly free from solid matter in
suspension, but, on the other hand, there are waters, like those from
silt-bearing rivers, which carry large amounts. Observations upon the
Mississippi River at St. Louis have shown that the suspended matter
may reach as much as 1000 parts in one million, although the quantity
held in suspension is usually much less than that. Similar observations
have been made upon other silt-bearing streams. Such large proportions
of suspended solid matter are not usually found in streams used for
potable purposes, but there are few surface sources of water-supply
the water from which will not be sensibly improved by sedimentation in
settling-basins or reservoirs.
The process of sedimentation is usually preliminary to that of
filtration. If raw water, i.e., as it comes from its natural source,
is conducted directly to filtration-beds, the amount of solid matter
is frequently so great that the surface of the filter would be too
quickly clogged; hence it is advisable in almost every case to subject
to sedimentation any water which is designed to be treated subsequently
by filtration.
The degree of turbidity is usually measured by means similar to those
employed in gauging discoloration from vegetable matter. One method
devised by Mr. Allen Hazen, to which allusion will again be made, is
that in which the depth in inches is observed at which a platinum wire
1 mm. in diameter and 1 inch long can be seen. The degree of turbidity
is then represented by the reciprocal of that distance. The permissible
turbidity estimated in this manner is taken by different authorities
at different values running from .025 to .2. Water of this degree of
turbidity appears, when seen through a glass, to be practically clear.
The rapidity with which sedimentation can be performed depends greatly
upon the character and degree of comminution of the solid material.
If it is coarse, comparatively speaking, it will quickly fall to the
bottom; if the solid matter is clay of fine texture, it is dissipated
through the water in an excessively high degree of diffusion and
will remain obstinately suspended. This has been found to be the
case at some points with the Ohio River water. Ordinarily sufficient
sedimentation can be accomplished where the water remains at rest
from twenty-four to forty-eight hours; in general, observations as
to this matter, however, must be applied very cautiously. Water of
the Mississippi River at St. Louis has been found to deposit nearly
all of its sediment within twenty-four hours. At Cincinnati, on the
other hand, the Ohio River water carries so fine a sediment that on
an average not more than 75 per cent of it will be deposited in three
days by unaided subsidence. Again, at Omaha the water of the Missouri
River has been found to be turbid at the end of seventy-two hours.
In some cases, as with the waters of the Delaware and Schuylkill at
Philadelphia, a greater amount of subsidence has been found to exist at
times at the end of twenty-four hours than after forty-eight hours. It
is obvious that some special conditions must have produced such results
that would not ordinarily occur in connection with the operation of
sedimentation.
=213. Sedimentation Aided by Chemicals.=—In cases where simple
unaided subsidence proceeds too slowly it can be accelerated by the
introduction of suitable chemicals. At Cincinnati, for instance, it
was found advantageous to introduce into the water before flowing into
the settling-basins a small amount of alum or sulphate of alumina,
depending upon the degree of turbidity, the average being about 1.6
grains per gallon, rising to perhaps 4 grains in floods. By these
means a few hours of aided sedimentation would produce more subsidence
than could be obtained in several days without the chemicals. A
similar recommendation has been made for the purpose of improving the
water-supply for the city of Washington, D. C., from the Potomac River.
In other cases between 5 and 6 grains of lime per gallon have produced
effective results.
=214. Amount of Solid Matter Removed by Sedimentation.=—Under adverse
conditions, or with sediment which remains obstinately suspended, not
more than 25 to 50 per cent of the solid material will be removed
by sedimentation, but when the process is working satisfactorily,
sometimes by the aid of chemicals acting as coagulants, 90 to 99 per
cent even of the solid material may be removed. The operation of
sedimentation has another beneficial effect in that the solid matter
when being deposited carries down with it large numbers of bacteria,
which, in some cases, have been observed to be 80 or 90 per cent of
the total contents of the water. In other words, the subsidence of the
solid matter clears the water of a large portion of the bacteria.
=215. Two Methods of Operating Sedimentation-basins.=—Sedimentation
is carried on in two ways, one being the “fill-and-draw” method and
the other the “continuous” method. In the former method a basin or
reservoir is first filled with water and then allowed to stand while
the subsidence goes on for perhaps twenty-four hours. The clear water
is then drawn off, after which the reservoir is again filled. In the
continuous method, on the other hand, water is allowed to flow into
a single reservoir or series of reservoirs through which it passes
at an extremely low velocity, so that its contents will not entirely
change within perhaps twenty-four hours or more. In this method the
clear water is continuously discharging at a comparatively low rate,
the velocity in the reservoir being so small that the solid matter may
be deposited as in the fill-and-draw method. Both of these methods
are used, and both are effective. The choice will be dependent upon
local conditions. In the continuous method the solid matter is largely
deposited nearer the point of entrance into the reservoir, but more
generally over the bottom in the fill-and-draw method. The velocity
of flow in the reservoirs of the continuous method generally ranges
between 0.5 inch and 2.5 inches per minute. Occasionally the velocity
may be slightly less than the least of these values, and sometimes one
or two inches more than the maximum value.
=216. Sizes and Construction of Settling-basins.=—The sizes of the
settling-basins will obviously depend to a considerable extent upon the
daily consumption of water. There is no general rule to be followed,
but the capacity of storage volume of those actually in use run
from less than 1 to possibly 14 or 15 days’ supply. Under ordinary
circumstances their volumes may usually be taken from 5 to 6 or 8 days’
supply. Their shape should be such as to allow the greatest economy
in the construction of embankments and bottoms. They may generally
be made rectangular. Their depths is also a matter, to some extent,
of constructive economy. The depth of water will usually be found
between about 10 and 16 feet, it being supposed that possibly 2 or 3
feet of depth will be required for the collection of sediment. These
basins must be water-tight. The bottom surfaces may be covered with
concrete 6 to 9 inches thick, with water-tight firm puddle 12 to 18
inches thick underneath, resting on firm compacted earth. The inner
embankment surfaces or slopes may be paved with 10- or 12-inch riprap
resting on about 18 inches of broken stone over a layer of puddle of
equal thickness with the bottom and continuous with it. Occasionally
the bottom and sides may be simply puddled with clay and lined with
brick or riprap pavement, laid on gravel, or broken stone. It is only
necessary that the sides and bottoms shall be tight and of such degree
of hardness and continuity as to admit of thorough cleaning.
The bottoms of sedimentation-basins may advantageously not be made
level. In order to facilitate cleaning away the solid matter settling
on them, a valley or depression may be formed along the centre line to
which the two portions of the bottom slope. A grade in this channel or
central valley of 1 in 500 with slopes on either side of 1 in 200 or 1
in 300 will be effective in the disposition of the solid matter. At the
lowest end of the central valley there should be suitable gates through
which the accumulated sediment can be moved out of the basin. This
sedimentary matter will in many cases be soft mud, but its movement
will always be facilitated by the use of suitable streams of water. The
frequency of cleaning will depend upon the amount of sediment carried
by the water and upon its accumulation in the basin. Whenever its depth
ranges from 1 to 2 or 3 feet it is removed.
Complete control of the entrance of the water to and its exit from
the basin must evidently be secured by suitable gates or valves and
other appliances required for the satisfactory operation of the basin.
In some cases the cost of sedimentation-reservoirs with concrete
bottoms and sides has risen as high as $9000 per million gallons of
capacity; but where the cheaper lining has been used, as in the case
of reservoirs at Philadelphia, the range has been from about $3300 to
about $4300.
=217. Two Methods of Filtration.=—After the process of sedimentation
is completed there will necessarily always be found the remains of
organic matter and certain other polluting material which should be
removed before the water is allowed to enter the distributing system.
This removal is accomplished usually by filtration through clean sand,
but occasionally through porous material, such as concrete slabs,
porcelain, or other similar material. The latter processes are not much
used at the present time, and they will not be further considered.
The filtration of water through sand is carried on by two distinct
methods, one called slow sand filtration and the other rapid sand
filtration. In the first method the water is simply allowed to filter
slowly through beds of sand from 2 to 3 or 5 feet thick and suitably
arranged for the purpose. In the second method special appliances and
conditions are employed in such manner as to cause the water to flow
through the sand at a much more rapid rate. The method of slow sand
filtration will first receive attention.
=218. Conditions Necessary for Reduction of Organic Matter.=—The most
objectionable class of polluting materials includes organic matter
which from one source or another finds its way into natural waters.
Such material has originally constituted or formed a part of living
organisms and chemically consists of varying proportions of carbon,
oxygen, hydrogen, and nitrogen. As found in public water-supplies it
is usually in some stage of decomposition. The chemical operations
taking place in these decompositions are more or less complicated, but
in a general way it may be said that the first step is the oxidizing
of the carbon which may produce either carbon monoxide or carbon
dioxide and a combination of nitrogen with hydrogen as ammonia. When
the conditions are favorable, i.e., when free oxygen is present, the
ammonia may be oxidized by it, thus producing nitric acid and water.
If, as is generally the case, suitable other substances, as alkalis,
are present, the nitric acid combines with them, forming nitrates more
or less soluble and essentially innocuous. It is therefore seen that
the complete result is a chemical change from the original organic
matter, offensive and possibly dangerously polluting, to gaseous and
solid matter, the former escaping from the water and the latter either
passing off unobjectionably in a soluble state or precipitating to
the bottom as inert mineral matter. In order that these processes may
be completely effective, two or three conditions are necessary, i.e.,
sunlight, free oxygen, and certain species of that minute and low class
of organisms known as bacteria, the nature and conditions of existence
of which have been scientifically known and studied within a period
extending scarcely farther back than ten or fifteen years. The precise
nature of their operations and their relations to the presence of the
necessary oxygen, or just the parts which they play in the process of
decomposition, are not completely known, although much progress has
been made in their determination. It is positively known that their
presence and that of uncombined oxygen are essential. Certain species
of these bacteria will live and work only in the presence of sunlight
and oxygen; these are known as aerobic bacteria. Other species,
forming a class known as anaerobic bacteria, live and effect their
operations in the absence of sunlight and oxygen in that offensive
mode of decomposition which takes place in cesspools and other closed
receptacles for sewage and waste matter. They play an essential part in
what promises to be one of the most valuable methods of sewage-disposal
in which the septic tank is a main feature.
=219. Slow Filtration through Sand—Intermittent Filtration.=—In the
slow sand filtration method of purifying the water of a water-supply
the aerobic bacteria only act. In order that their operations may be
completed, free oxygen and sunlight are essential requisites, and the
first of these is found in every natural water which can be considered
potable. Any water which does not contain sufficient free oxygen for
this purpose is to be regarded with suspicion, and generally cannot be
considered suitable for domestic purposes. The amount of uncombined
oxygen contained in any potable natural water is greatly variable and
changes much with the period of exposure in a quiet state, as well
as with pressure and temperature. In the river Seine it has averaged
nearly 11 parts in a million throughout the year, being lowest in July
and August and highest in December and January. It has been found in
the experimental work of the Massachusetts State Board of Health that
free or dissolved oxygen in potable water may vary from 8.1 parts
at 80° Fahr. to 14.7 parts by weight at 32° Fahr. in 1,000,000 at
atmospheric pressure.
[Illustration: FIG. 4.]
[Illustration: No. 1. CROSS-SECTION AT NORTH END OF BED.]
[Illustration: No. 2. CROSS-SECTION AT BEGINNING OF PIPE UNDERDRAIN.]
[Illustration: No. 3. CROSS-SECTION AT SOUTH END OF BED.]
[Illustration: No. 4. CROSS-SECTION AT END OF LOWEST GRAVEL UNDERDRAIN.]
[Illustration: No. 5. LONGITUDINAL SECTION OF A BED, AT WESTERLY END OF
FILTER.
TYPICAL SECTIONS OF UNIT BEDS IN LAWRENCE CITY FILTER.
APRIL, 1901.
COPIED FROM PLAN FURNISHED BY A.D. MARBLE, CITY ENGINEER.]
In some cases where liability to dangerous contamination exists it may
be advisable to increase the available supply of oxygen in the water by
using a slow sand filter intermittently, as has been done at Lawrence,
Mass. Instead of permitting a continuous flow of water through the
sand, that flow is allowed for a period of 6 to 12 hours only, after
which the filter rests and is drained for perhaps an equal period.
During this intermission another filter-bed is brought into use in the
same manner. Alternating thus between two or more filters, the flow in
any one is intermittent. In this manner the oxygen of the air finds its
way into the sand voids of each drained filter in turn and thus becomes
available in the presence of suitable species of bacteria for reducing
the organic matter in the water next passing through the filter.
Intermittent filters operated in this manner are not much used, but the
most prominent instance is that at Lawrence, Mass. At that place the
water after being filtered is pumped to a higher elevation for use in
the distribution system. The pumps have been run nineteen hours out of
the twenty-four, and the water is shut off from the filters five hours
before the pumps stop. The gate admitting water to the filter is open
one hour before they start. Nine hours of each day the filter does not
receive water, and rests absolutely about four hours.
=220. Removal of Bacteria in the Filter.=—The grains of the sand at
and near the surface of a slow sand filter, within a short time after
its operation is begun, acquire a gelatinous coating, densest at the
surface and decreasing rapidly as the mass of sand is entered. This
gelatinous coating of the grains is organic in character and probably
largely made up of numerous colonies of bacteria whose presence is
necessary for the reduction of the organic matter. It is necessary
to distinguish between these species of bacteria and those which are
pathogenic and characteristic of such diseases as typhoid fever,
cholera, and others that are water-borne. Every potable surface-water
and possibly all rain-water carry bacteria which are not pathogenic and
which apparently accumulate in dense masses at and near the surface of
the slow sand filter. As the water finds its way through the sand it
loses its organic matter and its bacteria, both those of a pathogenic
and non-pathogenic character. Potable water, therefore, is purified and
rendered innocuous by the removal in the filter of all its bacteria,
including both the harmless and dangerous.
=221. Preliminary Treatment—Sizes of Sand Grains.=—In designing
filtration-works consideration must be given to the character of water
involved. There are waters which when standing in open reservoirs
exposed to the sunlight will develop disagreeable tastes and odors, and
it may be necessary to give them preliminary treatment especially for
the removal of such objectionable constituents.
The character and coarseness of the sand employed are both elements
affecting its efficiency as a filtering material. It should not
be calcareous, for then masses of it may be cemented together and
injure or partially destroy the working capacity. Again, if it is
too coarse and approaches the size of gravel, water may run freely
through it without experiencing any purification. Much labor has been
expended, especially by the State Board of Health of Massachusetts,
in investigating the characteristics of sand and the sizes of grains
best adapted to filter purposes. In that work it has become necessary
to classify sands according to degrees of fineness or coarseness.
The diameter of a grain of sand in the system of classification
employed means the cube root of the product of the greatest and least
diameters of a grain multiplied by a third diameter at right angles
to the greatest and least. The “effective” size of any given mass of
sand means the greatest diameter of the finest 10 per cent of the
total mass. There is also a term called the “uniformity coefficient.”
The uniformity coefficient is the quotient arising from dividing
the greatest diameter of the finest 60 per cent of the mass by the
greatest diameter of the finest 10 per cent of the same mass. These are
arbitrary terms which have been reached by experience as convenient for
use in classifying sands. Evidently absolute uniformity in size will be
indicated by a uniformity coefficient of 1, and the greater the variety
in size the greater will be the uniformity coefficient. Sands taken
from different vicinities and sometimes even from the same bed will
exhibit a great range in size of grain.
[Illustration: FIG. 5.—Sizes of Grain or Fineness of Sand.]
Fig. 5 represents the actual variety of size of grain as found in
eight lots of sand among others examined in the laboratory of the
Massachusetts State Board of Health. The vertical scale shows the per
cent by weight of portions having the maximum grains less in diameter
than shown on the horizontal line. The more slope, like No. 5 or 6,
the greater is the variety in size of grain. Those lines more nearly
vertical belong to sands more nearly uniform in size of grain.
=222. Most Effective Sizes of Sand Grains.=—Investigations by the
Massachusetts State Board of Health indicate that a sand whose
effective diameter of grain is .2 mm. (.008 inch) is perhaps the most
efficient in removing organic matter and bacteria from natural potable
waters. At the same time wide experience with the operation of actual
filters seems to indicate that no particular advantage attaches to
any special size of grain, so long as it is not too fine to permit
the desired rate of filtration or so coarse as to allow the water to
flow through it too freely. Experiments have shown that effective
sizes of sand from .14 to .38 mm. in diameter possess practically
the same efficiency in a slow sand filter. The action of the filter
is apparently a partial straining out of both organic material and
bacteria, but chiefly the reduction of organic matter in the manner
already described and probably the destruction to a large extent of
the bacteria, especially those of a pathogenic nature, although at the
present time it is impossible to state the precise extent of either
mode of action.
=223. Air and Water Capacities.=—Another important physical feature of
filter-sands, especially in connection with intermittent filtration, is
the amount of voids between the grains. When the intermittent filter is
allowed to drain, so that the only water remaining in it is that held
between the grains by capillary attraction, generally at the bottom
of the filter unless the sand is very fine, the volume of the water
which remains in the voids is called the water capacity of the sand.
The remaining volume between the grains is called the air capacity of
the same sand. It is evident that the air capacity added to the water
capacity will make the total voids between the sand grains.
[Illustration: FIG. 6.]
Fig. 6 shows the amount of air and water capacities of the same sands
whose sizes of grains are exhibited in Fig. 5. The depth of the sand is
supposed to be 60 inches, as shown on the vertical line at the left of
the diagram, while the percentages of the total volume representing the
amounts of voids is shown on the horizontal line at the bottom of the
diagram. Both air and water capacities for each sand are shown by the
various numbered lines partially vertical and partially inclined. It
will be observed that the fine sands No. 2 and No. 4 have large water
capacities, the water capacity being shown by that part of the diagram
lying below and to the left of each line. It will be noticed that No.
5 sand is made up of approximately equal portions of fine and coarse
grains, the former largely filling the voids between the latter. This
mixture, as shown by the No. 5 line, gives a very high water capacity
and a correspondingly low air capacity. Obviously a sand with a high
water capacity has a correspondingly low air capacity, and in general
would not be a very good sand for an intermittent filter, since it
is the purpose of the latter to secure in the voids between the sand
grains as much oxygen as practicable whenever the filter may be at rest.
=224. Bacterial Efficiency and Purification—Hygienic Efficiency.=—As
the function of a filter is to remove as far as possible the organic
matter and bacteria of the applied water, there must be some criterion
by which its efficiency in the performance of those functions can be
expressed. The bacterial efficiency is represented by the ratio found
by dividing the number of bacteria after filtration in a prescribed
cubic unit, as a cubic centimeter, by the number which the same
volume of raw water held before being applied to the filter. This is
a rather misleading ratio, for the reason that the effluent water may
contain bacteria of certain species which grow in the lower portions
of a filter or in the drains which conduct the effluent from it.
It is possible, therefore, that bacteria may be found in a filter
effluent when all of the bacteria originally held in the water have
been removed. Hence the ratio expressing what is called the bacterial
purification arises from dividing the number of bacteria actually
removed from a cubic centimeter of water by the filter by the number
originally held by a cubic centimeter of raw water. The smaller the
first of these ratios the higher the degree of efficiency. Extended
experience, both in the filters of such laboratories as that of the
Massachusetts State Board of Health and with actual filters of public
water-supplies, show that under attainable conditions of operation 98
to 100 per cent of all the bacteria originally found in the water may
be removed.
There is also used the term hygienic efficiency which is used in
connection with slow sand filters. This means simply the per cent of
pathogenic bacteria removed by the filter, and there is good reason to
believe that it is at least as high as the bacterial purification.
=225. Bacterial Activity near Top of Filter.=—The work of removal of
bacteria and organic matter has been found by extended investigations
to be performed almost entirely within 6 or 8 inches of the top surface
of the sand; indeed the most active part of that operation is probably
concentrated within less than 3 inches of the surface. At any rate the
retained bacteria and nitrogenous matter are found to decrease very
rapidly within a foot from the upper surface, below which stratum the
quantity is relatively very small and its rate of decrease necessarily
slow. A little of this nitrogenous or gelatinous matter is found to
surround to a slight extent the sand grains found at the bottom of the
filter. Some authorities have considered that the more steady uniform
efficiency of the deeper filters is due to this effect.
=226. Rate of Filtration.=—The rate at which water can be made to
flow through a slow sand filter is of economical importance, for the
reason that the higher the rate the less will be the area required
to purify a given quantity per day. Foreign engineers and other
sanitary authorities advocate generally slower rates of filtration
than American engineers are inclined to favor. The usual rate in
Europe is not far from 1.6 to 2.5 million gallons per acre per day.
There is also considerable range in this country, and the rate may
reach 3 million gallons per acre per day. Indeed a considerable number
of tests have shown that for short periods of time, at least, some
waters may be efficiently filtered at rates as high as 7 to 8 million
gallons per acre per day, but probably no American engineer is ready
to introduce such high rates as yet. As a matter of fact the rate will
depend considerably upon the character of water used. Clear water from
mountain lakes and streams uncontaminated and carrying little solid
material may be filtered safely and properly at much higher rates of
filtration than river or other waters carrying more sediment and more
organic matter. This principle is recognized both in Europe and in this
country. It would appear from experience that slow sand filters at
the present time with rates of 2.5 to 3 million gallons per acre per
day may be employed for practically any water that may be considered
suitable for a public supply, and that with these rates high degrees of
both bacterial purification and hygienic efficiency may be reached.
=227. Effective Head on Filter.=—Inasmuch as the depth of sand ranges
from perhaps 3 to 5 feet the water will experience considerable
resistance in flowing through it. The distance in elevation between
the water surface over the filter and that of the water as it leaves
the filter measures the loss of head experienced in passing through
the sand and the drainage-passages under it. It has been maintained
by some foreign authorities that this loss of head should be not
more than 24 to 30 inches; that a greater head would force the water
through the sand at such a rate as to render desired purification
impossible. Experience both in the laboratory and with public filters
in this country does not appear to sustain that view of the matter;
considerably greater heads than 30 inches have been used with entirely
satisfactory results both as to the removal of organic matter and
bacteria. It appears to be best so to arrange the flow of water through
the sand and the underdrains as to avoid in either a pressure below
the atmosphere, as in that case some of the dissolved air in the water
escapes and produces undesirable disturbances in the sand, resulting
in reduced efficiency. No precise rule can be given in respect to this
feature of filtration, but it seems probable that satisfactory results
may be obtained under proper working of filters with a loss of head
not greater than the depth of water on the filter added to the depth
of sand in it, although that maximum limit would ordinarily not be
reached. The depth of water on the filter may be taken from 3 to 5
feet. In this country it is seldom less than the least of these limits,
and perhaps not often equal to the greater limit.
=228. Constant Rate of Filtration Necessary.=—Care should be taken in
the operation of filters to avoid any sudden change in the texture
or degree of compactness of the sand. At the times when workmen
must necessarily walk over the surface they should be provided with
special broad-based footwear, so as to produce as little effect of
this kind as possible where they step. Sudden changes in the degree
of compactness cause correspondingly sudden changes in the rate of
filtration, and such changes produce a deterioration of efficiency.
This may be due to two or three reasons. Possibly such changes may open
small channels through which water finds its way too freely; or the
breaking of the gelatinous bond between the grains of sand may operate
prejudicially. At any rate it is essential to avoid such sudden changes
and maintain as nearly uniform a rate of filtration over the entire
filter as possible. Again, the age of a filter affects to some extent
its efficiency. A month or two of time is required, when a new filter
is started, to attain what may be called its normal efficiency. Even
after that length of time the filter gains in its power to retain and
destroy bacteria. This action is particularly characteristic of filters
formed of comparatively coarse sand.
=229. Scraping of Filters.=—More or less solid inert as well as organic
matter accumulates on the surfaces of the slow sand filters, so that
at the end of proper periods of time, depending upon the character
of the water filtered, this surface accumulation must be scraped off
and removed together with the sand into which it has penetrated. In
scraping the filter it is impossible to remove less than .25 or .5
inch of sand, and at least .5 to .75 inch is removed whenever a filter
is scraped. Sometimes 1 or 2 inches may be removed. This sand may be
washed and again placed upon the filter for use. The operation of
scraping exhibits a fresh sand surface to the applied water. It has
been held, particularly by foreign authorities, that this operation of
scraping militates against the efficiency of the filter for the time
being. The investigations of the Massachusetts State Board of Health
and other experiences in this country do not confirm that view which
is based on the assumption that the top nitrogenous film is essential
to efficiency. These investigations have shown that this film is not
necessary in intermittent filters; that in many instances no diminution
of efficiency has resulted from a removal of the film to a depth of
.3 inch; that even the presence of that film has not given efficiency
to coarse sand when the coating was thick enough to completely clog
the filter; and, further, that the material of this nitrogenous
film is found at a depth of several inches below the surface. It is
practically certain that the scraping to depths not exceeding 1 inch
have no sensible effect upon the efficiency under proper management and
operation of the filters. This is particularly true if the thickness of
sand is from 3 to 5 feet. It is undoubtedly true that with very shallow
sand filters from 1 to 2 feet in depth the scraping of the surface may
have some effect upon bacterial efficiency.
It has been the custom in connection with some European filters to
waste the water which first passes through after cleaning, but the
usual practice in this country is to fill slowly the filter with
filtered water from below and, after the sand is submerged, to permit
it to stand a little while before use. Care taken in this manner will
insure an efficiency to a freshly scraped filter sufficient to avoid
any wastage.
=230. Introduction of Water to Intermittent Filters.=—Where
intermittent filters are used it is of the greatest importance to
conduct the water to them so as not to disturb the sand on their
surfaces. This can readily be done in a number of ways. If the shape
of the filter is not oblong, it will be advisable to form a number of
main drains or passages in the sand from which smaller depressions or
passages near together may lead the water to all parts of the surface.
The flowing of the first water through these depressions will permit
the entire surface to be covered so gradually as not to disturb the
sand grains, and it is essential that such means or their equivalent
be employed. If the filter is long and narrow in shape, the main
ditch along one of the longer sides, with depressions at right angles
to it or across the filter and near together, will be sufficient
to accomplish the desired purpose. Obviously when filters are not
intermittently used such precautions are not needed.
=231. Effect of Low Temperature.=—In the early days of the use of
sand filters in this country it was frequently supposed that the low
temperature of the winter caused decreased bacterial purification and a
decrease in power to reduce organic material. It now appears that such
is not the case. The effects of low temperature, such as is experienced
in winters of this climate, may be overcome by temporarily covering the
filters so that heavy ice cannot form and produce disturbances in one
way or another prejudicial to efficiency of operation. The agencies
which operate to reduce efficiency in cold weather are no longer
believed to be those due to low temperature. They are rather indirect
and mechanical, and may be readily overcome by the prevention of the
formation of ice.
=232. Choice of Intermittent or Continuous Filtration.=—The process of
slow sand filtration when continuous has been shown by experience to
be entirely effective for ordinary potable waters, but in those cases
where the amount of dissolved oxygen may be low and where the amount
of organic matter is relatively high it may be advisable to resort to
intermittent filtration. Neither method, however, can be depended upon
to render potable a water which has been robbed of its free oxygen
by an excessive amount of contaminated organic matter. Nor can these
processes be expected to remove coloring matter produced by peaty
soils or other conditions in which large amounts of vegetable matter
have been absorbed by the water. The methods, therefore, have their
limitations, although their field of application is sufficiently wide
to cover nearly all classes of potable water.
=233. Size and Arrangement of Slow Sand Filters.=—Among the first
questions to arise in the design of slow sand filters are their size
and arrangement. The total area will be determined by the total daily
draft and the rate of filtration. Rates of filtration running from
2.5 to 3 million gallons per acre per day, or even more, have been
found satisfactory and are customary in this country. Having given,
therefore, the total daily quantity required, it is only necessary to
divide that by the rate of filtration per acre and the result will be
the number of acres required for the total filter-bed surface. This net
area, however, is not sufficient. Unless there is requisite storage of
filtered water to meet the variation in the hourly draft for the day,
the capacity of the filters must be sufficient to meet the greatest
hourly rate, which must be taken at least 1½ times the average hourly
demand during the day; indeed this is only prudent in any case.
Again, it is necessary to divide the total filter surface into small
portions called beds, so that one or more of them may be withdrawn from
use for cleaning or repairs, while a sufficient filter-area remains in
operation to supply the greatest hourly draft. This surplus area will
usually run from 5 to 20 per cent of the total area of the filter-beds,
although for small towns and cities it may be much more. The sizes of
the filter-beds will depend upon the local circumstances of each case.
It is evident that as each single bed must have its individual set of
appliances and its separating walls, the purpose of economy will be
best served by making the beds as large as practicable. At the same
time they must not be made too large, for in that case the portion
out of use might form so large a percentage of the total area as to
increase unduly the cost of the entire plant. A size of bed varying
between .5 and 1.5 acres is frequently and perhaps generally found
in foreign filtering-plants. If filter-beds range in area from .5
acre to 2 acres, the latter for large plants, the purposes of economy
and convenience in administration will probably be well served. The
grouping of the beds is an important consideration and will depend
somewhat, at least, upon the shape of the plot of ground taken for the
filters. It is advisable that the inlets to the different beds should,
as far as possible, discharge from a single inlet-pipe or main. This
will generally be most conveniently accomplished by making the beds
rectangular in shape, grouped on each side of the supply-main, with
their longest dimensions at right angles to it. This arrangement is
illustrated by the grouping of the filter-beds in the Albany plant,
shown in Fig. 7. In the case of a single oblong bed, like that at
Lawrence, Mass., shown in Fig. 4, page 284, its relatively great length
and small width makes it possible to run the main supply along one
side, from which branch depressions with concrete bottoms enable the
water to be distributed uniformly over its surface in the manner shown
in the figure. It is further necessary to group the filter-beds, pumps,
sand-cleaning appliances, and other portions of the plant, so that
the ends of economy and efficient administration may be served in the
highest degree. It is always necessary that these features of the whole
filtration system should be carefully kept in view in laying out the
entire plant.
=234. Design of Filter-beds.=—The preparation of the site for a group
of filtration-beds also involves the consideration of a number of
principal questions. In the first place, the depth required for the
sand and underdrains will not be far from 5 feet, and there must be a
suitable bottom prepared below the collecting-drains. Again, the depth
of water above the sand may vary from 3 to 5 feet, making the total
depth, including the bottom, of the filter proper about 10 or 11 feet,
and this may represent the depth of excavation to be made. If the
material on which the filter to be built is soft, it may be necessary
to drive piles to support the superincumbent weight. The bottom must be
made water-tight. This can be done either by the use of a layer of well
rammed or packed clay, 1 to 2 feet in thickness, carrying 6 or 8 inches
of concrete, or by a surface of paved brick or stone. If the sides of
the filter-beds are of embankments with surface slopes, the latter may
be protected in the same manner. If the sides are of walls of masonry,
concrete is an excellent material to be used for the purpose.
[Illustration: FIG. 7.—Sedimentation-basin and Filter-beds at Albany,
N. Y.]
[Illustration: Filtration-plant at Albany, N. Y.]
In designing the sides of filters or of the piers projecting up
through the sand for the support of the roof, in case there is one, it
is imperative that care be taken to prevent water from flowing down
through the joints between the sand and the sides of piers or the
masonry sides of the filter-beds. There should be no vertical joint
of that character, but the faces of masonry in contact with the sand
should both slope and be made in steps, so that any settlement of the
sand will tend to close the joint, while the steps will prevent flow.
Nor should there be angles in which sand is to be packed; filleted
corners are far preferable and should be used.
=235. Covered Filters.=—It has become the custom where the best results
are expected in cold climates, if not in all cases, to cover filters
with masonry roofs of domes and cylindrical or groined arches supported
on masonry columns. Such roofs are usually covered with earth to a
depth of 1 to 2 or 3 feet. They prevent any injurious action on the
sides of the filters produced by thick ice or the effects of such
ice upon the upper portions of the sand. In summer they also protect
against the baking and cracking of the upper surface of the sand when
exposed to the sun and prevent, to a considerable extent, the growth
of algæ in different portions of the beds. They are expensive, filters
with masonry covers costing once and a half to twice as much as open
filters, but they enhance the sanitary value of the water. The height
of the masonry roof must be about 2 to 3 feet above the upper surface
of the water and high enough to offer convenient access to the sand
when it is to be cleaned and renewed. The length of span for the arches
or domes is seldom more than 12 or 15 feet.
=236. Clear-water Drain-pipes of Filters.=—After the water has passed
through the sand it must be withdrawn from the bottom of the filter
with as little resistance as practicable. This necessitates, in the
first place, the bottom of the filter to be so shaped as to induce
the flow of the filtered water toward the lines of drain-pipes which
are laid to receive it. These pipes consist of the main members and
the branches, the main members being laid along the centres of the
beds and the branches running from them. The bottoms of the filters,
therefore, should be formed with depressions in which the main pipes
are laid, and with such grades as to expedite the movement of the water
flowing through the branches. If the bottoms are of concrete, they can
advantageously be made of inverted arches or domes, the drain-pipes
being laid along the lines of greatest depression. In such cases the
loads produced by the weight of the roof are more nearly uniformly
distributed over the bottom. The sizes of the drains will be dependent
upon the areas from which they withdraw water. It is advisable to make
them rather large, in order that the water may flow through them more
freely. They seldom need exceed 6 or 8 inches. They are preferably made
of salt-glazed vitrified pipes laid with open joints, around and in the
vicinity of which are placed gravel or broken stone, the largest pieces
with a maximum diameter of 1 to 2 inches. The largest broken stone or
coarsest gravel is near the pipe and should decrease in size as the
drain-pipe is receded from, so that the final portions of the gravel
farthest removed from the drains will not permit the filter-sand to
pass into it. When properly designed and arranged, the loss of head in
passing from the farthest points of a filter-bed to the point of exit
from the filter will not exceed about .01 to .02 of a foot.
[Illustration: Interior of Covered Filter at Ashland, Wis.]
=237. Arrangement of the Sand at Lawrence and Albany.=—Above this
gravel is placed the filtering-sand, about 4 feet thick in the Albany
filter and 3 to 4 feet thick in the filter at Lawrence, Mass. The sand
in the Albany filter was specified to have not “more than 10 per cent
less than .27 mm.” in diameter and “at least 10 per cent by weight
shall be less than .36 mm.” in diameter. Over the entire floor was
spread not more than 12 inches of gravel or broken stone, the lower
7 inches consisting of broken stone or gravel with greatest diameter
varying from 1 inch to 2 inches; the remaining 5 inches of the lower
1 foot was composed of broken stone or gravel decreasing from 1 inch
in greatest diameter to a grain a little coarser than that of the
sand above it. In all cases, sand for the filter-bed should be free
from everything that can be classed as dirt, including clay, loam,
and vegetable matter. Furthermore, it should be free from any mineral
matter which might change the character of the water and render it less
fit for use.
[Illustration: Partially Filled Covered Sand Filter showing Drain-pipe.]
This filtering-sand is usually placed in position with a horizontal
surface. At Lawrence, however, it was placed with a wavy surface, the
horizontal distance between the crests of two consecutive waves being
30 feet, the concrete gutter for admitting the water being half-way
between, all as shown in the illustrations. The sand of this filter
was of two grades, the coarser sand having an effective size of 0.3
mm. (.118 inch) and the finer an effective size of 0.25 mm. (.098
inch). The two different sizes of sand are seen not to be arranged
in horizontal layers, but so that the finer is over the drains and
the coarser between. The No. 70 sand is capable of passing 70 million
gallons per acre per day with a head on it equal to the depth of sand,
while the No. 50 sand can pass 50 million gallons per acre per day
with a head on it equal to its depth. There appears to be no special
advantage in placing the sand in filters other than in horizontal
layers with an effective size practically uniform.
=238. Velocity of Flow through Sand.=—The velocity with which water
will flow through a given depth of sand with a known depth or head
above the surface of the latter has been carefully investigated by the
Massachusetts State Board of Health with the following results:
_v_ = the velocity at which a solid column of water,
whose section equals in area that of the bed of sand,
moves downward through the sand in meters per day; this
is practically the number of million gallons passing
through the sand per acre per day.
_c_ = a constant, having the value of 1000 for clean sand,
and 800 for filter-sand after having been some time in use.
_d_ = the effective size of the sand-grain in millimeters.
_h_ = the head lost by the water in passing through the sand
at the rate v; this is the effective head of water producing
motion through the sand.
_l_ = the thickness of the sand bed.
_t_ = the temperature of the water in degrees Fahr.
The velocity _v_, as determined by experiment, takes the following form:
_h_ (_t_ + 10)
_v_ = _cd²_ --- (--------).
_l_ ( 60 )
This formula cannot be used for the flow of water through all sands of
all thicknesses and under all circumstances. It is limited to effective
diameters of sand between .1 and 3 mm., having a uniformity coefficient
not greater than 5. _h_ and _l_ may be taken in any unit as long as
both are expressed in the same unit, since the ratio of the two
quantities will then not be affected. If the effective head of water
on the filter or the head lost is equal to the thickness of the bed of
sand, the ratio of _h_ divided by _l_ will be 1. In case the formula is
used to express the quantity of water flowing through the sand per acre
per day, it must be remembered that _v_ will be the number of million
gallons and not the total number of gallons. The formula can only be
used when the sand is well compacted and where the voids of the sand
are entirely filled with water.
=239. Frequency of Scraping and Amount Filtered between Scrapings.=—The
frequency of the scraping of filters will depend upon the amount of
organic matter in the water and upon the rate of filtration. Between
the years 1893 and 1900 the periods between scrapings of the Lawrence
filter ranged generally from 20 to 32 days, although periods as small
as 13 or 19 are found in the records. The quantity of water passed
between scrapings varies generally from 67 million to 90 million
gallons, although it fell as low as 49 millions and rose as high as
109 millions. In the case of the Albany filter-plant, up to the end of
the year 1900 the shortest period between scrapings was about 15 days
and the longest about 42 days, the smallest quantity of water passing
through any filter between scrapings being 26,735,000 gallons and the
largest 76,982,000 gallons. The operation of the Albany filters for
the year 1901 shows that the average run of a bed was 26 days between
scrapings, with a total of 70,000,000 gallons per acre for that period.
These figures represent about the usual workings of slow sand filters
at the present time, the period between scrapings running usually
between 15 and 30 days, and the quantity from 30 million gallons per
acre to 100 million gallons per acre.
[Illustration]
[Illustration: Filters for City of Albany, N. Y.]
=240. Cleaning the Clogged Sand.=—The clogged sand scraped from the top
of the filters at the periods of cleaning is removed to a convenient
point where appliances and machinery are available for washing it. This
is an item of some importance in the administration of filters, as the
sand which is removed and washed is at a later period replaced upon the
filter-bed. Various methods have been tried for the purpose of cleaning
sand efficiently and economically. The continuous ejector sand-washer,
one set of which is used at Albany, is probably as efficient as any
machine yet devised. It is shown in Fig. 8. It will be observed that
the dirty sand is fed to the machine at one end into a hopper-shaped
receptacle. In the bottom of this hopper is a nozzle through which
water is discharged from a pipe running along the entire bottom of the
machine. This jet of water forces the sand upward through a suitable
pipe into a reservoir which discharges the sand and water into another
hopper, and so on through the series of five. Evidently there may be
any number of hoppers in the series, a jet of water being provided at
the bottom of each. In this manner the sand and water are thoroughly
mixed together and compelled to flow upward from each hopper to the
next, the dirty water overflowing also from each hopper into a tank
underneath, whence it runs to waste. The clean sand and water flow out
of the machine at the end opposite to that at which they entered. After
the washed sand is dried it is ready to be replaced in the filter.
=241. Controlling or Regulating Apparatus.=—It is essential to the
proper working of a slow sand filter that the amount of water admitted
to and passing through it shall be as nearly uniform as practicable.
This necessitates controlling or regulating apparatus, of which there
are two general classes, the one automatic and the other worked by
hand. There are a considerable number of appliances of both classes.
The filtered water flows from the end of the drains to one or two
small tanks formed by suitable masonry walls immediately outside of
the filter-beds and rises to a level determined by the loss of head
in passing through the filter. The difference in elevation between
the water surface over the sand and that in the filtered water-tanks
shows the effective head which causes the water to flow through the
sand. The object of the controlling or regulating appliances is to keep
that head as nearly constant as possible. Both the hand and automatic
appliances preserve the value of that head by maintaining constant
discharges through either vertical or horizontal orifices, the orifices
themselves being movable. They may be rectangular or other orifices
with horizontal lips or crests. If the control is automatic it is
accomplished usually by a float which raises and lowers the orifice in
such a way as to maintain a constant difference of level between the
filtered and the unfiltered water. The figures illustrate both types of
regulating appliances, the actions of which will be readily understood.
[Illustration: FIG. 8.—Ejector Sand-washer.]
[Illustration: FIG. 9.—Ball-float Regulator of Rate of Filtration.]
[Illustration: FIG. 10.—Regulator in Use in Zurich, Switzerland. M.
Peter, Engineer.]
=242. Cost of Slow Sand Filters.=—The cost of both the open and
covered slow sand filters will obviously vary according to the cost of
labor and materials at their sites. The original cost of the Lawrence
filter, about 2.44 acres in total area, was nearly $25,000 per acre.
The cost of covered filters, so far as constructed in this country,
varies from about $44,000 to nearly $51,000 per acre excluding the
pipe, pumping plants, and sedimentation-basins. The Albany covered
filters cost about $38,000 per acre including filtering materials, but
excluding excavation, pumps, buildings, sedimentation-basins, piping,
and sand-washing machinery, or nearly $46,000 per acre including those
items except pumps and sedimentation-basins. The roof, included in
the preceding estimate, cost about $14,000 per acre. The smaller the
filters the greater the cost per acre, as a rule, as would be expected.
A single open filter at Poughkeepsie and three open filter-beds at
Berwyn, Pa., cost respectively $42,000 and $36,000 per acre, the
former being little less than .7 acre in area and the latter having an
aggregate area of a little more than one half acre. A covered filter at
Ashland, Wis., consisting of three beds of one sixth acre each, cost at
the rate of about $70,000 per acre.
[Illustration: FIG. 11.—Regulating Apparatus Designed by Allen Hazen
for the Albany Filters.]
[Illustration: FIG. 12.—Regulator of Rate of Filtration.]
=243. Cost of Operation of Albany Filter.=—The cost of operating
the Albany filter, including only the costs of scraping, removing
sand, refilling, incidentals, lost time, and washing the sand during
seventeen months ending December 29, 1900, was $1.66 per million
gallons filtered. The cost of removing the sand (excluding scraping),
washing, and refilling was $1.21 per cubic yard. The total cost of
operating the entire filter-plant, including all items, for the year
1900 was $4.52 per million gallons filtered. This covers all expenses,
including pumping, superintendence, and laboratory, which can be
charged to the operation of the filter-plant. The average removal of
albuminoid ammonia at Albany for the year 1900 was 49 per cent and
of the free ammonia 78 per cent of that in the raw water, while the
average bacterial removal was over 99 per cent, running from 98.3 per
cent to 99.6 per cent. The volume of water used in washing the sand was
about twelve and a half times the volume of the sand. Each cubic yard
of sand washed, therefore, required twelve and a half cubic yards of
water.
[Illustration: FIG. 13.—Regulator Designed by W. H. Lindley for the
Filters at Warsaw, Poland.]
=244. Operation and Cost of Operation of Lawrence Filter.=—It was
originally intended that the Lawrence filter should be worked
intermittently. The Merrimac River water, which is used by the city of
Lawrence, was known to carry at certain periods of the year sufficient
typhoid germs received from the city of Lowell to produce at least
mild epidemics. The intermittent operation was considered necessary to
furnish the filter with the requisite oxygen to destroy beyond a doubt
all pathogenic bacteria. The increasing demands of water consumption
during the years that have elapsed since filtration began in 1894 have
seriously modified these conditions, so that the intermittent feature
of operation of the filter is no longer very prominent. During 1898,
for instance, the filter was drained only four to thirteen times
per month, with an average of eight monthly drainings. In 1899 the
drainings were more frequent, varying from five to fourteen per month
and averaging eleven times. Finally, in 1900, the monthly drainings
ranged from three to thirteen, with an average of eight. It may be
considered, therefore, that the Lawrence filter occupies a kind of
intermediate position between intermittent and continuous operation.
The total cost of operating the filter at Lawrence, including scraping
and washing of sand, refilling, removal of snow and ice, and general
items in the period from 1895 to 1900, both inclusive, varied from a
minimum of $7.70 per million gallons to $9.00 per million gallons. If
the removal of snow and ice be omitted, these amounts will be reduced
to $5.10 and $6.90 respectively. The cost of washing the sand only in
the Lawrence filter during the same period varied from 45 to 67 cents
per cubic yard. The volume of water required for that washing varied
from ten to fourteen times the volume of sand.
=245. Sanitary Results of Operation of Lawrence and Albany
Filters.=—The average number of bacteria in the Merrimac River water
applied to the filter during the period 1894 to 1899, both inclusive,
varied from about 1900 per cubic centimeter to 34,900, and the
percentage of reduction attained by passing the water through the
filter varied in the same period generally from 97 to 99.8 per cent,
with an average of about 99.1 per cent.
In the city of Lawrence the average number of cases of typhoid
fever per 10,000 of population has been about one third, since the
introduction of filtered water, of the number of cases which existed
prior to the installation of the filters, and less than one fourth as
many deaths. A large number of the cases of typhoid occurring after the
installation of the filter have been traced to the use of unfiltered
water, and it is probable that all or nearly all could be similarly
accounted for.
In the city of Albany the experience had been quite similar. The
average number of deaths per year from typhoid fever for ten years
before the introduction of filtered water was 84, while in 1900, with
the filter in operation, the total number of deaths was 39. These
figures are sufficient to show the marked beneficial effect of filtered
water on the public health.
[Illustration: Jewell Filter.]
=246. Rapid Filtration with Coagulants.=—It has been seen that the rate
of filtration through open sand filters does not usually exceed 2 to
4 million gallons per acre per day under ordinary circumstances. Much
greater rates would clog the sand and produce less efficient results.
Experience has also shown that such methods cannot be depended upon to
remove from water coloring matter of a vegetable origin or very finely
divided sediment. In order to accomplish these ends it is necessary to
employ suitable chemicals which, acting as coagulants, may accomplish
results impracticable in the open filter. Resort has therefore been
made first to the adoption of suitable coagulants and then to such
increased heads or pressures as to force the water through the sand
at rates from 25 to 30 or even 50 times as great as practicable in
slow sand filtration. These rapid sand filters are called mechanical
filters. If the water is forced through them under pressure, they
consist of closed tanks in which sand is placed so as to leave
sufficient volume above it for the influent water and, supported upon
a platform carrying perforated pipes, strainers, or equivalent details
through which the filtered water may flow into a suitable system of
effluent pipes in the lower part of the filter. If water is forced
through the sand by the required head, the upper part of the filter may
be open, but of sufficient height to accommodate it. The same filtering
material, clean sand, is used as in the slow filters; the only
differences, aside from the higher rate of filtration, are the greater
head and the introduction of a coagulant to the water. The depth of
sand used may vary from 2 to 4 feet. The thickness of a relatively fine
sand may be less than that of a coarser sand.
=247. Operation of Coagulants.=—The coagulant which has been found to
give the best results is ordinary alum or sulphate of aluminum. If
sulphate of aluminum is dissolved in water containing a little lime or
magnesia, aluminum hydrate and sulphuric acid are formed. The aluminum
hydrate is a sticky gelatinous substance which gathers together in a
flocculent mass the particles of suspended matter in the water, and it
also adheres to the grains of sand when those masses have settled to
the bottom. This flocculent, gelatinous mass covers the sand and passes
into its voids. As the water is forced through it the bacteria and
suspended matter are held, leaving a clear effluent to pass through.
Other coagulants are used, such as the hydrate of iron, but it costs
more than alum and is not so effective in removing color, although
it is an excellent coagulant for removing turbidity. Physicians have
made objection to the use of alum for this purpose, on the ground that
any excess might pass into distribution-pipes and so be consumed by
the water-users to the detriment of health. While it is possible that
further experience may show that there is material ground for this
objection, it has thus far not been found to be so. It is, however,
essential that only the necessary amount of alum should be used and
that there may be a sufficient amount of alkali to combine with the
sulphuric acid. Otherwise the acidulated water may attack the iron and
lead pipes and so injure the water and produce serious trouble. It
can only be stated that the method and operation of these mechanical
filters have thus far been sufficiently successful to avoid any of
these difficulties.
[Illustration: The Jewell Filter-plant at Norristown, Penn.]
=248. Principal Parts of Mechanical Filter-plant—Coagulation and
Subsidence.=—The principal parts of a complete mechanical filter-plant
in the order of their succession are a solution-tank, a measuring-tank,
a sedimentation-basin, and a filter. In case of great turbidity
the sedimentation may be completed in two stages, the first in a
settling-basin prior to receiving the coagulant, and the second in
another basin subsequent to the coagulation. The tanks are usually
of wood, although they may be of steel. The solution-tank is a
comparatively small vessel in which the alum is dissolved. The solution
is then run into the measuring-tank, from which it flows into the water
at a constant rate maintained by suitable regulating apparatus. It is
imperative for the successful working of the mechanical filter-plant
that the coagulant be introduced to the water at a uniform rate.
This rate will obviously depend upon the character of the water. The
coagulating solution runs from the measuring-tank into the pipe through
which the water to be filtered flows and in which it first receives
the alum. The water and the coagulating solution are thus thoroughly
mixed and flow into the sedimentation-basin. The subsidence which is
provided for in this basin may be omitted in very clear waters which
carry little solid matter, but the operation of the filter itself will
be more satisfactorily accomplished if as much work as feasible is done
before reaching it. The mixture must remain in this basin a sufficient
length of time to allow such subsidence as can reasonably be attained.
It appears from experience in this part of the work that it is not well
to introduce the coagulant too long before the water enters the filter,
especially if the water be fairly clear. In the case of the presence
of finely divided solid matter, however, sufficient time must be
permitted for the necessary settlement. A period ranging in length from
½ hour to 6 or 8 hours may be advantageously assigned to this part of
the operation, the shorter period for clear waters and the longer for
very turbid waters. It has been suggested that two applications of the
coagulant might be beneficial, the principal portion being given to the
water before entering the sedimentation-basin and the other just before
the waters enters the filter. The work of the filter, especially with
turbid waters, may be much reduced by simple subsidence for a period
of perhaps 24 hours before receiving the coagulant, the secondary
subsidence taking place in the settling-basin in the manner already
described. Duplicate solution- and measuring-tanks will be required in
order that the process may be continuous while one set is out of use.
In this process it is absolutely essential also that the coagulant
should be of the best quality, inferior grades having been found to be
unsatisfactory in their operation.
=249. Amount of Coagulant—Advantageous Effect of Alum on Organic
Matter.=—The amount of sulphate of alumina will vary largely with the
quality of water. In the investigation made by Mr. Fuller in connection
with the Ohio River supply for the city of Cincinnati, he found that
with very slight turbidity only ¾ grain was required per gallon of
water, but that a high degree of turbidity required as much as 4.4
grains per gallon, with intermediate amounts for intermediate degrees
of turbidity. It was estimated that these quantities would correspond
to an average annual amount of about 1.6 grains per gallon. In case
there should be a period of three days of subsidence preliminary to
filtration, he estimated that for the greater part of the time the
amount of alum would vary from 1 to 3 grains per gallon. Occasionally
more and sometimes less would be required.
Alum has some specially valuable qualities in connection with this
class of purification work. It combines with coloring matter,
particularly that which has been acquired from contact of the water
with vegetation, and precipitates it. It seems to combine also, to some
extent, with the organic matter carried by the water and thus enhances
the efficiency of filtration.
=250. High Heads and Rates for Rapid Filtration.=—The principal work
of investigation of filtration in mechanical or pressure filters has
been made for the cities of Pittsburg, Cincinnati, Louisville, and
Providence, R. I. In the experimental work of those investigations
rates of filtration ranging from 46 million to 170 million gallons per
acre per day have been employed with essentially the same efficiency.
This is a practical result of great importance, particularly if in
the continued use of these filters on a large scale a satisfactorily
high efficiency can be reached and maintained. It was observed that
the number of bacteria in the effluent varied with that in the raw
water. It was also noticed that similarly to the operation of slow sand
filters the rate of filtration should not be changed suddenly, as that
is likely to cause breaks in the sand and militate against continued
efficiency.
In his experimental work at Cincinnati Mr. Fuller found that with
fine sand an available head on the filter of 12 feet gave economical
results. He also states that “high rates are more economical than low
ones, and that the full head which can be economically used should be
provided. Just where the economical limit of the rate of filtration is
can only be determined from practical experience with a wider range of
conditions than exist here, but there seem to be no indications that
the capacity of a plant originally constructed on a medium rate basis
(100 million to 125 million gallons per acre daily) could not readily
and economically be increased, as the consumption demanded, to rates at
least as high as the highest tried here (170 million gallons per acre
daily), provided the full economical increase in loss of head could be
obtained.”
=251. Types and General Arrangement of Mechanical Filters.=—These
mechanical or pressure (by gravity) filters have until lately been
constructed by companies owning patents either on the process or on
the different parts of the filters. The fundamental patent, however,
protecting rapid sand filters with the continuous application of
a coagulant has expired and the city of Louisville, Ky., is now
constructing rapid sand filters different in design from those
heretofore used. The types that have been most common heretofore are
the Jewell subsidence gravity filter, the Continental gravity filter,
the New York sectional-wash gravity filter, and others. They all
possess the main feature of accelerating the rate of filtration by
pressure, either in a closed tank (rarely) with comparatively small
water volume above the sand or by an open filter with sufficient head
of water above the sand to accomplish the high rate desired. This
latter method is that now generally used, as by it the requisite
steadiness of head or pressure can be secured. The closed type is
subject to objectionable sudden changes of pressure which prevent
or break uniform rates of filtration. The sand is supported upon a
platform with a suitable system of pipes fitted with valves or gates
for the withdrawal of the filtered water, the space below the platform
forming a small sedimentation-chamber. They are usually constructed in
comparatively small circular units, so that one or more of a group may
be withdrawn from operation for the purposes of cleaning or repairs
without interfering with the operation of the others. This system of
small units, gives some marked practical advantages, as housing is
readily accomplished, and if necessary the plant may be easily removed
from one point to another.
[Illustration: Continental Filter.]
It is obvious that with the large amount of water forced through
a given area of filter-bed the sand will become clogged within a
comparatively short time, requiring washing and replacing. Mr. Fuller
found at Cincinnati that the periods between washings when fine sand
was used in the filters ranged from 8 to 24 hours, with an average of
15, but with coarse sand the average became 20, with a range of from
6 to 36 hours. The time required for washing the sand at Cincinnati
was 20 minutes for coarse or 30 minutes for fine. At Providence Mr.
Weston found that the average time of washing was about 11 minutes.
The cleaning is accomplished partially by stirring the sand with
revolving arms, as shown in the accompanying figures, but generally
by forcing the water in a reverse direction through the sand and
allowing the wash-water either to run to waste or to be again purified.
The filters are designed for the purpose of cleaning by the reversal
of the direction of the flow of water. Latterly the sand has been
cleaned by forcing compressed air at a low pressure through it and the
superimposed water. The passage of the air or water upward through the
sand produces such a commotion among the grains that they rub against
each other and clean themselves of the adhering material, allowing it
to be carried off by the water above the sand. Both methods are much
used and are satisfactorily effective for the purpose.
It was found at Cincinnati that 4 to 9 per cent, with an average of 5
per cent, of filtered water was required for washing the fine sand, and
only 2 to 6 per cent, with an average of 3 per cent, for the coarse
sand of the mechanical filters used in Mr. Fuller’s experiments. Mr.
Weston has found about the same figures in his experimental work at
Providence. The wash-water need not be wasted at all if it is pumped
back into the subsidence-tanks.
It has been found in some cases that the efficiency of the filters
after washing is not quite normal, and that possibly 2 or 3 per cent
of the water must be wasted unless it is allowed to run back into
the subsidence-tanks and again pass through the filter. Under such
circumstances it has required 20 to 30 minutes of operation of the
filter after washing to regain its normal efficiency.
=252. Cost of Mechanical Filters.=—The cost of these mechanical filters
has been found to range as high as a rate of $500,000 per acre, which
is probably about ten times as much as the rate of cost for the slow
sand filters. On the other hand, the efficiency of the mechanical
filters may be as high as the other class, with a rate of filtration
from thirty to fifty times as great, and with a cost of operation less
than that of the slow sand filters. The cost of the filters per million
gallons of filtered water may, therefore, be reduced to perhaps one
fourth of that of the slow sand type.
=253. Relative Features of Slow and Rapid Filtration.=—It is premature,
even unnecessary, to make a comparison between the slow and rapid sand
filters. The former are well adapted to a large class of potable waters
in which there is not too much or too finely divided solid matter and
in which the coloring from organic origin is not serious. They have
the advantage of requiring no chemicals and are capable of attaining a
high degree of efficiency. The average rate of filtration may be taken
about 3,000,000 gallons per acre per day. The rapid sand filter, on the
contrary, requires the application of a coagulant, but has thirty to
fifty times the capacity of the other class. It is better adapted to
the removal of turbidity and color, and when properly operated it gives
a high efficiency. A sufficiently extended experience has not yet,
however, been attained to enable a complete statement to be made as to
the entire field to which they may be adapted. They have certainly been
shown to possess valuable qualities in a number of respects, and they
are undoubtedly destined to play an important part in the purification
of waters.
PART IV.
_SOME FEATURES OF RAILROAD ENGINEERING._
CHAPTER XXI.
=254. Introductory.=—The first step toward the construction of a
railroad is the location of the line, which requires as an initiative
a careful ocular examination of the general vicinity of the proposed
road, supplemented by simple and approximate instrumental work rapidly
performed. Following this reconnaissance, as it is called, more
complete surveys and examinations are made both in the field and on the
maps plotted from the data of the field-work. The prosecution of this
series of operations produces the final location, together with the
accumulation of such maps, profiles, and other data as may be required
in the construction of the road-bed, bridges, and other structures
constituting the complete railroad line with its ballast and track in
place ready for traffic.
The ultimate purpose of any railroad line is the transportation of
passengers and freight under conditions, including those of a physical
nature connected with the road as well as the rates received, leading
to profitable returns. Competition or other circumstances attending the
traffic of a given road will fix the maximum rates to be charged for
transportation. It is the business, first, of the civil engineer so to
locate and design the road and, second, of the manager so to conduct
the transportation as to make the margin of profits the greatest
possible. It will be the purpose of this lecture to consider in a
general way only some of the features of a railroad and its operation
which are related directly to civil-engineering.
[Illustration: The Royal Gorge.]
=255. Train Resistances.=—It is a fact confirmed by constant daily
experience that, however nicely the machine impelling the railroad
train or the tracks supporting the cars may be built, considerable
frictional and other resistance is offered to the movement of the train
when the latter passes over a perfectly level and straight track.
A considerable portion of the cost of transportation is expended in
overcoming this resistance. When the line fails to be either level
or straight other resistances of magnitude are developed; they are
called the resistances of grades and curves: and it is the business of
the civil engineer so to design the railroad as to reduce these two
classes of resistance to an absolute minimum, in view of certain other
conditions which must be concurrently maintained.
=256. Grades.=—The grade of a railroad is expressed usually in this
country by the number of feet through which 100 feet of length of line
rises or falls, or by some expression equivalent to that. If, for
instance, the line rises 1.5 or 2 feet in 100, it is said to have an
ascending grade of 1.5 or 2 per cent. Or if the line falls the same
amount in the same length, it is said to have a descending grade of
1.5 or 2 per cent. It is evident that a grade which descends in one
direction would be an ascending grade for trains moving in the opposite
direction, so that grades favoring traffic in one direction oppose it
in the other. Hence, other things being equal, that road is the most
advantageous for the movement of trains which has the least grade. The
grades of railroads seldom exceed 2 or 2.5 per cent, although, as will
presently be shown, there are some striking exceptions to that general
observation. The actual angles of inclination of railroad tracks
from a horizontal line are therefore as angles very small, but their
disadvantages for traffic increase rapidly.
A simple principle in mechanics shows that if the railroad train with
a weight _W_ moves up a 2 per cent grade, one component of the train
weight acts directly against the tractive force of the locomotive or
other motive power. If _a_ is the angle of inclination of the track
to a horizontal line, this opposing component will have the value _W_
sin _a_. When angles are small their sines are essentially equal to
their tangents. Hence, in this case, sin _a_ would have the value .02
or ¹/₅₀ of the train weight. If the weight of the train were 500 tons,
which is a rather light train for the present time, this opposing force
would be 10 tons, or 20,000 pounds, which, as we shall see later on, is
more than one half of the total tractive force of any but the heaviest
locomotives built at the present day. This simple instance shows the
advantage of keeping railroad grades down to the lowest practicable
values.
One of the most economical freight-carrying roads in the United States
is the Lake Shore and Michigan Southern of the New York Central system,
running from Buffalo to Chicago. Its maximum grade is 0.4 of 1 per
cent. The maximum grade of the N. Y. C. & H. R. R. R. is 0.75 of 1 per
cent between New York City and Albany and between Albany and Buffalo,
1.74 per cent at Albany, 1.12 per cent at Schenectady, and 1 per cent
at Batavia. Pushers or assistant locomotives are used for heavy trains
at the three latter points. The maximum grade of the Pennsylvania R. R.
on the famous Horseshoe Curve between Altoona and Cresson is 1.8 per
cent. It is advantageous, whereever practicable, to concentrate heavy
grades within a short distance, as in the case of the New York Central
at Albany, and use auxiliary engines, called pushers or assistants.
Some of the heaviest grades used in this country are found on the
trans-continental lines where they pass the summits of the Rocky
Mountains or the Sierras. In one portion of its line over a stretch of
25.4 miles the Southern Pacific R. R. rises 2674 feet with a maximum
grade of 2.2 per cent; also approaching the Tehacipi Pass in California
the maximum grade is about 2.4 per cent. At the Marshall Pass on the
Denver & Rio Grande R. R. there is a rise of 3675 feet in 25 miles with
a maximum grade of 4 per cent. The Central Pacific R. R. (now a part of
the Southern Pacific system) rises 992 feet in 13 miles with a maximum
grade of 2 per cent. The Northern Pacific R. R. rises at one place 1668
feet in an air-line distance of 13 miles with a maximum grade of 2.2
per cent. Probably the heaviest grade in the world on an ordinary steam
railroad is that of the Calumet Mine branch of the Denver & Rio Grande
R. R., which makes an elevation of 2700 feet in 7 miles on an 8 per
cent grade and with 25° curves as maximum curvature. These instances
are sufficient to illustrate maximum railroad grades found in the
United States.
=257. Curves.=—Civil engineers in different parts of the world have
rather peculiar classifications of curves. In this country the railroad
curve is indicated by the number of degrees in it which subtend a chord
100 feet in length. Evidently the smaller the radius or the sharper the
curvature the greater will be the number of degrees between the radii
drawn from the centre of a circle to the extremities of a 100-feet
chord. American civil engineers use this system for the reason that
the usual tape or chain used in railroad surveying is 100 feet long. A
very simple and elementary trigonometric analysis shows that under this
system the radius of any curve will be equal to 50 divided by the sine
of one half of the angle between the two radii drawn to the extremities
of the 100-feet chord. In other words, it is equal to 50 divided by
the sine of one half the degree of curvature. The application of this
simple formula will give the following tabular values of the radii for
the curves indicated:
Curve. Radius in Feet.
1° 5729.65
2° 2864.93
3° 1910.08
4° 1432.69
5° 1146.28
6° 955.36
7° 819.02
8° 716.78
9° 637.27
10° 573.69
12° 478.74
15° 383.06
20° 287.91
=258. Resistance of Curves and Compensation in Grades.=—Inasmuch as
the resistance offered to hauling the train around a curve increases
quite rapidly as the radius of curvature decreases, it is obvious
that in constructing a railroad the degree of each curve should be
kept as low as practicable, and that there should be no more curves
than necessary. While no definite rule can be given as to such
matters, curves as sharp as 10° (573.69 feet radius) should be avoided
wherever practicable. It is not advisable to run trains at the highest
attainable speeds around such curves, nor is it done. Inasmuch as curve
resistance has considerable magnitude, as well as the resistance of
grades, it is natural that wherever curves occur grades should be less
than would be permissible on straight lines or, as they are called,
tangents. If a maximum gradient is prescribed in the construction of
a railroad, that gradient will determine the maximum weight of train
which can be hauled on the straight portions or tangents of the road.
If one of these grades should occur on a curve, a less weight of
train could be handled by the same engine than on a tangent. Hence it
is customary to reduce grades by a small amount for each degree of
curvature of a curve. This operation of modifying the grades on curves
so as to enable a locomotive to haul the same train around them as up
the maximum grade on a tangent is called compensating the curves for
grade. There is no regular rule prescribed for this purpose, because
the combination may necessarily vary between rather wide limits in
view of speed, condition of track, and other influencing elements.
The compensation, however, has perhaps frequently been taken as lying
between .03 and .05 per cent of grade for each degree of curvature. In
other words, for a 5° curve the grade would be .15 to .25 per cent less
than on a tangent. This compensation for grades is carefully considered
in each case by civil engineers in view of experience and such data as
special investigations and general railroad operation have shown to be
expedient.
[Illustration: FIG. 1. GRAVEL BALLAST]
[Illustration: FIG. 2. STONE BALLAST
NEW YORK CENTRAL & HUDSON RIVER RY.]
[Illustration: FIG. 3. PENNSYLVANIA RY.]
=259. Transition Curves.=—High speeds for which modern railroads are
constructed have made it necessary not only to protect road-beds, but
also to make the passage from tangents to curves as easy and smooth as
possible. This is accomplished by introducing between the curve and
the tangent at each end what is called a “transition” curve. This is a
compound curve, i.e., a curve with varying radius. At the point where
the tangent or straight line ceases the radius of the transition curve
is infinitely great, and it is gradually reduced to the radius of the
actual curve at the point where it meets the latter. By means of such
gradual change of curvature the trucks of a rapidly moving train do
not suddenly pass from the tangent to the curve proper, but they pass
gradually from motion in a straight line to the sharpest curvature over
the transition curve. The rate of transition is fixed by the character
of the curves, which have been subjected to careful analysis by civil
engineers, and they can be found fully discussed in standard works on
railroad location.
[Illustration: FIG. 4.—Baltimore Belt-line Tunnel, B. & O. Ry.]
=260. Road-bed, including Ties.=—Not only the high rates of speed of
modern railroad trains but the great weights of locomotives and cars
have demanded a remarkable degree of perfection in the construction of
the road-bed and in the manufacture of rails. The favorite ballast at
the present time for the best types of road-beds is generally broken
stone, although gravel is used. The first requisites are a solid
foundation and perfect drainage whether in cuts or fills. Figs. 1,
2, 3, and 4 show two or three types of road-bed used by the New York
Central and Hudson River R. R., the Pennsylvania R. R., and a special
type adopted by the B. & O. for the belt-line tunnel at Baltimore.
These sections show all main dimensions and the provision made for
drainage. The general depth of ballast is about 18 inches, including
the drainage layer at the bottom. The total width of road-bed for a
double-track line varies frequently between 24 and 25 feet, while the
width of a single-track line may be found between 13 and 14 feet. In
the cross-sections shown the requirements for drainage are found to be
admirably met. Timber ties are almost invariably used at the present
time in this country, although some experimental steel ties have
been laid at various points. Fig. 5 shows the steel tie adopted for
experiment on the N. Y. C. & H. R. R. R. within the city limits of New
York. The time will undoubtedly come when some substitute for timber
must be found, but the additional cost of steel ties at the present
time does not indicate their early adoption.
[Illustration: FIG. 5.]
[Illustration: FIG. 6.]
[Illustration: Cañon of the Rio Las Animas, near Rockwood.]
=261. Mountain Locations of Railroad Lines.=—The skill of the civil
engineer is sometimes severely taxed in making mountain locations of
railroads. Probably no more skilful engineering work of this kind has
ever been done than in the crossings of the Rocky Mountains and the
Sierras in this country by trans-continental railroad lines, although
more striking examples of railroad location for short distances may
perhaps be found in Europe or other countries. The main problem in such
cases is the making of distance in order to attain a desired elevation
without exceeding maximum grades, such as those which have already
been given. Most interesting engineering expedients must sometimes
be resorted to. One of the oldest of these is the switchback plan
shown in Fig. 6. This is probably the simplest procedure in order to
make distance in attaining elevation. The line is run up the side of
a mountain at its maximum grade as far in one direction as it may be
desirable to go. It then runs back on itself a short distance before
being diverted so as to pass up another grade in the reverse direction.
This zigzagging of alignment may obviously be made to attain any
desired elevation and so overcome the summit of a mountain range. The
old switchback coal road near Mauch Chunk, Pa., is one of the oldest
and more famous instances of the method, which has many times been
employed in other locations.
[Illustration: FIG. 7.]
A more striking method, perhaps, is that of loops by which the
direction of a line or motion of a train on it is continuous. Distance
is made by a judicious use of the topography of the locality so as to
run the line as far up the side of the valley as practicable and then
turn as much as a semicircle or more, sometimes over a bridge structure
and sometimes in tunnel, so as to give further elevation by running
either on the opposite side of the valley or on the same. A succession
of loops or other curves suitably located will give the distance
desired in order to reach the summit.
=262. The Georgetown Loop.=—Fig. 7 shows one of these spiral or loop
locations on the Georgetown branch of the Union Pacific Railroad
in Colorado. It is a well-known and prominent instance of railroad
location of this kind. On the higher portion of this loop system
included in the figure there is a viaduct on a curve which crosses the
line 75 feet above the rail below it and 90 feet above the water. This
location is a specimen of excellent railroad engineering. The length
of line shown in the figure, including the spiral, is 8½ miles, and it
cost $265,000 per mile exclusive of the bridges.
=263. Tunnel-loop Location, Rhætian Railways, Switzerland.=—In Figs.
8 and 9 are shown two portions of the Albula branch of the Rhætian
Railways, Canton Graubünden, southeastern Switzerland. The line
connects the valleys of the Albula and the Inn, the former being one of
the branches of the Rhine and the latter of the Danube; it therefore
cuts the divide between the watersheds of those two rivers. It is a
3.28-feet gauge single-track road, and is built largely for tourist
traffic, as the scenic properties of the line are remarkable.
The maximum grade on this line is 3.5 per cent. Over one portion of the
line 7.8 miles long one third of that distance is in tunnel and 15 per
cent of it on viaducts. The radii of the centre lines of the tunnels
are 460 and 394 feet, while the lengths of the tunnels range from 1591
to 2250 feet, with a maximum grade in them of 3 per cent. The weight of
rails used is 50 pounds per yard on grades of 2.5 per cent or less, but
for heavier grades 55-pound rails are employed. The cross-ties are of
mild steel and weigh 80 pounds each except in the long Albula tunnel,
where treated oak ties are used as being better adapted to the special
conditions existing there. It will be observed that in each case the
line rises from the left-hand portion of the figure toward the right.
[Illustration: FIG. 8.]
[Illustration: FIG. 9.]
The tunnels are represented by broken lines, and they are in every
instance on circular curves. Fig. 9 represents the line running from
a point on the east side of the Albula River through a heavy cut and
then across the valley of the Albula into a tunnel 2250 feet long.
The line then runs chiefly in cuts to a point where there are two
tunnels, one over the other; indeed the line over-laps itself in loops
and tunnels a number of times in that vicinity. That portion of the
road shown in Fig. 8 is less remarkable than the other, although it
exhibits extraordinary alignment. This example of railroad location
is one of the most striking among those yet completed. It would
appear to indicate that no topographical difficulties are too great
to be overcome by the civil engineer in railroad location in a most
rugged and precipitous country. Obviously such a line could not be
economically operated for heavy freight traffic.
Railroad lines frequently lead through mountainous regions affording
some of the grandest scenery in the world accessible to the travelling
public. In this country the Canadian Pacific, the Northern Pacific, the
Great Northern, and the Rio Grande Western probably exhibit the most
remarkable instances of this kind.
CHAPTER XXII.
=264. Railroad Signalling.=—The birth of the art of railroad signalling
was probably coexistent with that of the railroad. At the very outset
of the movement of railroad trains it became imperative to insure to
a given train the sole use of the single track at schedule periods.
Both head-to-head and rear-end collisions were liable to occur on main
tracks, as well as false meetings at branches and cross-overs.
=265. The Pilot Guard.=—One of the earliest if not the earliest
of systematic procedures in England to accomplish the safe use of
a railroad track involved the employment of the “pilot guard” on
single-track roads. The pilot was an employé whose duty it was to
accompany every train over a stated section of the line. The authority
to start trains was lodged in him. When it became necessary to start
two or three trains from the same point and in the same direction, it
was also his duty to issue to each train conductor what was called a
pilot ticket, equivalent to a modern train order to run the train over
the section under his control. In that case he was obliged to accompany
the last train to the other end of his section, and no more trains
could move over that section in the same direction until his return
to his first station. As no train could pass over the section without
either him or his pilot ticket, it is clear that the system could
prevent head-to-head collisions, but in itself it is not sufficient to
eliminate rear-end collisions. This system is still employed in Great
Britain on some short branch lines.
=266. The Train-Staff.=—Another method nearly as old as the preceding
is that of the train-staff, used in an improved form at the present
time on some single-track roads. No train under this system can
pass over any given section of the line unless it carries the staff
belonging to that section, the staff being a piece of wood or metal 1
to 1¼ inches in diameter and 18 to 20 inches long. In order to cover
the case of two or more trains starting in the same direction at one
end of a section before running a train in the opposite direction,
tickets were issued, the staff being taken by the last train. The
proper operation of this method, like that of the preceding, would
prevent head-to-head collisions, but is not sufficient in itself to
prevent one train running into the rear of another while both are
proceeding in the same direction in the same section.
=267. First Basis of Railroad Signalling.=—These and other similar
systems answered fairly well the more simple requirements of early
railroad operation. Strictly speaking they are not methods of
signalling, although it may be said that each train is a signal in
itself. With the development of railroad business it was found that
other methods better adapted to a more efficient and rapid movement
of trains were imperative. It was in response to the advancing
requirements of the railroad business that the first approach to
what is now so well known as the block system of signalling was made
in 1842. An English engineer, subsequently, Sir W. F. Cooke, stated
the following sound principles as to the basis of efficient railroad
signalling:
“Every point of a line is a dangerous point which ought to be covered
by signals. The whole distance ought to be divided into sections, and
at the end as well as at the beginning of them there ought to be a
signal, by means of which the entrance to the section is open to each
train when we are sure that it is free. As these sections are too long
to be worked by a traction rod, they ought to be worked by electricity.”
The main features of railroad signalling, as thus set forth, have
continued to characterize the development of the block system from
that early day to the present. The electrical application to which
reference is made in the preceding quotation was that of the needle,
which by its varying position could indicate either “line clear” or
“line blocked.” In 1851 electric bells were used in railroad signalling
on the Southeastern Railway of England. Various other developments were
completed from time to time in Great Britain until the Sykes system
of block signalling was patented in 1875. One of the main features of
the system, and perhaps the most prominent, was the control of the
track signals at the entrance end of the block by the signalman at the
advance end. He exerted this control by electrically operated locks.
About 1876 the Pennsylvania Railroad introduced the block system into
the United States, which has since been greatly developed in a number
of different forms, and its use has been widely extended over many if
not most of the great railroad systems of the country. It is not only
used for the movement of trains, but also for the protection of such
special danger-points as switches, cross-overs, junctions, drawbridges,
heavy descending grades, sharp curves, and other points needing the
protection which a well-designed block system affords.
=268. Code of American Railway Association.=—The code of the American
Railway Association gives the following definitions among others
pertaining to the block system:
_Block._—A length of track of defined limits, the use of which by
trains is controlled by block signals.
_Block Station._—The office from which block signals are operated.
_Block Signal._—A fixed signal controlling the use of a block.
_Home Block Signal._—A fixed signal at the entrance of a block to
control trains in entering and using said block.
_Distant Block Signal._—A fixed signal of distinctive character used in
connection with a home block signal to regulate the approach thereto.
_Advance Block Signal._—A fixed signal placed in advance of a home
block signal to provide a supplementary block between the home block
signal and the advance block signal.
_Block System._—A series of consecutive blocks controlled by block
signals.
_Telegraph Block System._—One in which the signals are operated
manually upon telegraphic information.
_Controlled-Manual Block System._—One in which the signals are operated
manually, and by its construction requires the co-operation of a
signalman at both ends of the block to display a clear signal.
_Automatic Block System._—One in which the signals are operated by
electric, pneumatic, or other agency, actuated by a train or by certain
conditions affecting the use of a block.
=268a. The Block.=—It is seen by these definitions that what may be
called the unit in railroad signalling is the “block”; it may be of
almost any length from a few hundred feet to 6 or 8 miles, or even
more. On a single-track railroad it may evidently extend from one side
track or passing-place to another. Over portions of lines carrying
heavy traffic it may be a half-mile or less. The length of block will
depend, then, upon the intensity and kind of traffic, the physical
features of the line, such as curvature, grade, sidings, cross-overs,
and other similar features, the location, whether in cities, towns, or
open country, as well as upon other elements affecting conditions of
operation which it is desirable to attain.
=269. Three Classes of Railroad Signals—The Disc.=—The signals used
in railroad operation may mainly be divided into three classes:
semaphores, banners, and discs. In general they may convey information
by form, position, and color. The disc is used by causing it to appear
and disappear before an aperture, usually a little larger than itself,
in a case standing perhaps 10 or 12 feet high alongside the track, and
is admirably typified in the Hall electric signal. On account of its
shape, the case in which the disc is operated is frequently called
the banjo, as it is quite similar in shape to that musical instrument
placed in a vertical position, the key end resting on the ground.
=270. The Banner Signal.=—The banner signal is usually operated by
rotation about a vertical axis, frequently in connection with switches.
Its full face painted red, exposed with its plane at right angles to
the track, indicates “danger” or “stop.” With its face turned parallel
to the track, showing only its edge to approaching trains, a “clear”
line or “safety” is indicated.
In the present development of railroad signalling the banner and disc
patterns have a comparatively limited application, although, on the
whole, they are largely used. The banner signal is mostly employed in
the manual operation of switches, turn-outs, and cross-overs, and for
other local purposes, particularly on lines of light traffic.
[Illustration: FIG. 10.—Semaphore Signals.]
=271. The Semaphore.=—The semaphore is now mainly used in connection
with block signalling. Like many other appliances in railroad
signalling it was first used in England, by Mr. C. H. Gregory, about
1841. Its name is derived from the combination of two Greek words
signifying a sign-bearer. It consists of a post varying in height
from about 3 to 35 or 40 feet, carrying an arm at its top from 3 to
5 feet long, pivoted within a foot or 18 inches of one end, the long
end suitably shaped and painted and the other arranged with a lens so
that when operated at night in connection with a lamp it may exhibit a
properly colored light. The post of the semaphore is placed alongside
the track so as to be on the right-hand side of an approaching train,
the long arm rising and falling as a signal away from the track and in
a plane at right angles to it. The other arm of the semaphore signal
may be connected by wires or rods and light chains running over pulleys
with suitable levers and weights operated either in a near-by signal
cabin or by a signalman stationed near the semaphore itself; or it may
be operated by electric or pneumatic power, as in many of the later
installations. The semaphore may, therefore, be operated at the post or
by suitable appliances at a distance.
[Illustration: Semaphore on Pennsylvania Railroad.]
=272. Colors for Signalling.=—The colors used either for painted
signals for daylight exposure or for coloring lenses for night
signalling are red, white, and green, as ordinarily employed in
this country; red signifying “danger” or “stop,” white signifying
“safety” or “clear track,” and green signifying “caution” or “proceed
with train under control,” indicating that a train may go forward
cautiously, expecting to find an obstruction or occupied track. In
England green is largely employed to indicate “safety” or “clear
track,” on the ground that a white light is so similar to any other in
its vicinity that the latter may too easily be mistaken for a signal.
While there is some diversity of views in this country on that point,
the consensus of engineering opinion seems to favor the retention of
the white for the track safety signal.
=273. Indications of the Semaphore.=—It is evident that a semaphore
affords facilities of form, position, and color in its use for the
purpose of signalling. The horizontal position is the most striking
for the semaphore arm, as it then extends at right angles to the post
and to the right or away from the track; this position is, therefore,
taken to indicate “danger” or “stop.” No train may, therefore, proceed
against a horizontal semaphore arm.
It might at first sight appear that the vertical position of the
semaphore arm close against the post could be taken to indicate
“safety” or “clear track” or “proceed,” but experience has shown that
such a position may be injudicious, except under special conditions
where it has lately been employed to make that indication. If the
semaphore arm should be knocked or blown from the ordinary post,
the engineman of an approaching train probably would not be able to
detect the actual condition of things and might accept the appearance
of the semaphore as indicating a clear line, thus justifying himself
in proceeding at full speed, while the signalman in his cabin might
have placed the signal at “danger.” A position of the semaphore arm,
therefore, at an angle of 65° or 70° below the horizontal is usually
taken as a safety signal. This position is in marked contrast to the
horizontal arm and at the same time makes the absence of the semaphore
arm impossible without immediate detection from an approaching
locomotive. After dark the semaphore in a position of danger exhibits
a red light through the lens in its short arm when the long arm is at
the “danger” position or horizontal. Similarly, when the long arm is in
the safety position a white light is exhibited through the lens in the
shorter arm, so that the respective conditions of clear or obstructed
track are made evident to the engineman as well by night as by day on
his approach to the semaphore.
In some of the latest signal work three positions of the semaphore
arm on one post, known as three-position block signalling, have been
employed. In this system a special post, frequently on a signal bridge
over the track, permits the vertical position of the semaphore arm
to indicate “clear track,” while the diagonal or inclined position
below the horizontal indicates “caution.” In the Mozier three-position
signal a diagonal or inclined position above the horizontal indicates
“caution” an addition to the two usual positions of “stop” and “clear.”
These are the elements, so to speak, of railroad signalling at the
present day. They are combined with various appliances and in various
sequences, so as to express all the varied conditions of the track
structure which affect the operation of the road or the movement of
trains upon it. These combinations and the appliances employed in them
are more or less involved in their principal features and complicated
in their details, although the main principles and salient points are
simple and may easily be exhibited as to their mode of operation and
general results. In this treatment of the subject it will only be
possible to accomplish these general purposes without attempting to set
forth the mechanical details by which the main purposes of railroad
signalling are accomplished.
=274. General Character of Block System.=—It is evident from what has
already been stated that the block system of signalling involves the
use of fixed signals located so as to convey promptly to approaching
trains certain information as to the condition of points of danger
approached. Furthermore, this system of signals is designed and
operated on the assumption that every point is to be considered as a
danger-point until information is given that a condition of safety
exists. The usual position of signals, or what may be called the normal
position, is that of “danger,” and no position of “safety” is to be
given to any signal except to permit a train to pass into a block whose
condition of safety or clear track is absolutely assured. These are
the ground principles on which the signal systems to be considered are
designed and operated, although there are some conditions under which
the normal signal position may be that of safety.
=275. Block Systems in Use.=—The block systems now in general use are:
The Manual, in which the signals at each end of each block are wholly
controlled and operated by the signalman at each signal point.
The Controlled-Manual, in which the signals at the entrance to each
block are controlled either electrically or in some other manner by
the signalman at the other extremity of that block, but are operated
subject to that control by the signalman at the entrance of the block.
The Auto-Manual, in which the signals are generally operated and
controlled as in the Manual or Controlled-Manual, except that they are
automatically returned to the danger position as the rear car of a
moving train passes them.
The Automatic, in which the operation of the signals is wholly
automatic and generally by electricity, or by a combination of electric
and pneumatic mechanism. In this system no signalmen are required.
The Machine, which is a controlled block system for single-track
operation and in which machines operated electrically with detachable
parts, as staffs, are employed in connection with other fixed signals
alongside the track.
The main features of these various systems of blocking are, in
respect to their signalling, the same, but the means for actuating or
manipulating the signals and the conditions under which moving trains
receive the necessary instructions are different. They all have the
same main objects in view of improving railroad operation by enhancing
both safety and facility of train movement.
“Absolute” blocking is that system of block signalling which absolutely
prevents one train passing into a block until the preceding train is
entirely out of it, or, in other words, until the block is absolutely
clear.
“Permissive” blocking is, strictly speaking, the violation of the true
block system of signalling, since under it a train may under certain
precautionary conditions enter a block before the preceding train has
passed out of it.
=276. Locations of Signals.=—In proceeding to locate signals along a
railroad line it is imperative to recognize the preceding purposes
as controlling motives. Signals must be seen readily and clearly in
order to be of the greatest service to the enginemen of approaching
trains, and their positions must be selected with that end in view.
Locations of switches, cross-overs, junctions, and other similar track
features will control the locations of the signals which are to protect
them. The main or home signal in these special cases may usually be
placed from 50 to 200 feet from the point which is to be governed, the
so-called “distant” signal being placed about 2000 feet for level track
back of the main or home signal.
=277. Home, Distant, and Advance Signals.=—A complete system of signals
employed in blocking includes first of all the so-called “home” signal
at each extremity of a block, then at a distance of 2000 to 2500 feet
back from the home signal is placed the “distant” signal. The latter
is thus approached and passed before reaching the home signal. On the
other side of the “home” signal at least a maximum train length into
a block about to be entered by a moving train is placed the “advance”
signal. The distance of the advance signal from the home signal may
be 1500 to 2500 feet. As a moving train approaches the end of a
block it first meets the distant signal, the purpose of which is to
indicate what the engineman may expect to find at the home signal. If
the distant signal is in the danger position, he will pass it with
caution and place his train under control so as to be able to stop at
the home signal. If he finds the distant signal in a safety position,
indicating the same position of the home signal, he may approach the
latter without reducing speed, confident that the next section is clear
and ready for him. The advance signal forms a kind of secondary or
supplementary block into which the train, under certain conditions,
may enter when the block in which it is found is obstructed, but no
train may pass the advance signal unless the entire block is clear
except when, under permissive working, the train proceeds with caution,
expecting to find the track either obstructed or occupied. This group
of three signals—the distant, the home, and the advance—taken in
the order in which the moving train finds them, is located at each
extremity of the block. Although the home signal is said to control the
movement of trains in a block at the entrance to which it is found, as
a matter of fact it appears that the advance signal in the final event
holds that control.
=278. Typical Working of Auto-Controlled Manual System.=—The mode of
employing these signals can be illustrated in a typical way by the
diagrams, Figs, 11, 12, and 13, which exhibit in a skeleton manner
Pattenall’s improved Sykes system which belongs to the Auto-Controlled
Manual class. In these figures the end of block 1, the whole of blocks
2 and 3, and the beginning of block 4 are shown. Stations _A_, _B_,
and _C_ indicate the extremities of blocks. The signals _S_, _Sʹ_,
and _S″_ are the home signals, while _D_, _Dʹ_, and _D″_ indicate
distant signals, and _A_, _Aʹ_, and _A″_ advance signals. As the
diagrams indicate, the stretch of double-track road is represented
with east- and west-bound tracks. In order to simplify the diagrams,
signals and stations are shown for one track only; they would simply
be duplicated for the other track. The signal cabin is supposed to be
located at each station, and at that cabin are found the levers and
other appliances for working the signals operated there, the signals
themselves being exposed alongside the track. In each signal cabin
there is an indicator, as shown at _I_, _Iʹ_, and _I″_. On the face
of each indicator there are two slots, shown opposite the lines _E_
and _F_. In the upper of these slots appears either the word “Clear”
or “Blocked.” In the lower slot appears either the word “Passed” or
“On.” The significance of these words will appear presently. On this
indicator face at _P_, _Pʹ_, and _P″_ are located electric push-buttons
called plungers. The operation of the levers indicated at _L_, the
counterweights _d_, and the locking detail _l_ are evident from an
inspection of the figure, and need no special explanation. It is only
necessary to state that the locking-device _l_ holds the bar _bc_ until
it is released at the proper time, and that the counterweight may then
return the lever from its extreme leftward position to that at the
extreme right, at the same time placing the semaphore arm _S_ in the
position of danger. It is particularly important to bear in mind this
last observation. The counterweight is the feature of the system which
always holds the semaphore arm in the position of danger, making that
its normal position, except when it is put to safety for the passing of
a train.
[Illustration: FIG. 11.]
[Illustration: FIG. 12.]
[Illustration: FIG. 13.]
If a westward train is represented in Fig. 11 at _T_ as approaching
station _A_ to enter the block 2, both the distant signal _D_ and
the home signal _S_ being at danger, the system is so arranged that
the signalman at station _A_ cannot change those signals, i.e., to a
position of safety, until the signalman at station _B_ permits him to
do so. If the signalman at station _A_ desires to open block 2 for
the entrance of the train _T_, he asks the signalman at station _B_
by wire to release the lock _l_ to enable him to do so. If there is
no train in block 2, the signalman at station _B_ pushes the button
_P′_ or “plunges” it. This raises the lock _l_ at station _A_ and the
signalman immediately pulls the lever _L_ to its extreme leftward
position, throwing both the signals _S_ and _D_ to the position of
safety or clear, indicated by the dotted lines at _S_². At the same
time the indicator _E_ at station _A_ shows the words “Clear to _B_,”
while the slot _Fʹ_ at _B_ shows the words “On from _A_.” The signals
at stations _B_ and _C_ are supposed to be in their normal position of
danger, and the indicator _E′_ at station _B_ shows the words “Blocked
to _C_.” The home and distant signals _Sʹ_ and _Dʹ_ are now at danger,
but the train _T_ may enter block 2 and proceeds to do so, it being
remembered that the signalman at station _A_ cannot move the lever _L_,
as it has passed out of his control; not even the signalman at station
_B_ can give him power to do so. The train _T_ now passes station _A_
into block 2. As the last car passes over the point _G_ its wheels
strike what is called a track-treadle, an appliance having electrical
connection with the lock _l_. The effect of the wheels of the last car
of the train passing over the treadle at _G_ is to release lock _l_,
enabling the signalman at station _A_ immediately to raise the arms _S_
and _D_ to the position of danger. It is to be observed that he cannot
do this until the entire train has passed into block 2; nor, since his
plunger is locked by the same treadle at _G_, can he signal “Safety” or
“Clear” to the entrance of block 1. Hence no train can enter block 1 to
collide with the rear end of the train just entering block 2. When the
signalman at station _A_ has raised his signal _S_ to danger, it again
passes out of his control, indeed out of both his control and that of
the signalman at _B_, until the last car of the train passes over the
treadle _Gʹ_ at the entrance of block 3.
The train has now passed into block 2 and is approaching station _B_.
The signalman at _B_ asks _C_ by wire to release the lever _Lʹ_, and if
block 3 is clear, _C_ plunges at _P″_.
_C_ then throws his lever _Lʹ_ so as to place the home and distant
signals _Sʹ_ and _Dʹ_ at safety. The condition of things will then be
shown by Fig. 12. As soon as the last car of the train has passed over
the treadle at _Gʹ_ his lever _Lʹ_ will be released and he can then
throw the lever to the danger position, raising the home and distant
signals _Sʹ_ and _Dʹ_ to the horizontal. After the danger position is
assumed by the home signal _Sʹ_, as well as the distant signal _Dʹ_, he
has no power over them until the signalman at station _C_ confers it on
him by plunging the button _P″_.
While the train has been in block 2, the indicator _Iʹ_ has shown
“Blocked to _C_” and “Train on from _A_,” but as the train passes _B_
the indicator reads “Blocked to _C_” and “Train passed from _A_,”
while the indicator _I″_ at _C_ reads “Blocked to _D_” and “Train on
from _B_.” This condition of the signals and trains is shown by Fig.
13. Also, when the last car passes over the treadle _Gʹ_, but not till
then, _B_ may permit _A_ to admit a train to enter block 2 should _A_
so desire. Finally, when the train approaches _C_, the signalman at
that point asks _D_ to enable him to permit the train to enter block 4,
and _C_ confers the power by plunging if that block is clear. Fig. 13
exhibits the corresponding signals at _C_.
This sequence of operations is typical of what takes place in this
particular block signal system at the limits of every successive block,
and differs only in details characteristic of this system from those
which are performed in any other block signal system.
=279. General Results.=—It is seen first that no signalman can operate
a signal until the condition in the block ahead of him is such as to
make it proper for him to do so, and then he can only indicate what
is necessary for the safe entrance of the train into that block.
Furthermore, immediately on the passage of the train past his home
signal he must put the latter to danger or the counterweight may do it
for him, the train itself when in a safe position having conferred the
requisite power upon him. The signalman at the advance end of the block
always knows when the train is about to enter it, for he is obliged
to give his permission for that entrance. His indicator shows this
result, and will continue to show it until the train passes out of the
block. It is to be observed that the upper openings marked _E_ on the
indicator give information of the condition of the block in advance,
while the lower openings give information of the block in the rear.
It is particularly important to notice that after the signalman at the
advance end of a block has “plunged” his plunger remains locked and it
cannot be released until the train admitted to the block covered by
the plunger has completely passed out of that block, permitting the
track-treadle at the entrance to the next block to unlock the plunger.
This feature makes it impossible for one train to enter a block until
the preceding train has passed out of it.
If the permissive system of using a block be employed, in which the
train is permitted to enter that block before a preceding train leaves
it, the treadle gives no protection against a rear-end collision with
the first train. In such an exigency other devices must be used or the
following train must proceed cautiously, expecting to find the track
occupied.
=280. Distant Signals.=—Thus far the distant signals have been
treated incidentally only. They may be operated concurrently with
or independently of the home signal in such a way that if danger is
indicated, the distant signal gives its indication prior to that of the
home signal. In this manner protection is given to the rear of a train
approaching a block against the home signal set at “danger.” After the
obstruction is removed and the block cleared, the home signal is set at
“safety” before the distant signal is cleared.
=281. Function of Advance Signals.=—The advance signals are used when
for any purpose it is desired to form a short block in a regular block.
If, for instance, block 3 in Fig. 11 were obstructed by a train stopped
by some failure of a locomotive detail, a train approaching station _B_
in section 2 against the home signal _Sʹ_ set at “danger” would be
obliged to stop before entering block 3. It might then be permitted to
enter the latter block, to be stopped by the advance signal _Aʹ_ set at
“danger” or under instructions to pass it cautiously, expecting to find
the track obstructed. It is thus seen that the advance signal creates
what may be called an emergency block, and in reality finally controls
the movement of trains in the block in which it is located. It would
never be cleared unless the home signal were first cleared, nor would
it be set at “danger” unless the home signal gave the same indication.
The preceding operation of the block system of signalling controls the
movement of trains along a double-track line.
[Illustration: FIG. 14.]
=282. Signalling at a Single-track Crossing.=—A somewhat similar
sequence of signal operations controls train movements at a crossing,
whether single- or double-track. Fig. 14 illustrates the use of
signals required for the safe movement of trains at a single-track
railroad crossing, which is supposed to be that of a north-and-south
line crossing obliquely an east-and-west line. Precisely the same
arrangement of signals operated in the same manner would be required
if the crossing were at the angle of 90°. The signal cabin is placed,
as shown, as near as practicable to the actual intersection of tracks.
Trains may pass in either direction on either track, but in every
case they would be governed by the signals at the right-hand side of
the track as seen by the engineman. There will therefore be a set of
signals on both sides of each track, each set governing the movement
of trains in its own direction. Each home signal may be placed about
350 feet from the actual intersection, and each distant signal 1200
to 1500 feet from the home signal, or 1550 feet to 1800 feet from the
intersection. Each advance signal must be at least as far in advance
of the home signal as the maximum length of train, since it may be
used to stop a train, the rear car of which should completely pass the
home signal. In their normal positions every home signal should be set
at “danger,” carrying with them the distant signals giving the same
indication. The advance signals must also indicate “danger” with the
home signal. No train can then pass the crossing until the home and
distant signals indicate a clear line for it, the other signals at the
crossing, except possibly the advance signal, being set at “danger.”
If for any reason it is desired to hold the train after it is entirely
free of the crossing, the advance signal would also indicate “danger.”
It is thus seen that if the signals are properly set and obeyed, it is
impossible for two trains to attempt a crossing at the same time. It is
not an uncommon occurrence, however, for an engineman to run his train
against the danger signal, and in order to make it impossible for the
train to reach the crossing even under these circumstances a derailing
device is used. This derailing arrangement is shown in Fig. 14, about
300 feet from the crossing, although it may be placed from 300 to 500
feet from that point. Its purpose is to derail any train attempting
to make the crossing against the danger signal. The operation of the
derail is evident from the skeleton lines of the figure. When the home
signal is at danger the movable part of the derailing device is at this
point turned so as to catch the flanges of the wheels as they attempt
to pass it. The train is thus thrown upon the cross-ties at such a
distance from the crossing as will produce a stop before reaching it.
When the home signal is at safety the derail operated with the signal
is closed and the line is continuous. This combination of signals and
derail coacting serves efficiently to prevent collisions at crossings,
although trains may be occasionally derailed in accomplishing that end.
The preceding explanations of the use of signals and derail apply to
a train that may approach the crossing in either direction on either
track, as is obvious from an inspection of the diagram itself.
=283. Signalling at a Double-track Crossing.=—In the case of a
double-track crossing, the arrangement of signals and derails is
precisely the same as for a single-track crossing, each set of signals
shown in Fig. 15 covering one track. In other words, the line of single
track is to take the place of each rail with its set of signals in
that figure. There will be but four derails, one for each track only
on the approach to the crossing. The working of the signals with the
derails is precisely the same as has already been explained for the
single-track crossing.
[Illustration: FIG. 15.]
[Illustration: FIG. 16.]
=284. Signalling for Double-track Junction and Cross-over.=—Fig. 16
represents a skeleton diagram of signals required for a junction of
two double-track roads and a cross-over. This arrangement covers the
use of switches. The location of signals and signal cabin as shown is
self-explanatory, after what has already been stated in connection with
single- and double-track crossings. It will be observed that the home
signals for both the west-bound main and branch tracks are identical
in location, and are shown by the solid double flag, the distant
signal being shown by its notched end at a considerable distance back
of the double home signal. It will, furthermore, be observed that
at each home signal there is a derailing-switch interlocked, in the
lock-and-block system presently to be explained, with the home signals
operated simultaneously with them. If, therefore, an engineman attempts
to run his train past a home signal set at danger, the result will be
the derailment of his train, thus brought to rest before it can make
any collision with another. It is obvious in this case that if the
switches from the main to the branch tracks or at the extremities of
the cross-over are worked independently, they must be operated directly
in connection with the signals. For complete protection they should be
interlocked with the signals so that it would be impossible to clear
any signal without simultaneously setting the switches consistently
with those signals. The diagram exhibits clearly the indications which
must be made in order to effect any desired train movement at such a
junction of tracks.
=285. General Observations.=—Similar arrangements of signals, derails,
or switches must be made wherever switches, cross-overs, and junctions
are found, the detailed variations of those signals and switches being
made to meet the individual requirements of each local case. The
combinations of switches and switch-signals frequently become very
complicated in yards where the tracks are numerous and the combinations
exceedingly varied, in order to meet the conditions created by the
movement of trains into and out of the yard.
The preceding explanations are intended only to give a clear idea
of the main features of signalling, in order to secure the highest
degree of safety and facility in the movement of trains over a modern
railroad. While they exhibit the external or apparent combinations of
signals for that purpose, they do not touch in detail and scarcely
in general upon the mechanical appliances found in the signal cabin
and along the tracks required to accomplish the necessary signal
movements. The considerations in detail of those appliances would cover
extended examinations of purely mechanical, electrical, pneumatic, and
electro-pneumatic combinations too involved to be set forth in any but
the most extended and careful study. They have at the present time been
brought to a wonderful degree of mechanical perfection and afford a
field of most interesting and profitable study, into which, however, it
is not possible in these general statements of the subject to enter.
[Illustration: FIG. 17.]
=286. Interlocking-machines.=—The earliest machine perfected for
use in this department of railroad signalling was the Saxby and
Farmer interlocking-machine, first brought out in England and
subsequently introduced in this country between 1874 and 1876. This
machine has been much improved since and has been widely used. Other
interlocking-machines have also been devised and used in this country
in connection with the most improved systems of signalling, until
at the present time a high degree of mechanical excellence has been
reached.
The interlocking-machine in what is called the lock-and-block system of
signalling is designed to operate signals, or signals in connection
with switches, derailing-points, or other dangerous track features, so
as to make it impossible for a signalman to make a wrong combination,
that is, a combination in which the signals will induce the engineman
to run his train into danger. The signals and switches or other track
details are so connected and interlocked with each other as to form
certain desired combinations by the movement of designated levers in
the signal cabin or tower. These combinations are predetermined in
the design and connections of the appliances used, and they cannot
be changed when once made except by design or by breakage of the
parts; they cannot be deranged by any action of the signalman. He
may delay trains by awkward or even wrong movement of levers, but he
cannot actually clear his signals for the movement of a train without
simultaneously giving that train a clear and safe track. As has been
stated, he cannot organize an accident. Figs. 17 and 18 show banks or
series of levers belonging to interlocking-machines. As is evident
from these figures, the levers are numerous if the machine operates
the switches and signals of a large yard, for the simple reason
that a great many combinations must be made in order to meet the
requirements of train movements in such a yard. The signalman, however,
makes himself acquainted with the various combinations requisite for
outgoing and incoming trains and the possible movements required
for the shifting or hauling out of empty trains. He has before him
diagrams showing in full the lever movements which must be made for
the accomplishment of any or of all these movements, and he simply
follows the directions of the diagrams and his instructions in the
performance of his duty. He cannot derange the combinations, although
he may be slow in reaching them. The locking-frame which compels him
to make a clear track whenever his signals give a clear indication
to the engineman lies below the lower end of the levers seen in the
figures. The short arms of the levers carry tappets with notches
in their edges into which fit pointed pieces of metal or dogs; the
arrangement of these notches and dogs is such as to make the desired
combinations and no others. It will be observed that a spring-latch
handle projects from a point near the upper end of each lever where
the latter is grasped in operating the machine. This spring-latch
handle must be pressed close to the lever before the latter can be
moved. The pressing of the spring-latch handle against the lever
effects a suitable train of unlocking before which the lever cannot
be moved and after which it is thrown over to the full limit and
locked there. The desired combination for the movement of the train
through any number of switches may require a similar movement of a
number of levers, but the entire movement of that set, as required,
must be completely effected before the signals are cleared, and when
they are so cleared the right combination forming a clear track for
the train, and that one only, is secured. These meagre and superficial
statements indicate in a general way, however imperfectly, the ends
attained in a modern interlocking-machine. They secure for railroad
traffic as nearly as possible an absolutely safe track. They eliminate,
as far as it is possible to do so, the inefficiency of human nature,
the erratic, indifferent, or wilfully negligent features of human
agency, and substitute therefor the certainty of efficient mechanical
appliances. In some and perhaps many States grade crossings are
required by statute to adopt measures that are equivalent to the most
advanced lock-and-block system of signalling. So vast has become
railroad traffic upon the great trunk lines of the country that it
would be impossible to operate them at all without the perfected modern
systems of railroad signalling. They constitute the means by which all
train movements are controlled, and without such systems great modern
railroads could not be operated.
[Illustration: FIG. 18.]
The swiftly moving “limited” express passenger trains, equipped with
practically every luxury of modern life, speed their way so swiftly
and smoothly over many hundreds of miles without the incident of an
interruption, and in such a regular and matter-of-fact way, that the
suggestion of an intricate system of signalling governing its movements
is never thought of. Yet such a train moves not a yard over its track
without the saving authority of its block signals. If the engineman
were to neglect even for a mile the indication of the semaphore, he
would place in fatal peril the safety of his train and of every life in
it.
=287. Methods of Applying Power in Systems of Signalling.=—The
mechanical appliances used in accomplishing these ends are among the
most efficient in character and delicate yet certain in motive power
which engineering science has yet produced. The electric circuit formed
by the rails of the track plays a most important part, particularly in
securing the safety of the rear of the train in making it absolutely
certain whether even rear cars that may have broken away have either
passed out of the block or are still in it. The electric circuit in one
application or another was among the earliest means used in railroad
signalling. Electric power is also used in connection with compressed
air for the working of signals. Among the latest and perhaps the most
advanced types of lock-and-block signalling is that which is actuated
by low-pressure compressed air, the maximum pressure being 15 pounds
only per square inch. The compressed air is supplied by a simple
compressor, and it is communicated from the signal cabin to the most
remote signal or switch by pipes and suitable cylinders fitted with
pistons controlled by valves, thus effecting the final signal or switch
movements. It has been successfully applied at the yard of the Grand
Central Station in New York City and at many other similar points. In
this connection it is interesting to observe that while the original
Saxby and Farmer interlocking-machine was installed from England in
this country, as has already been observed, about 1875, American
engineers have within a year reciprocated the favor by furnishing and
putting in place most successfully in one of the great railroad yards
of London the first low-pressure pneumatic lock-and-block system[8]
found in Great Britain.
[8] By Standard Railroad Signal Company of Troy, N. Y.
=288. Train-staff Signalling.=—The lock-and-block system gives
the highest degree of security attainable at the present time for
double-track railroad traffic, but the simpler character of the
single-track railroad business can be advantageously controlled by a
somewhat simpler and less expensive system, which is a modification
of the old train-staff method. It is one of the “machine” methods of
signalling. The type which has been used widely in England, Australia
and India, and to some extent in this country is called the Webb and
Thompson train-staff machine, shown in Fig. 19. It will be observed
that the machine contains ten staffs (18 to 20 inches long and 1 to 1¼
inches in diameter), but as many as fifteen are sometimes used. These
staffs can be removed from the machine at one end of a section of the
road at which a train is to enter, only by permission from the operator
at the farther end of the section. If the station at the entrance to
that section is called _A_, and the station at the farther end _X_, the
following description of the operation of the instrument is given by
Mr. Charles Hansel in a very concise and excellent manner:
[Illustration: FIG. 19.—Webb and Thompson Train-staff Machine.]
“When a train is ready to move from _A_ to _X_ the operator at _A_
presses down the lever which is seen at the bottom of the right-hand
dial, sounding one bell at _X_, which is for the purpose of calling
the attention of the operator at _X_ to the fact that _A_ desires to
send a train forward. The operator at _X_ acknowledges the call by
pressing the lever on his instrument, sounding a bell in the tower at
_A_. The operator at _A_ then asks permission from _X_ to withdraw
staff by pressing down the lever before mentioned three times, giving
three rings on the bell at _X_, and immediately turns his right-hand
pointer to the left, leaving it in the horizontal position pointing to
the words ‘For staff,’ indicating that he desires operator at _X_ to
release his instrument so that he can take a staff or train order from
it. If there is no train or any portion of a train between _A_ and _X_,
the holding down of the lever at _X_ closes the circuit in the lock
magnets at _A_, which enables the operator at _A_ to withdraw a staff.
As soon as this staff is removed from _A_, _A_ turns the left-hand
pointer to the words ‘Staff out,’ and in removing this staff from the
instrument _A_ the galvanometer needle which is seen in the centre
of the instrument between the two dials vibrates, indicating to the
operator at _X_ that _A_ has withdrawn his staff. _X_ then releases
the lever which he has held down in order that _A_ might withdraw a
staff and turns his left-hand indicator to ‘Staff out,’ and with this
position of the instrument a staff cannot be withdrawn from either one.
“The first method of delivering this staff to the engineer as a train
order was to place it in a staff-crane, which crane was located on the
platform outside of the block station. With the staff in this position
it has been found in actual practice that the engineman can pick it up
while his train is running at a speed of 30 miles per hour. A second
staff cannot be removed from _A_ nor a staff removed from _X_ until
this staff which was taken by the engineman in going from _A_ to _X_
is placed in the staff instrument at _X_; consequently the delivering
of a staff from _A_ to the engineman gives him absolute control of the
section between _A_ and _X_.
“This train order staff also controls all switches leading from the
main line between _A_ and _X_, for with the style of switch-stand which
we have designed for the purpose the trainman cannot open the switch
until he has secured the staff from the engineman and inserted it in
the switch-stand, and as soon as he throws the switch-lever and opens
the switch he fastens the train-staff in the switch-stand, and it
cannot be removed until the switchman has closed and locked the switch
for the main line. When this is done he may remove the train-staff and
return it to the engineman. It will thus be seen that this train order,
in the shape of a staff, gives the engineman absolute control over the
section, and also insures that all switches from the main line are set
properly before he can deliver the train-staff to the instrument at _X_.
“In order that the operator at _X_ may be assured that the entire train
has passed his station, we may divide the staff in two and deliver one
half to the engineman and the other half to the trainman on the caboose
or rear end of the train, and it will be necessary for the operator at
_X_ to have the two halves so that he may complete the staff in order
to insert it into the staff instrument at _X_, as it is impossible to
insert a portion of the staff; it must be entirely complete before it
can be returned to the staff instrument.”
Instead of using the entire staff as a whole or in two parts, Mr.
Hansel suggests that one or more rings on the body of the staff be
removed from the latter and given to the engineman or other trainman to
be placed upon a corresponding staff at the extreme end of the section.
This would answer the purpose, for no staff can be inserted in a
machine unless all the rings are in their proper positions. These rings
can be taken up by a train moving at any speed from a suitable crane at
any point alongside the track.
For a rapid movement of trains on a single-track railroad under this
staff system an engineman must know before he approaches the end of the
section whether the staff is ready for delivery to him. In order to
accomplish that purpose the usual distant and home signals may readily
be employed. The distant signal would show him what to expect, so that
he would approach the entrance to the section either at full speed or
with his train under control according to the indication. Similarly,
electric circuits may be employed in connection with the staff or rings
in the control of signals which it may be desired to employ.
The electric train-staff may also be used in a permissive block system,
the section of the track between stations _A_ and _X_ constituting
the block. In Fig. 19, showing the machine, a horizontal arm is seen
to extend across its face and to the right. This is the permissive
attachment which must be operated by the special staff shown on the
left half of the machine about midway of its height. If it is desired
to run two or three trains or two or three sections of the same train
from _A_ before admitting a train at _X_ in the opposite direction,
the operator at _A_ so advises the operator at _X_. The latter then
permits _A_ to remove the special staff with which the extreme
right-hand end of the permissive attachment is unlocked and a tablet
taken out. This tablet is equivalent to a train order and is given
to the train immediately starting from _A_. A second tablet is given
in a similar manner to the second section or train, and a third to
the third section. The last section of train or train itself starting
from _A_ takes all the remaining tablets and the special staff for
insertion in the machine at _X_. In this manner head-to-head collisions
are prevented when a number of trains are passing through the block
in the same direction before the entrance of a train in the opposite
direction. This system has been found to work satisfactorily where
it has been used in this country, although its use has been quite
limited. Evidently, in itself, it is not sufficient to prevent rear-end
collisions in a block between trains moving in the same direction. In
order to avoid such collisions where a train falls behind its schedule
time or for any reason is stopped in a block, prompt use must be made
of rear flagmen or other means to stop or to control the movement of
the first following train.
[Illustration: FIG. 20.]
The most improved form of high-speed train-staff machine is shown in
Fig. 20, as made and installed by the Union Switch and Signal Company
and used by a number of the largest railroad systems of the United
States. In these machines the staffs are but a few ounces in weight.
CHAPTER XXIII.
=289. Evolution of the Locomotive.=—The evolution of the steam
locomotive may be called the most spectacular portion of the
development of railroad engineering. The enormous engines used at
the present time for hauling both heavy freight and fast passenger
trains possess little in common, in respect of their principal
features, with the crude machines, awkward in appearance and of little
hauling capacity, which were used in the early part of the nineteenth
century in the beginning of railroad operation. The primitive and
ill-proportioned machine, ungainly in the highest degree, designed and
built by Trevithick as far back as 1803, was a true progenitor of the
modern locomotive, although the family resemblance is not at first very
evident. Several such locomotive machines were designed and operated
between 1800 and 1829 when Stevenson’s Rocket was brought out. The
water was carried in a boiler on a wagon immediately behind the engine,
and the steam-cylinder in those early machines was placed almost
anywhere but where it now seems to belong. The Rocket has some general
features of resemblance to the machines built seventy years later, but
when placed side by side it might easily be supposed that seven hundred
years rather than seventy had elapsed between the two productions of
the shop.
After the famous locomotive trial in which Robert Stevenson distanced
his competitors, the design of the locomotive advanced rapidly, and
it was but a few years later when the modern locomotive began to be
accurately foreshadowed in the machines then constructed. This was true
both in England and the United States.
The first steam locomotive in this country is believed to be the
machine built by John Stevens at Hoboken, N. J., in 1825 and operated
in 1825-27. This locomotive has practically the arrangement of boiler
and cylinder which is found upon the modern contractors’ engines used
for pile-driving, hoisting, and similar operations. It would certainly
be difficult to imagine that it had any relation to the great express
and freight locomotives of the present day. The rectilinear motions
of the piston were transformed into the rotary motion of the wheels
by means of gearing consisting of a simple arrangement of cog-wheels.
About the same time a model of an English locomotive called the
Stockton and Darlington No. 1 was brought to the United States by Mr.
William Strickland of Philadelphia. The next important step in American
locomotive development was the construction of the locomotive “John
Bull” for the Camden and Amboy Railroad Company in the English shops
of Stevenson & Company in the years 1830-31. This machine has the
general features, although not the large dimensions, of many modern
locomotives. The cow-catcher is a little more elaborate in design and
far-reaching in its proportions than the similar appendage of the
present day, but the general arrangement of the fire-box and boiler,
the steam-cylinders, the driving-wheels and smoke-stack is quite
similar to a modern American locomotive. This machine, “John Bull,” and
train made the trip from New York City to Chicago and return under its
own steam in 1893. It was one of the prominent features of the World’s
Columbian Exposition. It rests in the National Museum at Washington,
where it is one of the most interesting early remains of mechanical
engineering in this country. One of the cars used in this train was
the original used on the Camden and Amboy Road about 1836. Its body
was used as a chicken-coop at South Amboy, N. J., for many years, and
was rescued from this condition of degradation for the purpose of the
Exposition trip in 1893. The original driving-wheels had locust spokes
and felloes, the hubs and tires being of iron.
The locomotive “George Washington” was built, as a considerable
number have been since, with one driving-axle, and was designed to
be used on heavy grades. This machine was built by William Norris &
Sons of Philadelphia, who were the progenitors of the present great
establishment of the Baldwin Locomotive Works. While the development
of the locomotive was subjected to many vicissitudes in principles,
general arrangement, and size in order to meet the varying requirements
of different roads as well as the fancies or more rational ideas of the
designers, its advance was rapid. As early as 1846 we find practically
the modern consolidation type, followed in 1851 by the ordinary
eight-wheel engine of which thousands have been constructed within
the past fifty years. The first Mogul built by the Baldwin Locomotive
Works was almost if not quite as early in the field. Both these types
of machines carry the principal portion of their weight upon the
driving-wheels and were calculated to yield a high tractive capacity,
especially as the weights of the engines increased. The weight of the
little “John Bull” was but 22,425 pounds, while that of the great
modern machine may be as much as 267,800 pounds, with 53,500 pounds on
a single driving-axle.
=290. Increase of Locomotive Weight and Rate of Combustion of
Fuel.=—The development of railroad business in the United States has
been so rapid as to create rigorous exactions of every feature of a
locomotive calculated to increase its tractive force. Any enhancement
of train-load without increasing the costs of the train force or other
cost of movement will obviously lead to economy in transportation.
In order that the locomotive may yield the correspondingly augmented
tractive force the weight resting upon the drivers must be increased,
which means a greater machine and at the same time higher working
pressures of steam. This demands greater boiler capacity and strength
and a proportionately increased rate of combustion, so as to move the
locomotive and train by the stored-up energy of the fuel transformed in
the engine through steam pressure. The higher that pressure the greater
the amount of energy stored up in a unit of weight of the steam and the
greater will be the capacity of a given amount of water to perform the
work of hauling a train. The greater the weight of train moved and the
greater its speed the more energy must be supplied by the steam, and,
again, that can only be done with a correspondingly greater consumption
of fuel. In the early days of the small and crude machines to which
allusion has already been made the simplest fuel was sufficiently
effective. As the duties performed by the locomotive became more
intense a higher grade of fuel, i.e., one in which a greater amount of
heat energy is stored per unit of weight, was required. Both anthracite
and bituminous coal have admirably filled these requirements. The
movement of a great modern locomotive and its train at an average
rate of 30 to 60 miles per hour requires the combustion of fuel at a
high rate and the rapid evaporation of steam at pressures of 180 to
225 or more pounds per square inch. The consumption of coal by such a
locomotive may reach 100 pounds per minute, and two barrels of water
may be evaporated in the same time. This latter rate would require over
a gallon of water per second to be ejected through the stack as exhaust
steam. Some of the most marked improvements in locomotive practice have
been made practically within the past six or seven years in order to
meet these exacting requirements.
While the operations of locomotives will obviously depend largely upon
quality of fuel, speed, and other conditions, the investigations of
Prof. W. F. M. Goss and others appear to indicate that 12 to 14 pounds
of water per hour may be evaporated by a good locomotive boiler per
square foot of heating surface, and that 25 to 30 pounds of steam will
be required per indicated horse-power per hour.
=291. Principal Parts of a Modern Locomotive.=—The principal features
of a modern locomotive are the boiler with the smoke-stack placed on
the front end and the fire-box or furnace at the rear, the tubes, about
2 inches in diameter, through which the hot gases of combustion pass
from the furnace to the smoke-stack, the steam-cylinders with their
fittings of valves and valve movements, and the driving-wheels. These
features must all be designed more or less in reference to each other,
and whatever improvements have been made are indicated almost entirely
by the relative or absolute dimensions of those main features. The
boiler must be of sufficient size so that the water contained in it
may afford a free steam production, requiring in turn a corresponding
furnace capacity with the resulting heating surface. The latter is
that aggregate surface of the interior chambers of the boiler through
which the heat produced by combustion finds its way to the water
evaporated in steam; it is composed almost entirely of the surfaces
of the steel plates of the fire-box and of the numerous tubes running
through the boiler and parallel to its centre, exposed to the hot gases
of combustion and in contact with the water on the opposite sides of
those plates. Evidently an increase in size of the fire-box with the
correspondingly increased combustion will furnish a proportionally
larger amount of steam at the desired high pressure, but an increase
in the size of the fire-box is limited both in length and in width. It
is found that it is essentially impracticable for a fireman to serve a
fire-box more than about 10 feet in length. The maximum width of the
locomotive limits the width of the fire-box.
[Illustration: FIG. 21.]
=292. The Wootten Fire-box and Boiler.=—As the demand arose for an
enlarged furnace the width of the latter was restricted by the width
between the driving-wheel tires, less than 4 feet 6 inches. That
difficulty was overcome by what is known as the Wootten fire-box, which
was brought out by John E. Wootten of the Philadelphia and Reading
Railroad about 1877, and has since been developed and greatly improved
by others. The Wootten boiler with its sloping top and great width
extending out over the rear driving-wheels presented a rather curious
appearance and was a distinct departure in locomotive boiler design.
Fig. 21 shows an elevation and two sections of the original Wootten
type of boiler. It will be noticed that in front of the fire-box there
is a combustion-chamber of considerable length, 2½ to 3 feet long. This
boiler was first designed to burn the poorer grades of fuel, such as
coal-slack, in which the combustion-chamber to complete the combustion
of the fuel was thought essential. By Wootten’s device, i.e., extending
the boiler out over the driving-wheels, a much greater width of
fire-box was secured, but the height of the locomotive was considerably
increased. It cannot be definitely stated just how high the centre of
the locomotive boiler may be placed above the track without prejudice
to safety in running at high speeds, but it has not generally been
thought best to lift that centre more than about 9½ feet above the
tops of rails, and this matter has been held clearly in view in the
development of the wide fire-box type of locomotive boilers.
Like every other new form of machine, the Wootten boiler developed some
weak features, although there was no disappointment in its steaming
capacity. It will be noticed in the figure that the plates forming that
part of the boiler over the fire-box show abrupt changes in curvature
which induced ruptures of the stay-bolts and resulted in other
weaknesses. This boiler passed through various stages of development,
till at the present time Figs. 22 and 23 show its most advanced form,
which is satisfactory in almost or quite every detail. The sudden
changes in direction of the plates in the first Wootten example have
been displaced by more gradual and easy shapes. Indeed there are few
features other than those which characterize simple and easy boiler
construction. The enormous grate area is evident from the horizontal
dimensions of the fire-box, which are about 120 inches in length by
about 106 inches in breadth. The boiler has over 4000 square feet of
heating surface and carries about 200 pounds per square inch pressure
of steam. The combustion-chamber in front of the fire-box has been
reduced to a length of about 6 inches, just enough for the protection
of the expanded ends of the tubes. The barrel of the boiler in front of
the fire-box has a diameter of 80 inches and a length of about 15 feet.
The grate area is not far from 100 square feet. The improvements which
have culminated in the production of this boiler are due largely to Mr.
Samuel Higgins of the Lehigh Valley Road.
[Illustration: FIG. 22.]
[Illustration: FIG. 23.]
=293. Locomotives with Wootten Boilers.=—Fig. 24 exhibits a
consolidation freight locomotive of the Lehigh Valley Railroad, having
the boiler shown in Figs. 22 and 23. This machine is one of the most
efficient and powerful locomotives produced at the present time. The
locomotive shown in Fig. 25 has a record. It is one used on the fast
Reading express service between Philadelphia and Atlantic City during
the season of the latter resort. It has run one of the fastest schedule
trains in the world and has attracted attention in this country and
abroad. Its type is called the Atlantic and, as the view shows, it is
fitted with the Wootten improved type of boiler. It will be noticed
that the wide fire-box does not reach out over the rear drivers, but
over the small trailing-wheels immediately behind them. This is a
feature of wide locomotive fire-box practice at the present time to
which recourse is frequently had. There is no special significance
attached to the presence of the small trailing-wheels except as a
support for the rear end of the boiler, their diameters being small
enough to allow the extension of the fire-box over them without unduly
elevating the centre of the boiler.
[Illustration: FIG. 24.]
The cylinders of these and many other locomotives are known as the
Vauclain compound. In other words, it is a compound locomotive, there
being two cylinders, one immediately over the other, on each side. The
diameter of the upper cylinder is much less than that of the lower.
The steam is first admitted into the small upper cylinder and after
doing its work there passes into the lower or larger cylinder, where
it does its work a second time with greater expansion. By means of this
compound or double-cylinder use of the steam a higher rate of expansion
is secured and a more uniform pull is exerted upon the train, the first
generally contributing to a more economical employment of the steam,
which in turn means a less amount of fuel burned for a given amount of
tractive work performed.
[Illustration: FIG. 25.]
In the early part of November, 1901, an engine of this type hauling a
train composed of five cars and weighing 235 tons made a run of 55.5
miles between Philadelphia and Atlantic City at the rate of 71.6 miles
per hour, the fastest single mile being made at a rate of a little less
than 86 miles per hour.
The power being developed by these engines runs as high as 1400 H.P. at
high speeds and 2000 H.P. at the lower speeds of freight trains.
The chief economic advantage of these wide fire-box machines lies in
the fact that very indifferent grades of fuel may be consumed. Indeed
there are cases where fuel so poor as to be unmarketable has been used
most satisfactorily. With a narrow and small fire-box a desired high
rate of combustion sometimes demands a draft strong enough to raise
the fuel over the grate-bars. This difficulty is avoided in the large
fire-box, where sufficient combustion for rapid steaming is produced
with less intensity of blast.
=294. Recent Improvements in Locomotive Design.=—Concurrently with the
development of the Wootten type of boiler, other wide fire-box types
have been brought to a high state of excellence. In reality general
locomotive progress within the past few years has been summed up by Mr.
F. J. Cole as follows:
(_a_) The general introduction of the wide fire-box for burning
bituminous coal.
(_b_) The use of flues of largely increased length.
(_c_) The improvements in the design of piston-valves and their
introduction into general use.
(_d_) The recent progress made in the use of tandem compound cylinders.
[Illustration: FIG. 26.]
The piston-valve, to which reference is made, is a valve in the shape
of two pistons connected by an enlarged stem or pipe the entire length
of the double piston, the arrangement depending upon the length of
steam-cylinder or stroke; it may be 31 or 32 inches. This piston-valve
is placed between the steam-cylinder and the boiler, and is so moved
by eccentrics attached to the driving-wheel axles through the medium
of rocking levers and valve-stems as to admit steam to the cylinder at
the beginning of the stroke and allow it to escape after the stroke is
completed. Fig. 26 shows a section through the centre of one of these
piston-valves. It will be noticed that the live steam is admitted
around a central portion of the valve, and that the steam escapes
through the exhaust-passages at each end of the piston-valve. This type
of valve is advantageous with high steam pressures for the reason that
its “blast,” i.e., the steam pressure, does not press it against its
bearings as is the case with the old type of slide-valve, the wear of
which with modern high steam pressures would be excessive, although
under more recent slide-valve design this objection does not hold.
[Illustration: FIG. 27.]
=295. Compound Locomotives with Tandem Cylinders.=—The tandem
compound locomotive, as recently built, is a locomotive in which
the high-pressure cylinder is placed immediately in front of the
low-pressure cylinder and in line with it. In the Vauclain type it
is necessary to have a piston-rod for each of the two cylinders, one
above the other, each taking hold of the same cross-head. In the tandem
arrangement with the two cylinders each in line, but one piston-rod is
required. An example of a locomotive with this tandem arrangement of
compound cylinders will be shown farther on.
[Illustration: FIG. 28.]
Figs. 27 and 28 show two sections, one transverse and one longitudinal,
of a type of large fire-box boiler built by the American Locomotive
Works at Schenectady. The diameter of the barrel of the boiler in front
of the fire-box is about 5 feet 8 inches, while the clear greatest
width of the fire-box is 5 feet 4½ inches. The length of the latter is
8 feet 7 inches, making a total grate area in this particular instance
of over 45 square feet. There are 338 2-inch tubes, each 16 feet in
length. The total length over all of the boiler is 31 feet ½ inch. The
result of such a design is an arrangement by which a large grate area
is secured and a corresponding high rate of combustion without a too
violent draft. In designing locomotive boilers for bituminous coal
one square foot of grate area is sometimes provided for each 60 to 70
square feet of heating surface in the tubes.
[Illustration: FIG. 29.]
=296. Evaporative Efficiency of Different Rates of Combustion.=—In the
development of this particular class of locomotive boilers it is to be
remembered that as a rule the highest rates of combustion frequently
mean a decreased evaporation of water at boiler pressure per pound of
fuel. Modern locomotives may burn over 200 pounds of coal per square
foot of grate area per hour, and in doing so the evaporation may be
less than 5 pounds of water per pound of fuel. On the other hand, when
the coal burned does not exceed 50 pounds per square foot of grate area
per hour, as much as 8 pounds of water may be evaporated for each pound
of coal. It is judicious, therefore, to have large grate area, other
things being equal, in order that the highest attainable efficiency in
evaporation may be reached.
=296a. Tractive Force of a Locomotive.=—The tractive force of a
locomotive arises from the fact that one solid body cannot be moved
over another, however smooth the surface of contact may be, without
developing the force called resistance of friction. This resistance is
measured by what is called the coefficient of friction, determined only
by experiment. The resistance of friction and this coefficient will
depend both upon the degree of smoothness of the surface of contact
and on its character. If surfaces are lubricated, as in the moving
parts of machinery, the force of friction is very much decreased, but
in the absence of that lubricant it will have a much higher value.
The coefficient of friction is a ratio which denotes the part of the
weight of the body moved which must be applied as a force to that body
in order to put it in motion against the resistance of friction. In
the case of lubricated surfaces this ratio may be as small as a few
hundredths. In the case of locomotive driving-wheels and the track on
which they rest this value is usually taken at .2 to .25.
There are times when it is desirable to increase the resistance of
friction between locomotive drivers and the rails. For this purpose a
simple device, called the sand-box, is frequently placed on the top of
a locomotive boiler with pipes running down from it so as to discharge
the sand on the rails immediately in front of the drivers. The sand is
crushed under the wheels and offers an increased resistance to their
slipping.
The tractive force of a locomotive may also be computed from the
pressure of steam against the pistons in the steam-cylinders. If the
indicated horse-power in the cylinder be represented by H.P., and
if all frictional or other resistance between the cylinder and the
draw-bar be neglected, the following equality will hold:
Draw-bar pull × speed of train in miles }
per hour × 5280 } = H.P. × 33,000 × 60.
If _S_ = speed in miles per hour, and if _T_ = draw-bar pull, then the
preceding equality gives
375 × H.P.
_T_ = ----------.
_S_
This value of the “pull” must be diminished by the friction of the
locomotive as a machine, by the rolling resistance of the trucks and
tender, and by the atmospheric resistance of the locomotive as the head
of the train. Prof. Goss proposes the following approximate values for
these resistances in a paper read before the New England Railroad Club
in December, 1901.
A number of tests have shown that a steam pressure of 3.8 pounds per
square inch on the piston is required to overcome the machine friction
of the locomotive. Hence if _d_ is the diameter of the piston in
inches, _L_ the piston-stroke in feet, and _D_ the diameter of driver
in feet, while _f_ is that part of the draw-bar pull required to
overcome machine friction, the following equation will hold:
π_d_²
_f_.π_D_ = 3.8 -----× 2_L_ × 2.
4
_d²L_
∴ _f_ = 3.8 ------.
_D_
Again, if _W_ be the rolling load in tons on tender and trucks
(excluding that on drivers), and if _r_ be that part of the draw-bar
pull required to overcome the rolling resistance due to _W_, then
experience indicates that approximately, in pounds,
( _S_ )
_r_ = (2 + --- )_W_.
( 6 )
As before, _S_ is the speed in miles per hour.
Finally, if _h_ be that part of the draw-bar pull in pounds required to
overcome the head resistance (atmospheric) of the locomotive, there may
be written approximately
_h_ = .11_S_².
The actual draw-bar pull in pounds available for moving the train will
then be
375 H.P. _d_²_L ( S_ )
_t = T - f - r - h_ = -------- - 3.8------ - _W_(2 + ----) - .11_S_².
_S D_ ( 6 )
The maximum value of _t_ should be taken as one fourth the greatest
weight on drivers.
If _H_ is the total heating surface in square feet, and if 12 pounds of
water be evaporated per square foot per hour, while 28 pounds of steam
are required per horse-power per hour, then
12_H_ 375H.P. 161_H_
H.P. = ----- and -------- = ------.
28 _S S_
Hence
161_H d²L_ ( _S_ )
_t_ = ----- - 3.8----- - _W_(2 + ----) - .11_S²_.
_S D_ ( 6 )
The actual draw-bar pull in pounds may then be computed by this formula.
Some recent tests of actual trains (both heavy and light) on the N.
Y. C. & H. R. R. R. between Mott Haven Junction and the Grand Central
Station, New York City, a distance of 5.3 miles, by M. Bion J. Arnold,
by means of a dynamometer-car, gave the actual average draw-bar pull
per ton of 2000 pounds as ranging from 12 to 25 pounds going in one
direction and 12.1 to 24 pounds in the opposite direction. There were
eight tests in each direction, and the greatest speed did not exceed 30
miles per hour.
As the diameter of the driver appears in the preceding formulæ, it may
be well to state that an approximate rule for that diameter is to make
it as many inches as the desired maximum speed in miles per hour, i.e.,
70 inches for 70 miles, or 80 inches for 80 miles, per hour.
=297. Central Atlantic Type of Locomotive.=—Fig. 29 represents what is
termed the Central Atlantic type (single cylinder) of engine, which
is used for hauling most of the fast passenger trains on the New York
Central and Hudson River Railroad. The characteristics of boiler and
fire-box are such as are shown in Figs. 27 and 28.
The cylinders are 21 inches internal diameter, and the stroke is 26
inches. The total grate area is 50 square feet, and the total heating
surface 3500 square feet. The total weight of the locomotive is 176,000
pounds, with 95,000 on the drivers. It will be observed that the total
weight of locomotive per square foot of heating surface is scarcely
more than 650 pounds, which is a low value. The boiler pressure
carried may be 200 pounds per square inch or more. The tractive force
of this locomotive may be taken at 24,700 pounds. There is supplied
to these engines, among others, what is called a traction-increasing
device. This traction-increaser is nothing more nor less than a
compressed-air cylinder secured to the boiler, so that as its piston
is pressed outward, i.e., downward, it carries with it a lever, the
fulcrum of which is on the equalizing-lever of the locomotive frame,
the other or short end of the lever being attached to the main bar of
the frame itself. This operation redistributes the boiler-load on the
frame, so as to increase that portion which is carried by the drivers.
This has been found to be a convenient device in starting trains and
on up grades. In the present instance the traction-increaser may be
operated so as to increase the load on the drivers by about 12,000
pounds. It is not supposed to be used except when needed under the
circumstances indicated.
[Illustration: FIG. 30.]
A number of indicator-cards taken from the steam-cylinders of these
engines hauling the Empire State Express and other fast passenger
trains on the Hudson River Division of the N. Y. C. & H. R. R. R.,
show that with a train weighing about 208 tons while running at a
speed of 75 miles per hour 1323 H.P. was developed. Fig. 30 shows
these indicator diagrams. With a train weighing 685 tons 1452 H.P. was
indicated at a speed of 63 miles per hour.
=298. Consolidation Engine, N. Y. C. & H. R. R. R.=—One of the heaviest
wide fire-box compound consolidation engines recently built for the New
York Central freight service is shown in Fig. 31. It will be noticed
that there is but one cylinder on each side of the locomotive, and
that they are of different diameters. One of these cylinders, 23 inches
inside diameter, is a high-pressure cylinder, and the other, 35 inches
inside diameter, is a low-pressure cylinder, the stroke in each case
being 34 inches. The total grate area is 50.3 square feet, the fire-box
being 8 feet long by 6 feet 3 inches wide. The total heating surface
is 3480 square feet. The diameter of the barrel of the boiler at the
front end is 72 inches, and the diameter of the drivers 63 inches. The
pressure of steam in the boiler is 210 pounds per square inch. The
total weight of the locomotive is 194,000 pounds, of which 167,000
rests upon the drivers. These engines afford a maximum tractive force
of 37,900 pounds. This engine is typical of those used for the New York
Central freight service. They have hauled trains weighing nearly 2200
tons over the New York Central road.
[Illustration: FIG. 31.]
=299. P., B. & L. E. Consolidation.=—The consolidation locomotive shown
in Fig. 32 is a remarkable one in that it was for a time the heaviest
constructed, but its weight has since been exceeded by at least two of
the Decapod type built for the Sante Fé company. It was built at the
Pittsburg works of the American Locomotive Company for the Pittsburg,
Bessemer and Lake Erie Railroad to haul heavy trains of iron ore. The
total weight is 250,300 pounds, of which the remarkable proportion of
225,200 is carried by the drivers. The tender carries 7500 gallons
of water, and the weight of it when loaded is 141,100 pounds, so that
the total weight of engine and tender is 391,400 pounds. The average
weight of engine and tender therefore approaches 7000 pounds per
lineal foot. This is not a compound locomotive, but each cylinder has
24 inches inside diameter and 32 inches stroke, the diameter of the
driving-wheels being 54 inches. The boiler carries a pressure of 220
pounds, and the tractive force of the locomotive is 63,000 pounds.
[Illustration: FIG. 32.]
A noticeable feature of this design, and one which does not agree with
modern views prompting the design of wide fire-boxes, is its great
length of 11 feet and its small width of 3 feet 4¼ inches. There are
in the boiler 406 2¼-inch tubes, each 15 feet long, the total heating
surface being 3805 square feet.
=300. L. S. & M. S. Fast Passenger Engine.=—The locomotive shown in
Fig. 33 is also a remarkable one in some of its features, chief among
which is the 19 feet length of tubes. It was built at the Brooks works
of the American Locomotive Company for the Lake Shore and Michigan
Southern Railroad. The total weight of engine is 174,500 pounds, of
which 130,000 pounds rests upon the drivers. The rear truck carries
23,000 pounds and the front truck 21,500 pounds. This is not a compound
engine. The cylinders have each an inside diameter of 20½ inches, and
28 inches stroke. As this locomotive is for fast passenger traffic, the
driving-wheels are each 80 inches in diameter, and the driving-wheel
base is 14 feet. The fire-box is 85 × 84 inches, giving a grate area
of 48½ square feet and a total heating surface of 3343 square feet.
There are 285 2¼-inch flues, each 19 feet long. The tender carries 6000
gallons of water. Cast and compressed steel were used in this design
to the greatest possible extent, and the result is shown in that the
weight divided by the square feet of heating surface is 52.18 pounds.
[Illustration: FIG. 33.]
=301. Northern Pacific Tandem Compound Locomotive.=—The diagram shown
in Fig. 34 exhibits the outlines and main features of a tandem compound
locomotive to which allusion has already been made. It was built at
Schenectady, New York, in 1900, for the Northern Pacific Railroad, and
was intended for heavy service on the mining portions of that line.
The diameters of the high- and low-pressure cylinders are respectively
each 15 and 28 inches, with a stroke of 34 inches, while the boiler
pressure is 225 pounds per square inch. The total weight of the machine
is 195,000 pounds and the weight on the drivers 170,000 pounds, the
diameter of the drivers being 55 inches. As the figure shows, it
belongs to the consolidation type. The fire-box is 10 feet long by 3.5
feet wide, giving a grate area of 35 square feet, with which is found
a total heating surface of 3080 square feet. There are 388 2-inch
tubes, each 14 feet 2 inches long. These engines are among the earliest
compound-tandem type and have been very successful. Other locomotives
of practically the same general type have been fitted with a wide
fire-box, 8 feet 4 inches long by 6 feet 3 inches wide, with the grate
area thus increased to 52.3 square feet.
[Illustration: FIG. 34.]
=302. Union Pacific Vauclain Compound Locomotive.=—The next example
of modern locomotive is the Vauclain compound type used on the Union
Pacific Railroad. It is a ten-wheel passenger engine and one of a
large number in use. The weight on the drivers is 142,000 pounds,
and the total weight of the locomotive is about 185,000 pounds. The
high-pressure cylinder has an inside diameter of 15½ inches, while the
low-pressure cylinder has a diameter of 26 inches. The stroke is 28
inches and the diameter of the driving-wheels 79 inches. On the Union
Pacific Railroad the diameter of the driving-wheel varies somewhat with
the grades of the divisions on which the engines run.
[Illustration: FIG. 35.]
In some portions of the country, as in Southern California, oil has
come into quite extended use for locomotive fuel.
=303. Southern Pacific Mogul with Vanderbilt Boiler.=—The locomotive
shown in Fig. 36 belongs to the Mogul type, having three pairs
of driving-wheels and one pair of pilots. It is fitted with the
Vanderbilt boiler adapted to the use of oil fuel. The locomotives of
which this is an example were built for the Southern Pacific Company,
and they have performed their work in a highly satisfactory manner.
They are not particularly large locomotives as those matters go at the
present day, as they carry about 135,000 pounds on the drivers and
22,000 pounds on the truck, giving a total weight of 157,000 pounds.
The characteristic feature of the machine is its adaptation to the
burning of oil, which requires practically no labor in firing, although
the services of a fireman must still be retained.
[Illustration: FIG. 36.]
=304. The “Soo” Decapod Locomotive.=—It has been seen that the results
of Trevethick’s early efforts was a crude and simple machine, with what
might be termed, in courtesy to that early attempt, a single pair of
drivers. Subsequently, as locomotive evolution took place, two pairs
of drivers coupled with the horizontal connecting-rod were employed.
Then the Mogul with the three pairs of coupled drivers was used, and
at or about the same time the consolidation type with four pairs of
coupled drivers was found adapted in a high degree to the hauling of
great freight trains. The last evolution in driving-wheel arrangement
is exhibited in Fig. 37. It belongs to what is called the Decapod type.
As a matter of fact, five pairs of coupled driving-wheels have been
occasionally used for a considerable number of years, but this engine
is the Decapod brought up to the highest point of modern excellence.
As shown, it uses steam by the Vauclain compound system, the small or
high-pressure cylinder being underneath the low-pressure cylinder. They
have been built by the Baldwin Locomotive Works for the Minneapolis,
St. Paul and Sault Ste. Marie Railroad Company, on what is called the
“Soo Line.” It has given so much satisfaction that more of this type
but of greater weight are being built for the same company. This engine
was limited to a total weight of 215,000 pounds, with 190,000 pounds on
the drivers.
[Illustration: FIG. 37.]
[Illustration: FIG. 38.]
[Illustration: FIG. 39.]
[Illustration: FIG. 40.]
=305. The A., T. & S. F. Decapod, the Heaviest Locomotive yet
Built.=—The heaviest locomotive yet constructed, consequently occupying
the primacy in weight, is that shown in Fig. 38. It is a Decapod
operated with others of its type by the A., T. & S. F. Company near
Bakersfield, California. It is a tandem compound coal-burner, as shown
by the illustration, the high-pressure cylinder being in front of the
low-pressure. The dimensions of cylinders are 19 and 32 × 32 inches
stroke, and the driving-wheels are 57 inches in diameter. The total
height from the top of stack down to the rail is 15 feet 6 inches,
while the height of the centre of the boiler above the rails is 9 feet
10 inches. Figs. 39 and 40 show some of the main boiler and fire-box
dimensions. There are 463 2¼-inch tubes, each 19 feet long. The total
heating surface is 5390 square feet, about one eighth of an acre, the
length of the fire-box being 108 inches and the width 78 inches. The
heating surface in the tubes is 5156 square feet, and in the fire-box
210.3 square feet; the grate surface having an area of 58.5 square
feet. The boiler is designed to carry a working pressure of 225 pounds
per square inch, the boiler-plates being ¹⁵/₁₆ inch, ⁹/₁₆ inch, and ⅞
inch thick, according to location. As shown by the illustrations, the
boiler is what is termed an extended wagon-top with wide fire-box. The
total weight of the locomotive itself is 267,800 pounds, while the
weight on the driving-wheels is 237,800 pounds, making 47,560 pounds
on each axle. The tractive force of this locomotive is estimated to be
over 62,000 pounds.
=306. Comparison of Some of the Heaviest Locomotives in Use.=—The
following table gives a comparison of the heaviest locomotives thus
far built, as taken from the _Railroad Gazette_ for January 31, 1902,
revised to September 1, 1902.
COMPARISON OF HEAVIEST LOCOMOTIVES.
---------------------+----------------+-------------+-------------
| Atchison, | Pittsburg, | Union
| Topeka | Bessemer & | Railroad.
| & Santa Fé. | Lake Erie. |
---------------------+----------------+-------------+-------------
Name of builder | Baldwin | Pittsburg | Pittsburg
Size of cylinders |19 & 32 × 32 in.|24 × 32 in. |23 × 32 in.
Total weight | 267,800 lbs. |250,300 lbs. |230,000 lbs.
Weight on drivers | 237,800 lbs. |225,200 lbs. |208,000 lbs.
Driving-wheels, diam.| 57 in. | 54 in. | 54 in.
Heating surface | 5,390 sq. ft. |3,805 sq. ft.|3,322 sq. ft.
Grate area | 58.5 sq. ft. |36.8 sq. ft. |33.5 sq. ft.
---------------------+----------------+-------------+-------------
| Illinois | Lehigh
| Central. | Valley.
---------------------+----------------+----------------
Name of builder | Brooks | Baldwin
Size of cylinders | 23 × 30 in. | 18 & 30 × 30 in.
Total weight | 232,200 lbs. | 225,082 lbs.
Weight on drivers | 193,200 lbs. | 202,232 lbs.
Driving-wheels, diam.| 57 in. | 55 in.
Heating surface | 3,500 sq. ft. | 4,104 sq. ft.
Grate area | 37.5 sq. ft. | 90 sq. ft.
---------------------+----------------+----------------
These instances of modern locomotive construction are impressive,
especially when considered in contrast with the type of engine in use
not more than fifty years ago. They indicate an almost incredible
advance in railroad transportation, and they account for the fact that
a bushel of wheat can be brought overland at the present time from
Chicago to New York City, a distance of 900 miles, for about one third
of the lowest charge for delivering a valise from the Grand Central
Station in the city of New York to a residence within a mile of it.
PART V.
_THE NICARAGUA ROUTE FOR A SHIP-CANAL._
=307. Feasibility of Nicaragua Route.=—The feasibility of a ship-canal
between the two oceans across Nicaragua has been recognized almost
since the discovery of Lake Nicaragua in 1522 by Gil Gonzales de Avila,
who was sent out from Spain to succeed Balboa, after the execution of
the latter by Pedro Arias de Avila at Acla on the Isthmus of Panama.
=308. Discovery of Lake Nicaragua.=—Gil Gonzales set sail from the
Bay of Panama in January of that year northward along the Pacific
coast as far as the Gulf of Fonseca. He landed there and proceeded to
explore the country with one hundred men, and found what he considered
a great inland sea, as we now know, about 14 miles from the Pacific
Ocean at the place of least separation. The country was inhabited,
and he found a native chief called Nicarao, who was settled with his
people at or near the site of the present city of Rivas. As he found
it a goodly country, fertile and abounding in precious metals, he
immediately proceeded to take possession of it for his sovereign, but
the Spanish explorer was sufficiently gracious to the friendly chief
to name Lake Nicaragua after him. From that time the part of Nicaragua
in the vicinity of the lake received much attention, and the Spaniards
made conquest of it without delay. Among those who were the earliest
visitors was a Captain Diego Machuca, who, with two hundred men under
his command, explored Lake Nicaragua in 1529 and constructed boats
on it, a brigantine among them. He seems to have been the first one
who entered and sailed down the Desaguadero River, now called the San
Juan, and one of the rapids in the upper portion of the river now
bears his name. He pursued his course into the Caribbean Sea and sailed
eastward to the Isthmus of Panama.
[Illustration: Map of American Isthmus, showing Proposed Canal Routes.]
=309. Early Maritime Commerce with Lake Nicaragua.=—Subsequently
sea-going vessels passed through the San Juan River in both directions
and maintained a maritime trade of some magnitude between the shores
of Lake Nicaragua and Spain. Obviously these vessels must have been
rather small for ocean-going craft, unless there was more water in the
San Juan River in those early days than at present. There are some
obscure traditions of earthquakes having disturbed the bed of the river
and made its passage more difficult by reducing the depth of water in
some of the rapids; but these reports are little more than traditionary
and lack authoritative confirmation. It is certain, however, that the
marine traffic, to which reference has been made, was maintained for
a long period of years, its greatest activity existing at about the
beginning of the seventeenth century. It was in connection with this
traffic probably that the city of Granada at the northwestern extremity
of the lake was established, perhaps before 1530.
=310. Early Examination of Nicaragua Route.=—Although the apparently
easy connection between the Caribbean Sea and Lake Nicaragua, together
with the proximity of the latter to the Pacific coast, at once
indicated the possibility of a feasible water communication between
the two oceans, probably no systematic investigation to determine a
definite canal line was made until that undertaken by Manuel Galisteo
in 1779 under the instruction of Charles III., who was then on the
throne of Spain. Galisteo made a report in 1781 that Lake Nicaragua
was 134 feet higher than the Pacific Ocean, and that high mountains
intervened between the lake and the ocean, making it impracticable
to establish a water communication between the two. In spite of the
discouragement of this report a company was subsequently formed under
the patronage of the crown to construct a canal from Lake Nicaragua
along the Sanoa River to the Gulf of Nicoya, but nothing ever came of
the project.
=311. English Invasion of Nicaragua.=—The country was invaded in 1780
by an English expedition sent out from Jamaica under Captain Horatio
Nelson, who subsequently became the great admiral. He proceeded up
the San Juan River, and after some fighting captured by assault Fort
San Juan at Castillo Viejo. Nelson and his force, however, were ill
qualified to take care of themselves in that tropical country where
drenching rains were constantly falling, and he was therefore obliged
to abandon his plan of taking possession of Lake Nicaragua and returned
instead to Jamaica. The tropical fevers induced by exposure reduced
the crew of his own ship, two hundred in number, to only ten after his
return to Jamaica, and he himself nearly lost his life by sickness.
=312. Atlantic and Pacific Ship-canal Company.=—Subsequently to this
period the Nicaragua route attracted more or less attention until Mr.
E. G. Squier, the first consul for the United States in Nicaragua,
negotiated a treaty between the two countries for facilitating the
traffic from the Atlantic to the Pacific Ocean by means of a ship-canal
or railroad in the interest of the Atlantic and Pacific Ship-canal
Company, composed of Cornelius Vanderbilt, Joseph L. White, Nathaniel
Wolfe, and others. It was at this time that the Nicaragua route became
prominent as a line of travel between New York and San Francisco.
Ships carried passengers and freight from New York to Greytown, then
trans-shipped them to river steamboats running up the San Juan River
and across the southerly end of the lake to a small town called La
Virgin, whence a good road for 14 miles overland led to the Pacific
port of San Juan del Sur. Pacific coast steamships completed the trip
between the latter port and San Francisco.
=313. Survey and Project of Col. O. W. Childs.=—This traffic stimulated
the old idea of a ship-canal across the Central American isthmus on the
Nicaragua route to such an extent that Col. O. W. Childs, an eminent
civil engineer, was instructed by the American Atlantic and Pacific
Ship-canal Company to make surveys and examinations for the project
of a ship-canal on that route. The results of his surveys, made in
1850-52, have become classic in interoceanic canal literature. He
concluded that the most feasible route lay up the San Juan River from
Greytown to Lake Nicaragua, across that lake, and down the general
course of the Rio Grande on the west side of Nicaragua to Brito on the
Pacific coast. This is practically identical with the route adopted by
the Isthmian Canal Commission now (1902) being discussed in Congress.
=314. The Project of the Maritime Canal Company.=—The project planned
by Col. Childs, like those which preceded it, had no substantial issue,
but the general subject of an isthmian canal across Nicaragua was, from
that time, under almost constant agitation and consideration more or
less active until the Maritime Canal Company of Nicaragua was organized
in February, 1889, under concessions secured from the governments
of Nicaragua and Costa Rica by Mr. A. G. Menocal. This company made
a careful examination of all preceding proposed routes, and finally
settled upon a plan radically different in some respects from any
before considered. The Caribbean end of the canal was located on the
Greytown Lagoon west of Greytown. From that point the line followed
up the valley of the Deseado River and cut across the hills into the
valley of the San Juan above its junction with the San Carlos. A dam
was to be constructed across the San Juan River at Ochoa, below the
mouth of the San Carlos, so as to bring the surface of Lake Nicaragua
down to that point. From its junction with the San Juan River the canal
line followed that river to the lake, across the latter to Las Lajas,
and thence down the Rio Grande to the Pacific coast at Brito. It was
contemplated under this plan to carry the lake level to a point called
La Flor, 13.5 miles west of the lake, and drop down to the Pacific
from that point by locks suitably located. After partially excavating
the canal prism for about three quarters of a mile from the Greytown
Lagoon, constructing a line of railroad up the Deseado valley, as well
as a telegraph line, and doing certain other work preparatory to the
actual work of construction, the Maritime Canal Company became involved
in financial difficulties and suspended operations without again
resuming them.
[Illustration: Breakwater of the Maritime Canal Company. The closed
former entrance to Greytown harbor is shown on the left.]
=315. The Work of the Ludlow and Nicaragua Canal Commissions.=—In
1895 and again in 1897 two commissions were appointed by the
President of the United States to consider the plans and estimates
of the Maritime Canal Company in the one case, and the problem of a
ship-canal on the Nicaragua route in the latter. Neither of these
commissions, however, had the funds at its disposal requisite for a
full and complete consideration of the problem. In 1899, therefore,
the Isthmian Canal Commission was created by Act of Congress, and
appointed by the President of the United States, to determine the most
feasible and practical route across the Central American isthmus for a
canal, together with the cost of constructing it and placing it under
the control, management, and ownership of the United States. This
commission consisted of nine members, and included civil and military
engineers, an officer of the navy, an ex-senator of the United States,
and a statistician. It was the province and duty of this commission to
make examinations of the entire isthmus from the Atrato River in the
northwestern corner of South America to the western limits of Nicaragua
for the purpose of determining the most feasible and practical route
for a ship-canal between those territorial limits. This brings the
general consideration of the isthmian canal question to the Nicaragua
route in particular, to which alone attention will be directed in this
part.
=316. The Route of the Isthmian Canal Commission.=—The Isthmian Canal
Commission adopted a route practically following the San Juan River
from near Greytown to the lake, across the latter to Las Lajas on
its westerly shore, and thence up the course of the Las Lajas River,
across the continental divide into the Rio Grande valley, and down the
latter to Brito at the mouth of the Rio Grande on the Pacific coast.
As has already been stated, this is practically the line adopted by
Col. Childs almost exactly fifty years ago. It is also essentially the
route adopted by the Nicaragua Canal Commission appointed in 1897,
and which completed its operations immediately prior to the creation
of the Isthmian Canal Commission. The amount of work performed in the
field under the direction of the commission can be realized from the
statement that twenty working parties were organized in Nicaragua with
one hundred and fifty-nine civil engineers and other assistants, and
four hundred and fifty-five laborers.
=317. Standard Dimensions of Canal Prism.=—By the Act of Congress
creating it, the latter commission was instructed to consider plans
and estimates for a canal of sufficient capacity to accommodate the
largest ships afloat. In order to meet the requirements of those
statutory instructions the commission decided to adopt 35 feet as the
minimum depth of water in the canal throughout its entire length from
the deep water of one ocean to that of the other, wherever the most
feasible and practical route might be located, the investigations of
the commission having shown that the final location to be selected must
narrow down to a choice between the Panama and the Nicaragua routes.
It was further decided by the commission that the standard width of
excavation at the bottom of the canal should be 150 feet, with 500 feet
for the ocean entrances to harbors, and 800 feet in those harbors.
Greater widths than that of the bottom of standard excavations were
also adopted for river and lake portions. The slopes of the sides of
the excavation were determined to be 1 vertical on 1½ horizontal for
firm earth, but as flat as 1 vertical on 3 or even 6 horizontal for
soft mud or silt in marshy locations. In rock cutting below water the
sides of the excavation would be vertical, but as steep as 4 vertical
on 1 horizontal above water.
[Illustration]
[Illustration: Standard Sections adopted by the Isthmian Canal
Commission.]
The longest ship afloat at the present time (1902) is the Oceanic of
the White Star Line, and its length is about 704 feet. The widest
ships, i.e., the ships having the greatest beam, are naval vessels,
and at the present time none has a greater beam than about 77 feet. In
order to afford accommodation for further development in both length
and beam of ships without leading to extravagant dimensions, the
commission decided to provide locks having a usable length of 740 feet
with a clear width of 84 feet. These general dimensions meet fully the
requirements of the law, and were adopted for plans and estimates on
both the Panama and Nicaragua routes.
=318. The San Juan Delta.=—The entire Central American isthmus
is volcanic in character, and this is particularly true of the
country along the Nicaragua route with the exception of the lowlands
immediately back of the ocean shore line in the vicinity of Greytown.
From the latter point to Fort San Carlos, where the San Juan River
leaves the lake, is approximately 100 miles. With the exception of
the 15 miles nearest to the seacoast the San Juan River runs mostly
through a rugged country with high hills densely wooded on either
side. The soil is mostly heavy clay, although the bottom of the valley
immediately adjacent to the river is largely of sandy silt with some
mixture of clay. Between the hills back of Greytown and the seacoast
the country is almost a continuous morass covered with coarse grasses
and other dense tropical vegetation, but with a number of small
isolated hills projecting up like islands in the surrounding marsh,
and interspersed with numerous lagoons. All this flat country has the
appearance of forming a delta through which a number of mouths of the
San Juan River find their way. One of these, called the Lower San Juan,
empties into the Greytown Lagoon, but the main mouth of the San Juan,
called the Colorado, branches from the main river at the point where
the Lower San Juan begins, about 13 or 14 miles from the ocean. The
Colorado itself is composed of two branches, and at the place where it
empties into the sea there are a number of long narrow lagoons parallel
to the seashore, appearing to indicate comparatively recent shore
formation. Again, a small river called the Rio San Juanillo leaves the
main river 3 or 4 miles above the junction of the lower San Juan and
the Colorado, and pursues a meandering course through the low marshy
grounds back of Greytown, and finally again joins the Lower San Juan
near the town. This marshy lowland is underlaid by and formed largely
of dark-colored sand brought down mostly from the volcanic mountains of
Costa Rica by two rivers, the San Carlos and the Serapiqui, the former
joining the San Juan about 44 miles and the latter about 23 miles from
the sea.
[Illustration: Greytown Lagoon (formerly Greytown Harbor), showing
Greytown in the Distance.]
=319. The San Carlos and Serapiqui Rivers.=—Both those Costa Rican
rivers are subject to sudden and violent floods, and they bring down
large quantities of this volcanic sand, the specific gravity of which
is rather low. The San Carlos bears the greater burden of this kind.
In fact its bed, even when not in a state of flood, is at many points
at least composed of moving sands. Both rivers are clear-water streams
except in high water stages. Below the junction of the San Carlos the
San Juan is necessarily in times of floods a large bearer of silt and
sand, but above that point it carries little or no sediment. There are
no streams of magnitude which join the San Juan between the lake and
the San Carlos.
=320. The Rapids and Castillo Viejo.=—About 54 miles from the ocean
are the Machuca Rapids, and from that point to a distance of about 75
miles from the ocean other rapids are found, the principal of which are
the Castillo and the Toro. The Castillo Rapids are at the point called
Castillo Viejo, where there is located an old Spanish fort on the top
of the high hill around the base of which the river flows. The town of
Castillo Viejo has a small population of perhaps 500 to 600 people.
It is a place with historical associations, to which reference has
already been made. It was here that Captain (afterwards Admiral) Nelson
captured the Spanish fort in 1780. It is a place of some importance
in connection with the river traffic in consequence of necessary
transhipment of freight and passengers to overcome the rapids.
=321. The Upper San Juan.=—The upper reaches of the San Juan within
about 20 miles of the lake are bordered with considerable marshy
ground. In the vicinity of its exit from the lake there is a wide strip
of soft marshy country around the entire southeastern shore.
=322. The Rainfall from Greytown to the Lake.=—The entire country
between Greytown and the lake is intensely tropical, and the vegetation
is characteristically dense. It is particularly so at Greytown, where
the total annual rainfall sometimes reaches as much as 300 inches.
It rains many times in a day, and nearly every day in the year. The
strong easterly and northeasterly trade winds, heavy-laden with the
evaporation from the tropical sea, meet the high ground in the vicinity
of Greytown and precipitate their watery contents in frequent and heavy
showers. The general course of the San Juan valley is a little north
of west or south of east, and the trade winds appear to follow the
course of the valley to the lake. The rainfall steadily decreases as
the seashore is left behind, so that at Fort San Carlos, the point of
exit of the river from the lake, the annual precipitation may vary from
75 to 100 inches. There is no so-called dry season between the lake and
the Caribbean Sea, although at Fort San Carlos the rainfall is so small
between the middle of December and the middle of May that that period
may perhaps be considered, relatively speaking, a dry season. It is
evident, therefore, that all the conditions are favorable to luxuriant
tropical growths over this entire eastern portion of the canal route,
and the coarse grasses, palms, and other tropical vegetation found in
it are indescribably dense. The same general observation is applicable
to the forest and undergrowth throughout the entire course of the river
from Greytown to Fort San Carlos. All of the high ground is heavily
timbered, with undergrowth so dense that no survey line can be run
until it is first completely cut out. That observation holds with added
force throughout the swampy country adjacent to the seashore. All the
heavy forest growth carries dense vines and innumerable orchids, which
so cover the trunks and branches of trees as in many places completely
to obscure them.
[Illustration: The Maritime Canal Company’s Canal Cut leading out of
Greytown Lagoon.]
=323. Lake-surface Elevation and Slope of the River.=—The lake surface
has an area of about 3000 square miles and varies in elevation with the
amount of rainfall in its basin from about 97 or 98 to perhaps 110 feet
above the ocean. The average elevation can probably be taken at about
104 feet above the sea. The length of the lake is about 103 miles,
with a greatest width of 45 miles. The area of its watershed is about
12,000 square miles. Inasmuch as the length of the San Juan River from
the ocean to the lake is but a little more than 100 miles, its average
fall is seen to be about 1 foot per mile. The greatest slope of the
river surface is at Castillo Rapids, where it falls about 6 feet in ⅜
of a mile. At the Machuca Rapids it falls about 4 feet in 1 mile. From
the foot of Machuca Rapids to the mouth of the San Carlos, a distance
of a little over 15 miles, the surface of the river falls about 1 foot
only. This pool, with practically no sensible current, is called Agua
Muerte, or Dead Water. The relatively great depth of this pool shows
conclusively that the upper San Juan, i.e., above the mouth of the San
Carlos, carries no silt, otherwise the pool would be filled; in other
words, that part of the San Juan River is not a sediment-bearer. The
slope of the river surface in the Toro Rapids, about 27 miles from the
lake, gives a fall of 7³/₁₀ feet in 1⁷/₁₀ miles.
=324. Discharges of the San Juan, San Carlos, and Serapiqui.=—In
times of heavy floods the San Carlos River may discharge as much as
100,000 cubic feet per second into the San Juan, but such floods have
a duration of a comparatively few hours only. Its low water-discharge
may fall below 3000 cubic feet per second. The maximum outflow of the
lake during a rainy season or a season of heavy rainfall probably never
exceeds about 70,000 cubic feet per second, but that rate of discharge
may continue for a number of weeks. The low water-discharge of the San
Juan above the mouth of the San Carlos may fall below 10,000 feet per
second, or 13,000 feet per second below the mouth of the San Carlos but
above that of the Serapiqui.
=325. Navigation on the San Juan.=—From what has been said of the
San Juan River it is evident that in times of low water no boats
drawing more than about 5 or 6 feet can navigate it, and most of the
river boats draw less than that amount. In times of low water no
boat can navigate the Lower San Juan drawing more than about 2½ to 3
feet of water. Nor, again, can the ordinary river boats pass up the
rapids at Castillo except at high water. It is necessary, therefore,
that the larger boats used on the river confine their trips on the
one hand between the mouth of the Colorado and Castillo, and on the
other between Castillo above the rapids to Fort San Carlos. It is the
custom, therefore, to transfer passengers and freight from boats below
the rapids at Castillo by a short tramway to other boats in waiting
above the rapids at that point. Boats pass up Machuca and Toro rapids
at practically all seasons, but sometimes with difficulty.
In order to meet the exigencies of low water in the Lower San Juan
a railroad called the Silico Lake Railroad, with 3 feet gauge, has
been constructed from a point opposite the mouth of the Colorado,
called Boca Colorado, to Lake Silico in the marshes back of Greytown,
a distance of about 6 miles. Light-draft boats connect Lake Silico
with Greytown for the transfer of passengers and freight. The type of
light-draft steamboat used on the San Juan River is the stern-wheel
pattern, so much used on the western rivers of this country, the
lower deck carrying the engines and boilers as well as freight, while
the upper deck, fitted with crude staterooms, furnishes a kind of
accommodation for passengers.
=326. The Canal Line through the Lake and Across the West Side.=—The
little town of Fort San Carlos on a point raised somewhat above the
lake where the San Juan River leaves the latter is the second place
on the entire river from Greytown where any population may said to be
found, and probably not more than 400 or 500 people even there. Its
position is on the north side of the river, at the extreme southeastern
end of the lake, commanding a fine view of the water and the country
bordering it in that vicinity. To the westward lie the Solentiname
Islands, a group a short distance to the north of which the sailing
line for the canal in the lake is located. After passing this group
of islands that line deflects a little toward the south, so that its
course westward is but a little north of west, straight to a point
near to and opposite Las Lajas on the westerly shore of the lake,
southwest from the large island on which Ometepe and Madeira are
located; indeed those two volcanic cones, the former still active,
constitute the entire island. The point called Las Lajas is at the
mouth of a small river of that name which discharges any sensible
amount of water only during the wet season; it is located not more
than 10 miles from Ometepe, and affords a most impressive view of that
perfect volcanic cone rising almost an exact mile above the water. The
general direction of the canal route is a little west of south from Las
Lajas on the lake to Brito on the ocean shore. The line follows the
Las Lajas about a mile and a half only of the 5 miles from the lake in
a southwesterly direction to the point where the continental divide
is crossed. The elevation of the divide at this place is about 145
feet only above sea-level. The line then descends immediately into the
valley of the Rio Grande and follows that stream to its mouth at Brito.
[Illustration: The Maritime Canal Company’s Railroad near Greytown.]
=327. Character of the Country West of the Lake.=—The country on the
west side of the lake exhibits a character radically different from
that on the easterly side, i.e., between the lake and the Caribbean.
It is a country in which much more population is found. While there
are no towns along the 17 miles of the route from Las Lajas to Brito,
the old city Rivas, containing perhaps 12,000 to 15,000 people, is
about 6 miles from Las Lajas, and the small towns of San Jorge, Buenos
Ayres, Potosi, as well as others, are in the same general vicinity.
Plantations of cacao and various tropical fruits abound, and there
is a large amount of land under cultivation. It is largely a cleared
country, so that far less dense forest areas are found.
There are two distinct seasons in the year, the wet and the dry, the
latter extending from about the middle of December to the middle of
May. The annual rainfall is extremely variable, but in the vicinity
of Rivas it may run from 30 or 40 to nearly 100 inches. The country
is of great natural beauty, and one which, under well-administered
governmental control, would afford many places of delightful
residence. The trade winds blow across the lake from east to west with
considerable intensity and great regularity. They produce a beneficial
effect upon the climate and render atmospheric conditions far more
agreeable than in that part of Nicaragua in the vicinity of Greytown.
It will be remembered that Rivas is the city where the American
filibuster Walker was taken prisoner by the Costa Ricans and
Nicaraguans and shot in 1857.
=328. Granada to Managua, thence to Corinto.=—At the northwestern end
of the lake is located the attractive city Granada, sometimes called
the “Boston of Nicaragua.” A reference to a map of Nicaragua will
show that a short distance north of Granada is the river Tipitapa,
which connects Lake Nicaragua with Lake Managua, the latter lying 18
miles to the northwest of the former. A railroad connects Granada
with the city of Managua, which is the capital of Nicaragua, running
on its way through the city of Masaya, chiefly noted for the volcano
of the same name located near by, and which has been subjected to a
most destructive eruption. The old lava-flow still shows its path of
destruction by a broad black mark extending many miles across the
country. A railroad connects Lake Managua at Momotombo with the Pacific
port of Corinto.
=329. General Features of the Route.=—It is thus seen that the proposed
route of the Nicaragua Canal lies first along the valley of the San
Juan River, then across the lake, cutting the continental divide west
of the latter at the low elevation of 145 feet above the sea, thence
following the valley of the Rio Grande to the Pacific Ocean at Brito.
From Greytown to Castillo the San Juan River is the boundary between
Nicaragua and Costa Rica, and concessions from both governments would
be necessary for that part of its construction. From Castillo to the
Pacific Ocean the route lies entirely in Nicaraguan territory, and the
only concession necessary for that portion of the line would be from
the government of Nicaragua. From Castillo to and around the southern
end of the lake the boundary-line is located 3 miles easterly from the
river, following its turns, and the same distance from the lake shore,
all by an agreement recently reached between the two governments. The
summit level of the canal would therefore be the surface of the water
in Lake Nicaragua, which is carried down to Conchuda, 52 miles from
the lake on the San Juan River toward the east, by a great dam located
there, and to a lock between 4 and 5 miles from the lake toward the
west. Hence the summit level would stretch throughout a distance of
about 126 miles, leaving a little more than 46 miles on the Caribbean
end and about 12 miles on the Pacific end of the regular canal section.
The 50-mile stretch from the lake to the point where the canal cuts the
San Juan River near Conchuda is a canalized portion of the San Juan
River, as a large amount of excavation must be done there in order to
give the minimum required depth of 35 feet. The points of river bends
or curves are in some cases cut off by excavated canal section in order
to shorten the line and reduce the curvature. Considerable portions
of the line in the lake, particularly near Fort San Carlos, would be
excavated. For several miles in the latter vicinity large quantities of
silt and mud must be removed, as the lake is shallow and the bottom is
very soft. The entrance into the western portion of the canal at Las
Lajas requires a large amount of rock excavation, as the shore and bed
of the lake there are almost entirely of rock.
[Illustration: Scene on the San Juan River.]
=330. Artificial Harbor at Greytown.=—The preceding observations are
mostly of a general character, and give but little consideration to
the engineering features of the canal construction. In considering
the canal as a carrier of ocean traffic probably the first inquiry
will be that relating to harbors. In reality there is no natural
harbor at either end of the Nicaragua route. Fifty years ago there
was an excellent harbor at Greytown into which ships drawing as much
as 30 feet found ready entrance, and within which was afforded a
well-protected anchorage. As early as that date, however, a point of
land or sand-pit was already pushing its way northward in consequence
of the movement of the sand along the beach in that direction, and
in 1865 it had nearly closed the entrance to the harbor. For many
years that entrance has been entirely closed, and now what was
once the protected harbor of Greytown is a shallow body of water,
completely closed, and known as the Greytown Lagoon. There is a narrow,
circuitous, and shallow channel leading from it out to an opening in
the sand-bar, which may be navigated by boats drawing not more than 2
or 3 feet, and by means of which freight and passengers are taken from
steamers, which are obliged to anchor in the offing. Occasionally heavy
storms break through this strip of sand between Greytown Lagoon and
the ocean, and for a short time form a shallow entrance to the former.
The sand movement in that vicinity northward or westward is so active
that it is but a short time before such openings are again closed.
The deepest water in the lagoon probably does not exceed 8 or 10 feet
at the present time, and the most of it is much shallower. The tidal
action at Greytown is almost nothing, as the range of tide between high
and low is less than 1 foot. The mean level of the Caribbean Sea is the
same as that of the Pacific Ocean.
Under these circumstances it is necessary to create what is practically
a new harbor at Greytown, and that work is contemplated in the plans
of the Isthmian Canal Commission. The canal line is found entering the
lagoon about 1 mile northwest of Greytown, where a harbor is planned
having a length of 2500 feet and a width of 500 feet, increased at
the inner end to 800 feet to provide a turning-basin. The entrance to
this harbor from the ocean will be dredged to a width of 500 feet at
the bottom, and it will be protected outside of the beach-line by two
jetties, the easterly about 3000 feet long, and the westerly somewhat
shorter. These jetties would “be built of loose stone of irregular
shape and size, resting on a suitable foundation,” the largest,
constituting the covering, weighing not less than 10 to 15 tons each.
These jetties would be carried 6 feet above high water and have a top
width of 20 feet. The trade winds, which blow from the easterly and
northeasterly, would have a direction approximately at right angles to
that of the easterly jetty, and ships making the entrance of the canal
would consequently be protected against them while between the jetties.
The easterly of these jetties would act as an obstruction against the
westerly movement of the sand, but it is practically certain that a
considerable amount of the latter would be swept into the channel,
and possibly to some extent into the harbor, necessitating dredging
a considerable portion of the time. The commission estimates that
the maintenance of the entrance and harbor would require an annual
expenditure of $100,000.
=331. Artificial Harbor at Brito.=—The harbor at Brito presents a
problem of a different kind. There is absolutely no semblance of a
harbor there at the present time (1902); it is simply a location on the
sandy beach of the ocean protected against swells from the west by a
projecting rocky point called Brito Head, the Rio Grande River emptying
into the ocean just at the foot of Brito Head, between it and the canal
terminus. The entire harbor and its entrance would be excavated in
the low ground of that vicinity, composed mostly of sand and silt,
although there would be a little rock excavation. The entrance to the
harbor would be dredged 500 feet wide at the bottom, and be protected
by a single jetty on the southeasterly side. The harbor itself would
be excavated back of the present beach; it would have a length of 2200
feet and a width of 800 feet. As the depth of water increases rather
rapidly off shore, the 10-fathom curve is found at about 2200 feet from
low-water mark, hence the jetty would not need to be more than probably
1800 to 2000 feet long. In this vicinity the water is usually smooth;
indeed but few storms annually visit this part of the coast. The
conditions are quite similar to those found on the coast of Southern
California. There is little sand movement in this vicinity, and the
annual expenditures for maintenance of the harbor and entrance would be
relatively small; the commission has estimated them at $50,000.
=332. From Greytown Harbor to Lock No. 2.=—The canal line, on leaving
the harbor at Greytown, is found in low marshy ground for a distance of
about 7 miles, the excavation being mainly through the sand, silt, mud,
and vegetable matter characteristic of that location. Throughout almost
this entire distance the natural surface is but little above sea-level.
The first ground elevated much above this marshy country is known as
the Misterioso Hills, in which Lock No. 1 is founded, having a lift
of 36½ feet and raising the water surface in the canal by that amount
above sea-level. Another stretch of marshy country, but not quite so
wet as the preceding, follows for a distance of about 11 miles, when
the Rio Negro Hills rise abruptly to an elevation of a little over 150
feet above sea-level. At this point is located Lock No. 2, with a lift
of 18½ feet. This lock is about 21 miles from the 6-fathom line off
Greytown. The canal line here practically reaches the San Juan River,
the latter lying a considerable distance easterly of the canal, between
this point and the ocean. Between Greytown and Lock No. 2 embankments,
never reaching a greater height than 10 to 15 feet, are required to
keep the water in the canal at various locations along the low ground.
These embankments do not necessarily follow parallel to the centre
line of the canal route, but are planned to connect hills, or rather
high ground, so as to reduce their length and give them a more stable
character than if they were located close to the canal excavation.
While some embankments will still be found above Lock No. 2, they are
few, and even lower than those already noticed. From Lock No. 2 to Lake
Nicaragua the route of the canal lies practically along the San Juan
River, the chief exception to that statement being the cut-off in the
vicinity of the Conchuda dam.
[Illustration: Lock No. 1, Nicaragua Route, about Seven Miles from
Greytown.]
[Illustration: Telegraph Office at Ochoa on the San Juan River.]
=333. From Lock No. 2 to the Lake.=—Inasmuch as both the Serapiqui and
San Carlos rivers flow from Costa Rican territory into the San Juan,
that is, from its right bank, the canal line necessarily is located
along the northerly or left bank of that river. At a distance of 23
miles from the ocean the canal line cuts through what are called the
Serapiqui Hills opposite the mouth of the river of that name, and at
a distance of a little over 26 miles from the ocean it pierces the
Tamborcito Ridge, where is found the deepest cutting on the entire
route. The total length of cut through this ridge is about 3000 feet,
but its greatest depth is 297 feet, and it consists largely of hard,
basaltic rock. The next lock, or Lock No. 3, is found about 17 miles
from Lock No. 2, or 38 miles from the sea, and it has, like Lock No. 2,
a lift of 18½ feet, raising the surface of the water in the canal to an
elevation of 73½ feet above the sea. Continuous heavy cutting through
what are called the Machado Hills brings the line to Lock No. 4, at
a distance of a little less than 41 miles from the ocean. This lock
has a lift varying from 30.5 to 36.5 feet, inasmuch as it raises the
surface of the water in the canal to the summit level in the lake. The
maximum lift of 36.5 feet would be required when the lake level stands
at an elevation of 110 feet above the sea, and 30.5 feet when the same
surface stands at an elevation of 104 feet above the sea. Although the
water surface in the canal level above this lock is identical with the
summit level in the lake, the canal line again runs through continuous
heavy cutting for a distance of 5 miles before it reaches the canalized
San Juan. This portion of the line between Lock No. 4 and the San Juan
River is called the Conchuda cut-off, for the reason that the point
called Conchuda, where the great dam is located, is but 3 miles down
the river from the point where the canal enters it. From Conchuda
to the lake, as has already been stated, the canal line follows the
course of the San Juan River, which must be canalized by considerable
excavation of earth and rock, both along the bed and in cut-offs. The
greater part of this cutting must obviously be on that portion of the
river toward the lake, as that is the highest part of the river-bed in
its natural condition.
=334. Fort San Carlos to Brito.=—The distance from the point of
entrance of the canal into the San Juan River near Conchuda to Fort
San Carlos on the shore of Lake Nicaragua is about 50 miles, while the
distance across the lake on the canal line is 70.5 miles, which brings
the line to Las Lajas on the southwesterly shore of the lake.
There is considerable heavy cutting through the continental divide
between the lake and the first lock westerly of it, i.e., Lock No. 5.
The maximum cutting is but 76 feet in depth, and the average is but
little less than that for nearly 3 miles. This lock is located a little
less than 10 miles from the lake and nearly 176 miles from the 6-fathom
line off Greytown. The place at which this lock is located is known as
Buen Retiro. The lift of Lock No. 5 varies from 28½ feet as a maximum
to the minimum of 22½ feet, bringing the water surface in the canal
down to 81½ feet above mean ocean level. Lock No. 6 is located but
about 2 miles west of Lock No. 5, and also has a lift of 28½ feet. The
line now runs along the course of the Rio Grande to the ocean, Lock No.
7 being also 2 miles west of Lock No. 6, again with a lift of 28½ feet.
The last lock on the line, or Lock No. 8, but a mile from the Pacific
Ocean, and about 182 miles from the Caribbean Sea, has a maximum lift
of 28½ feet, and a minimum lift of 20½ feet, the range of tide in the
Pacific Ocean being but 8 feet at Brito. There are thus four locks
between the lake and the Pacific Ocean, each having a possible lift of
28½ feet.
[Illustration: Surveying Party of the Isthmian Canal Commission on the
San Juan River.]
The entire distance between the 6-fathom lines in the two oceans is
183.66 miles.
=335. Examinations by Borings.=—Obviously it is of the greatest
importance that such structures as the locks and dams required in
connection with this canal route should be founded on bed-rock. In
order to determine not only such questions, but the character of all
materials to be excavated from one end of the route to the other, a
great number of borings were made along the canal line, not only by the
water-jet process, but also with the diamond drill. By means of the
latter, whenever it was so desired, cores or circular pieces could be
taken out of the bed-rock so as to show precisely its character at all
depths. These borings, both through earthy material by the jet and into
bed-rock by the diamond drill, were made at suitable distances apart
along the centre line of the canal, and in considerable numbers, closer
together at proposed lock and dam sites. By these means every lock on
the line has certainly been located on bed-rock, as well as the great
dam at Conchuda. In addition to this the commission has been able to
classify the material to be excavated, so that if the canal should be
built every contractor would know precisely the character and quantity
of the various materials which he would have to deal with.
=336. Classification and Estimate of Quantities.=—The following table
is arranged to exhibit a few only of the principal items of excavation,
so as to give an approximate idea at least of the magnitude of the work
to be done:
Dredging 130,920,905 cu. yds.
Dry earth 47,440,316 ”
Soft rock 14,029,170 ”
Hard rock 24,151,214 ”
Rock under water 2,780,040 ”
Embankment and back-filling 8,389,960 ”
Clearing 6,831 acres.
Stone-pitching 250,089 sq. yds.
Concrete, excluding retaining-walls 3,400,840 cu. yds.
Concrete in retaining-walls 424,321 ”
Cut-stone 22,272 ”
Steel and iron,
excluding cast-iron culvert lining 61,735,230 lbs.
Cast-iron culvert lining 19,286,000 ”
Brick culvert lining 34,542 cu. yds.
Cost of lock machinery $1,600,000
Excavation in coffer-dam 9,907 cu. yds.
Pneumatic work 145,557 ”
Piling 415,600 lin. ft.
Rock fill in jetties 451,500 cu. yds.
Clay puddle, bottom and side 936,800 ”
=337. Classification and Unit Prices.=—The classification of the
material to be excavated, both on the Nicaragua and Panama routes, was
one to which the commission gave very thoughtful study no less than to
the prices to be used in making the estimates. The following table,
taken from pages 67 and 68 of the commission’s report, exhibits the
classification and the prices adopted by the commission for purposes of
its estimates:
Removal of hard rock, per cu. yd. $1.15
Removal of soft rock, per cu. yd. .80
Removal of earth, not handled by dredge, per cu. yd. .45
Removal of dredgable material, per cu. yd. .20
Removal of rock, under water, per cu. yd. 4.75
Embankments and back-filling, per cu. yd. .60
Rock in jetty construction, per cu. yd. 2.50
Stone-pitching, including necessary backing, per sq. yd. 2.00
Clearing and grubbing in swamp sections of Nicaragua,
per acre 200.00
Other clearing and grubbing on both routes, per acre 100.00
Concrete, in place, per cu. yd. 8.00
Finished granite, per cu. yd. 60.00
Brick in culvert lining, per cu. yd. 15.00
All metal in locks, exclusive of machinery and culvert
linings, per lb. .075
All metal in sluices, per lb. .075
Cast-iron in culvert lining, per lb. .04
Allowance for each lock-chamber for operating machinery 50,000.00
Additional allowance for each group of locks
for power-plant 100,000.00
Price of timber in locks, per M B. M 100.00
Sheet-piling in spillways, per M B. M 75.00
Bearing piles in spillways, per lin. ft. .50
Average price of pneumatic work for the Bohio dam, below
elevation—30, per cu. yd. 29.50
Caisson work for the Conchuda dam, in place, per cu. yd. 20.00
Single-track railroad complete with switches, stations,
and rolling stock, per mile of main line 75,000.00
There are evidently other more or less uncertain expenditures,
depending upon all possible conditions affecting the cost of such work,
including those of climate, police, and sanitation. In order to cover
such expenditure the commission determined to add 20 per cent to all
its estimates of cost on both routes, and that percentage was so added
in all cases.
=338. Curvature of the Route.=—Among the engineering features of
a ship-canal line it is evident that curvature is one of great
importance. Small steam-vessels may easily navigate almost any
tortuous channel, but it is not so with great ocean steamships. On the
other hand, it may require very deep and expensive cutting to reduce
the curvature of the route, as curves are usually introduced to carry
the line around some high ground. It is necessary, therefore, to make
a careful and judicious balance between these opposing considerations.
The commission wisely decided to incur even heavy cutting at some
points for the purpose of avoiding troublesome curvature on the
Nicaragua route. The table on page 415, taken from page 135 of the
commission’s report, gives all the elements of curvature for the entire
line.
[Illustration: Boring Party of the Isthmian Canal Commission on a Raft
in the San Juan River.]
From the description of the line as given, it is evident that much
curvature must be found in spite of the most judicious efforts to avoid
it, and the table indicates that condition. Yet the amount of curvature
may be considered moderate for a location through such a country as
Nicaragua. The smallest radius is seen to be a little over 4000 feet.
The result may be considered satisfactory for such a difficult canal
country, although the total amount of curvature is rather formidable.
+-----------+---------+---------+------------------+
| Number of | Radius. | Length. | Total Degrees of |
| Curves. | | | Curve. |
+-----------+---------+---------+------------------+
| | Feet. | Miles. | ° ′ ″ |
| 2 | 17,189 | 1.53 | 26 51 10 |
| 8 | 11,459 | 6.80 | 179 31 50 |
| 4 | 8,594 | 4.31 | 151 40 50 |
| 1 | 8,385 | 1.43 | 51 44 30 |
| 2 | 7,814 | 1.90 | 73 28 30 |
| 1 | 7,759 | 1.73 | 67 16 50 |
| 5 | 6,876 | 4.64 | 204 34 40 |
| 2 | 5,927 | 2.40 | 122 41 20 |
| 16 | 5,730 | 11.08 | 584 47 40 |
| 2 | 5,289 | 2.27 | 129 45 50 |
| 1 | 5,209 | 1.15 | 66 38 30 |
| 2 | 5,056 | 1.22 | 73 17 40 |
| 1 | 4,982 | .82 | 49 49 00 |
| 3 | 4,911 | 2.75 | 169 36 00 |
| 1 | 4,297 | .63 | 44 19 50 |
| 1 | 4,175 | .81 | 58 20 40 |
| 4 | 4,045 | 3.82 | 285 25 40 |
+-----------+---------+---------+------------------+
| 56 | | 49.29 | 2,339 50 30 |
+-----------+---------+---------+------------------+
=339. The Conchuda Dam and Wasteway.=—The most important single
engineering feature of the whole plan is the dam at Conchuda. The
ordinary low-water elevation in the river at the dam site may be taken
at about 55 feet above the sea. Inasmuch as the greatest elevation of
the water in the lake is supposed to be about 110 feet, it will be
seen that its surface will be but 55 feet above the present elevation,
making its maximum depth at that point about 105 feet if there should
be no fill on the up-stream side of the dam, inasmuch as the present
depth of water in the river at the stage assumed is about 50 feet.
This dam would be a structure of concrete masonry with cut-stone facing
only at a few points where it would be advisable to use that material.
A large part of the flood discharge, or the discharge of other surplus
water, would be made over a properly designed crest of the dam; hence
its outline would be that shown in the accompanying figure, shaped
so as to prevent the overflowing sheet of water from damaging the
structure. This dam will be founded upon pneumatic caissons, and the
borings made by the commission show that the deepest of them would
reach satisfactory bed-rock at no greater depth than 25 feet below
sea-level, or about 80 feet below the ordinary stage of water in the
river. The construction of this dam therefore would involve no unusual
operations, but it would all be performed within the more usual and
easy limits of the pneumatic process of constructing foundations. The
masonry crest of this dam would be finished at the elevation of 97
feet above sea-level, or about 13 feet below the highest elevation of
water in the lake. The length of that part of this masonry dam, located
on pneumatic caissons, would be 731 feet, but the total length of the
entire masonry structure would be 1310 feet. The total length of crest,
including the masonry piers on it, over which the surplus waters would
flow, would be 810 feet, but there are twenty piers 9 feet thick, so
that the net length of crest available for overflow of waste-waters
would be about 630 feet. The piers to which reference is made are those
required for the support of the movable gates of the Stoney type which
would be employed to regulate the discharge over the dam. The maximum
elevation of the tops of these piers required for the support and
operation of the Stoney gates is 132 feet above sea-level. The masonry
dam thus furnished with movable gates can be used in times of flood
to prevent the water of the lake rising above about 110 feet above
sea-level. In times of low rainfall or during the dry season the gates
would prevent the escape of water needed for storage.
[Illustration: Castillo Viejo, on the San Juan River, about
thirty-seven miles from the lake and at the Castillo Rapids. The old
fort is shown on the right at the summit of the hill.]
The total available length of crest on this masonry dam is not
sufficient to exercise all the control that is needed to keep the lake
within desired limits, and the commission was obliged to avail itself
of a low depression or saddle between the hills less than a half-mile
easterly of the dam site. The depression affords an additional total
length of crest of 1239 feet, or, taking out thirty-one piers, each 9
feet wide, a net available length of 960 feet, making in combination
with the crest of the main dam a total net available length of 1590
feet. The total wastage over these two structures, i.e., the main dam
at Conchuda and the Conchuda wasteway on the Costa Rican side of the
river, may be at the rate of 100,000 cubic feet per second, with a
maximum depth over the crest of 7 feet, which is sufficient to meet the
demands of the heaviest rainfall in the lake basin.
The plans and elevations on pages 421, 423, and 424 show all the main
features of both the Conchuda dam and wasteway as designed by the
commission.
=340. Regulation of the Lake Level.=—One of the most important
engineering questions connected with the consideration of the Nicaragua
route is that of the regulation or control of the surface of the water
in Lake Nicaragua constituting the summit level of the canal.
As has already been stated, the drainage-basin of the lake, about
12,000 square miles in area, is subjected to an annual wet season
extending from about the middle of May to the middle of December,
the dry season extending over the remaining portion of the year. The
average annual rainfall over the entire lake basin is not accurately
known, although the Isthmian Canal Commission maintained rainfall
records at several points on the lake shore and at other points in the
basin during periods of 1½ to 2 years, and records running back over
periods of perhaps 12 to 15 years are available from Rivas, Granada,
and Masaya. Fortunately, also, both the Nicaragua and the Isthmian
Canal Commissions maintained gauging-stations at various points on the
San Juan throughout the periods of service of these commissions, so
that the discharges of the river could be known from accurate measures
at various seasons for at least two or three years. These observations,
although not as extended as could be desired, yield sufficient data
for a comparatively thorough treatment of the subject of lake-surface
control.
Obviously throughout the rainy season of the year, except during years
of low rainfall, some water would necessarily be wasted from the lake
because its retention would raise the surface of the lake too high,
causing damage, floods, or injurious overflows at various places around
the lake shore. On the other hand, unless some water were stored from
the rainy periods or wet seasons there would not be sufficient in
the lake to supply during the dry period of the year, or during low
rainfall years, the requisite quantity for the wastage of evaporation
from its surface and for the operation of the canal, and at the same
time maintain the minimum depth of water of 35 feet required in the
canal. It was necessary, therefore, to design at least the general
features of such regulating-works as would prevent the lake from rising
too high in wet periods, and from falling too low in dry periods or low
rainfall years.
[Illustration: Village of Fort San Carlos at Entrance to the San Juan
River. Lake Nicaragua is on the right and San Juan River in the middle
ground.]
=341. Evaporation and Lockage.=—The observations of both commissions
show conclusively that the average evaporation from the surface of Lake
Nicaragua is about 60 inches or 5 feet per year, varying from perhaps a
maximum of 6 inches per month to a minimum of possibly about 4 inches
per month. Furthermore, careful estimates of the quantity of water
required for the purposes of the canal, on the supposition that about
10,000,000 tons of traffic would pass through it annually, including
lockage, leakage through the gates of the locks, evaporation, power
purposes, and other incidentals, show that about 1000 cubic feet of
water per second must be provided. Whatever may be the character of the
season, therefore, there must be at least sufficient water stored in
the lake to provide for the wastage of evaporation from the lake and
canal surfaces and for the proper operation of all the locks throughout
the length of the canal. The superficial area of Lake Nicaragua is but
little less than 3000 square miles. The quantity of water required for
the operation of the canal, amounting to 1000 cubic feet per second,
would, for the entire year, make a layer of water over the lake surface
of less than 5 inches in thickness. In other words, the operation of
the canal, for a traffic of about 10,000,000 tons annually, requires an
amount of water less than one twelfth of that which would be evaporated
from the lake surface during the same period.
=342. The Required Slope of the Canalized River Surface.=—The dam
located at Conchuda and fitted with suitable movable gates affords
means of accomplishing the entire lake-surface control. That dam is
located, however, nearly 53 miles from the lake, and in order that the
requisite discharge may take place over it during the rainy season
there must be considerable slope of the water surface in the canalized
river from the lake down to the dam. It was necessary, therefore, to
compute that slope, from data secured by the commission, with the
lake surface at various elevations between the minimum and maximum
permitted. These slopes were found to be such that the difference in
elevations of the surface of the water at the dam and in the lake might
vary from about 6 to 9 feet, those figures representing the total fall
for the distance of 53 miles.
=343. All Surplus Water to be Discharged over the Conchuda Dam.=—The
Nicaragua Commission contemplated the construction of dams not only on
the San Juan River at Boca San Carlos, about 6 miles below Conchuda,
but also another a few miles west of the lake at La Flor, so as to
discharge the surplus waters at both points, but by far the largest
part over the dam at Boca San Carlos. The Isthmian Canal Commission,
however, decided to build no dam on the west side of the lake, but to
discharge all the surplus waters over the dam at Conchuda.
[Illustration: The Active Volcano Ometepe in Lake Nicaragua, showing
Clouds on Leeward Side of the Summit. The crater is nearly eleven miles
from the canal line.]
=344. Control of the Surface Elevation of the Lake.=—The rainfall
records in the lake basin have shown that a dry season beginning
as early as November may be followed by an extremely low rainfall
period, which in turn would be followed by a dry season in natural
sequence, lasting as late as June. It may happen, therefore, that
from November until a year from the succeeding June, constituting a
period of nineteen months, there will be a very meagre rainfall in the
lake basin, during which the precipitation of the seven low rainfall
wet months may not be sufficient even to make good the depletion of
evaporation alone during the same period. It would be necessary, then,
at the end of any wet season whatever, i.e., during the first half of
any December, or in November, to make sure of sufficient storage in the
lake to meet the requirements of the driest nineteen months that can
be anticipated. That condition was assumed by the commission, and the
elements of control of the lake surface, in its plans, are such as to
afford resources to meet precisely those low-water conditions.
[Illustration: Plan of Conchuda Dam Site, showing Location of Boring.]
The commission’s study of these features of the Nicaragua Canal problem
resulted in plans of works to prevent the surface of the lake ever
falling below 104 feet above sea-level, or rarely if ever rising higher
than the elevation of 110 feet above the same level, thus making the
possible range of the lake surface about 6 feet between its lowest and
its highest position.
Obviously at the end of a dry season the gates at the dam will always
be found closed, and there will be no water escaping from the lake
except by evaporation and to supply the needs of canal operation. It
is equally evident that the gates will also remain closed so as to
permit no wastage during the early part of the wet season. As the wet
season proceeds the surface of the lake will rise toward, and generally
quite to its maximum elevation; the operation of wasting over the
weirs will then commence. The time of beginning of this wastage will
depend upon the amount and distribution of the rainfall during the
wet period. Indeed no wastage whatever would be permitted during such
a low-water wet season as that shown by the records of 1890, which
was almost phenomenal in its low precipitation. The rainfall for the
entire drainage-basin would be impounded in the lake in that case, and
it would then fall short of restoring the depletion resulting from
evaporation and requirements of the canal. On the other hand, during
such a wet season as that of 1897 wastage would begin at an early date.
In general it may be said that neither the rate nor the law of the rise
of water surface in the lake can be predicted. There will be years when
no wastage will be permitted, but generally considerable wastage will
be necessary in order to prevent the lake rising above the permissible
highest stage.
[Illustration: Profile of Site of Conchuda Dam showing Borings.]
Detailed computations based upon the statistics of actual rainfall
records in the basin of Lake Nicaragua may be found by referring to
pages 147 to 152 of the Report of the Isthmian Canal Commission, and
they need not be repeated here. Those computations show among other
things that October is often a month of excessive rainfall, and that
the greatest elevation of the lake surface is likely to follow the
precipitation of that month. Hence the greatest discharge of surplus
waters over the Conchuda dam may be expected in consequence of the
resulting run-off or inflow into the lake. Those computations also
show that at long intervals of time the lake surface might reach an
elevation of nearly 112 feet above sea-level for short periods, causing
the discharge in the canalized river or over the Conchuda dam to reach
possibly 76,000 cubic feet per second, the elevation of the water at
the dam being 104 feet above sea-level. Furthermore, the Sabalos River
and one or two other small streams, emptying into the San Juan above
the dam, might concurrently be in flood for at least a few hours and
augment the discharge over the dam to 100,000 cubic feet per second.
The regulating-works at the dam, consisting of the movable (Stoney)
gates, were devised by the commission to afford that rate of discharge,
an aggregate net or available length of overflow crest at the dam and
wasteway of 1590 feet being necessary for that purpose with a depth of
water on the crest not exceeding 7 feet.
[Illustration: CONCHUDA DAM. SECTION SHOWING CAISSONS]
[Illustration: CONCHUDA DAM. DIAGRAM SHOWING ARRANGEMENT OF SLUICE GATE]
The commission states on page 156 of its report:
“While, therefore, no detailed instructions can be set
forth regarding the condition of the sluices at the
wasteway on specified dates, the general lines of their
operation should be stated below, viz.:
“1. A full lake with surface probably a little above
110 feet on December 1.
“2. Wasteway sluices closed at least from about
December 1 to some date in the early portion of the
succeeding rainy season, or throughout that season if
it be one of unusually low precipitation.
“3. A variable opening of wasteway sluices, if
necessary, during the intermediate portion of the rainy
season, so as to maintain the lake surface elevation
but little, if any, below 110 at the beginning of
October.
“4. The operation of wasteway sluices during October
and November so as to reach the 1st of December with a
full lake, or lake elevation probably a little above
110 feet.”
It is thus seen that while the measures for control and regulation are
entirely feasible, they are not sharply defined, nor so simple that
some experience in their operation might not be needful for the most
satisfactory results.
=345. Greatest Velocities in Canalized River.=—It is necessary to
ascertain whether the velocities induced in the canalized portions
of the San Juan River would not be too high for the convenience of
traffic during the highest rainfall season. The following table and the
succeeding paragraph, taken from the commission’s report, show that no
sensible difficulty of this kind would exist.
--------------+-------------------------+----------------------
| Elevation of Water at Dam.
Elevation of +-------------------------+----------------------
Lake. | 103 Feet. | 104 Feet.
--------------+------------+------------+-----------+-----------
| Feet per | Miles per | Feet per | Miles per
Feet. | Second. | Hour. | Second. | Hour.
110 | 4.16 | 2.8 | 3.9 | 2.7
111 | 4.51 | 3.1 | 4.2 | 2.9
112 | 4.85 | 3.3 | 4.5 | 3.1
--------------+------------+------------+-----------+----------
“The discharge of the river corresponding to the velocity of 2.7 miles
per hour is 63,200 cubic feet per second; while that corresponding to
3.3 miles per hour is 77,000 cubic feet per second. These estimated
high velocities will occur but rarely, and they will not sensibly
inconvenience navigation. In reality they are too high, for the reason
that while the overflow at the minimum river section materially
increases the areas of those sections, it has been neglected in this
discussion.”
[Illustration]
[Illustration: Brito, at the Pacific Terminus of the Nicaragua Route,
showing the mouth of the Rio Grande on the left and the easterly side
of Brito Head.]
=346. Wasteways or Overflows.=—At a number of places on the route
there are some small streams which must be taken into the canal, and
which when in flood require that certain wasteways or overflows from
the canal prism should be provided at or near where such streams are
received. These wasteways are simply overfall-weirs with the crests
at the elevation of the lowest water surface in the canal prism. The
principal works of this kind are on the east side of the lake and
involve a total drainage area or area of watershed of about 107 square
miles. Ample provision has been made by the commission for all such
structural features.
=347. Temporary Harbors and Service Railroad.=—Before actual work
could be begun at either end of the Nicaragua route temporary harbors
would have to be constructed both at Greytown and at Brito to enable
contractors to land plant and supplies or other material. These
temporary harbors would probably require no greater depth of water
than 18 feet, but they would be works of considerable magnitude, and
provision was made for them in the commission’s estimate of cost.
Again, a service railroad of substantial character would have to be
built from Greytown up to Sabalos, approximately half-way between the
Conchuda dam and Fort San Carlos, as well as from the west shore of the
lake to Brito, making a total line of about 100 miles. The commission
estimated the cost of this railroad and its rolling stock at $75,000
per mile.
=348. Itemized Statement of Length and Cost.=—The following table gives
the lengths of the various portions of the canal and the principal
items of its cost, so arranged as to show the classification of the
various items of the total sum to be expended for all purposes during
the construction of the entire work.
The commission estimated the total time required in preparing for and
performing the actual construction of the work at eight years, but the
writer believes that at least two years more should be allowed for the
work.
------------------------------------------------+------+------------
|Miles.| Cost.
------------------------------------------------+------+------------
Greytown harbor and entrance | 2.15| $2,198,860
Section from Greytown harbor to lock No. 1, | |
including approach-wall to lock | 7.44| 4,899,887
Diversion of Lower San Juan | | 40,100
Diversion of San Juanillo | | 116,760
Lock No. 1, including excavation | .20| 5,719,689
Section from lock No. 1 to lock No. 2, including| |
approach-walls, embankments, and wasteway | 10.96| 6,296,632
Lock No. 2, including excavation | .20| 4,050,270
Section from lock No. 2 to lock No. 3, including| |
approach-walls, embankments, and wasteway | 16.75| 19,330,654
Lock No. 3, including excavation | .20| 3,832,745
Section from lock No. 3 to lock No. 4, including| |
approach-walls, embankments, and wasteway | 2.77| 4,310,580
Lock No. 4, including excavation | .20| 5,655,871
Section from lock No. 4 to San Juan River, | |
including approach-wall and embankments | 5.30| 8,579,431
Conchuda dam, including sluices and machinery | | 4,017,650
Auxiliary wasteway, including sluices, | |
machinery, and approach-channels | | 2,045,322
San Juan River section | 49.64| 23,155,670
Lake Nicaragua section | 70.51| 7,877,611
Lake Nicaragua to lock No. 5, including | |
approach-wall to lock and receiving-basins for| |
the Rio Grande and Chocolata | 9.09| 19,566,575
Diversion of the Las Lajas | | 199,382
Lock No. 5, including excavation | .20| 4,913,512
Dam near Buen Retiro | | 125,591
Section from lock No. 5 to lock No. 6, including| |
approach-walls and wasteway | 2.04| 3,259,283
Lock No. 6, including excavation | .20| 4,368,667
Section from lock No. 6 to lock No. 7, including| |
approach-walls, embankments, and wasteway | 1.83| 2,309,710
Diversion of Rio Grande | | 176,180
Lock No. 7, including excavation | .20| 4,709,502
Section from lock No. 7 to lock No. 8, including| |
approach-walls, embankments, and wasteway | 2.43| 1,787,496
Diversion of Rio Grande | | 117,580
Lock No. 8, including excavation | .20| 4,920,899
Section from lock No. 8 to Brito harbor, | |
including approach-wall | .23| 553,476
Brito harbor and entrance, including jetty | .92| 1,509,470
Railroad, including branch line to Conchuda | |
dam site, at $75,000 per mile | | 7,575,000
Engineering, police, sanitation, and general | |
contingencies, 20 per cent. | | 1,644,010
+------+------------
Aggregate |183.66|$189,864,062
------------------------------------------------+------+------------
PART VI.
_THE PANAMA ROUTE FOR A SHIP-CANAL._
=349. The First Panama Transit Line.=—The Panama route as a line
of transit across the isthmus was established, as near as can be
determined, between 1517 and 1520. The first settlement, at the site
of the town of old Panama, 6 or 7 miles easterly of the present city
of that name, was begun in August, 1517. This was the Pacific end of
the line. The Atlantic end was finally established in 1519 at Nombre
de Dios, the more easterly port of Acla, where Balboa was tried and
executed, having first been selected but subsequently rejected.
The old town of Panama was made a city by royal decree from the throne
of Spain in September, 1521. At the same time it was given a coat of
arms and special privileges were conferred upon it. The course of
travel then established ran by a road well known at the present time
through a small place called Cruces on the river Chagres, about 17
miles distant from Panama. It must have been an excellent road for
those days. Bridges were even laid across streams and the surface was
paved, although probably rather crudely. According to some accounts it
was only wide enough for use by beasts of burden, but some have stated
that it was wide enough to enable two carts to pass each other.
=350. Harbor of Porto Bello Established in 1597.=—The harbor of
the Atlantic terminus at Nombre de Dios did not prove entirely
satisfactory, and Porto Bello, westerly of the former point, was made
the Atlantic port in 1597 for this isthmian line of transit. The harbor
of Porto Bello is excellent, and the location was more healthful,
although Porto Bello itself was subsequently abandoned, largely on
account of its unhealthfulness.
[Illustration: PROFILE OF PANAMA ROUTE]
[Illustration: PROFILE OF NICARAGUA ROUTE
Profiles of the two Canal Routes. The horizontal scales are different,
but the vertical scales are the same.]
=351. First Traffic along the Chagres River, and the Importance of the
Isthmian Commerce.=—As early as 1534, or soon after that date, boats
began to pass up and down the Chagres River between Cruces and its
mouth on the Caribbean shore, and thence along the coast to Nombre de
Dios and subsequently to Porto Bello. The importance of the commerce
which sprang up across the isthmus and in connection with this isthmian
route is well set forth in the last paragraph on page 28 of the report
of the Isthmian Canal Commission:
“The commerce of the isthmus increased during the century and Panama
became a place of great mercantile importance, with a profitable trade
extending to the Spice Islands and the Asiatic coast. It was at the
height of its prosperity in 1585, and was called with good reason
the toll-gate between western Europe and eastern Asia. Meanwhile the
commerce whose tolls only brought such benefits to Panama enriched
Spain, and her people were generously rewarded for the aid given by
Ferdinand and Isabella in the effort to open a direct route westward to
Cathay, notwithstanding the disadvantages of the isthmian transit.”
=352. First Survey for Isthmian Canal Ordered in 1520.=—This commercial
prosperity suggested to those interested in it, and soon after its
beginning, the possibility of a ship-canal to connect the waters of the
two oceans. It is stated even that Charles V. directed that a survey
should be made for the purpose of determining the feasibility of such
a work as early as 1520. “The governor, Pascual Andagoya, reported
that such a work was impracticable and that no king, however powerful
he might be, was capable of forming a junction of the two seas or of
furnishing the means of carrying out such an undertaking.”
=353. Old Panama Sacked by Morgan and the Present City Founded.=—From
that time on the city of Panama increased in wealth and population in
consequence of its commercial importance. Trade was established with
the west coast of South America and with the ports on the Pacific
coast of Central America. In spite of the fact that it was made by
the Spaniards a fortress second in strength in America only to old
Cartagena, it was sacked and burned by Morgan’s buccaneers in February,
1671. The new city, that is the present city, was founded in 1673, it
not being considered advisable to rebuild on the old site.
[Illustration: View of the Harbor of Colon.]
=354. The Beginnings of the French Enterprise.=—The project of a
canal on this route was kept alive for more than three centuries by
agitation sometimes active and sometimes apparently dying out for
long periods, until there was organized in Paris, in 1876, a company
entitled “Société Civile Internationale du Canal Interocéanique,” with
Gen. Etienne Türr as president, for the purpose of making surveys and
explorations for a ship-canal between the two oceans on this route.
=355. The Wyse Concession and International Congress of 1879.=—The work
on the isthmus for this company was prosecuted under the direction
of Lieut. L. N. B. Wyse, a French naval officer, and he obtained for
his company in 1878 a concession from the Colombian Government,
conferring the requisite rights and privileges for the construction of
a ship-canal on the Panama route and the authority to do such other
things as might be necessary or advisable in connection with that
project. This concession is ordinarily known as the Wyse concession.
A general plan for this transisthmian canal was the subject of
consideration at an international scientific congress convened in Paris
in May, 1879, and composed of 135 delegates from France, Germany, Great
Britain, the United States, and other countries, but the majority of
whom were French. This congress was convened under the auspices of
Ferdinand de Lesseps, and after remaining in session for two weeks a
decision, not unanimous, was reached that an international canal ought
to be located on the Panama route, and that it should be a sea-level
canal without locks. The fact was apparently overlooked that the range
between high and low tides in the Bay of Panama, about 20 feet, was so
great as to require a tidal lock at that terminus.
=356. The Plan without Locks of the Old Panama Canal Company.=—A
company entitled “Compagnie Universelle du Canal Interocéanique”
was organized, with Ferdinand de Lesseps as president, immediately
after the adjournment of the international congress. The purpose of
this company was the construction and operation of the canal, and it
purchased the Wyse concession from the original company for the sum
of 10,000,000 francs. An immediate but unsuccessful attempt was made
to finance the company in August, 1879. This necessitated a second
attempt, which was made in December, 1880, with success, as the entire
issue of 600,000 shares of 500 francs each was sold. Two years were
then devoted to examinations and surveys and preliminary work upon the
canal, but it was 1883 before operations upon a large scale were begun.
The plan adopted and followed by this company was that of a sea-level
canal, affording a depth of 29.5 feet and a bottom width of 72 feet. It
was estimated that the necessary excavation would amount to 157,000,000
cubic yards.
The Atlantic terminus of this canal route was located at Colon,
and at Panama on the Pacific side. The line passed through the low
grounds just north of Monkey Hill to Gatun, 6 miles from the Atlantic
terminus, and where it first met the Chagres River. For a distance
of 21 miles it followed the general course of the Chagres to Obispo,
but left it at the latter point and passing up the valley of a small
tributary cut through the continental divide at Culebra, and descended
thence by the valley of the Rio Grande to the mouth of that river where
it enters Panama Bay. The total length of this line from 30 feet depth
in the Atlantic to the same depth in the Pacific was about 47 miles.
The maximum height of the continental divide on the centre line of the
canal in the Culebra cut was about 333 feet above the sea, which is a
little higher than the lowest point of the divide in that vicinity.
Important considerations in connection with the adjacent alignment made
it advisable to cut the divide at a point not its lowest.
[Illustration: Old Dredges near Colon.]
=357. The Control of the Floods in the Chagres.=—Various schemes were
proposed for the purpose of controlling the floods of the Chagres
River, the suddenness and magnitude of which were at once recognized as
among the greatest difficulties to be encountered in the construction
of the work. Although it was seriously proposed at one time to control
this difficulty by building a dam across the Chagres at Gamboa, that
plan was never adopted, and the problem of control of the Chagres
floods remained unsolved for a long period.
=358. Estimate of Time and Cost—Appointment of Liquidators.=—It was
estimated by de Lesseps in 1880 that eight years would be required for
the completion of the canal, and that its cost would be $127,600,000.
The company prosecuted its work with activity until the latter part of
1887, when it became evident that the sea-level plan of canal was not
feasible with the resources at its command. Changes were soon made in
the plans, and it was concluded to expedite the completion of the canal
by the introduction of locks, deferring the change to a sea-level canal
until some period when conditions would be sufficiently favorable to
enable the company to attain that end. Work was prosecuted under this
modified plan until 1889, when the company became bankrupt and was
dissolved by judgment of the French court called the Tribunal Civil
de la Seine, on February 4, 1889. An officer, called the liquidator,
corresponding quite closely to a receiver in this country, was
appointed by the court to take charge of the company’s affairs. At
no time was the project of completing the canal abandoned, but the
liquidator gradually curtailed operations and finally suspended the
work on May 15, 1889.
=359. The “Commission d’Etude.”=—He determined to take into careful
consideration the feasibility of the project, and to that end appointed
a “commission d’études,” composed of eleven French and foreign
engineers, headed by Inspector-General Guillemain, director of the
_Ecole Nationale des Ponts et Chaussées_. This commission visited
the isthmus and made a careful study of the entire enterprise, and
subsequently submitted a plan for the canal involving locks. The cost
of completing the entire work was estimated to be $112,500,000, but
the sum of $62,100,000 more was added to cover administration and
financing, making a total of $174,600,000. This commission also gave
an approximate estimate of the value of the work done and of the plant
at $87,300,000, to which some have attached much more importance than
did the commission itself. The latter appears simply to have made the
“estimate” one half of the total cost of completing the work added to
that of financing and administration, as a loose approximation, calling
it an “intuitive estimate”; in other words, it was simply a guess
based upon such information as had been gained in connection with the
work done on the isthmus.
[Illustration: The Partially Completed Panama Canal, about eight miles
from Colon.]
=360. Extensions of Time for Completion.=—By this time the period
specified for completion under the original Wyse concession had nearly
expired. The liquidator then sought from the Colombian Government an
extension of ten years, which was granted under the Colombian law dated
December 26, 1890. This extension was based upon the provision that a
new company should be formed and work on the canal resumed not later
than February 28, 1893. The latter condition was not fulfilled, and a
second extension was obtained on April 4, 1893, which provided that the
ten-year extension of time granted in 1890 might begin to run at any
time prior to October 31, 1894, but not later than that date. When it
became apparent that the provisions of this last extension would not
be carried out an agreement between the Colombian Government and the
new Panama Company was entered into on April 26, 1900, which extended
the time of completion to October 31, 1910. The validity of this last
extension of time has been questioned.
=361. Organization of the New Panama Canal Company, 1894.=—A new
company, commonly known as the new Panama Canal Company, was organized
on the 20th of October, 1894, with a capital stock of 650,000 shares
of 100 francs each. Under the provisions of the agreement of December
26, 1890, authorizing an extension of time for the construction of
the canal, 50,000 shares passed as full-paid stock to the Colombian
Government, leaving the actual working capital of the new Panama
Company at 60,000,000 francs, that amount having been subscribed in
cash. The most of this capital stock was subscribed for by certain
loan associations, administrator, contractors, and others against whom
suits had been brought in consequence of the financial difficulties
of the old company, it having been charged in the scandals attending
bankruptcy proceedings that they had profited illegally. Those suits
were discontinued under agreements to subscribe by the parties
interested to the capital stock of the new company. The sums thus
obtained constituted more than two thirds of the 60,000,000 francs
remaining of the share capital of the new company after the Colombian
Government received its 50,000 shares. The old company had raised by
the sale of stock and bond not far from $246,000,000, and the number
of persons holding the securities thus sold has been estimated at over
200,000.
=362. Priority of the Panama Railroad Concession.=—The Panama Railroad
Company holds a concession from the Colombian Government giving it
rights prior to those of the Wyse concession, so that the latter could
not become effective without the concurrence of the Panama Railroad
Company. This is shown by the language of Article III of the Wyse
concession, which reads as follows:
“If the line of the canal to be constructed from sea to sea should
pass to the west and to the north of the imaginary straight line which
joins Cape Tiburon with Garachine Point, the grantees must enter into
some amicable arrangement with the Panama Railroad Company or pay an
indemnity, which shall be established in accordance with the provisions
of Law 46 of August 16, 1867, ‘approving the contract celebration on
July 5, 1867, reformatory of the contract of April 15, 1850, for the
construction of an iron railroad from one ocean to the other through
the Isthmus of Panama.’” It became necessary, therefore, in order to
control this feature of the situation, for the old Panama Company
to secure at least a majority of the stock of the Panama Railroad
Company. As a matter of fact the old Panama Canal Company purchased
nearly 69,000 out of the 70,000 shares of the Panama Railroad Company,
each such share having a par value of $100. These shares of Panama
railroad stock are now held in trust for the benefit of the new Panama
Canal Company. A part of the expenditures of the old company therefore
covered the cost of the Panama Railroad Company’s shares, now held in
trust for the benefit of the new company.
=363. Resumption of Work by the New Company—The Engineering Commission
and the Comité Technique.=—Immediately after its organization the new
Panama Canal Company resumed the work of excavation in the Emperador
and Culebra cuts with a force of men which has been reported as
varying between 1900 and 3600. It also gave thorough consideration
to the subject of the best plan for the completion of the canal. The
company’s charter provided for the appointment of a special engineering
commission of five members by the company and the liquidator to report
upon the work done and the conclusions to be drawn from its study. This
report was to be rendered when the amount expended by the new company
should reach about one half of its capital. At the same time the
company also appointed a “Comité Technique,” constituted of fourteen
eminent European and American engineers, to make a study of the entire
project, which was to avail itself of existing data and the results of
such other additional surveys and examinations as it might consider
necessary. The report rendered by this committee was elaborate, and it
was made November 16, 1898. It was referred to the statutory commission
of five to which reference has already been made, which commission
reported in 1899 that the canal could be constructed within the limits
of time and money estimated. On December 30, 1899, a special meeting
of the stockholders of the new company was called, but the liquidator,
who was one of the largest stockholders, declined to take part in it,
and the report consequently has not received the required statutory
consideration.
[Illustration: The Excavation at the Bohio Lock Site.]
=364. Plan of the New Company.=—The plan adopted by the company placed
the minimum elevation of the summit level of the canal at 97½ feet
above the sea, and a maximum at 102½ feet above the same datum. It
provided for a depth of 29½ feet of water and a bottom width of canal
prism of about 98 feet, except at special places where this width was
increased. A dam was to be built near Bohio, which would thus form an
artificial lake with its surface varying from 52.5 to 65.6 feet above
the sea. Under this plan there would be a flight of two locks at
Bohio, about 16 miles from the Atlantic end of the canal, and another
flight of two locks at Obispo about 14 miles from Bohio, thus reaching
the summit level, a single lock at Paraiso, between 6 and 7 miles from
Obispo, a flight of two locks at Pedro Miguel about 1.25 miles from
Paraiso, and finally a single lock at Miraflores, a mile and a quarter
from Pedro Miguel, bringing the canal down to the ocean elevation.
The location of this line was practically the same as that of the
old company. The available length of each lock-chamber was 738 feet,
while the available width was 82 feet, the depth in the clear being
32 feet 10 inches. The lifts were to vary from 26 to 33 feet. It was
estimated that the cost of finishing the canal on this plan would be
$101,850,000, exclusive of administration and financing.
In order to control the floods of the Chagres River, and to furnish a
supply of water for the summit level of the canal, a dam was planned to
be built at a point called Alhajuela, about 12 miles from Obispo, from
which a feeder about 10 miles long, partly an open canal and partly in
tunnels or pipe, would conduct the water from the reservoir thus formed
to the summit level.
=365. Alternative Plan of the New Panama Canal Company.=—Although
the plan as described was adopted, the “Comité Technique” apparently
favored a modification by which a much deeper excavation through
Culebra Hill would be made, thus omitting the locks at both Obispo and
Paraiso, and making the level of the artificial Lake Bohio the summit
level of the canal. In this modified plan the bottom of the summit
level would be about 32 feet above the sea, and the minimum elevation
of the summit level 61.5 feet above the sea. This modification of plan
had the material advantage of eliminating both the Obispo and Paraiso
locks. The total estimated cost of completing the canal under this plan
was about $105,500,000. Although the Alhajuela feeder would be omitted,
the Alhajuela reservoir would be retained as an agent for controlling
the Chagres floods and to form a reserve water-supply. The difference
in cost of these two plans was comparatively small, but the additional
time required to complete that with the lower summit level was probably
one of the main considerations in its rejection by the committee having
it under consideration.
=366. The Isthmian Canal Commission and its Work.=—This brings
the project up to the time when the Isthmian Canal Commission was
created in 1899 and when the forces of the new Panama Canal Company
were employed either in taking care of the enormous amount of plant
bequeathed to it by the old company or in the great excavation at
Emperador and Culebra. The total excavation of all classes, made up to
the time when that commission rendered its report, amounted to about
77,000,000 cubic yards.
The work of the commission consisted of a comprehensive and detailed
examination of the entire project and all its accessories, as
contemplated by the new Panama Canal Company, and any modifications of
its plans, either as to alignment, elevations, or subsidiary works,
which it might determine advisable to recommend. In the execution of
this work it was necessary, among other things, to send engineering
parties on the line of the Panama route for the purpose of making
surveys and examinations necessary to confirm estimates of the new
Panama Canal Company as to quantities, elevations, or other physical
features of the line selected, or required in modifications of
alignment or plans. In order to accomplish this portion of its work the
commission placed five working parties on the Panama route with twenty
engineers and other assistants and forty-one laborers.
[Illustration: The French Location for the Bohio Dam.]
=367. The Route of the Isthmian Canal Commission that of the New
Panama Canal Company.=—The commission adopted for the purposes of
its plans and estimates the route selected by the new Panama Canal
Company, which is essentially that of the old company. Starting from
the 6-fathom contour in the harbor of Colon, the line follows the low
marshy ground adjoining the Bay of Limon to its intersection with the
Mindi River; thence through the low ground continuing to Gatun, about
6 miles from Colon, where it first meets the Chagres River. From this
point to Obispo the canal line follows practically the general course
of the Chagres River, although at one point in the marshes below Bohio
it is nearly 2 miles from the farthest bend in the river, at a small
place called Ahorca Lagarto. Bohio is about 17 miles from the Atlantic
terminus, and Obispo about 30 miles. At the latter point the course of
the Chagres River, passing up-stream, lies to the northeast, while the
general direction of the canal line is southeast toward Panama, the
latter leaving the former at this location. The canal route follows up
the general course of a small stream called the Camacho for a distance
of nearly 5 miles where the continental divide is found, and in which
the great Culebra cut is located, about 36 miles from Colon and 13
miles from the Panama terminus. After passing through the Culebra cut
the canal route follows the course of the Rio Grande River to its mouth
at Panama Bay. The mouth of the Rio Grande, where the canal line is
located, is about a mile and a half westerly of the city of Panama. The
Rio Grande is a small, sluggish stream throughout the last 6 miles of
its course, and for that distance the canal excavation would be made
mostly in soft silt or mud.
Although the line selected by the French company is that adopted by the
Isthmian Canal Company for its purposes, a number of most important
features of the general plan have been materially modified by the
commission, as will be easily understood from what has already been
stated in connection with the French plans.
=368. Plan for a Sea-level Canal.=—The feasibility of a sea-level
canal, but with a tidal lock at the Panama end, was carefully
considered by the commission, and an approximate estimate of the
cost of completing the work on that plan was made. In round numbers
this estimated cost was about $250,000,000, and the time required to
complete the work would probably be nearly or quite twice that needed
for the construction of a canal with locks. The commission therefore
adopted a project for the canal with locks. Both plans and estimates
were carefully developed in accordance therewith.
=369. Colon Harbor and Canal Entrance.=—The harbor of Colon has been
fairly satisfactory for the commerce of that port, but it is open to
the north, and there are probably two or three days in every year
during which northers blow into the harbor with such intensity that
ships anchored there must put to sea in order to escape damage.
The western limit of this harbor is an artificial point of land
formed by material deposited by the old Panama Canal Company; it
is called Christoph Colon, and near its extreme end are two large
frame residences built for de Lesseps. The entrance to the canal is
immediately south of this artificial point. The commission projected a
canal entrance from the 6-fathom contour in the Bay of Limon, in which
the harbor of Colon is found, swinging on a gentle curve, 6560 feet
radius, to the left around behind the artificial point just mentioned
and then across the shore line to the right into the lowland southerly
of Colon. This channel has a width of 500 feet at the bottom, with
side slopes of 1 on 3, except on the second curve, which is somewhat
sharper than the first, where the bottom width is made 800 feet for a
length of 800 feet for the purpose of a turning-basin. This brings the
line into the canal proper, forming a well-protected harbor for nearly
a mile inside of the shore line. The distance from the 6-fathom line to
this interior harbor is about 2 miles. The total cost of constructing
the channel into the harbor and the harbor itself is $8,057,707, and
the annual cost of maintenance is placed at $30,000. The harbor would
be perfectly protected from the northers which occasionally blow with
such intensity in the Bay of Limon, and it could readily be made in all
weathers by vessels seeking it.
=370. Panama Harbor and Entrance to Canal.=—The harbor at the Pacific
end of the channel where it joins Panama Bay is of an entirely
different character in some respects. The Bay of Panama is a place
of light winds. Indeed it has been asserted that the difficulties
sometimes experienced by sailing-vessels in finding wind enough to
take them out of Panama Bay are so serious as to constitute a material
objection to the location for a ship-canal on the Panama route. This
difficulty undoubtedly exists at times, but the simple fact is to be
remembered that Panama was a port for sailing-ships for more than two
hundred years before a steamship was known. The harbor of Panama, as
it now exists, is a large area of water at the extreme northern limit
of the bay, immediately adjacent to the city of Panama, protected from
the south by the three islands of Perico, Naos, and Culebra. It has
been called a roadstead. There is good anchorage for heavy-draft ships,
but for the most part the water is shallow. With the commission’s
requirement of a minimum depth of water of 35 feet, a channel about 4
miles long from the mouth of the Rio Grande to the 6-fathom line in
Panama Bay must be excavated. This channel would have a bottom width
of 200 feet with side slopes of 1 on 3 where the material is soft.
Considerable rock would have to be excavated in this channel. At 4.41
miles from the 6-fathom line is located a wharf at the point called La
Boca. A branch of the Panama Railroad Company runs to this wharf, and
at the present time deep-draft ships lie up alongside of it to take on
and discharge cargo. The wharf is a steel frame structure, founded upon
steel cylinders, carried down to bed-rock by the pneumatic process.
Its cost was about $1,284,000. The total cost of the excavated channel
leading from Panama harbor to the pier at La Boca is estimated by the
commission at $1,464,513. As the harbor at Panama is considered an open
roadstead, it requires no estimate for annual cost of maintenance.
[Illustration: The Bohio Dam Site.]
=371. The Route from Colon to Bohio.=—Starting from the harbor of
Colon, the prism of the canal is excavated through the low and for the
most part marshy ground to the little village called Bohio. The prism
would cut the Chagres River at a number of points, and would require a
diversion-channel for that river for a distance of about 5 miles on the
westerly side of the canal. Levees, or protective embankments, would
also be required on the same side of the canal between Bohio and Gatun,
the Chagres River leaving the canal line at the latter point on its way
to the sea.
=372. The Bohio Dam.=—The principal engineering feature of the entire
route is found at Bohio; it is the great dam across the Chagres River
at that point, forming Lake Bohio, the summit level of the canal. The
new Panama Canal Company located this dam at a point about 17 miles
from Colon, and designed to make it an earth structure suitably paved
on its faces, but without any other masonry feature. Some borings had
been made along the site, and test-pits were also dug by the French
engineers. It was the conviction of the Isthmian Canal Commission,
however, that the character of the proposed dam might be affected
by a further examination of the subsurface material at the site.
Consequently the boring parties of the Commission sunk a large number
of bore-holes at six different sections or possible sites along the
river in the vicinity of the French location. These borings revealed
great irregularity in the character and disposition of the material
below the bed and banks of the river. In some places the upper stratum
of material was almost clear clay, and in other places clear sand,
while all degrees of admixture of clay and sand were also found. At
the French site the bed-rock at the deepest point is 143 feet below
sea-level, with large masses of pervious and semi-pervious sand,
gravel, and mixtures of those materials with clay. Apparently there is
a geological valley in the rock along the general course of the Chagres
River in this vicinity filled with sand, gravel, and clay, irregularly
distributed and with all degrees of admixture, large masses in all
cases being of open texture and pervious to water. The site adopted by
the commission for the purposes of its plans and estimates is located
nearly half a mile down the course of the river from that selected by
the new Panama Canal Company. The geological valley is nearly 2000 feet
wide at this location, but the deepest rock disclosed by the borings
of the commission is but 128 feet below sea-level. The actual channel
of the river is not more than 150 feet wide and lies on the extreme
easterly side of the valley. The easterly or right bank of the river at
this place is clean rock and rises abruptly to an elevation of about 40
feet above the river surface at ordinary stages. The left or westerly
bank of the river is compacted clay and sand, and rises equally as
abruptly as the rocky bank of the other side, and to about the same
elevation. From the top of the abrupt sandy clay bank a plateau of
rather remarkable uniformity of elevation extends for about 1200 feet
in a southwesterly direction to the rocky hill in which the Bohio
locks would be located. The rock slope on the easterly or northerly
bank of the river runs down under the sandy river-bed, but at such an
inclination that within the limits of the channel the deepest rock is
less than 100 feet below sea-level.
[Illustration]
[Illustration]
[Illustration: Profile of Bohio Dam Site, selected for Plans and
Estimate, with section of Dam.]
After the completion of all its examinations and after a careful study
of the data disclosed by them, the commission deemed it advisable to
plan such a dam as would cut off absolutely all possible subsurface
flow or seepage through the sand and gravel below the river surface.
It is to be observed that such a subsurface flow might either disturb
the stability of an earth dam or endanger the water-supply of the
summit level of the canal or both. The plan of dam finally adopted
by the commission for the purposes of its estimates is shown by the
accompanying plans and sections. A heavy core-wall of concrete masonry
extends from bed-rock across the entire geological valley to the top
of the structure, or to an elevation of 100 feet above sea-level, thus
absolutely closing the entire valley against any possible flow. The
thickness of this wall at the bottom is 30 feet, but at an elevation
of 30 feet below sea-level its sides begin to batter at such a rate as
to make the thickness of the wall 8 feet at its top. On either side of
this wall are heavy masses of earth embankment of selected material
properly deposited in layers with surface slopes of 1 on 3. As shown
by the plans, the lower portions of the core-wall of this dam would
be sunk to bed-rock by the pneumatic process, the joints between the
caissons being closed and sealed by cylinders sunk in recesses or
wells, also as shown by the plans.
=373. Variation in Surface Elevation of Lake.=—The profile of this
route shows that the summit level would have an ordinary elevation of
85 feet above the sea, but it may be drawn down for uses of the canal
to a minimum elevation of 82 feet above the same datum. On the other
hand, under circumstances to be discussed later, it may rise during
the floods of the Chagres to an elevation of 90 or possibly 91 or 92
feet above the level of the sea. The top of the dam therefore would be
from 8 to 10 feet above the highest possible water surface in the lake,
which is sufficient to guard against wash or overtopping of the dam by
waves. The total width of the dam at its top would be 20 feet, and the
entire inner slope would be paved with heavy riprap suitably placed and
bedded.
=374. Extent of Lake Bohio and the Canal Line in It.=—This dam would
create an artificial lake having a superficial area during high water
of about 40 square miles. The water would be backed up to a point
called Alhajuela, about 25 miles up the river from Bohio. For a
distance of nearly 14 miles, i.e., from Bohio to Obispo, the route of
the canal would lie in this lake. Although the water would be from 80
to 90 feet deep at the dam for several miles below Obispo, it would
be necessary to make some excavation along the general course of
the Chagres in order to secure the minimum depth of 35 feet for the
navigable channel.
[Illustration: Location of the Proposed Alhajuela Dam on the Upper
Chagres.]
=375. The Floods of the Chagres.=—The feature of Lake Bohio of the
greatest importance to the safe and convenient operation of the canal
is that by which the floods of the river Chagres are controlled or
regulated. That river is but little less than 150 miles long, and its
drainage area as nearly as can be estimated, contains about 875 square
miles. Above Bohio its current moves some sand and a little silt in
times of flood, but usually it is a clear-water stream. In low water
its discharge may fall to 350 cubic feet per second.
As is well known, the floods of the Chagres have at times been regarded
as almost if not quite insurmountable obstacles to the construction
of a canal on this line. The greatest flood of which there is any
semblance of a reliable record is one which occurred in 1879. No direct
measurements were made, but it is stated with apparent authority that
the flood elevation at Bohio was 39.3 feet above low water. If the
total channel through which the flood flowed at that time had been as
large as at present, actual gaugings or measurements of subsequent
floods show that the maximum discharge in 1879 might have been at the
rate of 136,000 cubic feet per second. As a matter of fact the total
channel section in that year was less than it is at the present time.
Hence if it be assumed that a flood of 140,000 cubic feet per second
must be controlled, an error on the safe side will be committed. Other
great floods of which there are reliable records are as follows:
1885 Height at Bohio 33.8 feet above low water.
1888: ” ” ” 34.7 ” ” ” ”
1890: ” ” ” 32.1 ” ” ” ”
1893: ” ” ” 28.5 ” ” ” ”
The maximum measured rate of the 1890 flood was 74,998 cubic feet per
second, and that of 1893, 48,975 cubic feet per second. It is clear,
therefore, that a flood-flow of 75,000 cubic feet per second is very
rare, and that a flood of 140,000 cubic feet per second exceeds that of
which we have any record for practically forty years.
=376. The Gigante Spillway or Waste-weir.=—It is obvious that the dam,
as designed by the commission, is of such character that no water must
be permitted to flow over its crest, or even in immediate proximity to
the down-stream embankment. Indeed it is not intended by the commission
that there shall be any wasteway or discharge anywhere near the dam. At
a point about 3 miles southwest of the site of the dam at Bohio is a
low saddle or notch in the hills near the head-waters of a small stream
called the Gigante River. The elevation of this saddle or notch is such
that a solid masonry weir with a crest 2000 feet long may readily be
constructed with its foundations on bed-rock without deep excavation.
This structure is called the Gigante spillway, and all surplus
flood-waters from the Chagres would flow over it. The waters discharged
would flow down to and through some large marshes, one called Peña
Blanca and another Agua Clara, before rejoining the Chagres. Inasmuch
as the canal line runs just easterly of those marshes, it would be
necessary to protect it with the levees or embankments to which
allusion has already been made. These embankments are neither much
extended nor very costly for such a project. The protection of the
canal would be further aided by a short artificial channel between the
two marshes, Peña Blanca and Agua Clara, for which provision is made
in the estimates of the commission. After the surplus waters from the
Gigante spillway pass these marshes they again enter the Chagres River
or flow over the low, half-submerged country along its borders, and
thence through its mouth to the sea near the town of Chagres, about 6
miles northwest of Gatun.
=377. Storage in Lake Bohio for Driest Dry Season.=—The masonry crest
of the Gigante spillway would be placed at an elevation of 85 feet
above the sea, identically the same as that which may be called the
normal summit level of the canal. It is estimated that the total uses
of water in the canal added to the loss by evaporation, taken at six
inches in depth per month, from the surface of the lake will amount
to about 1070 cubic feet per second if the traffic through the canal
should amount to 10,000,000 tons per annum in ships of ordinary size.
This draft per second is the sum of 406 cubic feet per second for
lockage, 207 for evaporation, 250 for leakage at lock-gates, and 200
for power and other purposes, making a total of 1063, which has been
taken as 1070 cubic feet per second. The amount of storage in Lake
Bohio between the elevations of 85 and 82 feet above sea-level, as
designed, is sufficient to supply the needs of that traffic in excess
of the smallest recorded low-water flow of the Chagres River during the
dry season of a low rainfall year. The lowest monthly average flow of
the Chagres on record at Bohio is 600 cubic feet per second for March,
1891, and for the purposes of this computation that minimum flow has
been supposed to continue for three months. This includes a sensible
margin of safety. In not even the driest year, therefore, can it be
reasonably expected that the summit level of the canal would fall below
the elevation of 82 feet until the total traffic of the canal carried
in ships of the present ordinary size shall exceed 10,000,000 tons.
If the average size of ships continues to increase, as will probably
be the case, less water in proportion to tonnage will be required for
the purposes of lockage. This follows from the fact that with a given
tonnage the greater the capacity of the ships the less the number
required, and consequently the less will be the number of lockages made.
[Illustration: The Eastern Face of the Culebra Cut.]
=378. Lake Bohio as a Flood controller.=—On the other hand it can be
shown that with a depth of 5 feet of water on the crest of the Gigante
spillway the discharge of that weir 2000 feet long will be at the rate
of 78,260 cubic feet per second. If the flood-waters of the Chagres
should flow into Lake Bohio until the head of water on the crest of
the Gigante weir rises to 7½ feet, the rate of discharge over that
weir would be 140,000 cubic feet per second, which, as already shown,
exceeds at least by a little the highest flood-rate on record. The
operation of Lake Bohio as a flood controller or regulator is therefore
exceedingly simple. The flood-waters of the Chagres would pour into the
lake and immediately begin to flow over the Gigante weir, and continue
to do so at an increasing rate as the flood continues. The discharge
of the weir is augmented by the increasing flood, and decreases only
after the passage of the crest of the flood-wave. No flood even as
great as the greatest supposable flood on record can increase the
elevation of the lake more than 92 to 92½ feet above sea-level, and
it will only be at long intervals of time when floods will raise that
elevation more than about 90 feet above sea-level. The control is
automatic and unfailingly certain. It prevents absolutely any damage
from the highest supposable floods of the Chagres, and reserves in
Lake Bohio all that is required for the purposes of the canal and
for wastage by evaporation through the lowest rainfall season. The
floods of the Chagres, therefore, instead of constituting the obstacle
to construction and convenient maintenance of the canal heretofore
supposed, are deprived of all their prejudicial effects and transformed
into beneficial agents for the operation of the waterway.
=379. Effect of Highest Floods on Current in Channel in Lake
Bohio.=—The highest floods are of short duration, and it can be stated
as a general law that the higher the flood the shorter its duration.
The great floods which it is necessary to consider in connection
with the maintenance and operation of this canal would last but a
comparatively few hours only. The great flood-flow of 140,000 cubic
feet per second would increase the current in the narrowest part of
the canal below Obispo to possibly 5 feet per second for a few hours
only, but that is the only inconvenience which would result from
such a flood discharge. That velocity could be reduced by additional
excavation.
=380. Alhajuela Reservoir not Needed at Opening of Canal.=—Inasmuch
as this system of control, devised and adopted by the Isthmian Canal
Commission, is completely effective in regulating the Chagres floods;
the reservoir proposed to be constructed by the new Panama Canal
Company at Alhajuela on the Chagres about 11 miles above Obispo is not
required, and the cost of its construction would be avoided. It could,
however, as a project be held in reserve. If the traffic of the canal
should increase to such an extent that more water would be needed for
feeding the summit level, the dam could be built at Alhajuela so as to
impound enough additional water to accommodate, with that stored in
Lake Bohio, at least five times the 10,000,000 annual traffic already
considered. Its existence would at the same time act with substantial
effect in controlling the Chagres floods and relieve the Gigante
spillway of a corresponding amount of duty.
=381. Locks on Panama Route.=—The locks on the Panama route are
designed to have the same dimensions as those in Nicaragua, as was
stated in the lecture on that route. The usable length is 740 feet
and the clear width 84 feet. They would be built chiefly of concrete
masonry, while the gates would be of steel and of the mitre type.
=382. The Bohio Locks.=—The great dam at Bohio raises the water
surface in the canal from sea-level in the Atlantic maritime section
to an ordinary maximum of 90 feet above sea-level; in other words,
the maximum ordinary total lift would be 90 feet. This total lift is
divided into two parts of 45 feet each. There is therefore a flight
of two locks at Bohio; indeed there are two flights side by side, as
the twin arrangement is designed to be used at all lock sites on both
routes. The typical dimensions and arrangements of these locks, with
the requisite culverts and other features, are shown in the plans and
sections between pages 396 and 397, Part V. They are not essentially
different from other great modern ship-canal locks. The excavation for
the Bohio locks is made in a rocky hill against which the southwesterly
end of the proposed Bohio dam rests, and they are less than 1000 feet
from it.
=383. The Pedro Miguel and Miraflores Locks.=—After leaving Bohio
Lake at Obispo a flight of two locks is found at Pedro Miguel, about
7.9 miles from the former or 21½ miles from Bohio. These locks have a
total ordinary maximum lift of 60 feet, divided into two lifts of 30
feet each. The fifth and last lock on the route is at Miraflores. The
average elevation of water between Pedro Miguel and Miraflores is 30
feet above mean sea-level. Inasmuch as the range of tide between high
and low in Panama Bay is about 20 feet, the maximum lift at Miraflores
is 40 feet and the minimum about 20. The twin locks at Miraflores bring
the canal surface down to the Pacific Ocean level, the distance from
those locks to the 6-fathom curve in Panama Bay being 8.54 miles. There
are therefore five locks on the Panama route, all arranged on the twin
plan, and, as on the Nicaragua route, all are founded on rock.
=384. Guard-gates near Obispo.=—Near Obispo a pair of guard-gates are
arranged “so that if it should become necessary to draw off the water
from the summit cut the level of Lake Bohio would not be affected.”
=385. Character and Stability of the Culebra Cut.=—An unprecedented
concentration of heavy cutting is found between Obispo and Pedro
Miguel. This is practically one cut, although the northwesterly end
toward Obispo is called the Emperador, while the deepest part at the
other end, about 3 miles from Pedro Miguel, is the great Culebra cut
with a maximum depth on the centre line of the canal of 286 ft. On page
93 of the Isthmian Canal Commission’s report is the following reference
to the material in this cut: “There is a little very hard rock at the
eastern end of this section, and the western 2 miles are in ordinary
materials. The remainder consists of a hard indurated clay, with some
softer material at the top and some strata and dikes of hard rock. In
fixing the price it has been rated as soft rock, but it must be given
slopes equivalent to those in earth. This cut has been estimated on
the basis of a bottom width of 150 feet, with side slopes of 1 on 1.”
When the old Panama Canal Company began its excavation in this cut
considerable difficulty was experienced by the slipping of the material
outside of the limits of the cut into the excavation, and the marks of
that action can be seen plainly at the present time. This experience
has given an impression that much of the material in this cut is
unstable, but that impression is erroneous. The clay which slipped
in the early days of the work was not drained, and like wet clay in
numerous places in this country it slipped down into the excavation.
This material is now drained and is perfectly stable. There is no
reason to anticipate any future difficulty if reasonable conditions
of drainage are maintained. The high faces of the cut will probably
weather to some extent, although experience with such clay faces on the
isthmus indicates that the amount of such action will be small. As a
matter of fact the material in which the Culebra cut is made is stable
and will give no sensible difficulty in maintenance.
[Illustration: The Culebra Cut.]
=386. Small Diversion-channels.=—Throughout the most of the distance
between Colon and Bohio on the easterly side of the canal the French
plan contemplated an excavated channel to receive a portion of the
waters of the Chagres as well as the flow of two smaller rivers,
the Gatuncillo and the Mindi, so as to conduct them into the Bay
of Manzanillo, immediately to the east of Colon. That so-called
diversion-channel was nearly completed. Under the plan of the
commission it would receive none of the Chagres flow, but it would be
available for intercepting the drainage of the high ground easterly
of the canal line and the flow of the two small rivers named, so that
these waters would not find their way into the canal. There are a few
other small works of similar character in different portions of the
line, all of which were recognized and provided for by the commission.
=387. Length and Curvature.=—The total length of the Panama route from
the 6-fathom curve at Colon to the same curve in Panama Bay is 49.09
miles. The general direction of the route in passing from Colon to
Panama is from northwest to southeast, the latter point being about
22 miles east of the Atlantic terminus. The depression through which
the line is laid is one of easy topography except at the continental
divide in the Culebra cut. As a consequence there is little heavy
work of excavation, as such matters go except in that cut. A further
consequence of such topography is a comparatively easy alignment, that
is, one in which the amount of curvature is not high. The smallest
radius of curvature is 3281 feet at the entrance to the inner harbor at
the Colon end of the route, and where the width is 800 feet. The radii
of the remaining curves range from 6234 feet to 19,629 feet.
The following table gives all the elements of curvature on the route
and indicates that it is not excessive:
+-----------------+-------+-------+----------------+
|Number of Curves.|Length.|Radius.|Total Curvature.|
+-----------------+-------+-------+----------------+
| | Miles | Feet. | ° ′ |
| 1 | 0.88 |19,629 | 14 17 |
| 1 | .48 |13,123 | 11 04 |
| 4 | 4.22 |11,483 | 111 32 |
| 15 | 11.61 | 9,842 | 355 50 |
| 4 | 2.44 | 8,202 | 90 20 |
| 2 | 1.67 | 6,562 | 77 00 |
| 1 | .73 | 6,234 | 35 45 |
| 1 | .82 | 3,281 | 75 51 |
| +-------+-------+----------------+
| | 22.85 | | 771 39 |
+-----------------+-------+-------+----------------+
=388. Principal Items of Work to be Performed.=—The principal items
of the total amount of work to be performed in completing the Panama
Canal, under the plan of the commission, can be classified as shown in
the following table:
Dredging 27,659,540 cu. yds.
Dry earth 14,386,954 ”
Soft rock 39,893,235 ”
Hard rock 8,806,340 ”
Rock under water 4,891,667 ”
Embankment and back-filling 1,802,753 ”
----------
Total 97,440,489 ”
Concrete 3,762,175 cu. yds.
Granite 13,820 ”
Iron and steel 65,248,900 lbs.
Excavation in coffer-dam 7,260 cu. yds.
Pneumatic work 108,410 ”
=389. Lengths of Sections and Elements of Total Cost.=—The lengths of
the various sections of this route and the costs of completing the work
upon them are fully set forth in the following table, taken from the
commission’s report, as were the two preceding:
TOTAL ESTIMATED COST.
--------------------------------------------+---------+------------
| Miles. | Cost.
--------------------------------------------+---------+------------
Colon entrance and harbor | 2.39 | $8,057,707
Harbor to Bohio locks, including levees | 14.42 | 11,099,839
Bohio locks, including excavation | .35 | 11,567,275
Lake Bohio | 13.61 | 2,952,154
Obispo gates | | 295,434
Culebra section | 7.91 | 44,414,460
Pedro Miguel locks, including excavation | |
and dam | .35 | 9,081,321
Pedro Miguel level | 1.33 | 1,192,286
Miraflores locks, including excavation | |
and spillway | .20 | 5,781,401
Pacific level | 8.53 | 12,427,971
Bohio dam | | 6,369,640
Gigante spillway | | 1,209,419
Peña Blanca outlet | | 2,448,076
Chagres diversion | | 1,929,982
Gatun diversion | | 100,000
Panama Railroad diversion | | 1,267,500
+---------+------------
Total | 49.09 | 120,194,465
Engineering, police, sanitation, and general| |
contingencies, 20 per cent. | | 24,038,893
+---------+------------
Aggregate | |$144,233,358
--------------------------------------------+---------+------------
The item in this table called Panama Railroad diversion affords
provision for the reconstruction of the railroad necessitated by the
formation of Lake Bohio. That lake would submerge the present location
of the railroad for 14 or 15 miles.
[Illustration: The Culebra Cut with Steamer Deutschland in it.]
=390. The Twenty Per Cent Allowances for Exigencies.=—It will
be observed that in the estimates of cost of the canal on both
the Nicaragua and the Panama routes, 20 per cent is allowed for
“engineering, police, sanitation, and general contingencies.” For the
purposes of comparison the same percentage to cover these items was
used on both routes. As a matter of fact the large amount of work
which has already been performed on the Panama route removes many
uncertainties as to the character of material and other features of
difficulty which would be disclosed only after the beginning of the
work in Nicaragua. It has therefore been contended with considerable
basis of reason that a less percentage to cover these uncertainties
should be employed in connection with the Panama estimates than in
connection with those for the Nicaragua route. Indeed it might be
maintained that the exigencies which increase cost should be made
proportional to the length of route and the untried features. On the
other hand, both Panama and Colon are comparatively large centres
of population, and, furthermore, there is a considerable population
stretched along the line of the Panama Railroad between those points.
The climate and the unsanitary condition of practically every centre
of population in Central America and on the isthmus contribute to the
continual presence of tropical fevers, and other diseases contingent
upon the existing conditions of life. It is probable, among other
things, that yellow fever is always present on the isthmus. Inasmuch as
the Nicaragua route is practically without population, the amount of
disease existing along it is exceedingly small, there being practically
no people to be sick. The initial expenditure for the sanitation of
the cities at the extremities of the Panama route, as well as for
the country between, would be far greater for that route than on the
Nicaragua. This fact compensates, to a substantial extent at least,
for the physical uncertainties on the Nicaragua line. Indeed a careful
examination of all the conditions existing on both routes indicates the
reasonableness of applying the same 20 per cent to both total estimates
of cost.
=391. Value of Plant, Property, and Rights on the Isthmus.=—The
preceding estimated cost of $144,233,358 for completing the Panama
Canal must be increased by the amount necessary to be paid for all the
property and rights of the new Panama Canal Company on the isthmus. A
large amount of excavation has been performed, amounting to 77,000,000
cubic yards of all classes of materials, and nearly all the right of
way has been purchased. The new Panama Canal Company furnished the
commission with a detailed inventory of its entire properties, which
the latter classified as follows:
1. Lands not built on.
2. Buildings, 2431 in number, divided among 47
subclassifications.
3. Furniture and stable outfit, with 17 subclassifications.
4. Floating plant and spare parts, with 24
subclassifications.
5. Rolling plant and spare parts, with 17 subclassifications.
6. Plant, stationary and semi-stationary, and spare parts,
with 25 subclassifications.
7. Small material and spare parts, with 4 subclassifications.
8. Surgical and medical outfit.
9. Medical stores.
10. Office supplies, stationery.
11. Miscellaneous supplies, with 740 subclassifications.
The commission did not estimate any value for the vast amount of plant
along the line of the canal, as its condition in relation to actual use
is uncertain, and the most of it would not be available for efficient
and economical execution of the work by modern American methods.
Again, a considerable amount of excavated material along some portions
of the line has been deposited in spoil-banks immediately adjacent to
the excavation from which it was taken, and would have to be rehandled
in forming the increased size of prism contemplated in the commission’s
plan.
In view of all the conditions affecting it, the commission made the
following estimate of the value of the property of the new Panama Canal
Company, as it is now found on the Panama route:
Canal excavation $21,020,386
Chagres diversion 178,186
Gatun diversion 1,396,456
Railroad diversion (4 miles) 300,000
-----------
22,895,028
Contingencies, 20 per cent 4,579,005
-----------
Aggregate 27,474,033
Panama Railroad stock at par 6,850,000
Maps, drawings, and records 2,000,000
-----------
$36,324,033
The commission added 10 per cent to this total “to cover omissions,
making the total valuation of the” property and rights as now existing,
$40,000,000.
In computing the value of the channel excavation in the above
tabulation it was estimated that “the total quantity of excavation
which will be of value in the new plan is 39,586,332 cubic yards.”
=392. Offer of New Panama Canal Company to Sell for $40,000,000.=—In
January, 1902, the new Panama Canal Company offered to sell and
transfer to the United States Government all its property and rights on
the isthmus of every description for the estimate of the commission,
viz., $40,000,000. In order to make a proper comparison between the
total costs of constructing the canal on the two routes it is necessary
to add this $40,000,000 to the preceding aggregate of $144,233,358,
making the total cost of the Panama Canal $184,233,358. It will be
remembered that the corresponding total cost of the Nicaragua Canal
would be $189,864,062.
[Illustration: The Railroad Pier at La Boca, the Panama end of the
Canal.]
=393. Annual Costs of Operation and Maintenance.=—It is obvious that
the cost of operating and maintaining a ship-canal across the American
isthmus would be an annual charge of large amount. A large organized
force would be requisite, and no small amount of material and work
of various kinds and grades would be needed to maintain the works in
suitable condition. The commission made very careful and thorough
studies to ascertain as nearly as practicable what these comparative
costs would be. In doing this it gave careful consideration to the
annual expenditures made in maintaining the various ship-canals of
the world, including the Suez, Manchester, Kiel, and St. Mary’s Falls
canals. The conclusion reached was that the estimated annual costs of
maintenance and operation could reasonably be taken as follows:
For the Nicaragua Canal $3,300,000
For the Panama Canal 2,000,000
----------
Difference in favor of Panama $1,300,000
=394. Volcanoes and Earthquakes.=—Much has been written regarding the
comparative liability to damage of canal works along these two routes
by volcanic or seismic agencies. As is well known, the entire Central
American isthmus is a volcanic region, and in the past a considerable
number of destructive volcanic eruptions have taken place at a number
of points. There is a line of live volcanoes extending southeasterly
through Nicaragua and Costa Rica. Many earthquake shocks have occurred
throughout Nicaragua, Costa Rica, and the State of Panama, some
of which have done more or less damage in large portions of those
districts. At the same time many buildings which have been injured have
not been substantially built. In fact that has generally been the case.
Both routes lie in districts that are doubtless subject to earthquake
shocks, but there is little probability that the substantial structures
of a canal along either line would be essentially injured by them. The
conclusions of the commission as to this feature of the matter are
concisely stated in three paragraphs at the top of page 170 of its
report:
“It is possible and even probable that the more accurately fitting
portions of the canal, such as the lock-gates, may at times be
distorted by earthquakes, and some inconvenience may result therefrom.
That contingency may be classed with the accidental collision of ships
with the gates, and is to be provided for in the same way, by duplicate
gates.
“It is possible also that a fissure might open which would drain the
canal, and, if it remained open, might destroy it. This possibility
should not be erected by the fancy into a threatening danger. If
a timorous imagination is to be the guide, no great work can be
undertaken anywhere. This risk may be classed with that of a great
conflagration in a city like that of Chicago in 1871, or Boston in 1872.
“It is the opinion of the commission that such danger as exists from
earthquakes is essentially the same for both the Nicaragua and Panama
routes, and that in neither case is it sufficient to prevent the
construction of the canal.”
The Nicaragua route crosses the line of live volcanoes running from
northwest to southeast through Central America, and the crater of
Ometepe in Lake Nicaragua is about 11 miles only from the line. The
eruptions of Pelée and Soufriere show that such proximity of possible
volcanic action may be a source of great danger, although even the
destruction by them does not certainly indicate damage either to
navigation or to canal structures at the distance of 11 miles. Whatever
volcanic danger may exist lies on the Nicaragua route, for there is no
volcano nearer than 175 miles to the Panama route.
=395. Hygienic Conditions on the Two Routes.=—The relative
healthfulness of the two routes has already been touched upon. There
is undoubtedly at the present time a vast amount of unhealthfulness
on the Panama route, and practically none on the Nicaragua route, but
this is accounted for when it is remembered, as has also been stated,
that there is practically no population on the Nicaragua route and
a comparatively large population along the Panama line. There is a
wide-spread, popular impression that the Central American countries
are necessarily intensely unhealthful. This is an error, in spite of
the facts that the construction of the Panama Railroad was attended
with an appalling amount of sickness and loss of life, and that records
of many epidemics at other times and in other places exist in nearly
all of these countries. There are the best of good reasons to believe
that with the enforcement of sanitary regulations, which are now well
understood and completely available, the Central American countries
would be as healthful as our Southern States. A proper recognition of
hygienic conditions of life suitable to a tropical climate would work
wonders in Central America in reducing the death-rate. At the present
time the domestic administration of most of the cities and towns of
Nicaragua and Panama, as well as the generality of Central American
cities, is characterized by the absence of practically everything which
makes for public health, and by the presence of nearly every agency
working for the diseases which flourish in tropical climates. When
the United States Government reaches the point of actual construction
of an isthmian canal the sanitary features of that work should be
administered and enforced in every detail with the rigor of the
most exacting military discipline. Under such conditions, epidemics
could either be avoided or reduced to manageable dimensions, but
not otherwise. The commission concluded that “Existing conditions
indicate hygienic advantages for the Nicaragua route, although it is
probable that no less effective sanitary measures must be taken during
construction in the one case than in the other.”
=396. Time of Passage through the Canal.=—The time required for
passing through a transisthmian canal is affected by the length, by
the number of locks, by the number of curves, and by the sharpness
of curvature. The speed of a ship, and consequently the time of
passage, is also affected by the depth of water under its keel. It
is well known that the same power applied to a ship in deep water
of unlimited width will produce a much higher rate of movement than
the same power applied to the same ship in a restricted waterway,
especially when the draft of the ship is but little less than the
depth of water. These considerations have important bearings both upon
the dimensions of a ship-canal and upon the time required to pass
through it. They were most carefully considered by the commission, as
were also such other matters as the delay incurred in passing through
the locks on each line, the latter including the delay of slowing or
approaching the lock and of increasing speed after passing it, the
time of opening and closing the gates, and the time of emptying and
filling the locks. It is also evident that ships of various sizes will
require different times for their passage. After giving due weight
to all these considerations it was found that what may be called an
average ship would require twelve hours for passing through the Panama
Canal and thirty-three hours for passing through the Nicaragua Canal.
Approximately speaking, therefore, it may be stated that an average
passage through the former waterway will require but one third the time
needed for the latter.
[Illustration: A Street in Panama.]
=397. Time for Completion on the Two Routes.=—The time in which an
isthmian canal may be completed and ready for traffic is an element of
the problem of much importance. There are two features of the work to
be done at Panama, each of which is of sufficient magnitude to affect
to a controlling extent the time required for the construction of the
canal, viz., the Bohio dam and the Culebra cut. Both of these portions
of the work may, however, be prosecuted concurrently and with entire
independence of each other. There are no such features on the Nicaragua
route, although the cut through the divide west of the lake is probably
the largest single work on that route. In considering this feature of
the matter it is well to observe that the total amount of excavation
and embankment of all grades on the Nicaragua route is practically
228,000,000 cubic yards, while that remaining to be done on the Panama
route is but little more than 97,000,000 cubic yards, or 43 per cent
of the former. The accompanying figures show the relative quantities of
total excavation, concrete, iron, and steel required in construction
along the two routes, as well also as the total amounts and radii of
curvature.
[Illustration: Diagrams comparing some of the main Elements of the two
Routes.]
The commission has estimated ten years for the completion of the
canal on the Panama route and eight years for the Nicaragua route,
including in both cases the time required for preparation and that
consumed by unforeseen delays. The writer believes that the actual
circumstances attending work on the two routes would justify an
exchange of these time relations. There is great concentration of
work in the Culebra-Emperador cut on the Panama route, covering about
45 per cent of the total excavation of all grades (43,000,000 cubic
yards), which is distributed over a distance of about 7 miles, with
the location of greatest intensity at Culebra. This demands efficient
organization and special plant so administered as to reduce the
working force to an absolute minimum by the employment of machinery
to the greatest possible extent. A judicious, effective organization
and plant would transform the execution of this work into what may be
called a manufactory of excavation with all the intensity of direction
and efficiency of well designed and administered machinery which
characterizes the concentration of labor and mechanical appliances in
great manufacturing establishments. Such a successful installation
would involve scarcely more advance in contract operations than was
exhibited, in its day, in the execution of the work on the Chicago
Drainage-canal. By such means only can the peculiar difficulties
attendant upon the execution of great works in the tropics be reduced
to controllable dimensions. The same general observations may be
applied to the construction of the Bohio dam, even should a no more
favorable site be found.
The greatest concentration of excavation on the Nicaragua route is
between the lake and the Pacific, but it constitutes only 10 per cent
of the total excavation of all grades, and it can be completed in far
less time than the great cut on the Panama route. If this were the
only great feature of work besides the dam, the time for completion
of work on this route would be materially less than that required for
the Panama crossing. As a matter of fact, there are a succession of
features of equivalent magnitude, or very nearly so, from Greytown
nearly to Brito, extending over a distance of at least 175 miles,
requiring the construction of a substantial service railroad over a
considerable portion of the distance prior to the beginning of work.
This attenuation of work requires the larger features to be executed in
succession to a considerable extent, or much duplication of plant and
the employment of a great force of laborers, practically all of whom
must be foreigners, housed, organized, and maintained in a practically
uninhabited tropical country where many serious difficulties reach a
maximum. It is not within the experience of civil engineers to execute
by any practicable means that kind of a programme on schedule time.
The weight of this observation is much increased when it is remembered
that the total volume of work may be taken nearly twice as great in
Nicaragua as at Panama, and that large portions between Lake Nicaragua
and the Caribbean Sea must be executed in a region of continual and
enormous rainfall. It would seem more reasonable to the writer to
estimate eight years for the completion of the Panama Canal and ten
years for the completion of the Nicaragua Canal.
=398. Industrial and Commercial Value of the Canal.=—The prospective
industrial and commercial value of the canal also occupied the
attention of the commission in a broad and careful study of the
elements which enter that part of the problem. It is difficult if not
impossible to predict just what the effect of a transisthmian canal
would be either upon the ocean commerce of the United States or of
other parts of the world, but it seems reasonable to suppose from the
result of the commission’s examinations that had the canal been in
existence in 1899 at least 5,000,000 tons of the actual traffic of
that year would have been accommodated by it. The opening of such a
waterway, like the opening of all other traffic routes, induces the
creation of new traffic to an extent that cannot be estimated, but it
would appear to be reasonable to suppose that within ten years from the
date of its opening the vessel tonnage using it would not be less than
10,000,000 tons.
[Illustration: View of Panama.]
The Nicaragua route would favor in distance the traffic between our
Atlantic (including Gulf) and Pacific ports. The distances between
our Atlantic ports and San Francisco would be about 378 nautical
miles less than by Panama. Between New Orleans and San Francisco
this difference in favor of the route by Greytown and Brito would be
580 nautical miles. It must be remembered, however, that the greater
time by at least twenty-four hours required for passage through the
Nicaragua Canal practically obliterates this advantage, and in some
cases would throw the advantage in favor of the Panama waterway. This
last observation would hold with particular force if for any reason
a vessel should not continue her passage, or should continue it at a
reduced speed during hours of darkness, which could not be escaped on
the Nicaragua Canal, but might be avoided at Panama. For all traffic
between the Atlantic (including Gulf) ports and the west coast of
South America the Panama crossing would be the most advantageous. As a
matter of fact, while there may be some small advantage in miles by one
route or the other for the traffic between some particular points, on
the whole neither route would have any very great advantage over the
other in point of distance or time; either would serve efficiently the
purposes of all ocean traffic in which the ports of the United States
are directly interested.
The effect of this ship waterway upon the well-being of the United
States is not altogether of a commercial character. As indicated by
the commission, this additional bond between the two portions of the
country will have a beneficial effect upon the unity of the political
interests as well as upon the commercial welfare of the country. Indeed
it is the judgment of many well-informed people that the commercial
advantages resulting from a closer touch between the Atlantic and
Pacific coasts of the country are of less consequence than the unifying
of political interests.
In a final comparison between the two routes it is to be remembered
that the concession under which the new Panama Company has been and
is now prosecuting its work is practically valueless for the purposes
of this country. It will therefore be necessary to secure from the
republic of Colombia, for the Panama route, as well as from the
republics of Nicaragua and Costa Rica, for the Nicaragua route, such
new concessions as may be adequate for all the purposes of the United
States in the construction of this transisthmian canal. The cost of
those concessions in either case must be added to the estimated total
cost of the work, as set forth, in order to reach the total cost of the
canal along either route.
=399. Comparison of Routes.=—Concisely stating the situation, its main
features may be expressed somewhat as follows:
Both routes are entirely “practicable and feasible.”
Neither route has any material commercial advantage over the other as
to time, although the distance between our Atlantic (including Gulf)
and Pacific ports is less by the Nicaragua route.
The Panama route has about one fourth the length of that in Nicaragua;
it has less locks, less elevation of summit level, and far less
curvature, all contributing to correspondingly decreased risks peculiar
to the passage through a canal. The estimated annual cost of operation
and maintenance of the Panama route is but six tenths that for the
Nicaragua route.
The harbor features may be made adequate for all the needs of a canal
by either route, with such little preponderance of advantage as may
exist in favor of the Panama crossing.
The commission estimated ten years for the completion of the Panama
Canal and eight years for the Nicaragua waterway, but the writer
believes that these relations should be exchanged, or at least that the
time of completion for the Panama route should not be estimated greater
than for the Nicaragua.
The water-supply is practically unlimited on both routes, but the
controlling or regulating works, being automatic, are much simpler and
more easily operated and maintained on the Panama route.
The Nicaragua route is practically uninhabited, and consequently
practically no sickness exists there. On the Panama route, on the
contrary, there is a considerable population extending along the entire
line, among which yellow fever and other tropical diseases are probably
always found. Initial sanitary works of much larger magnitude would be
required on the Panama route than on the Nicaragua, although probably
as rigorous sanitary measures would be required during the construction
of the canal on one route as on the other.
The railroad on the Panama route and other facilities offered by a
considerable existing population render the beginning of work and the
housing and organization of the requisite labor force less difficult
and more prompt than on the Nicaragua route.
The greater amount of work on the Nicaragua route, and its distribution
over a far greater length of line, involve the employment of a
correspondingly greater force of laborers, with greater attendant
difficulties, for an equally prompt completion of the work.
The relative seismic conditions of the two routes cannot be
quantitatively stated with accuracy, but in neither case are they of
sufficient gravity to cause anxiety as to the effects upon completed
canal structures.
Concessions and treaties require to be secured and negotiated for the
construction of the canal on either route, and under the conditions
created by the $40,000,000 offer of the new Panama Canal Company
this feature of both routes appears to possess about the same
characteristics, although the Nicaragua route is, perhaps, freer from
the complicating shadows of prior rights and concessions.
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