WORKS OF PROF. WALTER LORING WEBB PUBLISHED BY JOHN WILEY & SONS. Railroad Construction. — Theory and Practice. A Text-book for the Use of Students in Colleges and Technical Schools. Fourth Edition. Revised and Enlarged. 16mo. xvi + 777 pages and 234 figures and plates. Morocco, $5.00. Problems in the Use and Adjustment of Engineer- ing: Instruments. Forms for Field-notes; General Instructions for Extended Students' Surveys. 16mo. Morocco, $1.25. The Economics of Railroad Construction. Small 8vo. Second Edition, vii +347 pages, 35 figures. Cloth, $2.50. The American Civil Engineers' Pocket Book (Author of Section on Railroads.) Large 16mo. Morocco, $5.00. THE ECONOMICS OF RAILROAD CONSTRUCTION BY WALTER LORINTG WEBB, C.E. Member American Society of Civil Engineers; Member American Railway Engineering Association; Assistant Professor of Civil Engineering (Railroad Engineering) in the University of Pennsylvania, 1893-1901; etc. SECOND EDITION, THOROUGHLY REVISED FIRST THOUSAND NEW YORK JOHN WILEY & SONS London: CHAPMAN & HALL, Limited 1912 D° ^V Copyright, 1906, 1912, BY WALTER LORING WEBB, THE SCIENTIFIC PRESS ROBERT DRUMMOND AND COMPANY BROOKLYN, N. Y. CI.A327767 CONTENTS. Introduction PART I. FINANCIAL AND LEGAL ELEMENTS OF THE PROBLEM. CHAPTER I. Railroad Statistics 4 Mileage, 4. Capitalization, 10. Public service of railways, 11. Employees, 12. Accidents, 12. Use of statistical averages, 15. CHAPTER IL The Organization of Railroads 16 Economic justification of railroad projects, 16. Basis of ownership of railroad property, 17. Charters, 19. General railroad laws, 20. General railroad law of the State of New York, 21. CHAPTER III. Capitalization 25 Stock, 25. Funded debt, 26. Dividends on stock, 29. Interest on bonds, 31. Taxes, 32. Small margin between profit and loss, 36. Variation in dividends due to small variations in business done, 39. Practical limitations of capitalization, 40. Principles which should govern the amount of capital to be raised, 41. CHAPTER IV. The Valuation of Railway Property 43 Objects, 43. Nominal valuation, 43. Cost-of-replacing- property method, 45. Valuation of physical properties and iv CONTENTS. PAGE franchise, 47. Stock-market valuation, 49. Valuation by capitalizing the net earnings, 49. Legal Control, 54. Basis of freight-rates, 54. Direct competition, 57. Indirect competition, 58. Justification of special commodity rates, 60. Low rates on low-grade freight, 60. Federal Control: Origin, 61. Necessity for control, 62. Pooling, 63. Traffic associations, 64. Consolidation, 65. State Control: Scope and limitations, 66. CHAPTER V. Estimation of Volume of Traffic 68 Primary considerations, 68. Methods of estimating volume of traffic, 70. Seasonal variations, 72. Estimate of earnings per mile of road, 74. Estimate of tributary population, 76. Estimate by comparison with other roads, 77. Actual esti- mation of the sources of revenue, 78. Statistics of average traffic, 80. Train mile statistics, 82. Proportions of various classes of commodities carried, 82. Conditions which Affect Volume of Traffic : Proximity to sources of traffic, 84. Estimation of effect of location of station at a distance from a business center, 86. Extent of monopoly in railroad business, 87. PART II. OPERATING ELEMENTS OF THE PROBLEM. CHAPTER VI. Operating Expenses Classification of operating expenses, 89. Average operating expenses per train-mile, 91. Itemized classification of oper- ating expenses, 99. Maintenance of Way and Structures: Track material, 99. Roadway and track, 100. Maintenance of track structures, 101. Maintenance of Equipment: Superintendence of equipment, 102. Repairs, renewals and depreciation of steam locomotives, 102. Repairs, renew- als and depreciation of electric locomotives, 103. Repairs, renewals and depreciation of passenger-train cars and of freight cars, 104. Electric equipment; floating equipment; work equipment; shop machinery and tools; power plant equip- ment; miscellaneous items, 105. Traffic, 105. Transpor- tation: Yard engine expenses, 105. Road engine-men, 106. Fuel for road locomotives, 107. Water, lubricants and CONTENTS. other supplies, 108. Road trainmen, 108. Train supplies and expenses, 109. Clearing wrecks, loss, damage and injuries to persons and property, 109. Operating joint tracks and facilities, Dr. and Cr., 110. Switching charges, 112. Other items, 112. Estimation of the effect on operating expenses of a change in alinement, 112. Reliability of such estimates, 113. CHAPTER VII. Motive Power 116 Economics of the Locomotive : Total cost of power by the use of locomotives, 116. Renewals of locomotives, 117. Repairs of locomotives, 119. Wages of road enginemen, 122. Fuel for locomotives, 124. Water-supply — impurities, 127. Methods of water purification, 130. Pumping water, 131. Lubricants for road locomotives, 132. Comparative cost of various types of locomotives, 133. Statistics on locomotives, 134. The Economics of Heavy Locomotives : The problem stated, 135. Economy effected by handling a given traffic with one less train, 137. Maintenance of way and structures, 138. Maintenance of equipment, 139. Transportation, 141. Numer- ical illustration, 144. CHAPTER VIII. Economics of Car Construction 146 Weight of cars, 147. Ratio of live load to dead load, 147. Economics of high-capacity cars, 148. Use of air- or train- brakes, 150. Use of automatic couplers, 151. Draft-gear, 151. Spring draft-gear, 152. Friction draft-gear, 155. CHAPTER IX. Track Economics 159 Rails: Rail wear — theoretical, 159. Rail wear — statis- tics, 162. Rail-wear statistics on the Northern Pacific R. R., 164. Relation of rate of rail wear to the life-history of the rail, 166. Rail wear on curves, 168. Economics of Ties: Importance of the subject, 171. Methods of deterioration and failure of ties, 171. The actual cost of a tie, 172. Chem- ical treatment of ties, 174. Comparative value of cross-ties vi CONTENTS. PAGE of different materials, 175. Economy due to form of tie, 180. Protection against wear by using tie-plates, 181. Use of screw-spikes, 182. Use of dowels, 184. CHAPTER X. Train Resistance 186 Classification of the various forms, 186. Resistances in- ternal to the locomotive, 187. Velocity resistances, 188. Wheel resistance, 190. Grade resistance, 192. Curve resist- ance, 195. Brake resistance, 196. Inertia resistance, 197. Train-resistance formulae, 200. Comparison of the above formulae, 204. Dynamometer tests, 205. CHAPTER XI. Momentum Grades 208 Velocity head, 208. Practical use of Table XX, 210. Accuracy of the above statement, 212. Utilization of Table XX, 215. Momentum Diagrams and Tonnage Ratings: Tonnage rating, 217. Tonnage rating of locomotives, 217. Tonnage rating for a given grade and velocity, 219. Accelera- tion curves, 221. Retardation curves, 225. Practical utili- zation of these diagrams, 227. Another tonnage-rating formula (Henderson), 231. PART III. PHYSICAL ELEMENTS OF THE PROBLEM. CHAPTER XII. Distance 233 Relation of distance to rates and expenses, 233. The conditions other than distance that affect the cost; reasons why rates are usually based on distance, 234. Variable effect on expenses of extent of change in distance, 235. Effect of Distance on Operating Expenses: Effect of changes in distance on maintenance of way, 236. Effect on maintenance of equipment, 238. Effect on conducting trans- portation, 242. Road enginemen, 242. Fuel, 242. Minor engine supplies, 245. Train-supplies and expenses, 246. Signals, flagmen, and gatemen, 246. Telegraph expenses, 246. Estimate of total effect on expenses of small changes in CONTENTS. vii PAGE distance (measured in feet); also estimate for distances measured in miles, 248. Effect of Distance on Receipts: Classification of traffic, 249. Method of division of through rates between the roads on which through traffic is carried, 250. Effect of a change in the length of the road on its receipts from through-competitive traffic, 252. Application of the above principle, 254. General conclusions regarding a change in distance, 254. Justification of decreasing distance to save time, 256. Effect of change of distance on the business done, 256. CHAPTER XIII. Curvature 258 General objections to curvature, 258. Financial value of the danger of accident due to curvature, 259. Effect of curvature on traffic, 260. Effect of curvature on the operation of trains, 261. Limiting the use of heavy engines, 262. Effect of Curvature on Operating Expenses: Relation of radius of curvature and of degrees of central angle to operating expenses, 262. Effect of curvature on maintenance of way, 265. Renewals of ties, 266. Renewals of rails, 266. Repairs of roadway, 267. Effect of curvature on main- tenance of equipment, 267. Repairs and renewals of locomo- tives, 267. The repairs and renewals of shop machinery, 268. Effect of curvature on conducting transportation, 269. Flag- men, 269. Estimate of total effect per degree of central angle, 270. Numerical illustration, 272. Reliability and value of the above estimate, 275. Compensation for Curvature: Reasons for compensation, 276. The proper rate of compensa- tion, 279. The limitations of maximum curvature, 281. CHAPTER XIV. Minor Grades 284 Two distinct effects of grade, 284. Basis of the cost of minor grades, 286. Meaning of " rise and fall," 287. Classi- fication of minor grades, 289. Effect on operating expenses, 291. Renewals of ties, 291. Renewals of rails, 291. Road- way and track, 292. Maintenance of equipment, 292. Con- ducting transportation, 293. Estimate of cost of one foot of change of elevation, 293. Numerical illustration, 295. viii CONTENTS. CHAPTER XV. PAGE Ruling Grades 297 Definition, 297. Choice of ruling grade, 298. Maximum train-load on any grade, 299. Proportion of traffic affected by the ruling grade, 301. Financial value of increasing the train-load, 303. Maintenance of equipment, 304. Con- ducting transportation, 306. Numerical illustration, 307. CHAPTER XVI. Pusher Grades 311 General principles underlying the use of pusher-engines, 311. Numerical illustration of the general principle, 312. Equating through grades and pusher grades, 313. Method of operation of pusher grades, 318. Length of a pusher grade, 322. The cost of pusher-engine service, 322. Numerical illustrations of the cost of pusher service, 324. CHAPTER XVII. Balancing Grades for Unequal Traffic 327 Nature of the subject, 327. Illustrations in the balancing of grades, 328. Principles on which the theoretical balance must be computed, 328. Numerical illustration, 330. Re- liability of calculations of this nature, 331. Index > 333 THE ECONOMICS OF EAILEO AD CONSTRUCTION. INTRODUCTION. Owing to the diversity of opinion existing among rail- road men as to the proper scope of a book on railroad economics, a word of introduction is necessary. (^Railroad economics, in its broadest sense, covers the entire subject of railroad engineering, from the most simple feature of railroad surveying to the weightiest questions of railroad practice or legislation which could be brought before the Interstate Commerce Commission, Congress, or the United States Supreme Court.) While it is of course desirable that an engineer should have as broad a knowledge as possible of every phase of railroad management and legis- lation, it should not be forgotten that his primary work is that of construction, maintenance, and operation. If the railroad engineer should develop into the railroad president, the larger questions must be answered, but even in such a case an encyclopedia of railroad science would not cover the ground with which he should be familiar. It is assumed that those who read or study this book are already familiar with the mechanical processes used in railroad surveying and construction ; that they know how to survey a line (when the economic questions of its loca- tion have been decided), and how to build a line as thus 2 THE ECONOMICS OF RAILROAD CONSTRUCTION. laid out. Of course many of the simpler economic prin- ciples will have been included in any good course in sur- veying and construction. But such courses do not usually include an exhaustive exposition of the reasons why cer- tain grades should be adopted, or why a certain large expenditure for a tunnel, bridge, or other special con- struction-may (or may not) be justifiable. The justifica- tion of improvements by changes in alinement also comes within the scope of the engineer. The constructing engineer should also know enough of the work of opera- tion to understand the effect on operation of constructive details. This requires a knowledge of operating expenses, locomotive and car construction, train-resistance, and the operation of heavy trains on grades. Even then the con- structive engineer is not equipped for his work until he has dipped into law and finance — until he understands the legal method of organization and the methods of the world of railroad finance. Rising still higher, the railroad man is sometimes con- fronted with an apparent conflict between a policy which would best serve the public, and a policy which would afford greater immediate profit to the stockholders. , Probably such conflicts are more apparent than real. History has invariably shown that the prosperity of a railroad is closely bound up with that of the community which it serves, and that in the long run the interests of the stockholders are best promoted by policies which give the best possible service to the public. This book is therefore written from the standpoint of the constructing or operating engineer. The railroad lawyer or legislator would find little or nothing in it which he can use, and much in which he is not interested. Even the professor of social economics will find that it is written from the technical standpoint rather than from the social viewpoint, and yet (as before mentioned) it will be em- INTRODUCTION. 3 phasized that the best social standpoint will also prove to be the best technical standpoint. The practicable size of this book has also been consid- ered. An adequate discussion of railroad legislation alone would more than fill a book of this size. Therefore legis- lation and kindred subjects are only considered very briefly, and almost exclusively as they affect qu3stions which must be answered by a railroad engineer. The author wishes to acknowledge his indebtedness to many engineers throughout the country who have fur- nished him with some very valuable technical information. The sources of such information have each been indicated during its discussion. Those familiar with recent railroad literature, especially the books dealing with railroad legislation, the regulation of rates, etc., will appreciate the author's indebtedness to some of them. The chapters of this book dealing with kindred subjects attempt to give an abridged outline of some of the most salient features of these valuable addi- tions to railroad science. For more complete discussions the student should read the following: "Railway Legisla- tion in the United States/' by Dr. B. H. Meyer; "Restric- tive Railway Legislation/' by H. S. Haines; "American Railway Transportation," by E. R. Johnson; "The Ele- ments of Railway Economics/' by W. M. Acworth; "Rail- road Transportation," by A. T. Hadley; and "American Railroad Rates/' by W. C. Noyes. The preparation of the second edition has required a very extensive revision and even the rewriting of several sections and the compilation of revised tables in order to make the computations correspond with the classifica- tion of operating expenses now used by the Interstate Commerce Commission. But the general principles used are the same as those laid down in the first edition. PART I. FINANCIAL AND LEGAL ELEMENTS OF THE PROBLEM. CHAPTER I. RAILROAD STATISTICS. i. Mileage. — A study of the growth of railroad mileage during a period of years will reveal many instructive features of railroad progress. In the following chapter will be given several tables of statistics showing the growth of the railroad industry, especially during later years. From such tables it is possible to draw conclusions, regard- ing the present status of railroad business and its probable future growth, which will be of considerable value to the railroad engineer in understanding many of the problems which must be solved. But it should not be forgotten that the proper interpretation of statistics is not easy, and that wrong conclusions may readily be drawn from them. An endeavor will be made to point out some of the legitimate conclusions which these statistics indicate. In Table I is given the mileage in the United States for each year from 1870 to 1910, the increase for each year, the number of miles of line per 100 square miles of terri- tory, the number of miles of line per 10,000 inhabitants, and the total railway capital per mile of line. The figures for the year 1888 and later are taken from the reports of the Interstate Commerce Commission. Those for previous 4 RAILROAD STATISTICS. o years have been taken from various sources, chiefly the annual issues of Poor's Manual. The figures given in the later issues of Poor's Manual do not agree exactly with those from the Interstate Commerce Commission, although the agreement is sufficiently close for any deductions which we may here wish to draw from the figures. It should be noted that the " number of miles of line " does not consider whether the road has one track, two, three, or four, nor that a mile of line in one place may be worth ten or twenty times a mile of line in some other place. The growth of the mileage may be most readily studied by an inspection of Fig. 1. The steeper the line, the more rapid has been the growth in mileage. The annual in- crease arid its fluctuations are more readily seen in Fig. 2. For several years after the "boom " times of 1870 to 1873 but little was done, until another boom began about 1878-9. This culminated in 1882 and dropped suddenly in 1884-5. After the panic year of 1893 but little was done until 1898-9. Then another boom started which had its culmination in 1906. The panic of 1907 was fol- lowed by the usual slump. The " number of miles of line per 100 square miles of territory " is shown graphically in Fig. 3. Since the area considered is constant, the number constantly increases. The rate of growth is indicated by the steepness of the " mileage curve " and also by the ordinates of the " dif- ferential curve." The differences are given in column 4 of Table I. In column 5 of Table I is shown the " number of miles of line per 10,000 inhabitants." The number reached a maximum in 1893. The check in railroad building caused by the panic of that year caused a gradual reduction in the ratio, which meant that the population was growing faster than the building of railroads. This tendency was not checked until 1899. After that year the prosperity C) THE ECONOMICS OF RAILROAD CONSTRUCTION. of the country again so increased that it could afford more miles of railroad per 10,000 inhabitants. Apparently following an inevitable law, the next local maximum 250 000 200000 §150 0Q0 100000 50000 ! I jm w a bl 3 _5 c >> ^& a ■J ( B ."' 2 & > p, V 33 ,<" - c 'E 3 = o £ 55 £ - ■5 A ■°. p £. r- ^ -< bJC ■~ s - •r. : _o pq Steepness bf ine indicates - >- rate of new construction s > p — -c -7. — y > S 1 1870 1 2 3 4 5 6 7 8 91! 2 3 4 5 6 7 8 91890.1 2 3 4 5 6 7 8 919001 2 3 4 5 6 7 8 91910 Fig. 1. — Total railroad mileage in the United States. in this figure was reached in the fateful year 1907. and since then there has been another slump. The " total railway capital per mile of line " has re- mained fairly constant. Disregarding the value given for 1870, which is of somewhat doubtful accuracy, the remaining figures are marvelously uniform, until the last few years, when the enormous and revolutionary improve- ments in road-bed, track, rolling stock and structures have demanded a substantial increase in capitalization. But the great development in the essential value of the roads of the country between 1875 and 1900, with no increase in capitalization per mile, was accomplished chiefly by making improvements out of earnings and perhaps occasionally by requiring fuller payments on stock subscriptions. In general, the capitalization has become a truer measure of money invested than it was, RAILROAD STATISTICS. M o o o o g 8 OS s-1 o s e "P 2! a SI imp fol owi Dg] Pan c ^- S Boom Ye irs / SI ami )fol low ngr Boo m u< /* X N s, Inl atic D p rect din ?P£ nic — - — ■ • o Pa lie i'ea • Ski mp foil >wi »g I ani : J ° Bo< jin ' reai a ^1 ^ Slu np folic iwii g:P anic CO 8 THE ECONOMICS OF RAILROAD CONSTRUCTION. ui © ux -s £ CD »-* O ® Mi ea i » c 4 1 i I f E Diff . c 5 O 8 k \ 3 o \ \ \ "Pai ie y •ar \ Oi OS 1 \ Slump a£ er i uric \ \ / \ ^ M \ v '4>, § % S >*N 4 r oom yea 1 ^» ¥ ^ >■" -*" r S" I •^ r? i -3 $v y (91 < ^ A l-» > o Pai ic-y •ar— SI umi aft* v pa nic \ \ . g \ \ 1 \ \ T ) i \ « / \ S \ f \ ] y \ • \ J f \ fn I 1 k Panic year Slump Partial recovery Effect of Anti-railroad legislation RAILROAD STATISTICS. Table I. — Railroad Statistics. 1 Year. 2 Mileage. 3 Annual increase. 4 Number of miles of line per 100 square miles of territory. 5 Number of miles of line per 10,000 inhabitants. 6 Total railway- capital per mile of line. 1870 71 72 73 74 1875 76 77 78 79 1880 81 82 83 84 1885 86 87 52,914 60,293 66,171 70,268 72,383 74,096 76,808 79,089 81,776 86,497 93,349 103,145 114,713 121,454 125,379 128,967 136,338 142,776 6,070 7,379 5,878 4,097 2,117 1,711 2,712 2,280 2,629 4,746 6,886 9,796 11,568 6,741 3,825 3,588 7,371 6,438 Diff. 178 25 2.03 ^ 2.23 'fi 2.37 - 14 244 .06 2.50 Q9 2.59 ■$ 2.66 -^ 2.75 Va 2.91 it 3.14 oq 3.47 ■»» 3.86 ^ 4.09 fo 4.22 \l 4.34 9 , 4.59 -;2 481 :S 13.72 15.18 16.19 16.71 16.76 16.74 16.87 16.94 17.08 17.65 18.61 20.06 21.77 22.51 22.71 22.83 23.61 24.19 $44,255 59,726 55,116 57,136 60,944 61,534 60,791 60,699 58,916 58,070 58,624 60,645 60,830 61,592 60,886 60,897 60,564 58,093 *1888 89 1890 91 92 93 94 1895 96 97 98 99 1900 01 02 03 04 1905 06 07 08 09 1910 149,902 157,759 163,597 168,403 171,564 176,461 178,709 180,657 182,777 184,428 186,396 189,295 193,346 197,237 202,472 207,977 213,904 218,101 224,363 229,951 233,678 236,869 240,439 7,126 7,857 5,838 4,806 3,161 4,898 2,247 1,949 2,119 1,652 1,968 2,898 4,051 3,892 5,234 5,505 5,927 4,197 6,262 5,588 3,727 3,191 3.605 496 .26 O . ZZ c\(\ 5.51 lfi 5.67 \l 5.78 ;.JJ lit ;>>>>^- / /?777 60" - ^5?^ 1rfm//;A ''^fofs. \1/ 50 IE 1 1 I "^s. i£ Percentage oj stocktaking NO dividend ■> / 40 y, (below the shaded 1 me) ""-*-< >—, — i : 1 \ y^^Z+X^ ,^^95 vfr 30 '/, X L-*-t4^ *■•"% ^ -, « i^ j*&»Xvfi Wr>ia2+7-k 1 • 20 v^' v " ^-.ftiX 1 ^ r ,Vs 1 ' i 5* _lj J&*\ rq£#r 1 10 ■ > '/, 1 '"/.A. ■ •■:...■'■ ; . •/•,.;■- 1888 9 1890 12 3 4 5 1900 12 3 4 5 6 9 1910 Fig. 5. — Percentage of stocks paying no dividends; also average rate paid by dividend-paying stocks. dividends has been reduced to about 35%, and yet the last few years have been the most prosperous years known in railroad history. There is some mitigation of the above gloomy view when we consider that a large proportion, if not the total, of the stock of many small branch railroads is owned by the larger trunk lines, with which they connect, in their corporate capacity. The larger railroads utilize these smaller roads as feeders which add to the earnings of the main line. Even though the earnings directly assignable to the branch line are not sufficient to earn more than enough to pay the operating expenses and the CAPITALIZATION. 31 interest on the bonds, the larger railroad company as owner is securing a return on its investment, in the indirect form of through- business furnished to its main line, which adds to the receipts of the main line far more than the added business costs. The fact that about 30% of all railroad stocks outstanding are owned by railways in their corporate capacity, and that some of it brings an indirect, if not direct, return, materially modifies the above statement regarding stocks which do not pay dividends. * If we analyze the situation with respect to different sections of the country, we find a very marked differ- ence. Group VII, comprising the region between the Rocky Mountains and the Missouri River, has the best record regarding roads which failed to declare divi- dends, less than 8.5% having failed to do so. Over 40% of the stock in that group paid from 7 to 8 per cent. The largest amount of stock belongs to Group II; in this group a large percentage paid from 4 to 8 per cent. The Pacific States, Group X, are erratic, over 80% paying no dividends while 1|% paid over 10%. 15. Interest on bonds. — The record of the payment of interest on bonds is of necessity far better than that of paying dividends on stock. Excluding equipment trust obligations from consideration, less than 4J% of the bonds defaulted their interest. Although the very large bulk of bonds pay from 3 to 6% interest, there is a con- siderable percentage which pays 7 or 8% and even a little over. Considering the railroads of the United States as one system (and thus eliminating the intercorporate pay- ments made to a railroad which owns the bonds of another road), the net interest on the funded debt for 1903 and 1904 required a little over 14% of the gross earnings from * The figures in this and the following paragraphs were taken from the I. C. C. report for the year ending June 30, 1904. 32 THE ECONOMICS OF RAILROAD CONSTRUCTION. operation. Even this figure is a considerable reduction from the corresponding figures for previous years, owing largely to the general policy of refunding railroad secur- ities at a lower rate of interest. Although there is a very large variation in individual cases of the proportion of gross earnings which must be paid out for interest on the funded debt, it is remarkable that such a large percentage of all railroads expend nearly the same proportion of their gross earnings in this way. This uniformity seems to be regardless of the length of the road, except that, the larger the system, the greater the probability that the average figure will be approached. The largest variations from average figures occur with very small branch fines which are operated under special operating conditions and financial agreements. 1 6. Taxes. — The item of taxes is usually included under fixed charges. For the year ending June 30, 1904, the total amount paid in taxes by the railroads of the United States amounted to $61,658,373. Of this amount $1,324,- 808 was paid upon property owned by railroad corpora- tions but not used in operation. If we deduct this from the total, we have, as the amount of this expense assigned to operation, $60,333,565. The commercial valuation of railroad property as given by the Bureau of the Census for the same year, was $11,244,852,000. Upon this basis the average rate of taxation would amount to about $5.37 per thousand. The basis of the assessment of these taxes is somewhat variable, although over 70% is assessed on what is considered to be " the value and of real personal property." About 10% more of the tax was computed on the basis of the market value of the stocks and bonds or on a valuation of the road, which is based on the actual earnings, dividends, or other results of operation. In all States and Territories of the Union the first system is used, but in some States a second system is employed to CAPITALIZATION. 33 supplement the first. In addition to the above systems, which may be called ad- valorem taxes, about 18% of the taxes collected were based on some special system of taxa- tion, such as a tax on the gross or net earnings, revenue ? or dividends. Sometimes a tax is paid on the amount of traffic, or on some physical property of the road operated, or on some special privilege which has been granted. Sometimes there is a special taxation on stocks, bonds, loans, etc. The amount of these taxes per mile of line of course depends chiefly upon the actual valuation of the road per mile, but it also depends upon the system of taxation in the various States and Territories. In the State of Massa- chusetts, where the valuation of the railroad per mile of line is very high, we would expect a high tax-rate per mile, but it is apparently far higher on the basis of actual valuation than in other States, since it amounts to $1426 per mile. Connecticut comes next with $1114 per mile. In the State of New Jersey, where the actual valuation of the railroads is nearly, if not quite, as high as in any other State, the amount of taxes per mile of line is $798, while in New York and Pennsylvania it is $581 and $482 respectively. In some of the Southern States, where the valuation of the railroads per mile of line is comparatively low, we find, as might be expected, a low tax-rate per mile, that in Florida being $150 and in Alabama $182. In Texas the rate is only $110, and in Indian Territory it amounts to only $19. The average for the whole United States is $301 per mile. The corresponding figures for June 30, 1910, show the very great change made in six years, not only in the average amount of taxes per mile for the whole United States ($301 to $431) but also in the average amounts per mile collected in each State. A small part of this increase was of course due to actual increase in real value, and 34 THE ECONOMICS OF RAILROAD CONSTRUCTION. Taxes per Mile of Line of the Railways of the United States, by States and Territories, for the Fiscal Years Ending June 30, 1904, to 1910. State. Alabama Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts. . . Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire . . New Jersey New York North Carolina. . . North Dakota . . . Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina. . . South Dakota. . . . Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Arizona Dist. of Columbia, New Mexico United States 1904. 1905. 1906. 1907. 1908. 1909. $182 $186 $190 $218 $295 $298 168 208 224 224 241 234 317 319 325 390 494 498 278 286 295 287 289 300 1114 1259 1220 1339 1593 1686 336 303 310 391 340 421 153 140 170 176 187 198 152 139 158 166 196 194 237 256 244 233 312 288 418 441 453 472 441 463 458 455 451 481 490 518 208 212 217 233 230 242 277 272 305 296 343 309 333 373 333 366 333 369 239 239 241 218 245 253 219 251 262 292 314 314 384 430 597 620 675 711 1426 1472 1083 1525 1394 1500 316 333 554 398 396 424 262 285 389 429 388 381 195 201 197 214 214 242 201 204 209 206 187 196 221 232 240 271 298 289 223 224 240 429 309 311 381 242 235 265 283 291 326 318 333 358 379 402 798 848 1047 2047 1926 2166 581 617 671 686 672 800 185 171 176 177 211 213 223 251 264 265 265 297 468 478 519 569 576 187 599 460 272 248 211 228 297 446 482 336 645 510 554 552 937 1049 1128 1100 1204 1243 156 159 167 176 224 226 103 107 107 101 153 182 254 244 263 267 298 301 110 109 118 153 243 189 216 264 313 320 381 375 148 149 161 172 205 189 301 322 334 376 385 369 236 256 354 415 549 507 230 224 214 413 471 467 285 331 387 414 409 440 164 162 165 141 216 230 135 135 130 142 148 157 979 1349 1459 1480 944 1036 116 112 147 139 154 180 $301 $303 $349 $367 $382 $401 1910. $297 277 508 306 1867 482 208 206 345 501 521 253 344 312 250 301 742 1484 469 461 250 230 356 335 388 629 2290 877 220 341 611 499 444 587 1302 233 211 326 196 383 251 400 685 463 440 384 158 1562 254 $43 n CAPITALIZATION. 35 this merely illustrates the truth of the statement made in §1 that the intrinsic value of the roads per mile has increased, in spite of an almost stationary capitalization per mile. Nevertheless the bulk of the increase in taxa- tion per mile has evidently been due to a flat intention to increase the assessments, perhaps in the belief that railroads have not hitherto paid their due proportion of taxes. The chief interest of the engineer in this subject is to make a prediction as to the probable tax on some road yet to be constructed. A glance at the table shows two tilings: (a) The tax assessments in many States are very uncertain. For example, the drop from $1472 in 1905 to $1083 in 1906, followed immediately by the increase to $1525 in 1907, in Massachusetts, was the result of radical changes in the system of taxation and unques- tionably not due to any corresponding changes in real valuation. (6) Although a few States, such as Colorado, Kentucky, Nevada and Arizona, have made comparatively slight changes in the taxes per mile, nearly all of the States have not only greatly increased the taxes but even multiplied them by two or three, as in the cases of Mary- land, New Jersey, Washington and West Virginia. There- fore, in attempting to predict the future taxes on a railroad, the tendency of the State to increase the taxes per mile, as shown by the yearly changes in the table, should be considered. Fortunately the reports of the Interstate Commerce Commission now state the amount of taxes actually paid by nearly every railroad in the United States. The general table regarding taxes also shows the gross amounts paid in each State on each of several bases of taxation. The great bulk of the taxation is an ad -valorem tax on the value of real and personal property, although in some States, notably Minnesota, the taxes are specific 36 THE ECONOMICS OF RAILROAD CONSTRUCTION. on gross or net earnings, revenue or dividends. Although a definite knowledge of the tax laws for the particular State would facilitate a closer prediction, a study of the taxes paid by some road of the same State which cor- responds closely with the proposed road, considering also the method of taxation indicated by the general table, should enable an engineer to predict the taxes as closely as necessary. 17. Small margin between profit and loss. — The gross revenue received by a railroad is applied first to the payment of operating expenses. As an average for the whole United States this amounts to approximately 65%. From the remainder must be paid the interest on the funded debt and current liabilities, and also the taxes. This will take about 20% more, but it is not even permitted to use all of the remainder for dividends, since a very large fund is needed for permanent improvements and for bolstering up weak branch lines which are not paying their expenses but which are operated because of their indirect or their future value. It will thus be seen that the dividends are only paid out of the last small percentage of the gross earnings. Since there is so much variation in the financial condition of railroads, from one which is unable to pay its operating expenses to another which is declaring dividends on watered stock, we may learn something by studying the statistics of all the railroads of the United States " considered as a system." This last phrase refers to the fact that, since such a considerable proportion of railway stoGk is held by railway companies in their corporate capacity, there is a very large percentage of payments made to and by railroad companies which are merely intercorporate payments. By deducting those payments, which would appear as receipts in the accounts of one road and as expenses in the accounts of another, we may prepare a statement such as would be made up if all the railroads of the country were actually combined CAPITALIZATION. • 37 into one system. Another condition which somewhat complicates the situation is due to the fact that railroads are also the owners of property which brings in an income totally independent of their work as common carriers. In 1904 this " clear income from investments" amounted to nearly $50,000,000, although it was only 2|% of the gross earnings, but such income has been ignored in the following statements. The tabular form below gives the gross earnings of the railroads of the country considered as one system for the year ending June 30, 1904 (using even millions throughout). The actual amount of surplus available for "adjustment and improvements" was nearly $50,000,000 in excess of the $94,000,000 surplus gi venin the table, on account of the added sources of income not included in " gross earnings from opera- tion." It should be noted that in the above case the divi- dends were taken from the last 9.3% of the gross earnings. Earnings from passenger service. $ 444,000,000 " freight " 1,379,000.000 " " other sources. .... . 152,000,000 Gross earnings from operation. $1,975,000,000 Subtracting operating expenses 1,339,000,000 We have as net earnings 636,000,000 Out of these earnings were paid, Taxes $ 62,000,000 Interest on debt and on current lia- bilities 296,000,000 and then dividends 184,000,000 542,000,000 leaving a surplus of 94,000,000 The dividends actually paid averaged less than 3% on the total capital stock. That which has been called surplus may almost be considered in the light of an expense, since it was not considered wise to increase the dividends beyond the amount actually paid. The average revenue per passenger per mile amounted to 2.006 c. The revenue 38 THE ECONOMICS OF RAILROAD CONSTRUCTION. per ton of freight per mile amounted to .780 c. If the passenger and freight receipts, as well as the rates on mail, express, etc., had been cut clown 10% without any increase in business the amount available for dividends would have been entirely wiped out. Even cutting them down 5% under the same conditions would have cut the dividends in two. It may thus be readily seen that there is but a small margin between large dividends and no dividends, which will be produced by comparatively small differences in rates. Of course the above should not be interpreted as meaning that a difference in the amount of business done will have the same effect on dividends. Although to a very con- siderable extent it is true that when times are hard and business is slack, so that the amount of traffic is reduced, the gross expenses of the railroads are cut down, they cannot be cut down in strict proportion to the reduction in traffic. It will be shown later on that the cost of running an extra train is by no means equal to the average cost of running all trains. To put it more concretely a railroad which is regularly running 20 trains per day each way can run one additional train per .day each way for much less than yu of the average cost. Vice versa, the saving which is made by running one less train, because the traffic has been cut down, is less than -%\ of the average cost. If, therefore, a road is doing a certain gross amount of business which requires say 20 trains per day, a change of policy which increases or diminishes the amount of business done will increase or diminish the gross receipts in strict proportion to the change in the business, but the change in operating expenses will be far less. If the business is reduced say 10%, the gross receipts are reduced 10%, while the operating expenses are reduced probably not more than 4 or 5%, 'and the probable result is that all money which otherwise might be devoted to dividends has been entirely wiped out. On the other CAPITALIZATION, 39 hand, an increase in business of 10% will not increase the operating expenses more than 4 or 5%, and therefore the amount for dividends may be nearly doubled. This fact may be made still clearer by a concrete example. 18. Variation in dividends due to small variations in business done. — Assume that by changes in the alinement the business obtained has been increased or diminished 10%. Assume that the operating expenses are 67% of the gross receipts. Assume that the amount required for taxes, for the interest on the bonds, and for such demands for permanent improvements, working capital, etc., as are considered essential before dividends can be paid amount to 28%. We will have a balance left of 5% available for dividends. Assume a change of policy by which a 10% increase of business is obtained. As an approximate figure we may say that this additional business may be carried at a cost of 40% of the average cost of the traffic. We will also assume that the reduc- tion of 10% in traffic reduces the expenses by a similar amount. The comparative effect may therefore be stated as follows: Business increased 10%. Business decreased 10%. Operating exp. = 67 Fixed charges, ete = 28 67[1 + (10%X4C Income Available for dends )%)] =69.68 =28.00 67[1-(10%X40%)] Income Deficit = 64.32 = 28.00 95 Total income. ... 100 97.68 110.00 92.32 ..90.00 Available for divi- dends 5 divi- 12.32 . 2.32 The above comparison is useful chiefly to indicate a principle rather than as a computation of definite value. It indicates in one case that an increase in business which may be obtained perhaps by mere changes in manage- ment more than doubles the amount available for dividends. On the other hand, a decrease in business, which may be 40 THE ECONOMICS OF RAILROAD CONSTRUCTION. due solely to poor business management, not only wipes out a dividend but actually creates a deficit . The numerical accuracy of the calculations of course depends on the estimate that the additional business only increases the cost for handling by 40% of the average cost. While the cost of running additional trains will be more than 40% of the average cost per train-mile, the cost of running additional cars in a train, which is not actually limited by grade, will be far less than the proportional cost of an additional train. The additional cost is still less when the manager secures traffic to move in the direction in which the traffic is ordinarily least. It is still less when the freight is carried in cars which would otherwise return empty. In fact under the last condition the added receipts are almost pure profit and the additional cost is so insignificant that it might almost be neglected. There- fore the estimate of 40%, as used in the above calculation, might be considered as a conservative average. If the increase in business can only be obtained by an increased expenditure which will make a permanent addition to the fixed charges, the above method of calculation will show whether the improvement is justifiable. The accuracy of the calculations will then depend on the accuracy with which the future increase of business may be predicted, but if the increase in receipts is greater than the addition to the fixed charges, and particularly if it is very much greater, there can be but little question as to the value of the proposed improvement. 19. Practical limitations of capitalization. — Theoretic- ally there is a definite limit to the proper capitalization of every railroad project. Even if it is possible to obtain from a credulous public more capital (in the form of bonds) than the project requires, the effect is to burden the road with unnecessary " fixed charges" for bond interest. If more stock is subscribed for and paid in than can profitably be used, the usual result is wasteful CAPITALIZATION. 41 expenditure, and the inevitable result is a decrease in the rate of dividends. In either case the credit of the road is impaired by the reduction in net earnings. The result of the over-capitalization may be actually financial embarrassment. The other extreme is far more common. The project may fail to attract the capital necessary to build the road properly and to operate it until its normal traffic income is being regularly obtained. If the obtainable capital is exhausted before the road is put in operation the loss to the projectors is very great and is sometimes nearly or quite total. In anticipation of such a predica- ment a road is sometimes opened for traffic, using rails or ties which are too light, using little or no ballast, uncom- pleted earthwork having narrow cuts and no ditches and very narrow embankments, and many other devices for reducing the cost of the road before traffic-trains are run. To some extent such measures are justifiable, but it should always be remembered that it is frequently very expensive " economy" and that the operating expenses are thereby increased — often to such an extent as to wipe out an easily obtainable profit. Although it is unfor- tunately true that the engineer of the road must make the best of the capital which is furnished him for the work, be it great or small, yet the recommendations of the engineer should largely control the efforts to secure capital. The engineer should be competent to recommend how much capital may profitably be spent to secure the greatest rate of net return on the capital invested. 20. Principles which should govern the amount of capi- tal to be raised. — (1) The project should secure sufficient capital to insure the proper completion of the road and its operation until the normal traffic income is obtained. An estimate of this amount can readily be made and the projectors should not be satisfied with anything less. It might even be stated more strongly to say that the 42 THE ECONOMICS OF RAILROAD CONSTRUCTION. projectors are foolish to embark on the enterprise unless they have a reasonable certainty of raising this amount. (2) The surveys may develop the fact that some addi- tional expenditure may permit an improvement on the line as originally laid out. An illustration of this (elabor- ated in Chapter XV) is the reduction of the rate of the ruling grade, which is shown to have a definite financial value. The criterion in such a case is this: If the im- provement is unquestionably justifiable, on the basis of a reasonable capitalization of the annual saving in operating expenses, then the improvement should be made, unless there is danger that the total available capital is limited and that the whole enterprise may become imperiled by an expenditure which is not absolutely essential even though desirable. (3) In considering such a case as the above, the pos- sibility of merely deferring the extra expenditure without ultimately abandoning work already done must be con- sidered. In some cases the plan as actually constructed becomes practically a finality, which cannot be changed except at prohibitive loss. Under such conditions the best plan (from the operating standpoint) must be insisted on. (4) On the other hand, no change or " improvement' ' should be adopted, unless it can be demonstrated that the change itself will be financially justifiable. It is not sufficient that its cost will not wreck the enterprise. (5) The engineer can usually count on the fact that unless the money market is abnormally disturbed by panic conditions any enterprise which is really meri- torious can command sufficient capital to float it, if it is properly exploited. Even an improvement to the original plan can command capital if it has sufficient merit, although this may be more difficult than to raise the original sum asked for. CHAPTER IV. THE VALUATION OF RAILWAY PROPERTY. 21. Objects. — There are several objects for which a valuation is placed on railway property. The method of making the valuation as well as the value arrived at is apt to depend very largely on the purpose for which it is made. An estimate may be made for the purpose of taxation. Another and very different estimate may be made by the agents of individuals or a corporation who are contemplating buying the property. Legislatures may wish to obtain a valuation which may be used as a basis for some form of railroad legislation. The fact that some railroad properties have become very valuable and have returned very large profits to their promoters has caused a general belief throughout the country that railroad earnings are far higher than a fair return on their valuation will justify. This has resulted in the demand that railway rates should be reduced so that the net earnings will be more nearly in proportion to the true valuation of the road. Some of the methods of appraising railroad property will be here discussed. 22. Nominal valuation. — The nominal valuation of a railroad property is the sum of the par values of its stocks and bonds. On the basis that a bond is a mere evidence of indebtedness and that it represents money which has been used to create the property, the bondholder may be considered as one of the owners of the road and that 43 44 THE ECONOMICS OF RAILROAD CONSTRUCTION. his rights and control of the property are merely some- what different from those of a stockholder. If the capital stock is not fully paid, then of course the true valuation must be considered as the sum of the paid-in capital together with the bonds and other liabilities. Of course such figures are very approximate and are discussed chiefly on account of their simplicity. When the road is first constructed, such figures ought to be a fair repre- sentation of the value of the physical property, provided expenditures have been cautiously and efficiently made. Such a valuation does not assign any value to the fran- chise or the charter of the road. A railroad property is very different from any other form of landed property. A tract of land, averaging about four rods in width and an indefinite number of miles in length, is di- verted from its original use as farmland or other pur- poses and devoted to a particular use. A very large amount of money is spent in grading, in the construction of tunnels and the building of bridges, and the construction of the road-bed and track. Except for the comparatively insignificant value of the rails, which may be torn up and sold as second-hand rails, or the value of steel bridges, which may be removed and erected elsewhere or sold for scrap, all the money which is spent for me construc- tion of the road is absolutely sunk beyond hope of recla- mation. It can only be used for one purpose, and the value of the property as an investment is represented by its earning capacity when used for its one sole purpose of being a common carrier. Thereafter its value is really represented, not by the amount of money which has been sunk in the enterprise, but by the capitalized value of the road as an organization for earning money in one par- ticular way — that of a "common carrier.' ' If the road is well located for obtaining business, which is virtually the same as saying that it has a valuable franchise, then THE VALUATION OF RAILWAY PROPERTY. 45 it will probably earn dividends on a comparatively small expenditure of capital. On the other hand, if there is but little business to be done, its earnings will be small, no matter how much the road may have cost. We may thus see that the amount which has been spent on the construction of the road does not necessarily bear any relation to the real value of the railroad property. Prac- tically the two values will ordinarily approach equality. If the amount of money which has been spent is far higher than is justified by its earning capacity, it simply indicates that the expenditure has been foolishly made. If, on the other hand, it is far less, then it means that the promoters have seized an unusual golden opportunity. It would seem unnecessary to point out any further fallacies in the method of valuation from the amount of money spent in construction, if it were not for the fact that so many people still cling to some such method. Such a method sometimes gives values which are far too great, while in other cases they are far too small. To quote from one writer on the subject: "The commercial value has nothing to do with its cost. If John Smith buys a hotel for $1,000,000 and, although a good hotel man, cannot make more than $50,000 a year out of it, and wants to sell, the commercial value is probably not over $500,000." A hotel man might go into a wilderness, select a site for a hotel on land which costs him practically nothing, build a summer resort at a comparatively small expenditure, and in a few years create a custom and give his hotel a name and reputation which would make his hotel property exceedingly valuable and worth many times its original cost. Under such conditions, the market value of that hotel would have little or no rela- tion to its actual cost. 23. Cost-of-replacing-property method. — There is a large class of people who think that a road should be valued 46 THE ECONOMICS OF RAILROAD CONSTRUCTION. according to the cost of replacing the property at the present time, i.e., buying the right-of-way, constructing the road-bed and track, and providing its equipment. There are several causes which will operate to make such a valuation very unfair. Such a valuation takes no account whatsoever of the earning capacity of the road. A railroad may be so well located that its annual earnings are very large, so large that the public values its stocks and bonds, as quoted in the stock-market, at a very high figure, and yet the cost of duplicating that road in every particular at present-clay prices might be very much less than the market price of its securities. As another reason, it is almost invariably found that any business enterprise, whether it is a factory or a rail- road, which has been in existence for a series of years long enough for a considerable part of its construc- tion to have been renewed by methods which were not in vogue when the structure was originally built, has had a total amount of money spent on it which is very far in excess of the amount which would replace it at the present day. It would certainly be unfair to say that, because a railroad-cut, for example, which was originally dug out by hand labor at a high price per cubic yard could now be taken out with steam-shovel methods at one-half the cost, therefore those who had paid the high prices for the original work should now have the railroad earnings scaled clown until they give merely a return on the cheapened method of construction. This method is usually advocated by those who wish to make it a basis for radical legislation which shall reduce railroad charges until they merely pay the cost of opera- tion plus a comparatively insignificant return on what it would cost under present methods to reconstruct the road. Such methods seem to lose sight entirely of the fact that the element of risk in railroad construction is THE VALUATION OF RAILWAY PROPERTY. 47 very great, and that, as given in a previous chapter, a very large proportion of railroad stock pays absolutely no dividends. Therefore it is but just that the permissible earnings of railroads should be made high enough to compensate for the great risk which is run by capitalists who build railroads. 24. Valuation of physical properties and franchise. — In Michigan and Wisconsin the railroads of the State have all been valued by a corps of engineers, appointed by the State, who adopted a systematized method of making an actual valuation of the property as it exists. Of course the method was largely an estimate of the cost of repro- duction, allowance being made, however, in those elements such as rails, etc., which are subject to wear and deprecia- tion, for the " present value." The various elements of cost of a road were classified, and those elements which were subject to depreciation were examined particularly, while making the appraisal, to determine their present value. For the railroads of Michigan, the total cost of reproduction of construction and equipment was given as $202,716,262, while the present value was given as only $166,398,156, or 81.4% of the value when new. Switch- ties and cross-ties were allowed a present value of only 53.9% of the cost of reproduction. Telegraphs and telephones were allowed only 52%, while, on the other hand, right-of-way, real estate, and grading were allowed their full value, 100%. Although this work was under- taken by the State with the idea of furnishing a basis for a more uniform system of taxation, "it very soon became necessary to publish an order excluding all thought of taxation in connection with the results to be obtained." "The commissioners required of us only the cost of repro- duction and the present value of this road, reserving to themselves any adjustments of these values that might be thought necessary to secure uniformity of taxation." 48 THE ECONOMICS OF RAILROAD CONSTRUCTION. There was added to the " present value" of these proper- ties the sum of $35,814,043 as the value of the " non- physical" properties. The non-physical property is sup- posed to include among other things the following: "1. It includes the franchise " (a) To be a corporation. " (6) To use public property and employ public author- ity for corporate ends. "2. It includes the possession of traffic not exposed to competition, as, for example, local traffic. "■3. It includes the possession of traffic held by estab- lished connections, although exposed to competition, as, for example, through-traffic that is secured because the line in question is a link in a through-route. "4. It includes the benefit of economies made possible by increased density of traffic. "5. It includes a value on account of the organization and vitality of the industries served by the corporation, as well as the organization and vitality of the industry which renders the service; this value consequently is, in part, of the nature of an unearned increment to the corporation." (From report of Professor Henry C. Adams.) The value of the non-physical properties was obtained by deducting from the gross earnings from operation the operating expenses, exclusive of taxes, which gives the net income from operation. Adding to this the net income from corporate investments would give the total available corporate income. From this is deducted an annuity, based at 4% of the mean value of the physical elements, which then gives the remainder available for other pur- poses. From this was deducted further the taxes on the physical elements at 1% of their mean value, also the rentals on property not covered by the appraisal, also the interest on current liabilities, and also the cost of permanent improvements which were charged to income. THE VALUATION OF RAILWAY PROPERTY. 49 Subtracting these deductions from the remainder obtained above, we have a surplus (or deficit) which is capitalized at 7%. This gives such a value of the non-physical ele- ments that it yields a net income of 6% after the payment of taxes of 1%. It is a very curious coincidence that when the value of the non-physical properties of the railroads of Michigan, as it was actually computed accord- ing to the above method, was added to the "present value," the sum total agreed with the cost of reproduc- tion to within a quarter of 1%. It is probable, however, that this should be considered as a coincidence rather than as an illustration of a general law. 25. Stock-market valuation. — A far more accurate method of valuation is to determine the average market value of the stocks and bonds of the road for a period of time which is long enough to cover the speculative fluc- tuations of the stock-market. There is one very strong reason for considering this as a true valuation. The market price for railroad securities is determined as a compromise between two opposing classes of financiers, one of which is interested in raising the price as high as possible, the other in making it as low as possible. Such men are experts in valuation. They make it their life-long business. The compromise value which is offered and accepted between these two classes of experts may therefore be considered as the true valuation of the property, provided we can succeed in eliminating from the price the effect of fluctuations due to speculative excite- ment. The combined value of these securities (stocks and bonds) represents the value placed upon the earning capacity of the railroad. 26. Valuation by capitalizing the net earnings. — This method requires two steps: the determination of, first, the income to be capitalized, second, the rate of capitaliza- tion. The determination of the income to be capitalized is 50 THE ECONOMICS OF RAILROAD CONSTRUCTION. not very difficult, although it requires some modification from the "net earnings" as reported by the railroad companies, with which it should be identical. The diffi- culty arises from the variation in the methods of railroad companies, in keeping their accounts. The net earnings represent the difference between the gross earnings and the amount properly assignable to operating expenses. For the purpose of this investigation such taxes as are paid are allowed as operating expenses so that the remainder represents the total which can be applied as a return in whatever form to the capital which has been invested. The chief difficulty lies in the variation among railroad accountants, in charging expenditures for permanent improvements. One company may purchase additional rolling-stock and charge the entire cost to operating expenses. Others will charge the entire sum to the capital account. If the new equipment is partially to replace old and antiquated equipment, some will adopt the plan of charging the value of the replaced cars or locomotives to operating expenses and charge the remainder to the capital account. The last method is undoubtedly the correct method to adopt, since any permanent addition to the equipment of the road should be charged to capital account and not to operating expenses. Assuming that we have the rate of capitalization, if we divide the net income of the road by this rate of capitalization it will then give a valuation of the property which represents its actual financial worth. The determination of the proper rate of capitalization is very difficult and must be determined according to some fixed rule rather than by assigning an arbitrary value. A minute difference in the rate of capitalization will produce a very large difference in the resulting value of the road. The method adopted by the United States Department of Commerce and Labor may be very briefly indicated as follows: THE VALUATION OF RAILWAY PROPERTY. 51 The market quotations on the securities of each railroad were studied for a period of over six months previous to a given date; even this period was extended in the case of abnormal fluctuations. The details of each issue of debt, the amount outstanding, the rate of interest, the dates of the payment of interest, and the date of maturity were determined. The effect of accrued interest and expected dividends on the prices of securities was allowed for. Since the record of sales only includes a very small proportion of the railroad securities in existence, even the bid and ask prices, which resulted in no sales, were considered. Under usual conditions the bid price repre- sents the lower limit of the market value of the security. The ask price represents the upper limit and the difference represents the zone within which bargaining takes place. On the general principle of adopting a lower valuation in case of doubt, the bid price was used as the basis upon which to value the securities considered. The actual return to a bondholder on a bond which matures at a given time is a very complicated mathematical function of the annual interest rate and of the length of time still remaining for the bond to run. Sets of tables are published which give the average rate per cent in annual return on bonds purchased at various prices above or below par. The rate of annual return on bonds of the road, on the basis of their market price and the date of their maturity, was then figured for each issue of bonds. Multiplying this rate by the actual market value of the bonds gives the virtual annual return to the investor. Dividing the sum total of these annual returns by the sum total of the market values then gives the average rate of income on the bonds which were actually sold or on which bidding prices had been determined. The valuation of the funded debt, which was not quoted on the stock-market, was estimated by giving it a valuation corresponding with 52 THE ECONOMICS OF RAILROAD CONSTRUCTION. other similar securities. Multiplying these values by the same rate per cent per annum will give the annual return on the unlisted securities. We can then add up the values for the actual (or probable) market value of all the funded debt of the road and also the computed annual return to the investor and, by dividing the return by the total market value, we obtain the average annual return in rate per cent per annum. The market price of the stocks, together with their actual dividends, are similarly obtained, but there must be added to the market price of these stocks an estimate which will represent tht undivided profits which have not been returned to the stockholders in the form of dividends. "No well-managed corporation divides at any one time among its stockholders the precise amount of its gain since its last preceding dividend. Such a proceeding is not only impractical but also impossible, for the reason that it is impossible to tell precisely what the corporation gains have been during such a period. . . . The physical property has, to at least some extent, changed its identity during the period; the credits and obligations, of the corporation have prob- ably changed; the general aspects of its business oppor- tunities have almost certainly changed; and all of these together have correspondingly modified the value of its physical property." Some of these improvements can be definitely allowed for. For example, the average annual expenditures for permanent improvements which have been made during a period of say five years should be added as though it were a dividend, since it might be considered as a dividend paid to the stockholder and immediately reinvested by him in the capital stock of the road. Similarly, variations in the profit-and-lc«s account, as indicated by the general balance-sheet, can be allowed for by considering the average annual change in the profit-and-loss item for a period of years. Even if THE VALUATION OF RAILWAY PROPERTY. 53 there had been a loss each year a steady reduction in that loss may be considered as an average increase in the profit account. Another item to be added is due to the fact that the sum of the actual annual payments of interest and guar- anteed dividends may amount to more than the computed annual return based on the market price of the bonds. This annual excess must be added in order to compute the actual annual return to the investors of the road. In fact the only object of computing the annual return, based on the market price and the time of maturity of the bonds, was that a proper average rate could be obtained on which to compute the return on the unquoted securities. There is still one other item which may need to be added: if the returns on the common stock are based on the present rate of dividends, but the dividends have varied during a period of say five years, which is the period adopted for the annual averages of betterment, etc., we must consider that a reduction in some rate of declared dividend means that so much money has been added to the profit-and-loss account of the road, and therefore the average amount of this difference, spread out during a period of say five years, represents the average addition (or deduction) which must be made to or from the average income of the road. Taking the summation of these average returns and dividing it by the summation of the market (and computed) prices of all forms of the securities of the road, we determine the actual average annual return in rate per cent on those securities. Dividing the net earnings of the road by this computed rate of capitalization then gives the valuation of the entire property. 54 THE ECONOMICS OF RAILROAD CONSTRUCTION. Legal Control. 27. The subject of the legal control of railroad cor- porations by the federal, State, and municipal govern- ments is so very broad that several volumes would be required to adequately discuss even the present condi- tion of such regulation. A large part of the subject (the making of rates) is usually considered to be entirely outside of the province of the engineer, since the engineer is never called on to make rates or to revise them. But there are many cases where a knowledge of the method actually employed by railroad managers in making and revising rates, and the control which has already been exercised by the State and federal governments over rate- making, will give the engineer a much clearer idea of the influence which rate-making has on many of the problems which daily come before him. It may be more accurate to say that he should understand how little rate-making is affected by such variations in engineering design as he is able to control. In the next few pages an attempt will be made to very briefly state a few of the fundamental principles regarding the methods of rate-making and the control of rates which is exercised by the State and federal governments. 28. Basis of freight-rates. — The usual method of setting a price on a manufactured commodity is to determine from actual experience what is the cost of manufac- turing the commodity and to acid to such cost an amount which will pay a reasonable return on the capital invested, and also pay a reasonable return to the manufacturers to compensate them for their time, skill, and knowledge of the business. If the manufactured article is secured by patents and is in great demand, the profit added to the cost of the manufacturing will be correspondingly large, and yet even this is considered right since the owners THE VALUATION OF RAILWAY PROPERTY. 55 of a valuable invention are entitled to a corresponding profit on the invention. Ever since legal control of railroad-rates has been suggested there has been an effort to establish a basis of cost of transportation, so that by adding a reasonable amount, which will pay for the use of the capital, a proper charge may be deter- mined, and that the railroad shall be enjoined from attempt- ing to collect any greater charge for such transportation. A consideration of some of the facts already stated, together with demonstrations made in subsequent chapters, will show that the cost of transportation is a very variable quantity. It will be shown that, even though we deter- mine from statistics of the whole country that the average cost of transporting one ton per mile is about .5 c, we cannot therefore say that the cost of transporting one ton for one mile on any particular railroad and under all conditions will be .5 c. or even approximately so. Even if we were to establish from the statistics of any one given road that the average annual cost of transporting freight on that road amounted to a certain figure, it would be neither fair nor equitable to say that all traffic should be charged according to this figure, that no traffic should be taken at any less figure, nor that any charge could be made at any greater figure. To a very considerable extent it is true that railroad expenses are independent of the amount of business done. The fixed charges must be paid regardless of the amount of business, if the road is kept solvent. The cost of maintaining the road-bed and track is very largely independent of the amount of traffic. Whether there are twenty trains per day each way or only one, the amount of track-work which is necessary to keep the road up to a given standard will not be propor- tional to the number of trains. Although the fuel bill will vary more nearly in accordance with the amount of traffic, it will be by no means strictly in accordance with 56 THE ECONOMICS OF RAILROAD CONSTRUCTION. it. The practical result of all this is that railroad profits are subjected to "the law of increasing returns." The first half of the business which is done costs a large pro- portion of the total ; the final ten per cent is almost clear profit. A railroad is very often compelled to accept some of its business at a rate which is much lower than the average rate or it cannot get the business at all. It can handle the additional business at a net additional cost which will be less than the amount received for it and hence can make a profit on such business. Under such conditions the business is profitable. If it is attempted to increase the charge for this low-grade business to the average rate for all business it will not get it at all. If it is attempted to reduce the charges on its local non- competitive business to the lower average rate actually received the road cannot pay its expenses and must go bankrupt. These facts may be illustrated by a very simple concrete example, in which the figures make no pretense of accuracy and are given merely for the purpose of illustrating a principle. Suppose that a road is hand- ling 80,000 tons of non-competitive freight per year, for which it receives $1 per ton; suppose that it has an opportunity of handling 80,000 additional tons of com- petitive freight at the rate of 60 cents per ton; its gross receipts are therefore $128,000. The competition is such that it must accept the competitive freight on the basis of 60 cents or refuse it altogether. It is therefore handling 160,000 tons of freight at an average rate of 80 cents per ton. Assume that it could handle its non-competitive business alone at a total expenditure, for operating ex- penses and fixed charges, of 90% of the amount received or $72,000 for the 80,000 tons. Assume that the extra business, whose cost is confined to comparatively small additions to the cost of maintenance of way, maintenance of rolling stock, and the expenses of conducting transpor- THE VALUATION OF RAILWAY PROPERTY. 57 tation, costs but 50 centt • jer ton. The additional busi- ness is therefore handled at a cost of $40,000, and the entire traffic at a total expenditure of $112,000, which leaves a net profit of $16,000 on the business. Although the competitive business is handled at a far less rate than the non-competitive business the net profit on that part of the business alone is $8000, which is as great as the profit on the non-competitive business. If, in response to attempts to enforce uniform rates, the charges were cut down to the uniform basis of $128,000 on 160,000 tons of freight or an average price of 80 cents per ton, we would find that the additional competitive freight could not be obtained at all. The road would then be compelled to -attempt to pay its operating expenses by handling the 80,000 tons of freight at 80 cents, which would give a rev- enue of only $64,000 when the actual expenses, including fixed charges, are supposed to cost $72,000. Such a condition of affairs could only lead to bankruptcy. The condition of competition is one that a road is forced to meet. 29. Direct competition.— A road that is already bank- rupt is usually the one which most recklessly breaks established rates and starts a rate war. Such a road will enter the most reckless competition in order to obtain business under any conditions. A rate which will pay operating expenses, even though it necessitates a default of the interest on the bonds and, of course, pays no dividends, is doing better than to remain idle, since, if it pays the operating expenses, it is at least maintaining its road-bed and track in some sort of condition. There- fore such a road will try to obtain business at any rate which will actually pay the operating expenses. The solvent road which is so situated that it must meet the compe- tition of the roacl which is recklessly cutting rates has forced upon it the alternative of accepting business at 58 THE ECONOMICS OF RAILROAD CONSTRUCTION. much less than its usual rates, or refusing it altogether. If the general manager can estimate that such business can be handled at a rate which will more than cover the additional operating expenses, he is justified in accepting the business, especially since it will actually prove a source of profit to the road. It is claimed that these who ship their freight on the non-competitive high rates are helping to pay the freight of others. This is not true, since the others will not pay anything to the road except at the reduced rate. As a matter of fact, it might even be said that the low-rate shipper helps to pay the freight of the high-rate shipper, since the profits of the road are increased by the payments made by the low-rate competitive shipper, thus enabling the road to reduce the rates of the high-rate non-competitive shipper. We are thus led to the conclusion that freight-rates are not, and cannot be, based on any rational estimate of the cost of service. The railroads really charge "what traffic will bear," and this charge is determined very largely by causes over which the railroads have little or no control. This will be discussed later. 30. Indirect competition. — It has frequently been stated in this book that the prosperity of a railroad company is very intimately connected with that of the community which it serves. A large part of the business of a rail- road is freight business. The freight business of a rail- road depends on the business prosperity of its customers. Commercial competition requires that a manufacturer shall not only manufacture his goods as cheaply as his competitors, but that he shall also be able to deliver the goods at the very door of his customers as cheaply as another manufacturer. Since a very considerable item in this total cost is the cost of transportation, it becomes a matter of business for the railroad to assist the manu- facturer by making the freight-rate, if possible, at such a THE VALUATION OF RAILWAY PROPERTY. 59 figure that it will permit the manufacturer to meet the competition of others. If the manufacturer cannot do this, he cannot do business at all, and the railroad com- pany loses his business altogether. This course of reason- ing is the justification of the discriminations which have been practiced by railroad companies in favor of certain shippers. These shippers could not do business profitably, except at certain freight-rates which were below the normal. The railroads could handle such business as extra business at a profit, and could make more money on such an arrange- ment than by not handling the business at all. Of course- there are reasons which make such discriminations unjust as well as illegal, especially when these methods have been used to build up the wealth of great monopolies. A treatise of this sort is not the place to discuss discrimi- nations, but the above statements have been made to show why discriminations may be profitable to the rail- road company. The indirect competition furnished by other railroads, who are trying to build up their own prosperity by building up the prosperity of the shippers along their lines, is one of the most potent causes to reduce freight-rates, even to a shipper who has absolutely no choice except to ship his goods on the one road which passes his place of business. The railroad company is therefore virtually compelled to reduce its freight-rates to a point where they will pay the operating expenses and leave as much margin as possible on the capital invest- ment. It will thus be seen that a profit which is made out of the low-grade competitive business will actually enable the railroad management to reduce the freight- rate on the so-called non-competitive business, if it is found necessary to do so in order that the local shipper may meet the competition of another shipper on a rail- road perhaps 200 miles away. 60 THE ECONOMICS OF RAILROAD CONSTRUCTION. 31. Justification of special commodity rates. — In the following chapter the methods of estimating the volume of traffic of a new railroad enterprise will be discussed. The discussion there chiefly concerns the methods of estimating the volume of the business. Although the freight-rates obtainable on such business will usually bear some relation to the similar rates charged by other railroads, the rates will not necessarily be identical. In fact the estimator must have sufficient knowledge of commercial business to know the market prices of com- modities in the markets reached by his road, and to know, for example, the market price of hay in a certain city and the rate that may be charged for transporting hay which will leave to the farmer a sufficient amount per ton to encourage him to raise and haul hay to the railroad for shipment. If the freight-rate charge is excessive, so that there is but little object for the farmer to raise hay, the railroad will lose such business altogether. It would be preferable for it to charge a lower rate per ton than is charged for other merchandise, rather than to discourage and lose the business altogether. 32. Low rates on low-grade freight. — The preceding paragraph furnishes the basis of the justification of an apparent discrimination between different kinds of freight. From the operating standpoint it costs just as much to haul a ton of coal as to haul a ton of furniture or expensive machinery, and yet the universal custom is to handle coal, broken stone, and similar products which have compara- tively little value per ton, at a much cheaper rate than articles of higher value. This is partly done on the general principle that the traffic will bear a higher value. In the case of coal, viven the low freight-rate is a large proportion of the total value of the coal. In the case of machinery or dry-goods, the freight charge is compara- tively ins'gnificant. The shipment of low-grade, bulky THE VALUATION OF RAILWAY PROPERTY. 61 freights would be considerably discouraged by a marked increase in the freight-rates. The much higher rates which are charged on high-grade freight is such a small proportion of their total value that their use is not appre- ciably limited by the freight-charges. As a conclusion of this very brief discussion on freight- rates, it may be said that the fundamental principle of freight-rates is that the charge is made in accordance with what traffic will bear — interpreting this phrase to mean that the prosperity of the railroad is bound up with the prosperity of the community served, and that the railroad will have more business and obtain a greater profit by encouraging the business and permitting the prosperity of the community. And it will best accomplish this by reducing its freight-rates to the point which will so en- courage business that the return to the railroad company will be a maximum. Federal Control. 33. Origin. — The authority for the control of railroads by the federal government is based not only on the principle of the governmental control of "common carriers," but also on the provision of the Constitution that Congress has the power to regulate the commerce between States. It is quite probable that this provision was inserted in the Constitution chiefly, if not entirely, with the idea of preventing the collection of import and export duties on merchandise passing between the States. Railroads were non-existent at that time, were hardly even dreamed of, and certainly the framers of the Constitution had not the slightest conception of the present railroad situation. Nevertheless on this very slender basis has been built up the elaborate series of decisions which have been rendered by the U. S. Supreme Court in the many recent 62 THE ECONOMICS OF RAILROAD CONSTRUCTION. railroad cases. Of course it required no authority greater than that of common law for Congress to deal with railroads as common carriers which are subject to its jurisdiction. Inasmuch as the consolidation of railroads during recent years has made every important railroad system enter two or more States, there is but little railroad traffic in the country which is not subject to federal control. Federal control has been exercised partly as a result of the very extensive grants of public land which have been donated to railroad companies to encourage the building of im- portant roads, such as the Union Pacific Railroad. The authority of Congress to control railroads even to the making of reasonable freight-rates has been thoroughly affirmed by decisions of the U. S. Supreme Court. The control exercised by Congress over railroads has been principally centered on the regulation of freight- rates. In addition to this, acts have been passed to regulate the use of safety appliances, such as automatic couplers, air-brakes, etc. 34. Necessity for control. — A private shipper has but little hope of satisfaction if he considers that a given freight-rate on a shipment of goods is unreasonable. If the goods have already been shipped, the charge must be paid before the goods can be recovered at the other end. Theoretically the law provides that he can complain to the Interstate Commerce Commission that the charge is unreasonable. Although the Interstate Commerce Com- mission is empowered to order a railroad to reduce its charge to " reasonable rates," it does not 'have the power to state what a reasonable rate shall be. Regardless of the Interstate Commerce Law, the shipper can bring an action against a railroad company in an ordinary court upon the complaint that a rate is unreasonable, and if he can establish the point, the railroad must refund whatever has been proven to be the excess. But when the THE VALUATION OF RAILWAY PROPERTY. 63 cost of such proceedings is taken into consideration, there is no object for the shipper to bring such an action cither before the courts or the Interstate Commerce Commission. Even the powers of the Interstate Commerce Commission have been so limited by the decisions of the Supreme Court that the shipper has very little recourse under the present conditions of the law. The railroad company is protected by the constitutional provision that rates cannot be reduced to such an extent as to make them "confiscatory." But since it would be practically impossible to demonstrate that any individual rate would be confiscatory, the provision is of little prac- tical use to the railroads. The reasonableness of a rate is very difficult to prove, except by a comparison with similar rates under similar conditions. The chief provi- sion of the Interstate Commerce Act is what is commonly called the " long-and-short-haul clause," which forbids a railroad from charging more for a short haul than for a long haul in the same direction and under similar condi- tions, the short haul being included within the long haul. The words "under similar conditions" have been the loophole which has practically nullified the long-and- short-haul clause. The railroads have successfully main- tained the existence of a difference in operating conditions which justifies them in accepting some shipments of com- petitive freight at less rates than other shipments of non- competitive freight on which the haul was actually some- what less. 35. Pooling. — Unrestricted competition on competitive freight has proved very disastrous to railroad companies, especially when they have endeavored to prevent their business from slipping away from them by reducing their rates in order to meet competition below the point where it even paid the actual additional cost of operation. To avoid such cutthroat competition many competing rail- 64 THE ECONOMICS OF RAILROAD CONSTRUCTION. roads formed what were called pools, under which they agreed to maintain rates and to insure to each of the competing roads their proportion of the freight business. The passenger pools were sometimes arranged in the same way. The proportions assigned to each road were determined by the actual business of that road during the previous year. The pools were of two kinds, money pools and traffic pools. On the basis of the money pools, each road was allowed an agreed share of the total receipts on the business done by all the roads, almost regardless of the work which it actually did. Some slight adjust- ment was made by allowing roads which had handled more than their rated share of business a small extra amount which would partially compensate them for the extra work which they actually did. But the compensa- tion was purposely made so small that it would be no object for the railroad to attempt to get more than its share of business. The traffic pools were managed so that the actual traffic of the roads would be kept at the prearranged ratios, this being accomplished by diverting traffic to roads which showed a tendency to fail to get their due share. Since shippers usually object to the diversion of their freight shipments, certain large shippers, who were called "eveners," consented to allow their shipments to be diverted to any route so as to even up the traffic to the different roads. Of course they were allowed con- cessions in the freight-rate on account of this arrangement. But as pooling was popularly supposed to be detrimental to competition, it was declared illegal by federal legisla- tion and has been discontinued. 36. Traffic associations. — It has been attempted to maintain competitive freight-rates between railroads by means of traffic associations. The traffic associations which have been formed have adopted uniform systems of classification together with uniform systems of freight- THE VALUATION OF RAILWAY PROPERTY. 65 rate charges which would prevent rate-cutting. The many attempts in this direction have been rendered in- effectual, because the railroads themselves would not abide by the schedules. One freight agent would suspect (justly or otherwise) that another freight agent was cut- ting rates and he would proceed to meet the cut. A rate war would soon be in progress, which would probably disrupt the association. Even traffic associations were declared illegal, on the ground that they were " in restraint of trade." Traffic associations are still in existence, but their powers have been legally curtailed. Any attempt in their by-laws to discipline any road for an infraction of their rules is declared illegal. All agreements regarding rates are merely " gentlemen's agreements" and this gives no guarantee of immunity from a rate war. 37. Consolidation. — Pooling and traffic associations having been declared illegal, the only method left to prevent competing roads from ruining each other finan- cially by means of rate wars was to cut off all incentive for competition by consolidation. Even this has been somewhat prevented by legal provisions against the con- solidation of parallel or competing lines. But such pro- hibitions have not prevented the elimination of competi- tion by combinations of groups of capitalists who so control the roads on the principle of " community of interests" that there is practically no such thing as an active competition which has an effect in cutting down rates. Consolidation has already progressed to such an extent that the great railroads of the country are now combined into a very few groups and are owned or con- trolled by a comparatively small number of men. Since the reduction in rates through active competition is now practically hopeless, the only means of preventing the railroad from being the sole judge of how much it shall demand from a helpless shipper appears to lie in the 66 THE ECONOMICS OF RAILROAD CONSTRUCTION. power of Congress to directly specify what a traffic-rate shall be. This power appears to be only limited by the common-law rule that " it must be reasonable/' which, of course, includes the constitutional provision that "it must not be confiscatory." State Control. 38. Scope and limitations. — The scope of State control is somewhat the same as that of federal control, but it has different limitations. It must be subject to federal control and cannot apply to any traffic except that in the State. Like the federal control its authority is based chiefly on the principle of a governmental control of common carriers. The control actually exercised by the States applies chiefly to police regulations as to their physical condition. Railroad charters are usually granted by State legislatures. These have already been discussed in Chapter II. The control by the States of such matters as grade crossings, etc., has also been referred to. Comparatively few of the States have interfered with the rates which shall be charged by a railroad, except as it has been done in the charters of the railroad. Even the limitations imposed by the charters are frequently so much higher than the rates which the railroad company themselves see fit to charge, that it cannot be said to have any influence on rate- making. Space is too limited to discuss the so-called " granger legislation, " which was the all-important political controversy in the Northwestern States several years ago. The prevalent opinion that freight-rates were extortionately high produced very drastic legislation, cutting down the charges which the railroads were permitted to make. The legislation went too far, and the result was financial embarrassment and even bankruptcy for many of the roads. Much of this legislation has since been repealed. Some THE VALUATION OF RAILWAY PROPERTY. 67 of the State Railroad Commissions, notably that of Texas, have been active in recent years in regulating the charges made by the railroads. It remains to be seen whether this action will prove beneficial alike to the railroads and to the communities. Other elements of State control have already been discussed in Chapter II. CHAPTER V. ESTIMATION OF VOLUME OF TRAFFIC. 39. Primary considerations. — The economic considera- tions underlying the building of railroads are now funda- mentally different from those existing fifty or sixty years ago. In 1840. the number of miles of railroad in the United States was 2818. In seventy years that mileage was multiplied by nearly 87. At that time the number of miles of line per 10,000 square miles (100 miles square) of territory was only 9.5. Now it is 808. At that time nearly the whole country was virgin territory, and it was not a question of the ultimate success of a road, provided it was constructed with a decent regard for sound engineer- ing principles, but a mere question of time before the country would develop sufficiently to support the road. In a broad way we may now say that the railroads of the country are built. The great trunk lines have developed practically all of the available east and west routes,' at least between the Atlantic and the Middle West, and all of the necessary lines from north to south. More tracks will doubtless be built, but they will be the expansion of one- and two-track lines into four, or even six-track roads, or the construction of short stretches of expensive recon- struction to obtain low-grade lines. If irrigation succeeds in transforming parts of the great West from deserts into fertile farms, there will probably be an enormous increase in railroad building in the West, but even this will be 68 ESTIMATION OF VOLUME OF TRAFFIC. 69 under different circumstances and conditions from those under which our railroads were built during the period from 1860 to 1890. If we examine a railroad map of the United States, it will not be easy to find a spot in the New England States (except Maine), in the Middle Atlan- tic States, or in the States around the Great Lakes, which is '20 miles from any railroad. If we consider that the whole country was gridironed with railroads running north and south and east and west at a distance apart of 25 miles, only one point in each square would be as far as 12.5 miles from any road. Such squares would have 50 miles of road for 625 square miles of territory or 8 miles per 100 square miles of territory. The average for the whole United States (8.08) is even now greater than this. Maine is the only State east of the 95th meridian in which the number is less than 8. The practical meaning of the above is that the rail- road building of the future in the eastern part of the United States will probably be confined to the con- struction of comparatively short cross-country lines whose chief purpose is to give additional facilities to sections of territory which already have railroad lines within ten to twenty miles. This again means that a railroad will not usually be able to monopolize all traffic in the territory through which it passes and for as many miles back from the railroad as railroad influence may be considered to extend, but that it must directly compete with other roads for its traffic. Of course it will have a virtual monopoly on sources of traffic which are so near to its line that no other road could obtain such traffic except at a prohibitive sacrifice, but it will mean that for some distance out of large cities, which are entered by. several railroads from approximately the same direc- tion, the traffic will be largely competitive. It will fre- quently be found that a very large proportion of the 70 THE ECONOMICS OF RAILROAD CONSTRUCTION. traffic of a railroad is competitive traffic and that the strictly non-competitive traffic, the local traffic which it picks up from its own immediate territory, is compara- tively unimportant. On this account we must largely modify the methods of estimation which would have been proper many years ago and also estimates based on the history of roads which have been long established, since in general those roads began under traffic considera- tions which are different from those of a new road of the present day. 40. Methods of estimating volume of traffic. — We may first begin with the most rapid, easy, and approximate methods which have their value, because their rapidity and simplicity renders them easy to apply and they at least form a valuable check on other and more elaborate methods. In Table III are shown the gross "earnings Table III. — Gross and Per-capita Railroad Earnings — Whole United States. Year. Gross earnings from operation (millions) . Population (thousands) . Earnings per capita. 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 $1,073 1,075 1,150 1,122 1,247 1,314 1,487 1,589 1,726 1,901 1,975 2,082 2,326 2,589 2,394 2,419 2,751 67,800 69,100 70,400 71,700 73,000 74,300 75,995 77,592 79,190 80,788 82,385 83,983 85,581 87,179 88,777 90,375 91,972 $15.83 15.55 16.33 15.65 17.08 17.95 19.56 20.48 21.80 23.53 23.97 24.79 27.18 29.70 26.97 26.77 29.91 ESTIMATION OF VOLUME OF TRAFFIC. 71 from operation " for the whole United States for each year, from 1894 to 1910 inclusive, and in the next column the actual or estimated population. Dividing one by the other we have the average earnings per capita for the whole United States. It is interesting to note from this the comparatively low value of these receipts in 1894, which immediately followed the panic year of 1893, and how, by an almost uniform rise, the receipts increased with the boom times until 1907. Then, notwithstanding the growth in population, the gross earnings dropped nearly 200 millions and the average per capita dropped nearly three dollars. Since then they have recovered even more than that loss per capita, and now the per capita earnings are nearly double those in 1894. A study of the last column shows that, barring fluctuations, a nor- mal increase in per capita earnings may always be expected. These values, after all, are but average values, and are the average of the whole ten sections into which the area of the United States is divided by the Interstate Commerce Commission. By reference to the map of the United States shown in Fig. 4, it will be seen that -the whole ter- ritory of the United States is divided into groups. These groups are found to vary considerably in the character of their population, its density, the number of miles of railroad per hundred square miles of territory, and in the amount contributed per capita. In Table IV are shown the gross earnings for the year 1900 as divided among the different groups. Unfortunately the report of the Interstate Commerce Commission for 1910 does not contain similar data for that year, but the figures given, although now somewhat out of date, will still illustrate the principle. The figures in the last column are not based on data which are so accurate that the figures may be considered to be precise, but the errors involved are certainly small 72 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table IV. — Statistics of Mileage and Gross Earnings in Differ- ent Sections of the United States (1900). Number of miles of line Number of Gross earn- Mileage. per hundred miles of line ings per mile ings per square miles per 10,000 capita. of inhabitants. operated. territory. Group I. . . . 7,622 12.30 13.63 $12,392 $17.31 II 21,481 19.88 12.91 16,514 21.55 Ill 23,403 18.66 24.38 9,273 23.14 IV 11,894 8.53 20.71 5,250 10.39 V 22,672 7.57 21.05 5,323 10.62 VI 43,448 11.73 34.31 6,727 23.74 VII 10,930 2.64 66.49 5,233 35.05 VIII 23,775 6.51 37.80 5,363 20.30 IX 12,233 3.74 30.78 4,664 13.97 X 15,889 2.09 51.13 6,349 30.49 United States. . 193,346 6.51 25.44 $ 7,722 $19.67 and the figures are amply accurate for our purpose. The figures are seen to vary considerably from the average receipts per head of population for the whole United States. As a general statement it is true that the estimated earnings for a road to be constructed in the territory of any one of these ten sections would be given more accurately by the average figure for that section than by the figure given for the whole United States. Such a figure has its value as a first trial and preliminary estimate of the probable traffic of a road. 40A. Seasonal variations. — The earnings of a road, its operating expenses, and therefore its net revenue, vary from month to month throughout the year, and the variations are remarkably uniform during successive years. This variation is well shown in Fig. 5a, in which the lines show the actual variations in dollars per mile of line for the year 1911. The shaded areas show the maximum variation of each line during the preceding three years. This shows that the maximum revenue invariably occurs ESTIMATION OF VOLUME OF TRAFFIC. Fig. 5a. 73 Fig. 5a. — Seasonal variations in revenues and expenses. 74 THE ECONOMICS OF RAILROAD CONSTRUCTION. during October. The expenses are also a maximum, which practically means that expenses which may be somewhat controlled, such as extraordinary maintenance expenses, are purposely timed when the revenues to meet them are maximum. The revenues drop rather steadily until February and controllable expenses are likewise regulated accordingly. There is always a small increase in March and a drop in April, after which the rise begins for the big Fall business. The monthly variation in the operating ratio is also shown. The maximum is of course in January or February, when revenues are the lowest. 41. Estimate of earnings per mile of road. — It is some- times attempted to quickly estimate the probable earnings per mile of road by a comparison of the earnings per mile of existing roads which are similarly situated. The gross earnings per train-mile for every railroad in the United States are given in the statistics of the Interstate Com- merce Commission. We will consider first the gross earnings per mile of road and per train-mile for the ten greatest railroad systems of the country and will also consider similar figures for ten small railroads which are chosen at random, except that their mileage is invariably less than 100 miles and also that they are all independent railroads, and therefore it need not be considered that their gross earnings are dependent upon their relationship to a larger trunk system. These figures are given in Table V. An inspection of these figures will show that the gross receipts per mile of road are exceedingly variable, even for roads in the same section of the country and of approxi- mately the same mileage. On the one hand, it will be seen that the earnings per mile of road of the five small roads in Group II are all very much smaller than the average per mile of road for that group. The earnings per mile of road evidently bear a close relation to the frequency of the train service, and this of course is exceedingly variable. ESTIMATION OF VOLUME OF TRAFFIC. 75 Table V. — Gross Earnings per Mile of Road and per Train-mile for Great and Small Roads (1C04). No. in Mileage. Gross annual receipts. Gross earn- ings Re- port. Per mile of road. Per mile of road for that group. per train- mile. Whole United States 220,112 $9,306 $1.94 5? Canadian Pacific C. B. &Q Chicago & Northwestern . Southern Railway C. R. I. & P 8,382 8,326 7,412 7,197 6,761 5,619 5,031 4,489 4,374 4,229 $5,540 7,640 7,190 6,270 5,580 8,300 8,330 8,080 10,710 4,860 $1.92 141? 2.04 1407 1.71 939 1.49 1433 1.64 1534 1383 Northern Pacific A. T. & S. F 2.66 2.17 1471 Great Northern 2.94 1242 Illinois Central. . 1.58 975 Atlantic Coast Line.. .... Average of ten 1.67 $ 7,250 $1 98 78 134 349 374 396 486 660 769 1239 1835 Montpelier & Wells River. Somerset Railway Co ... . Hunt. & Broadtop Mt . . . Lehigh & New England. . Ligonier Valley Newburgh, Dutch. & Conn. Susquehanna & N. Y. . . . Detroit & Charlevoix . . . Harriman & Northeast'n Galv., Hous. & Henderson Average of ten. 44 42 66 96 11 59 55 51 20 50 $ 4,095 2,960 11,560 1,990 6,570 2,910 3,625 1,770 4,510 7,560 13,994 13,994 ] 1 - 20,187 11,863 6,679 5,443 $1 45 1.35 f 1.82 | 1.14 i 2.06 | 1.08 1 1.74 2.11 2.73 3.29 $4,755 $1.88 There is hardly a possibility of uniformity until we deter- mine the average revenue per train-mile, which is also given in Table V. In this case, however, there is a uni- formity which is really remarkable in spite of the varia- tions which are seen. It may be noted that the average revenue per train-mile for the large roads is much more nearly uniform and that it closely approximates to the average value for the whole United States as might have been expected. The revenue per train-mile from the smaller roads, while it covers a far larger range than in the case of the larger systems, is nevertheless a figure with some 76 THE ECONOMICS OF RAILROAD CONSTRUCTION. limitations. It seldom drops below $1, and the cases are rare where it rises above $3. But even such a figure is of but little value until the proper number of train- miles per year may be determined, and this after all brings us back to the point where we started, viz., the determination of the amount of traffic from which we may obtain an idea as to the number of trains. It is perfectly true, as elaborated later, that on roads of very small traffic the number of trains will not be strictly proportional to the number of passengers carried nor to the gross number of the tons of freight. Nevertheless, if the number of trains is increased in order to encourage traffic, the revenue per train-mile will be reduced, although it is sometimes a wise proceeding to do so. 42. Estimate of tributary population. — Having decided on some estimate for the receipts per head of tributary population, even if it is only for a preliminary and rough estimate, the next step is to determine the number of the tributary population. A large map with a scale of say one mile to the inch is of considerable assistance in determining this. On this map, which may be one of the easily obtainable railroad maps or a set of maps such as are published by the U. S. Geological Survey, we may see the location of all existing railroads. The proposed road will probably pass to some extent through territory considered exclusively its own. If it passes through a valley, so that it is separated on either side by high hills from the valleys occupied by other railroad lines which are perhaps ten miles away, it may reasonably claim all of the population within the valley through which it passes. The population of this area may be determined with sufficient accuracy from census records or other sources. Where the road passes through towns which are already served by one or more lines, it is not right to consider that the entire population of that town ESTIMATION OF VOLUME OF TRAFFIC. 77 will contribute per annum the average per-capita quota. In fact it would be more nearly true to say that the per- capita quota multiplied by the population of the town will be distributed amoi.g all the roads concerned in the relative proportion of their importance. Or, in other words, if we divide the po[ ulation of the town into parts which are proportional to the relative importance of the roads, we may consider that the income from that town will equal that proportion cf the total population multiplied by the average per-capita figure. By thus computing the tributary population for each section of the road we may multiply the sum total by the assumed per- capita figure and obtain a rough estimate of the gross receipts. 43. Estimate by comparison with other roads. — Still another method of estimating the gross revenue from operation is to obtain the figures of the gross revenue of an existing road which is operating under conditions which are similar to. those of the proposed line. This might be done by saying that since the existing line has gross receipts of so much per mile, and since the proposed line will have very similar advantages, the receipts per mile of road should be substantially the same. Perhaps a still better method than the above would be to estimate the tributary population of the existing road by the method indicated in the last section. An estimate should then be made of the population which would be tributary to the proposed line. Dividing the gross receipts of the existing line by its tributary population would give a fairly reliable estimate of per-capita receipts from such a community. Multiplying this figure by the tributary population of the proposed line would then give a fairly close estimate of its probable revenue. Probably the greatest danger underlying the above method comes from the inaccuracy of the assumption that the existing 78 THE ECONOMICS OF RAILROAD CONSTRUCTION. road and the proposed road will operate under similar conditions or that their tributary populations will have equal revenue-producing capacities. An experienced man may however use this method by making a suitable allowance when he considers that the proposed road will be more valuable or less valuable than the line with which it is compared. Even though this method is confessedly inaccurate and subject to error, it should generally be utilized, because it is nearly always possible to obtain sufficient data for the purpose with but little trouble, and the results obtained are a valuable check on the results which will be computed by the other methods. 44. Actual estimation of the sources of revenue. — Prac- tically the only accurate method of making any such computations is to study the entire territory which will be served by the road and estimate in detail the amount of business which will be obtained from every manu- facturing plant, mine, lumber-camp, and even every farm. Through country districts and through towns which are not already served by a railroad such an estimate is not very difficult. Generally the errors will be on the safe side, unless rendered valueless by a gross exaggeration of the expected increase in business. A factory which can do business without railroad facilities will frequently multiply its business many times when it is connected with the outside world by a railroad which passes its doors. It is usually safe to estimate a freight-charge not only on the entire present output of the factory, bnt to even consider that the factory will grow and furnish a much larger amount of business. An experienced estimator will soon estimate the probable yield of the farms which are within five miles of the road and what would be the probable market for the produce when it became possible to ship it by rail. In estimating what farms should be thus included the distance from the ESTIMATION OF VOLUME OF TRAFFIC. 79 farm (perhaps in an opposite direction) to another rail- road and also the nature of the roads and the hills should be taken into consideration. It is usually possible to predict with certainty that a farmer who had previously hauled his entire output over a steep hill for a distance of seven or eight miles to an existing road will transfer his entire business to the new road because the new road will be only three miles away and the grade is downhill. It may even be justifiable to consider that the farmer will produce more of certain kinds of crops, since the accessibility to the markets produced by the proposed road will encourage him and will enable him to make profits w 7 hich were unobtainable before. Of course the estimator must have sufficient knowledge of mercantile values to know what are the probable markets, not only for farm-produce, lumber, and minerals, but also for manufactured products. The estimator will consider each proposed station on the road in turn and will estimate (considering first the freight business) that the farms within reach of that station will annually bring to that station so many tons or car-loads of various kinds of farm-produce which will probably be shipped to a certain market, or at least will be shipped from that station to one or the other of the termini of the road where. they will connect with other lines. Multiplying that tonnage of produce by a suitable freight-rate for the distance will determine the receipts for those items. Each lumber tract, each mine and each factory should be considered in the same way. Unless there is some place along the line where certain products are consumed the traffic of this kind will usually run from the local station to one or the other of the termini. Of course there will be a small' amount of local freight traffic between stations along the line, but this is usually a comparatively small proportion of the business done. 80 THE ECONOMICS OF RAILROAD CONSTRUCTION. 45. Statistics of average traffic. — Statistics show that the proportion of the passenger revenue to the total earnings is roughly constant, and yet it varies considerably in the different groups. This is best shown in Table VI. Table VI. — Public Service of Railways, by Groups (1900). ^ o° ^ 0) a C TO O bfl "p. C3 1 Passenger service. Freight service. of pas- s carried ile per f line. u B ex' 3 c . 50 C C CXl .11 of tons ght ear- ne mile ile of 3 Si ■43 c S-i >- c C (B O C asg 60 >— »'§ ° £ . tIC D O O en-* c. £ "2 r 1 O — ca a-^ R 1- rC«wT3 j_ 0, m "*"'S 03 u p "3 M 03 3»iOC go.S £& § C c;=i |S Ph w £ < t3 QTCJ o <§• L — ° ( > { ) c J -J L. < ) ( > i 1 : > ( ( 33 ^ 33 4 4 : ) U jfif m ife 1 >n n | i i U N 1 a c ( aM 1 > N c co ) ) o 1 If ) i o o o o o o 158 THE ECONOMICS OF RAILROAD CONSTRUCTION. the draft-gear is in tension the coupler, which is rigidly attached to B, is drawn to the left, drawing the follower Z with it. Compression is then exerted through the gear mechanism to the follower A which, being restrained by the shoulders RR, against which it presses, causes the gear to absorb the compression. The coil-spring C forces the eight wedges n against the eight corresponding segments E. The great compression of these surfaces against the outer shell produces a friction which retards the compression of the gear. The total possible movement of the gear, as determined by an official test, was 2.42 inches, when the maximum stress was 180,000 pounds. The work done in producing this stress amounted to 18,399 foot-pounds. Of this total energy 16,666 foot-pounds, or over 90%, represents the amount of energy absorbed and dissipated as heat by the frictional gear. The remaining 10% is given back by the recoil. The main release spring K is used for returning the segments and friction strips to their normal position after the force to close them has been removed. It also gives additional capacity to the entire mechanism. The auxiliary spring L releases the wedge D, while the release pin M releases the pressure of the auxiliary spring L against the wedge during frictional operation. If we omit from the above design the fric- tional features and consider only the two followers A and Z, separated by the springs C and K, acting as one spring, we have the essential elements of a spring draft- gear. In fact this gear acts exactly like a spring draft- gear for all ordinary service, the frictional device only acting during severe tension and compression. CHAPTER IX. TRACK ECONOMICS. In this chapter will be discussed some of the items of the cost of track construction and maintenance, which are so large and important that they should be studied with great care, in order to discover any possible economies. Chief among these items are the costs of rails and ties. A very brief study of the subject will show that variations in the weight and character of the rolling-stock, the rate of grade, the amount and sharpness of curvature, etc., will modify the expenditure which may, with the best economy, be made on these two items. Rails. 99. Rail wear — theoretical. — Definite information on this subject is very difficult to obtain. If rails were only renewed when a certain proportion of their total weight had been worn away — say one-quarter of the head or about 10% of the total weight — then it would be a com- paratively simple matter to estimate the effect of aline- ment on rail wear. But it frequently, if not generally, happens that rails on tangents are removed, not on account of wear on the head, but on account of failure at the joints. When the steel of a rail is comparatively soft and duc- tile, the effect of concentrated wheel-pressure is to cause an actual flow of the metal, so that it will spread outside of its original outline, as is shown in the figure. The burr 159 160 THE ECONOMICS OF RAILROAD CONSTRUCTION. on the inside of the head will generally be worn off by the occasional pressure of a wheel-flange against the rail. The top of the rail will be worn with a slight slope to the inside, which corresponds somewhat with the coning of the wheels. Fig. 11 shows the usual outline of a worn rail on the outside of curves. The wear is largely on the inner side of the head, the side of the head being practically gone before the top of the rail is much worn. The inside rail of a curve will wear to about the same form as a rail on a tangent, as shown in Fig. 12, but the wear is much faster. Fig. 11. Fig. 12. Fig. 13. Rail wear on curves is due chiefly to two causes: slip- ping due to unequal length of the rails and grinding of the side of the head by the wheel-flanges. (a) Longitudinal slipping. When a pair of wheels which are not rigidly attached to their axle run around a curve (see Fig. 13), the outer wheel must roll a distance T0L ^r 2 and the inner wheel will roll a distance of -^&\ 360 c 2~a° LTZOL 36U 9- 360° This shows The difference equals -w^>(r 2 -ri) or that when the wheels are fixed for any one gauge (g), the slipping is proportional to the number of degrees of central angle, equals ca°, and is independent of the radius. This slipping must be accomplished by the inner wheel slip- ping forward or the outer wheel slipping backward, or by a combination of the two which will give the same total amount of slipping. It is quite probable that the most of TRACK ECONOMICS. 161 the slipping occurs on the inner rail, and that this accounts for the great excess of rail wear on the inner rail of a curve over that on a tangent. (b) Lateral slipping. The two (or three) axles of car- trucks and the two or more driving-axles of a locomotive •are always set exactly parallel to each other. This is clone so that each pair of wheels shall mutually guide the other and maintain each axle approximately perpendicular to the rails. If the two axles of a truck are not exactly parallel, the truck has a constant tendency to run to one side, producing additional track resistance, rail wear, and wheel-flange wear. When two pairs of wheels with parallel axles are on a curve, the planes of at least one pair of wheels must make an angle with the tangent to the rails. When the radius of the curve is very short compared with the length of the wheel-base (as generally occurs at the street-corners of street-railways), then both axles will make angles with the normals to the curve, as shown in Fig. 14. The normal case for ordinary railroad work with easy curvature is that shown in Fig. 15, in which the rear axle stands nearly or quite normal to the curve, while the front axle makes an angle a° with the normal, Fig. 14. Fig. 15. Fig. 16. and the plane of the wheel makes an angle of a° with the rail. The relative position of the outer front wheel and the rail is shown more clearly, although in an exaggerated way, in Fig. 16. The wheel tends to roll from a to b. Therefore, in moving along the track from a to c, it rolls 162 THE ECONOMICS OF RAILROAD CONSTRUCTION. the distance ab and slides laterally the distance be, which equals ac sin a. In the usual case (Fig. 15) sin a = t+r. When t = 5' and r = 5730', the radius of a 1° curve, a = 0° 03'. For the usual radii of railroad curves a will vary almost exactly with the degree of the curve. For example, on a 6° curve, using a 5-foot wheel-base, a=0°18' and sin a = .0052. For each 100 feet traveled along a 6° curve, the lateral slip of the front wheels is 0.52 foot, or about 6i inches. If the rear axle remains radial there is no lat- eral slipping of the rear wheels. It can readily be seen that when the angle a is large, the wheel-flange continually grinds the side of the head of the rail. The larger the angle the more direct and destructive is the grinding action. ioo. Rail wear — statistics.— It is very difficult to ob- tain reliable figures regarding rail wear and especially of the rail wear on curves. Such figures as are obtainable are almost hopelessly contradictory. The author has corresponded with the Chief Engineers or Engineers of Maintenance of Way of several prominent railroads in the hope of collecting such data. Very few satisfactory answers were obtainable. Usually the answers gave merely the average total life of rails on tangents and on various curves. It should not be forgotten that almost the only value of the figures quoted below lies in the statement of the relative life on the various curves of any one division of a road where the rails are of the same kind and are subject to exactly the same train-loads. One such statement is given by Mr. W. B. Storey, Jr., Chief Engr. of the A. T. & S. F. Rwy. The statement gives the approximate times of rail removal of 75-lb. A. S. C. E. rails on mountain curves of that road, on which the freight-trains are hauled by " Santa Fe " engines, which are decapods with trailing wheels, and have a very long wheel-base. TRACK ECONOMICS. 163 Table XIII. — Life (in Months) of Rails on Mountain Curves- A. T. & S. F. Rwy. 10° 8° 6° 5° 4° 3° Outer rail Inner rail 9 mo. 18 mo. 15 24 24 4S 40 60 56 72 /6 to 8 I yrs. The relative life of these rails is better appreciated by a consideration of the curves of Fig. 17. 120 100 GO 40 \ \ \ \ \ \ \ \ \ \ \ X C \ ^S % Vs '^ X T % ^ Fig. 1' 7° Degree of curve. Total rail life in months. m A similar statement was furnished by Mr. A. C. Shand, Chief Engr. of the P. R.R. This statement does not differentiate between the wear on the outer and inner rails. It gives the average life of 100 rails which are sub- ject to the very heavy traffic of their main line. 164 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table XIV. — Life (in Months) of 100-lb. Rails — Main Line, P. R.R. Tangent 1° 2° 4° 6° 8° 9° 120 mo. 96 GO 30 20 14 9 The curve indicating these values has also been shown in Fig. 17. A comparison of these rates of wear apparently indicates that, although the rate of rail wear is less (under the given conditions) on the A. T. & S. F. than on the P. R.R., the reduction in rail life, by increasing the curvature from 4° to 9°, is far greater on the A. T. & S. F. than on the P. R.R. More important, however, is the agreement of both curves that they are concave upward. A considerable part of rail wear is independent of whether the track is curved or straight. The rails on a curved track are subject to all forms of wear which reduce the life of rails on a straight track and much other wear in addition. If we draw a straight horizontal line through the "120," the vertical distance down to the P. R.R. curve at any point indicates the reduction in the life of the rail on account of curvature. This reduction is less per degree of curve as the curvature is sharper. Although we clo not know where the "tangent" ordinate belongs for the A. T. & S. F. curves, it is evident that the same principle holds good. This only verifies the theoretical deduction previously made that the longitudinal slipping (and the amount of rail wear it causes) is independent of the radius. ioi. Rail-wear statistics on the Northern Pacific R.R. — Some five-year tests have just been made on the Northern Pacific Railroad to determine the actual wear of rails under a measured amount of traffic. Apparently one object of the investigation was to determine the effect of variation in the chemical composition of the rails. A TRACK ECONOMICS. 165 pair of each of five types of rails were tested in each of eight situations; six of them being on the Pacific division and two on the Minnesota division. No attempt will be made here to analyze the effect of variation of chemical composition, but, since one of each kind of rail was used in each locality, the average of all rails for each locality will be considered as the typical rail for such an aline- ment and grade. The rails were actually weighed each year for five years, so that their actual loss in weight during each year's wear could be determined. The tonnage passing over these rails was systematically recorded. It varied for these eight localities between 27,021,227 and 29,862,738 tons. For uniformity in each case, the wear was reduced to the uniform basis of 10,000,000 tons. Even though the wear is not strictly proportional to the tonnage, the variation between 27,021,227 and 29,862,738 is not large enough. to cause any serious error from this source. The wear of the rails on the tangents in per cent per 10,000,000 tons' duty is given in the following tabular form. Table XV. — Rail Wear on Tangents, Northern Pacific R.R. Five pairs of rails on first tangent, Pacific div, ; grade, 0.3%. Five pairs of rails on second tangent. Pacific div. ; grade, 0.525%. Five pairs of rails on third tangent, Minnesota div, ; grade chiefly level at bot- tom of sag. Pet. loss in four years. Pet. loss per 10,000,000 tons' duty. Pet. loss in four years. Pet. loss per 10,000,000 tons' duty. Pet. loss in four years. Pet. loss per 10,000,000 tons' duty. 1.800 2.336 1.806 2.015 1.706 .603 .783 .605 .676 .572 .960 .900 1.360 1.256 1.807 .346 .324 .490 .452 .391 .451 .825 1.135 .822 .280 .167 .305 .420 .304 .104 .648 .401 .260 It may be at once noticed that the average loss in per cent per 10,000,000 tons' duty on the first tangent was 166 THE ECONOMICS OF RAILROAD CONSTRUCTION. 0.648%; on the second tangent it was only 0.401%. In the endeavor to discover the cause of the uniformlv increased wear of the rails on the first tangent over that on the second tangent, the grade of the two tangents was considered, but the grade of the first tangent was 0.3%, while that of the second tangent was 0.525%. As rail wear is usually greater on steep grades than oh flat grades, owing to the slipping of the driving-wheels when climbing the grades, or the possible skidding of the wheels when moving down the grade with brakes set, the results are here relatively contrary to what we would expect. The only apparent explanation of the increased rail wear on the 0.3% grade is that it occurs near the bottom of a very long down grade, where a train might have acquired a high velocity and where the wheels might have skidded in the attempt to hold the train, or where engines, hauling a train up grade, are doing their utmost (perhaps by using sand) to obtain a sufficiently high velocity to carry their trains by momen- tum over the long grade. In the case of the 0.525% grade this tangent occurs at the very upper end of the grade, where the velocity in either direction is probably lower than the average. Whether this is the true explanation, the relative wear on these two tangents for all makes of rails is uniformly as stated above. 102. Relation of rate of rail wear to the life-history of the rail. — The figures obtained during the above-described tests of rails on the Northern Pacific Railroad afford some very instructive and apparently reliable data regarding the rate of rail wear in its relation to the life-history of the rail. The rails were taken up and weighed each year for a period of four or five years; the loss of weight in pounds for each yearly interval then becomes known. It is usually stated that rail wear is comparatively small during the first half of the life of the rail and that the rate of wear grows in geometric ratio. It is usually sup- TRACK ECONOMICS. 167 posed that this is more especially true of rails on sharp curves than on easy curves or on tangents. A study of the tabular values given in the report is interesting in this respect, for the figures seem to contradict this theory. The annual losses on the outer rails of 10° and 10° 30' curves were as follows : Table XVI. — Yearly Wear (in Pounds) of Outer Rails — Sharp Curves. 1st Year. 2d Year. 3d Year. 4th Year. 5th Year. r 10° curve; grade, J 0.128% ] I 13.75 11.75 13.25 5.75 9.75 13.75 9.75 9.75 7.25 7.25 11.75 9.75 9.75 1.75 5.75 18.25 12.0 16.5 4.5 7.0 21.0 13.5 21.25 11.25 15.75 Average 10.85 13.75 13.5 10.75 12.0 12.25 9.55 7.75 11.65 16.55 \ 10° 30' curve; grade, j 0.3%... | I 7.75 5.25 7.75 4.25 4.75 10.25 9.25 15.25 4.75 9.75 5.5 19.25 15.0 15.0 7.5 19.25 6.25 15.0 2.5 6.25 Average 12.45 5.95 9.85 12.45 9.85 Similar figures for the wear of rails on tangents are given in Table XVII. So many rails are involved in the above tests that we can hardly ignore the indications given by the averages espe- cially when the different lines of averages seem to vary by an approximately similar law. Apparently rail wear during the first year is greater than during the second and third years; during the fourth year it increases to about the same as during the first year, while the wear during the fifth year is usually far greater. If we ignore the three abnormally low values given for the fifth year on 10° 30' curves, the average of the other seven values is 16.71 pounds per year, which is an increase over the fourth 168 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table XVII. — Yearly Wear (in Pounds) of Rails on Tangents. Grade. 0.3%.. 0.525%. 0.3%... 0.525%. 0.3%.., 0.525%. 0.3% . . . 0.525%. 0.3%.. 0.525%. Average, . 3% . . 0.525% General average. 1st Year. 3.0 3.25 2.5 0.25 1.50 4.75 2.0 2.25 3.75 3.50 1.75 2.75 6.25 5.25 3.25 2.75 2.75 4.25 2.5 1.0 3.82 2.10 2.96 2d Year. 25 25 25 25 75 3.25 2.75 2.25 2.25 3.75 75 75 0.25 75 25 75 75 25 1.75 2.82 2.90 3d Year. 3.0 2.75 0.75 0.50 2.25 2.25 0.25 0.0 0.75 4.75 0.75 0.25 1.5 4.25 0.75 0.25 75 75 5 2.75 2.80 0.67 1.74 4th Year. 5th Year 3.25 2.25 1.50 4.75 6.50 4.25 0.50 0.75 2.50 4.50 1.0 0.50 25 75 75 25 5 25 0.25 3.5 3.80 1.87 2.84 6.0 2.25 9.0 7.0 2.25 6.25 8.50 10.25 1.25 2.25 2.25 2.0 3.25 1.75 5.75 14.0 6.25 7.5 4.75 6.25 3.90 6.97 5.94 year such as we might expect. It may be noticed in passing that all of the rails on the 10° curves were noted as being "badly worn" and that the rails on the 10° 30' curves were actually replaced. The rails on the 10° 30' curve averaged 648 pounds in weight and they had lost an average of nearly 50 pounds, or about 8%, before being replaced. The rails on the 10° curve averaged 579 pounds in weight and they had lost a little over 56 pounds apiece, which was little over 8% on their weight. They had not been actually renewed, although they were indicated as "badly worn." 103. Rail wear on curves.— In Table XVII is given an analysis of the figures furnished for the rail wear on various curves of the Pacific division of the Northern TRACK ECONOMICS. 169 Pacific Railroad. The method adopted was to determine the percentage loss in four years. This percentage was divided by the tonnage (varying between 27,021,227 and 29,862,738 tons) to reduce it to the uniform basis of the wear for 10,000,000 tons' duty. By dividing the quantities in column 3 by the average percentage loss (0.525%) on two tangents subject to the same traffic, of this same division, we have the ratio of the rail wear on a curve to the rail wear on the average tangent. Subtracting one from each one of the quantities in column 4 we have Table XVIII. — Rail Wear on Curves — Northern Pacific R.R., Pac. Div. Degree of curve. Pet. loss in four years. Pet. loss 10,000,000 tons' duty. Col. 3 -f-.525. Excess over one. Excess per degree. Average excess per degree. r I 4° 31' • 2.675 2.970 2.912 1.781 1.877 0.964 1.070 1.049 0.642 0.676 1.838 2.038 1.999 1.223 1.288 0.838 1.038 0.999 0.223 0.288 .185 .230 .221 .049 .064 ■ .150 5° 0' h 3.500 3.271 4.349 2.857 4.450 1.173 1.096 1.450 0.957 1.491 2.235 2.087 2.761 1.823 2.840 1.235 1.087 1.761 0.823 1.840 .247 .217 .352 .165 .368 1 • .270 f 1 10° 0' . . . . 1 1 I 5.150 4.417 6.205 2.087 3 . 122 1.855 1.590 2.238 0.751 1.124 3.534 3.030 4.265 1.430 2.141 2.534 2.030 3.265 0.430 1.141 .253 .203 .326 .043 .114 • .188 f 10° 30' . . . { [ 6.200 6.022 5.610 3.704 3.795 2.080 2.020 1.882 1.241 1.272 3.960 3.850 3.588 2.365 2.423 2.960 2.850 2.588 1.365 1.423 .282 .272 !247 .130 .136 1 \ .213 1 J the excess wear, which may be considered due to curva- ture alone. By dividing these quantities in column 5 by the degree of the curve we have the excess per degree. 170 THE ECONOMICS OF RAILROAD CONSTRUCTION. The average of the five values in each case is given in column 7. The significance of these numbers in column 7 may be interpreted as follows: .150, for example, means that the excess wear per degree of curve on the 150 various rails of the 4° 31' curve averaged -^-— of the wear on an average tangent. The other figures in the last column are to be interpreted similarly. The 4° 31' curve was on a 0.525% grade, the 5° curve was on a 0.3% grade, the 10° curve was on a 0.128% grade, and the 10° 30' curve was on a 0.3% grade. The rate of grade on these curves evidently does not account for the variations in these values. It is quite apparent that the rail wear per de- gree of curve for the sharper curves does not increase with the curvature, and it is more than likely that it dimin- ishes, as was indicated by the diagrams given in § 100. A similar computation was made from the results of the wear on a 3° curve on the Minnesota division. See Table XIX. Table XIX.- -Rail Wear on Curves — Northern Pacific Railroad Minnesota Division. Degree of curve. Pet. loss in four years. Pet. loss 10,000,000 tons' duty. Col. 3 + .260. Excess over one. Excess per degree. Average excess per degree. r i 3° 0' j I 1.208 1.030 1.538 1.314 1.637 .447 .392 .569 .487 .613 1.718 1.507 2.188 1.872 2.358 0.718 0.507 1.188 0.872 1.358 .239 .169 .396 .291 .453 1 • .310 Here the average excess per degree amounted to 31% of the rail wear on the tangent. The average percentage of excess per degree on the curves of the Pacific division was 20. f Oi for the one curve on the Minnesota division it was 31%; allowing the average for the four curves a weight of four and giving a weight of one for the curve TRACK ECONOMICS. 171 on the Minnesota division, the weighted mean is 22.6%. Anticipating a demand in a future chapter (Chapter XIII) for the effect of curvature on the cost of the renewal of the rails, we might state, as an approximate average figure, that, since the excess rail wear per degree of curve does not seem to increase with the curvature, it is a safe conclusion to say that it varies with the degree or curva- ture, and that therefore the excess rail wear on a 10° curve will be 226% of the rail wear on a tangent. Economics of Ties. 104. Importance of the subject. — The cost of rails is frequently the largest single item in the cost of constructing a railroad, the cost of the ties usually being less than one- half the cost of the rails. This familiar fact is apt to cause the engineer to lose sight of the fact that the relative cost for maintenance is reversed. For the last three years the average cost of maintaining ties on the railroads of the country has been over three times the cost of main- taining the rails. The amount actually spent in 1910 was over $55,000,000, or over 3% of the total operating expenses. The enormous number of ties annually con- sumed in track maintenance is so depleting the forests of the country that the price of timber has advanced very greatly during the last few years, and it has become a question of national importance which is engaging the attention of the United States Government. Therefore any method which will increase the life of a wooden tie is a matter of great importance, not only to the railroads but also to the community in general, since the whole lumber industry has been very largely affected by the use of timber for railroad-ties. 105. Methods of deterioration and failure of ties. — The failure of ties is due to some one or to a combination of a large number of causes. First, the wood may decay. 172 THE ECONOMICS OF RAILROAD CONSTRUCTION. Second, the wood may be so soft that the holding power of the spikes may be small and this requires that the spikes must be frequently re-driven in order to hold the rails. Since th'i tie must be placed symmetrically under the rails, the available area for driving spikes is very limited, and it sometimes happens that an otherwise sound tie must be taken out because it has been " spike-killed." Third, the tie may be so soft that it is crushed by the concen- trated pressure of the rail-flange and especially by the pressure of the outer flange of the outer rail on curves. This form of destruction is largely obviated by the com- paratively inexpensive device of tie-plates. 1 06. The actual cost of a tie. — The actual cost of a tie equals the total of several items, of which the first cost is but one item. It must be transported from the place of sale and delivery to the road to the place where it is to be used. A certain amount of, track-labor is necessary to place the tie in the track. A considerable amount of track-labor is necessary to maintain the track at a proper surface. The amount of this labor will depend considerably on the length, width and weight of the tie, since a large heavy tie has such a hold in the ballast that it is not so easily disturbed by the passage of trains. Since the cost of track-labor is such a very important item in the total cost of a tie, a tie which can be kept in the track for a greater length of time and with less work for maintenance may be far more econom- ical in the long run than a tie which has cost less money. The annual cost of a system of ties may be considered as the sum of (a) the interest on the first cost, (b) the annual sinking-fund that would buy a new tie at the end of its life, and (c) the average annual cost of maintenance for the life of the tie which includes the cost of laying and the considerable amount of subsequent tamping that must be done until the tie is fairly settled TRACK ECONOMICS. 173 in the road-bed. The following very conservative estimate of the relative cost of untreated ties and ties which have been treated chemically is given as follows: the cost of the untreated tie is estimated at 40 c, while the cost of the chemical treatment is assumed to be 25 c, making the total cost of the treated tie 65 c. The life of the untreated tie is assumed to be seven years and that of the treated tie fourteen years. The annual interest on the first cost estimated at 4% will therefore be 1.6 and 2.6 c. respectively. The sinking-fund at 4% which would renew each tie at the given cost at the end of its estimated life will be 5.1 and 3.6 c. respectively. The average an- nual cost of maintenance is very difficult to estimate, but, since we are seeking a comparison rather than a definite estimate of cost, all that we need to know is the excess of the cost of one method of construction over the other. Owing to the impracticability of giving a definite figure for item (c) we will assume that it balances for the two methods, but with the understanding that the advantage is very distinctly with the treated tie and that the advan- tage extends not only to the comparative cost of track- work but also the indefinite saving in operating expenses, due to less jar of the rolling-stock on a smoother track, less cost of repairs, less consumption of energy by the locomo- tive, and all the advantages of a smoother track. Collect- ing these items we have the tabulated form as follows: Untreated tie. Treated tie. Original cost Life (assumed at). Item (a) — interest on first cost at 4%. . ' ' (b) — sinking-fund at 4% tl (c) — (considered here as balanced). Average annual cost (except item (c)). 40 cents 7 years 65 cents 14 years 1 . 6 cents 5.1 " 2 . 6 cents 3.6 " 6 . 7 cents 6 . 2 cents 174 THE ECONOMICS OF RAILROAD CONSTRUCTION. 107. Chemical treatment of ties. — The methods of chemical treatment of ties will not be here discussed, as they may be found in numerous text-books. It is not easy to obtain an accurate estimate of the effect of chemical treatment, unless reliable figures showing the total life in the track of a very large number of ties are obtainable. It frequently happens that, owing to some imperfection in the tie or some error in its treatment, a treated tie may not last even as long as a wooden untreated tie. It is only by obtaining the average figures for a very large number of ties (at least several thousand) that a true measure of the economy of chemical treatment can be obtained. The lack of accurate figures is due largely to the fact that it is practically a difficult matter to keep track of the actual life of the ties. Chalk-marks, and even numbers stamped with dies, are easily obliterated in a few years. Marking the ties with tacks arranged to form letters seems to be the best method, and it has therefore been largely adopted by railroads which have determinedly made a study of this question. But such a method involves trouble and work which few roads have been willing to make.. Even when figures have been obtained regarding the life of ties, it will be found that, of a lot of ties which are supposed to be uniform and whose average life is supposed to be say seven years, a considerable percentage of the ties may need to be removed in two or three years, while a very considerable percentage of them may still be in the track after 12 or 15 years' service. Similar figures are found for the life of chemically treated ties, some of them requiring removal after a very few years' service, while others will last much longer than could be claimed by the promoters of that particular sys- tem of tie treatment. It therefore becomes necessary in comparing the life of untreated ties with treated ties, or in comparing the life of ties treated with different methods TRACK ECONOMICS. 175 of treatment, to compare the percentages of removals after a given period of years. It practically amounts to the same thing to determine for each kind of tie or each method of treatment a curve, showing the number of ties as one set of ordinates, and their corresponding life for the other. The comparison of such curves will show which manner of treatment gives the best results. 108. Comparative value of cross-ties of different mate rials. — Through the courtesy of Mr. W. C. dishing, Chief Engineer of Maintenance of Way, Pennsylvania Lines West of Pittsburg, S. W. System, the author is enabled to quote very largely from a paper published by him in Bulletin No. 75 of the American Railway Engineering and Main- tenance of Way Association. Mr. Cushing made an investigation, with a view to determining, as closely as possible, the relative value of concrete and steel cross-ties, taking cost and prospective life into account, as com- pared with the wooden cross-ties at present in use. The author states that "some of the data used are costs estab- lished from actual practice and from reliable information given, while in other cases assumptions have been made after examining the most reliable information available. It is quite true, of course, that these figures cannot be considered as absolutely correct, but it is believed by the writer that they are fairly trustworthy." The author develops his values on the basis of the formula proposed by Mr. S. Whinery, in the "Railroad Gazette " for November 11, 1904. In order to eliminate any difference due to variability of tie-spacing, all results have been reduced to the cost per linear foot of track. This annual cost per linear foot of track may be ex- pressed algebraically thus : Let x = the required annual cost of ties per linear foot of track: 176 THE ECONOMICS OF RAILROAD CONSTRUCTION. c = the first cost in the track per linear foot of track; v = the value of the worn-cut tie per linear foot of track; L = the useful life of the tie in years. i = the rate of interest = the interest on $1.00 for one year; s = an annual payment into a sinking-fund which at i rate of interest for L years will amount to one dollar (s can be taken directly from tables such as that on page 16 of Kent's Mechanical Engineers' Pc iket-book) : Then x = ci+(c — v)s. If v = 0, then x = c(i + s). On the basis of the above formula, Mr. Cushing made three tabulations which have not been copied. Table I shows the "cost delivered which a white-oak tie lasting 10 years must reach before it will be economical to use any of the ties heading the columns." The ties considered in this table were made of white oak untreated, inferior woods treated with zinc-chloride and zinc- tannin, but using no tie-plates, also ties of inferior woods using tie- plates and treated with zinc-chloride, zinc-tannin, zinc- creosote, and with creosote costing 30 and 85 cents per tie, also steel ties costing $1.75 and $2.50; also con- crete ties costing $1.50 and $2.25. Table II shows "how long ties of different materials must last in order to be as economical as white oak costing 70 cents and lasting ten years." Table III shows "first cost which can be paid for different kinds of ties in order to be as economical as white oak costing 70 cents and lasting ten years." The kinds of tie considered and also their chemical treatment, if any, are the same in Tables II and III as were stated for Table I. From these various tables Mr. Cushing made the fol- lowing deductions. TRACK ECONOMICS. 177 DEDUCTIONS FROM TABLE I. (1) With white-oak ties costing 70 cents delivered on the railroad, it is economical at the present time to buy inferior woods at a price not to exceed 50 cents, have them treated with zinc-chloride or zinc-tannin, lay them in the tracks without the use of tie-plates (except where it is necessary to use them on oak ties), and use a standard railroad spike. A life of ten (10) or eleven (11) years has been found to be a maximum for such ties without the use of tie-plates and better fastenings, and if the life of ten (10) years is not attained, there will be that much loss to the company. (2) When a white-oak tie reaches a cost of 86 or 87 cents delivered on the railroad, it will be economical to use the zinc-creosote process, or straight creosote cost- ing 30 cents, if the tie costs 46 cents delivered on the rail- road and will last (16) sixteen years; or it will be econom- ical to use straight creosoting. costing 85 cents for treat- ment if the tie can be made to last thirty (30) years, which is French practice, before the oak tie reaches a cost of 80 cents delivered on the railroad. In both of these cases it is assumed that tie-plates, wood screws, and heli- cal linings are used because ties cannot be made to last more than ten (10) or twelve (12) years without the use of proper fastenings, since, otherwise, the tie will be de- stroyed by mechanical wear. It is necessary, therefore, to use improved fastenings when we expect to obtain a life of ties greater than ten (10) or eleven (11) years. It will also be economical to use a steel tie costing $1.75 delivered if it will last twenty (20) years. (3) When the white-oak tie reaches a cost of 90 cents delivered on the railroad, it will be economical to use either ties of inferior woods treated with zinc-tannin if a life of fourteen (14) years can be obtained, the improved 178 THE ECONOMICS OF RAILROAD CONSTRUCTION. fastenings being used, or a concrete tie costing $1.50 if it will last twenty (20) years. (4) When the price of white-oak ties reaches $1, it will be economical to use a steel tie costing $2.50 if it will last thirty (30) years, a concrete tie costing $2.25 if it will last thirty (30) years, or an inferior wood tie treated with zinc-chloride if a life of twelve (12) years can be obtained. DEDUCTIONS FROM TABLE II. (5) With ties of inferior woods costing 46 cents deliv- ered on the railroad we must obtain a life of from eighteen (18) to twenty (20) years, whether treated with zinc- chloride, zinc-tannin, or zinc-creosote, to make them as economical as white-oak ties costing 70 cents. It is assumed, of course, that they must have the most ap- proved fastenings in order to attain an age as great as that. (6) With inferior woods costing 46 cents delivered on the railroad, and if the creosoting costs 30 cents, it will be necessary for us to obtain a life of twenty-one (21) years in order to make them as economical as white-oak ties costing 70 cents delivered. (7) With inferior wood ties costing 46 cents delivered, and with the creosote treatment costing 85 cents, as in French practice, it will be necessary for us to obtain a life of thirty-six (36) years from the ties in order to make them as economical as white-oak ties costing 70 cents delivered. (8) With steel ties costing $1.75 each delivered, it will be necessary for us to obtain a life of twenty-eight and one-half (28J) years in order to have them as economical as white-oak ties costing 70 cents delivered. This price is a little less than the cost of the Buehrer steel ties in the tracks at Emsworth. TRACK ECONOMICS. 179 (9) With concrete ties costing $1.50 each delivered, it will be necessary for them to last twenty-eight (28) years before they will be as economical as the white-oak ties costing 70 cents delivered. (10) With steel ties costing $2.50 delivered and concrete •ties costing $2.25 delivered, which are approximately the prices of the Seitz steel tie and the Buehrer concrete tie in the tracks at Emsworth, it is necessary for them to last over fifty (50) years each in order to make them as eco- nomical as the white-oak ties costing 70 cents delivered. DEDUCTIONS FROM TABLE III. (11) In order to make treated inferior woods as economi- cal as white oak costing 70 cents delivered, when the treated ties are equipped with proper fastenings in order to make them last as long as has been found practicable by experience, we can only afford to pay for the ties deliv- ered on the railroad, 10 cents each when treated with zinc- chloride; 20 cents each when treated with zinc-tannin or creosoted at 30 cents; 23 cents each when treated with zinc-creosote, and 29 cents each when creosoted in accord- ance with French practice. (12) In order to make them as economical as white-oak ties costing 70 cents delivered, we can only afford to pay $1.48 each for steel ties which last twenty (20) years, and $1.79 each when lasting thirty (30) years. (13) In order to make them as economical as white-oak ties costing 70 cents delivered, we can only afford to pay, as first cost of concrete ties delivered, $1.15 each if they last twenty (20) years, and $1.57 each if they last thirty, (30) years. (14) We know nothing about the life of concrete ties, and it is at least very desirable to experiment with them for yard and side tracks, even though we do not use them in the main tracks, because they might lie undisturbed in 180 THE ECONOMICS OF RAILROAD CONSTRUCTION. yard tracks for many more years than they would in main tracks. (15) When white-oak ties are costing 70 cents delivered (about present prices), we can afford to buy inferior oak and other hard woods at 45 to 50 cents (present prices) and have them treated with the zinc-tannin or zinc-chloride processes, and only use common spike fastenings. 109. Economy due to form of tie. — The standard practice in this country, especially in parts of it where rigid economy in the use of ties is not essential, is to use a tie with a rectangular cross-section. An attempt at economy has been made by adopting a form of tie which would permit a greater number of ties to be sawed from the same tree trunk. The Great Northern Railroad has been experi- menting with triangular ties, cut by sawing the maximum Fig. 18. — Method of cutting four triangular ties from one tree. Fig. 19.— Method of cutting two triangular ties from one tree. square obtained from a tree trunk into four parts by cutting through the diagonals. In this way four trian- gular ties would be obtained from a tree trunk, as shown TRACK ECONOMICS. 1S1 in Fig. 18, from which only two rectangular ties could be obtained. If the tree trunk is so small that the cross- sections of the ties would be too small when cut in this form, then two triangular ties would be cut from the trunk, as shown in Fig. 19. When tie-plates are used, the upper corners of an ordinary rectangular tie are of little use, and there is but little, if any, objection to sawing the tie so as to leave off the corners, as shown in Fig. 20. While the method of triangular ties is un- questionably economical as to the number of ties which can be produced from given sizes of timber, the ties themselves are objectionable, since the wood is apt to split and check very badly, and the durability is very greatly diminished. Economy is also possible by studying the exact dimensions of each log to determine whether it is possible to cut planks from the slabs on the outside. Formerly the slabs were wasted. The increase in the cost of lum- ber has justified the effort to save them. no. Protection against wear by using tie-plates. — Although it is found that a soft-wood tie is more easily impregnated with chemicals, and thereby insured against rapid decay, the tie is not thereby protected against mechanical wear of the rail on the tie. This wear is largely prevented by use of tie-plates. Tie-plates originally had a flat lower surface, but, since the plates were made very thin, it was found that they buckled under the pressure of the rail. It was then thought necessary to use some form of corrugation or prong which shou? J fasten the tie-plate in the tie, It has been found tha* even these corrugations will not secure the plate solidlv Fig. 20. — One tie and one or more planks from one tree. 182 THE ECONOMICS OF RAILROAD CONSTRUCTION. to the tie, but that the plate will rock on the tie with the movement of the rail, thereby enlarging the hole made by the corrugation or prong. It has been found in many cases that this actually led to abnormal wear and decay immediately under the tie-plate, which caused the removal of the tie when it was otherwise perfectly sound. On this account the Southern Pacific and the Pennsylvania Railroads, as well as most European rail- roads, have adopted tie plates which have no corruga- tions or prongs on the lower surface. During recent years experiments have been made on European railroads, and to some extent in this country, on the use of very thin strips of creosoted wood, which are placed immediately under the rails. These strips are as wide as the base of the rail, as long as the width of the tie, and not more than | inch thick; sometimes they are as thin as J inch. They are very cheap and can readily be renewed. The theory of their advantage is based on the fact that the inevitable wave-motion of the rail on the tie results either in the rail sliding over the tie-plate or in the tie-plate rocking over the tie. As long as the tie-plate rigidly retains its hold on the tie there is little or no trouble; but when the tie-plate becomes loose, then it moves on the tie and wears it as has been described. The wooden tie-plate will invariably stick to the wooden tie and the rail will slide over the tie-plate. The wear then consists entirely of that due to the rail sliding over the tie-plate, and this results merely in wearing out the wooden tie-plate, which is readily and cheaply renewed. in. Use of screw-spikes. — The ordinary track-spikes are very largely responsible for the removal of ties, since they induce decay around the spike-hole even if the tie is not spike-killed by the frequent re-driving of spikes. Even the treated ties are ruined by the spikes, especially TRACK ECONOMICS. 183 when the ties have been treated with a chemical which is soluble in water, since the water will soak into the spike-hole and leach the chemical, which then leaves the wood-fibers unprotected and subject to decay. The best substitute for spikes, and the method which has been fre- quently adopted, is the screw-spike. Although the details of their design as adopted by various roads have a con- siderable variation, they all agree es- sentially in having a length of about five or six inches; have a square or hexagonal head so that they can be screwed with a suitable wrench; they taper to a blunt point, and have a screw-thread similar to those used for any wooden screw. Of course one es- sential to the form of the head is that it shall have a flange wide enough to extend over the base of the rail and thus hold it down. It is essential that a hole, somewhat smaller than the diam- eter of the spike, shall be previously drilled into the tie. When a large number of screw-spikes are to be placed, the work is accomplished by a drilling-machine, which not only does the work more accurately but with greater speed. It has been found by actual test that such machines can put in two screw-spikes while three ordinary spikes are being driven. Even the additional time required is much more than saved by the reduction in track-work made possible by the use of screw-spikes. Although the holding-power of screw-spikes, compared with ordinary spikes, varies with the character of the wood, the average of a large number of tests showed that the relative holding-power of screw-spikes and common spikes in white oak was as Fig. 21. Screw-spike. 184 THE ECONOMICS OF RAILROAD CONSTRUCTION. 1.87 : 1, while in long-leaf pine the ratio was as 4.63 .1. This shows that screw-spikes are especially advantageous in soft-wood ties, which are so readily subject to spike- killing. ii2. Use of dowels. — Another device for retarding the destruction of ties is the invention of a French engineer and consists in using a creosoted piece of wood, into which Fig. 22. — Wooden dowels for ties. the spike, which may be either a common spike or a screw- spike, is inserted. A cylindrical hole is first bored into the tie; following this a shaper cuts a screw-thread in the sides of the hole already bored; the wooden dowels, which are already provided with a corresponding screw- thread, are then screwed in the tie. Since the upper part of the dowel is conical, the dowel is readily screwed down until it fits the hole, and there is no danger that water will soak in around the dowel. After the dowel is in place, another machine cuts it off even with the top of the tie. The dowel has a hole through the center which is bored the proper size for the insertion of the screw-spike. TRACK ECONOMICS. 185 Usually a hole the proper size is provided, even when com- mon spikes are to be used. It is found that the compara- tive resistance to displacement, both lateral and vertical, when dowels are used with soft-wood ties is very remark- able, as it very largely increases the holding-power of the spikes and thus retards one of the most common causes of tie deterioration. CHAPTER X. TRAIN RESISTANCE 113. Classification of the various forms. — The various resistances which must be overcome by the power of the locomotive may be classified as follows: (a) Resistance and losses internal to the locomotive, which include friction of the valve-gear, piston- and connecting- rods, journal friction of the drivers, also all the loss due to radiation, condensation, friction of the steam in the passages, etc. In short, these resistances and losses are the sum total of the lost energy by which the power at the circumference of the drivers is less than the power developed by the boiler. (b) Velocity resistances, which include the atmospheric resistances on the ends and sides of the train, the oscilla- tion and concussion resistances due to uneven track, etc. (c) Wheel resistances, which include the rolling friction between wheels and the rails of all the wheels (including the drivers), also the journal friction of all the axles except those of the drivers. (d) Grade and curve resistances, which include those resistances which are due to grades and curves and which are not found on a straight and level track. (e) Brake resistances. These consist of that very con- siderable proportion of the power developed by the loco- motive, which is consumed by the brakes. (/) Inertia resistances. From one standpoint the energy 186 TRAIN RESISTANCE. 187 expended in overcoming inertia, should not be considered as a train resistance, since it is stored up in the train as kinetic energy which is afterward utilized in doing useful work, or it is consumed by the application of brakes; but, in a discussion of the demands on the tractive power of the engine, one of the chief items is the energy required to rapidly give to a starting train its normal velocity, and therefore this item must be considered, since a discussion of train resistances is virtually a discussion of the power required from the locomotive to overcome all the resis- tances. 114. Resistances internal to the locomotive. — These are the resistances which do not tax the adhesion of the drivers to the rails. If the engine were considered as lifted from the rails and made to drive a belt placed round the drivers, then all the* power that reached the belt would be the power that is ordinarily available for adhesion, while the remainder would be that consumed internally by the engine. The modern locomotive testing- plant mounts the locomotive on a series of wheels placed immediately under the driving-wheels. The motion of the driving-wheels turns the wheels on which they rest, and thereby operates dynamometers which measure the power developed. The locomotive itself is rigidly secured against any horizontal motion. The power developed in the cylinders may be obtained by taking indicator-diagrams which show the actual steam-pressure in the cylinder at any part of the stroke. From such a diagram the average unit steam-pressure is easily obtained, and this average pressure multiplied by the length of the stroke and by the net area of the piston gives the energy developed by one half-stroke of one piston. Four times this product, divided by 550 and multiplied by the number of revolutions per second, gives the " indicated horse-power." Even this calculation gives merely the power behind the piston, which is several 188 THE ECONOMICS OF RAILROAD CONSTRUCTION. per cent greater than the power which reaches the circum- ference of the drivers, owing to the friction of the piston, piston-rod, cross-head, connecting-rod bearings, and driv- ing-wheel journals. By measuring the amount of water used and turned into steam and by noting the boiler pressure, the energy possessed by the steam used is readily computed. The indicator-diagrams will show the amount of steam that has been effective in producing power in the cylinders. The steam accounted for by the indicator-diagrams will ordi- narily amount to from 80 to 85% of the steam developed by the boiler; the other 15 or 20% represents the loss of energy due to radiation, condensation, etc. The power consumed by the engine in frictional resistances is con- siderably greater when the engine is hauling a train than when it is merely running light. It has been estimated that an engine when running light will consume about 11% of the power which it will develop when it is working to the limit of its capacity in hauling a train, but it has also been determined that when it is doing its maximum work about 15 to 16% of the power developed by the pistons is consumed by the engine, leaving about 84 to 85% for the train. This may be determined by a compari- son of the energy developed by the pistons, as computed from the indicator-diagrams, with the amount of energy transmitted behind the tender as measured by a dyna- mometer at the rear of the tender. 115. Velocity resistances, (a) Atmospheric. — These con- sist of the head and tail resistances and the side re- sistance. The head and tail resistances are nearly con- stant for all trains of given velocity, varying but slightly with the varying cross-section of engines and cars. The side resistance varies with the length of the train and the character of the cars, whether box-cars or flats. Vestibul- ing the cars of passenger-trains has had a considerable TRAIN RESISTANCE. 189 effect in reducing the side resistances by preventing much of the eddying of air-currents between the cars, although this is one of the least of the advantages of vestibuling. Atmospheric resistance is generally assumed to vary as the square of the velocity, and, although this may be nearly true, it has been experimentally demonstrated to be at least inaccurate. The head resistance is frequently as- sumed to vary as the area of the cross-section, but this has been definitely demonstrated to be very far from true. A freight-train, composed partly of flat-cars and partly of box-cars, will encounter considerably more atmospheric resistance than a train consisting exclusively of either type of car, other things being equal. On account of the extreme variation in the making-up of freight-trains no accurate figures regarding atmospheric resistance would be of much value, and this probably explains why more effort has not been made to obtain accurate determinations of this form of resistance. In the comparatively few experiments which have been made, the head resistance has been assumed to vary as the cross-sectional area and also as the square of the velocity. The results obtained by different experimenters have been so discordant as to be of little value. The discrepancies are due to the fact that both of the assumptions regarding the variation of the atmospheric resistances are inaccurate. (b) Oscillatory and concussive. — These resistances are considered to vary as the square of the velocity. Probably this is nearly, if not quite, correct, on the general principle that such resistances consist of a series of impacts. The laws of mechanics tell us that the force of impact varies as the square of the velocity. These impacts are due to irregularities in the track and to the effect of the yielding of the rails and ties in a ballast which is not homogeneous in character nor absolutely uniform in its elasticity. Even though it were possible to make a precise determination 190 THE ECONOMICS OF RAILROAD CONSTRUCTION". of the amount of this resistance in any particular case, the value obtained would only be true for that particular piece of track and for the particular degree of excellence or defect which the track then possessed. The general improvement in track maintenance during late years has had a large influence in increasing the possible train-load by decreasing the train resistance. The expenditure of money to improve track will give a road thus improved an advantage over a competing road with a poorer track by reducing train resistance and thus reducing the cost of handling traffic. Although it is almost impossible to determine accurately the effect of a given expenditure in track improvement in reducing track resistance, it is significant to note that the resistances per ton which were measured by experimenters even 25 years ago were far higher than those obtained on the improved tracks of the present day. 116. Wheel resistance. — (a) Rolling friction of the wheels. To determine experimentally the rolling friction of wheels, apart from all journal friction, is a very difficult matter and has never been satisfactorily accomplished. Another practical difficulty is that the rolling resistance on a track is more or less intimately connected with the yielding of the rail, which is due not only to its own elasticity but to the yielding under it of the ties and ballast. Theory as well as practice shows that the higher and more perfect the elasticity of the wheel and of the surface on which it rolls the less will be the rolling friction. The determina- tion, even if it could be made, would be chiefly of theoretic interest. The rolling friction is only a very insignificant part of the total train resistance. From the nature of the case no great reduction of the rolling friction by any device is possible. The use of harder rails with higher elasticity would probably have some effect in reducing it, but this effect would be so very small that it should hardly TRAIN RESISTANCE. ♦ 191 be considered in comparison with the effect of that added hardness and elasticity on the cost of the rails and the rate of rail wear. (b) Journal friction of the axles. The energy used up in this form of resistance has been studied quite ex- tensively by means of the measurement of the force required to turn an axle in its bearings under various conditions of pressure, speed, extent of lubrication, and temperature. It may be measured quite accurately by loading a pendulum with any desired weight and hanging the pendulum on to the axle. The axle is then turned at any desired speed of rotation, which is easily measured. The deviation of the pendulum from the vertical position gives a measure of the circumferential resistance. The following laws have been fairly well established: (1) The coefficient of friction increases as the pressure diminishes. (2) It is higher at very slow speed, gradually diminishing to a minimum at a speed corresponding to a train velocity of about 10 miles per hour, then slowly in- creasing with the speed. (3) It is very dependent on the perfection of the lubrication, it being reduced to J or j\ when the axle is lubricated by a bath of oil rather than by a mere pad or wad of waste on one side of the journal. (4) It is lower at high temperatures and vice versa. The practical effect of these laws is shown by the observed facts that (1) loaded cars have a far less resist- ance per ton than unloaded cars. (2) When starting a train the resistance may be as much as 16 or even 20 pounds per ton, notwithstanding the fact that the velocity resistances are practically zero. At a speed of two miles per hour it will drop to about one-half of this figure, and at seven miles per hour the resistance of loaded cars will drop to between 4 and 5 pounds per ton. (3) The journal resistance is so very greatly reduced by higher tempera- ture (which results from the increased velocity) that it 192 ^HE ECONOMICS OF RAILROAD CONSTRUCTION. largely neutralizes the increase in the velocity resistances, and tends to make the total resistance uniform for a con- siderable range of low velocities, say between 7 and 35 miles per hour. (4) As a corollary to the above, it is found that the resistance at any given speed, say 20 miles per hour, is less, if the velocity has been reduced to that figure from some higher velocity, than it is if the velocity has been increased to 20 miles per hour from a lower velocity. (5) It has been observed that freight-train loads must frequently be cut down in winter by about 10 or 15% of the loads that the same engine can haul over the same track in summer. This is doubtless due chiefly to the reduction of temperature of the journal-bearings and the consequent addition to the journal resistance, in spite of the fact that the tractive resistance will probably be less over a hard frozen road-bed, provided that the track has been kept in uniform surface. Roller bearings for cars have been used to some extent. It has been found that they very greatly reduce the start- ing resistance, but that their advantages grow less and less as the velocity increases. The effect of the adoption of this device on car repairs and maintenance has not yet been determined on a large scale, and the ultimate economy is still uncertain. 117. Grade resistance. — The amount of this may be computed with mathematical exactness. Since the trac- tive resistances are computed separately, we merely have to compute the tendency of the wheels to roll down the grade, or the resistances to pulling them up the grade, which are exactly equal when the frictional resistance is zero or when it is otherwise provided for. Assume that a ball or cylinder (Fig. 23) is being drawn up an inclined plane. If we represent its weight by W, as measured graphically by the line W in the figure, then N will measure the normal pressure against the plane, and G will measure TRAIN RESISTANCE. 193 the force required to draw it up the plane with a uniform velocity. It also measures the tendency of the weight to roll down the plane. From similar triangles we may write the proportion Wh G:W::h:d or G = -j- (1) In the diagram d is very much larger than c, but, as will Fig. 23. — Grade resistance. be shown, c is so nearly equal to d on all practicable rail- road grades that there is no appreciable error in substitu- ting c for d, and write the equation G Wh But — equals the rate of grade. Therefore we have the very simple and mathematically exact relation that the grade resistance G = W times the rate of grade. In order to appreciate exactly the extent of the approximation in assuming that the slope distance equals its horizontal projection, the per- centage of the slope distance to the horizontal projection is given in the tabular form on page 186. Incidentally the tabular form show^ the amount of error involved when we measure with the tape lying on the ground instead of holding it horizontally. Since almost all railroad grades are less than 2% (where the error is but .02 of 1%) and anything in excess of 4% is unheard-of for normal construction, the error in the approximation is generally too small fcr practical consideration. 194 THE ECONOMICS OF RAILROAD CONSTRUCTION. Grade in per cent, 1 2 3 4 5 Slope dist. ^ 100.005 100.020 100.045 100.08C 100.125 nor dist. Grade in per cent. Slope dist. nor. dist. X100. 100. 18C 100.24,' 100.319 100.404 10 100.499 If the rate of grade is 1:100, G equals JFXttTo, i-e., G = 20 pounds per ton ; therefore, for any per cent of grade, (r = (20x per cent of grade) pounds per ton. When mov- ing up and down grade this force G must be overcome in addition to all the other resistances. When moving down a grade the force G assists the motion, and the net force tending to move the car or train down the grade equals G minus the resisting forces. If the resisting forces are less than G, then the train will keep moving down the grade, and its velocity will increase until the added resist- ance to increased velocity just equals G. The train will then move at this uniform velocity as long as such con- ditions remain constant. If the resistance of a train averaged 6 pounds per ton for a velocity of 20 miles per hour and the train were started on a down grade of 0.3% at this velocity, then it would move indefinitely at this speed down such a grade. If a train were started down a 1% grade at a velocity of say 10 miles per hour, the grade force will equal 20 pounds per ton on the 1% grade. Under such conditions the velocity of the train would in- crease until the velocity resistances would equal 20 pounds per ton. The precise speed at which this will occur de- pends on whether cars are loaded or empty and on various other conditions which affect train resistance, but the velocity would probably be very high, perhaps 60 or 70 miles per hour. Since this would be too great a speed for TRAIN RESISTANCE. 195 safety with freight-cars, a 1% grade of indefinite length can never be operated without the use of brakes. As developed later in the chapters on Grade, the necessary use of brakes on a down grade is one of the objections to grade, in addition to the resistance to moving up the grade. 118. Curve resistance. — It is exceedingly difficult to obtain experimental data showing the resistance in pounds per ton which is due to curvature. Mr. J. F. Aspinall, an English engineer, who has made many elaborate experi- ments on train resistance, has commented on this difficulty substantially as follows: When the experimental train enters the curve the engine encounters the additional resist- ance first, which decreases its velocity slightly, and the draw-bar pull actually diminishes instead of increases. As the train gradually moves on to the curve, the draw-bar pull increases until it will settle to some definite value after the entire train is on the curve; but, unless the curve is very long or the speed very slow, the engine will begin to leave the curve very soon afterward. On the track on which Mr. Aspinall conducted his experiments, these con- ditions existed to such an extent that no reliable compu- tations of the curve resistance were possible. Mr. G. R. Henderson uses the value 0.5 pound per ton per degree of curve. This is based on the assumption that the resistance varies directly as the degree of curvature. Although precise figures for the curve resistance are so scarce, it is definitely known that the total curve resistance does not increase as fast as the degree of curve. While the values given by Mr. Henderson's formula may be sufficiently precise for ordinary easy curvature, the appli- cation of such a figure to the curves of 90'' radius on the New York Elevated road would mean a resistance due to curvature alone of about 34 pounds per ton. The curve resistance on these curves is far less than this figure. Al- though this is a very extreme case, it is a valuable check, 196 THE ECONOMICS OF RAILROAD CONSTRUCTION. since it shows the tendency of the increase of the resist- ance with an increase in the degree of the curve. This conclusion is also corroborated by the theoretical con- siderations already given, that the portion of the curva- ture resistance which is due to longitudinal slipping is absolutely independent of the radius. It is quite probable that the curvature resistance on sharp curves is also de- pendent on the velocity of the train, but, unfortunately, there is no experimental data by which such a conclusion can be definitely corroborated. Searles makes an allowance of 0.448 pound per degree of curve per gross ton of 2240 pounds. He does not state the derivation of the value, nor how a value is obtained to the third significant figure, but, considering that such a value is the equivalent of precisely 0.4 pound per ton of 2000 pounds or a frictional coefficient of precisely .0002, it is possible that the apparently precise value may be based on a comparatively loose approximation. 119. Brake resistances. — The fact that grades may be so steep that they cannot be safely operated, when mov- ing down the grade, without the use of brakes has been referred to in § 117. The energy consumed by brakes is hopelessly lost without any compensation. The kinetic energy possessed by the train is transformed into heat. All such energy is wasted and, in addition to this, a very considerable amount of steam is drawn from the boiler to operate the air-brakes which consume the power already developed. When trains are required to make frequent stops and yet maintain a high average speed, a considerable amount of power is consumed in applying the brakes. It has been demonstrated that engines, drawing trains in sub- urban service, making frequent stops and yet developing high speed between stops, will consume a very large pro- portion of the total power developed by the use of brakes. The brakes consume the power already developed and TRAIN RESISTANCE. 197 stored in the train as kinetic or potential energy, while the operation of the brakes requires additional steam- power from the engine. It should therefore not be for- gotten that, in some kinds of service especially, the power required from the locomotive may be many times the amount of power which is required merely to overcome mere track and grade resistance. 120. Inertia resistance. — The two forms of train resist- ance, which, under some circumstances, are the greatest resistances to be overcome by the engine, are the grade and inertia resistances, and fortunately both of these resistances may be computed with mathematical precision. The problem may be stated as follows: What constant force P (in addition to the forces required to overcome the grade and various frictional resistances, etc.) will be required to impart to a body a velocity of v feet per second in a distance of s feet? The required number of foot- pounds of energy is evidently Ps. But this work imparts W v 2 a kinetic energy which may be expressed by -5—. Equat- Wv 2 ing these values, we have Ps = -77— , or Wv 2 P =W (2) " The force required to increase the velocity from vi to v 2 W may likewise be stated as P = ^-(v 2 2 -vi 2 ). Substituting in the formula the values W = 2000 lbs. (one ton), # = 32.16, and s = 5280 feet (one mile), we have P = . 00588 {v 2 2 -v x 2 ). Multiplying by (5280-3600) 2 to change the unit of veloc- ity to miles per hour, we have P = .01267(F 2 2 -7 1 2). 198 THE ECONOMICS OF RAILROAD CONSTRUCTION. But this formula must be modified on account of the rotative kinetic energy which must be imparted to the wheels of the cars. The precise additional percentage depends on the particular design of the cars and their loading, and also on the design of the locomotive. Con- sider, as an example, a box car, 60,000 lbs. capacity, weighing 33,000 lbs. The wheels have a diameter of 36", and their radius of gyration is about 13". Each wheel weighs 700 lbs. The rotative kinetic energy of each wheel is 4877 ft. -lbs. when the velocity is 20 miles per hour, and for the eight wheels it is 39,016 ft.-lbs. For greater pre- cision (really needless) we may add 192 ft.-lbs. as the rota- tive kinetic energy of the axles. When the car is fully loaded (weight, 93,000 lbs.) the kinetic energy of transla- tion for 20 miles per hour is 1,244,340 ft.-lbs.; when empty (weight, 33,000 lbs.) the energy is 441,540 ft.-lbs. The rotative kinetic energy thus adds (for this particular car) 3.15% (when the car is loaded) and 8.9% (when the car is empty) to the kinetic energy of translation. The kin- etic energy which is similarly added, owing to the rotation of the wheels and axles of the locomotive, might be simi- larly computed. For one type of locomotive it has been computed to be about 8%. The variations in design, and particularly the fluctuations of loading, render useless any great precision in these computations. For a train of "empties " the figures would be high, probably 8 to 9%; for a fully loaded train it will not much exceed 3%. Wel- lington considered that 6% is a good average to use (actu- ally used 6.14% for " ease of computation"), but con- sidering (a) the increasing proportion of live load to dead load in modern car design, (b) the greater care now used to make up full train-loads, and (c) the fact that full train-loads are usually the critical loads, it would appear that 5% is a better average for the conditions of modern practice. Even this figure allows something for the higher TRAIN RESISTANCE. 199 percentage for the locomotive and something for a few empties in the train. Therefore, adding 5% to the co- efficient in the above equation, we have the true equation P = .0133(F 2 2 -Fi 2 ), (3) in which V 2 and Vi are the higher and lower velocities respectively in miles per hour, and P is the force required per ton to impart that difference of velocity in a distance of one mile. If more convenient the formula may be used thus : 70.224 Pi= L —(V 2 2-V 1 *), .... (4) in which s is the distance in feet and Pi is the correspond- ing force. As a numerical illustration, the force required per ton to impart a kinetic energy due to a velocity of 20 miles per hour in a distance of 1000 feet will equal 70.224(400-0) Pl= 1000 =28 lbs., which is the equivalent (see § 117) of a 1.4% grade. Since the velocity enters the formula as V 2 , while the distance enters only in the first power, it follows that it will require four times the force to produce twice the velocity in the same distance, or that with the same force it will require four times the distance to attain twice the velocity. As another numerical illustration, if a train is to increase its speed from 15 to 60 miles per hour in a distance of 2000 feet, the force required (in addition to that required for all the other resistances) will be „ 70.224(3600-225) __„ P 2000 = 1 18.50 lbs. per ton. 200 THE ECONOMICS OF RAILROAD CONSTRUCTION. This is equivalent to a 5.9% grade, and shows at once that it would be impossible, unless there were a very heavy down grade, or that the train was very light and the engine very powerful. 121. Train-resistance formulae. — Train-resistance for- mulae are usually empirical and are based on one of two forms : R=c +f v, ) R=c+fV« \ w in which R is the resistance per ton, / is a coefficient to be determined, V equals the velocity in miles per hour, and c is a constant also to be determined. Formulae of the second class, which include some power of V represented by the exponent n, usually employ the second power, but there are some variations even from this. These formulae disregard grade and curve resistances, inertia resistance, and the active resistance (or assistance) ' of the wind as distinct from mere atmospheric resistance. In short, they are supposed to give the resistance of a train moving at a uniform velocity over a straight and level track, there being no appreciable wind. It may readily be seen that, since grade and curvature resistances and the active pres- sure of the wind furnish resistances which are indefinitely variable, all general formulae must necessarily ignore these elements. The quantity c represents those elements of resistance which are supposed to be constant, or so nearly constant that their variation with velocity may be ignored. The journal friction and the rolling friction are generally considered as belonging to this class. The velocity re- sistances are usually assumed to vary as the square of the velocity, and for such formulae it only becomes necessary to determine the value of the coefficient / to obtain the value of this term. Very few resistance formulae take any account of any variation in train-load, whether the cars TRAIN RESISTANCE. 201 are loaded or empty, and whether (in freight- trains) they consist entirely of box cars, of flat cars, or a combination of all kinds. It is well known that all these elements have a very material influence on the actual train resistance, so much so that a formula which ignores such influences must be considered as very approximate. Out of a great multitude of formulae which have been proposed, a few have been selected for discussion, the formulae having been modified (if necessary) to bring them to a uniform basis for comparison, in which case R equals the total resistance in pounds per ton of 2000 pounds. (a) Baldwin Locomotive Works' formula : R = 3+l (6) This formula has the merit of extreme simplicity, but since, as shown above, extreme simplicity is incompatible with accuracy, the most that can be claimed for such a formula is that it is approximately accurate for ordinary trains and for a considerable range of velocity. Evidently appreciating the fact that the formulae is not applicable to high velocities, the following modification has been suggested for velocities between 47 and 77 miles per hour : R* = 1.5+0.2V (7) (b) Wellington's formulae. A very simple formula ascribed to Wellington is as follows : #=4+0.00557 2 (8) Although this formula is more simple than the formulae immediately following, it is evidently impossible for it to be accurate for all conditions. Wellington devised a series * The Baldwin Locomotive Works deny the authorship of formula 7. The real author is at present unknown. 202 THE ECONOMICS OF RAILROAD CONSTRUCTION. of formula which should distinguish between the character of the loading, whether it was carried in box cars or flat cars, or whether the cars were loaded or empty. The formulse also allow for the variation due to the weight of the train. Assuming that the constants have been prop- erly chosen, these formulse ought to give very much closer results than are obtainable by any other formula here quoted. R = .577 3.9 + .00657 + -^ 647 3.9 + .00757 + -^- .577 6.0 +.00837 +-|p- .647 6.0 + .01067 + -|p- . . for loaded flat cars, . . for loaded box cars, . . for empty flat cars, . . for empty box cars. (9) It should, however, be noted that a train consisting partly of box cars and partly of flat cars will have a higher resist- ance than is shown by any of the above formulse (and not a mean value), on account of the increased atmospheric resistance acting on the irregular form of the train, (c) Barnes's formula: £ = 4 + 0.167. (10) It may be noted that Barnes's formula is identical with Wellington's simpler formula when the velocity is 29 miles per hour, but gives higher values for lower velocities and lower values for higher velocities. (d) Aspinall's formula: £ = 2.23 + y* 56.9+0.0311L (11) TRAIN RESISTANCE. 203 This formula declares that the resistance varies as the | power of the velocity, and also inserts the extra term L, which denotes the length of the train in feet. This con- stitutes another method of allowing for the variation in the resistance due to the loading of the train. There is reason, however, to doubt the correctness of the form of this equation, since, if the train were comparatively long (as it might be with a train of empties), the denominator of that fraction would be increased, the fraction itself would be decreased, and the resistance per ton would be less. It is well known that the contrary would be the case, since of two trains with the same actual gross weight, one consisting of loaded cars and therefore comparatively short, and the other a comparatively long train of empty cars, the short train of loaded cars will have a less total resistance and therefore (in this case) a less resistance per ton. In addition, a long train will have a somewhat greater atmospheric resistance than a short train of equal weight, and this will increase still more the unit resistance per ton. As Aspinall's tests were made on the basis of English rolling-stock, their values are hardly applicable to American practice. (e) Searles's formula: £ = 4.82+0.005367 2 0.00048 V 2 (weight of engine and tender) 2 gross weight of train * ^ ' This formula does not take account of differences in the form of the train (whether box cars or flats) which would affect the atmospheric resistance. Neither does it take into account the relation of length to weight, or whether the cars are loaded or empty. Considering as before two trains, one of which is short and heavily loaded, and the other a long train of empties, the weight of engine and 204 THE ECONOMICS OF RAILROAD CONSTRUCTION. tender and the gross weight of the train might be the same in both cases, and yet the resistance per ton for the train of empties would be considerably higher than for the train of loaded cars, although this formula gives them the same figure. 122. Comparison of the above formulae. — For the pur- poses of comparison, we will compute the train resistance per ton according to the above formula? for a locomotive weighing 130 tons and with 2043 tons behind the tender moving at the rate of seven miles per hour. The resist- ances would be as follows : (a) Baldwin: 22 = 3 + g- = 4.16. (Jo) Wellington: R = 4 + .0055F 2 = 4.27. (c) Barnes: R =4 + .167 = 5.12. (d) Aspinall: The formula is not strictly applicable, as before stated, but the comparison will be interesting. We will assume that the 2043 actual tons behind the tender, loaded two contents to one tare, consist of 44 cars. Assuming that the cars have a total length between coupler ends of 37 feet, the length of the train would be 1628 feet, Adding 62 feet for the engine, we would have L = 1690 feet. The formula then becomes 25 6 22 = 2.23 + ^-^,-^ = 2.23 + .234 = 2.46. 56.9+52.6 (e) Searles: 22 = 4.82+0.262+0.183 = 5.265. Applying Wellington's more accurate formula, and assuming first that the cars were loaded box cars, we would have 72 = 3.9+0.367 + 0.014 = 4.28. If the cars were loaded flat cars, the resistance would be 22 = 3.9+0.318+0.013 = 4.231. TRAIN RESISTANCE. 2C5 It may be noted that these last two values agree fairly closely with Wellington's more general formula. The actual results obtained during Dennis's experiments were i.7 pounds, which is a fair average between the low values given by Baldwin and Wellington and the higher values given by Barnes and Searles. The value given by Aspin- all's formula is apparently inapplicable. Comparing these formulae for a fast passenger-train, the results will be given below. Assume that the train con- sists of six cars weighing 60,000 pounds each and that it is drawn by a locomotive whose total weight is 280,000 pounds. The train has a total length of 430 feet. We will compute, according to these formulae, its resistance at 50 miles per hour. (a) Baldwin, Eq. 6: #=3 + 8.3 = 11.3. (b) Wellington: # = 4 + 13.75 = 17.75. (c) Barnes: # = 4+8 = 12. (d) Aspinall: # = 2.23+9.64 = 11.87. (e) Searles: # = 4.82+13.40 + 73.5 = 91.72. It may be noted that the first three formulae agree about as closely as they did for the slow freight-train, and that even Aspinall's formula, although based on English prac- tice, gives a result which is very close to the average. It is seen, however, that Searles 's formula gives a result which is out of all proportion to the other results. Al- though the formula is stated by its author "to give the re- sistance per ton for all trains, whether freight or passenger, and at any velocity under ordinary circumstances," it is evidently inapplicable to the assumed case unless we admit that the other formula? are worthless. 123. Dynamometer tests. — Tests to obtain the resist- ance of trains are usually made by placing a dynamometer car between the locomotive and the body of the train. 206 THE ECONOMICS OF RAILROAD CONSTRUCTION. The coupler between the car and the locomotive includes a dynamometer attachment which automatically records at any instant the actual pull on the draw-bar. Appar- ently this ought to solve the problem very easily and accurately, but in practice it is found that the interpreta- tion of the dynamometer records is not easy and is liable to misconstruction, unless care is taken to make several allowances. One of the practical difficulties in interpret- ing the results of dynamometer experiments is to deter- mine the actual velocity, especially when the velocity is not regular. Speed-recorders are supposed to indicate the velocity at any instant, but they are not very accurate even when the velocity is uniform, and they are especially inaccurate when the velocity is fluctuating. When the velocity of the train is decreasing, the kinetic energy of the train is being turned into work, and a force transmitted through the dynamometer is less than the amount of the resistance which is actually being overcome. Therefore, unless the indication of the dynamometer is carefully cor- rected by adding to it the force calculated according to formula 4, which equals the force which is really assisting the train when its velocity is reduced from V 2 to Fi in a distance s, the indication of the dynamometer will not represent the force required to overcome the resistances actually encountered by the train. On the other hand, when the velocity is increasing, the dynamometer indicates a larger force than is required to overcome the*resistances, but the excess force is being stored up in the train as kinetic energy. In such a case, the force P 1; calculated from formula 4 on the basis of the differences of velocities in any assumed distance s, must be subtracted from the dynamometer record in order to obtain the force necessary to overcome the train resistances. Grade has a similar effect, and the force indicated by the dynamometer may be greater or less than that required at the given velocity TRAIN RESISTANCE. 207 on a level by the force which is derived from, or is turned into, potential energy. Since grade, either ascending or descending, is usually found in the track, the actual grade of the road-bed must be known and allowed for at all points. Curvature must likewise be allowed for, as it has a constant retarding force. Usually the allowance per ton is 0.5 pound. CHAPTER XI. MOMENTUM GRADES. 124. Velocity head. — When a train starts from rest and acquires its normal velocity, it overcomes not only the usual track resistances (and perhaps curve and grade resistances), but also performs work in accumulating a large amount of kinetic energy. Such work is not neces- sarily lost. In fact there need not be the loss of a single foot-pound of such energy, provided it is not necessary to dissipate the energy by the application of brakes. If for a moment we consider that a train runs without any friction, then, when running at a velocity of v feet per second, it possesses a kinetic energy which would raise v 2 it to a height of h feet, when h = ^~, in which g is the ac- celeration of gravity which equals 32.16 feet per second in a second. Still ignoring friction, the train would climb a grade until it had attained an elevation of h feet above the point where its velocity was v. When it had climbed a height of h! feet (less than h) it would have a velocity v 1 =\/2g(h — h'). As an illustration assume that v = 30 miles per hour =44 feet per second. Then /i = ~- = 30.1 feet. Still assuming that there is no friction, the kinetic energy in the train would carry it up a grade until it had attained an elevation of 30.1 feet, or 208 MOMENTUM GRADES. 2C9 it would carry it for two miles up a grade of 15 feet per mile or half a mile up a grade of 60 feet per mile. When the train had climbed 20 feet there would still be 10.1 feet left of velocity head, and its velocity would be v = \/2g(10.1) =25.49 feet per second = 17.4 miles per hour. But these figures must be slightly modified, on account of the revolving- wheels, of the train, as already discussed in § 120. When train velocity is being acquired part of the work done is spent in imparting the energy of rotation to the driving-wheels and various truck- wheels of the train. Since these wheels run on the rails and must turn as the train moves, their rotative kinetic energy is just as effective (so far as it goes) in being transformed back into useful work. The proportion of this rotative energy to the kinetic energy of translation has already been computed in § 120, in which the corrective value of 5% has been adopted. 5280 Since v equals »„ m 7 = 1.4667 V, in which v equals the velocity in feet per second and V equals the velocity in miles per hour, and since v 2 equals 2.151 V 2 we may write Velocity head v 2 in ft. per sec. 2.151T 72 in m. per h. no _,. T7<) — = 0. 03344 k 2 64.32 64.32 Adding 5% for the rotative kinetic energy of the wheels = 0.00167F 2 The correct velocity head therefore =0.0351 IV 2 On account of the great usefulness of these values, as explained later, the velocity-head for velocities varjdng from 10 to 50 miles per hour have been computed as shown in Table XX. Part of these figures were obtained by interpolation, and the final hundredth may be in error by one unit, but it may readily be shown that the final 210 THE ECONOMICS OF RAILROAD CONSTRUCTION. hundredth is of no practical importance. It is also true that the chief use made of this table is with velocities much less than 50 miles per hour. 125. Practical use of Table XX. — The previous demon- stration has been made under the assumption, many times repeated, that the frictional resistances to the movement of the train are zero. The same law will hold if we may assume that the engine is doing an amount of work which at all times is just equal to that required to overcome such resistances. It has been found that the tractive resistances (which here include all resistances except those due to grade) are nearly independent of velocity for a very considerable range of velocity, which includes the most common freight-train velocities. It is also assumed that the draw-bar pull is uniform for these various veloc- ities. This last assumption is virtually the same as assum- ing that the tractive power of the drivers is independent of velocity, and that the engine is capable of varying its output measured in horse-power indefinitely. None of these assumptions are strictly true, but a thorough appreciation of this method of calculation will assist very materially in studying the value and use of momentum grades, since the error is practically inappreciable when operating small sags and humps, and does not become of very great value except in extreme cases. We will first apply the method to some practical cases on the basis, as before stated, that the tractive resistances are independent of velocity, and that the pull on the draw-bar of the loco- motive is constant. Assume that a train is passing A (see Fig. 24) running at a velocity of 15 miles per hour. Assume that the throttle is not changed nor any brakes applied, and that the engine is capable of increasing its horse-power, so that, in spite of its increased velocity on the succeeding down grade, it is still able to exert the same draw-bar pull. At A its velocity head is that due to MOMENTUM GRADES. 211 Table XX. — Velocity Head (representing the Kinetic Energy) of Trains moving at Various Velocities. Velocity m. per h. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 11 12 13 14 3.51 4. 25 5.06 5.93 6.88 3.58 4.33 5.15 6.02 6.98 3.65 4.41 . 5.23 6.12 7.08 3.72 4.49 5.32 6.21 7.19 3.79 4.57 5.41 6.31 7.29 3.87 4.65 5.50 6.40 7.39 3.95 4.73 5.58 6.50 7.49 4.02 4.81 5.67 6.59 7.60 4.10 4.89 5.75 6.69 7.70 4.17 4.97 5.84 6.78 7.80 15 16 17 18 19 7.90 8.99 10.15 11.38 12.68 8.00 9.10 10.27 11.50 12.81 8.11 9.21 10.39 11.63 12.95 8.22 9.32 10.51 11.76 13.08 8.33 9.43 10.63 11.89 13.22 8.44 9.55 10.75 12.02 13.35 8.55 9.67 10.87 12.15 13.49 8.66 9.79 10.99 12.28 13.63 8.77 9.91 11.12 12.41 13.77 8.88 10.03 11.25 12.55 13.91 20 21 22 23 24 14.05 15.49 17.00 18.58 20.23 14.19 15.64 17.15 18.74 20.40 14.33 15.79 17.30 18.90 20.57 14.47 15.94 17.46 19.06 20.74 14.61 16.09 17.62 19.22 20.91 14.75 16.24 17.78 19.38 21.08 14. 89 16.39 17.94 19.55 21.25 15.04 16.54 18.10 19.72 21.42 15.19 16.69 18.26 19.89 21.59 15.34 16.84 18.42 20.06 21.77 25 26 27 28 29 21.95 23.74 25.60 27.53 29.53 22.12 23.92 25.79 27.73 29.73 22.30 24.10 25.98 27.93 29.93 22.48 24.28 26.17 28.13 30.13 22.66 24.46 26.36 28.33 30.34 22.84 24.65 26.55 28 . 53 30 . 55 23.02 24.84 26.74 28.73 30.76 23.20 25.03 26.93 28.93 30.97 23.38 25.22 27.13 29.13 31.18 23.56 25.41 27.33 29.33 31.39 30 31 32 33 34 31.60 33.74 35.95 38.23 40.58 31.81 33.96 36.17 38.46 40.82 32.02 34.18 36.39 38.69 41.06 32.23 34.40 36.62 38.92 41.30 32.44 34.62 36.85 39.15 41.54 32.65 34.84 37.08 39.38 41.78 32.86 35.06 37.31 39.62 42.02 33.08 35.28 37.54 39.86 42.26 33.30 35.50 37.77 40.10 42.51 33.52 35.72 38.00 40.34 42.76 35 36 37 38 39 43.01 45.51 48.08 50.72 53.42 43.26 45.76 48.34 50.99 53.69 43.51 46.01 48.60 51 . 26 53 . 96 43.76 46.26 48.86 51 . 53 54.23 44.01 46.52 49.12 51 . 80 54.51 44.26 46.78 49.38 52.07 54.79 44.51 47.04 49.64 52.34 55.07 44.76 47.30 49.91 52.61 55.35 45.01 47.56 50.18 52.88 55.63 45.26 47.82 50.45 53.15 55.91 40 41 42 43 44 56.19 59.03 61.94 64.92 67.98 56.47 59.32 62.23 65.22 68.29 56.75 59.61 62.52 65.52 68.60 57.03 59.90 52.82 55.82 58.91 57.31 60.19 33.12 66.12 69.22 57.59 60.48 63.42 66.43 69.53 57.87 60.77 63.72 66.74 69.84 58.16 61.06 64.02 67.05 70.15 58.45 61.35 64.32 67.36 70.46 58.74 61.64 64.62 67.67 70.78 45 43 47 48 49 50 71.10 74.30 77.57 SO. 91 34.32 87.79 71.42 74.62 77.90 SI. 25 S4.66 S8.14 71.74 74.94 78.23 81.59 85.00 88.49 72.06 75.26 78.56 SI. 93 S5.34 S8.85 72.38 75 . 59 78.89 82.27 85.69 89.20 72.70 75.92 79.22 82.61 86.04 S9.55 73.02 76.25 79.55 82.95 86.39 89.91 73.34 76.58 79.89 83.29 86.74c 90.26 < 73.66 76.91 SO. 23 S3. 63 37.09 50.61 73.98 77.24 80.57 83.97 87.44 90.97 212 THE ECONOMICS OF RAILROAD CONSTRUCTION. 15 miles per hour or 7.90 feet. At B it has gained 20 feet more, and its velocity is that due to a velocity head of 27.90 feet, or nearly 28.2 miles per' hour. Upon climbing the grade BC, when it reaches the point B', it has given up its velocity head, due to the additional 20 feet, and its velocity head is again 7.90. At the point C, which is 4 feet higher than B' ', its velocity head is only 3.90, which "Virtual Profile Train vel. 10.5 m. per n. Train veL 15 -ini. pe Fig. 24. — Relation of virtual and actual profile through a sag and over a hump. corresponds to a speed of about 10.5 miles per hour. As the train starts down the grade CD its velocity continues to increase from 10.5 miles per hour, and when it has reached C it has again recovered the 4 feet of velocity head and will again be moving at the velocity of 15 miles per hour. If at this point the grade again becomes level, the train will continue to move on as before at a velocity of 15 miles per hour. It will have been practically unin- fluenced by the presence of the combined sag and hump. 126. Accuracy of the above statement. — The late A. M. Wellington, in giving a detailed solution of a problem substantially like the above, declared that he had taken velocity and dynamometer records in hundreds of cases of trains that were operated substantially as above, and that he had found that for all practical purposes the draw- bar pull was constant, whether the velocity was great or small, and that the velocity at the foot of the sag or at the summit of the hump was substantially in accordance MOMENTUM GRADES. 213 with the theoretical figures obtained for the particular case. In a paper read before the American Society of Civil Engineers on December 3, 1902, by Mr. A. C. Dennis, the statement was made that, as a result of tests aggregating thousands of miles of train operation, he found that freight-train resistance, when duly corrected for existing curvature and grade and for change in velocity, was sub- stantially a uniform quantity at about 4.7 pounds per ton for loaded trains between the velocities of 7 and 35 miles per hour. Since the velocities in the above example are well within these limits, there would be little or no error due to variation of tractive resistances. Assume that the train in the above problem weighs 1500 tons. Let us assume that it approached the point A on a level track, and that it was moving at a velocity of 15 miles per hour, which is at the rate of 22 feet per second. Assuming that the tractive resistance is 4.7 pounds per ton, we would have, as the total horse-power developed at the speed of 15 miles per hour, 1500X4.7X22 550 =282 H ' P - According to the assumption of a uniform draw-bar pull, when the train reached the bottom of the sag it would be moving at a velocity of 28.2 miles per hour, and it must therefore be developing 530 H.P. When it has moved up the succeeding grade and has reached the summit of the hump, the velocity is assumed to be 10.5 miles per hour instead of 15, and the horse-power re- quired at this velocity will be only 197.4. Although the horse-power developed by a locomotive may vary be- tween rather wide limits, the range of this variation is subject to definite limitations. At a very low velocity the tractive power is absolutely limited by the frictional resistance between the driving-wheels and the rails. Al- 214 THE ECONOMICS OF RAILROAD CONSTRUCTION. though the coefficient of friction will not ordinarily exceed 25%, there are some cases where, by the use of sand, a coefficient approximating one-third may be obtained. Therefore the weight on the drivers multiplied by 25% is usually a limiting measure of the tractive power of the locomotive. At very low velocities the maximum horse- power of the locomotive is therefore limited by the prod- uct of the maximum tractive power and the velocity which the locomotive can develop. At some speed, which is usually over 10 to 15 miles per hour, it not only becomes impossible for the locomotive to develop steam fast enough to supply the cylinders at full stroke, but it also becomes far more effective to use the steam expansively. The maximum tractive force which can be developed by an engine for one complete revolution of a driver equals Theoretical tractive force (diam. piston) 2 X av. steam-pr. X stroke diameter of drivers The effective steam-pressure is considerably less than this, and none of the above quantities are variable except the pressure. If the effective steam-pressure in the cylin- der is reduced, as must be the case when the steam is used expansively, then the effective tractive power is unques- tionably reduced. In spite of the reduction in effective steam-pressure, it is possible that the speed may become so high that the horse-power developed is greater, in spite of the reduced draw-bar power, than it was before. Never- theless, the draw-bar pull certainly does decrease with increased velocity. The speed at which it will begin to decrease depends on the ability of the boiler to develop steam rapidly. In Fig. 26 is shown in a diagram the reduc- tion in tractive power with increase of velocity of the consolidation locomotive with which Mr. A. C. Dennis made the tests above referred to. It will be noticed in MOMENTUM GRADES 215 this particular case that the draw-bar pull commenced to decrease immediately, and that at 14 miles per hour the tractive force had reduced to 75%. 127. Utilization of Table XX. — Locomotive engineers very soon learned to utilize the advantage of "a run at the hill," and found that whenever they were able to approach a hill with a high velocity they would be able to draw up that hill a considerably heavier train than could be hauled if they started from rest or at a low veloc- ity at the bottom of the hill. This advantage, however ; is limited by the length of the hill, and it really becomes a question of the difference of elevation which can be sur- mounted by virtue of the kinetic energy stored in the train when it reaches the bottom of the hill. As the train (a) Hump in track otherwise level. (b) Hump on a grade otherwise uniform. (c) Sag on a grade otherwise uniform. Fig. 25. — Sags and humps on grades otherwise uniform. climbs the hill and its velocity diminishes, the tractive force will increase rather than diminish, the tractive re- sistance will diminish rather than increase (assuming that 216 THE ECONOMICS OF RAILROAD CONSTRUCTION. the velocity does not decrease to less than 7 miles per hour), and therefore the kinetic energy can all be utilized in overcoming the elevation. About the only exception to this occurs when a freight-train has been forced to attain such a high velocity at the bottom of a hill that the reserve boiler-power has been overtaxed, and the boiler-pressure falls because the boiler is unable to produce steam with sufficient rapidity, but this will be largely a matter of the way the engine is handled. In a very simple case, such as the mere insertion of a hump either on an otherwise level track or on an otherwise uniform grade, such as is illus- trated in Fig. 25 (a) or (6), whenever we can rely on a train reaching that hump with a sufficient velocity, and with the engine doing an amount of work which would carry it along the uniform grade at that velocity, Table XX will show whether that hump can be surmounted so that the velocity at the summit of the hump will still be within practicable limits, say 10 miles per hour. The other case (c) in Fig. 25 cannot always be determined accurately by this table, although the table may be de- pended on to give an approximate result, unless the case is very extreme. If a sag is very deep, one of several things may happen. First, the velocity at or near the bottom of the sag may become so great that steam must be shut off and brakes applied in order to prevent the train from attaining an objectionably high velocity. In such cases the table is not supposed to apply, since an express condition of the table is that the tractive force exerted by the engine is uniform. Second, even if it is attempted to operate the engine so that the tractive force is uniform, it may become impossible, as explained above, for the boiler to make steam fast enough to develop such power. If that full amount of power is not developed at the bottom of the sag, then the full amount of kinetic energy will not be developed, which will be necessary to permit the train MOMENTUM GRADES. 217 to surmount the steeper grade and reach the upper end of the sag with its original velocity. Whether this will be the case can best be determined by means of momentum diagrams, such as will be described later. Momentum Diagrams and Tonnage Ratings. 128. Tonnage rating. — The following demonstration is based very largely on the admirable paper by Mr. A. C. Dennis, M. Am. Soc. C. E., which has been previously re- ferred to. The paper as originally presented is very much condensed, and is not easy to be understood by those who have little or no knowledge of the subject. The state- ments and numerical illustrations have therefore been amplified in the endeavor to present a somewhat difficult subject in a simple form. 129. Tonnage rating of locomotives. — Dennis's experi- ments indicated that the draw-bar pull of the particular locomotive tested, after being corrected for inertia, grade, and curvature, when drawing a train of empty box cars, averaged about 8.9 pounds per ton. The variation from this figure between the velocities of 7 and 30 miles per hour did not exceed 0.1 pound per ton. On the other hand, the tractive resistance to loaded cars was very uniform at 4.7 pounds per ton when the " tare- weight," or weight of the empty cars, was one-third of the total weight. Since train-loads are made up of loaded, partially loaded, and empty cars, the only practicable method of uniform ton- nage rating is to equate live load and tare-weight to a uniform basis of resistance. Since empty cars showed a resistance of 8.9 pounds per ton, and since the resistance per ton was lowered to 4.7 when the cars were loaded with a live load twice the tare-weight, we may write an equa- tion as follows, in which R = the resistance in pounds per ton due to the live load, 218 THE ECONOMICS OF RAILROAD CONSTRUCTION. from which we may derive 72 = 2.6. The reasonableness of this view becomes more apparent when we consider that the total tractive resistance consists of the summation of several resistances, some of which (such as atmospheric resistance) are independent of weight, and some of which (such as axle resistance) are decreased per ton by an increase in weight. According to the above figures, a 50-car train of empties, weighing 15 tons each, would have a tractive resistance of 50x15x8.9=6675 pounds. If each car was loaded with 15 tons, we would have an additional tractive resistance of 50x15x2.6 = 1950 pounds, or a total of 8625 pounds. Loading on 15 more tons per car would add another 1950 pounds, making a total of 10,575 pounds. But the total tonnage would then be 2250 and the average resistance would be 4.7 pounds per ton. The tonnage rating is then given by multiplying the tare-weight by a factor such that the " rating ton," as it is called, multiplied by 2.6 will equal the actual tare- weight resistance per ton. But since the grade resistance per ton is a definite quantity, we cannot use the increased hypothetical equivalent in tons in allowing for the actual grade resistance. This factor therefore depends on the rate of grade. For example, on a 0.4% grade the tractive resistance for a " rating ton " is 2.6 pounds; the grade resistance is 8 pounds, the total is 10.6. A ton of tare has a resistance of 9.0 and has a grade resistance of 8.0, or a total of 17. This is 160% of a rating ton. The corre- sponding figures for other grades are as given in Table XXL In Fig. 26 is shown the actual tractive power of the MOMENTUM GRADES. 219 Table XXI. — Ratio of Tare Tons to Rating Tons for Various Grades. Grade in per cent. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Tare ton Rating ton 346% 239% 197% 174% 160% 151% 144% 139% 134% 131% 128% Grade in per cent. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Tare ton Rating ton" 128% 126% 124% 123% 121% 120% 118% 117% 117% 116% 115% locomotive used in Mr. Dennis's tests. The curve of trac- tive power was obtained by adding to the actual dyna- mometer pull the grade and rolling resistance of the loco- motive and tender. The curve represents average values; the maximum values were about 1000 pounds higher. 130. Tonnage rating for a given grade and velocity. — We will first compute the tonnage rating for this locomo- tive on the basis of a velocity of 7 miles per hour and for a 0.4% grade. The tractive power, as obtained from Fig. 26, for this speed is 28,200 pounds. The grade and tract- ive resistance for a rating ton on this grade is (8.0+2.6) or 10.6 pounds per ton. At 7 miles per hour, the locomo- tive could therefore handle (28,200 -10.6) or 2660 gross rating tons. The actual weight of the locomotive and tender was 130 tons. On a 0.4% grade this is the equiva- lent of (160%, X 130) =208 rating tons, which leaves 2452 rating tons behind the tender. The actual load behind the tender will depend on the character of the car loading. Assume first that all cars were empty, then the actual loading would be 2452 -1.60 = 1529 tons. If the live load exactly equaled the tare, we would have for each two tons one ton of live load and (1x1.60) rating tons of 2 tare. The actual tonnage would be r + 1.60 2452 = 1886 220 THE ECONOMICS OF RAILROAD CONSTRUCTION. tons. If the live load is twice the tare, the actual tonnage 3 would be X2452=2043 tons. The above calcula- 2 + 1.60 tions are on the basis of 7 miles per hour. If the speed were increased to 25 miles per hour, the tractive power R ' 30000 £We- ^ ^, 3000C X M 2 O NjJ \ u > o o > o o £"2 Operating on level. Operating on + 0.4% grade. Operating on -1.0% grade. fcH s >> u s oo . 0,03 03 8 * or? Sv 03 O "O a; o:' s 1 _03 H3 2.C0 03 9^1 0) S a K3 Is"! cj 0> a O <~ 03* c si o 03 c ■+3 3 o o go, o > P £o a QQ JOS s o H a> o P "e3 O H 51 s "5 o H 1 2 3 4 5 6 7 8 9 10 ii 12 13 1 30,300 .03 0.035 23,400 8 8 2,100 90 90 76,600 2 2 2 30,000 .14 .105 23,100 24 32 1,800 310 400 76,300 7 9 3 29,800 .32 .18 22,900 42 74 1,600 600 1,000 76,100 13 22 4 29,500 .56 .24 22,600 56 130 1,300 980 1,980 75,800 17 39 5 29,100 .88 .32 22,200 77 207 900 1,890 3,870 75,400 23 62 6 28,700 1.26 .38 21,800 91 298 500 4,040 8,910 75,000 27 89 7 23,200 1.72 .46 21,300 115 413 74,500 33 122 8 27,600 2.25 .53 20,700 136 549 73,900 38 160 9 27,000 2.84 .59 20,100 156 705 73,300 43 203 10 26,400 3.51 .67 19,500 183 888 72,700 49 252 11 25,700 4.25 .74 18,800 209 1,097 72,000 55 307 12 24,900 5.06 .81 18,000 239 1,336 71,200 60 367 13 24,000 5.93 .87 17,100 270 1,606 70,300 66 433 14 23,100 6.88 .95 16,200 312 1,918 69,400 73 506 15 22,200 7.90 1.02 15,300 355 2,273 68,500 79 585 16 21,200 8.99 1.09 14,300 405 2,678 67,500 86 671 17 20,100 10.15 1.16 13,200 467 3,145 66,400 93 764 18 19,000 11.38 1.23 12,100 541 3,686 65,300 100 864 19 17,900 12.68 1.30 11,000 628 4,314 64,200 108 972 20 16,800 14.05 1.37 9,900 737 5,051 63,100 115 1,087 21 15,700 15.49 1.44 8,800 870 5,921 62,000 123 1,210 22 14,900 17.00 1.51 8,000 1,004 6,925 61,200 131 1.341 23 14,100 18.53 1.58 7,200 1,167 8,092 60,400 139 1,480 21 13,400 20.23 1.65 6,500 1,350 9,442 59,700 147 1,627 25 12,900 21.95 1.72 6,000 1,524 10 8 966 59,200 154 1,781 26 12,400 23 . 74 1.79 5,500 1,730 12,696 58,700 162 1,943 27 11,900 25.60 1.86 5,000 1,979 14,675 58,200 170 2,H3 28 11,400 27.53 1.93 57,700 178 2,291 29 10,900 29.53 2.00 57,200 186 2,477 30 10,400 31.60 2.07 56,700 194 2,671 somehow acquired a velocity of 30 miles per hour, the tractive power of that engine at that velocity is 10,400 pounds. Assume that it then strikes a +0.4% grade. The tractive resistance per rating ton is 8.0+2.6, or 10.6 pounds per ton. The tractive force required is therefore 28,200 pounds. The deficit at this velocity is 17,800 pounds, which must be considered as a retarding force. MOMENTUM GRADES. 227 As before, since the difference of velocity heads for 29 and 30 miles per hour equals 2.07 feet, the distance This gives the point on the +0.4% retardation curve in the ordinate over 29 miles per hour. The numerical woik of computing all of these values for one curve can best be accomplished by a series of three columns, such as col- umns 5, 6, and 7 in Table XXII, following the preliminary set of columns from 1 to 4. Each retardation curve will require a similar set of columns. Figs. 27, 28, and 29 are copies of the diagrams prepared by Mr. A. C. Dennis in illustrating the article above referred to. It will be found t!nat the distances given in columns 7, 10, and 13 of Table XXII agree substantially with the value of the ordinal cs given in these diagrams. Such discrepancies as do exist are due to the fact that the tractive power of the engine has been measured to scale from the diagram Fig. 26, which indicates the tractive power. 133. Practical utilization of these diagrams. — Borrow- ing the example given by Mr. Dennis, assume that our locomotive has been loaded with 2452 rating tons behind the engine, which is the requirement for a +0.4% grade at 7 miles per hour. Suppose that a start has been made on a level grade 5000 feet long, followed by 4000 feet of 0.6% grade, followed by 3000 feet of -0.2% grade. Since the train starts on a level and is loaded on the basis of a +0.4% grade, we must follow its course for 5000 feet on the acceleration curve marked " level " in the diagram of Fig. 27. This curve has an ordinate corresponding to 5000 feet when the train is moving at a velocity of 20 miles per hour. This is therefore the velocity of the train when it strikes the +0.6% grade. The course of the Distance iu Feet Distance in Feet 228 MOMENTUM GRADES. 229 train must then be studied from the retardation curve for 0.6%. This curve has an ordinate of 3600 on the 20 miles per hour line. Incidentally we may remark that if this train had started from any point with a velocity of 30 miles per hour up this grade, its velocity would have dropped to 20 miles per hour in 3600 feet. 4000 feet further gives us 7600 feet. The point on this curve which has an ordinate of 7600 feet occurs at about 8 miles per hour. The train then passes the summit at this velocity and starts on a —0.2% grade, which will evidently be an acceleration curve. Eight miles per hour on this grade corresponds to about 400 feet. Adding 3000 we have 3400 feet, which on this curve corresponds to a velocity of nearly 21 J miles per hour. The only apparent difficulty in the above demonstra- tion is the fact that, when the train is starting, the resist- ance is far higher than the resistance which has been found to be so uniform at velocities above 7 miles per hour. Whether this would be compensated by the fact that at very slow velocities the tractive force may be largely increased by the use of sand is not very certain. Mr. Dennis's diagram showing the tractive force at veloci- ties but little above zero do not show any marked increase in the tractive force at very low velocities. The above method cannot be considered as precise, except on the basis that at very low velocities the resistance is no greater than at somewhat higher velocities, which is certainly not the case. These diagrams are probably very reliable for variations of freight-train velocities between 7 and 30 miles per hour. They are useful in obtaining the behavior of a train through a sag or over a hump. They are prob- ably not so reliable when considering the movement of a train which starts from rest. In the numerical case just considered the velocity of the train at the end of the level grade of 5000 feet would probably be less than 20 miles Distance in Feet o © © © © Distance in Feet MOMENTUM GRADES. 231 per hour, since the resistance at starting would be con- siderably greater. If, however, it had somehow acquired that velocity of 20 miles per hour at the beginning of the +0.6% grade, its behavior over that grade and down the following grade would certainly be about as computed. 134. Another tonnage-rating formula (Henderson). — The following formula has been proposed by Mr. G. R. Henderson, and has the merit of great simplicity com- bined with practical agreement with the more complicated formulae based on elaborate tests. Let R = the resistance of the train or the pull at the tender draw-bar in pounds; T = the number of tons back of the tender, including cars and contents; (7 = the number of cars in the train; P = rate of grade in per cent. For speeds up to 12 miles per hour R = T (3.5+20P)+50C. Applying this formula to a numerical case, let us assume three trains, one a train of empties, the second half filled, and the third of full cars, a full load being assumed as twice the weight of the car. The first train has 45 empties, each weighing 20 tons; the second train has 28 cars, each weighing 20 tons and carrying 20 tons of freight; the third train has 20 cars, each weighing 20 tons and carrying 40 tons of freight. Then the draw-bar pulls on a leve* would be as follows : R = (900X3.5) +(50X45) =5400, #= (1120X3.5) +(50X28) =5320, R = (1200 X 3.5) + (50 X 20) = 5200. 232 THE ECONOMICS OF RAILROAD CONSTRUCTION. The resistances per ton are 6, 4.75, and 4.33 respect- ively. It may be noted that the above values per ton are not as high for empty cars as those given by Mr. Dennis's tests, although the values for loaded cars agree fairly well. PART III. PHYSICAL ELEMENTS OF THE PROBLEM. CHAPTER XII. DISTANCE. 135. Relation of distance to rates and expenses. — Rates are usually based on distance traveled, on the apparent hypotheses that each additional mile of distance adds its proportional amount not only to the service rendered but also to the expense of rendering it. Neither hypothesis is true. The value of the service of transporting a passenger or a ton of freight from A to B is a more or less uncertain gross amount, depending on the necessities of the case and independent of the exact distance. Except for that very small part of passenger traffic which is undertaken for the mere pleasure of traveling, the general object to be at- tained in either passenger or freight traffic is the trans- portation from A to B, however it is attained. A mile greater distance does not improve the service rendered; in fact it consumes valuable time of the passengers and delays and perhaps deteriorates the freight. From the standpoint of service rendered, the railroad which adopts a more costly construction, and thereby saves a mile or more in the route between two places, is thereby fairly entitled to additional compensation rather than have it cut down, as it would be by a strict mileage-rate. The 233 234 THE ECONOMICS OF RAILROAD CONSTRUCTION. actual value to a passenger of being transported from New York to Philadelphia depends on his individual require- ments, which may vary from a mere whim to the most imperative necessity. In one case the money value approaches zero ; at the other extreme, money could hardly measure the loss if the trip were impossible. If the pas- senger charge between New York and Philadelphia were raised to $5, $10, or even $20, there would still be some passengers who would pay it and go, because to them it would be worth $5, $10, or $20, or even more. Therefore, when they pay $2.50 they are not necessarily paying what the service is worth to them. The service rendered can- not therefore be made a measure of the charge, nor is the service rendered proportional to the miles of distance. The idea that the cost of transportation is proportional to the distance is much more prevalent and is in some respects more justifiable but it is still far from true. This is especially true of passenger service. The extra cost of transporting a single passenger is but little more than the cost of printing his ticket. Once aboard the train, it makes but little difference to the railroad whether he travels one mile or a hundred. Of course there are cer- tain very large expenses due to the passenger traffic which must be paid for by a tariff which is rightfully demanded, but such expenses have but little relation to the cost of an additional mile or so of distance inserted between stations. The same is true to a slightly less degree of the freight traffic. As shown later, the items of expense in the total cost of a train-mile, which are directly affected by a small increase in distance, are but a small proportion of the total cost. 136. The conditions other than distance that affect the cost; reasons why rates are usually based on distance. — Curvature and minor grades have a considerable influ- ence on the cost of transportation, as will be shown in DISTANCE. 235 detail in the succeeding chapters, but they are never con- sidered in making rates. Ruling grades have a very large influence on the cost, but they, are likewise disre- garded in making rates. An accurate measure of the effect of these elements is difficult and complicated, and would not be appreciated by the general public. Mere distance is easily calculated; and the railroads therefore adopt a tariff which pays expenses and profits, even though the charges are not in accordance with the expenses or the service rendered. An addition to the length of the line may (and generally does) involve curvature and grade as well as added dis- tance. In this chapter is considered merely the effect of the added distance. The effect of grade and curvature must be considered separately, according to the methods outlined in succeeding chapters. The additional length considered is likewise assumed not to affect the. business done nor the number of stations, but that it is a mere addition to length of track. 137. Variable effect on expenses cf extent of change in distance. — It will be developed later that the actual added expense of increasing the length of the line will depend very largely on the amount of that increase. An engineer frequently has occasion to make a slight change in the alinement which may make a difference in the length of the line at that place of a very few feet. It is demon- strable that certain items in the expense of operation will be absolutely unaffected by such a change, while other expenses will be increased nearly, if not quite, in their full proportion. On the other hand, if the change of line amounts to several miles, a very much larger proportion of the expenses will be increased in their full proportion. If the question of substituting an entirely different loca- tion on a division of approximately 100 miles was being considered, then, so far as distance itself was concerned 236 THE ECONOMICS OF RAILROAD CONSTRUCTION. (ignoring for the moment the question of curvature, grades, etc., which must be considered separately), the expenses of transporting freight over either of those two lines would be more nearly proportional to the exact mile- age. This phase of the question will be considered in detail later on. Effect of Distance on Operating Expenses. 138. Effect of changes in distance on maintenance of way. — The items of maintenance of way are more nearly affected in proportion to the distance than any other group of items. In fact it will be easier to note the exceptions from a full 100% addition for all increases of distance. The cost of track labor, which is such a large percentage of the total cost of Item 6 (see Table IX in Chapter VI), and also the cost of all track material, will vary almost exactly in accordance with the distance. If the track-labor was so perfectly organized that there were no more laborers than could precisely accomplish the necessary work, working full time, then any additional labor would necessarily require a greater expenditure for laborers. Although a division of a road is divided into sections of such a length that a gang of say six or seven men will be employed as steadily as possible in maintain- ing the track in proper condition, the addition of a few feet of track would not probably have the effect of increas- ing the number of sections, nor would it even require the addition of another man to the track-gang. It might require a little harder work in maintaining a section, it might even mean a slight lowering in the standard of work done in order that the whole section should be covered. The fact remains that the cost of track-labor will not inevitably and necessarily be increased in a strict propor- tion to the increase in distance. On the other hand, it would not be wise to rely on any definite reduction or DISTANCE. 237 discount from the full 100% of work required, since to do so implies that, with the lessened distance there would be some loafing on the part of the track-gang, or that with the added distance the men would be overworked or would be compelled to slight their work. The items, renewals of rails and renewals of ties, should certainly be considered as changing in direct proportion to the distance. Therefore it is only safe to allow the full 100% addition for Items 1 to 7. The repairs and renewals of tunnels, bridges, culverts, fences, road crossings, signs, cattle-guards, buildings and fixtures, docks and wharves, etc. (Items 8 to 17), may perhaps be considered in the same way, although there are some of these items on which the effect is more doubtful. If a proposed change in line does not involve any difference in the number of streams crossed, then the number of the bridges and culverts will not be altered, and although the size may be altered, the effect of the change on the cost for repairs will probably be too insignif- icant for notice. For small changes of distance it may very readily happen that no bridge or culvert is involved. For great changes of distance, especially those which would involve an entire change of route for a distance of many miles, it might be proper to consider Item 9 to be affected fully 100 %. Although Items 9 and 10 are small, averaging about 1.8%, the error involved in these items by consider- ing that the change amounts to 100% for great distances and zero for small distances will be almost inappreciable. For Items 11 to 13 the full 100% will be allowed for all changes of distance, for the same reason as previously given for repairs of roadway. Item 16 will usually be absolutely unaffected by a small change in distance, since it does not usually involve any buildings or fixtures, Larger changes of distance will probably require some change in the number of minor buildings required, but 238 THE ECONOMICS OF RAILROAD CONSTRUCTION. such buildings will be the more insignificant buildings, and we are therefore making ample allowance, if, under ordinary conditions, we estimate that 20% of the average cost of all buildings (which include terminals, etc.) is allowed for this item. Under ordinary conditions Item 17 will be absolutely unaffected by any changes in aline- ment which the engineer may make. An addition to distance will not usually affect the telegraph system, except as it adds to the number of telegraph-poles and to the amount of wiring and pole fixtures. Therefore any addition to distance will not add more than 50% to the average cost of Item 14. Items 18 to 21 are insig- nificant in amount, and can hardly be said to be affected by any small difference in distance which would ordinarily be measured in feet. Larger differences, which are meas- ured in miles and which may involve, for instance, all the blank forms required for the reports of an additional sec- tion-gang, additional pay-rolls, etc., will be increased to practically their full proportion. Therefore there is but little error involved in allowing 100% on these items for changes of distance measured in miles. 139. Effect on maintenance of equipment. — The rela- tion between an increase in length of line and the expenses of Items 24, and 46 to 50 are quite indefinite. In some respects they would be unaffected by slight changes of distance, and yet it is difficult to prove that the expenses should not be considered proportionate for the distance. For example, the added train-mileage will increase repairs of rolling-stock, and will therefore hasten the deterioration and increase the cost of " repairs and renewals of shop machinery and tools" (Item 46). Fortunately, all these items are so small, even in the aggregate, that little error will be involved, whatever decision is made. It will there- fore be assumed that these items are affected 100% for large additions in distance and 50% for small additions. DISTANCE. 239 Items 40 to 42 are evidently unaffected by any change of distance. Electrical equipment, items 28-30 and 37-39, which are used on so few steam railroads, is ignored in this discussion. There only remain the four groups of items, the repairs, renewals and depreciation of steam locomotives and of passenger and freight-cars and of work equipment. The deterioration of rolling stock, which requires its repair and finally its ultimate abandonment and therefore renewal, is caused by a combination of a large number of causes, of which the mere distance they travel on the road is but one cause. They deteriorate first with age; second, on account of the strains due to stopping and starting; third, on account of the strains and wear of wheels due to curved track; fourth, on account of the additional stresses due to grade and change of grade, and fifth, on account of the work of pulling on a straight level track. In addition to this, locomotives suffer considerable deterioration due to expansion and contraction, especially of the fire-box when the fires are drawn and the fire-box and boiler become cold, and again when the fire is started up. A large part of the expenses of maintaining passenger-cars is the expense of painting, which is a matter of mere time. Considering that the changes of distance, whose economic value the engineer tries to compute, will never make a difference in the number of round trips the engine or car would make in a day or month, the added distance which may be traveled does not add to the exposure of the car to the weather. There- fore, whatever deterioration of the car paint is due to weather, it will be incurred regardless of whether the length of the division of the road is 100 miles or 99 or 101. That element of the cost of car maintenance is absolutely inde- pendent of the precise length of that division of the road. On the other hand, the wear of car- and engine- wheels, although largely affected by curvature, is certainly affected 240 THE ECONOMIC OF RAILROAD CONSTRUCTION. to some extent by wear on a straight tangent. To deter- mine the proportion of total wear due to these various causes is a matter of estimation and judgment. An approach to accuracy may be made by a compilation of the shop records of rolling-stock, repairs, showing the amount which is spent in various kinds of repairs, and estimating as closely as possible what is the cause of each form of deterioration. A check on any such estimate is the consideration that the total deterioration is simply the summation of the deterioration clue to all causes com- bined. It is therefore a question of dividing 100% into as many portions as there are contributing causes, and to assign to each cause its relative importance in per cent, so that the sum total shall reach 100. A. M. Wellington, Table XXIII. — Distribution of the Cost of Engine Repairs to its Various Contributing Causes. (Copied from Wellington.) Item. Boiler Running gear Machinery Mountings Lagging and painting. . Smoke-box, etc Tender: Running gear Body and tank Total. Total cost of item. 20.0 20.0 30.0 Distribution. » x o> u c3 'Van; Fig. 32. — Effect of uncompensated curvature. makes an angle with BN equal to the equivalent grade resistance of the curve DE, and the angle of DE with the horizontal line represents a grade on which the resistance would be the equivalent of the total resistance on the curve DE, and then we have the line EF parallel to the line BN. The average resistance throughout that stretch of track would evidently be represented by the line AF, and therefore the angle FAN represents the grade which would cause a resistance equal to the average resistance actually caused by the curves. This figure therefore illustrates the fact that if the grade of a stretch of track, consisting of curves and tangents, is kept actually uniform, the virtual grade of that track is somewhat higher than the actual grade. If it becomes necessary for trains to stop on these curves, then the full effect of the resistance is encountered and the virtual grade would be as repre- sented by the lines BC and DE. If it is possible to operate the trains throughout that stretch of track without any stops, then the virtual grade would be reduced approxi- mately to the grade AF, since the trains would regain on 278 THE ECONOMICS OF RAILROAD CONSTRUCTION. the tangents a portion of the energy which was lost on the curves. If, on the other hand, the rate of grade is reduced on the curves, so that the actual grade is as shown by the line ABCDEF in Fig. 33, the reduction of the grade on Fig. 33. — Grade virtually uniform, with compensated curves. the curves being just equal to the difference of grade which will represent the added resistance of the curves, then the virtual grade of the entire stretch of line will be as represented by the line AG. In laying out a ruling grade which is to carry a line to a summit, the compensation for curvature must unques- tionably be provided, but it adds a complication which is also illustrated in Fig. 33. An engineer is frequently required to " develop " his line in order to have the neces- sary length for a given elevation to be overcome, in order that the grade shall be kept within some chosen limita- tion; but if the grades are actually reduced on the curves, the total horizontal distance required to overcome a ver- tical elevation of HG at the rate of grade shown by the tangent AB equals AH, but the distance actually required when the curves are compensated is something more, and is represented by the line AK in Fig. 33. The problem is further complicated, owing to the fact that the necessary additional distance can only be obtained by additional "development," which of itself usually implies additional CURVATURE. 279 curvature, and perhaps a great deal of it. In order to compensate this additional curvature there is required a still further increase in horizontal distance. The locating engineer therefore is confronted by the problem of intro- ducing considerable added length of track and perhaps considerable added curvature, in order to obtain a ruling grade on which the resistance is virtually constant through- out, whether on a tangent or on a curve, and on which the maximum resistance does not exceed that of the chosen ruling grade for the line. Nevertheless, consider- ing the supreme importance of avoiding an increase in the ruling grade (as will be developed later) and the compara- tive unimportance of an increase in distance or curvature, such a method is literally the only correct method to follow. 1 80. The proper rate of compensation. — This evidently is the rate of grade of which the resistance just equals the resistance due to the curve. Unfortunately for the sim- plicity of our calculations curve resistance is variable. It is greater for very low velocities. It depends somewhat on the detailed construction of the rolling-stock, although fortunately the differences in this respect are not great. When starting a train the curve resistance may amount to two pounds per ton per degree of curve. Such a resist- ance is equivalent to that encountered on a 0.1% grade. On this account the compensaton for a curve which occurs at a known stopping-place for the heaviest trains should be 0.1% per degree of curve. On the other hand, the compensation required for very fast trains may be as low as 0.02% or 0.03% per degree of curve. But these trains are not the trains which are usually limited by grade. It is the comparatively slow and heavy freight-trains which must be chiefly considered in the study of ruling grades. Therefore from 0.04% to 0.05% must be used as the rate of compensation for average conditions. Even 280 THE ECONOMICS OF RAILROAD CONSTRUCTION. these figures must be considered as only applicable to the ordinary and usual degrees of curvature. It has been found that the resistance on the excessively sharp curvature used on street-railways or on elevated railroads is far less per degree of curve than the above figures would indicate. This is due to the fact that the actual resistance on a curved track is the sum of a number of resistances, some of which are virtually independent of the rate of curvature. Curves which occur immediately below a known stopping-place for all trains need not be compensated, for the extra resistance of the curve will reduce by that amount the work required from train- brakes in stopping the train. On the other hand, if a curve occurs just above a stopping-place it is a serious matter and should be amply compensated. In either case the down-grade traffic is not affected and therefore need not be considered. Although the suggested rate of compensation (0.04% or 0.05%) is possibly somewhat excessive, it has been recommended on the general prin- ciple that it is preferable that the compensation should be somewhat ample in order that it shall be sufficient for all cases. It is quite possible, however, that the excessive rate of compensation might require a steeper grade on the tangents, in order that the desired summit shall be reached in a given horizontal distance. In such cases the rate of compensation should be reduced to 0.035% or even 0.03%. Rules for compensation may therefore be stated as follows: (1) On the upper side of a stopping-place for the heaviest trains compensate 0.10% per degree of curve. (2) On the lower side of such a stopping-place do not compensate at all. (3) Ordinarily compensate about 0.05% per degree of curve. (4) Reduce this rate to 0.04% or even 0.03% per degree CURVATURE 281 of curve, if the grade on the tangents must be increased in order to reach the required summit. (5) Reduce the rate somewhat for curvature above 8° or 10°. (6) Curves on minor grades need not be compensated, unless the minor grade is so heavy that the added resistance of the curve would make the total resistance greater than that of the ruling grade. 181. The limitations of maximum curvature. — What is the maximum degree of the curvature which should be allowed on any road? Unquestionably there is no definite limit. If any limitation is made it depends on the general character of the country and on the amount of traffic which may be immediately expected. As an extreme case in the justifiable use of sharp curvature, we may con- sider a portion of the line from Denver to Leadville, Colo. The traffic that was expected on the line was so meager, and the general character of the country was so forbidding, that a road built according to the usual standards would have cost very much more than would have been justified by the expected traffic. The lines as adopted cost about $20,000 per mile, and yet in a stretch of 11.2 miles there are about 127 curves. One is a 25° 20' curve, 24 are 24° curves, 25 are 20° curves, and 72 are sharper than 10°. If 10° had been made the limit (a rather high limit accord- ing to usual ideas), it is probable that the line would have been found impracticable (except with prohibitive grades), unless four or five times as much per mile had been spent on it, and this would have ruined the project financially. As an illustration of the other extreme, we may con- sider some of the improvements which have been recently made on the P. R.R. between Philadelphia and Pittsburg. Millions of money have been spent in the effort to reduce distance, curvature, and grade. The reduction of curva- ture has been very largely in the form of eliminating 282 THE ECONOMICS OF RAILROAD CONSTRUCTION. degrees of central angle, but it also has taken the form of increasing the radius of curvature, so that the running of express-trains at a speed of 60 miles per hour will be facilitated. This is one of the comparatively rare cases where an increase in the radius of curvature justifies a considerable expenditure. Another illustration of the use of sharp curvature by a line of heavy traffic is given by the case of the B. & 0. R.R. in its line at Harper's Ferry. For many years the traffic of this road passed over two curves, one with a radius of 300 feet (19° 10') and then over a 400-foot curve (14° 22'). During recent years this sharp curvature has been materi- ally reduced by means of some very expensive tunneling, but the fact that the engineers of this line very wisely con- cluded to run the traffic of a great trunk line over such sharp curves shows how foolish it is for an engineer to sacrifice money or sacrifice gradients in order to reduce the rate of curvature on a road which at its best will be a line of very small traffic. Many locating engineers have started out to locate a line with instructions that their maximum rate of curvature must not exceed 6°. Pos- sibly it would be better to say that no limitation should be imposed. It is far better to operate a road on a 10° or 15° curve in some one place, provided that the cost of avoiding such a curve will be very large. This is especially true for the light-traffic roads, which constitute such a large proportion of our mileage, and which will probably constitute the great bulk of the roads yet to be constructed. Of course such belittling of the effects of curvature may be, and sometimes is, carried to an extreme and cause an engineer to fail to give to curvature its due consideration. Degrees of central angle should always be reduced by all the ingenuity of the engineer, and should only be limited by the general relation between the financial and topo- graphical conditions of the problem. Easy curvature is CURVATURE. 283 in general better than sharp curvature and should be adopted when it may be done at a small financial sacrifice, especially since it reduces the length of the line. Never- theless the engineer should not give undue prominence to curvature in comparison with the other features of aline- nimt, which are really of far greater importance. He should remember that so far as the cost of track-work is concerned, there is little if any saving in this respect, and that the extra cost of operating trains on curves is very nearly independent of the radius of curvature. Of course the trains cannot be operated at high speed on sharp curves, but if the road is a minor road such a condition will have almost no effect on the operation of trains. Above all, the engineer should not waste the capital of the road (which is usually limited) in an effort to avoid curvature, when any spare funds may more profitably be expended in making reductions of grade which will be of vastly greater financial value. CHAPTER XIV. MINOR GRADES. 182. Two distinct effects of grade. — The effects of grade on train expenses are of two distinct kinds. One possible effect is very costly and should be limited even at considerable expenditure. The other is of comparatively little importance, its cost being slight. As long as the length of a train is not limited by the power of the engine, the occurrence of a grade on a road merely means that the engine is required to develop so many foot-pounds of work in raising the train so many feet of vertical height. For example, if a train weighing 600 tons (1,200,000 pounds) climbs a hill 50 feet in height, the engine per- forms, in addition to the work due to mere tractive resist- ance and curvature, the extra work of creating 60,000,000 foot-pounds of potential energy. If this height is sur- mounted in two miles of horizontal distance (grade of 25 feet per mile) and in six minutes of actual time (20 miles per hour), the extra work accomplished by the engine is done at the rate of 10,000,000 foot-pounds per minute, which is about 303 horse-power. But the disadvantages of such a rise are always largely compensated. Except for the fact that one terminus of a road may be higher than the other, every up grade is followed more or less directly by a down grade, which is operated partly by the potential energy acquired during the previous climb. But when we consider the trains running in both directions, even the 284 MINOR GRADES. 285 difference of elevation of the termini is largely neutralized. If we could eliminate altogether the waste of energy in the use of brakes, where brakes are used to control the train on grades, we would then find that the net effect of minor grades on their operation in both directions would be zero. Whatever was lost on any up grade would be regained on the succeeding down grade or on the return trip. On the very lowest grades, the limits of which are defined later, we may consider this to be literally true, viz., that nothing is lost by their presence. It is unneces- sary to use brakes on these, grades, except for such use as would be made if the line were level. Whatever energy is temporarily lost in climbing any grade is either imme- diately regained on a subsequent down grade or is regained on the return trip. The other effect of grade is that it may so limit the length of trains that more trains will be required to handle a given traffic. The receipts from traffic are a perfectly definite sum which is independent of the number of trains. The cost of handling the traffic will be nearly propor- tional to the number of trains. Anticipating a more com- plete discussion, it may be said, as an example, that in- creasing the ruling grade from 1.20% (63.36 feet per mile) to 1.55% (81.84 feet per mile — an increase of about 18.5 feet per mile) will be sufficient to increase the required number of trains for a given gross traffic about 25%, i.e., five trains will be required to handle the traffic which four trains would have handled before at a cost slightly more than four-fifths as much. Since the gross receipts remain the same and the operating expenses have been increased nearly 20%, the effect on dividends is readily imagined. On the other hand, a reduction of the grade, which will enable four trains to handle an amount of traffic which have required five trains on the heavier grade, will have a corresponding influence in decreasing 286 THE ECONOMICS OF RAILROAD CONSTRUCTION. the operating expenses and will justify a large expenditure to accomplish this result. 183. Basis of the cost of minor grades. — The basis of the computation of this least objectionable form of grade is as follows: The resistance to the movement of a train on a straight level track is variable, depending on the velocity, the number and character of the cars, and on the character of the road-bed and track. No one figure that can be stated may be considered accurate for all cases, but for average conditions and for average velocities we may consider that the round number of 10 pounds per ton is a reasonable figure. This value agrees fairly well with the results of some dynamometer tests made by Mr. P. H. Dudley, using a passenger-train of 313 tons running at about 50 miles per hour. It also agrees with Searles's formula (based on experiments) for the resist- ance of a freight-train with 40 cars running 25 miles per hour. Using the very approximate resistance formula published by the " Engineering News," which makes the 7 N resistance in pounds per ton equal to (2+^-), in which V is the velocity in miles per hour, this value would be true for a train moving at a speed of 32 miles per hour. A comparison of the three cases mentioned above shows at once the wide variations in the values given by different formulae. Therefore this value of 10 pounds per ton may be considered to be as nearly correct for an average value as any other one value that can be chosen. Ten pounds per ton is the grade resistance of a 0.5% grade, or a grade of 26.4 feet per mile. On this basis a 0.5% grade will just double the tractive resistance on a straight level track. We may compute, as in the previous chapter, the cost of doubling the tractive resistance for one mile, but, since the extra resistance is due to lifting the train through 26.4 feet of elevation, we may divide the extra cost of a MINOR GRADES. 287 mile of 0.5% grade by 26.4 and we will have the cost of one foot of difference of elevation. If the rate of grade is not so great that it has an effect in limiting the length of trains, we may then say that the cost of this one foot of difference of elevation is independent of the rate of grade. On account of the compensating character of the effect of grade in the operation of trains down the grade or in the operation of a train down the other side of an elevation which has just been climbed, we must consider the total effect of one foot of rise and fall. Although we may say in a general way that the cost of one foot of rise and fall is independent of the rate of grade, it is true, as will be seen, that the cost of a foot of rise and fall of a very light grade is very much less than the cost of a foot of a much heavier grade. 184. Meaning of " rise and fall." — In the simplest case a rise and fall of so many feet means a rise from the start- ing-point to a summit and a return to the same level, as is shown in Fig. 34. For instance, in Fig. 34 (a) is indi- cated a rise and fall of BD above the level AC, but (6) and (c) may be considered just as much cases of rise and fall. In (c) the line AB is actually an up grade, and yet we may consider it as a virtual drop. If a freight- train is moving up the grade in (&) and the engine is doing the work which will carry it steadily up the grade ADC, it encounters additional resistance on the extra grade AB, and must either work much harder or it will continue to lose velocity. If it has sufficient momentum to carry it over the point B it will then continue on the grade BC, which, although an up grade, is so much less than the grade DC that the engine will do more work than is re- quired on such a grade and hence will gain velocity. This is essentially the same case as though a train were moving uniformly along the level (case a) and encountered the hump ABC. The case is essentially the same in (c). 288 THE ECONOMICS OF RAILROAD CONSTRUCTION. Although AB is actually an up grade, it is so much less than the grade ADC that if a train were running up that grade with the engine doing an amount of work which would carry it uniformly up the grade ADC, the resist- ance on the lesser grade AB will be so much less that the train will actually gain velocity and acquire a momentum which will enable it to climb the still steeper grade BC, so that by the time it reaches C it will have practically the same velocity which it had at A. We are therefore iitmlliiiiimuiumiiitiil Fig. 34.— Types of "rise and fall". justified in considering that whether the train passes over a hump which is superimposed on an otherwise uniform grade, whe'ther level or not, or goes through a sag which occurs in what would otherwise be a uniform grade, we may consider that in all cases the train is encountering what we denominate as "rise and fall." When the line runs through a stretch of several miles with very light grades, all of which are well within the ruling grade, there is in general no possibility of doing anything which will MINOR GRADES. 289 favorably affect the grade. Practically all that we can do is to remove what is virtually a hump or a sag in what is otherwise a nearly uniform grade or level. 185. Classification of minor grades. — The additional cost of one foot of rise and fall is not altogether indepen- dent of the rate of grade. We can, however, divide grades into three groups, within which we may say that the cost of a foot of rise and fall is practically uniform. In the first class are grades which may be operated without changing the work of the engine, and which have practically no other effect than a harmless fluctuation of the velocity, but a grade which belongs to this class, when considering a fast passenger-train, will belong to another class when considering a slow and heavy freight-train, and, since it is the slow and heavy freight-trains which must be chiefly considered, a grade will usually be classified with respect to them. The limit of class A therefore depends on the maximum allowable speed, and also depends on the length of the grade and the depth of the sag. If it is permissible to operate all trains through the sag without making any change in the handling of the engine, without changing the throttle-valve or the position of the links, and espe- cially without the use of brakes,, then the effect of the sag on the operation of trains is possibly zero, and the sag or hump has no financial importance. The above conditions assume that the engine is working uniformly throughout, that all potential energy which is lost on the steeper grade is regained on the lighter grade. In the case of a sag the change in potential energy merely comes in reversed order. If train resistance and tractive effort were actually inde- pendent of velocity, the assumption that class A has no influence on train expenses would be almost theoretically precise. The operation of momentum grades has been considered in Chapter XL In classifying a sag or a hump we must therefore consider whether trains which run over 290 THE ECONOMICS OF RAILROAD CONSTRUCTION. or through it may be operated without changing any operating conditions. We will very often discover that passenger-trains may be so operated, while freight-trains will need to be handled differently. Therefore such a hump or sag will be classified as belonging to class A for pas- senger-trains, and to class B or possibly class C for freight- trains. The next classification (B) applies to grades on which a change of operating conditions becomes necessary. On the clown grade it becomes necessary to partially, if not entirely, close the throttle, in order that the velocity shall not become too great. On the other hand, the up grade is so steep that the engine must work considerably harder, consume more coal, and perhaps operate with a longer cut-off and therefore less economy than is possible on the lighter grades. As long as brakes are not used there is no actual loss of energy, except that steam will probably be wasted by being blown through the safety-valve while the train is running down the grade with the throttle closed. The chief disadvantage is due to the uneconomical working of the train on the heavier up grade. On the down grade the losses in fuel consumption, due to radia- tion, etc., will become a much larger percentage than usual of the useful work actually obtained from the engine. The third class (C) includes humps which are so high and sags which are so deep that brakes must be applied on the down grade in order to prevent excessive velocity. The loss by the application of brakes is very heavy. The brakes require power for their application which is a con- siderable tax on the locomotive. The use of brakes causes wear of the brake-shoes and of the wheel-tires, which hastens the deterioration of the rolling-stock. Their use destroys the kinetic or potential energy which had pre- viously been created, while the tax on the locomotive on the corresponding ascending grade is very great. MINOR GRADES. 291 It may be seen that the classification of these humps and sags is more a matter of the total height of the hump or the depth of the sag rather than the rate of grade. The sag or hump which has a comparatively steep grade on both sides may be almost harmless if the grades are short, or (which amounts to the same thing) if the height or depth is small. On the other hand, a comparatively light grade may become of importance because it is so deep. It is not usual, however, that a sag or hump could be classified in class C if the grade is very light, since it requires a considerable grade to cause a train to attain a dangerous velocity when the steam is turned off. Exces- sively long sags or humps are practically outside of the line of problems which may thus be considered. 186. Effect on operating expenses. — As in the previous chapter we may at once throw out a large proportion of the items of expense of an average train-mile. In " main- tenance of way and structures." Items 2 to 6 will be variously affected according to. the classification of grades. The other items are evidently unaffected. 187. Item 3. Renewals of ties. — The extra wear of ties on grades is considered by Wellington as being some- what compensated by the improved drainage of the road- bed which is found on a track which is not quite level, the better drainage tending to increase the life of the ties. On this account Wellington made an allowance of 5% increase for class C and no increase for the other classes. 188. Item 4. Renewals of rails. — Observations of rail wear on heavy grades show that the wear is much greater than on level tangents. The heavy grades of a mountain division of a road are usually operated with shorter trains or with the help of pusher-engines, and in such cases the proportion of engine tonnage to the total is much greater than on minor grades, and, since the engine has much greater effect on rail wear than an equal total tonnage of 292 THE ECONOMICS OF RAILROAD CONSTRUCTION. cars, partly on account of the use of sand and excess of engine tonnage, the grade will have a marked effect on rail wear. But such circumstances apply to ruling grades and very little, if at all, to minor grades. The use of sand on up grades and the possible skidding of wheels on down grades will wear the rails considerably. Even the slipping of the drivers, although sand is not used, will wear the rails. Wellington allows 10% increase for class C and 5% for class B. 189. Item 6. Roadway and track. — It is very plain that a large proportion of the subitems are absolutely unaffected by minor grades. In fact it is a little difficult to ascribe any definite increase to any subitem. Rail wear is somewhat increased and this will have some effect in in- creasing the track-work. Wellington allows 5% increase as a liberal estimate for class C, and makes no allowance for classes A and B. Items 2 and 5 are allowed the same. 190. Maintenance of equipment. — It is evident that none of these items will be affected except repairs and renewals and depreciation of road engines and cars. The chief effect on these items will evidently be the repairs and renewals of wheels and brake-shoes. The draw-bars are also apt to suffer somewhat, on account of the increased work which they are required to do. It would appear that the extra stress on the locomotive mechanism will have some effect on locomotive repairs, and the expense of boiler repairs may be increased on account of the greater range of the demands on it. It would seem as if such effects would be quite large, but if the records of engine and car repairs on mountain divisions and on compara- tively level divisions of the same road are examined and compared, there appears to be no such difference as might be expected. Considering the very small proportion of locomotive and car repairs which are affected at all by such circumstances, and also the very small percentage MINOR GRADES. 293 of these subitems which can be said to be affected by these two classes of minor grades, Wellington allows only an increase of 4% on each of these four items for class C and 1% for class B. This is reasonable in view of the 19% allowed for grades and curvature (Table XXIII) of which 13% was estimated for curves, leaving only 6% for all grades. 191. Conducting transportation. — It is apparent that the only items in conducting transportation which will be affected will be the four items of engine-supplies (82 to 85). As in Chapter XIII, since we are considering that the resistance is doubled, we will assume that there is an increase of 44% as the cost of the extra fuel used in climb- ing 26.4 feet, but the total cost of both rise and fall is to be considered. In class B, although steam is shut off; fuel will be wasted by mere radiation. On this account we will add 5%. For class C we must allow in addition the energy spent in applying the brakes, which we may assume as 5% more. Therefore we will allow 49% for class B and 54% for class V. The other small items of supplies, 83, 84, and 85, will be estimated similarly. The items of general expense are evidently unaffected. 192. Estimate of cost of one foot of change of elevation. — Collecting the above estimates we have Table XXVI, showing that the percentage of increase for operating grades of classes B or C will be 5.85% and 7.71% respect- ively on the average cost of a train-mile. On the basis of an average cost of $1.50 per train-mile, the additional cost for the 26.4 feet of rise and fall in one mile would bs 8.77 c. and 11.56 c, or 0.33 c. and 0.44 c. per foot for the two classes respectively. For each train per day each way per year the value per foot of difference of elevation is For class B: 2x365 X$0.0033 = $2.41. For class C: 2x365x$0.0044 = $3.21. 294 THE ECONOMICS OF RAILROAD CONSTRUCTION. In assuming the number of trains running over a given grade the character of the trains must be carefully con- sidered, since it will quite frequently happen that a hump or sag must be classified as belonging to class C, so far as heavy freight- trains are concerned, but may be classified as B or perhaps even A, the harmless class, for passenger- trains. The above values should likewise be modified when the trains are run only 313 days per year instead of 365. Table XXVI. — Effect on Operating Expenses of 26.4 Feet of Rise and Fall. Item (abbreviated.) Normal average. Claas B. Class C. Item number. a"6 U 03 Cost per mile per cent. S 03 U 03 P4 eS § Jo O C3 03 2 Ballast 0.50 3.10 0.92 1.13 7.53 6.91 5 0.05 5 5 10 5 5 02 3 Ties 15 4 Rails 0.09 5 6 Other track material Roadway and track (All other items) 0.06 0.38 Maintenance of way 20.09 0.05 0.70 25-27, 31-36, 43-45 1 Locomotives, passenger cars, > freight- cars and work-cars . (All other items) 21.24 1.50 1 0.21 4 0.85 Maintenance of equipment. . 22.74 0.21 0.85 53-60 Traffic 3.08 82-85 Fuel and other supplies for road engines 11.41 39.03 49 5.59 54 6.16 (All other items) Transportation 50.44 5.59 6.16 106-116 General expenses 3.65 100.00 5.85 7.71 MINOR GRADES. 295 193. Numerical illustration. — Assume that the grade of a railroad in crossing a river valley includes a sag 5000 feet long and with a depth in the center of 40 feet. Assume that freight-trains would ordinarily approach this sag at a velocity of 20 miles per hour. The velocity head at 20 miles per hour, as found in Table XX, is 14.05 feet. Add- ing the depth of the sag, 40 feet, we would have the velocity head at the bottom of the sag, 54.05 feet, which corre- sponds to a velocity of over 39 miles per hour. The exten- sive adoption of automatic couplers and train-brakes have permitted the use of much higher freight-train speeds than were permissible some years ago. Even though it might be considered safe to run the train through the sag at a speed of nearly 40 miles per hour, it is unquestionable that a freight-engine could not develop steam fast enough to exert a constant draw-bar pull up to a speed of 39 miles per hour. There would therefore be a very considerable loss from the theoretical operation of such a sag as de- scribed above, and we must consider that the sag will not belong to class (A), at least for freight-trains. If a pas- senger-train approached this sag at a velocity of 30 miles per hour, the velocity head then being 31.60 feet, its velocity head at the bottom of the sag would be 71.60, which would correspond to a velocity of over 45 miles per hour. If the passenger-engine were so lightly loaded that its draw-bar pull at the top of the sag was quite small, and its boiler capacity was so large that it could develop this light draw-bar pull even at a speed of 45 miles per hour, then for such trains we could consider the sag as belonging to class (A), the harmless class. Assume that after an analysis of the character of the trains using the sag, we find there are six trains per day each way in the operation of which the sag should be classed as class (C), and eight other trains per day each way for which it should be classed as class (B). It should be noted that it is not 2C6 THE ECONOMICS OF RAILROAD CONSTRUCTION. essential to fill up the sag altogether and make it level. If we fill up only the lower 20 feet, which will not ordinarily cost more than one-fourth to one-third as much as filling up the upper 20 feet, the sag would probably become harmless for all classes of trains. We w 1 therefore compute the value of reducing the depth of the sag 20 feet. We will have the added cost of operating this 20 feet as follows : Eight trains, class (B) 8 x20x$2.41 = $385.60 Six " " (C) 6x20x$3.21 = $385.20 Total annual saving $770.80 Capitalizing this at 5%, we have $15,416 as the justifiable expenditure to fill up the lower 20 feet of this sag. Of course the amount of earthwork required to make this fill can be readily computed. In the case of a new road we would have merely this additional cost to the original plan of construction. If such a plan is considered with the intention of improving an old line, the cost of raising the track, and all the added expense involved in maintain- ing the track so that traffic may continue to run over it, will have to be added as part of the cost of improvement. The cost of such an improvement is a comparatively simple matter to determine. The above demonstration, even though it is based on data which is approximate, is at least a measure of the value of the improvement, which is far better than having no measure at all. In applying the method outlined above to any particular case, the problem must be studied from the beginning with refer- ence to all the available figures of cost as applied to the given road. The figures given above for the value of one foot of rise and fall of either class should not be used in general for all cases, and in fact should never be used ex- cept as an approximate method for computing the value of a change in the proposed location of a new road where there is no data on which to base more accurate calculations. CHAPTER XV. RULING GRADES. 194. Definition. — Ruling grades are those which limit the weight or length of a train of cars which may be hauled by one engine. They are frequently, although not neces- sarily, the steepest grades on the road. It is sometimes possible by a mere change in the method of operating the trains to very greatly reduce what must technically be considered the ruling grade of the road. When one or two grades on the road are considerably higher than all other grades, it is possible to use assistant engines on those grades, and thereby very greatly increase the weight or number of cars in a through-train load over the entire line. The weight of train will then be limited by the next lower grade, which may be a grade which offers but little more than one-half the total resistance of the grade which is operated by pusher-engines. This enables the train-load to be practically doubled. Such grades, which are called pusher grades, will be considered in a succeeding chapter. When a grade is very short and it is never necessary to stop a train while on the grade, it is frequently possible to load up an engine with a far greater number of cars than could be run up an indefinite grade of that length. This has already been discussed in the chapter on Momentum Grades. These are the most common exceptions to the general statement that the ruling grade is usually the maximum grade of the road. 297 298 THE ECONOMICS OF RAILROAD CONSTRUCTION. The selection of the general route of the road usually determines more or less definitely the ruling grade of the road, except as that may be modified by " development." The rate of ruling grade should bear some relation to the general character of the road which is to be built. A second-class or third-class road, which at its best will never be anything more than a branch line, is not justified in spending much money to reduce a ruling grade. On the other hand, a great trunk line is thoroughly justified in spending enormous sums in the construction of tunnels, deep cuts, high embankments or viaducts, in order to reduce the rate of the ruling grade. In this chapter we will endeavor to determine the financial relation between the lowest permissible grade and the money which may profitably be spent to secure it. 195. Choice of ruling grade. — A little consideration re- garding the practical operation of- trains will show that it is impracticable for an engine to drop off or pick up cars in accordance with the grades which may be encountered along the line. The nearest approach to this is to divide a long road into divisions. At the termini of each division are located freight-yards at which the cars are assorted, and, if necessary, the train-load is increased or diminished, according to the capacity of the engines which are to haul the trains over the succeeding division. The locating engineer cannot determine the proper rate of ruling grade for a line until after the belt of country through which the road is to pass has been thoroughly surveyed, and he can study the project as a whole. There are usually a dozen or more points within a distance of 100 miles through which a railroad is almost compelled to pass, and which must be considered as governing points, unless there is very urgent reason why the road should not go through them. The selection of the rate of grade then becomes a problem of determining the best route between jeach pair of consecu- RULING GRADES. 299 live governing points. If the natural grade between two consecutive points is very high, and much higher than the grades between other consecutive ruling points, it may be advisable to immediately decide to operate the especially steep grade with pusher-engines, and thereby make it .possible to use a much lower rate for the ruling grade. The endeavor should be made to cut down all grades which would naturally be somewhat higher than the other grades until a considerable number of grades have been determined, all of which are approximately equal and which cannot be materially reduced without a large expenditure. On the one hand, it will not pay to spend any amount of money to reduce a grade below this maxi- mum which has been selected, although, on the other hand, it will pay to spend considerable to cut clown the rate of grade on one or two grades which are higher than the gen- eral maximum. In this way may be determined, after considerable study, some limit of grade which can be used at all points without an extravagant expenditure of money, and yet which could not be reduced, on account of the large number and length of the grades which would be involved, without an extravagant expenditure of money. The engineer is frequently confronted with a definite prob- lem substantially as follows: The rate of ruling grade at one or two places on the line is naturally at some definite figure, say, 1 .4% . By spending an easily computable sum of money the line may be modified so that the ruling grade is reduced to perhaps 1 .0% . The engineer must then consider the traffic to be run over the road, and must compute the effect on the operating expenses of reducing the rate of grade. If the annual saving in operating expenses,when capitalized materially exceeds the cost of obtaining the lower grades, it will probably be justifiable to construct them. 196. Maximum train-load on any grade. — The tractive power of a locomotive, and especially the reduction of the 300 THE ECONOMICS OF RAILROAD CONSTRUCTION. effective tractive power with increase in velocity, has already been discussed in previous chapters. It is ex- pected that on ruling grades a train runs slowly if necessary. Fortunately the tractive power of a locomotive is greatest when the speed is slow, and when very nearly the full theoretical adhesion of the drivers to the rails can be counted on. In Table XXVII are given the tractive powers of locomotives of a wide range of types and weights and with various ratios of adhesion. Almost any loco- Table XXVII. — Tractive Power of Various Types of Standard- gauge Locomotives at Various Rates cf Adhesion. Type of Locomotive. Atlantic, 4-4-2 Atlantic, 4-4-2, four-cyl- inder compound Pacific, 4-6-2 Pacific, 4-6-2 Ten-wheel, 4-6-0 Prairie, 2-6-2 Consolidation, 2-8-0. . . . Consolidation, 2-8-0 Mikado, 2-8-2 Total weight of engine and tender. Lbs. 340,000 368,800 343,600 403,780 321,000 366,500 214,000 366,700 405,500 Tons. 170.0 184.4 171.8 201.9 160.5 183.2 107.0 183.3 202.7 Weight of engine only. 199,400 206,000 218,000 236,700 201,000 212,500 120,000 221,500 259,000 Weight on the drivers. 105,540 115,000 142,000 151,900 154,000 154,000 106,000 197,500 196,000 Tractive power when ratio of adhesion is 1/4 9/40 26,385 23,740 25,875 31,950 34,180 34,650 34,650 23,850 44,440 44,100 28,7501 35,500 37,975! 38,500 38,500| 26.500 49,375; 49,000 1/5 21,100 23,000 28,400 30,380 30,800 30,800 21,200 39,500 39,200 motive will be sufficiently similar to one of these given in this table, so that the tractive force here given may be used for calculations, at least approximately. In Table XXVIII is shown the total train resistance in pounds per ton for various grades and for various values of track resistance. By a combination of these two tables the net train-load on any grade under given conditions may be quickly determined. For example, a consolidation engine, weighing 214,000 pounds and having 106,000 on the drivers, will have a tractive power of 23,500 pounds when the effective adhesion is J. When it is moving slowly up a 1.2% grade the grade resistance is 24 pounds per ton, and if the tractive resistance on a level is 6 pounds per RULING GRADES. 301 ton the total train resistance per ton will be 30 pounds. Dividing 26,500 by 30, we have 883 tons as the gross train-load. Subtracting 107 tons, the weight of the engine and tender in working order, we will have 776 tons as the net load. A much better way of considering this will be on the basis of rating tons, as already explained in Chapter XI, but, whatever the method adopted, Tables XXVII and XXVIII are accurate as long as the velocity is so slow that the boiler capacity is not overtaxed, and as long as the proper ratio of adhesion and the actual tractive resist- ance on a level are chosen for use in the tables. 197. Proportion of traffic affected by the ruling grade. — Very many light-traffic roads are not fortunate enough to have a traffic which is materially affected by the rate of ruling grade. Passenger-trains are very seldom affected, unless the volume of traffic is so great that the number of cars attached to one engine approaches the limit which one engine is able to haul. The comparatively high speed usually demanded of passenger-trains means that the locomotive must have high steaming power to haul even light loads. Such light loads do not require very great tractive force, and therefore the tax on the adhesion of the drivers is correspondingly small. When a passenger- train reaches an unusually heavy grade, the effect of the grade is usually confined to reducing the speed of the train. On any road but a trunk line such a slight reduc- tion of speed has almost no financial value. We may therefore make the general statement that for all light- traffic roads the passenger-trains need not be considered as being affected by the rate of ruling .grade. Local freight-trains may sometimes be considered in the same way. It frequently happens that the local freight is sent out over the line with a far less number of cars than could be hauled by one engine, and therefore the ruling grades cannot be considered as affecting these trains. Whatever 302 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table XXVIII. — Total Train Resistance per Ton (of 2000 Pounds) on Various Grades. When tractive resist- When tractive resist- Grade. ance on a level in Grade. ance on a level in pounds per ton is pounds per ton is Rate Feet Rate Feet per per 6 7 8 9 10 per per 6 7 8 9 10 cent. mile. cent. mile. 0.00 0.00 6 7 8 9 10 2.00 105.60 46 47 4£ 4g .50 .05 2.64 7 8 9 10 11 .05 108.24 47 48 49 5C 51 .10 5.28 8 9 10 11 12 .10 110.88 48 49 50 51 52 .15 7.92 9 10 11 12 13 .15 113.52 49 50 51 52 53 .20 10.56 10 11 12 13 14 .20 116.16 50 51 52 53 54 0.25 13.20 11 12 13 14 15 2.25 118.80 51 52 52 53 53 54 54 55 55 .30 15.84 12 13 14 15 16 .30 121.44 56 .35 18.48 13 14 15 16 17 .35 124.08 53 54 55 56 57 .40 21.12 14 15 16 17 18 .40 126.72 54 55 56 57 58 .45 23.76 15 16 17 18 19 .45 129.36 55 56 57 58 59 0.50 26.40 16 17 18 19 20 2.50 132.00 56 57 58 59 60 .55 29.04 17 18 19 20 21 .55 134.64 57 58 59 60 61 .60 31.68 18 19 20 21 22 .60 137.28 58 59 60 61 62 .65 34.32 19 20 21 22 23 .65 139.92 59 60 61 62 63 .70 36.96 20 21 22 23 24 .70 142.56 60 61 62 63 64 0.75 39.60 21 22 23 24 25 2.75 145.20 61 62 63 64 65 .80 42.24 22 23 24 25 26 .80 147.84 62 63 64 65 66 .85 44.88 23 24 25 26 27 .85 150.48 63 64 65 66 67 .90 47.52 24 25 26 27 28 .90 153.12 64 65 66 67 68 0.95 50.16 25 26 27 28 29 .95 155.76 65 66 67 68 69 1.00 52.80 26 27 28 29 30 3.00 158.40 66 67 68 69 70 .05 55.44 27 28 29 30 31 .05 161.04 67 68 69 70 71 .10 58.08 28 29 30 31 32 .10 163.68 68 69 70 71 72 .15 60.72 29 30 31 32 33 .15 166.32 69 70 71 72 73 .20 63.36 30 31 32 33 34 .20 168.96 70 71 72 73 74 1.25 66.00 31 32 33 34 35 3.25 171.60 71 72 73 74 75 .30 68.64 32 33 34 35 36 .30 174.24 72 73 74 75 76 .35 71.28 33 34 35 36 37 .35 176.88 73 74 75 76 77 .40 73.92 34 35 36 37 38 .40 179.52 74 75 76 77 78 .45 76.56 35 36 37 38 39 .45 182.16 75 76 77 78 79 1.50 79.20 36 37 38 39 40 3.50 184.80 76 77 78 79 80 .55 81.84 37 38 3C 40 41 4.00 211.20 86 87 88 89 90 .60 84.48 38 39 40 41 42 4.50 237.60 96 97 98 99 100 .65 87.12 39 40 41 42 43 5.00 264.00 106 107 108 109 110 .70 89.76 40 41 42 43 44 5.50 290.40 116 117 118 119 120 1.75 92.40 41 42 43 44 45 6.00 316.80 126 127 128 129 130 .80 95.04 42 43 44 45 46 6.50 343.20 136 137 138 139 140 .85 97.68 43 44 45 46 47 7.00 369 . 60 146 147 148 149 150 .90 100.32 44 45 46 47 48 8.00 422.40 166 167 168 169 170 1.95 102.96 45 46 47 48 49 9.00 475.20 186 187 188 189 190 2091210 2.00 105.60 46 47 48 49 50 10.00 528.00 206 207|208 RULING GRADES. 303 business is done by the road in handling bulky freight, such as coal, ore, or timber, is usually handled in train- loads which are made as heavy as the power of the engine on the grades of the road will permit. All such trains are directly affected by the rate of ruling grade. Therefore, in counting the number of trains which are affected by the ruling grade, we must usually count all coal-, lumber-, and ore-trains, and all through freight-trains which are run from one terminus of the division to another, as well as passenger-trains, if any, which are actually limited in length or weight by the grade. 198. Financial value of increasing the train-load. — The gross receipts obtained for transporting a given amount of freight is a definite sum which is independent of the number of train-loads required to handle it. On the other hand, the cost of a train-mile is nearly constant. If it were actually so, we could say at once that the cost of handling the traffic would be proportional to the number of trains, and that the saving of even one train-load, or of handling in four trains what would otherwise require five train-loads, would reduce the operating expenses pro- portionally. The problem is a very similar one to that already worked out in Chapter VII, but with a very important difference in some of the conditions. In both cases the object to be gained is the reduction in the number of trains to handle a given gross tonnage of freight traffic In the case worked out in Chapter VII, this is accom- plished by merely increasing the power of the locomotives, so that a given amount of traffic can be handled in three trains instead of four, or in six trains instead of seven, the grades of the road being the same in each case. By the method discussed in this chapter, the grade is so reduced that an engine of given type may haul a larger number of cars, and therefore a certain gross amount of freight ton- nage can be handled in three trains instead of four, or in 304 THE ECONOMICS OF RAILROAD CONSTRUCTION. six trains instead of seven, using engines of the same type and weight. In the first case, the power of the engine is increased; in the second case, the demand on its capacity is reduced by a reduction in the grade. We will estimate as before the difference in the cost of operating, say, four light trains on heavy grades, or three heavier trains on the lighter grades. In either case the gross tonnage of cars, with their contents, is supposed to be the same. The difference consists in the cost of operat- ing the extra engine and also the extra cost for train service, etc., which is a function of the number of trains on the road rather than of their tonnage. The additional cost of maintenance of way is confined to the effect of the extra engine, and this will evidently effect only Items 2 to 6 and 9. On the basis that an engine produces one- half of the track deterioration, we may allow 50% of these items as the total effect on maintenance of way. 199. Maintenance of equipment. — The effect on main- tenance of equipment will be practically confined to the re- pairs, renewals and depreciation of steam locomotives (Items 25 to 27) and the same items for freight cars (Items 34 to 36). Very few roads have a passenger traffic which is affected by the rate of the ruling grade, since, for the encouragement of traffic, passenger-trains are usually added to the schedule in advance of the physical capacity of a locomotive to haul one or more additional cars. There- fore, in general, no allowance need be made for any effect on passenger-trains, or on the maintenance of the passenger- cars. But the cost of maintaining the freight-cars is actually reduced by having more trains and less cars per train. This means that, although the maximum draw- bar pull will be the same in both cases, and will equal the maximum capacity of the locomotive, while on the ruling grades, the draw-bar pull while on the light grades, level track and down grades, which may mean 90% of RULING GRADES. 305 the length of the road, will average very much less. It is impossible to make an accurate estimate of the amount of this saving which would be generally applicable. Well- ington estimated it at 10%. Considering the very large proportion of freight-car maintenance charges which are evidently independent of draw-bar pull, the estimate is probably large enough and the error in adopting that figure is not very great. Although, for either system of grades, the locomotive is supposed to work to its full capacity while on the ruling grades, there is also some saving for each locomotive when hauling a lighter train over the light grades, level sections and down grades. If, on account of the reduction in average draw-bar pull, the repairs of each of four loco- motives were reduced 5% below the repairs of the three locomotives which could haul the same number of cars over lower ruling grades, then the repairs of the four locomotives would cost 4X95, or 380 compared with 3 X 100, or 300 for the three locomotives. This would mean that the additional locomotive should be assigned an added expenditure of 80% of the average cost for one. If the saving by the reduction of grade was only half as much, or one train in eight, so that seven trains were required to do the work of eight on the steeper grade, then the saving per engine would be correspondingly less. If it were 2.5% instead of 5, we would have, for the cost of eight engines, 8X97.5, or 780 compared with 7X100, or 700 for the seven engines. Again, we would have 80% as the additional net cost of the repairs on the addi- tional engine. Of course the above estimates of 5% and 2.5%, as the saving on one engine, are merely guesswork, but the above demonstration shows that if the saving in repairs is proportional to the reduction in number of trains which is made possible by the reduction of grade, as is quite probable, then the cost of the repairs of the 306 THE ECONOMICS OF RAILROAD CONSTRUCTION. extra engine is the same, whether it is one engine out of four, or one engine out of eight, or one engine out of any other number. Therefore, although the estimate of 5% per engine as made above is a guess, it is probably near enough to the truth, so that there is comparatively little error in using the figure of 80% for the additional cost of repairs of the additional engine. 200. Conducting transportation. — Items 61-79, chiefly yardwork, will be practically unaffected. Items 80 and 81 will be given their full value. The additional cost for the fuel for the added engine may be computed some- what on the same basis as the cost of engine repairs. The fuel used by four engines will average somewhat less than that used by three engines, since the four engines will do far less work on the level and on very light grades, while on the heavier grades the engines are working to the limit of their capacity in either case. The loss of heat, due to radiation and the other causes, which 7 m m are independent of the direct work done by the engine m hauling, will be the same in either case. These causes have already been discussed in § 142. It is impossible to make any general calculations as to the relative consump- tion of fuel in the two cases, since so much depends on the proportion of track which is level or which has a very light grade. If the four engines operating lighter trains each burn 5% less fuel than three engines operating heavier trains, we will find, by the same method as before, that the extra engine may be charged with 80% of the average fuel consumption of the other three engines. If, as before, we assume that this variation in fuel consump- tion is proportional to the variation in the number of trains required to handle a given traffic, then the extra engine would be responsible for 80% of the average fuel consumption, regardless of whether the number of trains saved was one in four or one in ten. Although it is true RULING GRADES. 307 that the value 80% is a mere guess, that no general value is obtainable, and that the value for any particular and special case could only be computed with great diffi- culty, it is evident that the error is not very great, and we will therefore assume 80% as the fuel consumption assign- able to the extra engine. The consumption of other engine-supplies, water, oil, waste, etc., is not strictly pro- portional to the consumption of fuel, but we will assume it to be so in this case, and that 80% of Items 83-85 are allowable for the extra engine. Items 88 to 94, which concern train-service, will be considered as varying according to the number of train- miles, and we will therefore add 100% for all these items. Items 97 and 98 will be allowed 50%. Items 99, 101 to 103, which refer to damages, might be considered from one standpoint to be unaffected, while from other stand- points the effect might be considered as 100%. The risk of train operations varies very largely with the number of trains, and yet in some respects the danger is independent of whether there are 15 or 20 cars in a train. There will be little error in assigning 50% extra for this item. Items 104 and 105 will be allowed 100% of their net value. The general expenses are evidently unaffected. Collecting these various items we have Table XXIX. If we assume that the average cost of a train-mile is $1.50, then the operating value per mile of saving the use of the additional engine equals 41.63% of $1.50, or 62.45 c. 201. Numerical illustration. — As a practical illustration of the figures in Table XXIX assume that the ruling grade on a given line is 1.4% (73.92 feet per mile). Assume that only 8 trains per day out of a total of 20 trains of all kinds are to be considered as affected by the rate of the ruling grade. Assume that it has been discovered that with the expenditure of $300,000 a change of alinement may be 308 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table XXIX. — Additional Cost of Operating a Given Freight Tonnage with (n+1) Engines on Heavy Ruling Grades INSTEAD OF WITH 71 ENGINES ON LIGHTER GRADES. Item number. Item (abbreviated) Normal average. Per cent affected. Cost per mile, per cent. 2 3 4 5 6 9 Ballast, Ties Rails, Other track material, Roadway and track, Bridges, trestles and culverts (All other items) 14.89 5.20 50 7.45 Maintenance of way 20.09 7.45 25-27 Steam locomotives 8.61 10.15 3.98 80 -10 6.89 34-36 Freight cars -1.01 (All other items) Maintenance of equipment 22.74 5.88 53-60 Traffic 3.08 80 Road enginemen 6.08 1.72 11.41 9.66 0.57 2.82 0.02 18.16 100 100 80 100 50 50 100 6.08 81 82-85 Enginehouse expenses, road .... Fuel, and other supplies for road engines 1.72 9.13 88-94 Train service, etc 9.66 97,98 99, 101, 103 104, 105 Stationery, printing, etc Loss, damage, etc Operating joint tracks, net (AH other items) 0.28 1.41 0.02 Transportation 50.44 28.30 106-116 General expenses 3.65 100.00 41.63 made which will reduce the ruling grade to 1%. Is such an expenditure justifiable under the circumstances? It has been shown in the chapter on Train Resistance that the actual tax on the locomotive depends quite largely on the RULING ^GRADES. 309 ratio of live load to tare. Therefore the only comparison which can justifiably be made as the basis for planning construction is to assume the same conditions of loading for both cases. For this comparison we will assume the resistances taken from Mr. Dennis's paper, as already referred to in Chapter XI, §§ 123-133. The grade and tractive resistance for a rating ton on the 1.4% grade would be (23.0 + 2.6), or 30.6 pounds per ton. The tract- ive power, as given for Mr. Dennis's locomotive at the speed of 7 miles per hour, is 28,200 pounds. The gross rating tons which could be hauled at this speed therefore equals (28,200-^30.6), or 922 gross rating tons. The ratio of a tare ton to a rating ton on a 1.4% grade equals 121% (see § 129). The actual weight of the locomotive and tender was 130 tons. On the 1.4% grade the resistance of the locomotive would be that due to (121% X 130) = 157 rating tons. Subtracting this from 922, we have 765 rating tons behind the locomotive. On the basis that the live load is twice the tare, the actual weight of cars with their loading would equal X 765 = 715 tons. 2 + 1.21 Since § of this weight consists of live load, the actual weight of live load carried in one train behind such an engine up the 1.4% grade is 477 tons. But, since we are assuming that these cars are loaded to the limit of their capacity, or at least to the same ratio of that limit, we will consider 715 tons as the total weight for both grades of the freight and of the cars which carry it. On a 1% grade the ratio of tare ton to rating ton is 128%. On this grade the locomotive has the equivalent weight of (128% X 130) = 166 rating tons. The eight trains, each of which are assumed to have a gross weight for cars and 310 THE ECONOMICS OF RAILROAD CONSTRUCTION. live load of 715 tons, will therefore weigh 5720 tons. On a 1% grade this will be the equivalent of 3 5720 -^ 2+128 = 6254 rating t0nS# The grade and tractive resistance for a rating ton on a 1% grade equals (20.0 + 2.6), or 22.6 pounds per ton. This locomotive at seven miles per hour can therefore handle 28,200-22.6 = 1248 rating tons. Subtracting 166 rating tons for the locomotive, we have left 1082 rating tons behind the tender as the capacity of one engine. Dividing 6254 by 1082, we have something less than 6, which shows that 6254 rating tons could be handled by six such engines with a margin of 238 rating tons. We may therefore say that, as the effect of reducing the ruling grade from 1.4% to 1%, the eight trains, which are affected by the rate of the ruling grade, can now be handled by six engines, and that there will be the saving due to the reduction of two trains. If these trains were operated 365 days per year, the annual saving on the basis of 62.5 c. per train-mile will be 2x0.625x365 = 1456.25 per mile of length of that division. If the division is 100 miles long, the annual saving is $45,625. Capitalizing this at 5% we have an additional justifiable expenditure of $912,500. Since this is over three times the computed expenditure, which can be readily estimated as the cost of effecting this reduction in ruling grade, it would appear that the improvement is thoroughly justified, especially since future traffic will probably increase rather than diminish the value of the improvement. CHAPTER XVI. PUSHER GRADES. 202. General principles underlying the use of pusher- engines. — Whenever a road is laid out merely with the idea of passing through certain predetermined points and constructing the road as cheaply as possible, the usual result is that there will be a great variety of grades differ- ing by small amounts from a level up to the actual maxi- mum. In such cases it will usually happen that the term " ruling grade " will apply to only one or two grades along the entire length of the road. The length and weight of heavy trains will therefore be limited by these ruling grades, as already explained in the previous chapter. The obvious policy in such cases is to cut down these heaviest grades until some limit is reached, at which these heavy grades are so numerous and so long that any further reduc- tion is financially, if not physically, impossible. The economics of such reduction of the ruling grade has already been considered in a previous chapter. It frequently happens that there are one or two grades along the line on which the tractive resistance is nearly, if not quite, twice the tractive resistance of 'any other grades on the line. In such cases the adoption of pusher grades becomes economical. If by using assistant engines to assist the heaviest trains over one or two steep grades, we are actu- ally able to double the length or weight of our freight- trains, there is evidently an enormous saving, even though 311 312 THE ECONOMICS OF RAILROAD CONSTRUCTION. it requires the services of pusher-engines which are used for no other purpose. 203. Numerical illustration of the general principle. — In the following illustration the refinements regarding the hauling capacity of locomotives, as determined by rating tons, have been ignored. Assume that at one point on a road there is a grade of 1.9%, which is five miles long. Assume that all other grades are less than 0.92%. Assum- ing that all trains are to be operated by one engine through- out that division, the net capacity of a consolidation engine, weighing 107 tons, with 53 tons on the drivers, ^0 adhesion, and six pounds per ton for normal resistance, will be 435 tons on the 1.9% grade. This is therefore the maximum net train-load allowable with that type of engine. Assume that this 1.9% grade has a length of five miles, and that the whole division is 100 miles long. By using pusher-engines on this five-mile grade the net train-load can be doubled. These 870 tons can also be hauled by one engine up the 0.92% grades. Making a rough comparison, which is free from details and allow- ances, we may say (a) Ten trains per day over a 100-mile division hauling 435 tons net per train will require 1000 engine-miles per day, which will haul 4350 net tons. (b) Utilizing pusher-engines on the steep grade, the same tonnage of 4350 tons may be handled in five trains of 870 tons each behind the locomotive. The engine mileage will be 5X100 miles of the through-engines plus 2x5x5 pusher-engine miles, which makes a total of 550 engine- miles per day, instead of 1000, to handle a given traffic. The advantages of this method are numerous. (1) There is not only a large saving in the number of ergine- miles, but it may even mean a saving in the number of locomotives, since it may require the purchase and use of ten locomotives in place of seven. (2) The throrgh- PUSHER GRADES. 313 engines, vhich are hauling 870 tons along the easier grades, are working more nearly to the limit of their capacity for a large part of the distance, and therefore are doing their work more economically. The work of overcoming the normal track resistances of so many loaded cars over so many miles of track, and of elevating so many tons of train weight through the differences of elevation of the several points of the line, is approximately the same what- ever the exact route. If the grades are so made that fewer engines, which are working more constantly to nearly the limit of their capacity, can accomplish the work as well as more engines, which are doing but little work for a considerable proportion of the time, the economy is very apparent and unquestionable. Wellington ex- presses it very concisely: " It is a truth of the first impor- tance that the objection to high gradients is not the work which the engines have to do on them, but it is the work which they do not do when they thunder over the track with a light train behind them, from end to end of a division, in order that the needed power may be attained at a few scattered points where alone it is needed. " 204. Equating through grades and pusher grades. — The above problem was purposely chosen with figures in which the pusher grade and the through grade were exactly balanced or equated. When it has once been decided that pusher grades should be used, . then the problem of grade reduction is modified to the extent of concentrating effort and attention on the reduction of grades which may be less than the rate of the pusher grade, and to reduce them to the limit of the equated through grade. In other words, if it is decided to retain the 1.9% pusher grade, any inter- mediate grade between 1.9% and 0.92%, such as 1.4%, must necessarily be treated in one of four ways: (a) it must be reduced to 0.92%; (6) it might be operated as a pusher grade; (c) it might be operated as a through grade, 314 THE ECONOMICS OF RAILROAD CONSTRUCTION. which virtually means that all train-loads are reduced to itie 1.4% basis; (d) a fourth possible method would be to use two pusher-engines on the steepest grade, as described below. Of course the first method is the proper method to adopt, if it can be done with a reasonable expenditure of money. The method of pusher grades is only applicable when it is possible to modify the system of grades on the road, so that there is an abrupt change from grades which are to be operated as pusher grades down to through grades which correspond with these pusher grades. A somewhat unusual solution of a problem in pusher grades is given by the possibility of using two pusher- engines on some grades and one pusher-engine on corre- spondingly lower grades. Working out such a method on the basis of the engine previously considered, and assum- ing that the 1.9% grade is the grade for two pusher-engines, we might determine the corresponding grades for one pusher and for through engines as follows : Tractive power of three engines = 106,000 XAX 3 = 71,550 pounds. Resistance on 1 .9% grade = 6 + (20 X 1 .9) = 44 lbs. per ton 71 ,550 -h 44 = 1626 = gross load in tons. 1626- (3 X 107) = 1305 = net load in tons. 1305 +(2X107) = 1519 = gross load on the one-pusher grade. Tractive power of two engines = 47,700 lbs. 47,700 -r-1519 = 31. 40 = possible tractive force in lbs. per ton. (31 .40 - 6) - 20 = 1 .27% = permissible grade for one pusher. 1305+ 107 = 1412 = gross load on the through grade. Tractive power of one engine = 23,850 lbs. 23,850-^1412 = 16.89 = possible tractive force in lbs. per ton. (16.89-6) 4- 20 = 0.54% = permissible through grade PUSHER GRADES. 315 On account of its simplicity the above problem has been worked out on the basis that the normal tractive resist- ance is uniformly six pounds per ton, and also that the normal adhesion of the drivers is i 9 TF . On the basis of these figures the grades for one, two, and three engines are precisely as given above. Using other types of engines and assuming other values for the resistance and adhesion, the relation of these grades will change somewhat, although, as shown in the following tabular form, the variation will be but slight. Table XXX. — Relation of One-pusher and Two-pusher Grades to Through Grades, with Variations of the Ratios of Adhe- sion and Normal Resistance. Adhesion Resistance Load on Through One-pusher Two-pusher of drivers. per ton. drivers. grade. grade. grade. l 5 6 lbs. 53 tons. .54% 1.26% 1-86% i 7 " 53 " .54 1.29 1.92 TU 6 " 53 " .54 1.27 1.90 9 TO 7 " 53 " .54 1.31 1.96 1 6 " 53 " .54 1.28 1.93 1 4 7 " 53 " .54 1.32 2.00 The above form shows that increasing the resistance per ton and decreasing the adhesion have opposite effects on altering the ratios of these grades, and, as a storm would increase the resistance and decrease the adhesion, the changes in the ratio would be compensated, although the absolute reduction in train-load might be considerable. Another practical inaccuracy in the above calculations is obtained from the fact that the rating tonnage on the pusher-engine service is different from that on the through- engine service. To determine the effect on the above case, let us consider the original problem of using a 1.9% grade as a pusher grade using one pusher-engine. Adopting the same figures as before of 2.6 pounds as the resistance of a rating ton and 9 pounds as the resistance of a ton of tare, 316 THE ECONOMICS OF RAILROAD CONSTRUCTION. we have, on the 1.9% grade, a gravity resistance of 38 pounds per ton, and therefore a total resistance of 40.6 pounds per ton for a rating ton. The resistance of a tare ton will be 47 pounds; therefore, to change tare tons into rating tons for a 1.9% grade, we multiply the tare ton by 116% (see Table XXI, § 129). Assuming, as before, an adhesion of A of the 53 tons on the drivers, we have a tractive force of 23,850 pounds for one engine, or 47,700 for two engines. Dividing 47,700 by 40.6, we have 1175 rating tons for the whole train. The two engines weigh 214 tons, which is the equivalent of 248 rating tons. Sub- tracting this from 1175, we have 927 rating tons behind the two locomotives. Since the required through grade is still an unknown quantity, we must solve the problem by an assumption of the required through grade in order to determine the equivalent number of rating tons for one locomotive on the unknown grade. We know from the other solution that the through grade will probably be a little less than one per cent, but we know that it will probably be a little higher than the rate given by the other solution, since a locomotive has a higher resistance per ton than the average train resistance. The ratio of tare tons to rating tons on a one per cent grade is 128%, therefore the number of rating tons on the through grade must be very nearly 927 + (107 X 1 .28) = 1064 rating tons. Dividing this into 23,850, the tractive power of one locomotive, we have 22.40 the total tractive resistance for one rating ton. Subtracting 2.6, we have 19.8, which is the grade resistance of a 0.99% grade. This value is somewhat higher than the 0.92% grade previously worked out, as was to have been expected. It should be noted, however, that even this value depends on the constants, 2.6 pounds for the resist- ance of a rating ton and 9 pounds for the resistance of a tare ton, as deduced from Dennis's experiments. If the solution is worked out on the basis of other values, the re- PUSHER GRADES. 317 suits will probably be somewhat different. On the other hand, it is somewhat encouraging that, in spite of the radi- cal difference in the methods used, the difference in the final results are as small as given above. When separate methods give results which agree to a few hundredths of one per cent in the rate of the grade, we may consider that either are sufficiently accurate for practical use. In view of the variations in train resistance and the uncertainties of the relation between the resistance for a rating ton and the resistance of a tare ton, no table that can be devised will be accurate for all conditions. In Table XXXI is given the corresponding pusher grades for one- and two- pusher, for the same net load behind the locomotive for various through grades. These have been worked out for track resistance of six and eight pounds. The table is valuable in that it affords a very ready comparison of the relative rates of grade under the conditions named. On account of the extra resistance of the extra locomotive, the pusher grades are probably a few hundredths of one per cent too high, and a corresponding allowance should be made. As an illustration of the use of the table, let us answer the question of the permissible pusher grade when the through grade has already been estabished at 1.24%. If the road-bed is in good condition, we will assume the lower rate of track resistance or six pounds per ton. We will then interpolate between 2.34 and 2.50, and obtain 2.40% as the corresponding pusher grade. For the reason stated above, we should probably cut this down to about 2.3%. As another illustration, if a road has a few grades of 1.8% which are not of excessive length and yet which cannot be materially reduced except at excessive cost, we may consider the question of operating these few grades as pusher grades, assuming that all through grades can be reduced to the corresponding through-grade limit. Assum- 318 THE ECONOMICS OF RAILROAD CONSTRUCTION. ing again a track resistance of six pounds and interpolating for 1.8% for one pusher, we have the corresponding through grade of 0.86%. For the same reason as before, this should probably be increased to at least 0.90% to obtain the correct balance. The question then is transformed into the possibility of reducing all grades which are not to be operated as pusher grades, so that none are above the limit of 0.90%. If the road under consideration is already in operation, a closer value may be obtained by considering the actual capabilities of the locomotives employed and the track resistance as it actually exists. For preliminary calculations the above figures are prob- ably sufficiently accurate. It may be noted from Table XXXI that when the track resistance is increased from six to eight pounds per ton, the pusher grade correspond- ing to any through grade is increased. This is due to the fact that the net load which may be hauled on the through grade is considerably less, so much less that a larger part of the adhesion is available on the pusher grade to overcome grade resistance. 205. Method of operation of pusher grades. — Much of the economy in the operation of pusher grades depends on the method of operation, which in turn depends on the method of their construction. When it is decided that pusher grades are necessary, the ideal method of con- struction is to concentrate the steep grades into one con- tinuous rise. A turnout must be located very near the upper and lower ends of each pusher grade, so that the pusher-engine may be switched on and off the main track with a minimum of useless running. But the ideal arrange- ment of a continuous grade is not always practicable. It sometimes becomes necessary to lay out a pusher grade for a length of perhaps three or four miles, and then, after a mile or two of comparatively level track, another pusher grade several miles in length must be added. It will PUSHER GRADES. 319 Table XXXI. — Balanced Grades for One, Two, and Three Engines. Basis. — Through- and pusher-engines alike; consolidation type; total weight, 107 tons; weight on drivers, 53 tons; adhesion, ¥ 9 5 , giving a tractive force for each engine of 23,850 lbs.; normal track resistance, 6 and 8 lbs. per ton. Track resistance, 6 lbs Track resistance, 8 lbs, Through grade. Corresponding Corresponding Net load pusher grade for Net load pusher grade for for one same ne load. for one same net load. engine in engine in tons (2000 tons (2000 lbs). One Two lbs.). One Two pusher. pushers. pusher. pushers. Level. 3868 tons 0.28% 0.55% 2874 tons 0.37% 0.72% 0-10% 2874 ' ' 0.47 0.82 2278 " 0.56 0.98 0.20 2278 " 0.66 1.08 1880 " 0.74 1.23 0.30 1880 " 0.84 1.33 1596 " 0.92 1.47 0.40 1596 " 1.02 1.57 1384 " 1.09 1.70 0.50 1384 " 1.19 1.80 1218 " 1.27 1.92 0.60 1218 " 1.37 2.02 1085 " 1.44 2.14 0.70 1085 " 1.54 2.24 977 " 1.60 2.36 0.80 977 " 1.70 2.46 887 " 1.77 2.56 0.90 887 " 1.87 2.66 810 " 1.93 2.76 1.00 810 " 2.03 2.86 745 " 2.09 2.96 110 745 " 2.19 3.06 688 " 2.24 3.15 1.20 688 " 2.34 3.25 638 " 2.40 3.33 1.30 638 " 2.50 3.43 594 " 2.55 3.51 1.40 594 " 2.65 3.61 555 " 2.70 3.68 1.50 555 " 2.80 3.78 521 " 2.85 3.85 1.60 521 " 2.95 3.95 489 " 2.99 4.02 1.70 489 " 3.09 4.12 461 " 3.13 4.17 1.80 461 " 3.23 4.27 435 " 3.27 4.33 1.90 435 " 3.37 4.43 411 " 3.42 4.49 2.00 411 " 3.52 4.59 390 " 3.55 4.63 2.10 390 " 3.65 4.73 370 " 3.68 4.78 2.20 370 " 3.78 4.88 352 " 3.81 4.92 2.30 352 " 3.91 5.02 335 " 3.94 5.05 2.40 335 " 4.04 5.15 319 " 4.07 5.19 2.50 319 " 4.17 5.29 304 " 4.20 5.32 usually be more economical to operate the entire distance as a continuous pusher grade, in spite of the fact that for a mile or two the pusher-engine is utterly unnecessary. It 320 THE ECONOMICS OF RAILROAD CONSTRUCTION. would be very difficult to so arrange the schedule of trains that each section of such a pusher grade could be operated separately with separate engines and keep the engines continuously employed. Economy in pusher-engine ser- vice demands that each pusher-engine shall be working as nearly continuously as possible. On account of the great loss of economy that occurs when two sections of a pusher grade are separated by a mile or two of comparatively level track, the engineer can profitably expend considerable study and even surveying, by his corps of men, in the endeavor to so modify the line that the total required difference of elevation can be condensed into a single grade. It has been demonstrated elsewhere that the loss of energy incurred in stopping a heavy train is sufficient to run it along a level track for a mile or more. It is there- fore desirable to couple and uncouple the pusher-engine without stopping the train if it is possible. The pusher- engine takes its name from the frequent custom of using the assistant' engine literally as a pusher behind a freight- train, which enables it to accomplish its work without stopping the freight-train either at the top or bottom of the grade. For passenger service the assistant engine is always coupled ahead of the through engine, which means practically that the train must be stopped when the assistant engine is coupled on. The stop at the top of the grade is avoided by merely uncoupling the locomotive while running, and then running it ahead at increased speed on to a flying-switch, where a switchman is located so that the passenger-train passes the switch without stopping. When the traffic of a road is very heavy a pusher grade may have several pusher-engines, whose sole duty is to serve the trains on that grade. Under such conditions they can usually be operated economically. When the train service is comparatively light, the pusher-engines are PUSHER GRADES. 321 not so steadily employed, and the cost of the pusher-engine service is proportionally higher for each train assisted. If the pusher grade is located very near or even within a few miles of a large freight-yard, at which switching- engines are constantly employed, a considerable economy is frequently possible by employing the pusher-engines alternately as switching-engines in the yard and as pusher- engines on the pusher grade. A still further economy is possible on roads of very light traffic, where the use of a pusher-engine would be a luxury. On such roads the passenger-trains are usually very short and light, and therefore are probably not affected materi- ally by the rate of the ruling grade. On such roads also a delay of even 50% 'in the time of hauling a freight-train over the road is of comparatively small importance. In such cases the road can still be designed on the basis of pusher grades. The freight- train can be loaded up to the capacity of a single engine on all through grades which are less than the pusher grade. The freight-train can then be cut in two at the bottom of the pusher grade, and one half of the train can be taken up separately. The total engine mileage is no greater than with pusher-engine service, and in fact may be somewhat less, for reasons given in the next section. Almost the only objection is that due to the loss in time, and on a road of very light traffic this is a small matter. This method should not be forgotten, particularly in the design of light-traffic roads, since it has all the advantages of enabling a road to be designed, if necessary, on a pusher-engine basis, and yet if the traffic should ever increase, so that the delay, due to this method of operation, becomes objectionable, the normal method of pusher-engine service may be adopted. The engineer should not forget that the pusher- engine method must not be discarded simply because the road may not at first have an amount of traffic which 322 THE ECONOMICS OF RAILROAD CONSTRUCTION. would justify the ordinary method of pusher-engine service. 206. Length of a pusher grade. — The actual mileage traveled by pusher-engines for each train assisted must be something in excess of twice the distance between the sidings at the top and bottom of the grade. Usually a telegraphic station at both the top and the bottom of the grade is at least very convenient if not essential to safe and efficient operation. If a regular stopping-place of the road is located even a mile or two beyond the top or bottom of the pusher grade, it will usually be found advisable, in spite of the added mileage, to have the pusher-engine service begin at the station. When the assistant engine is uncoupled from the train while running, the siding must evidently be at some little distance beyond the top of the grade, so as to give ample opportunity for the assistant engine to run onto a siding and have the switch turned before the train passes. All of these allowances add to the length of the pusher-engine service, which therefore makes it considerably more than the nominal length of the pusher-engine grade as taken from a profile of the road. 207. The cost of pusher-engine service. — When we analyze the elements of cost, we will find that many of them are dependent only on time, while others are depend- ent upon mileage. Still others are dependent on both. Very much will depend on the constancy of the service, and this in turn depends on the train schedule and on a variety of local conditions which must be considered for each particular case. The effect of a pusher -engine on maintenance of way may be considered to be the same as the cost of an additional engine to handle a given traffic, as developed in § 198. The same total allowance for the expenses of maintenance of way (7.45%) will therefore be made. Although the cost of repairs and renewals of PUSHER GRADES. 323 engines is evidently a function of the mileage, and would therefore be somewhat less for a pusher-engine which did little work than for an engine which was worked to the limit of its capacity, yet it is only safe to make the same allowance as for other engines. Other items of mainte- nance of equipment are evidently to be ignored. The item of wages of enginemen will evidently depend upon the system employed on the particular road. Whatever the precise system the general result is to pay the enginemen as much in wages as the average payment for regular ser- vice, and therefore the full allowance for Item 80 will be made. Similarly we must allow the full cost of the items for engine-supplies. While the engine is doing its heavy work in climbing up the grade, the consumption of fuel and water is certainly greater than the average; but, on the other hand, on the return trip, when the engine is run- ning light, it probably runs for a considerable portion of the distance actually without steam, and therefore the consumption of fuel and water will nearly, if not quite, average the consumption for an engine running up and down grade along the whole line. That portion of fuel consumption which is due to radiation, blowing-off steam, and the many other causes previously enumerated, will be the same regardless of the work done. We therefore allow 100% for all of these items of engine-supplies. In general we must add 100% for Items 90, 91, and 94, the cost of switchmen and telegraphic service. While there might be cases where there would be no actual addition to the pay-rolls or the operating expenses on account of these items, we are not justified in general in neglecting to add the full quota for such service. Collecting these items we will have 45.05% of the average cost of a train- mile for the cost of each mile-run by the pusher-engine. Using the same figure as before, $1.50, for the cost of one train-mile, we have 67.57 c. for each mile-run. 324 THE ECONOMICS OF RAILROAD CONSTRUCTION. Table XXXII. — Cost for Each Mile of Pusher-engine Service. Item number. Itenr (abbreviated). Normal average. Per cent affected. Cost per engine mile, per cent. 2-6,9 25-27 Track material, labor, bridges . . Steam locomotives 14.89% 8.61 7.80 11.41 1.17 50 100 100 100 100 7.45 8.61 80,81 82-85 90, 91, 94 Road enginemen and engine- house expenses Fuel and other engine supplies . . f Signaling, flagmen, and tele- \ graph 7.80 11.41 1.17 45.05 208 Numerical illustrations of the cost of pusher service. — In § 204 we found that a through grade corresponding to a 1.9% pusher grade was 0.99%, or, in other words, that two engines of equal capacity could handle on a 1 .9% grade a train which could be hauled by one engine on a 0.99% grade. Suppose that we have a road or division 100 miles long, which has a traffic of ten trains per day each way which must be assisted by pusher-engines. Two of the grades, 5 and 6.5 miles respectively, are against the traffic in one direction, and the other grade,' with a length of 7.5 miles, is against the traffic in the other direc- tion. There will therefore be a total of 19 miles of pusher-engine grade, on which ten trains per day must be assisted. Suppose that these maximum grades have been limited by suitable development to 1.9%. Suppose that the other grades are less than 1% or are so little above it that, with a comparatively small expenditure, they may be reduced to 1% or to 0.99%. How much money could justifiably be spent to accomplish the reduc- tion of the other grades to keep them within the limit of PUSHER GRADES, 325 0.99%? There will be no object in cutting down these intermediate grades, unless by so doing we can double the train-load, eve-n though doubling the train-load adds the expense of operating the pusher service. If the traffic of the road is sufficient for ten trains, such as could be hauled with one engine over the 0.99% grades, it will require twenty such trains to haul that traffic with one engine over 1.9% grades. Therefore, utilizing the pusher-engine ser- vice will save the operation of ten trains per day each way. If this particular division of the road is 100 miles long, the annual saving by cutting down the number of trains from twenty to ten, computed as in the previous chapter, will be 10 X$0.625X 100x365 = $228,125. But this saving is accomplished only by the pusher service, which will cost 10x19x2x67.57 c. X 365 =$93,720 per year. Capitalizing the net saving, $134,405 at 5%, we have $2,688,010, which represents the amount which might jus- tifiably be spent in reducing all grades except the three pusher grades down to the limit of 0.99%. The above estimate may need to be modified somewhat as to the cost of the pusher service. If these three pusher grades were so widely separated that each must be operated independ- ently, then the pusher-engine mileage per day for the three grades would be 100, 130, and 150 miles respec- tively. Unless the schedules were favorably arranged for the pusher-engine service, it is quite possible that one engine might not be able to do the entire work on each of the grades. Freight-trains which require pusher-engine help usually move at a very low speed, probably less than 15 miles per hour, and at times not more than 10 miles 326 THE ECONOMICS OF RAILROAD CONSTRUCTION. per hour. One hundred and fifty miles per day for a pusher-engine implies a very well-arranged schedule, and therefore two pusher-engines might be needed instead of one. This would add considerably to the cost of the pusher-engine service. The cost of reducing these grades is a quantity which can be readily computed with all desired accuracy, therefore we can usually determine by an investigation like the above whether the plan of using a pusher-engine service is desirable, since the cost of reducing the grades might be very much less than the computed capitalization. In that case it would show that it would probably be justifiable to adopt such a policy and that any allowable inaccuracy in the method of esti- mating the difference in operating expenses would not alter the final result. On the other hand, if the cost of reducing the grades is materially greater than the capital- ized value, the proper method is again clearly indicated. When the two values are substantially equal, it shows that there is but little choice, and that the choice must probably be determined by the facility with which the money for the improvement can be obtained. In applying the above methods to any particular case, the values given above should be closely studied and revised to agree as nearly as possible with the local conditions. The value of the cost of a pusher-engine mile given above is to be considered as merely illustrative of what the cost will be under some conditions. Under other conditions the variation will be considerable, and a value which will correspond with the local conditions should be determined. CHAPTER XVII. BALANCING GRADES FOR UNEQUAL TRAFFIC. 209. Nature of the subject. — In the preceding chapters it has been tacitly implied that the extent of the traffic in the two directions is equal, and that it is just as desir- able to obtain a low grade in one direction as in the other. But it frequently happens that the freight traffic in one direction is far greater than the freight traffic in the oppo- site direction. Even on the main trunk lines running east and west, the east-bound ton-mileage has at times amounted to four or five times the west-bound ton-mileage. Be- tween the years 1851 and 1885 the east-bound ton-mileage on the Pennsylvania Railroad averaged 3.7 times the west-bound ton-mileage. As an actual consequence, the west-bound freight-trains consisted very largely of " empties." As another corollary, a locomotive which could haul a certain number of loaded cars up a grade of 0.6%, which was against the east-bound traffic, could just as easily haul such cars as were loaded, together with the empties, which must be returned, up a considerably steeper grade, say 1.0%. Under such conditions there is little or no object (from the ruling-grade standpoint) of making the grade against the west-bound traffic any less than 1% when the east-bound traffic is as steep as 0.6%. The two grades, 0.6 and 1.0, have been selected offhand as two grades which might balance each other under certain 327 328 THE ECONOMICS OF RAILROAD CONSTRUCTION. conditions of relative traffic in the two directions. They illustrate the principle involved that the ruling grades in opposite directions should not necessarily be equal, but should probably be made unequal. It now remains to determine what should be the relation between the luling grades in the two directions on any given road. 210. Illustrations in the balancing of grades. — This sub- ject is one that chiefly concerns the great trunk lines of the country, which are constructed almost regardless of cost and at grades which are reduced to a low figure by a great expenditure of money. A very large number of railroads, especially branch lines which run from a main road up into the mountains, have one terminus much higher than the other, are laid out largely as "surface lines," and are therefore laid on such grades as can be obtained with a minimum of constructive work. On such a road the heavy grades may be almost entirely in one direction, which may or may not be against the heavy traffic. Unless a road is of such importance that it can be largely rebuilt after its original construction, in order to correct the errors and deficiencies of the original work, we must consider the original location as a finality. It is frequently impossible to predict, with any great accuracy, what the traffic of the road will be, and especially that the traffic in one direction will be materially greater by any definite percentage than that in the other. The engineer is there- fore seldom justified in attempting to make precise cal- culations of this sort previous to the construction of a new road. 211. Principles on which the theoretical balance must be computed. — A little thought will show the truth of the following statements. First, the number of locomotives and passenger-cars running in each direction is necessarily equal. Second, the number of passengers carried in BALANCING GRADES FOR UNEQAL TRAFFIC, 329 opposite directions is practically equal. Even if we allow that there is a considerable immigrant traffic which in- creases slightly the load of passengers carried, it is useless to base any calculations on this, since the ratio of live load to dead load in passenger-cars is so very small that such a slight difference in the number of passengers carried in opposite directions as may exist can have absolutely no effect on the proper rate of grade. Third, empty cars have a greater resistance per ton than loaded cars; therefore, in computing the hauling capacity of a locomotive hauling so many tons of " empties," a larger figure must be used for the ordinary tractive resistances. This fact, so far as it goes, tends to equalize the differences in the two grades which might otherwise be computed. Fourth, owing to greater or less imperfections of management, a small per- centage of cars will run empty or partly full in the direction of the greatest traffic. Fifth, freight having great bulk and weight (such as grain, lumber, coal, etc.) runs from the rural districts to the cities and manufacturing dis- tricts. Sixth, freight from manufacturing districts, although it pays comparatively high freight-rates and is actually more profitable to handle, weighs far less, and occupies less bulk. Seventh, changes in traffic conditions which are more or less permanent will alter the direction of the hauling of bulk freight. For instance, a farming district which is largely a dairying country frequently will not raise as much feed (hay and grain) as is needed to feed the cattle, and we have the apparent paradox of importing grain and feed into a farming country. Eighth, a change in the character of the country may permanently alter the ratio of the freight tonnage in the two directions. Such changes are already discernible in the traffic of the east and west lines and also in the north and south lines. The discovery of extensive coal-fields in the western part of the United States has largely changed the direction of the 330 THE ECONOMICS OF RAILROAD CONSTRUCTION. movement of this class of bulk freight. The exhaustion of supplies of timber in one section and the development of that industry in another has also had material influ- ence in changing the relative flow of traffic. The develop- ment of the coal and iron industries in the South has largely changed the relative traffic flow in north and south lines. 212. Numerical illustration. — Assuming the same figures already considered in § 129, we will consider that the grade against the heaviest traffic and for fully loaded trains is 1%. The grade and tractive resistance for a rating ton on this grade is 22.6 pounds per ton. If the locomotive has a tractive power of 28,200 pounds, it can handle 1248 gross rating tons. The actual weight of the locomotive and tender is 130 tons; multiplying this by 128% for the 1% grade, we have 166 rating tons for the locomotive which leaves 1182 rating tons behind the tender. If the fully loaded trains have a live load equal to twice the weight of the cars, their actual tonnage will 3 be ~ — -7^X1182 = 1081 tons. This means that the cars 2-f- l.Zo weigh 360 tons and the freight 721 tons. Assume that the total live load carried in the opposite direction is but J of the above, we would then have 360 tons of cars and 240 tons of freight, which will aggregate 600 tons. To determine the rating tons corresponding to 600 actual tons of loading, we must make first a trial estimate of the grade in order to determine the value of a rating ton on that grade. We will assume as a trial that the grade is 1.6%. At this grade the ratio of a tare ton to a rating ton is 119%. Since the live load is J of a nominal full load, which means that it is § the weight of the cars, to reduce 600 actual tons to rating tons at 1.6% we must 2 +l divide 600 by z 3 ^ 1Q , which equals 668 rating tons. BALANCING GRADES FOR UNEQUAL TRAFFIC. 331 But on a 1.6% grade the 130-ton locomotive will have the equivalent weight of 155 rating tons. Adding this to 668 rating tons for the load behind the tender, we have 823 rating tons as the total weight of the train. If we divide the total tractive power 23,200 by 34.8, the tractive resistance of a rating ton on a 1.6% grade, we would have 811 as the total capacity in rating tons of the locomotive on the 1.6% grade. This agrees fairly well with 823, but it proves that the trial rate of grade, 1.6%, is a little too high. If we were to carry through another trial calcula- tion on the basis of 1.5%, we would find a far greater dis- crepancy in the other direction. Considering that our assumption of the probable weight of the loading in the direction of light traffic is at its best a gross approxima- tion, any over-refinement in these calculations is a mere waste of time. We may therefore say that, under the above conditions, a grade of 1% against the heaviest traffic will give as much resistance and require as much work of the engines as a grade of 1.6% against the assumed lighter traffic. 213. Reliability of calculations of this nature. — As before intimated, this is not a question which will ordina- rily concern the engineer of a light-traffic, cross-country road. The practical difficulty of predicting the relative amount of traffic on a road before it is constructed, and the probability that such figures, no matter how correct they might be in the early history of the road, will be permanently altered in the course of 20 or 50 years, means that very little reliability can be placed on such computa- tions except in a general way. The great east and west trunk lines, although they find that there are fluctuations in the relative amounts of traffic, have also discovered that, in a rough way, the east-bound traffic is permanently far greater than the west-bound traffic. The Pennsylvania Railroad, in the course of the carefully developed recon- 332 THE ECONOMICS OF RAILROAD CONSTRUCTION. struction of their line and the building of a low-grade line between Philadelphia and Pittsburg, have kept this prin- ciple in mind, and have uniformly designed the ruling grade against the east-bound traffic at a considerably lower figure than that against the west-bound traffic. The Canadian Pacific has already begun extensive reconstruc- tion of their line in order to follow this same principle. In an extreme case pusher grades may be used to accom- plish the same object, but this does not alter the principle involved. A pusher grade should always be considered as a special case of a ruling grade of a little over one-half the rate which is operated in a special way, and the above principle is one which applies to the relative rate of the ruling grade. Although the engineer of a light-traffic road may not find it justifiable to spend any added amount of money to follow this principle, he should keep it in mind and endeavor to so design his ruling grades to conform to this principle, if it may be done with little, if any, added expenditure. INDEX. Numbers refer to sections except where specifically marked pages (p.). Acceleration curves 131 Acceleration of trains, force required 120 Accidents, cost as affected by curvature 160-175 danger of, due to curvature 160 justification of unusual expenditure to avoid them 5 probability during any one railroad trip 5 proportion for which railroads are responsible 5 total number of killed and injured 5 Additional cost of operating a given freight tonnage with (n + 1) engines on heavy ruling grades instead of with n engines on lighter grades — Table XXIX p. 308 cost of operating a given freight tonnage with (n + 1) light engines instead of n heavier engines — Table XII p. 143 Adhesion of locomotive driving-wheels 126, 130 Air-brakes — see Brakes. Air resistance — see Atmospheric resistance. American type of locomotives, cost 83 Aspinall's formula for train resistance 121, 122 Assistant engines — see Pusher engines and Pusher grades. Atmospheric resistance 115 Automatic air-brakes, extent of use 94 couplers, extent of use 95 Average cost per train-mile for the whole United States — 1890- 1910— Table VII p. 91 Averages, statistical, danger in indiscriminate use 6 Balanced grades for one, two, and three engines — Table XXXI. p. 319 BALANCING GRADES FOR UNEQUAL TRAFFIC— Chap. XVII. determination of theoretical balance 211 nature of the subject 209 numerical illustration 212 Baldwin Locomotive Works' formula for train resistance 121, 122 Barnes's formula for train resistance. 121, 122 333 334 INDEX. Boiler, limitation of steaming capacity 126, 127 Bond, convertible, financial character 13 equipment trust, financial character 13 income, financial character 13 Bonds, interest, average rate 15 interest, percentage of defaulted interest 15 limitation of bonded debt 8 power of bondholders to demand foreclosure sale 8, 13 Brake resistances 119 Brakes, air- or train-, extent of use 94 Bridges and culverts, cost of renewals and repairs 54 • as affected by changes in alinement and operating conditions 86, 138, 164 Buildings and fixtures, cost of renewals and repairs 55 CAPITALIZATION— Chap. III. minimum required by State laws 10, 11 railroad, practical limitations 19 principles governing amount 20 Capital, railroad, growth for decennial periods 2 per inhabitant . 1 per line of mile 1 CAR CONSTRUCTION, economics of— Chap. VIII Car-mileage, cost 70 Cars' capacity of various types 91, 92 causes of deterioration 139 cost of repairs, renewals and depreciation 59, 139 as affected by changes in alinement 87, 139, 170, 190, 199 draft-gear 96-98 high capacity, economy 93 ratio of live load to dead load 92 Car-wheels, rotary kinetic energy of 120, 124 Charters, special privilages granted 9 Chemical treatment of ties 107 economics of 108 Classification of operating expenses 49-51 of traffic 151 Coal — see Fuel. Coaling stations, cost of operation 78 Commodities — proportions of various classes carried, Table VI, b p. 83 summary of selected, for year ending June 30, 1910, Table VI, c p. 83 Commodity rates, special, justification 31 INDEX. 335 Comparative cost of various sizes of standard gauge simple locomo- tives —Table XI p. 134 value of cross-ties of different materials 108 Condemnation proceedings, regulations regarding them 11 Compensation for curvature 179, 180 meaning and necessity 179 rate 180 Competition, direct, effect on rates 29 indirect, effect on rates 30 Concrete ties, economics of 108 Conducting transportation, cost of 62-71 cost of as affected by changes in dis- tance 140-149 as affected by curvature 172-175 minor grades 191 ruling grades 200 Consolidation locomotives, cost of 83 weight and tractive power 196 of railroad corporations 37 Constructive mileage, as used in payment of enginemen's wages . . 77 Control, Federal, of railroads 33-37 legal, of railroads 27-32 State, of railroads 38 Cost, comparative, of various types of locomotives 83 for each mile of pusher-engine service — Table XXXII ... .p. 324 of curvature, per degree of central angle 176 of handling a given traffic with one less train 85-89 of maintenance and operation of locomotives, 1908-1910, Table X p. 117 of one additional mile of distance per daily train per year. . . 150 of one additional foot of distance per daily train per year. . . 150 of pusher-engine service 207 numerical illustration 208 of renewals of rails 52 of ties 52, 104-112 of repairs and renewals of bridges and culverts 54 of fences, road-crossings and cattle- guards 54 of freight-cars 59 of locomotives 57, 75, 76 of passenger-cars 59 of repairs of roadway 52, 53 of ties, actual, as distinguished from first cost 106 per train-mile, average for United States 50 336 INDEX. Cost, total, of power, by the use of locomotives 74 Cresoted ties, economics of 107, 108 Cross-ties — see Ties. Culverts, cost of renewals and repairs 54 CURVATURE— Chap. XIII. effect in limiting length of trains 162 the use of heavy engines 162 on speed of trains 161 on traffic 161 limitations for maximum 181 objections to 159 Curve resistance 118 per degree of curve 118 Curves, cost per daily train per year of one degree of central angle 176 effect on rail wear 100-103 Cushing, W. C, author of demonstration of comparative value of cross-ties of different materials 108 Damages to persons and property, cost 69 Demurrage charges on detained cars 70 Dennis, A. C, author of demonstration on momentum diagrams and tonnage ratings 128-133 Determination of coordinates of velocity-distance curves for one type of locomotive— Table XXII p. 226 Discrimination in rates, effect on receipts and profits 30 DISTANCE— Chap. XII. compensation to cost of increased distance 153-154 effect of change in the length of the home road on its receipts from through-compet- itive traffic 153, 154 on business done 158 effect on operating expenses 138-150 receipts 151-156 justification of decrease to save time 157 relation to rates and expenses 135 Distribution of the cost of engine repairs to its various contributing causes— Table XXIII p, 240 Dividends on railroad stocks 14 railroad, variation due to variation in business 18 Docks and wharves, cost of repairs and renewals 55 Dowels, use in ties 112 Draft-gear 96-98 friction 98 spring 97 INDEX. 337 Dynamometer tests for train resistance 123 Earnings, railroad, estimation by comparison 43 detailed computation 44 gross amount from various sources 3, 17 per capita 40 per mile of road for large and small roads 41 per mile of road in various groups 40 • per train-mile for large and small roads 41 ECONOMICS OF CAR CONSTRUCTION.— Chap. VIII. Economics of change in distance, general conclusions 156 heavy locomotives . 84-89 high capacity cars 93 rails 99-103 the locomotive 74-83 ties 104-112 railroad, justification of methods of computation . 73, 178, 193 Economy of pusher grades 202, 203 Effect of curvature on operating expenses 163-177 of distance on receipts 151-155 on operating expenses of 26.4 feet of rise and fall — Table XXVI p. 294 of changes in curvature — Table XXV p. 271 of great and small changes in dis- tance—Table XXIV p. 247. Elimination of curvature, financial value 177 of distance, numerical illustration of financial value. . 177 Eminent domain, right of, inherent in railroad corporations 9-11 Employees, railroad, proportion of total population 4 total number in railroad service 4 wages paid 4, 64, 77 Enginemen, methods of payment of wages 64, 77, 141 English locomotives, mileage life 75 Estimates on economics, reliability 73, 178, 193 volume of traffic 40 ESTIMATION OF VOLUME OF TRAFFIC— Chap. V. Expenditure of money for railroad purposes, general principles . . 19, 20 Extra business, cost of handling 18-28 Federal control, constitutional basis 33 of rates 33-37 Fixed charges, character 15 338 INDEX. Fixed charges, ratio to total disbursements 13, 18 Formula for accelerated motion 131 tractive force '. 126 grade resistance 117 Formulae for inertia resistance 120 train resistance 121 Freight rates on bulky or low-grade freight 32 rational basis of determination 28 traffic, average haul per ton in miles *..... 45 number of tons carried one mile per mile of line 45 in a train 45 Friction draft-gear 98 journal, of axles 116 rolling, of wheels 116 Fuel for locomotives, cost 65, 78 for handling coal at coaling stations .... 78 of, as affected by changes in alinement 88, 142, 200 relative value of various kinds and grades. . . 78 Funded debt, ratio to total capitalization 13, 18 Grade — see Minor Grades, Pusher Grades, Momentum Grades, Ruling Grades, Balancing of grades for unequal traffic. Grade resistance 117 virtual 125 use, value, and misuse ., 126, 127 Grades, accelerated motion of trains on 120, 124, 127, 131 distinction between minor and ruling 182 minor — see Minor grades, pusher — see Pusher grades, ruling — see Ruling grades. Gross and per-capita railroad earnings, whole United States — Table III p. 70 Gross earnings per mile of road and per train-rnile for great and small roads (1904)— Table V p. 75 Henderson, G. R., tonnage-rating formula 134 Hitt, Rodney, economics of high-capacity cars 93 Humps in a grade, financial value of removal 186-193 operation of a train over them by means of momentum. . . 127 Impurities in water for boiler use 79 Incorporators, number required in various States 10 INDEX. 339 Inertia resistance 120 Injuries to persons, cost 69 Interstate Commerce Act 34 Journal friction of axles 116 Kinetic energy of trains 124-127 Law of increasing returns 28 Laws, general railroad 10 in State of New York 11 of journal friction 116 Life (in months) of 100-lb. rails— Main line, P. R. R.— Table XIV, p. 164 of rails on mountain curves — A. T. & S. F. Rwy. — Table XIII p. 163 Life of locomotives 75 Limitations of curvature 181 Local traffic, definition and distinction from through traffic 151 Location of terminals and stations at a distance from business centers, effect 46, 47 Locomotives, cost of fuel 65 of repairs, renewals and depreciation 57, 75, 76, 139 of various types 83 heavy, use on very sharp curvature 162 heavy vs. light 84-89 internal resistances 114 life of 75 statistics 83a repairs, distribution to various causes 139 repairs and renewals, as affected by changes in alinement 87, 139, 169, 190, 199, 207 tonnage rating 129-134 tractive power of various types — Table XXVII. . .p. 300 water-supply 66, 79-81 Long-and-short-haul clause, Interstate Commerce Act 34 Loss in traffic due to lack of facilities 46-48 Lubricants for locomotives 82 Maintenance of equipment, as affected by changes in curvature 168-170 distance 139 minor grades 190 ruling grades 199 pusher-engines 207 weight of engines 87 cost 56-60 340 INDEX. Maintenance of Way, as affected by changes in curvature 164-167 distance 138 minor grades 186-189 weight of engines 86 cost 52-55 and Structures, discussion of items 52-55 Map showing Interstate Commerce Commission division of railroads into groups 13 Marine equipment, cost of repairs and renewals 60 Maximum train-load on any grade 196 Metal ties, economics of 104-108 Mileage, car 70 life of locomotives 75 railroad, annual growth in the United States 1 per 100 square miles of territory 39 per 10,000 inhabitants 1 total in the United States 1 Miles of line per 100 square miles of territory 1 MINOR GRADES.— Chap. XIV. basis of cost 183 classification 185 distinctive character 182 effect on operating expenses 186-193 estimate of cost of one foot of change of elevation 192 numerical illustration of financial value of re- duction 1 93 Mogul locomotives, cost and dimensions 83 Momentum diagrams and tonnage ratings 128-134 MOMENTUM GRADES.— Chap. XI. Monopoly in railroad business, possible extent 48 MOTIVE POWER.— Chap. VII. National wealth and railway capital— Table II p. 10 Non-competitive traffic, extent of monopoly 48 Northern Pacific Railroad, rail-wear statistics 101-103 Objections to curvature 159 Oil, use for fuel for locomotives 78 OPERATING EXPENSES.— Chap. VI. Operating Expenses, classification 49, 51 per train-mile, as affected by changes in curvature 163-177 per train-mile, as affected by changes in distance 138-150 INDEX. 311 Operating Expenses, per train-mile, as affected by minor grades. 186-193 per train-mile, as affected by ruling grades. 199-201 per train-mile, as affected by weight of engine 85-89 per train-mile, average 50 per train-mile, fivefold distribution 49 method of distribution 51 on large and small roads, 1904, 1910— Table VIII p. 93 uniformity 50 Operation of trains, effect of curvature on 162 ORGANIZATION OF RAILROADS.— Chap. II. Oscillatory and concussive velocity resistances 115 Passenger-cars, cost of repairs, renewals and depreciation 59 -miles, total per year 3 traffic, average journey per passenger in miles 45 average number in train in various groups 45 number of passengers carried one mile per mile of line 45 proportion of earnings to total in various groups . 45 Population, tributary, estimate of 42 Pooling of railroad receipts 35 Pools, money 35 traffic 35 Profit and loss, dependence on variations in business done 18 small margin between 17 Projects, railroad, economic justification of 7 Property, private, appropriation of by railroads 10-1 1 railroad, basis of ownership 8 railroad, valuation, Chap. IV . Public service of railways, by groups (1900) — Table VI p. 80 ratios of various kinds 3 Purification of water-supply for boiler use 80 Pusher-engine service, cost 207 PUSHER GRADES.— Chap. XVI. length 206 method of operation 205 principles underlying use 202, 203 relation to corresponding through grades 204 Rail renewals, as affected by changes in distance 138 curvature 166 342 INDEX" Rail renewals, as affected by minor grades 188 weight of engines 86 Rails, cost of renewals 52 minimum weight permitted by law 11 Rail wear on curves — Northern Pacific R. R., Minnesota Div. — Table XIX p. 170 — Northern Pacific R. R., Pacific Div. — Table XVIII p. 169 per degree of curve 103 on tangents — Northern Pacific R. R. — Table XV p. 165 relation of rate to the life-history of the rail 102 statistics 100, 101 theoretical 99 Railroad property, basis of ownership 8 statistics — Table I p. 9 Rates, railroad, based on distance, reason 135-137 basis of determination 28 limitations 10 " reasonable ' ' — " confiscatory " 34 relation to distance 135, 136 Rating tons, meaning of 129 Ratio of tare tons to rating tons for various grades — Table XXI. . . p. 219 Relation of one-pusher and two-pusher grades to through grades, with variations of the ratios of adhesion and normal resistance — Table XXX p. 315 of radius of curvature and of degree of central angle to operating expenses 163 Renewals of locomotives 57, 75 Repairs and renewals of bridges and culverts, cost 54 of freight-cars, cost 59 of locomotives, cost 57, 75, 76 as affected by changes in operating conditions, 87, 139, 168, 190, 199 of passenger-cars, as affected by changes in operating conditions. .87, 139, 168, 190, 199 of passenger-cars, cost 59 Repairs of locomotives 57, 76 average cost per engine-mile 76 per thousand ton-miles 76 Repairs of roadway 53 as affected by changes in operating conditions, 86, 138, 167, 186-188 Resistance atmospheric 115 INDEX. 343 Resistance curve 118 grade 117 train, formulae for 121 Resistances due to brakes . 119 due to inertia 120 internal, to the locomotive 114 oscillatory and concussive 115 velocity 115 Retardation curves 132 Revenue, gross, distribution of 17 Rise and fall, technical meaning of 184 Roadway, cost of repairs 53 (See also Repairs of roadway.) Roller-bearings, advantages and use 116 Rolling friction of wheels 116 Rotative kinetic energy of wheels of train 120, 124 Road enginemen, wages paid 64, 77 RULING GRADES.— Chap. XV. definition 194 determination of 195 numerical illustration of value of reduction. . 201 proportion of traffic affected by them 197 Sags, operation of a train through them by means of momentum . . 127 Screw-spikes, use in ties Ill Searles's formula for train resistance 121 Seasonal variations in traffic 40a Service, railroad, value compared with cost 135-136 Shop machinery and tools, cost of repairs and renewals 60 Slipping of wheels on rails, lateral, effect on rail wear 99 longitudinal, effect on rail wear 99 Speed of trains, limited by sharp curvature 161 relation to tractive adhesion 130 Spring draft-gear 97 State control 9-11, 38 STATISTICS.— Chap. I. of mileage and gross earnings in different sections of the United States (1900)— Table IV p. 72 locomotive 83a train-mile — average in various groups for the year ending June 30, 1910— Table VI, a p. 82 traffic, average 45 Steel ties, economics of 108 Stocks, dividends on, percentage paying no dividends 14 344 INDEX. Stocks, per mile of line in various sections of the country 12 preferred, privileges and limitations 12 railroad, total for railroads of United States 12 Summary showing classification of operating expenses for the year ending June 30, 1910, and proportion of each class to total —Table IX pp. 95-97 Supplies, miscellaneous, for locomotives, cost 66, 82 Switching charges 70 engines, used in pusher-engine service 205 TABLES. — Numbers refer to pages, not sections. I. Railroad statistics 9 II. National wealth and railway capital 10 III. Gross and per-capita railroad earnings — whole United States 70 IV. Statistics of mileage and gross earnings in different sections of the United States (1900) 72 V. Gross earnings per mile of road and per train-mile for great and small roads (1904) 75 VI. Public Service of railways, by groups (1900) 80 VI a. Average train-mile statistics in various groups for the year ending June 30, 1910 82 VI b. Percentages of freight traffic movement tonnages, by class of commodity, originating on line of reporting roads 83 VI c. Summary of selected commodities for the year ending June 30, 1910 83 VII. Average cost per train-mile for whole United States — 1890-1910 91 VIII. Operating expenses per train-mile on large and small roads (1904 and 1910) 93 IX. Summary showing classification of operating expenses for the year ending June 30, 1910, and proportion of each class to the total. Large roads 95-97 IX a. Small roads 97, 98 X. Cost of maintenance and operation of locomotives, 1908- 1910 117 XL Comparative cost of various sizes of standard-gauge simple locomotives 134 XII. Additional cost of operating a given freight tonnage with (n-f-1) light engines instead of n heavier engines. ... 143 XIII. Life (in months) of rails on mountain curves 163 XIV. Life (in months) of 100-pound rails, main line P. R. R. . . 164 XV. Rail wear on tangents, Northern Pacific R. R 165 INDEX. 345 TABLES. — Numbers refer to pages not sections. XVI. Yearly wear (in pounds) of outer rails — sharp curves . . . 167 XVII. Yearly wear (in pounds) of rails on tangents 168 XVIII. Rail wear on curves, Northern Pacific R. R., Pac. Die. . 169 XIX. Rail wear on curves, Northern Pacific R. R., Minn. Die. 170 XX. Velocity head (representing the kinetic energy) of trains moving at various velocities 211 XXI. Ratio of tare tons to rating tons for various grades .... 219 XXII. Determination of coordinates of velocity-distance curves for one type of locomotive 226 XXIII. Distribution of the cost of engine repairs to its various contributing causes 240 XXIV. Effect on operating expenses of great and small changes in distance 247 XXV. Effect on operating expenses of changes in curvature . . . 271 XXVI. Effect on operating expenses of 26.4 feet of rise and fall 294 XXVII. Tractive power of -various types of standard-gauge loco- motives at various rates of adhesion 300 XXVIII. Total train resistance per ton (of 2000 pounds) on various grades 302 XXIX. Additional cost of operating a given freight tonnage with n + 1 engines on heavy ruling grades instead of with n engines on lighter grades 308 XXX. Relation of one-pusher and two-pusher grades to through grades, with variations of the ratios of adhesion and normal resistance 315 XXXI. Balanced grades for one, two, and three engines 319 XXXII. Cost for each mile of pusher-engine service 324 Tare ton, meaning of 129 Taxes, railroad, annual amount paid 16 average assessment per mile 16 average rate of taxation 16 method of assessment 16 Telegraph plant, cost of repairs and renewals 54 Terminals, effect of location on business 46 Through rates, method of division between the roads on which through traffic is carried 152 Through traffic, definition 151 effect of changes in distance on receipts 153 Tie-plates 109, 110 economics of 109 wooden 110 316 INDEX. Tie renewals, as affected by changes in operating conditions. 86, 138, 165, 187 Ties, actual cost as distinguished from first cost 106 chemical treatment 107 cost of renewals 52 form, economics of 109 methods of deterioration and failure 105 of different materials, comparative value 108 protection against wear 110 use of dowels 112 use of screw-spikes Ill Time, reduction in distance to save 157 Ton-miles per pound of coal burned in locomotives 78 Tonnage rating for a given grade and velocity 130 of locomotives 129-134 TRACK ECONOMICS.— Chap. IX. Trackmen, wages 53 Tractive power of various types of standard-gauge locomotives at various rates of adhesion — Table XXVII p. 300 Traffic associations 36 classification 151 effect of change of distance on 158 estimation of volume, Chap. V. facilities, effect on volume of business 46-48 proportion affected by the ruling grade 197 railroad, " necessary " and " unnecessary " 48 seasonal variations 40a Train-brakes — see Brakes. Train length, limitation by curvature 162 load, increase in, financial value of 198 maximum on any grade 196 men, wages 67 mile statistics 45a TRAIN RESISTANCE.— Chap. X. Train-resistance formula? 121 results compared 122 total per ton (of 2000 pounds) on various grades — Table XXVIII p. 302 Train service, cost 67 supplies and expenses, cost 68 wages — see Train service. Tributary population, estimation of 42 INDEX. 347 Valuation, based on capitalization of net earnings 26 cost of replacing property 23 par value of stocks and bonds 22 stock-market quotations 25 of a railroad's physical property and franchise 24 VALUATION OF RAILWAY PROPERTY.— Chap. IV. Velocity, effect on journal and rolling friction 116 tractive power 130 head 124 (representing the kinetic energy) of trains moving at various velocities — Table XX p. 211 Virtual profile, illustration 125 Volume of railroad traffic — see Earnings. traffic, conditions affecting it 46-48 Wages of engine-men 64. 77 trainmen 67 trackmen 53 Water-supply for locomotives, cost 66, 81 impurities 79 methods and cost of pumping 81 methods for purification 80 Wear of rails — see Rail wear. Weight of cars 91 Wellington's formula 3 for train resistance 121 Westinghouse friction draft-gear 98 Wheel resistance 116 Wheels, effect of rigidly attaching them to axles . 99 White-oak ties, economics of, compared with other kinds. 108 Wood, use for fuel for locomotives 78 Wooden tie-plates 110 Work-cars, cost of repairs, renewals and depreciation 60 Yard-engine expenses 63 Yearly wear (in pounds)of outer rails — Sharp curves — Table XVI, p. 167 of rails on tangents— Table XVII p. 168 OV 12 1912