The economic theory of the location of railways; an analysis of the conditions controlling the laying out of railways to effect the most judicious expenditure of capital

Front matter

m glory

625.1

THE

Preface

Only in a very figurative sense can this book be said to be a “ revised edition” of the little volume under the same title which the writer published ten years ago. The substance of the old book remains unchanged, so far as it went, but every page and sentence has been rewritten, except the dedication. The most important change in the nature of an addition is the much greater attention given to traffic and revenue questions, which are particularly likely to be underrated or forgotten. The mechanics of curve resistance have been discussed, it is hoped, more adequately than heretofore, and on a more solid basis of experimental fact, with some important practical questions which depend thereon. The theory of the effect of variations in velocity on the motion of trains is an entirely new addition, supplying one of the most important omissions of the former edition and of other engineering text-books. The theory of various details of the locomotive, which did not seem to have been elsewhere adequately discussed for the purposes of this volume, has been given, it is hoped, more fully and correctly than heretofore. Parts IV. and V. are entirely new.

On the other hand, the new edition has been abbreviated by omitting the discussions, some thirty in all, where reasons why the writer felt compelled to differ from some previously published conclusions or estimates were given in detail. This seemed necessary ten years ago, but at present it appeared as if the space might be better used.

The number of engravings has been increased from half a dozen to 313, the number of pages from 216 to 950, and the number of tables from 44 to 204. All of the tables, with a few exceptions noted in connection with each, are original computations of the writer or compilations from original sources of information. As practically all the work of preparing them, and of rewriting the text, has been done outside of those hours which are ordinarily and more rationally regarded as working hours, a long delay in republication has been unavoidable ; but if there be truth

PREFACE.

aai a

Gaough in the old antithesis of “easy writing” and “curst hard reading” to hold good when twisted wrong end to, there should be some compensation in store for any reader who may have chanced to be annoyed by the delay.

In order to adapt the volume to the more convenient use of all classes of readers, three sizes of type have been used :

Long Primer type is used for those parts of the volume which were deemed most likely to be such as every interested reader would wish to read, including those who desire only to ascertain the more important conclusions, free from technicalities.

Bourgeois type is used for discussions which relate more to the details of the subject than to principles, and hence may be passed over by those who are not engineers, or who are ready to take the reasons for what is printed in larger type for granted. Nevertheless, much of the matter which is printed in this smaller type, as for instance the long chapter on the locomotive engine and the whole of Part V., is among the most important in the book for the professional engineer.

Brevier type is used for minor notes and comments which it seemed essential or desirable to give, as of much possible importance to those wishing to look into the subject, or some particular branch thereof, with still gre.ater care, but which might otherwise be passed over.

The mathematical form of discussion has been intentionally avoided, first, because the book has been written for practical men as well as for students, and mathematical methods are apt to repel them ; and secondly, and chiefly, because mathematical methods of solution are not only inexpedient, but positively dangerous for the class of problems considered. When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions; but whenever the chief difficulty of a problem lies in the multiplicity and dubiousness of the premises themselves, and in reconciling them with each other, there is no safe course but to remain continuously on the solid ground of concrete fact. The invidious but simple task of proving this by instances the writer will not attempt.

To fully set forth in any one volume these premises for the correct laying out of railways, which include almost everything connected with their construction, operation, and finances, and vary in each case, would

PREFA CE.

IX be impossible. The purpose in view has been merely to give between the covers of one book whatever was necessary for some approach to a correct solution of every probable problem, which could not be found in other publications. This necessarily led to a large book, since this work still remains the only one on its subject in the language. Several of a somewhat similar nature have appeared in French and German since the first edition of this work was published, but from difference of operating conditions, and their profuse use of mathematics, the resemblance is not close.

The word “ton” in this volume means 2000 lbs., unless otherwise explicitly stated.

The term “ velocity-head ” has been borrowed from hydraulics to designate a somewhat different thing, which heretofore has had no name at all. The “ velocity- head ” of hydraulics and of this volume are closely related but not identical, and should not be confused.

Grades have been designated for the most part by their rate per cent and not by their rate per mile, in accordance with an increasing custom which may well become universal, as the more rational. The approximate rate per mile is given at once by multiplying the per cent by 50 (52.8).

Owing to the great number of tables, and the probability that others might be added in future editions, it was impossible to even attempt to refer in the text to all those which contained a given class of information. To insure doing this reference must be had to the Index, which it has been endeavored to make very complete.

Most of the computations of percentages, costs per mile, and the like, in this volume, were made with a slide-rule — an instrument too little known and used by engineers. Hence many errors of 1 or 2 in the third digit, or of one or two tenths of one per cent, probably exist, but, it is hoped, few of a more serious nature. The admirable computing instrument of Mr. Edwin Thachf.r, which would have insured greater accuracy with but little more trouble, was secured by the writer too late to be of much service.

The author will be at all times pleased to receive corrections of typographical or other errors, or supposed errors, extensions of any of the tables, or other similar matter.

A. M. W.

Tribune Building, New York, May, 1887.

Preface To The First Edition

The investigation of which this volume is the fruit had its origin in the preparation of a few notes for an anticipated location, and has since gradually expanded into a single magazine article, a short series of papers, and at last into a volume. Even the latter has been expanded far beyond the writer’s original intention by the close and, it is to be feared, tedious attention to detail which he found continually more needful ; and it is kept within its present dimensions only by excluding considerable matter and superficially considering or neglecting altogether a number of subjects which the writer deems of real importance for the correct conduct of location. In the improbable event that the sale of this volume should justify a thorough revision at some future day, he hopes to produce one more in keeping with the professional interest and importance of the subject, by rectifying the faults of omission and commission which he clearly perceives.

The writer does not intend to imply, however, that he has fallen into unacknowledged errors of fact or theory. All known errors have been frankly corrected as soon as discovered. For such others as may probably exist the writer can only hope that they will be regarded with that leniency which an exploration of a neglected field of labor may fairly ask. For such the present volume is, with all its imperfections. A recognition of the value of previous discussions of the same subjects would be a more welcome duty; but the writer deems it but simple justice to himself and his readers to declare frankly that, so far as his knowledge extends and he is competent to judge, all of the few existing discussions of the various leading topics of this volume are so superficial or so imperfect in method as to have little or no value as a guide for location. Some of them express correct views, and some of them will sometimes give correct results ; but none of them are trustworthy, and several of those which are given under distinguished names are incredibly defective. The various problems of location, in fact, have been disxii PREFACE TO THE FIRST EDITION.

cussed or neglected by technical writers with an airy lightness which would convince an unskilful reader that they were either too simple, or too unimportant, or too well understood, for any careful analysis. And yet there is no field of professional labor in which a limited amount of modest incompetency, at $150 per month, can set so many picks and shovels and locomotives at work to no purpose whatever.

As a natural consequence of this general negligence, all our railways are uneconomically located, most of them in respect to their general route and system of gradients, and all of them in respect to the minor details of alignment, and in many cases these errors are shockingly evident. ... In the care taken in this respect we are not advancing beyond, but rather falling below, the standard set up forty years ago, when the art of designing railways started out in this country with such brilliant promise. The works of Latrobe and Jervis and Thomson and Whistler show a truly remarkable ability, considering their early day, and bear the clearest marks of original and self-reliant thought : but the great men of that earlier day have no successors; for we have done nothing but copy them ill ever since, and a copyist is not a successor. We copy their errors, but we do not copy that admirable habit of personal investigation and far-sighted intellectual courage which created precedents, and has made the work of their hands — in despite of many faults — the high-water mark of American locating skill.

Contents

PAGE

Introduction, i

Part I. Economic Premises

CHAP.

I. The Inception of Railway Projects and Conditions

GOVERNING IT, 13

II. The Modern Railway Corporation 28

HI. The Nature and Causes connected with Location

WHICH MODIFY THE VOLUME OF RAILWAY REVENUE, . 48

IV. The Probable Volume of Traffic and Law of Growth

therein, 75

V. Operating Expenses, 106

[Maintenance of Way, 118; Fuel, 132; Repairs of Engines, 139; Repairs of Cars, 160; Train-wages, etc., 168; Summary, 180.]

Part II. The Minor Details Of Alignment

VI. The Nature and Relative Importance of the Minor

Details of Alignment, 185

VII. Distance, 195

[Effect on Operating Expenses, 198; Effect on Receipts, 21 1;

Law as to Connections, 219; Moral Effect of Short Line, 239.]

VIII. Curvature, 242

[Danger of Accident, 245; Statistics of Curvature, 259; Difficulty in Making Time, 268; Effect on Smooth Riding of Cars, 275;

XIV

CONTENTS.

CHAP. PAGE

Moral Effect to deter Travel, 276; Effect to obstruct the use of Heavy Engines, 278; Mechanics of Curve Resistance, 281 ; Rail-sections, 307; Effect on Operating Expenses, 313; Long Tangents, 324.]

IX. Rise and Fall, 327

[Classes of, 330; Laws of Accelerated and Retarded Motion,

331; Virtual Profiles, 346; Safe Limits of Undulations of Grades,

356; Limits of Classes, 366; Effect on Operating Expenses, 375; Estimating Amount of, 384; Vertical Curves, 385.]

Part III. Limiting Gra Die Nts And Curvature

X. The Relative Importance of Gradients, 395

XI. The Locomotive Engine, 399

[Tables of Standard Dimensions, 407; Running-Gear, 421;

Tractive Power, 434; The Locomotive Boiler, 449; The Cylinder Power, 457; Theoretical Gain by Expansion, 467; Causes of Loss of Efficiency, 470.]

XII. * Rolling-Stock, 485

XIII. Train Resistance, . . . . 492

[Freight-Train Resistance, 496; Starting Resistances, 511; Effect of Size of Wheel and Axle, 513; Velocity Resistances,

517; Train-Resistance Table, 524; Engine Friction, 530.]

XIV. The Effect of Grades on Train-Load, 536

[Table of Capacity of all Engines on all Grades, 544; Percentage of Change in Net Load from a Change in any Grade, 554]

XV. The Effect of Train-Load on Operating Expenses, 560 [Cost of Increasing Weight of Engines, 560; Cost of Increasing Number of Engines, 568; Proportion of Traffic affected by Rate of Ruling Grade, 576; Effect of a Difference in Ruling Grade, on the Cost of Distance, Curvature, and Rise and Fall,

XVI. Assistant Engines, 585

[Power of Assistant Engines, 591; Duty of Assistant Engines,

598; Cost of Assistant Engines, 601; Comparison of Pusher Grades with Uniform Gradients, 604.]

XVII. The Balance of Grades for Unequal Traffic, . . 608 XVIII. Limiting Curvature and Compensation therefor, . 620

CONTENTS.

XV

CHAP. PAGE

XIX. The Limit of Maximum Curvature, 635

[The Inherent Costliness of Sharp Curvature, 638; The Limiting Effect of Curvature, 645.]

XX. The Choice of Gradients, and Devices for Reducing Them, 659

[How to Project Low Grades, 660; How to Project Pusher Grades; — Easy Gradients, 666; Heavy Gradients, 669; Expedients for reducing the Rate and Cost of High Grades, 675; Great Inclines of the World, 699.]

Part IV. Larger Economic Problems

XXL Trunk Lines and Branch Lines 707

[Law of Geometric Increment of Traffic, 708; Trunk Lines, Non-Competitive, 718; Competitive Trunk Lines, 723; Branch Lines, 731.]

XXII. Light Rails and Light Railways 737

[Rails, 737; Expedient Economies, 748; Rails and Track Labor, 758.]

XXIII. The Economy of Construction 762

[Least harmful Economies, 764; Most harmful Economies,

768; Cross-ties, 775; Storms and Structures, 781.]

XXIV. The Improvement of Old Lines, 785

[Usual Defects, 787; Constructing Virtual Profile, 798; Remedying Defects, 799.]

XXV. Grade Crossings and Interlocking, 809

XXVI. Terminals, 818

Part V. The Conduct Of Location

XXVII. The Art of Reconnaissance, 831

XXVIII. Ocular Illusions 843

XXIX. When to make Surveys, 856

XXX. The Field-work of Surveys 860

XXXI. Topography : its Uses and Abuse 874

XXXII. Mapping and Projecting Location, 886

XXXIII. The Estimation of Quantities, 895

XVI

CONTENTS.

APPENDICES.

CHAP. PAGE

A. Experiments on the Resistances of Rolling-Stock, . . 909

B. Experiments with New Apparatus on Journal Friction

at Low Velocities, 913

C. The American Line from Vera Cruz to the City of

Mexico via Jalapa, with Notes on the Best Methods

OF SURMOUNTING HIGH ELEVATIONS BY RAIL, 925

[The usual List of Tables is omitted, as too voluminous. The tables and engravings are separately indexed at the back of the book.]

TO THE MORE IMPORTANT

RULES ; TABLES, FORMULAE, AND FINAL CONCLUSIONS,

WHICH MAY BE NEEDED

FOR IMMEDIATE APPLICATION.

“ It may be remarked that it was no part of the purpose of this volume to furnish a collection of mere rules, professing to require only an ability to read for their successful application. Rules can seldom be safely applied without a clear understanding of the principles on which they rest.”

— J. B. Henck, Preface to “ Field-Book.”

[ This index has purposely been ?nade and kept as brief as possible. It HAS NO CROSS-REFERENCES NOR DOUBLE references. For anything not found, see General Index, where the subjoined references are repeated, and for the most part in SMALL CAPITALS.]

Assistant Engines— page

Balance of grades for ....... 593

Cost of service ........ 602

vs. Uniform grades ....... 604

Branch Lines—

Rules for laying out ...... 733-6

Cable Railways ....... 686

Choice between close lines ...... 583

Construction-

Order of expedient economies ...... 764

Worst errors in . . . . . . . 768

Compensation for ....... 632 xviii INDEX TO CONCLUSIONS

Effect on accidents

PAGE . 258

“ expenses

.

. 321

“ use of heavy engines .

•

.

. 281

“ making time

•

.

. 274

“ smooth riding of cars .

•

•

.

. 275

Maximum limit of

•

•

•

•

. 653

Moral effect of

•

•

•

•

. 277

Curve Resistance—

Conclusions as to

•

•

•

•

. 304

Dead Weight-

Passenger, why tends to increase

•

•

•

•

• 567

Effect on competitive receipts

•

•

•

. 228

“ non-competitive receipts

*

ft

.

234-6

“ expenses

•

•

•

•

. 209

Increasing, to secure more traffic

•

•

•

•

. 238

Law as to connections

•

•

•

•

. 219

Moral effect of short line .

•

•

•

•

. 240

Freight-Train Speed .

•

•

•

•

. 371

Grade-Crossings—

And interlocking . . •

•

•

. 8II

Balance of, for unequal traffic, table

•

•

•

. 185

Effect on passenger traffic

•

•

•

. 580

“ train-load, law as to .

•

•

•

•

554-6

General law for choosing .

•

•

•

•

. 660

How to reduce in easy country .

•

•

.

. 665

Pusher grades, pros and cons for

•

•

•

• 669

Relative importance of gradients, example

•

• s

.

. 396

Train-load on all grades, table .

•

•

•

.

. 546

Trains affected by grades

•

•

•

•

. 576

Value of reducing grades

c

•

•

• 572

Growth of Traffic—

Geometric law as to

• ft

•

Proper allowance for

•

•

ft

•

Inclined Planes

•

•

•

•

. 686

Light Railways—

Proper direction for economy «

•

•

•

•

. 701

Location—

A priori basis for

•

•

•

. 10

General law for good

•

•

•

. 660

FOR IMMEDIATE APPLICATION.

XIX

Locomotives—

Adhesive traction limits .

Dimensions, etc. .

Train-load on all grades .

Long Tangents—

Value of .

Mapping Surveys

Minor Details-(Distance, Curvature Comparative importance and Rise anc

Fall.)

Narrow Gauge Old Lines—

Best manner of improving Usual defects to be corrected

Operating Expenses—

Percentages . .

Rails—

Proper form of . ,

“ weight of .

Reconnaissance-

Choice of lines to survey Fundamental rule for

Per head of population .

Rise and Fall-

Effect on operating expenses Estimating amount of Limits of classes .

Safe limits for

Sags-

In grade-lines, to what extent admissible Superelevation-

Proper rule for . . .

Surveys—

Choice of lines to run . . •

Switchbacks—

For thin traffic and great inclines • Termini—

Location of . • . .

Topography—

(Physical geography), Harmonizing line with (Mapping), Its uses and abuse .

Towns—

Loss from not going to .

. • 437

. 407-10

• • 544

. 324

. . 888

. . 186

. . 808

. . 179

. . 308

• 747, 761

. 857

. 835

. . 104

. 381

. 384

• • 374

. 363-8

. . 368

• . 301

• . 860

• • 950

. . 67

• • 655

. . 880

• • 63-4

Index To Conclusions

}CX

How to estimate the probable volume of

Train-mile—

Cost by items ....

Train Resistance-

Freight, amount .

Passenger, amount Trunk Lines-

Competitive, conditions of success Non-competitive, rule for laying out

Valley Lines-

And inundations . . . .

Merits of, for railway lines . .

Valleys—

Descending into ....

Vertical Curves—

Laying out . • . •

Length of . . . . o

Virtual Profile-

Nature and use of . « »

86, 95-102 . 179

. 502

. 518

. 720

. 682

. 387

, . 365

THE ECONOMIC THEORY OF THE LOCATION OF RAILWAYS.

Introduction

As the correct solution of any problem depends primarily on a true understanding of what the problem really is, and wherein lies its difficulty, we may profitably pause upon the threshold of our subject to consider first, in a more general way, its real nature ; the causes which impede sound practice ; the conditions on which success or failure depends ; the directions in which error is most to be feared. Thus we shall more fully attain that great prerequisite for success in any work — a clear mental perspective, saving us from confusing the obvious with the important, and the obscure and remote with the unimportant.

It would be well if engineering were less generally thought of, and even defined, as the art of constructing. In a certain important sense it is rather the art of not constructing ; or, to define it rudely but not inaptly, it is the art of doing that well with one dollar, which any bungler can do with two after a fashion.

There are, indeed, certain great triumphs of engineering genius — the locomotive, the truss bridge, the steel rail — which so rude a definition does not cover, for the bungler cannot attempt them at all ; but such are rather invention than engineering proper. There is also in some branches of engineering, as in

i

f v

IN TROD UCTION.

bridge-building, a certain other side to it, not covered by such a definition, which consists in doing that safely, at some cost 01- other, which the bungler is likely to try to do and fail. He therefore, in such branches, who is simply able to design a structure which will not fall down, may doubtless in some measure be called an engineer, although certainly not one of a very high type.

But to such engineering as is needed for laying out railways, at least, the definition given is literally applicable, for the economic problem is all there is to it. The ill-designed bridge breaks down ; the ill-designed dam gives way ; the ill-designed boiler explodes ; the badly built tunnel caves in, and the bungler’s bungling is betrayed. But a little practice and a little study of field geometry will enable any one of ordinary intelligence, without any engineering knowledge whatever in the larger sense, to lay out a railway from almost anywhere to anywhere, which will carry the locomotive with perfect safety, and perhaps show no obtrusive defects under what is too often the only test — inspection after construction from the rear end of a palace-car. Thus, for such work, the healthful checks which reveal the bungler’s errors to the world and to himself do not exist. Nature, unhappily, has provided no way for the locomotive — like Mr. Jingle’s intelligent pointer — to refuse to pass over an ill-designed railway as it refuses to pass over an ill-designed bridge.

Therefore, since there is no natural line between safety and danger to mark even so rude a distinction as that between the utterly bad and the barely tolerable, in the kind of engineering work we are to study, one may fairly say that the locating engineer has but the one end before him to justify his existence as such — to get the most value for a dollar which nature permits ; and but one failure to fear — that he will not do so. Except as his work necessarily involves the preliminary design of constructive details, he has no lives to save or imperil ; and the young engineer cannot too early nor too forcibly have it impressed upon his mind that it takes no skill worth speaking of to do such work after a fashion, unless in the comparatively few localities (rare in-

INTRODUCTION.

deed in the United States) where to get a reasonable line of any kind is something of a feat. His true function and excuse for being as an engineer, as distinguished from a skilled workman, begins and ends in comprehending and striking a just balance between topographical possibilities, first cost, and future revenue and operating expenses.

While this, in a certain sense, is peculiar to the branch of engineering we are to study, yet a curiously close analogy may be drawn, tending to show that it is as essentially true of all other branches of engineering as of this. For example, it is beyond doubt that the true reason for the striking progress in bridge-building in recent years has been, not that men have been driven into excellence by “the responsibility of human life” resting on them ; — for, after the types have once been invented, a relatively low order of engineering skill suffices to reduce that risk alone to a minimum. But the impelling force has been the keen competitive struggle to bring the first cost of every bridge as low as possible, and yet do nothing which shall injure its permanent efficiency and compel it to be speedily rebuilt ; nothing, in other words, which shall increase the future “ maintenance and operating expenses.” But whereas the “ operating expenses” of bad bridge-engineering come in a series of startling catastrophes which shock the community and dismay the moneyed interests concerned, causing good work to be appreciated and insisted on, and scaring off the amateurs and ’prentice hands from “ meddling and muddling,” after the manner of their kind, the operating expenses from bad railway location come by a gentle but unceasing ooze from every pore which attracts no attention, albeit resulting in a loss vastly larger than any possible loss from bad construction ; for it requires some training and experience even to appreciate the loss as existing, and still more of both to appreciate it as remediable. In fact no one can do so, except in the most general way, without special investigation of each special case. Errors which, even if committed, are not likely to be discovered, are rarely much feared, and at last the consciousness that there is danger of error becomes dulled.

IN TROD UCTION.

In these facts we have plain reasons why average practice in laying out railways should inevitably tend, as it does tend, to be and remain of a low grade. It is not difficult, in fact, to see reasons why it can never well be otherwise, except in degree, unless the progress of science should wholly change the nature of the work ; and a correct appreciation of how great is this danger, and why it exists, will greatly help to save the student from it.

The permanent difficulty lies in this : High efficiency in any art or calling in which many minds of no phenomenal gifts are engaged requires that every man’s work should be readily comparable either with a certain uniform standard or with the work of his fellows. In constructive engineering this is possible. Broadly speaking, a hundred-foot bridge is a hundred-foot bridge, the world over. It has everywhere to fulfil but two primary conditions : It must carry a certain nearly uniform load per foot, and it must not fall down. The same is in substance true of every form of constructive engineering. Every man’s practice therein, therefore, is comparable, and is compared, with the highest level of practice, the world over. Those most highly skilled are discovered and recognized. The moderately skilled perceive and correct their deficiencies. The hopelessly unskilled retire to other pursuits.

In laying out railway lines, and less strikingly in some other analogous kinds of engineering work, this is forever impossible. We cannot reduce the laws of topography, nor even of finance, to equations and formulae. Every line is a problem by itself, with its own peculiar physical and commercial conditions, so that the engineer is deprived of the aid to be had by comparing with, and copying the details of, the practice of others. Under these circumstances, the difference of conditions will be apt to be honestly accepted by the reader who may have sinned against good practice, and by all others concerned, as the reasons why another line, one hundred or one thousand miles off, should have cost so much less and yet be so much better worth owning than his own. He who has done well, therefore, is cut off from any

INTRODUCTION.

absolute knowledge and general recognition of that fact, and the guilty reader, who has done ill, is cut off from the still greater gain which would come to him from a revelation of where and wherein he has done ill. In most such cases each will have in some detail shown better judgment than the other ; but from the lack of unquestionable evidence of this, each is denied the instruction which he might otherwise receive from that fact, and so is in great danger of falling into the most natural and most human error, believing that all that he has done is good, which has not been proven to be bad, and so ceasing to make effort to improve upon what is good enough to pass, and merely multiplying errors with advancing experience, without really advancing in knowledge.

For these reasons the student should begin with the consciousness that the level of average practice in railway location, his own included, is by its nature restricted, not to the sum of the united abilities of all those who are or have been engaged in it, as in constructive engineering, but to the average individual level of capacity and knowledge. No more is needed than this undoubted fact to prove to demonstration that average practice is and must be, both comparatively and absolutely, of a pretty low grade ; and hence it becomes every one who may be entrusted with such work to have constantly before him the fact that he stands thus alone, and to scrutinize with the sternest skepticism, the conclusions which he may reach, remembering that his danger of grave errors of judgment is thereby multiplied many-fold. As he measures only by his own knowledge, all the work he does will naturally seem good even if really bad.

To the preceding, which may be called the subjective obstacles to good practice, must be added another and perhaps a greater one. Inasmuch as no one can even know for himself the absolute quality of his own skill in this particular branch of engineering, it is almost a natural corollary that corporations should very uniformly decline to take it for granted, by assuming that there are any measurable differences in qualifications for such work among those who have proved their competency in