m t M, M ■ 1 WSm I*MB^ •1 1 1 l&v ^" ^ Pl@ / ^^^ -^ Authors and Collaborators— Continued A. MARSTON, C. E. Dean of Division of Engineering and Professor of Civil Engineering, Iowa State College Member, American Societj' of Civil Engineers Member, Western Society of Civil Engineers De WITT V. MOORE Consulting Engineer and Architect Formerly District Engineer-:— Central District Division of Valuation Interstate Commerce Commission, Chicago Member, American Society of Engineering Contractors Member, Indiana Engineering Society W. HERBERT GIBSON, B. S., C. E. Civil Engineer Designer of Reinforced Concrete JAMES K. FINCH. C. E. Associate Professor of Civil Engineering, and Director of Summer School of Surveying, Columbia University, Now York HENRY J. BURT, B. S., C. E. General Manager for Ilolabird and Roche, Architects Member, American Society of Civil Engineers Member, Western Society of Civil Engineers Member, Society for the Promotion of Engineering Education RICHARD I. D. ASHBRIDGE Civil Engineer Member, American Society of Civil Engineers HERMAN K. HIGGINS Civil Engineer Associate Member, American Society of Civil Engineers Member, Boston Society of Civil Engineers Member, New England Water Works Association MemlK'r, American Railway P.ridge and lUiilding Association ALFRED E. PHILLIPS, C. E., Ph. D. Professor of Civil Engineering, Armour Institute of Technology Authors and Collaborators — Continued H. E. MURDOCK, M. E., C. E. Head of Department of Agricultural Engineering, Montana State College, Bozeman, Montana Formerly Irrigation Engineer, U. S. Department of Agriculture A. B. McDANIEL, B. S. Formerly Assistant Professor of Civil Engineering, University of Illinois Member, American Society of Civil Engineers Member, Society for the Promotion of Engineering Education Fellow, Association for the Advancement of Science Author of "Excavating Machinery" GLENN M. HOBBS, Ph. D. Secretary and Educational Director, American School of Correspondence Formerly Instructor, Department of Physics, University of Chicago American Physical Society THOMAS FLEMING, Jr., B. S., C. E. With Chester & Fleming, Hydraulic and Sanitary Engineers Associate Member, American Society of' Civil Engineers Memlier, New England Water Works Association Member, Engineers' Society of Pennsylvania CHARLES E. MORRISON, C. E., Ph. D. Formerly Instructor in Civil Engineering, Columbia University As.sociate Member, American Society of Civil Engineers Author of "Highway Engineering," "High Masonry Dam Design" EDWARD B. WAITE Formerly Dean, and Head, Consulting Department, American School of Cor- respondence American Society of Mechanical Engineers Boston Society of Civil Engineers C. A. MILLER, Jr. Associate Editor, American Technical Society Affiliated Member, Western Society of Engineers Member, American Association of Engineers Member, Illinois Society of Architects JESSIE M. SHEPHERD, A. B. Head, Publication Department, American Technical Society Authorities Consulted THE editors have freely consulted the standard technical literature of America and Europe in the preparation of these volumes. They de- sire to express their indebtedness, particularly, to the following eminent authorities, whose well-known treatises should be in the library of everyone interested in Civil Engineering. Grateful acknowledgment is here made also for the invaluable co- operation of the foremost Civil, Structural, Railroad, Hydraulic, and Sanitary Engineers and Manufacturers in making these volumes thoroughly repre- sentative of the very best and latest practice in every branch of the broad field of Civil Engineering. WILLIAM G. RAYMOND, C. E. Dean of the School of Applied Science and Professor of Civil Engineering in the State University of Iowa; American Society of Civil Engineers Author of "A Textbook of Plane Surveying," "The Elements of Railroad Engineering" JOSEPH P. FRIZELL Hydraulic Engineer and Water-Power Expert; American Society of Civil Engineers Author of "Water Power, the Development and Application of the Energy of Flowing Water" FREDERICK E. TURNEAURE, C. E., Dr. Eng. Dean of the College of Engineering and Professor of Engineering, University of Wisconsin Joint Author of "Public Water Supplies," "Theory and Practice of Modern Framed Structures," "Principles of Reinforced Concrete Construction" HENRY N. OGDEN, C. E. Professor of Sanitary Engineering, Cornell University Author of "Sewer Design" DANIEL CARHART, C. E. Emeritus Professor of Civil Engineering, University of Pittsburgh Author of "Treatise on Plane Surveying" HALBERT P. GILLETTE Editor of Engineering and Contracting; American Society of Civil Engineers; Formerly Chief Engineer, Washington State Railroad Commission Author of "Handbook of Cost Data for Contractors and Engineers" CHARLES E. GREENE, A. M., C. E. Late Professor of Civil Engineering, University of Michigan Author of "Trusses and Arches, Graphic Method," "Structural Mechanics' Authorities Consulted— Continued A. PRESCOTT FOLWELL Editor of Municipal Journal and Engineer; Formerly Professor of Municipal Engineer- ing, Lafayette College Author of "Water Supply Engineering." "Sewerage" IRVING P. CHURCH, C. E. Professor of Applied Mechanics and Hydraulics. Cornell University Author of "Mechanics of Engineering" PAUL C. NUGENT, A. M., C. E. Professor of Civil Engineering, Syracuse University Author of "Plane Surveying" FRANK W. SKINNER, C. E. Consulting Engineer; Associate Editor of The Engineering Record Author of "Types and Details of Bridge Construction" HANBURY BROWN, K. C. M. G. Member of the Institution of Civil Engineers Author of "Irrigation, Its Principles and Practice" SANFORD E. THOMPSON, S. B., C. E. American Society of Civil Engineers Joint Author of "A Treatise on Concrete, Plain and Reinforced' JOSEPH KENDALL FREITAG, B. S., C. E. American Society of Civil Engineers Author of "Architectural Engineering," "Fireproofing of Steel Buildings," "Fire Pre- vention and Fire Protection" AUSTIN T. BYRNE, C. E. Civil Engineer Author of "Highway Construction," "Inspection of Materials and Workmanship Em- ployed in Construction" JOHN F. HAYFORD, C. E. Expert Computer and Geodesist, U. S. Coast and Geodetic Survey Author of "A Textbook of Geodetic Astronomy" WALTER LORING WEBB, C. E. Consulting Civil Engineer; American Society of Civil Engineers Author of "Railroad Construction in Theory and Practice," "Economics of Railroad Construction," etc. Authorities Consulted— Continued EDWARD R. MAURER, B. C. E. Professor of Mechanics, University of Wisconsin Joint Author of "Principles of Reinforced Concrete Construction' HERBERT M. WILSON, C. E. Geographer and Former Irrigation Engineer, United States Geological Survey; American Society of Civil Engineers Author of "Topographic Surveying," "Irrigation Engineering," etc. MANSFIELD MERRIMAN, C. E., Ph. D. Consulting Engineer Formerly Professer of Civil Engineering, Lehigh University Author of "The Elements of Precise Surveying and Geodesy," "A Treatise on Hy- draulics," "Mechanics of Materials," "Retaining Walls and Masonry Dams," "Introduction to Geodetic Surveying," "A Textbook on Roofs and Bridges," "A Handbook for Surveyors," "American Civil Engineers' Pocket Book" DAVID M. STAUFFER American Society of Civil Engineers; Institution of Civil Engineers; Vice-President, Engineering News Publishing Co. Author of "Modern Tunnel Practice" CHARLES L. CRANDALL Professor of Railroad Engineering and Geodesy in Cornell University Author of "A Textbook on Geodesy and Least Squares" N. CLIFFORD RICKER, M. Arch. Professor of Architecture, University of Illinois; Fellow of the American Institute of Architects and of the Western Association of Architects Author of "Elementary Graphic Statics and the Construction of Trussed Roofs" ^- ^ W. H. SEARLES, C. E. Author of "Field Engineering" and "Railroad Spiral" HENRY T. BOVEY Late Rector of Imperial College of Science and Technology, London, England Author of "Treatise on Hydraulics" WILLIAM H. BIRKMIRE, C. E. Author of "Planning and Construction of High Office Buildings," "Architectural Iron and Steel, and Its Application in the Construction of Buildings," "Compound Riveted Girders," "Skeleton Structures," etc. Authorities Consulted— Continued IRA 0. BAKER, C. E. Professor of Civil Engineering, University of Illinois Author of "A Treatise on Masonry Construction," "Engineers' Surveying Instruments, Their Construction, Adjustment, and Use," "Roads and Pavements" JOHN CLAYTON TRACY, C. E. Assistant Professor of Structural Engineering, Sheffield Scientific School, Yale University Author of "Plane Surveying: A Textbook and Pocket Manual" FREDERICK W. TAYLOR, M. E. Joint Author of "A Treatise on Concrete, Plain and Reinforced' J. B. JOHNSON, C. E. Author of "Materials of Construction;" Joint Author of "Design of Modern Frame Structures" FRANK E. KIDDER, C. E., Ph. D. Consulting Architect and Structural Engineer; Fellow of the American Institute of Architects Author of "Architect's and Builder's Pocketbook," "Building Construction and Super- intendence, Part I, Masons' Work; Part II, Carpenters' Work; Part III, Trussed Roofs and Roof Trusses," "Strength of Beams, Floors, and Roofs" V» WILLIAM H. BURR, C. E. Professor of Civil Engineering, Columbia University; Consulting Engineer; American Society of Civil Engineers; Institution of Civil Engineers Author of "Elasticity and Resistance of the Materials of Engineering:" Joint Author of "The Design and Construction of Metallic Bridges," "Suspension Bridges, Arch Ribs, and Cantilevers" WILLIAM M. GILLESPIE, LL. D. Formerly Professor of Civil Engineering in Union University Author of "Land Surveying and Direct Leveling," "Higher Surveying' GEORGE W. TILLSON, C. E. Past President of the Brooklyn Engineers' Club; American Society of Civil Engineers; American Society of Municipal Improvements Author of "Street Pavements and Street Paving Material" CHARLES E. FOWLER Consulting Civil Engineer; Member, American Society of Civil Engineers Author of "Practical Treatise on Subaqueous Foundations" W. M. PATTON Late Professor of Engineering at the Virginia Military Institute Author of "A Treatise on Civil Engineering" ^ S 1 I o h T3-g ^ j= (1) e 5 a i ^1^ 3 ^ S-. For e w^ord OF all the works of man in the various branches of en- gineering, none are so wonderful, so majestic, so awe- inspiring as the works of the Civil Engineer. It is the Civil Engineer who throws a great bridge across the yawning chasm which seemingly forms an impassable obstacle to further progress. He designs and builds the skeletons of steel to dizzy heights, for the architect to cover and adorn. He burrows through a great mountain and reaches the other side within a fraction of an inch of the spot located by the original survey. He scales mountain peaks, or traverses dry river beds, survey- ing and plotting hitherto unknown, or at least unsurveyed, regions. He builds our Panama Canals, our Arrow Rock and Roosevelt Dams, our water-works, filtration plants, and prac- tically all of our great public works. C The importance of all of .these immense engineering projects and the need for a clear, non-technical presentation of the theoretical and practical developments of the broad field of Civil Engineering has led the publishers to compile this great reference work. It has been their aim to fulfill the de- mands of the trained engineer for authoritative material which will solve the problems in his own and allied lines in Civil Engineering, as well as to satisfy the desires of the self-taught practical man who attempts to keep up with modern engineer- ing developments. ^ Books on the several divisions of Civil Engineering are many and valuable, but their information is too voluminous to be of the greatest value for ready reference. The Cyclopedia of Civil Engineering offers more condensed and less technical treatments of these same subjects from which all unnecessary duplication has been eliminated; when compiled into nine handy volumes, with comprehensive indexes to facilitate the looking up of various topics, they represent a library admirably adapted to the requirements of either the technical or the practical reader. ^ The Cyclopedia of Civil Engineering has for years occupied an enviable place in the field of technical literature as a standard reference work and the publishers have spared no expense to make this latest edition even more comprehensive' and instructive. ^ In conclusion, grateful acknowledgment is due to the staff of authors and collaborators — engineers of wide practical ex- perience, and teachers of well recognized ability — without whose hearty co-operation this work would have been im- possible. Table of Contents VOLUME II Railroad Engineering . . .By Walter Loring Webbt Page *11 Railroad Surveys — Conflicting Interests — Reconnoissance — Use of Existing Maps — Surveying Methods — Elements of a Survey — Low Ruling Grades — Preliminary Surveys — Cross-Section and Stadia Methods — Composition of Parties — Re- surveys— Location Surveys— Selecting a Route— Simple Curves— Methods of Field Work — Locating Points by Deflections — Instrumental Work — Special Methods of Location— Obstacles to Location— Modifications of Location — Com- pound Curves— Transition Curves— Spiral between Tangent and Circular Curve —Spirals in Old Track— Vertical Curves— Construction— Earthwork— Slopes and Cross-Sections — Width of Roadbed — Ditches — Earthwork Surveys — Position of Slope Stakes — Computing the Volume — Level, Equivalent, and Three-Level Sections — Irregular Sections— Prismoidal Correction— Volume of Earthwork in Irregular Ground— Side- Hill Work— Borrow Pits — Correction for Curvature- Eccentricity of Center of Gravity— Methods of Excavating— Blasting— Formation of Embankments — Tunnel Surveys— Surveying Down-Shafts— Tunnel Design— Cross-Sections, Grade, Lining — Portals — Tunnel Construction — Trestles — Pile- Driving — Trestle Floor-Systems — Guard Rails — Fire Protection — Culverts — Cattle Passes— Water Supply— Turntables— Coaling Stations— Engine Houses- Cattle Guards— Track Construction— Ballast— Rails and Joints— Tie- Plates — Braces, Spikes, Bolts, Nut Locks— Laying Ties and Rails — Switches and Turn- outs — Crossings— Yards and Terminals— Signal Systems (Manual, Automatic, Electro- Pneumatic) — Semaphores — Interlocking — Track Maintenance — Work Trains— Railroad Finances: Capitalization, Stocks and Bonds, Gross Revenue, Fixed Charges. Net Revenue, Operating Expenses, Maintenance of Way and Structures, Maintenance of Equipment, Transportation Expenses — Economic Location: General Principles — Reliability and Value of Economic Locations — Distance: Relation to Rates and Expenses — Effect on Receipts — Curvature: Operating Disadvantages, Compensation for Curvature, Limitations — Grade: Distinction between Minor and Ruling Grades, Laws of Accelerated Motion, Virtual Profile, Train Systems, Locomotive Ratings, Units of Operation, Locomotive Types, Power Calculations, Effect of Grade on Tractive Power, Speed Curves — Pusher Grades: Economy, Operation of Pusher Engines, Cost of Service— Balance of Grades for Unequal Traffic EARTHWORK By A. B. McDaniel Page 301 Scrapers: Slip— Two-Wheel— Four- Wheel— Graders: Two- Wheel Blade— Four- Wheel Blade — Reclamation — Elevating — Cost of Operation — Power Shovels: Fixed and Revolving Platform T^pes: Platforms, Power Equipment, Excavating Equipment, Operation, Cost — Electrically Operated Shovels — Efficiency and Economy — Dry-Land Excavators: Stationary Scrapers — Revolving Excavators — Operation Cost — Templet, Wheel, and Tower Excavators — Walking Scoop Dredgea-r Walking Drag- Line Excavators Review Questions Page 439 Index Page 451 *For page numbers, see foot of pages, t For professional standing of author, see list of Authors and Collaborators at front of volume. ^ Xi CO 13 {H O o « O » RAILROAD ENGINEERING. PART I. RAILROAD SURVEYS. 1, General Principles. The engineer should have first, a thorough appreciation of the objects to be accomplished by the sxirveys. He should realize that, except in the rare cases where it is difficult to find arnj practicable line, very little engineering training or ability is required to lay out aline over which it would be physically possible to run trains. A line as laid out may violate all rules of location, may be expensive to operate and have disad- vantages which will discourage traffic, and yet trains can be run over it. From the infinite number of possible locations, the en- gineer must select the location which best satisfies the various con- flicting interests. His value as an engineer depends on his ability to interpret the natural conditions and design the line accordingly. This ability is only obtained by a thorough knowledge of the whole subject of railroad engineering, supplemented by practical expe- rience. It is therefore true that many of the following statements will not be thoroughly appreciated until the student has covered the whole subject and then reviews it. 2. Conflicting Interests. There are several classes of inter- ests, which are generally more or less conflicting, which affect the location of every line* (a) The initial cost should he a miniimun, but the cheap- est road generally has sharp curvature, steep grades and incon- venient location. (h) The oj?erating expenses per train mile should he a nilthlmun}, which is generally equivalent to saying that the curva- ture should be light and the grades low, but this is usually unob- tainable except at great cost. \^6') The location should he convenient to sources of traffic so that the maximum traffic will be obtained, but this is generally very costly. 2 RAILROAD ENGINEERING A little study will show the frequent conflict of tlie above conditions. When a proposed location evidently combines the above interests advantageously, instead of bringing them into con- flict, then there is no doubt as to the proper location, unless it affects unduly the adjacent location. The best engineering ability is a cheap investment when deciding on a location which requires a delicate balancing of the claims of several possible routes, each with its own combination of greater or less initial cost, greater or less operating expenses, and greater or less effect on the probable revenue of the road. RECONNOISSANCE SURVEYS. 3. Essential Problem. From the above considerations it may readily be seen that the first survey to be made (called the recon- noissance survey) consists essentially of a broad examination ot the country through which the road is expected to pass. Business considerations usually predetermine that the road is to connect certain termini and also pass through certain intermediate impor- tant towns or cities, but the problem consists in finding the best route between the predetermined points. When two consecutive predetermined points lie in the same valley or on the same bank of a river too large to be easily bridged, the location is self-evident. If the river is smaller, easily bridged, has sharp bends, with variable banks and important towns on either bank, it will usually require a close examination of each bank to determine where to cross if at all. When the two points are many miles apart, lie in different valleys, and are therefore separated by one or more sum- mits, the selection of the best route becomes more and more com- plicated as the number of possible routes becomes greater. It is generally true, although not invariably, that a cross-country route which includes the lowest summits and the highest loio^'point^ (such as river crossings) will give the best grades. Since the " ruling grade " is the most important physical consideration for the engineer, as will be developed later, the chief work of the reconnoissance survey (apart from considerations of probable traffic) is the determination of the elevations of summits and sags and the distance between them, together with the constructive character of the country. RAILROAD ENGINEERING 8 4. Utilization of Existing Maps. The U. S. Geological Survey lias already published contour iiiaj)s of a large part of the country which enable an engineer to select a line with even greater ease and certainty than he can from a reconnoissance map made for the purpose (as usually made), since the U. S. G. S. maps show the whole country and enable the engineer to rapidly com-- pare a dozen suggested routes instead of confining his attention to the (usually) limited area of the special map. The errors of the U. S. G. S. maps will seldom if ever be sufficient to vitiate the accuracy of the preliminary route laid out from them. Usually a brief study of the map will demonstrate that one (or perhaps two or three) general route has advantages so pronounced over all other possible routes that the choice is immediately made or is at least reduced to the comparison of two or three lines which are so nearly equal that closer and more detailed surveys are necessary to decide between them. County atlases are usually sufiiciently accurate for reconnoissance purposes to the extent of giving the relative horizontal positions of governing points of the survey. Elevations may be determined (as described later) and plotted on these maps. 5. Surveying Methods. When reliable contour maps are unavailable, some of the following methods may be used to fill out existing maps or to make a complete reconnoissance survey. The essential point is the rapid determination of those details from which one route is shown to be superior to another. Nothing useless should be surveyed and no time should be wasted on an unnecessary degree of accuracy. The physical characteristics of two routes have usually such differences that they are apparent even with rapid and approximate methods of surveying. If two routes are so nearly equal that a decisive choice cannot be made from the results of reconnoissance surveys, it shows that a more accurate survey should be made of both routes. 6. Elements. The three elements of the survey of any line are {a) the length, (J) the direction, and {c) the slope or the relative elevation of the two ends. Distance. The length is sometimes determined with sufficient accuracy by pacing, the steps being counted with a pedometer. In an open prairie country, where a buggy may be run, an odometer attached to a wheel will count the 4 RAILROAD ENGINEERING revolutions. An odometer on a wheel, attached to a frame and trundled like a wheelbarrow, has been used for the same purpose. A large telescope, mounted with a universal joint on a very light tripod, and fitted with stadia wires so adjusted that distances of 2,000 or even 2,500 feet can be read to the nearest 10 feet on a 10-foot rod, will give the distances between widely separated sta- tions with sufficient accuracy and extreme rapidity. Direction may be obtained with sufiicient accuracy with a compass — even of the pocket type. Leveling, Spirit leveling is too slow and ex- pensive for the rapid surveying here required. If stadia methods are used with an instrument provided for reading vertical angles, the inclination of all lines may be observed and the elevations of all stations computed. A still more rapid method of observing differences of elevation with sufiicient accuracy for the purpose is found in the use of an aneroid barometer, supplemented by another aneroid or preferably by a mercurial barometer. The mercurial, or the office aneroid, is kept at some ofticp whose elevation is known and observations are regularly taken (say every half hour) during the period when observations are being taken in the field with the field aneroid. The field aneroid is taken to each place, within a range of several miles, where elevations are desired. At each point there should be noted (see the form of notes below) the time, the described location, the aneroid reading and the temperature. If possible, duplicate readings should be taken on the trip to and from the office on all important points. The elevations of succeeding office locations made, may be determined with the field aneroid if necessary, but of course extra care should be taken with such work. Aneroids are usually "compensated for temperature," i.e.^ so adjusted that they will give a true reading regardless of temperature. If an aneroid has not been so adjusted, it should be carefully com- pared with a standard mercurial barometer under widely varying conditions of temperature and a tabular form should be made out for that aneroid showing the correction to be applied at any given temperature. On account of the expansion of mercury with tem- perature, and also the expansion (at a different rate) of the tube and cistern, all readings of the mercurial barometer must be "reduced to 32° F.," i.e.^ reduced to the reading it would have, if the temperature of the instrument were 32° F. This is readily ac- BAILROAD ENGINEERING 5 complished by means of Table XI.* At the office, each half -hourly observation should include the time, the ijeading of the scale show- ing the height of the mercury, the reading of the "attached ther- mometer" (the thermometer attaclied to the mercurial) and also the temperature of the external air. When the mercurialis in- doors these two temperatures may differ somewhat. When reduc- ing the observations interpolation should be made if necessary between the reduced office observations to determine the probable reading of the mercurial at the time of any given field observation. Determine from Table XII* the heights corresponding to the field reading and reduced office reading for each pair of observations. Their difference is the approximate difference of elevation of the office and of the place of the field observation. If necessary this may be corrected by an amount equal to the approximate differ- ence of elevation :imes a coefficient derived from Table XIII.* This coefficient is found opposite the number which gives the sum of the temperatures in the field and outside the office. The correction is frequently too small to be noticed. An approximate calculation will often show this, or will give a solution to the nearest foot, which is amply accurate. An aneroid, no matter how perfect, will seldom agree exactly with a mercurial barometer, and even if ad- justed to the same reading will soon indicate some discrepancy. It is therefore better to leave the adjustment undisturbed and apply corrections. The aneroid should therefore be compared with the mercurial before leaving headquarters for a day's work, and the readinors of both and their diiference should be recorded. Immediately after returning from the day's work the aneroid should again be compared. The absolute reading of the mercurial will probably be higher or lower, but the difference should be nearly the same, although it is found that an aneroid will lag somewhat behind its true reading, especially if it has been subjected to an extreme variation of pressure. All the field readings of the an- eroid should therefore be corrected by the mean of the initial and final differences. The method and the above explanation may be illustrated by the following numerical examples: 7. ' Examples. 1. Given a reading of 28.692 on a mer- *See Webb's "Trigonometric Tables," pubUshed by American School of Correspond- ence, Chicago, 111. Price, 50c, 6 RAILROAD ENGINEERING curial barometer, what is its reading when reduced to 32° F., the reading of the attached thernionieter being 68. 5"^ F.? In Table XI* under 28.5 and opposite 68", we find - .101. Under 29.0 and for 68° we find - .103. For 28.692 and 68° it evidently should be - .102 (to the nearest thousandth). Similarly for 28.692 and 69° we may derive - .105. For 28.692 and 68.5° it w^ould be the mean or - .1035, which we will call - .103 since it is useless to compute the correction closer than the nearest thousandth. Then since the correction is - .103, the corrected reading should be 28.589. With a little practice the interpolations, when necessary, may be made in far less time than it takes to describe it. 2. Verify the following reductions: Bar. reading. Temp. Reduced reading. 26.426 27.892 28.475 30.847 58° F. 78.5 85. 48.5 26.356 27.767 28.a30 30.792 3. Reduce the following readings: 27.294, 47°; 29.462, 87°; 26.230, 78.5°; 25.241, 62°; 26.481, 75°; 29.625, 89.5°; 30.942, 88.5°; 29.784, 46.5°; 28.386, 48°; 27.942, 74.5°. 4. Compute the barometric elevation corresponding to a reading of 28.589. From Table XII* the reading for 28.5 is 1397 and the difference for .01 is -9.5; therefore, for .089 the correction will be -9.5 X 8.9 = - 84.55, or in whole numbers - 85. Then 1397 - 85 == 1312, the corrected reading. 5. Verify the following elevations from the reduced read- ings: 26.356, 27.767, 28.330, and 30.792; i.e., 3528, 2107, 1560, and - 710. 6. Compute the barometric elevations corresponding to the reduced readings found by solving Example 3. 7. With an approximate difference of elevation of - 136 feet and field and ofiice temperatures of 62° and 67°, what is the true difference of elevation? 62 + 67 = 129. For 129° the coefii- cient is (by interpolation) + .0357. 136 X (+ .0357)= +4.8552. For this slight difference of elevation, the coefficient is far more accurate than necessary, and of course the correction is called + 5. ♦See Webb's "Trigonometric Tables," published by American School of Correspond- RAILROAD ENGINEERING The difference of elevation should be increased by 5, but the dif- ference is essentially negative. Therefore we have as the correc- tion -(+ 5). The true difference of elevation is - 136 - (-|- 5) = -141. 8. The following example shows not only the method of recording the observations but also the complete solution of a problem. Time. Mercurial Attached Reduction to Corrected External barometer. thermometer. 320 F. reading. thermometer. 7:00 A. M. 28.692 62° -.087 28.605 60° F. :30 .724 64 -.092 .632 62 8:00 .756 66.5 -.099 .657 64 :30 .782 68 -.102 .680 65 9:00 .824 69 -.105 .719 66 The observations taken in the field at this time were as given in the first four columns of the following tabular form. The other columns are computed later in the office. (Left-hand page of notes.) Time. Place. Aneroid. Therm. Corrected aneroid. Corrected mercurial. 7:00 A. M. Office. 28.743 .769 .860 .522 62° 63 65 66 28.605 7:20 8:10 8:50 R. R. Junction. Blue River Saddle in Beanpole ridge 28.631 .722 .384 .623 .665 .706 (Right-hand page of notes.) Ext. temp, office. Approx. field reading. Approx. office reading. Difference. Correction for temp. Difference of elevation. 62° 64 66 i27'3 1186 1508 1280 1240 1201 -54 + 307 -(+2) + 12 -56 + 319 8. Low Ruling Grades. It will be developed later that a low ruling grade is of prime importance. The approximate value of the ruling grade is determined from the reconnoissance survey. If the country is mountainous, it may be necessary to "develop" the line in order to reduce the grade. *• Development" here RAILROAD ENGINEERING RAILROAD EXGTNEERING ineans a deliberate increase in the length of the line between two predetermined points so that the rate of grade shall be as low as desired. The Georgetowni spiral, shown in Fig. 1, is perhaps the most famous example in this country of this general method. A study of the course of the track will illustrate several methods of taking advantage of the topography and attaining a considerable elevation although the grade is kept low. PRELIMINARY SURVEYS. 9. General Object. The reconnoissance survey has shown tliat the best location for the road will lie somewhere throuo^h a certain belt of country. In some places this belt may be very narrow, i.e., certain topographical features will determine that the road must pass through a strip but little if any wider than the roadbed requirements. In other places the choice of possible loca- tion is so widened that it is necessary to survey everything within reach of the backbone line of the survey. The willingness or finan- cial ability of the company to ignore minor topographical con- siderations and incur heavy expense in order to obtain economic advantages, may also widen the area of possible location. As a general statement, the width of the belt surveyed should so vary as to include all practicable locations along that general route. 10. Cross Section Method. A broken line is run which shall lie as near the expected location line as possible. The bear- ing and length of each segment of the broken line is determined and also all essential topographical features on either side. Bear- ings are sometimes taken only with a compass, which has the advantage of great rapidity but lessened accuracy. For more ac- curate work, true azimuth is carried along by means of back sights at previous stations. The azimuths between stations should be' checked by means of needle readings. It is advisable to determine exact azimuth at the beginning of a survey and at intervals of a few miles. This may be done by observations on Polaris (see Plane Surveying, Part II, Pages '95 to 97), or still better, by solar observations w4iich may be taken w^ith great accuracy at any time of day. Set stakes at each even 100 feet. In general the instru- ment stations will not occur at the even 100-foot distances, but the odd distance should always be carried on to the next course. The 10 RAILROAD ENOINEERINO stakes should be about fifteen inches long and about one-and-one quarter inches square. Stakes with a cross-section of one inch by one-and-one-half inches are preferred by some. The stakes indi- cating the 100-foot stations should be driven to within five inches of the ground. Stakes indicating the locations of the transit (called hubs) should be driven flush with the ground. A " witness stake" should then be driven three feet to the right and on this stake should be marked the station number and the "plus distance "; e.g.^ the stake might show 137 + 46, which would indicate that the stake was 46 feet beyond Sta. 137, and 13,746 feet from the start- ing point. Station stakes should be marked with the station number on the rear side of the stake. Immediately following the transit party, the level party should obtain the elevations above the datum plane of all stations and substations, ridges, sags, river banks and any point where the profile changes abruptly. 11. Cross Sectioning. Use a Locke level, resting on a five- foot stick, a 50-foot tape and a ten -foot rod graduated to feet and tenths. The cross-section party takes cross sections (usually) at every 100-foot stake, the cross section being made perpendicular to the backbone line of the survey at that place, as is indicated by the dotted lines in Fig. 2. It is desired to plot on the map con- tours at each five-foot interval above the datum plane. Let Fig. 3 represent a typical cross section. Set the level (on its five- foot stick) at the stake S. The elevation of this stake given by the level party is (say) 169.4. The level therefore has an elevation of l'''4.4. If the level rod is moved up hill until it is found (by trial) that 4.4 mark is on a level with the telescope, then the base of the rod must have a level of 170 and must be on the 170-foot contour. Measure the distance horizontally from stake to rod and record as shown in Fig. 4. Leaving the level rod at that point, carry the stick and level up the hill until a level line strikes the top of the rod. The base of the stick is evidently on the 175-foot contour. Measure and record the distance as before. Carry the level rod to that point and in a similar manner determine the 180 foot contour if desired. The 165-foot contour is evidently 9.4 feet below the telescope when on the 5 -foot stick at the center stake. The distance from the center to the 165-foot contour can thus be found. Lower contours can be similarly obtained. The results RAILROAD ENGINEERING 11 should be plotted in a note-book ruled in quarter- inch squares, each side of a square representing 25 feet. The work will then be plotted on the scale of 100 feet per inch. If the successive stations are plotted iip the page, the drawing will correspond with the points when looking ahead along the line. After plotting each section, the corresponding contours should be connected to form a sketch like Fig. 4. The crossing of the main line by a contour may be similarly determined. Fig. 4 is simply an enlarged detail of a sketch like Fig. 2. Although the Locke level is incapable of Fig. 2. accurate leveling work, any error that may be made by the above method is confined to the station where it occurs and is not carried on and made cumulative. With reasonable care such inaccuracies can be kept within desired limits, while the rapidity is far greater than a more accurate method. 12. Stadia Method. This consists simply of a stadia survey of a long and narrow belt of country by the same general methods as those employed in ordinary stadia- topographical surveys. One advantage of this method is that the levels can be carried along very successfully as a part of the stadia work, if particular care is taken to always obtain practical agreement in the vertical angles 12 RAILROAD ENGINEERING for the foresight and backsight between conse.mtive stations. This will generally permit more rapid work, as the progress of the whole party is sometimes limited by the progress of the level party. The added cost .__^Q^ j._. of tlie level party is also saved. It is here as- sumed that the details of stadia work have al- ready been studied and therefore no further dis- cussion will be given of this very simple appli- cation of the general previous method, the primary object of the survey is the preparation of a map sliowing the contours and required topographical features over tlie desired area. Fig. 3 method. As in tlie Fig. 4, 13. Party Required. It has been forcibly said that the only duty of the chief- of -jMvty is to ^'keep his eyes open". The selection of the best route for a road fo de|)ends on a close study of the country that if the chief-of-party is required to do the work RAILROAD ENGINEERING 13 of traDsitman, as is sometimes the case, the work of either position is apt to suffer. The work of the transitmaii is so exacting that he should not be required to spend any time in studying out a route. Beside these two, there should be two flagmen, two chain - men, one stakeman and two or more axemen — depending on the wooded character of the country. On stadia surveys the flagmen and chainmen may be replaced by two or more rodmen; it is also economical to have a recorder, as it facilitates the progress of the whole party. The cross-section party should consist of a level- man, recorder, and two tapemen. This party can be cut down to three, or in an emergency two, but it is uneconomical in the long run. The level party will consist of a leveler and rodman. If the party is camping out, a cook and one or more teamsters will usually be required to handle the camp equipage, as it is unwise to require the surveyors to spend their time in such work. 14. Re-surveys. Much of the defective location of raH- roads is due to (1)* deciding hastily on a general route, (2) then surveying a line through the belt with great detail and accuracy, (3) then locating the line substantially as first surveyed, because the line is fairly good (or at least not very bad), and also because of an unwillingness to throw away the detailed work of a large party for several weeks. Frequently a great amount of unneces- sary and wholly useless detail is surveyed and plotted during the reconnoissance and preliminary surveys. These surveys should only include those salient facts which instantly stamp a route as being inferior or superior to another. Usually the general loca- tion of a large part of a route is self evident or may be deter- mined after a brief examination. But there are generally places along the line where for a few miles a hasty examination of two or three lines is not only justifiable but is the only proper course. Two or more of these short loops may show advantages so evenly divided that a more elaborate survey is necessary to decide betw^een them. Even after the location survey has been made, or even after construction has begun, changes are often proper, but if the preliminary surveying has been well done only minor changes should be needed. A few hundred dollars spent on extra survey- ing is a wise investment considering the great probability of an immediate saving of as many thousands in construction or of an 14 RAILROAD ENGINEERING operating advantage whose annual value might be as great as the cost of the extra surveying. LOCATION SURVEYS. 15. Selecting a Route. *Much of the raih-oad location of the country has been done by picking out the line on the ground, even making it follow in places the backbone line of the prelim- inary survey, running from one course to the next by means of suitable curves. In the hands of a good engineer the method is not necessarily very bad, but it is much improved by the following modification. Paper location. The work of the preliminary sur- vey is carefully plotted from the transit notes and cross-section book to a scale of 200 feet per inch. On this map may be plotted one or more trial location lines. Each of these consists of circular curves joined by tangents. The location line must pass through any predetermined points and yet join them by lines w^hich will give the best location, considering the conflicting interests as described in section 1. Within the limits of the preliminary map several locations are generally possible and one great element of the value of such a map lies in the ease with which several routes may be laid out and compared. Profiles may be drawn for each line laid down by noting the intersection of the line, with each contour. Drawing on the profile the required grade line wull give a relative idea of the amount of earthwork required. The method is especially valuable when "development" is necessary. Although such a line must sometimes be laid out by a bold and apparently unsystematic trial of a route, yet some approach to a systematic solution may be made as follows: Assume that the maximum ruling grade has been determined as 1.2 per cent, and that the contours have, as usual, a five-foot interval. It will require 417 feet of 1.2 per cent grade to rise five feet. Set a pair of dividers so that they will step off spaces of 417 feet on the map. Starting on a contour at the required beginning of a grade, swing the dividers so that they will just reach the next contour and continue to step off such spaces. Joining these points, such a line would be a purely surface line, would probably be very crooked and otherwise unsuitable, but it probably would be sug- gestive of a practicable route* After locating on the map the best 24 RAILROAD ENGINEERING 15 obtainable line, it should then be transferred to the gronnd. Measure to scale the lengths af all "tangents" (the straight lines joining the curves), and the radii and lengths of all curves. Instead of scaling off the length of a curve, it may be more accu- rate to measure with a protractor, or with a scale of chords, the angle between the tangents at each end of the curve, and from the angle and the radius compute the length. Usually the located line will lie fairly close to the preliminary line — close enough so that tie lines may readily be run between them. These should be scaled from the map. To prevent the accumulation of error due to inaccuracies, the length (or radii) of curves or the length of tangents should be altered if necessary so as to make the location check on the ground with the positions of the stakes of the pre- liminary survey. The method of making such modifications will be taken up later. 16. Surveying Methods. Only the most precise work with a transit can be tolerated. The compass needle is only to be used as a check, but its use for this purpose should be insisted on, as it frequently detects a gross error. Transit stations should be marked by ''hubs" and "witness stakes" (Section 10). Reference stakes should also be set at places as near as possible to the princi- pal stations and yet outside of the line of all earthwork operations, so that at any stage of the construction the positions of the original stakes may be easily recovered. The link chain as a measurer has now been practically discarded for the steel tape. Fractions of a foot are measured in tenths and hundredths rather than in inches. The personnel of the party will be almost identical with that of the preliminary survey party except that the cross section party will be replaced by the slope-stake party, whose duties are similar, but who generally use a level on a tripod rather than a hand level. The description of the duties of the slope-stake party will be de- ferred to a later chapter. The leveling party should establish "bench-marks" at frequent intervals along the line. A spike driven in the roots of a large tree is one of the best and easiest es- tablished of marks in rural districts. A mark on any large masonry structure, such as a bridge abutment or a building, should be obtained when possible. Levels should be taken to hundredths of a foot on turning points and bench marks. Some engineers 25 16 RAILROAD ENGINEERING read to tlioiisandtlis of a foot, but when it is considered that one division of a level bubble Tisually corresj)onds to 30" of arc, and that at a distance of 150 feet a movement of 30" of arc will correspond to .0218 foot on the rod, an error of level amounting to a very small fraction of a division will make an error of several thousandths or even a hundredth. Therefore unless unusual care is taken in handling the level, it is a useless refinement to read the rod to thousandths. In reading elevations of the surface of the ground, the nearest tenth of a foot is sufficiently accurate. The complete details of location surveys can only be appreciated after the subject of railroad curves has been studied, and they will not therefore be further elaborated here. SIMPLE CURVES, * 17. Method of Measurement. The alignment of a track is the geometrical form of the line midway between the two rails. Such a center line may be a straight line, a simple curve or a curve of double curvature, but it simplifies matters to consider always the horizontal projection of such lines. \ Their vertical projections are considered ^^""mC separately when it is necessary. Curves are ^^((p m sometimes designated by their radius or by ^y(^ W\ the degrees and minutes subtended by a unit ^^■\;0 .« chord. Nearly all railroad curves have such ^"^v..,^^ Hf long radii that it is impracticable to use the ^"^"^^vj/ center. Therefore all work is done at the /8 ■p. ^ circumference in accordance w^ith geomet- rical principles which will now be described. If AB, Fig. 5, is a chord of unit length, then D is called \hQ degree of curve for the radius R. AO sin i D = i AB = -4 C 2 ^^ 2 (1) 26 KAIT.ROAD ENGINEERING wLicli becomes by inversion sin -^ D 2R (2) The length of the unit sub-chord varies somewhat with cus. torn. The abnost invariable practice in the United States is to use a unit chord length of 100 feet. Sul)stituting C = 100 in equa- tion 1, and successively assuming values from 0"^ 01' up to 12"^ 0' varying by single minutes, and with larger intervals for higher degrees which are very seldom used, the radius of almost any curve may be tabulated for ready and convenient use. Such a table is found in Table I*, which also gives the logarithm of each radius. A very common rule, which is approximate but accurate enough for many uses, is as follows, using the same notation as before: _5730 (3) i8. Sub=Chords. It often becomes necessary to lay oflp a chord length which is less than 100 feet and to know the angle subtended at the center. Since a chord is shorter than its arc, it also follows that the sum of the four equal chords in Fig. 6 is also shorter than the total arc although they are evidently longer than the 100' chord. But it is found more convenient to say that the chord has a rKjminal length (in this case) of 25 feet. As in equation (2) we may derive .1 c (4) Fig. 6. In which d is the angle subtending the sub-chord whose true length is c. By inversion we have c = 2 It sin^^ (5) Calling the nonnmal length c', we have the proportion r':100::^Z:D •See Webb's "Trigonometric Tables," published by American School of Correspond- eni'G r!hif:iy<>. TIL T»ric«. .Vh-. ^.^ 18 RAILROAD ENOTNEERING EXAMPLES FOR PRACTICE. 1. What is the true length of a chord of a 3^ 30' curve whose nominal length is 40 feet ? From the above proportion, 40 <^=Tqq^ = 0-40 X 3.5 = 1.4° = 1° 24'. Substituting in equa- tion 5, we have 6' =- 2 X 1637.3 X sin i (1° 24') = 40.005. Note that the excess over 40 feet is very small — about one- sixteenth of an inch. It is always small for low degrees of curva- ture. In the following example it is far greater. 2. What is the true length of a chord of a 12° curve whose nominal length is 60 feet? Ans. 60.070. In this case it would be a gross error to neglect to allow for this difference. i9. Length of a Curve. The length of a curve is always considered to be the quotient of lOOA -h D, in which A is the total central angle of the curve or the angle between the terminal tangents. The mean length of the two rails of a curve is always a little in excess of this, but the excess is always so small that it has no practical importance. It merely adds an insignificant amount to the length of rail required. Examjple. A 4° curve begins at Sta. 16 + 80 and runs to Sta. 21 + 35. The nominal length of the curve is 455 feet. The actual arc (which is the mean of the two rail lengths) is 4.55 X 4° X R X j^o = 455.09 which shows th:.t the excess in this case = .09 foot, a little over an inch. 20. Elements of a Curve. The follow- ing fundamental relations apply to all curves. See Fig. 7. The beginning of the curve, A, is called the point of curve ^ PC. The other Fig. 7. end of the curve at B is called the point of tangeney, PT. The intersection of the two tangents is called the vertex (Y). The central angle^ A, is the angle 3,t Y between the tangents, and it is equal to the angle at the center, O, between the radii drawn to the PC and PT. The RAILROAD ENGINEERING 19 two equal tangents AY and BV are called tangent distances, T. The chord AB is called the long chords LC. The'distance HG from the middle of the long chord to the middle of the arc is called the middle ordinate, M. The distance GV from the middle of the arc to the vertex is called the external distance, E. From trigonometry the following commonly used relations are easily derived. T = Rtan^A (6) LC = 2R8ingA (7) M-Rvers^A (8) E = R exsec -^ A (p) {Note. The versed sine, abbreviated to vers, and the exter- nal secant, abbreviated to exsec, are trigonometrical functions which are not commonly used except in railroad work, and some works on trigonometry omit their discussion. An inspection of the figure readily shows that vers a = \ - cos a, and that exsec a = sec a - 1.) From trigonometry we may derive the general equation that tan a -f- exsec a — cot-^«. Therefore, by dividing equation 6 by equation 9 and transposing we obtain Tr^Ecot i A (10) 21. Elements of a F Curve. The various elements of a curve are exactly proportional to the radius and nearly proportional to the degree of curve. Therefore if the tangents, external distances and long chords are computed from equations 6, 7 and 9 for var- ious values of A from 1° to 91°, varying by 10', then an approxi- mate value for any degree of curve and value of A may be found by taking out its value for a 1° curve (by interpolation if necessary) and then dividing that value by the degree of curve. For low degrees of curvature the inaccuracy of this method is usually small 20 RAILROAD ENGINEERING enough to ]ye neglected. Even for sharper curvature the values obtained are accurate enough for approximate work. For abso- lutely accurate values equations 6 to 9 should be used, but the tabular values, found in Table II*, may always be used as a check. 22. Numerical Examples. 1. What is the tangent distance of a 3' 10' curve whose central angle is IQ^ 26' ? Solution, log R = 8.25757 ^- A == 8' 18', log tan = 9.15956 Tangent = 261.30 log 261.80 = 2.41714 Approximate solution. Interpolating in Table II* between the values for A = 16° 20' and 16° 30' we have the value 827.86 as the tangent distance for a 1° curve when the central angle is 16° 26'. Dividing 827.36 by 3.1666 (3° 10') we have 261.27 as the approximate value. The inaccuracy is about one-hundredth of one per cent or in absolute value about three-eighths of an inch. 2. Compute the external distance and the long chord for the above curve, both accurately and approximately. 8. Two tangents make an angle of 18° 24'. It is desired to run a line which shall pass 21.2 feet from the vertex of the curve. What is the required radius and the resulting tangent distance? Indicated solution. The known quantities are E and A; from equation 10 we may derive T; then with T known and A a given quantity, we may compute R by an inversion of equation 6. METHODS OF FIELD WORK. 23. Location of Points by Deflections. The angle between a tangent to a curve at any point and a secant from that point to any other point of the curve, is measured by one-half of the arc between those points. It is also equal to one-half of the angle between the radii to those points. On this fundamental geomet- rical proposition depends the whole science of circular-curve loca- tion. As a corollary, the angle between two secants intersecting on a point of the curve is measured by one-half of the intercepted arc or by one-half of the angle between the radii drawn to the ends of the intercepted arc. Applying these statements to Fig. 8 we have *See Webb's "Trigonometric Tables," published by Amerieau School of Correspoud- IIAILROAD ENGINEERING 21 aOh = ^ aCh hOd = ^ IjQd If 0<^ = 100 feet, tlieii by definition, the angle OCt^ = D, and the angle TOc^ = ^ D. Likewise if the chord ab =^ 100 feet, then the angle aCb = D and the angle aOh = ^ D. ^^ is a subchord subtending the angle d, and the angle bOd = -^ d. Therefore if a transit is set up at the point O, any point of the curve may be determined by measuring the proper chord length from O in a direction **^'Nrf/ determined by swinging an angle from the / VM^ tangent OT equal to one-half of the angle / / Yo^ measured at C between O and the desired / / \\ point. But the measurement need not be // .^"'^ made directly from O if other points have c^- already been determined; b may be deter- mined from a land d from b. Since it is p. g generally impracticable to locate more than 500 feet of curve from any one point, on account of natural obstructions (and sometimes the distance is very short), the transit must be moved up to a new station already established on the curve. But the same principles will apply and may be repeated indefinitely. 24. Computing the Deflections. If the point of curve is less than 100 feet from the last regular station, the remainder of the 100 feet must be laid off as a subchord. One-hundred-foot chords are set off until a station is reached which is within 100 feet of the end of the curve or (numerically) until the degrees of central angle remaining is less than D. That remainder is the angle for the final subchord. The foregoing may be illustrated by a numerical case: A 4° curVe is to begin at Sta. 24 + 40. The central angle is 18° 40'. Compute the deflections. The first sta- 22 RAILROAD ENGINEERING tion point is 60 feet beyond the point of curve. The subchord angle is therefore iqqX ^"^ = 2-4° = 2° 24'. The deflection from the tangent is one-half of this or 1° 12'. The deflection for the P.T. is one-half of the total central angle or 9° 20'. Subtracting 1° 12' we have left 8° 08', which will allow for four deflections of 0° 08' 2° each and 0° 08' over, which will require a chord = ■ ^^ ■ X 100 = 6.67 feet. The curve will therefore end at Sta. 29 -f- 6.67. 18° 40' This may be verified or otherwise computed as follows: — -^ — = 4.66667, the total nominal length of the curve in station lengths of 100 feet. That is, the length will be 466.67. The first sub- chord is 60 feet; then four chords of 100 feet; then a final subchord of 6.67 feet. The deflections may be tabulated as follows: P.O. Sta. 24 + 40 0° 25 0° + r 12' =: r 12' 26 r 12' + 2° = 3° 12' 27 3° 12' + 2° = 5° 12' 28 5° 12' -h 2° = T 12' 29 7° 12' + 2° = 9° 12' 29 4- 6.67, , 9° 12' + 0° 08' =: 9° 20', which is one- half of 18° 40' as it should be. 25. Instrumental Work. The above numerical case is com- paratively simple. When the degree of curve is an odd quantity and when difiiculties of location require that the transit be set up at substations on the curve, then the numerical work, although worked out on precisely the same principle, is much greater and chances for numerical error are greater. The following rule for instrumental work is as simple as any for the simple cases and is far better for the more complicated cases. Compute the deflec- tions for all stations and substations as illustrated above. Set up the transit at the P.O., and locate from it all stations that may be conveniently reached. Then move up the transit to a forward station and use the following rule: W/)e7i the transit is set at any forward station^ hael'sight to ANY previous station with the i)lates set at the deflection angle RAILROAD ENGINEERING 23 for the station sighted at. Plunge the telescope and sight at any forward station with the deflection angle computed for that station. The student should verify for himself the truth of this rule by drawing out a simple case and noting the angles both for fore- sight and backsight for any station, when the transit is located at any station. Curve location requires extreme care on the part of field men, for a very slight inaccuracy is apt to be multiplied until the error is intolerable. The transit should be very carefully centered over hubs, which should be referred to points which will not be dis- turbed during construction. 26. Special Methods of Location. The above method, using a transit and tape, is the ordinary and preferable method, but it is Fig. 9. sometimes necessary to lay out a curve when a transit is not at hand and there are sometimes special conditions when a modifica- tion of the above method will be more accurate. The engineer must have learned the fundamental principles of curve location so thoroughly that he may decide on the best method to use and even to invent some modification which may best suit the special case in hand. A few of these special cases will be described. {a) Using tv;o transits. The location may run over swampy ground where accurate chaining is impracticable. Some point of the curve beyond the swamp may be located, perhaps by triangu- lation, by computing its angle of deflection and the length of the long chord (equation 7). The point beyond the swamp may or may not be the P. T. Then set up two transits simultaneously at the stations located on firm ground The deflection of each chord from 24 RAILROAD ENOINEERINO pa = 40 hi/ == V v in tlie tangent to the curve at tlie instrument point, or from tlie long chord, is a simple matter of geometry (see ^ 23). A rodman can locate each point by placing himself at points where he is simul- taneously in line for both transits. {!>) By tangential offsets. The solution of this as well as the following methods will be indicated by the lines in the figures. In each case the solution is an appli- cation of simple geometrical and ti'igo- nometrical principles. The solutions are somewhat lengrthened, althouo-h not essentially modified, when the curve begins or ends with a subchord. In Fig. 10, for example Oh' = Oa' + a'h' = 40 cos 0° 36' + 100 cos (1° 12' + 1° 30') 40 sin 0° 30' + 100 sin (1° 12' + 1" 30') and similarly for other points. (c) By middle ordinates. Compute first the length of a long chord for tivo stations and the middle ordinate of such a chord. For subchords, compute the long chord and middle ordinates for an angle twice that subtended by the subchord. These distances should be laid off on the ground as indicated in the illustration. In Fig. 11, Oa" is half the long chord for two stations and a"a equals the middle ordi- nate for such a loner chord. Lay off Oa on the tangent and measure ' out the offset «"<7. Meas- ure out aa' (= a" a) so that aa' is perpendicular to Oa\ and produce O*^^' to h. Oa" == Oa' = a'h. Thus is h located, and (?, cZ, etc.,. will be located similarly. In Fig. 12, an is half the long chord for twice the arc Oa^ and On is its middle ordinate. Compute similarly zy and z"z^ and lay off on the ground a and z. Compute, as in the regular case, aa! and za' ( — a'l>)\ h is then laid off as before. Fig. 11. RAILROAD ENGINEERING 25 (d) By offsets from the long chord. The geometry involved is apparent from an inspection of Fig. 13, in which is shown the general case of a cnrve beginning and ending with a subchord. All of the al)ove methods are mathematically perfect in theory, hut wlien curves are thus laid out without the aid of a transit the work is apt to he inaccurate unless unusual care is taken. 27. Obstacles to Location. As in the previous section, the problems are usually simple ex- amples in geometry and trigo- nometry, and the engineer must select the solution which will give the best result. () Point of cwrve, or point of tangent^ inaccessible. By making a diagram of the desired line with its obstructions, as in P'ig. 15, the known and unknown quantities are readily determined, also their geometrical relations. For example, in the illustration the position of V (on the ground) is known, as is also the distance 26 KAILROAD ENGINEERING Fig. 14. AV. Then the computed position of A is known. Assume some angle a such that K vers a = Ks = no = jjt/ where s is in an accessible position. Then ?is = sj) = H sin a and 71 and p can be located on the ground. Then, setting up a transit at n, and turning from the line 7ip an angle of a, the tangent is determined and the remainder of the curve can be run in as usual. If the P.T. is inac- cessible, the curve may be run in to some point 7n, from which, by similar calculations and field work, the point x is obtained, from which the tangent can be continued. (€) Middle part of ctrrve ohstructed. The curve may be run as usual to some point n (Fig. 16) which should preferably, although not necessarily, be an even station. At 7i a chord nvi may be run which will clear the obstruction. The angle between nrti and the tangent is one-half the angle measured by the arc nm. From equation 7, the length of nm may be computed and then measured off, thus es- tablishing the point m, from which the remainder of the curve is easily run in. As an illustration of the elasticity of this general method, it might under some conditions be easier to run the dotted curve having the same radius as the required curve could then be found by using the same geometrical principles used in §26 d. 28. Numerical Examples. Ail problems have hitherto been so very simple that nothing has been said about the details of solv- Fig. 15. RAILROAD ENGINEERING 27 ing numerical problems. But as problems become more compli- cated, the greater becomes the value of a systematic method of solu- tion, which may be readily reviewed, checked and studied for the discovery of a possible error. Logarithms should almost invariably be used for multiplication and division, for they are great time- savers. Even if the student is unaccustomed to them, it pays to become familiar with them. Such methods will be used in the following solutions and the student is urged to solve all such problems similarly. 1. In a case similar to that sketched in Fig. 14, ab was measured as 476.25; the angle Nah was measured as 24° 18', and the angle Yha 34° 22'. The curve is to be a 3° 30' curve. Its radius is therefore 1637.3. A = 24° 18' + 34° 22' = 58° 40'. Compute aK and iB. Logarithms. Equation 6. R (3° 30') 3.21412 tan-^A = tan 29° 20' 9.74969 2 T = 920.04 2.96381 3i„ 340 22, ah = 476.25 2.67783 ^^ ^ "^^ sin 58° 40"' log sin 34° 22' 9.75165 co-log sin 58° 40' 0.06836 aY = 314.74 2.49795 Tan AY = 920.04 aA. = 605.30 sin 24° 18' — ^'^ = ^^' oir. ^k- ±(^' cil = 476.25 2.67783 sin 58° 40' log sin 24° 18' 9.61438 co-log sin 58° 40' 0.06846 hY = 229.45 2.36068 Tan BY = 920.04 hB = 690.59 2. Example as in Fig. 15. D = 3° 20'. A = 23° 40'. It is estimated that at v, 180 feet back from Y, the line 7ip will prob- ably clear the obstruction at A; 71s is the difference between 180 and the computed tangent distance AY; 71s -j- R = sin a. Then nv = py — R vers a. Locate 7% by the offset -y??, and make a 28 RAILROAD ENGINEERING similar oflFset tit //. If this line does not clear tlie ol)struction, another value of a (probably greater) should be assumed and new values for A.v and vii computed. Compute the numerical values as above. 29. Modifications of Location, Only a few of the very many changes which are at times required will here be given. They are all solvable by a few principles of geometry and trigonometry. The oc- casion for many such changes is the ad- justment of the inaccuracies of a "paper location." (i) To move theforumrd' tangent par- allel to itself a distance x^ the radms remaining unehanged. See Fig. ' 17. Every point of the curve is moved par- allel to the first tangent a distance A A' = BB'==VV'-=00'. Fig. 16. AA'=: B'?^ X sin 7?BB' sin A («■) (^) To move the forward tangent parallel to itself the point of curvatiire remaining unehanged'. Since the central angle (A) is unchanged, the curve and all its parts are simply enlarged or reduced according to some ratio, as is apparent from Fig. 18. The known quantities are the change in the tangent x' (or a?"), the central angle A and the original radius R. YV' = Y'A sinZ/VV X' sin A (12) Then the new tangent distance A V = ^^ + VY'. The triangle BmB', being similar to the triangle AO' B', is isosceles and Viiii = B'm. Then the new radius Fig. 17. R' = R + mB = R + B'. vers B'/;vB = R4 vers A (13) RAILROAD ENGINEER IX(; 29 Tlie niodiiications of this solution, when the tangent is moved toward the center, are very simple and are apparent from the figure. (.?) To change the directioii of the forward tangent at the point of tangencxj. The central angle scaled off from the paper location miglit have an error which would be best corrected by this means. This solution is but one of a large class in which the central angle is modified. The required change (a) in the central angle is one of the given quantities. R, A, AV and BV are also known. In Fig. 19, A' = A - a; B-? = R vers A ; B.9 = R' vers A' R'=R vers A vers (A - a) Also, since A.? = R sin A and A'-y (14) Fig. 18. R' sin A', we have AA' A.S' = R' sin A' - R sin A (•5) 30. Examples. 1. Given a 4" 20' curve w^th a central angle of 18° 28'. It is required to move the forward tangent parallel to itself 12 feet. How much is the change of the P.O. (the distance A A' in Fig. 17) ? 2. Given the same curve as above, it is required to move the tangent tovKird the center 12 feet, but without changing the P.O. What wnll be the changes in the tangent distance and the radius? 3. Given the same curve as above, it is required to diminish the central angle by 0° 22', but retaining the same P.T. What will be the new radius and the change in the P.O.? Fig. 19. COMPOUND CURVES. 31. Definition. Compound curves consist of a succession of two or more curves of diflFerent radii which have a common tan- gent where they meet. They maxj be laid out by the same method 30 RAILROAD ENGTNEEKINO as simple curves, but there are certain geometrical relations exist- ing between the parts of a compound curve which greatly facili- tate the ccrmjmtations, especially when any modifications are required. In the following demonstrations 11^ and R^ will always represent the smaller and larger radii respectively, no matter which succeeds the other. A, and A., will always represent the corresponding central angles. Although R^ is always larger than Ii„ A2 may or may not be larger than A,. T2 is always adjacent to the larger radius H^ and is always larger than T^. 32. Mutual Relations of the Parts of a Compound Curve of Two Branches. The curve is illustrated in Fig. 20, in which AC and CB are the two curves with radii of ll^ and E., respectively. Therefore by the above definitions the other functions are as indicated in the figure. Produce the arc AC until the angle COj x = A^. Then, by similar triangles, the chord Cx produced must intersect B. Also, if xt is drawn parallel to CO2, it will equal B^ and the angle Then draw A.9 and xk perpendicular to Oj x. -e JTi^ 9^ ^ r-v \ \ \ / ."-^ Ri 0? Fig. 20. xi^ will equal A^. Then BA: — xt vers xtR = (K^ - R,) vers A2 xs = AGj vers AOj.'Z? = li^ vers A Am = AV sin AYm = Tj sin A A7n = Bk -i- xs T, sin A = Ej vers A + (E2 - I^.) vers A, (16) By drawing a few additional lines in the figure, it may similarly be proved that T2 sin A = R2 vers A - (K, - E,) vers Ai (17) By algebraic transformation we may derive from equations 16 and 17 the following useful relations. The details of the derivation of these equations is suggested as a profitable exercise for the student. K = K, + ^^^ Ti sin A - Ej vers A vers (A - A,) (18) RAILROAD ENGINEERING 31 R. = T, sin A vers A^ - T2 sin A (vers A - vers A,) vers Aj) (vers A - vers A.J (■9) vers Ao vers A, - (vers A SS, Modifications of Location. As in § 29, only a few of the most common modifications will be here illustrated. 1. To move the forward tangent imrallel to itself^ hut without changing the radii. From Fig. 21 we derive X = 0,.9 - O2V =- (R, - R,) cos A, - (R, - R,) cos A/, from which cos A./ = cos A.3 - R.-R, (20) Fig. 21. Fig. 21 shows the tangent as having been moved outward', in such a case the P.C.C. (which means the "point of compound curvature ") is moved backward along the sharper curve. If it is desired to move the tangent toward the center, the required equation may be found by transposing A.^ and A/ in equation 20. But in this case the sharper curve must be extended and the P.C.C. must be moved forvmrd. In case the larger radius comes first, the figure is apparently quite different, although a little study will show that the same principles apply. From Fig. 22 we derive X ^ o;h' - o,H = (R, - R,) cos a;- (R, - R,) cos A, from which we have cos A,' = cos A, + Ro-R. (21) Fig. 22 shows the tangent as having been moved outward ', in such a case the P.C.C. is moved forward along the easier curve which is extended. As before, if the tan- gent is moved invmrd, transpose A, and A/ in equation. The P.C.C. will then be moved hacMoard along the first curve. (5) To change the radius of one of the curves without rfmnging either tangent. The requirements will be apparent from a "pauer" solution. In Fig. 23 assume that the longer 32 KAILIIOAD ENGINEERING radius, which comes first, is to be shortened by an amount equal to 6-0^. The new center O' must lie somewhere on the arc whose center is O, and whose radius is Oj^. It also must lie on a line which is parallel to AY and distant from it by li./ which is equal to ^s - P.Cy.C. With 0/ as center, draw an arc from Oj to ni . With O.^ as center, draw an arc from Oj to m. It may be proved that inin' is parallel to AY. Draw the line Oi?i' perpendicular to AO2. (22) r)%yi = (TI2 - Rj) vers A.,; m'/i = (R/ - Rj) vers A./; vers A./ = j^^, — y>-( vei'S ^-^ [K, - R,) AA' = 0,,i - 0,/a' = (R, - 11,) sin A, - ( R; - R,) sin A,' (23) 34. Examples. 1. A 5^ 30' cnrve with a central angle of 16° 22' has a tangent distance of 1800 feet from the P.O. to the vertex. At the P.C.C. the curve compounds into an easier curve. The total central angle is 30° 18'. What is the radius of the easier curve, and what is tangent dis- tance ? Answer. The given quantities are R, the ^A^r^^/' radius, Aj, A, and T, ; the required quantities are R^ and To. By substituting the known quantities in equation 18 and then the computed valve of R,, in equa- tion 17, the required quantities are The student should perform this numerical work. A 2° 30' curve 450 feet long runs into a 5° 30' curve 260 feet long. It is required to move the forward tangent in 6.4 feet, but without changing either radius. Required the change in the P.C.C. Comment. The solution evidently requires the indicated modification of equation 21. It should be noted that a practical solution always requires that the resulting value of the cosine shall be less than unity, which mt^ans that x can never be greater than (R2 - R,), and also means that the sum of the cosines of the Fig. found. RAILROAD ENGINEERING 33 original angle and its modified angle shall be less than unity. The linear change in the P.C.C. may be found by the formula Linear change = (angular change in degrees) X (radius of curve) X -fcTi^o 3. Assume the same curve as in example 2, but that it is required to change the 2° 30' curve to a 2° curve without changing the tangents. Comment. Fig. 23 may be made to apply by transposing the new and old larger radii, and their corresponding central angles. Note that when such changes are made in equa- tion 22, the equation is unchanged. The effect on equation 23 is merely to change the algebraic sign, which means that the P.C.C. is moved hacl'ivard instead of forward. 4. Draw a figure corresponding to Fig. 23 but showing a change in the smaller radius Ji^. TRANSITION CURVES, 35. Transition Curve Systems. General Use. When a train, or any other mass, is in motion it requires a definite force to make it move in a curved path. If the two rails of a railroad curve are level transversely, this centripetal force can only be furnished by the pressure of the w^heel flanges against the outer rail. To avoid such a dangerous pressure, which would make high speed imprac- ticable, the outer rail is made higher than the other. But it is manifestly impracticable to suddenly raise the outer rail at the beginning of a curve and lower it as suddenly at the end of the curve. There must be a "run -off" of considerable length. If this run-off were placed exclusively on the tangent, there would be an objectionable jar because the cars were tipped on a straight track where there is no compensating centrifugal force. If the run-off were entirely on the curve there would be a jar, because the centripetal force would not become fully developed at the be- ginning of the curve; and, therefore, a transition curve is used at the beginning and end of the curve. The transition curve is one whose rate of curvature gradually increases from nothing to the rate of the central part of the curve. If the super-elevation of the outer rail is begun at the beginning of the transition curve and is grad- 34 - RAILROAD ENGINEERING ually increased as the curvature increases so that the proper super- elevation is attained at the end of the transition curve where the regular curve commences, then the theoretical requirements are satisfied. But there is another important reason for transition curves. On a curve the bogie trucks of a car make an angle with the axis of the car. If there were an instantaneous change from a straight track to the full degree of curvature the change of posi- tion of the truck would need to be accomplished in the time required for its train to run the distance between the truck centers of a car. For a high-speed train this distance would be covered in less than a second. On a transition curve this change of position is accomplished gradually and without jar. The amount of the required super-elevation will be discussed in the following sections. Varieties of Curves. A theoretically exact transition curve is very complicated and its mathematical solution very difficult. Many systems of curves have been proposed, all of which are objec- tionable for some one of the following reasons, as stated in a report by a Committee of the American Railway Engineering Association. "(1) If simple approximate formulas were used they were not sufficiently accurate. (2) Accurate formulas were too complex. (3) The curve could not be expressed by formulas. (4) Formulas were of the endless series class. (5) Complex field methods were required to make the field work agree with formulas with spirals of large central angles." The Committee then developed a method which gives results whose accuracy is beyond that of the most care- ful field work and yet which is sufficiently simple for practical use. The mathematical development is too elaborate to be detailed here but the working formulas, together with a condensation of the Tables will be given, together with an explanation of their practical use and application, with examples. The general form of these curves, whatever their precise mathe- matical character, is shown in Fig. 24. AVE are two tangents, joined by the simple circular curve ACB, having the center O. Assume that the entire curve is moved in the direction CO a distance 00' = CC' = BB' = AA'. At some point TS on the tangent, the spiral begins and joins the circular curve tangentiaUy at SC. The other spiral runs from CS to ST. The significance of these symbols RAILROAD ENGINEERING 35 may be readily remembered from the letters; T, S, and C signify tangent, spiral, and circular curve; T^ is the point of change from tangent to spiral, SC the point of change from spiral to curve, etc. At the other end of the circular curve, the letters are in the reverse order, the station numbers increasing from A to B. The meaning of each of the various symbols used is plainly indicated on the diagram, Fig. 24. The length of a spiral can only be computed on the basis of certain assumptions as to the desired rate of tipping the car, so as to avoid discomfort to passengers, and of course this depends on the expected velocity. There is also a limitation since the sum of the two spiral angles cannot exceed the total cen- tral angle of the curve. The 7n in im nm lengths recom- mended are as follows: On curves which limit the speed : 6° and over, 240 feet less than ()°, 5^ X speed in m.p.h. for elevation of 8 inches On curves which do not the speed : limit Fig. 24. 30 times elevation in inches, OR fX ultimate speed in m.p.h. X elevation in inches For example. (1) 5° curve which limits speed; speed limit 48 m.p.h. by interpolation in table, §41; 48X5J=256 feet minimum length. (2) 3° curve; maximum operating speed 60 m.p.h.; super- elevation .62 feet = 7.44 inches; 30X7.44= 223.2 feet; OR, §X60 X7.44 = 297.6 feet. Of course the higher value should be used, or say 300 feet as the minimum length. While it is generally true that the longer transition curves give easier riding, the spiral must 36 • RAILROAD ENGINEERING not reach the center point of the curve. Since it is approximately true that the spiral extends for equal distances on each side of the original point of curve, it is nearly true that two spirals, each having the same length as the original curve, would meet at the center. The length of a spiral should in general be far less than the length of the original curve. 36. Symbols. Besides the symbols whose significance is clearly indicated in Fig. 24, the following are defined : a — ^The angle between the tangent at the TS and the chord from the TS to any point on the spiral. A — ^The angle between the tangent at the TS and the chord from the TS to the SC. . b — The angle at any point on the spiral between the tangent at that point and the chord from the TS. B — The angle at the SC between the chord from the TS and the tangent at the SC. D — The degree of the central circular curve. A — The central angle of the original circular curve, or the angle between the tangents. <^ — ^The central angle of the whole spiral. <^i — The central angle of the spiral from the TS to the first spiral point. k — ^The increase in the degree of the curve per station on the spiral. L — ^The length of the spiral expressed in feet from the TS to the SC. s — ^The length of the spiral in stations from the TS to any given point. S — ^The length of the spiral expressed in stations from the TS to theSC. 37. Deflections. The field formulas for deflections are based on the following two equations a = 10ks^ minutes = —01 f o a = lOA-S^ minutes = -—(f) o The first deflection ai = 10ksi^ minutes. But k is the increase in RAILROAD ENGINEERING 37 degree of curve per station and since the degree of curve increases as the length A: = D-^S, S being expressed in stations. For point 1, since 8 = 10^, ai = 10 ( — \s^ = T>s, which may be expressed as the \10s/ degree of curve times the length of the chord in stations. For example, if the spiral is 400 feet long (L = 400 and S=4) and runs on to a 5° curve (D = 5), one chord is 40 feet long or s = A stations. Then ai = 5X0.4 = 2 minutes of arc for the deflection for the first chord point. And since the deflections are as the square of the number of stations, the deflections from TS to succeeding stations will be 4, 9, 16, 25, 36, 49, 64, 81, and 100 times 2 minutes, as shown in the second vertical column of Part A of Table- IV. The last deflection A = 100x2' = 200' = 3° 20' = J (10°) =i, which is the total central angle of the spiral. This result also checks the general equation "^ 2" 2 20000 200 Since DS_5X4 The deflections from any point of the spiral to any other point, either forward or backward, may be found by multiplying the value of a I (in this case 2') by the coefficients in the proper vertical column U V of that table. The values of the ratios — and — for even degrees C X Y and for A, — , ^, and — for half degrees are given in Parts B and C, Table IV. 38. Insertion of a Spiral between a Tangent and a Circular Curve. In Fig. 25 it has been necessary to make the distance MM' about 100 times its real proportional value in order to make the illustration distinct. The curve AMB is a simple circular curve joining the two tangents, such as would be used without spirals. If a suitable spiral is started at a suitable point Q, and run to some point Z, such that the total central angle of the spiral, ) tan — A+R tan— A = .T — R sin 4)-\-y tan —A+R cos (j) tan —A ^1 Zd (25) As a numerical solution of any problem will usually involve the determination of the value of A'N, equation 25 may be reduced from four terms to three as follows : Transform the equation above equation 25 to read VQ = a:+R (tan-^A sin in which L is the length of each spiral. (31) RAILROAD ENGINEERING 41 41. Example. Assume that a track has been laid with a 6° curve for 39° 50': It is desired to insert suitable spirals without altering the length of the old track. Solution. Unfortunately there is no method of solving this problem so as to obtain directly the revised value for the radius: The new radius will always be about 5 per cent shorter than the old. The larger the central angle, the less will be the difference. The only method is therefore to assume a value for R', solve equation 30, and then compare the lengths of the new and old lines. If the difference is so small that it may be neglected, the problem is solved. If not, a slight modi- fication of the new radius, such as experience in these computations will suggest, will usually give on a second trial a value which is sufficiently close. As a first trial for the above numerical case, wp will assume a 6° 20' curve for the new curve, and a 240 ft. spiral whose = 7° 36'. rr = 239.580 and ?/ = 10.60. Logarithms. X = 239 . 580 R' (6° 20') 2 . 95671 sin 7° 36' 9.12141 119.709 325.069 564.649 462.019 342.310 462.019 2.07812 R' 2.95671 cos 7° 36' 9.99617 tani-A 9.55909 2.51197 R =955.37 y= 10.60 944.77 2.97532 tan —A 9.5590'9 2.53442 AQ = 102.630 The length of the old curve from Q to Q' is 100 A, 10^39.83333^ D 6 2AQ= 2X102.630 = 663.889 205.260 869.149 42 RAILROAD ENGINEERING The length of the new curve from Q to Q' is 100^=100§i:f|=l^= 388.947 2L = 2 X 240 = 480.000 868.947 868.947 Difference in length = . 202 When it is considered that in that length of 869 feet there will be about 27 rail joints and that a stretching at each joint of about .0075 foot will make up for this difference of length, it might not be necessary to cut the rails. To illustrate the method of adjustment if a more accurate value for R' were required; note that in the above case the new curve is too short. If R' is diminished (say from D' = 6° 20' to D = 6° 24'), one term of equation 30 will be increased and one of them diminished, but the net change in the value of AQ is 3 . 403, which will decrease the length of the old curve by 6 . 806. But such a change in D' will decrease the length of the new line by 6 . 552. The revised length of the old line is, therefore, 862.343 and the revised length of the new line is 862 . 395 The revised difference is 0.052 The new line is now longer than the old, but the difference is insig- nificant (about one fortieth of an inch per joint). By interpolation D' = 6° 23' is the better value to use. There is another method of introducing a spiral into old track without even changing the central part of the curve. The spiral runs into a curve which is sharper than the original curve which then compounds into the old curve. The solution of this method consists in so choosing and locating the spiral and the sharper curve that it will compound into the original curve. The details of this method will not be here given because, although it involves less track work at the start, it is a more complicated alignment to maintain and the method is inferior to the one pre- viously given- RAILROAD ENGINEERING 43 On the basis of D' = 6° 20' (Equation 29) Logarithms. R(6°) 2.98017 1 . exsec —A 2i 8.80356 60.776 1.78373 905.13 965.906 R' cos 1 . secyA 2.95671 9.99617 0.02678 954.255 loga! = 2.97966 1.02530 11 .274 1 . secyA 0.02678 1.05209 965.529 965.529 m= 0.377 foot Note that the maximum lateral change in the track is less than five inches. On many railroads where there has been no pretense to using spirals the track foremen have produced nearly the same result in a rough uncertain way by throwing in the curve somewhat near the point of curve. This necessarily sharpens the curve further on, and thus substantially the same result is obtained as is described above but without any calculations or any theoretical accuracy. It is only by such means that a tolerable riding track can be produced when transition curves are not used. 42. yjsQ of Transition Curves with Compound Curves. It is shown in the last few sections that the lateral deviation involved by the use of spirals is very small. Since compound curves are usually employed only when the location is difficult, it is best to make the calculations as if no spirals were to be used, except that approximate allowances may be made for such lateral changes as will be required. Then the changes can be computed as follows. Theoretically there should be a transition curve between the two branches of a compound curve, but when a train is already on a curve and the wheels are pressing against the outer rail, it will cause but little jar to merely increase the curvature. The intro- 44 RAILROAD ENGINEERING duction of such spirals will not be here given. Transition curves need not be used in running on to curves which are easier than 3° and even 4"". Therefore if one branch of a compound curve is of easy curvature, as is frequently the case, it will not bie neces- sary to use a spiral at that end of the curve. Therefore two cases will be developed — using spirals at one end only, and at both ends. (r/) jSplral at one end onltj. The method of §38 may be adopted La hSO*--^! ^O by substituting Aj for ^ A in equa- tions 24 to 28. This would move the P.C.C. from M to M'. But since the two curves must be made to coincide, the sharper curve will be moved parallel to the tangent BV a distance of M'M, while the unchanged circular curve will be moved parallel to the tangent AY a distance MM^. Calling MM' = m^, we have. Fig. 27, % Fig. 27. M MM cos A. ^mr sin M/MM, sin (90° - A„) /M, = MM/ .* ',^. ' = m, ^ — T — ^ = m, -. — ^ sin M; M,M cos A, m. sin A (32) It should be noted that the new P.O. is at A' and that AA' = MM*, while the P.T. is changed from B to Q/, which equals BQj - QQ'. BQ, is found from equation 28 and Q/Qi = Mi'M4 is found from equation 32. (b) Spiral at hotk ends. Applying the method of §38 to each branch of the curve in turn by successively substituting A, and A^ for^ A, we will obtain values for m^ and m.^ which will in general differ considerably. But as before we may move each revised curve as shown in Fig. 28 and as computed in equations 34 and 35, Calling MM,' = m^ and MM/ = vi^, and noting chat the angle at M,' (see the detail) = 90° - A,, the angle at M/ RAILROAD ENGINEERING 45 == 90°- A_, and the angle at M3 = A, we have the following: M/M3 ^r ,^r sin (90^ - A,) ^ , cos A, . . sin A sin A m;m3 == M/M ^ sin (90° - A,) ' sin A = (v/^i - m,) cos A, sin A (35) As in the previous case, the position of the new point of the spiral is found in each case from one of the above quantities and the change computed from equation 28. Note that in one case the point of spiral is moved nearer to, and in the other case further away from, the vertex. 43. Example. Given a 7° 20' curve for 29° 40' followed by a 4° 10' curve for 25° 20'. Required to introduce suitable spirals. Using equation 24 suc- cessively with the two sets of figures w^e obtain mi = 5.506 and ?ri2= 1.930. Then {jni — m2) = 3.576. Substituting this value in equations 34 and 35 we obtain Ml Ms = 3.946 and Ms'Ms = 3.793. Using equation 28, calling —A = 25° 20', we compute AQ2 = 120.769. But we must add to this an amount equal to Mz'Ma = 3.793, which makes AQ2' = 124.562. Simi- larly, calling —A = 29° 40' in equation 28, we may compute BQi = 152.444. But from this must be subtracted M/M3 = 3.946, which makes BQ/ = 148.498. The actual lateral change from the original point M is equal to MMo'+Ms'Ms sin A2 = 1.930+1.623 = 3.553. The student should verify in detail all these calculations. Fig. 28. 46 RAILROAD ENGINEERING 44. Field Work. \Yhen spirals form part of the original location, it is a useless refinement to locate all the chord points before earth work has been done. It is then sufficient to locate the beginning and end of each spiral with perhaps one intermediate point in case the spiral is very long. During the resurvey which immediately precedes track work, when the roadbed is graded and flat, the intermediate points are readily inserted. Referring to Fig. 25, the point Q (or TS) would first be located at a distance VQ (see equation 25) from the point V. Assume, as in Fig. 25, a simple curve, 6°, with A = 32°, and at each end a spiral 240 feet long. Dur- ing the first location of the road it would be sufficient to locate the end of the spiral at point Z or SC. The deflection from the tangent when the instrument is at TS and is ''sighting at" SC is — = -;- o o (M) ^jQl^) ^-° •* = 2°24'. The ordinate X (QK in Fig. 25) is 239.623 and the distance out from the tangent KZ = z/ = 10.042. The total central angle to this point ( ^ ^*^' ('^ " yO x^=^h -f s{il + yj (38) But in each of these equations, both x and y are unknown quanti- ties, and it is impracticable to depend on a strictly mathematical solution. The simplest method is to find by trial the location of points which will satisfy the equations. An experienced man will 64 RAILROAD ENGINEERING 55 sometimes determine such a point in a single trial and generally the second trial will be sufficient. As a first approximation, we may note that a is at such a position that its x is ac = -^ J + sd. The added distance out to iti equals the added drop times s. As- sume that in Fig. 36, d = 7.7, J = 20 and s = l.b : 1. The dis- tance ae r= 10 -f (1.5 X 7.7) = 21.55. But experience will suggest that the required point i/i is about 8 feet lower down and therefore about (1.5" X 8) or 12 feet further out. As a first trial with the rod, the rod is placed at n', 34 feet out (21.55 + about 12), where a rod reading of b (= 10.6) is found. Subtracting k (^= 3.5) we have 7.1, the ''?/" of that point. Substituting this value of y in the first part of equation 37, we compute Xi to be 32.2. This is the point n in Fig. 36, at a distance x" (which is less than x) from the center. This shows that even 32.2 is too far out. Another trial is made at 30.2 feet, where the rod reading is found to be 9.3, which means that the y is 9.3 — 3,5 = 5.8, which substituted in the equation gives x = 30.25. This checks so closely with 30.2, that it may be considered satisfactory. On rough ground it is an utterly useless refinement to attempt to do work closer than the nearest tenth of a foot, for the almost un- avoidable inaccuracies will often have a greater effect than a change of even a tenth in such work. The above explanation is given in detail so as to show the method. Some such method is neces- sary for the inexperienced man, but even a short experience will enable a man to estimate the correction to his first trial very quickly and surely so that the second trial will be satisfactory, and without a detailed solution as above of all the work. In Figs. 36 and 37, the ground has been shown as having a practically uniform slope. The determination of the slope stake is not affected essentially by the nature of the ground between the center and the slope stakes. In Fig. 42 is shown a more compli- cated cross-section in which the elevation of each intermediate point above the roadbed and its distance from the center must be measured. These are determined by setting up the level so that it is higher than any point in the cross-section and noting its height above the stake at the center. This rod reading added to the given center cut d gives the height of the instrument above ,56 RAILROAD ENGINEERING the roadbed. This is called the H.I. Subtracting the rod read- ing for any point from the ILL gives the height of that point above the roadbed. In the case of a fill, which may be illustrated by turning Fig. 42 upside down, the level may be either above or below the roadbed. This modifies the above rule somewhat, but the same principle applies — determine the difference of elevation of each point of the surface of the ground and the roadbed, COMPUTING THE VOLUME. 53. Common Methods. Sometimes an approximate com- putation of the volume of the earthwork is made from the work of the preliminary survey, so as to get an approximate idea of the amount of earthwork on a route, and therefore its cost. To do this, a more or less approximate measure of each cross-section is taken and then the distance between any two cross-sections is multiplied by the half-sum of the two areas. The sum of all such products gives the total volume. Such a method is mathematically inaccurate, but the approximation in the cross-sectional areas, and some other reasons, will probably introduce still further inac- curacies. These various methods will be described in the order of increasing accuracy. 54. Level Sections. From Fig. 38 may readily be derived the equation Area = {a -^ ^^A' --y (39) If Aq is the area of the initial section and Aj, Ag, • • A^ be the areas of the succeeding and final sections, which are at a uniform ^/^//m/^Ammw/m/^'/ distance apart of 1, then the total I- -[- -i-i -H yffi^ volume will be wfdmjw ?--Y-' Volume = i- qA„ + 2 (A, + A, ^'^■''- .' + •• +A,.,) + AJ (40) Of course I is usually 100. The ^— for each section is a constant, and therefore the subtractive term issimply this constant multi- RAILROAD ENGINEERING 67 plied by the number of times the areas are used in the summation. Example. Given the center heights set down in the second column of the tabular form. Width of roadbed, 20 feet; slope, 1.5 : 1. Then d = 6.7. The remainder of the solution is evident. Sta. Center Height. (a + d) (a + d)2 (a-fd)2s ^ 42 43 44 45 46 1.4 2.6 4.3 8.9 3.1 8.1 9.3 11.0 15.6 9.8 65.61 86.49 121.00 243.36 96.04 98.41 129.731 181.50 365.04 J 144.06 X 98.41 r 259. 46 2 = 363.00 1 730.08 144.06 ah 6.7 X 20 = 67 1595.01 '8 X 67 =536. io5^:oi 1059 X 100 ~T">r2T~ 1961 cubic yards. The above method invariably gives results which are some- what too high, for the volume between two "level sections " is less than the length times the mean of the areas. When the areas are equal, the error is zero, but it. increases as the square of the differ- ence of the center cuts, or fills. But since sections are almost never truly level, the assumption that they are level will usually introduce an error largely in excess of the theoretical error. Some- times the above method is used, aided perhaps by tables, by taking center cuts, or fills, from a profile and assuming that the actual volume will be the equivalent of the volume computed as above.* Such a method has its value as a mean^ of comparing two routes, but the error is apt to be very great. 55. Equivalent Sections. The following method is some- times used when the cross -sections are irregular and especially when there is disinclination or inability to use a more accurate method. Each cross-section is plotted on cross-section paper. Then a thread (mn) is so laid that (by estimation) it equalizes the spaces al)ove and below it (see Fig. 39). The distances out from the center of the intersections of this mean line wnth the side slopes are scaled from the drawing and are here called £»i and x^. Since s is the slope ratio, s = Xi -t- mo = x^ ^^ nj). Then the required 58 RAILROAD ENGINEERING area equals the area mnop minus the triangles mso^ njjs, and the " grade triangle," which means that 1 / 'a;i+.rr )(. r) - ■t"l Xi av Xr ah TT 1 i+.i + 2 V . s > / S 2 s 2 2 .ri av ah (^ s 2 ^.w Area Note the simplicity of the form. When *^ = 1:1, the area equals the mere product of these two side distances minus the constant correc- tion -^<7J. The areas being computed, the volumes are obtained exactly as in equa- Fig. 39. tion 40. As in the previous section, it may readily be shown that the method of averaging end areas does not give correct results except in the special case when the distances to the right (or to the left) at adjacent stations are equal, and when these dis- tances are nearly equal the error is small. As an approximate method, it is very rapid and good. As before, the correction is usually negative,, i.e., the computed volume is too large. 56. Volume of a Prismoid. Fig. 40 represents in a perspective view a prismoid, formed between two triangles which lie in parallel planes. The surfaces which join the corresponding sides of the tri- angles are, in general, warped sur- faces. It may be proved that the 1'^^- ^^• volume of such a prismoid equals one-sixth of the perpendicular distance betw^een the parallel planes times the sum of the two eiid triangles and four times the middle triangle (cut by a plane parallel to the end planes and midway betw^een them). This may be stated algebraically as follows: RAILROAD ENGINEERING 59 Volume = !^^ /A, + 4A^ + A A (42) It may also be proved that the foririula holds good regardless of the values, relative or absolute, of ?>i, ^.^, h^ or h.^. Therefore it holds good when h^ = O, and the prismoid becomes a wedge. It also holds good when both h^ and h^ become zero and the prismoid, becomes a pyramid. But since the formula holds good for all these forms individually it holds good for them collectively, and since any prismoid, having bases of straight lines lying in parallel planes and with plane or warped surfaces connecting those ends, can be considered as made up of a collection of triangular prismoids, pyramids and wedges, the formula evidently holds for such a prismoid. If, in equation 42, A^ were the mean of A^ and A2, then we could obtain the true volume by averaging end areas. Some of the exceptional cases where this is true have already been men- tioned. In general it is a complicated and impracticable problem to compute the area of the middle section. But it is quite possi- l)le to compute the correction which must be applied to the result found by averaging end areas, and these methods w411 be used in the following more accurate solutions. Applying equation 42 to Fig. 40, we have Volume =^^l2 h h + ^ V 2 ^T' "^T^/ + 2 ^-' ^ J But the approximate volume, computed by averaging end areas, is Appr. vol. =-^(-y^», li, + -^ ^7^2) Subtracting tlie approximate volume from the true volume, we obtain the Correction = „ \{h^ - b.^) [h^ - h^)\ (43) 57. Three=Level Sections. When the ground is fairly uni- form so that it may be said without great inaccuracy that it slopes uniformly from the center to each slope stake, then the volume may be computed from the positions of these three points and the sections are called "three-level sections." The area of such a GO RAILROAD ENGINEERING section = ~^(^^ + ^^) '^^ — ^ab. If we consider two such adja- cent sections and compute the volume by the method of averaging end areas, we will obtain as the volume Vol. = -4-L('^ + ^^') f''' - ''^' + (^'' + ^n ^^^" - ^^'^^J Dividing by 27 to reduce immediately to cubic yards, we have when I = 100, 25 25 25 25 Vol. = ^ (v^ + d') w -^ab + -^ {a + (7") w'* --^ctt> (44) When it is desired to make the computation still more accurate, the prismoidal correction may be computed as follows. We may compute separately the pris- moidal correction for each of the two triangular prismoids. These two prismoids together include the triangular " grade prismoid" under the road- bed, but since there is no pris- moidal correction to the grade prismoid, such correction as may be computed applies solely to the volume actually excavated. Applying equation 43 to the dimensions in Fig. 41, we have for the left side Pris. Corr. -= p- [(^ + d') - (^ + ^/")] (^''i" - '^"lO. which reduces to = j-r (^d' - d") (^w{' - w{) For the right side, we may compute similarly Pris. Corr. = ^ {d' - d") (w^" - <) For the two triangles we have Pris. Corr. =. — (^' _ f7")[(7^?r + w^") - {w{ + Oj RAILROAD ENGINEERING 61 Making I = 100 and dividing by 27 to reduce to cubic yards we have OK Pris. Corr. = -^ {d' - d") {w" - lo) (45) An inspection of equation 45 will show that if either the center cuts or the total widths at two adjacent sections are equal or nearly so, the prismoidal correction is zero or is so small that it may be neglected. This frequently enables one to decide that the pris- moidal correction will evidently be so small that it will be useless to compute its exact value. It usually happens that when d' > d'\ in is also greater than w". This means that the correction com- puted from equation 45 will usually be negative^ which means that for three-level sections the results computed by averaging end areas will usually be too large. A very great economy of time and accuracy result from tabu- lating all the computations in earthwork. Such work can be readily reviewed to check it or to discover a supposed error. An illustration of such a solution is given below. 58. Numerical Example. Sta. Center. Left. Right. a + d w Yards. 52 53 54 + 65 55 3.1C 6.7C 10.6 C 15.5 C 8.7C 9.6C 1.2 C 11.1 14.7 18.6 23.5 16.7 40.2 47.4 59.1 68.4 51.3 413 645 1018 1488 793 702 1307 1397 674 26.4 11. 4C 13.8 4.2C 29.1 15.6 C 18.3 7.8C 35.4 19.0 C 23.7 10.6 C 40.5 12.4 C 27.9 5. 80 30.6 20.7 d' - d' 3.6 i-f 7.2 3.9 +11.7 4.9 1+ 9.3 +6.8 17.1 Pris. corr. I - 8 -14 - 9 -13 Roadbed 24' wide in cut. Approx. vol. = 4080 Slope 1.5 : 1. Pris. corr. = —44 h -44 i-^=«-» True vol. = 4041 •^o ah = 178 9.6C . In the above form, -^ — - in the third column means that the slope stake on the left side of Sta. 52 is 9.6 feet above the elevation of 02 RAILROAD ENGINEERING the roadbed which is here in cmt C; also that it is 20.4 feet out from the center. This notation is also used to indicate the posi- tion of "intermediate points," the numerator of the fraction giv- ing the depth of cut or fill (C or F) and the denominator the distance from the center. The other points in the third and fourth columns are to be interpreted similarly. Column 5 is found by adding a (^=8.0) to column 2; '^^ in each case is the sum of the two denominators in the same horizontal line; 413 (in column 6) 25 =^97 X 11.1 X 40.2. A short method of performing this mul- tiplication will be given later. The solution of equation 44 applied to this case is: Vol. = 413 - 178 + 045 - 178 = 702. Similarly 1397 -- ~^^ (1018 - 178 + 1488 - 178). and 074 = ^~ (1488 - 178 + 703 - 178). - 3.0 = 3.1 - 0.7 and -f 7.2 =- 47.4 ~ 40.2. - 8 = ?5 81 (- 3.6) X ( + 7.2) ; see equation 45. Note that in this case the prismodial correction is about 1 per cent of the total volume. The errors due to inaccurate cross-sectioning will frequently be more than this. The volume 4036 cubic yards is the 'precise vol- ume (barring the neglect of the fraction of a yard) of the prismoids given by the notes. Whether these prismoids actually represent the true volume of the earthwork depends entirely on the cross- sectioning and is entirely out of the hands of the computer. 25 59. Computation of Products. The products ^^<2 J maybe written j-t^. These products are always the combination of two variable terms and a constant. It thus becomes possible to con- struct tables which will give these products for any given height and width. CrandalPs Earthwork Tables are computed on this basis. But these products are also obtained with great ease by means of a slide rule, provided it is large enough to give the required accuracy. The 108 mark, being so constantly in use should have a special. mark so that it may be found without effort. RAILROAD ENGINEERING 63 As a numerical illustration, take the first of the above cases. Set the 108 mark of the upper scale on the 111 mark on the lower scale. Then look for the 402 mark on the upper scale and note that it is nearfy over the 413 mark on the lower scale. "While it is possible to devise set rules to determine the position of the decimal point, it is considered that a hasty mental solution of the problem will decide the point quicker and w4th less chance of error. For example — the product of the two variable quantities is always divided by 1.08, which means that the final result will be a little less than the simple product of the two variables, 11 X 40 = 440. Therefore 413 is evidently the correct result, rather than 25 41.3 or 4130. The products — - xy are similarly obtained since 25 1 81 ^^ ^^' ^^^ ^^ ^^^ mark can be used instead of the 108. For example, the slide rule shows that ^^ q 9 / '- — = - 8 to the nearest cubic yard. As to the decimal point — 3.6 -^ 3.24 is something more than one; therefore, the result is something more than 7.2. Therefore it is 8, rather than 80 or 0.8. If the student has neither tables nor slide rule, the multiplication of the two variables (in columns 5 and 6) and the division of the products by the constant 1.08, may be made so mechanical and systematic that it may be done quickly and accurately although it is much slow^er than the slide rule method. 60. Irregular Sections. The distance from the center and the height above or below the roadbed must be obtained for each break in the surface between the slope stakes. Then, in Fig. 42, by dropping perpendiculars from each point to the roadbed line, the total area is divided into a number of trapezoids, the sum of the areas of which (less the areas of the two triangles under the side slopes) equals the total area of the section. For Fig. 42, the area would be stated algebraically as follow^s: Area = \{r + *■) {f-g) + \- (.v + t) (j/ - A) + ^^(t+ d)h + y {d + '0)j + -3- (y + w) {k -j) - — w{l---^ h) 64 RAILROAD ENGINEERING Expanding this and collecting terms, of whicli many will cancel out, we Lave Area = -2^[_/*' + ^ (^ - ''') + J(^i(l- ^) + ^o +i {d - w) + -g- ^ {r + ^)]. (46) Although the above equation looks as if it applied only to the par- ticular case given, yet a little study of it will show that the terms follow a law so general that the reduced equation for the area of any section, no matter how complicated or how many points it may have, may be written out by a literal obedience of the follow- ing rule: Area equals one-lialf the sum of products ohto/med as follows : Fig. 42. The distance to each slope stake times the height above grade of the point next inside the slope stake; The distance to each interTuediate point in tarn tunes the height of the point just inside tninus the height of the point just outside; Finally^ one -half the width of the roadbed times the sum odd amount must go to the lower story, as is illustrated in Figs. Fig. 58. 59 and 60. Some plans have these stories absolutely independent of each other. This simplifies the construction and makes repairs easy, but the trestle will be lacking in stiffness. These illustrations should be studied with special reference to the design of the lateral bracing of the individual bents and also the longitudinal bracing of the trestle as a whole. Note that the lateral bracing always runs to some point where two or more pieces inter- sect, and when possible it is so designed that even the intermediate points are a common point for several pieces. A thorough bolting at these points greatly stiffens the structure. The span between the bents varies from 10 feet to 18 feet. For high trestles economy requires that the number of bents shall be reduced as much as possible, which means that the spans should be increased. But this increases the requirements for the floor sys- tem, and also the load to be carried by each bent. 18 feet is about the safe limit for railroad rolling stock on untrussed wooden floor beams. 87. Foundations. Trestles are frequently to be classed as "temporary" structures. Such will justify the use of a foundation of a more temporary character than could be tolerated for per- Fig. 59. 92 RAILROAD ENGINEERING manent work. When time is important and the ground soft, piles are sometimes driven and sawed off a little above the ground. They are so placed that a pile comes as nearly as possible under each post of the trestle. Of course, such foundations must be con- sidered as very temporary in character, as they will speedily decay to such an extent as to render them unsafe. Locust or chestnut are preferable for this purpose. ''''%KXNX X XXXX Xt i ff988.^ kV^-VF-V .z(5'-----*^---/S--->¥--/S- ->f ^J— -^--/fL? T-R.4-74- Detail of Stringer Joint. r I" t 3' T // %-B^lt ,„ Jl Section Through Floor. Fig 71. Standard Framed Trestle as led 3x/0x/80 Boat Sp!/f», fjr ' ' Notes on Tre stie Bents. 1 Height of Bent Length of Pjsts 5///S ^^ ofSnc I8ff. ZOft es ana 22ff. ^ ^ lift 16 ff. Wff 2 18 . 20 » 2 ?l . 20 » 20 . 2 ?J , ? 25. 22. 2 27. 22. 2 29. 28 . ?4. 2 4- 2 31. 30. ?4. 2 4 2 33. 32. 24, 2 [^_ ■^ RAILROAD ENGINEERING 99 as usual. Another method is to cover the stringers and caps with sheet metal. A very long trestle generally deserves the protection of a special watchman or track walker. ]\Ieans for fighting a fire when discovered are provided by reservoirs of water, made perhaps from halves of oil barrels, which are placed on the trestle at inter- vals of 300 feet. Three or four ties are made about 4 feet longer than the usual length. These form the floor of a platform, which, when provided with a railing, forms not only a place for the barrel, but also a refuge bay for the track walker, who may be on the trestle when a train is passing. 95. Choice of Timber. When a railroad is being run through a virgin country where timber is plentiful and there is frequent occasion for trestles, it pays to take a portable sawmill to the spot and saw the timber as required. Under such condi- tions any one of the various kinds of timber which are ever used for building purposes will answer. If necessary, the cross-sec- tions can be increased to correspond with the reduced strength of a weaker wood. But when the wood must be transported a con- siderable distance and it is practicable to choose among various kinds of w^ood, the selection should be made according to favorable qualities. Ties and guard rails should, if possible, be of oak. Stringers should be made of oak or pine. Since one of the chief uses of corbels is to relieve a dangerous pressure across the grain they should be made of the hardest wood obtainable, such as oak, hickory or ash. The bents of a framed trestle may be made of almost anything, but oak, pine or fir are preferable when obtain- able. If the sills are liable to become buried somewhat in the ground so that rain will not readily be shed, then some wood like cedar, which is very long-lived under ground, might be preferable, but the strength as posts will be somewhat less than that of oak. The chemical treatment of timber for trestles is seldom used, except for trestles which are partly immersed in water where the teredo navalis is found. Trestles are usually considered to be so cheap and temporary that conditions which would justify the additional expense of chemical treatment would also justify the immediate construction of a permanent structure of steel or stone. On the folding plate. Fig. 71, is shown the standard plans for a framed trestle as adopted by the Great Northern Railroad. 100 RAILROAD ENGINEERING Many of the details shown will verify those already mentioned, while in other cases the variations in detail represent practice equally good. The plate is well worthy of a long and close study. CULVERTS. 96. Pipe Culverts. The scarcity of stone suitable for mak- ing a "box" or "arch" culvert has led to the adoption for many localities of pipe culverts, the pipes being made of tile or iron, Fig. 72. Pipes have several very great advantages. Their form is hydraulically better than any rectangular form and the surface is Note! Where character of soil will permit, this concrete need not be used Fig. 72. Pipe Culvert. usually very much better than an ordinary masonry culvert. There- fore they will discharge a far greater volume of water than a box culvert of equal area. They are very easily placed without skilled labor. Sometimes they are set inside of a wooden box culvert temporarily placed during the construction of the road. When one pipe of the size which it is desired to use has insufficient area two or more pipes may be used side by side. This feature is of special value when the head room between the bed of the stream and the grade line is limited. Iron pipe usually has such inherent strength that there is little need for special care in securing a foun- dation for the pipe. A little block of concrete at each joint is suffi- cient for ordinary cases, but tile pipe requires a secure foundation. RAILROAD ENGINEERING 101 The danger to the pipe does not lie so much in the mere static pressure of the earthwork embankment above it as in the effect of settlement of a "green'* embankment. If the pipe is laid on the natural soil, which might be tolerated if it is very firm, a bed should be carefully scooped out so as to fit the pipe as closely as possible. A better plan is to place a thick layer of broken stone or brickbats and ram them to the proper form as a bed for the pipe. A still better plan is to place a layer of concrete under the whole length of the pipe. The required slope of the pipe depends somewhat on the accuracy of the laying and on the permanency of the work. A slope of 1 per cent is ample, provided the grade be made and maintained uniform, but the effect of settlement may be to change such a grade to a negative grade, which would pre- vent the water from being carried off. Some standard plans there- Fig. 73. Old-Rail Culverts. Fig. 74. fore require a grade as steep as 1 in 20. At each end of the pipe there should be a substantial head wall of masonry. Some stand- ard plans make this wall very large and heavy with elaborate wing walls. These are justifiable on the grounds of preventing the water at the upper end from scouring around the ends of the head wall or of preventing the outflowing water from scouring away the bed of the stream and thus undermining the lower head wall. An iron pipe can be used if necessary very close to the ties, but a tile pipe should have a cushion of at least three feet between the tile and the ties. The joints in the pipe should always be caulked. Clay puddle is much used for this purpose and when it is of good quality and the work well done, the results are satis- factory, but if clay puddle cannot be obtained it is better to use hydraulic cement. The cost of the cement is an insignificant item considering the value of the result. 102 RAILROAD ENGINEERING 97. 01d=Rail Culverts. These have an especial value when the head room between the bed of the stream and the rails is small, and when it is also necessary to provide for a considerable flow of water. The old rails, even when worn out as rails, still have a considerable strength as girders and a continuous layer of them is amply strong enough to carry the roadbed and the traffic over a six-foot opening. The rails may be bound together by means of tie rods run through the webs of the rails, but they may also be confined by stones at each end of the seat course on each abut- ment. Figs. 73 and 74. Another advantage of this form of opening, over the com- mon plan of supporting the ties on stringers or steel girders, is that in this plan the ballasted roadbed is continuous. This is a great advantage both from the standpoint of smooth riding and of safety. 98. Cattle Passes. When an embankment crosses a farm, cutting it in two, it becomes necessary for the road to provide a passage way through the embankment for the use of cattle and farm wagons. The cost of such a structure is compensated by the relief of the company from damages due to the cattle crossing the road at grade. These openings are sometimes built as large stone arch culverts or as old-rail culverts, especially if there is liable to be a storm-water flow throrugh them. Another method is to set two trestle bents at the requisite distance apart; 3-inch planks are set behind the bents to hold the earthwork embankment; the stringers are notched down so as to take up the thrust of the embank- ment. This method naturally applies to embankments which are from about 8 to 15 feet in height. The disadvantage incident to all wooden structures set in earth also applies here. There is also the disadvantage of a break in the continuity of the ballasted road- bed, as well as the danger due to an accident from fire destroying or weakening the structure. When the head room is limited, a first-class permanent construction can best be obtained by the "old-rail" method or something similar. i^.„^;ii^ RAILROAD ENGINEERING. PART II. MISCELLANEOUS STRUCTURES. 99. Water Supply. The railroads of the country spent in 1910 over $13,000,000 in supplying water to their locomotives. Part of this expense is due to the fact that a bad quality of water is so injurious to a locomotive boiler (as well as rendering it diffi- cult for the boiler to steam properly) that the added expense of procuring a suitable supply of naturally pure water or of purify- ing an impure supply is amply justified. A natural water supply is always more or less charged with calcium and magnesium car- bonates and sulphates in addition to impurities of almost any nature which come in as the refuse from factories, etc. Some of these impurities are comparatively harmless, especially if the quantity is not large. But the evaporation of the water precipi- tates the calcium and magnesium, which form deposits on the surface of the boiler. These deposits are injurious in two ways. In the first place the transfer of heat from the fire to the water is less free and there is thus a waste of energy, and in the next place the metal becomes overheated and perhaps "burned." The safety of the metal of a boiler depends on the free transfer of the intense heat of the fire to the comparatively low heat of the water or steam. The prevention of these deposits may be accomplished in one (or both) of two ways; the frequent cleaning of the boilers through the manholes and handholes provided for the purpose, and by the more or less perfect purification of the water before it enters the boiler. The location of the water stations must be at such places and intervals as the service demands. There must always be a supply at the extremities of each division and usually at intervals of 15 to 20 miles between. Of course these intervals are varied accord- ing to the location of convenient sources of supply. The frequent 104 RAILROAD ENGINEERING erection of municipal plants for water supply even in small places has led to the utilization of such plants, since a suitable supply for domestic use is usually satisfactory for boiler use, and since a reasonable charge to such a large consumer would generally be far less than the cost of maintaining a separate plant. In default of such supplies, a convenient intersecting stream, especially when combined with an existing but perhaps abandoned mill dam which will form a convenient storage reservoir, may be utilized. If the stream passes through a limestone region, the water may become so thoroughly impregnated with calcium compounds that a purify- ing plant will become a necessity and then there may arise the question of a choice between a conveniently located station with a necessary purifying plant and a less convenient location but a nat- ural supply of purer water. The chemical purification of water for railroad purposes has become a specialty and must be studied as such. Of course no attempt is made to produce chemically pure water as that would be unnecessarily costly. The reagents chiefly employed are quick- lime and sodium carbonate. The lime precipitates the bicarbon- ate of lime and magnesia in the water. Sodium carbonate gives, by double decomposition in the presence of sulphate of lime, carbonate of lime, which precipitates, and soluble sulphate of soda, which is non-incrustant. The precipitates settle to the bottom of the tank and are drawn off while the purified water is drawn from the upper portion of the tank. Such purification may be accom- plished for a few cents per thousand gallons. Still another method of preventing incrustation in the boiler is to introduce directly into the water tank a "non-incrustant" which, as its name implies, will so change the composition of the impurities that they will settle harmlessly and may be readily blown out. Pumping, Except when water is obtained from a municipal water supply it must be pumped into a tank or reservoir which is usually placed with its bottom 12 to 15 feet above the rails. The pumping may be done with a wind mill, which is very cheap but unreliable, or by an ordinary steam pump operated by a boiler fed with coal, or by a gasoline engine. The last method is becoming very popular, as the pumps require but little attention and the cost of operating them has been found to be as low as one-third or even RAILROAD ENGINEERING 105 one-fourth of the cost of steam pumping. And this is true in spite of the fact that a railroad can usually deliver slack coal or screenings at a pump house alone the line of the road at a cost that may not exceed 30 cents per ton. The cost of pumping to a track tank will usually run at from 2 cents to 6 cents per 1,000 gallons. Tanks. The construction of the piping from a tank and even of the tanks themselves has become a specialty by manufacturing firms who can make and sell them much cheaper than may be done by any ''home-made" method, and, therefore, the details of manufacture need not be here discussed. The tank must be so placed that its nearest face is about 8 feet 6 inches from the track center. When one tank is to serve several tracks or when the supply is taken from a city waterworks, a " stand- pipe" is necessary. This consists essentially of an up- right pipe which stands about 14 feet above the ground where it has a hori- zontal arm about 7 feet long. This elbow may be turned so that the arm is either par- allel or perpendicular to the track. As shown in Fig. 75, the valve mechanism is bur- ied underground and the roof of the pit is protected so that freezing shall be obviated. Track Tanks. The demands for high speed require that long runs shall be made without a stop even for water. Very long runs can only be made by taking on water while in motion from a track tank. These have a length of 1,200 to 1,500 feet and must be laid on a stretch of perfectly level track. A large item in the Fig. 75. Automatic Standpipe. 106 RAILROAD ENGINEERING expense of installing such a plant is the cost of the re-grading which is usually necessary to make the track perfectly level. On the ties and midway between the rails is a tank about 19 inches wide, 6 inches deep and as long as desired. This trough will be made of ^-inch steel plate, stiffened and reinforced with angle bars. Such tanks can only be used by engines which are provided with a scoop on the tender which is lowered at the proper time. The high speed causes the water to rush into the scoop with such velocity that it is easily carried to the top of the leader pipe and over into the tender tank. An inclined plane at each end of the trough automatically raises the scoop and when raised it is auto- matically caught and held so that there is no danger that the scoop shall catch in anything on the track. To prevent the water from freezing in the winter, steam jets should be blown into the water at every 40 to 50 feet of its length. The steam required for this may be many times as great as the steam required for pumping. The cost of such an installation will be upwards of $10,000 and the annual expense about $1,500. Of course these figures will vary with the circumstances. loo. Turntables. The turntable proper is an example in , structural engineering which is now almost universally made of structural steel in shops which make such .work their specialty. Therefore no discussion will be given of the table. But the table must be supported on a pivot which must have an adequate foun- dation which must be able to support a load of perhaps 200 tons. The table revolves in ti pit which is say 75 feet in diameter and which must have a retaining wall about it. Immediately inside of this wall is a circular track on which rollers on the under side of the turntable may run if the load is eccentric. Since this load on the rail may be large it must have an adequate support. If the turntlable must be located on what is originally sloping ground, the masonry may need to be quite deep and heavy, sincG the foundation for the pivot should be especially firm. If the subsoil is not self -draining, it should be thoroughly drained by a thorough sub-drainage and the pit should be drained by a pipe leading to a suitable outfall. A turntable is usually located as an adjunct to a roundhouse, but in any case the location should be made so that the switching that must be done before and after RAILROAD ENGINEERING 107 Bucket towcr fiUTOMATlC £LCCrR/C HOIST Fig. 300-Ton Reinforced Concrete Locomotive Coaling Plant, Provided with "Duplex' Shallow Pit Loader. Courtesy of Roberts and Schae/er Company, Chicago 108 RAILROAD ENGINEERING using the table shall be made a miniiiiiiin. The location of the turn- table in the yard is an item in the subject of Yards and Terminals. loi. Coaling Stations. The cost of removing ashes from the ashpan of a locomotive to a suitable dumping ground and of supplying the tender with coal may amount to a very considerable item unless special facilities are devised for doing the work cheaply as well as rapidly. Such facilities are especially necessary when the number of locomotives to be taken care of is very great. As will be seen from the vertical section of a Roberts and Schaefer concrete coal loader, Fig. 76, the coal car is placed over the 12-foot Fig. 78. Electrically Operated 2000-Ton Coaling Station Fourteen engines can be supplied simultaneously with coal, sand, and water. Courtesy of Link-Belt Company, Chicago pit, a hopper receiving the coal from the car and a traveling loader conveying it to the bucket hoist. By means of the hoist the coal is carried to the top of the tower and automatically dumped into the storage bins. In Fig. 77 is shown the plan view of the bucket pit. Another concrete coaling station built by the Link-Belt Com- pany is shown in Fig. 78. This has a capacity of 2,000 tons of coal and is also provided with sand bins and facilities for taking care of the cinders. 102. Engine Houses. On very small roads, where the num- ber of engines to be housed at any one place will never exceed five RAILROAD ENGINEERING 109 or six, a rectangular engine house with two or three parallel tracks is the cheapest form of construction. But as the number of engines to be provided for increases, and as space grows more valuable, the "roundhouse" is preferable. Considering the space, tracks and switches required to run a large number of tracks into a rectangular house, the roundhouse will accommodate more engines in proportion to the space required. A turntable is a necessary feature of a roundhouse, but since a turntable would naturally be located at any point on a road where an engine house was required the cost of the turntable should not be considered as an integral part of the cost of the roundhouse. Engine houses are used for the minor repairs which contin- ually form a part of the maintenance of any locomotive. There- fore a portion of the tracks should be provided with "pits" or spaces between the rails in which work may be done under the engine. The outer walls are preferably constructed of masonry, although wooden structures are not uncommon on cheaper roads. The roof framing should preferably be of wood, as iron trusses deteriorate very fast under the action of the gases of combustion from the engines. The effect of this is prevented as far as possi- ble by " smoke jacks," which are chimneys suspended from the roof so that they are immediately above the engine stack when each engine is placed where designed. The lower part of this chimney is made adjustable so that it may come down closely over the stack. The smoke jacks are variously made of galvanized iron (very short lived), vitrified pipe (too brittle), cast iron (very heavy), expanded metal and concrete, and even plain wood painted with "fireproof" paint. The floors are best made of brick; cinders are cheap but objectionable, wood is tolerable but lacks durability, concrete is almost an extravagance. Considering that the larger roundhouses may contain locomotives worth several hundred thousand dollars, fire protection is an important feature. One means to this end is the use of rolling steel shutters instead of wooden doors. In Fig. 79 is shown some of the details of what may be considered a typical roundhouse. The figure will illus- trate many of the points named above. 103. Cattle Guards. The prevalent opinion that a railroad company is responsible for the death or injury of any cattle which RAILROAD ENGINEERING 111 may stray on its right-of-way requires especial precautions that cattle, straying along a highway, shall not turn into the railroad right-of-way. The fundamental idea is a structure which is not Fig. 80. Climax Cattle Guard. an obstruction to trains but over which cattle will not pass. The old way was to use a pit about two feet deep and four feet wide Fig, 81. Sheffield Cattle Guard. across which the rails were supported on wooden stringers. But this form makes a break in the continuity of the roadbed and is a 112 RAILROAD ENGINEERING very fruitful source of accidents. This form lias, therefore, been definitely abandoned for "surface" cattle guards. Two forms of these are illustrated in Figs. 80 and 81. The variations in the surface adopted are multitudinous. Usually they are made of iron, sometimes of wood and sometimes of some form of tile or cement which is not subject to decay or rust. Any form must have in addition the fences extending from the sides of the right-of-way up to the ends of the ties. These fences will be "headed" by a short guard fence, as shown in the left of each of the figures, which will prevent cattle from stepping over the end of the fence. TRACK AND TRACK WORK flATERIALS. 104. Ballast. The ideal ballast must transfer the applied load over a large surface; it must hold the ties in place horizon- tally; it must carry off the rain water and thereby prevent freez- ing up in winter; it must be such that the ties may be readily adjusted to the true grade line and it must produce an elastic roadbed. The various materials used for ballast fulfill these con- ditions in variable degrees and at various costs. The most perfect and costly ballast is not necessarily the best for a light traffic road, but on the other hand many light traffic roads are increasing their operating expenses (unconsciously) in a vain attempt to cut them down by using a cheap form of ballast or none at all. The prin- cipal kinds used will be stated with a comment on each one. Mud. This means no ballast except the natural soil. Some- times the natural soil is sandy or gravelly and will make a very Fig. 82. Mud BaUast. good ballast where it occurs, but no matter how good the soil may be in some places, such a quality cannot be depended on to be con- tinuous throughout the line or even approximately so. Consider- ing that a heavy rain will in one day spoil the results of weeks of patient " surfacing " with mud ballast, it is seldom economical to use it if there is a gravel bed or other sources of ballast anywhere RAILROAD ENGINEERING 113 on the line of the road. If it must be used, then the drainage should be exceptionally perfect. The earth should be crowned over the ties in the center and the ditches on each side should be at least 20 inches bejow the base of the ties. This will facilitate the flow of water to the sides. Cinders. The advantages are. an almost perfect drainage, ease of handling, and cheapness, for, after the road is in opera- tion, their use is but the utilization of a waste product. The chief disadvantage lies in the dust produced as the particles are ground up by use. Incidentally, a light traflic road would require a long time to produce enough ashes to ballast the whole road, which would imply a long period of operation with no ballast at all. Slag. In certain places such ballast is very cheaply obtained as a waste product, it being given away for the hauling. It is free from dust and the drainage is perfect. Shells., fine coal^ etc. These are only used when their prox- imity makes them especially cheap. They become dusty in dry weather and correspondingly imperfect in their drainage qualities. They soon become but little better than " mud." Gravel. A large proportion of the railroad mileage of the country is laid with gravel ballast. This is because gravel beds are so frequently found on the lines of roads, from which the gravel Fig. 83. Gravel Ballast. may be dug with a steam shovel, loaded on to cars and hauled to any desired point where it is perhaps unloaded mechanically, the only strictly hand work in the whole operation being the tamping of the ballast in the track. Such methods make the cost per cubic yard very small. The gravel is easily handled and affords almost perfect drainage. If the gravel contains very fine stones or dirt, it should be screened over a half-inch screen to take the fine stuff out. Broken Stone. This is the best form of ballast obtainable, and usually the most expensive. Although hand-broken stone is preferable, the cost of machine crushed stone is so much less that it is almost exclusively used. They should be broken so that they 114 RAILROAD ENGINEERING will pass through a 1^-inch or 2-inch ring. It is most easily shoveled with forks, and this method has the additional advantage that the finest chips and dirt will be screened out. Such ballast holds the ties more firmly than any other form and hence is almost an essential for roads handling a great and heavy traftic at high speed. For a light trafiic road running few trains and these at very mod- erate speed, the use of rock ballast would be almost a useless lux- ury unless the broken stone were very cheap and gravel were expensive or unobtainable. Amount required. Good practice requires a depth of 12 inches of gravel or broken stone under the ties. With 6-inch X 8 -inch ties spaced 24 inches between centers, the amount between the ties will be equivalent to an additional depth of about 4 inches. If the ballast has an average w^dth of 10 feet, say 8 feet at the top and 12 feet at the bottom, then one mile of track will contain 2,607 cubic yards. Broken stone requires a little more than this since there should be a shoulder of ballast on the ends of the ties. (See Fig. 84.) Method of laying. When ballast is laid during the original construction of the road, the proper method is to haul the most of the ballast with carts or on the contractor's temporary track and spread it evenly to the level of the bottom of the ties. Then the ties and rails can be laid and a construction train can haul what- ever ballast is required for surfacing and tamping. When the ties and rails are laid on the bare subsoil and the construction trains with ballast are run over it, the rails are apt to become badly bent and kinked. A compromise between the above methods is to use light construction cars which may run on the standard gauge track without doing the injury that would be caused by standard loaded rolling stock. Cost, The cost of ballast depends on (a) the initial cost as it comes to the road, (h) on the distance from the source of supply to the place where used, and {p) on the method of handling. A RAILROAD ENGINEERING 115 little thought will show the variation in these items for different roads, and therefore any estimates of cost are necessarily approxi- mate. As an average figure the cost of broken stone ballast in the track may be computed as $1.25 per cubic yard, and the cost of gravel may be put at 60 cents. The cost of placing and tamp- ing gravel ballast is estimated at 20 to 24 cents, while the similar estimate for cinders is put at only 12 to 15 cents. The cost of loading gravel on cars, using a steam shovel, is estimated at 6 to 10 cents per cubic yard. 105. Ties. The cost of ties to a railroad is too apt to be superficially considered as the mere market price of the ties deliv- ered to the road. The true cost is the cost of the maintenance of suitable ties in the roadbed for an indefinite length of time. The first cost is but one item in the total cost. A cheap tie must be soon renewed. The labor of renewal is a considerable item of cost. The renewal disturbs the roadbed, which requires adjustment to keep it from getting uneven. The unavoidable unevenness of the roadbed has an actual although uncertain effect on operating ex- penses, increasing the fuel consumption and wear and tear on the rolling stock. It even has some effect on possible or -safe speed. In round numbers, if the cost of buying and placing a good tie is twice that of a cheap tie, and the good tie lasts twice as long as the cheap tie, the economics of the cases are nearly equal. But on the one hand we have the interest on the extra cost of the good tie for the lifetime of the cheaper tie and on the other hand we have the additional cost of maintenance of way when using the poorer ties and the indefinite increase of operating expenses due to a poor roadbed. The annual cost of a system of ties should there- fore be considered as the sum of {a) the interest on the first cost, Q)) the annual sinking fund that would buy a new tie at the end of its life, and (c) the average annual 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 settled in the roadbed, besides the regular track work due to the tie. Such a method of comparison is essential in considering the economics of chemically treated ties and untreated ties. Wood, A good tie must last as long as possible in the ground, must be hard enough not to be unduly affected by "rail-cutting," 116 RAILROAD ENGINEERING must be hard and tough enough to hold the spikes, and finally must be reasonably cheap. Throughout the United States some of the varieties of oak fulfill these conditions (on the whole) better than any other kind. Pine is the second choice, largely determined by its local cheapness. Cedar and chestnut come next, while red- wood, cypress, hemlock, tamarack and a few others have a lesser use. Redwood and cypress are as good as any from the standpoint of mere decay, but they are so soft that the rails cut them and spikes have but little holding power. Since spikes must be driven within a very small area on the face of the tie (for the tie must be placed symmetrically under the rails), when a spike is partially pulled up by the rail tending to turn over, the spike must be re- driven very near its former position. On a curve there is a very great force tending to turn the rail over, and when the holding power of the spikes is not very great, they must be frequently re-driven. Forcing them down in the same hole is almost useless. It thus happens that a tie of soft but durable wood will be ''spike- killed " long before any decay has set in. Redwood ties have been largely used in the West, and when they are protected by tie plates from rail-cutting, their life in a dry climate is very great, especially on tangents. Dimensions, Ties for standard gauge roads are 8 feet, 8 feet 6 inches, and occasionally 9 feet in length. They should be 6 inches to 7 inches thick, and if sawed should be 8 inches or 9 inches wide. If they are hewed, they should have a hewed face of Fig. 85. about the same amount. Sawed ties are a practical necessity on trestles and bridges, and elsewhere they are preferable. When ties are cut from large timber, as is now frequently the case, sawing is a necessity, but there is a general opinion that hewed " pole " ties are more durable than sawed ties. In any case the bark should be entirely removed before they are laid. Spacing. The most common spacing is 24 inches from cen- ter to center, which is the same as 15 per 30 -foot rail, which is a common way of stating it. As many as 20 per 30-foot rail are sometimes used if the ties are small, but as this means only 18 RAILROAD ENGINEERING 117 inches from center to center, the space left for tamping is small and the support to the rail may be even less than that given by larger ties with wider spacing and more perfect tamping. The spacing should not be exactly even as more support is needed at the joints. Two ties are placed so that the rail joint is evenly sup- ported by them. If the rail joints are " staggered," as is usual, two more joint ties are placed somewhat closer together near the middle of the opposite rail. The remaining ties of the allotment (say 15) per rail will be divided evenly in the remaining spaces. Rules for cutting. It should be required that hewed ties should have their two faces truly parallel; the trees should be reasonably straight, one rule being that a straight line passing through the center of one end and the center of the middle shall not pass outside of the other end ; they must not have severe splits or shakes; they should be cut in winter, or when the sap is down; they should be piled for at least six months before being used. When ties are furnished by farmers along the right of way, it is specified that the ties shall be neatly piled crosswise in piles on ground not lower than the rails, the piles to be at least seven feet from the rails. Rules for laying and reneuiing. The largest and best ties should be reserved for joint ties. Whenever spikes are drawn out, the hole should be plugged with a wooden plug which will prevent water from settling in the hole and thus causing rapid decay. Ties should always be laid at right angles to the rail and never obliquely. When renewals are to be made, the requi- sitions are to be based on an actual count of ties to be renewed and not as the result of any wholesale estimate. It is unwise to use a mixed variety of ties in the track so that their size, elasticity and durability are very dif- ferent. This will, by the variation in elasticity, cause rough riding. Cost, Local circumstances very greatly affect the cost, even for the same class of ties. Railroads sometimes succeed in monop- olizing the tie production in the territory through which they run by refusing to haul ties for any other customer or railroad, except at prohibitory rates, and control the price somewhat by refusing to pay more than the lowest limit at which the local people will Fig. 86. Wooden Tie Plug. 118 RAILROAD ENGINEERING supply the ties. The best ties procurable in a section can thus be procured for 45 to 50 cents per tie, and where common labor is very cheap this price is cut even to 25 cents. On the other hand, the very best of large oak ties will often cost 75 to SO cents. In view of the above variation in price, any estimates must depend on local conditions. io6. Rails. The form of rail section popularly known as the A.S.C.E. section, was adopted by a committee of the American the A.S.C.E. section, was adopted by a committee of the American Society of Civil Engineers in 1893, after a great deal of discus- sion and study. That form is now used by the most of the rail- roads of the country. The numer- ical dimensions and angles shown in Fig. 37 are constant for all weights of rail. The letters indi- cate the variable dimensions, which are given in the following tabular form : Pig. 87. Am. Soc. C. E. Standard Rail Section. Dimeir- sion, in inches. Weight per yard in pounds. 40 45 60 65 60 65 70 75 80 85 90 95 100 A B CifeD E F G 1% II % Iff 2 U m ItV 2% 3% H 2tV 2k if M 2U IH 2% n 4M 1/^ 4tV M 2% 1/^ 2tV If 4% 11 2JI IH 2M \\ 411 11 2|f 111 2X If 5 % 2% IX 2^ If 2% l|f 2% tV 5% If 2ff m 2H \\ 2|f 2% 5% li m About 1909 the American Railway Engineering Association proposed two types of sections (A and B). Series A is designed to meet the wishes of those who desire a rail with a comparatively thin head and high moment of inertia, and series B for those who believe that the head should be narrow and deep and that the moment of inertia is comparatively unimportant. The radius of the upper corner of the head is increased from \" to \" , The side of the head, instead of being left vertical, has a flare of 3° 35' for the A type and 3° for the B type. In 1914, the Rail Committee reported RAILROAD ENGINEERING 119 that the A.S.C.E. sections were still extensively used and appar- ently had not been largely replaced by the proposed new sections. The feature in rail design which has excited the most discussion is the radius of the upper corners of the head. Rail wear begins there and rails with sharp corners will wear longer than those with ..i*f Fig. 88, Rail Joint. larger radii. The rapidity of the rate of rail wear after the corner has worn off is one proof of this, and so from the maintenance of way standpoint sharp rail corners are desirable. But excessively sharp rail corners produce excessive wear on the flanges of the wheels, not only wearing out the wheels quickly but even rendering them dangerous and liable to cause a derailment. The compromise of yq" radius, adopted in the A.S.C.E. design, was increased to \" in the A.R.E.A. design. Weight, The weight of rail that should be used on any road is an exceedingly important financial and technical question. It is the largest single item of expenditure in the construction of a road, and the temptation to cut* down the item by 5 per cent or 10 per cent is very great. For all ordinary sizes the price per ton is uniform, and therefore a reduction in weight per yard means a corresponding reduction in the cost. But it should be considered that what is desired is a rail that has stiffness and strength^ no matter how much it weighs. Fig. 89. Weber Rail Joint. 120 RAILROAD ENGINEERING It can readily be proved that if all sizes of rails had exactly- similar cross -sections (which is nearly true) then the stiffness of a rail varies as the square of the weight and the strength varies as the f power. This means that if we add 10 per cent to the weight (and therefore to the cost) of the rail we are adding 21 per cent to the stiffness, and over 15 per cent to the strength. As a more concrete example, suppose that some desire to make the weight of the rail for a road 60 lb. per yard, and others wish to use a 70-lb. rail. At $30 per ton (of 2,240 pounds) the difference of cost w411 be $471.42 per mile of single track. But on the other hand, although the cost is increased by 16§ per cent, the strength is increased 26 per cent, and the stiffness is increased 36 per cent. The increase in stiffness is more than double the increase in cost. Unfortunately there is no ab- solute criterion as to the amount of stiffness or strength required since it depends largely on the unknown, uncertain and variable tamping of the ties and the support which the ties receive from the ballast. But the above relative figures hold good, and consid- ering that a stiff track means decreased rolling resistance, higher Fig. 90. Bonzano Rail Joint. Fig. 91. Continuous Rail Joint. speed and greater safety, a considerable increase in weight over that minimum on which it would be possible to run trains is not only justifiable but is a measure of true economy. As a general statement, it may be said that 60 lb. per yard is the lightest 132 RAILROAD ENGINEERING 121 weight which should be used on a standard gauge road running ordinary rolling stock, no matter how light the traffic. Roads with a fair business should have 70-lb. rails. The great trunk lines are relaying with 100-lb. rails on the heavy traffic divisions, and usually have as heavy as 85 -lb. rails on all but the small branches. Length. The standard specifications proposed by a committee of the American Railway Engineering and Maintenance of Way Association in 1902 contained this clause: "The standard length of rails shall be 33 feet. Ten per cent of the entire order will be accepted in shorter lengths, varying by even feet down to 27 feet. A variation of J-inch in length from that specified will be allowed." Fig. 92. Wolhaupter Rail Joint and Section Through Center. During late years much experimenting has been done with the idea of increasing the length of rail, and a considerable amount of rails of 45 and even 60 feet has been laid. These have the un- doubted advantage of saving a proportionate number of rail joints, which are always a source of trouble, but at the same time the allowance for expansion which must be made at every joint must be proportionately increased. The above recent standard specifica- tion apparently indicates that the increase in length has not proven desirable. 107. Rail Joints. The action of a heavy wheel rolling on an elastic rail is to cause a wave of elasticity to run in front of the point of contact. A perfect track is one that will keep that wave of elasticity perfectly uniform, which requires that the rail joint 122 RAILROAD ENGINEERING should have the same strength and stiffness as the rail. Only a welding of the rails, making them continuous, would accomplish this. Any rail joint which is as strong as the rail is necessarily much heavier and stiffer. Passing by the older forms which have now become obsolete, we have in Figs. 88 to 93 the forms which are now competing for adoption. The '' angle bar " is still used more than any other kind, but many of the other forms have demonstrated their reliability and fulfilment of the requirements as nearly as may be hoped for. Nearly all of these designs are used exclusively as "suspended" joints rather than as "sup- ported" joints, the difference being, as the name implies, that a suspended joint is placed between two ties so that each end of the joint has an equal bearing on the ties; a supported joint is set directly over a tie and hence must get practically its whole sup- Fig. 93. Atlas Suspended Rail Joint. port from that one tie, unless the joint is so long that it rests on the adjacent ties, thus making it a " three-tie" joint. Angle bars are usually about 26 inches long. Of course, the bars, of whatever kind, should be so made that they will fit closely under the head of the rail and also have a close fit on the top of the flange. This means that every rail joint must be made with special reference to the particular design of rail with which it is to be used and that it will fit no other design. For the smaller sizes of rails and on light traffic roads, four-bolt angle bars are used, but the longer and heavier bars are usually made with six holes. The holes are made in a somewhat elliptical form and the track bolt has a corresponding form immediately under the head. The bolt is thus prevented from turning when the nut is screwed on or off. The holes in the rail are made about J inch larger in 134 RAILROAD ENGINEERING 123 diameter than the bolt. This is to allow room for expansion of the rail due to temperature. Insulated Joints. Rails are very frequently used to form an electric circuit as part of the system of signaling. As an item in the system it is required that certain joints shall be so made that no current shall pass between adjacent rails. pv oped will not be so great that the rails may L ,y J ' not slide in the joints during temperature r I changes. On a straight track the contrac- tive pull due to a fall of temperature is so great that no possible gripping of the bolts could prevent slipping, but it is quite possi- ble that when rails expand, and especially when on a curve, the resistance to slipping might be so great that the track would bulge out of alignment instead of slipping at the joints. Such an effect does actually take place when the allowance for expansion is insufficient and the rails continue to expand after they have butted end to end. Another requirement is that the bolts shall not turn while the nut is being turned. This is accomplished by an enlargement of the bolt just under the head, as shown in Fig. 101. This fits fairly closely in a corresponding oval-shaped hole in the angle plate. The sizes shown in the figure are about what should be used with a 70 or 80-pound rail. Heavier rails require a longer bolt and one that is proportionately heavier. The type of rail joint used, and also the type of nut lock if any, will determine the required length of bolt, while the weight of rail should deter- mine the diameter. The diam- eters vary from £ inch to 1 inch, and the lengths from 3 inches to 5 inches. 112. Nut Locks. There are three types of nut lock — (^a) those which have an elastic cushion under the nut which absorbs the vibrations that would otherwise loosen the nut, (5) those by which the nut is made to grip the bolt (by some unusual device) so that vibration will be insufficient to loosen it, and (c) the "positive" type, in which the locks arepre- Fig. 102. Ajax Tail Washer. 138 RAILROAD ENGINEERING 127 vented from turning by some definite and positive mecLianical check. The '' Ajax Tail Washer," shown in Fig. 102, is a sample of the first class, although it also has some of the elements of the third class, since the sharp steel points will tend to bite into both the under side of the nut and^the side of the angle plate where it rests whenever there is a tend- ency for the nut to turn backward. These points merely drag and slip when the nut is being tightened. The Columbia nut lock, shown in Fig. 103, is a sample of the second class. The nut is compound, the inner piece being a four-sided frustum of a pyramid, the edges being rounded. This fits into a corresponding recess in the outer piece. The inner piece is also cut through so that it may be slightly squeezed together. The pyramidal form requires both pieces to turn to- gether. When the outer piece comes in contact with the angle plate it is forced back (relatively to the inner piece) which squeezes Fig. 103. Columbia Nut Lock. Fig. 104. Gordon Nut Lock. the inner piece together and causes it to grip the bolt. The more the nut is turned, the tighter the grip. The Gordon nut lock, shown in Fig. 104, is a sample of the third class, although it is designed to be used only w^ith the form of angle plate which is shown. In the form shown the square 128 RAILROAD ENGINEERING nuts must be turned until one edge is exactly on line. A one- eighth turn forward or back will always accomplish this. Thus when the bar is slipped in all nuts are absolutely prevented from turning. The above designs have been selected as mere samples of each class from a great multitude of designs of greater or less merit which are on the market. LAYING TRACK. 113. Surveying. After the earthwork is completed and the culverts and bridges are built, the center line of the track must be re-located on the roadbed surface of the fills and cuts. Reference points should have been established during the original survey so that by the intersection of two radii swung from permanently established points the beginnings and endings of all curves may be re-located. Then all intermediate stations should be filled in. A line of levels should then be run and the an-reement of these • RIGHT. WRONG. Fig. 105. Right and Wroug Method of Laying Ties. levels with the designed grade should be determined. If the levels of the cuts and fills has been followed with sufficient closeness during construction, there should be no discrepancy except that the levels of fills should be somewhat higher than that called for so as to allow for subsequent settlement. 114. Laying Ballast. This has already been discussed in §104, as has also the policy of laying the ties and rails first and then drawing the ballast in a construction train on the poorly supported track. 115. Laying Ties. If the ties have been sawed to an exact length, the alignment of one end will of course line up the other but when ties have been hewed and chopped off and sometimes even when they have been sawed, there is a range of several inches in their length and then it is required that they shall be aligned at one end or the other. A little stick may be furnished the track- RAILROAD ENGINEERING 129 men as a spacer, but with a little experience they will space the ties as closely to the required spacing as is necessary. The ties should always be laid with rings convex upward rather than con- cave. Of course a pole tie, when it is perfectly symmetrical, will be the same either way, but there is usually a choice, as is shown by the figure. When the rings are concave upward there is a greater chance for water to soak in and cause decay. Turning the tie the other way, the w^ater will shed off more freely. ii6. Laying Rails. Rails should be laid so that the joints are staggered as nearly as possible. This requires a half-rail length at the start. But the difference of length of the outer and inner rails of a curve will disturb the arrangement of the joints, no matter how perfectly it may start. These differences may be neu- tralized by selecting rails which are a foot or tw^o shorter than the usual length. But the occurrence of a switch will require a read- justment of the joints, and may require a rail cutting so as to bring a joint where desired. Yery short lengths of rail should be avoided. If a full length rail comes a few feet short of a point where a joint 'tnust be made, it should be cut so that both pieces shall have a fair length. The rails are first laid approximately in position and end to end. When placing the joints on the rails, allowance must be made for rail expansion due to temperature. The theoretical amount to be allowed is .0000065 of the length for each degree Fahrenheit. If it could be readily determined just what is the temperature of the rail (w^hich is possibly much higher than that of the air) at the time the rail is laid and. also the highest and lowest temperature that it will ever attain, the problem would be comparatively simple, but the fact that these quantities are so uncertain seem to render useless any attempt at an exact calculation and to justify the rough and ready rule of '-allowing -f^ inch for coldest w^eather, J-inch during the spring and fall, and J^ -inch during the very hottest w^eather." The allow^ance of yig-inch during the very hottest weather is apparently based on the idea that the rails should never be allowed to butt up against each other, for then any additional expansion will cause the rails to buckle. If a rail was laid when its actual temperature was 60° F., its length of 33 feet would be increased by about ^ inch if its temperature were raised to 130 RAILROAD ENGINEERING 120°, as might readily happen under a burning summer sun when the temperature of the air in the shade was perhaps 100°. A prac- tical method of making an allowance which would be sufficiently accurate would be as follows: Place a bulb thermometer (one without a metal frame) so that the bulb lies against the rail ana then cover it up so as to protect it from the air and so that it will assume the temperature of the rail as closely as possible. The expansion of a 33-foot rail for each degree is .0000065 X 33 X 12 =- .002574 inch. If w^e allow 120° (some allow 150°) as the maximum beyond which it is assumed that the temperature will never rise, then the difference between this maximum and the ascertained temperature of the rail, when multiplied by the above allowance per degree, equals the gap to be allowed at each joint. Strips of sheet metal of the required thickness should be furnished to the trackmen. These strips are placed temporarily between the rail ends which obviates any necessity for measuring on their part. When the joints have been bolted up, one line of rails is spiked so that they are at the proper distance from the ends of the ties. Then by using a "track gauge" at every other tie the other line of rails may be spiked down. The intermediate ties are then spiked. " Standard" gauge, which is in almost universal use in this country, is 4 feet 8^ inches = 4.708 feet. Although the gauging should be all right for these other ties, the gauge should be at hand to check the previous work, especially if it is on a sharp curve. Track instruc- tions frequently specify that rails should be previously bent before laying around curves, or in other words, that the rails should have the proper curve when lying freely on the ties. Of course the necessity for this increases with the degree of curvature, it being unnecessary for very easy curves. The practical trouble comes at the joints; the rails instead of having a common tangent will intersect at an angle which is de- structive both to the track and the rolling stock when trains are run at high speed. The ideal method is to have the rail bending done by rollers in a rolling mill and this method is almost a necessity for the very sharp curvature employed on some electric roads. The field method is to use a "rail bender" which bends the rail in RAILROAD ENGINEERING 131 lengths of about two feet and which must be operated very care- fully and skilfully to avoid ruining the rail. A rail is bent until, when a string is stretched from the inside of the head at one end to the inside of the head at the other end, the distance from the middle point of the string to the inside of the head at the middle of the rail is as computed below: In Fig. 106, since the triangles AOE and ADC are similar, AO : AE :: AD : DC, or E = -^ AD^ -f- X. When as is usual, the arc is very short compared with the radius, AD = -^ AB ^^' ^^^' very nearly. Making this substitution, we have Inverting the formula we have the formula required for present use: chord^ , , . , . X = -g^ (very nearly) (55) Although not mathematically accurate, the maximum error in any practical case is far within the attainable accuracy using a string. Example. What should be the middle ordinate for the outer rail (83 feet long) for a 6 degree curve ? We will call the chord 33 feet since the slight inaccuracy involved only tends to neutral- ize the inaccuracy of the fornriula. R = 955.37 + 2.35 = 957.72. Then 33^ (which equals 1089) divided by (8 X 957.72) = .142 foot or 1.70 inches. If a similar calculation is made for the inside rail the difference in the ordinate is less than .01 inch, which shows that unless the curvature is excessively sharp there is no need to make the allowance for half -gauge (2.35, as is done above) nor even to use great accuracy in the decimals. A table giving the middle ordinates for 33-foot rails for different degrees of curvature is a desirable part of the equipment of each track foreman. The spikes on the opposite sides of a rail should be driven " staggering," so that there will be less tendency to split the tie. The direction of the staggering should be reversed at the two ends of the tie, so as to prevent a loosening of the hold of the spikes, 132 RAILROAD ENGINEERING such as would occur if the reverse method were used and the tie were to become displaced and not perpendicular to the rails. Such an item of construction, while very simple, is of vital importance. 117. Surfacing. Track centers (stakes) having been placed in line, the alignment of the track is made perfect. The rail lay- ing should have been done with the rails a few inches below their proper gi-ade. Then jacks are placed under the ties (or rails, as most convenient) and the track is raised to grade, as given by grade stakes which should have been previously set. Using tamp- ing picks or shovels, the ballast is jammed under the ties until , . they are solid at the desired grade. Picks or ^m^ tamping bars are best for tamping broken J^ ^^ stone ballast, but gravel can be most easily |HL ^W tamped with shovels. fl^Bj^F^ 118. Super-elevation of the Outer Rail ^^^|V on Curves. It is one of the demonstrations ^^HT of physics that the force required to make a ^^g^ mass move in a circular path equals QiV^ -^ |H^ ^R, in which G is the weight, v the velocity ^H in feet per second, g the acceleration of the ^Ml force of gravity in feet per second in a sec- ^^^SSk. Olid, and R the radius of curvature. If the ^^^^^^P rails on a curve were level transversely, such a force could only be furnished by the pres- sure of the wheel flanges against the rail. To avoid this objectionable pressure, the outer rail is elevated until the inward component of the inclined wheel pressure equals the computed centripetal force required. In Fig. 108, oh may represent the resultant pressure on the rails at the same scale at which oc represents the weight G. Then ao is the required centripetal force. From similar triangles, we may write nn : sm w ao : oc. Call g = 32.17. Call R = 5730 -r- D, which is sufficiently accurate for the purpose. Call v == 5280 Y -^ 3600, in which V is the velocity in miles per hour. 77in is the distance between rail centers, which for an 80-lb. rail and standard gauge is 4.916 feet; sm is slightly less than this. As an average value, call it 4.900, which is its exact value when the superelevation is 4| inches. Calling sn = e, we have Pig. 107. Trip Ballast Gang Jack RAILROAD ENGINEERING 133 ao . ^^ Gv 1 e = S7/1 — — 4.9 — T^ -77- OG gli G e = .0000572V^D 4.9 X 528Q^V^D 32.17 X 3600^ X 5780 (56) >«-%c Studying the above formula, it will first be noticed that the required super-elevation varies as the square of the velocity, which means that a change of velocity of only 10 per cent would require a change of super-elevation of 21 per cent. Since train velocities over any road are so very variable, it shows that it is impossible to make any super-elevation fit all trains even approximately. There are several approximations in the above formula, but none of th3m will affect the result as much as a change of less than one per cent in the velocity. Practical Rules. A very simple and commonly used rule is to elevate one inch for each degree of curvature. This rule agrees with the above formula when the velocity is about 38 miles per hour. If a train is running slower than the speed for which the super-elevation was designed, the practical efiect is to relieve the pressure against the outer rail which still Q;xists in spite of super-elevation on account of the necessity of turning the groups of four or six wheels under a truck or engine. Therefore the better plan is to elevate for the fastest trains. Thirty-eight miles an hour is so near the max- imum for a light traffic branch line, that the above rule is very fair, although, of course, not so good as a more accurate one. Another rule, which is especially good for track maintenance when the track foreman may not even know the degree of curve, is developed as follows: Assume that a? in equation 55 is equal to e in equation 56, and we have Fig. 108. chor(P ~8R" .0000572 Y^D but since D = 5730 -^ R, we have chord' = 2.621 Y' and chord = 1.62 V (57) 134 RAILROAD ENGINEERING Assume that the limit of 50 miles per hour is set as the speed of the fastest trains, then chord = 1.62 X 50 = 81 feet. This means that if a string or tape, having a length of 81 feet, is stretched between two points at that distance apart on the inner head of the outer rail, the length of the ordinate at the middle of the string equals the required super-elevation for 50 miles per hour. Similar computations can be made and tabulated for all other desired speeds. On double track, since the speed on an ascending grade will almost certainly be less than the speed of trains coming down that grade, there should theoretically be a difference in the super-elevation to allow for this difference of speed. On some roads the track instructions contain specific instructions to allow for this. SWITCHES AND TURNOUTS. up. Switch Construction. The universal method of keep- ing the wheels of railroad rolling stock on the rails is to put Pig. 109. Stub Switch. Fig. 110. Point Switch. flanges on the inner edges of the w^heels. When the wheels are to be led away from the main track, it must be done by creating a new pathway for these flanges. This is done by leading the wheel flanges through the rails or by raising the wheels sufficiently so RAILROAD ENGINEERING 135 that they may pass over the rails. Both methods will be de- scribed. The method of leading the flanges through the rails is most commonly used since it does not require raising the rolling stock over the rail. \ AYhen the rails are first led out from the main track, it must be done by one of two general methods, the stub-switch method, illustrated in Fig. 109, or by the point-switch method, illustrated in Fig. 110. Of course these figures are only diagrammatic and it should be at once understood that in these figures as well as in many others in this chapter, it has been necessary to use very short radii, very wide gauge, and very large frog angles in order Fig. 111. Details of Point Switcli. to illustrate the principles by figures which are suitable for the page and which would at the same time be intelligible. The use of the stub switches is now confined to the cheapest of yard work or private switches which run off from sidings. They should never be used in any main track. Their construction may be implied from Fig. 109. The pair of movable rails are tied together at the proper gauge by tie rods. The two pairs of stub ends are of course fixed. The details of a point switch are illus- trated in Fig. 111. Note that one rail on each side is absolutely unbroken. The other rail has nearly all of the head cut away and a part of one flange. The other flange and the web, with that part of the head immediately over the web still remains. The tie rods which are clearly shown connect this pared-down rail with a 136 RAILROAD ENGINEERING similar rail on the other side. The last tie rod has an extension to which the switch rod from the switch stand is attached. The moving rail slides on tie plates which have rail braces on the outer ends which stiffen the rail against the unusual lateral strain to which it is subjected. The angle of these switch points varies from 0° 52' to 2° 36'. /Switch Stands, One type of switch stand, which also com- bines a semaphore (or signal which shows its position) is shown in Fig. 113. Switch Stand. Fig. 112. The mechanism is of course covered, the cover being indicated by the faint lines. The type shown is but one of a multitude for which there is no space here. Guard Bails. These are shown opposite the frogs in both Figs. 109 and 110. They obviate any danger of the wheel run- ning on the wrong side of the frog point and also save the frog point from excessive wear. The flange-way space between the heads of the guard rail and the wheel rail must therefore not exceed a definite quantity, which is made about two inches. Since this is less than the distance between the heads of two ordinary sized rails when placed base to base, to say nothing of any space RAILROAD ENGINEERING 137 for spikes, the base of the guard rail must be cut away somewhat. These guard rails are made from 10 to 15 feet long and are bent a few feet from each end so that there shall be no danger that a wheel flange shall strike the ends. Frogs. When the outer switch rail reaches the opposite main rail, the wheel flange must either pass through the head of the main rail or the wheel must be raised so that the flange may pass over the rail. The most commonly used frogs are those of the type of which the wheel flange passes through the head of the rail. The geometrical outline of such a frog is shown in Fig. 113. The frog number may be found by dividing the distance from the *' point " to any chosen place by the width of the frog at that place, or in the figure ch -f- ah. But since c is the imaginary intersection of the sides produced and is not easily determinable with accuracy on the frog, it is sometimes easier to measure the Fig. 113. Diagram of Frog. width at two places {ed and ah) and then divide the sum of those widths by the total distance sh\ this will give the same result as before. This measuring may be done with any convenient unit of length such as a pencil or a spike. Find the place where the width of the frog just equals the unit of length and then step off that distance to the " point." The fundamental objection to all frogs of this type is that they make a break in the main rail which causes a jar when a train is run over the frog at high speed. If the frog is made " stiff" as is illustrated in Fig. 114, the track has the advantage of being literally stiff, but the wheels have to run over the gap. The design shown in the figure aims to obviate any drop of the wheel at any point and this will be fairly accom- plished as long as the hardened steel faces can resist the wear which is very severe in the older and commoner designs. 138 RAILROAD ENGINEERING The '' spring-rail" frog, illustrated in Fig. 115, is an attempt to obviate the gap for main line trains. Wheel flanges running on to the switch force back a por- tion of the main track rail which is normally held in place by a heavy spring. Running on to the switch is supposed to be done at comparatively slow speed, which permits the rail to be forced back without danger of derailment. But since the main rail is kept in place by the pressure of a spring, the frog lacks the stiffness of a "stiff" frog. The method of raising the wheel and carrying it over the main rail is illustrated in Fig. 116, which shows one of the many devices to accomplish this end. The method has the very positive advantage of leaving the main track absolutely unbroken. In Fig. 117 is shown a method of avoiding a break even at the switch. The switch rails are at the level of the main rails at the switch point but gradually rise higher until the wheel flange is high enough to cross over the main rail. Such a switch must be operated at slow speed. 120. Mathematical Design. In all of the following demonstrations, the track lines repre- sent the gauge lines or the lines of the inside head of the rails. The older formulae, which are still in extensive use on account of their simplic- ity, all assume that the switch rails are bent to arcs of simple curves extending from the switch point to the frog, and that they are tangent to Section A-A Fig. 114. Anvil-face Frog. the main rails at the switch point. On account of its common use and also because it forms a fitting introduction to the more RAILROAD ENGINEERING 139 exact method, it will be given. In all of the fol- lowing demonstrations, the following notation will, for simplicity, be kept uniform. R will represent the radius of curvature of the main track, if it is curved, and r is the radius of the switch rails. F will always represent the frog angle, and a the gauge of the track. L will rep- resent the "lead" or the distance measured on the main track from the switch point B to the frog point F. The angle FDD in Fig. 118 equals the angle F, and BD is the versed sine of F to the radius FO. From this relation we may derive the equa- tion 2 ^ vers 1 ^ ^ also, since BF -^ BD = cot-^F, BD = g and BF = L, we have L = ^cot-^F (59) Also, L= [r -{- -jg) BinF (60) o 140 RAILROAD ENGINEERING and QT= 2r8m~^F (6l) All of the above formulae involve the angle F. Reference to Table III* will shov^' that with one chance exception the values of F are always odd and the accurate computation of their trigonometrical functions is tedious. Fig. 119 shows that the ratio of the length to width of a frog, or jr?^ -r- ah, which is called ??, is also equal to -p- cot -jy- F. This relation can be used to derive the following marvellously simple formulae: i 1 1 ^^H^^^^^^HS^^^^^^^^^^hVS 1 Fig. 116. 1 , 14 Since L = y cot-^ P^, and n = -— cot-^ F, we may at once derive the equation L = 2gn (62) But in Fig. 120 the line QZ, drawn midway between the rails, bisects DF at Z and also, since DQ is one-half of DB, QZ is one- half of BF or = -g-L. OQ = r and the angle ZOQ = -^ F. ♦See Webb's "Trigonometric Tables," pubUshed by American School of Correspond- ence, Chicago, 111. Price, 50c. RAILROAD ENGINEERING 141 Then r -^ -^Ti = cot -j- F, from which /' = nJj Combining equations 61 and 62, we have 7' = 2gn^ (63) (64) The above relations only lack the merit of correctness of application to make the whole subject very simple. They were first devised when stub switches were in universal use and although Fig. 117. it is theoretically possible to make a stub switch conform to these lines, it is impracticable even there. But with point switches, which are in almost universal use, the switch rail makes an angle varying from 0° 52' to 2° 36' with the main rail. The frog rails are also made straight. The effect of each of these changes, taken separately, is to shorten the lead. The combined effect is to shorten the lead from 15 to 25 per cent. In Fig. 121, DM represents the straight point rail and HF the straight frog rail, the two being connected by the 142 RAILROAD ENGINEERING arc MH, tangent to both. The central angle of this arc is there- fore (F - a), a being the angle (MDN) of the point rail. The chord MIX makes an angle with the main rails which equals Call FH =/and MN := A-. Then HM sin -^(F + a) = ^-/sin F-^. But HM = (^ + -g- ^) ^ sin -g- (F - a). Substituting this value of HM in the previous equation and solving for (^ + -9-^) we have ^-/sinF->^ Fig. 118. (^ -f 4 '^^) = 2 sin -^ (F + a) sin -^ (F - a) (65) _g -,/'sin ¥ -k cos a — cos F ST=2rsin-i(F-a) (66) ^ The lead BF = L = HM cos -i (F + a)+/cosF + DN Fig. 119 o"-- - .^> • 1 F I X ' \ .\ 1 A \ _\\ _, »'T -\f\ ^'' \ ^ \ ' i \ -B 1 Fig. 120. =:(^-/sin F-^)cot-^(F + a) +/ cos F + DN (67) If (^ + -9- ^) has already been computed numerically from equation 65, it will be more simple to compute L as follows: 1^'= 2(r + i- g) sin -i (F-a)cos-i (F + a)+/cosF + DN = C^ + "2- f/) (sin F - sin a) +/ cos F + DN (68) 154 RAILROAD ENGINEERING 143 If the lead is computed for a turnout from a straight track using a No. 9 frog, a straight point rail and frog rail of the dimen- sions given in the middle section of Table III*, it will be found that the lead becomes 72.61 instead of 84.75, the corresponding dimension assuming that the lead rails were circular through- out. Table III* was computed on the basis of the above equa- tions and the point switch di- mensions which are in general use. The two references to sec- tion numbers in the table are to se(^tions in Webb's "Railroad Construction," from which the tables were taken. 121. Turnout from the Outer 5ide of a Curved Track. the dimensions of a turnout, from a curved track on the basis of using straight point rails and straight frog rails, it not only renders the demonstration exceedingly complicated, but it would involve assumptions regarding the mechanical construction which probably would not be followed in practice. Therefore the following dem- onstration is given with the purpose of showing the effect on the Fig. 121. When it is attempted to compute Fig. 122. switch dimensions of curving the main track, the switch rails being circular throughout, and then drawing a reasonable inference as to the dimensions which should be followed for point switches from a curved main track. In the triangle FCD, in Fig. 122, we have *See Webb's "Trigonometric Tables," published by American School of Corresjwnd- ftTiffi. Phina.P-n Til. 'Pricfi. TtOc 1 kc 144 RAILROAD ENGINEERING (FC+CD) : (FC-CD) : : tan^ (FDC+DFC) : tan^(FDC -DFC); but \ (FDC + DFC) = 90° - -i- Q, and 4" (FDC - DFC) = ~ F; also FC+CD = 2R and FC-CD=^; .-. 2R : ; but <^ = (F - (9) then 1 /t. , 1 \ sin (9 , . The lead, BF = L - 2 (r + 4" ^) ^^^^ 4^ '^ (^0 A study of the three equations above will show that as the curvature of the main track increases and R grows less, tan 6 increases and ^increases. Then (F - 6) decreases and r increases. When Q = F, as it readily may, (F - ^) = and r becomes infin- ity, that is, the switch rails become straight. If 6 becomes greater than F, sin (F - 6) becomes negative and /' becomes negative. The interpretation of this is that the center of the switch track will be on the same side as the center of the main track. The figure will then correspond with Fig. 123 except that the positions of O and C and also of <^ and 6 will be transposed and also that " main track" should read "side track." Equations 73 and 75 will be the same as before, but equation 74 will be changed to If we call d the degree of curve corresponding to the radius r, D the degree of curve corresponding to the radius R, and d^ the degree of curve of a turnout from a straight track for the same frog angle F, it will be found that d ==d' -D very nearly. It RAILROAD ENGINEERING 145 will also be found that the " lead " as computed above and as com. puted for a straight track will agree to within a few inches and frequently to within a fraction of an inch. Example. Compute from the above equations the values of L and r (and then of d) for the cases when the main track has a 4° degree curve and when it has a 10° curve; solve them for num- ber 6, 9 and 12 frogs. This makes six cases. Compare them with values computed by the approximate rule. In all these cases it may be shown that the discrepancies are very small. If such calculations are made for very sharp curves and for very large frog angles (which must be considered as bad practice), the discrepancies would be considerable, but since such turnouts (if ever made) should be operated at very slow speeds, the errors would have but little practical importance. Therefore we are justified in applying the approximate rule for turnouts from a curved track — use the same "lead " as for straight track; the de- gree of curvature for the switch rails to the outside of the main track will be the difference of the degree of curve for the main track and the tabular value for the degree of curve of the switch rails; for a turnout to the inside of a curved main track it may be similarly shown that the proper degree of curve for the switch rails is the suirt of the degrees for the main track and the tabular value for the switch rails from a straight track. Also, since it may be shown that the effect of using straight point rails and straight frog rails is to shorten the lead and to lessen the radius in approximately the same proportion, it may be assumed without material error that we may apply the same rule 'as above, and instead of taking the values of " lead " and '' degree of curve " for the switch rails from the tabular form which uses circular switch rails throughout, we may take them from the revised form using straight switch rails and straight frog rails and apply the same rule. 122. Turnout from the Inner Side of a Curved Track. By the formation of precisely similar equations as were used in the previous section, we may derive the equation tan^e = ^ (73) 146 RAILROAD ENGINEERING From the triangle OFC we may derive OF : FC :: sin (9 : sin (F + 0\ from which (.+ |,) = (R-i-,) sin 6 The lead BF = L sin (F + ^) ^'^'^^ 2 (ll - 4 ^) '''' i ^ ^75) The details of the solution of the above equations should be worked out by the student; also a numerical dem- onstration of the fact, already referred to, that the degree of the turnout [d) is very nearly the sum of the degree of the main track (D) and the degree [d') of a turnout from a straight track when the frog angle is the same. It will be found that the discrepancy in these cases is somewhat larger than in the previous case, although it is still so small that it may be neglected when the curvature of the main track is small. An in- spection of the figure will show that when the curvature of the main track is sharp the curvature of the turnout is very excessive. Such conditions should be avoided if possible, that is, a turnout should o'^-'^lf not be located on the in- "*-^^ side of a very sharply ''^^^^ curved main track if it can be avoided. 123. Numerical Examples. 1. Deter- tJ ^-"- mine the lead and the ra- dius of curvature for a Fig. 124. turnout to the outside of a 4° 30' curve using a No. 8 frog and a point switch. 2. Determine the lead and the radius of a curvature for a turnout to the inside of a 3° 40' curve using a No. 7 frog and point switch. RAILROAD ENGINEERING 147 In each of the above examples use the switch point angles, length of switch point and length of straight frog rails as given in Table III*. 124. Connecting Curve from a Straight Track. The "con- necting curve " is that part of the siding between the frog and the point where the siding becomes parallel with the main track, or the distance FS in Fig. 124. Call d the distance between track centers. The angle FO,R must equal the angle F. If we call /•' the radius of the connecting curve, we may say (^'-4^) d vers FR 0"-4O sin F (76) (77) The distance FR may be shortened somewhat by the method indicated in Fig. 129. Theoretical accuracy would apparently re- quire that we should consider a short length of straight track at the point F. The effect may readily be shown to shorten the radius / and to shorten the distance FR by an amount exactly equal to the length of the straight frog rail, but in actual track laying such a procedure might be consid- ered a useless retinement. And therefore in this case as well as in the succeeding similar cases, the effect of the straight frog rail will be ignored. It should likewise be noted that the figure has been drawn for simplicity as if the switch rails were circular. But since the point O^ has no connection with the demonstra tion, it is immaterial what is the form of the switch rails back of F. the following similar demonstrations. 125. Connecting Curve from a Curved Track to the Outside. As in the previous case the only required quantities are the radius r of the connecting curve from F to S, Fig. 125, which *See Webb's •'Trigonometric Tables," published by American School of Correspond- Pig. 125. This same remark applies to 148 RAILROAD ENGINEERING must be determined from r and the angle (= F + "^/r). From the triangle CSF we may write CS + CF : CS - CF : : tan -i (CFS + CSF) : tan -^ (CFS - CSF) but-2-(CFS + CSF) = 90° --2"^; and since ehe triangle 0,SF is isosceles, ~ (CFS - CSF) =4-F. .-. 2R + F : sin (F + ^) 1 /t? , 1 \ sin ^ (F -f- ^) (79) Also FS Fig. 126. and finally that 126. Connecting Curve from a Curved Track to the Inside. ^^ There are three solutions accord- ing as F is greater than, equal to, or less than "^. In the first case, we may readily deduce, as in the previous section, from the tri- angle CFS (see Fig. 126) that (2R-6Z) :{d^g) :;cot-^^ 1 ; tan -g- F 1 2n(d-~g) (81) RAILROAD ENGINEERING 149 And as before, in equations 78 and 79, we may derive („4,)=(„_J.,);,J^ (82) and FS = 2 (r- ^ ^ )sin -i- (F - f ) (83) When yjr =1 Y, equation 80 will become tan 1 ^ 1 27i(d-g) ^ Y = ^^ = Q-^ — -j^ from which we may derive 2R-d 2n 2R 4.n^ {d - g) This equation gives the value of R which makes this condition possible. If we make F = "^ in equations 81 and 82, we find in the first case that /' is infinite, which means that the track is straight, and in the second case that FS = infinity times zero, which is "indeterminate." But from the figure itself we may readily see that FS =(E--^^/)sin^ (85) (84) Fig. 127. Also When F < "^ we may derive the value of tan -^ "^ to be the the same algebraically as in Equation 81, although the figure is so different. By the same method as before we may derive for the value of r the equation. Fig. 128. gin (^ - F) \°^^ FS = 2 (r + i- J,) sin 4 (^ - F) (87) 150 RAILROAD ENGINEERING 127. Crossover Between Two Parallel Straight Tracks. As in the previous cases, although the figures are drawn for simplicity with switch rails as simple curves, the demonstrations only involve the frog angles and the na- ture of the track beyond the frog. The better method is that shown by the full lines, when the track is straight between the frogs. But this consumes so much of the main track (many times what is indicated in the distorted figure) that a re- versed curve (as is indicated by the dotted curves) may be used. The length of the straight crossover track is RT. F,T sin F, + y cos F, = d d-g F,T sin g cot F, (88) The total distance along the track is DY = D,F, + YF, + FA = D,F, + XY - YF, + F,D, but XY =[d - g) cot F, and XF^ = ^ -f- sin F, .-. DV=D,F,+ {d -g) cot F,- ^^^+D.F, (89) If a reversed curve with equal frogs is used, we will have the construction as is indicated by the dotted lines, and we have vers 6 = also (90) Fig. 130. DQ = 2/'sin6> (91) If it should for any reason be necessary to use frogs of differ ent sizes, it may be done, but the point of reversed curve, instead 162 RAILROAD ENGINEERING 151 of being in the exact center, will be as is indicated in Fig. 130. In this case we will have /•j vers + f\ vers 6 = d .'. vers e = : — (92) The distance along the track will depend, as before, on the length of the "lead" for each switch. If it were circular, as indicated in the figure, we would have B.N-C/', +n)sin^(93) but the true lead for point switches would be less than this by the difference be- tween the true L and (/' + -^g) sin F. Therefore, this ^^' correction should be computed and subtracted for each switch. 128. Crossover Between Two Parallel Curved Tracks. In the previous case there is no practical limitation as to frog num. bers, but in this case there are limitations on what frogs are per. Fig. 132. missible. If the connecting track is straight, there are still three cases depending on the value of F2, as in section 121. Two of these cases are illustrated in Figs. 131 and 132. The following 152 RAILROAD ENGINEERING demonstrations apply to both figures. If one frog (F,) is chosen, then F2 becomes determined as a function of F,. If Fj is the angle for some even frog number, F2 will in general be an angle that does not correspond to any even frog number and therefore will need to be made to order. If F, is less than some limit, depending on the width (^d) between the parallel tracks, it will be impossible to have a straight connecting track, and at some other limitation it will be impossible to have the reversed curve connecting track shown later. In Figs. 131 and 132 assume F^ as known. Then FiH = g sec Fp In the triangle HOFg we have sin HF^O : sin F,HO : : HO : Yfi but sin F2HO = cos F, ; RFfi = 90° + F/, sin HF^O = cos F/, HO = R + -i^-.~^-.^secF,; F^O = R~~d +^g hi^ .•. cos Fg = cos F, -R +-^d--^(/-(/seGF, ^--^d +-2(/ (94) Knowing F^, 0^ is determinable from equation 69. To determine the relative position of the frogs F, and F2, HOF2 = 180° - (90° - FJ - (90° + F,) = F, - F./, then GF, = 2 (R Jr\d-\g) sini-(F, - F^) (95) RAILROAD ENGINEERING 153 If the connecting curve is made a reversed curve, as is shown in Fig. 133, the frogs F, and F2 may be chosen at pleasure (within rather close limitations, however), and this will usually permit the adoption of regular standard sizes and will not necessitate the mak- ing to order of special sizes. We may then consider that F^ and F2 are known and that they are equal or unequal as desired. Em- ploying formula 29 in Table XXX,* we may write: 2(S-0Q,)(S-00.) ve^sv- ^()(^^^ ^^y^y^^ in which ^ == T ^^^' ^ ^^^^' "^ ^^' ^'^ but OOi = R + -g- ^ - ^1 .'.S=^ (2R + 2r,) = R -{- r, S-00, = U -{- r,-R -^-^d-r,=-^d', S-00, = R^r,-R-^d^r, = r,-{-r,-^d; d {r, + r,-^d) ... vers ^ = J (96) {R-^d^r.^(K^^d-r) 00 R + -g- ^ - r, sin OO2 O, = sin ^ ytit = sin , (97) O, O, r, + 7\ ^ ^ O2 O, D == ^ + O, O^ o (98) NF,=.2(R--^.Z+ -|-^)sin4(^- e,-0,)(99) The chief advantages of the above method are tliat it not only permits the use of standard size frogs, but also uses up less of the main track between the extreme switch points. * Found in Webb's "Railroad Construction". 154 RAILROAD ENGINEERING 129. Problems in Switch Computation. 1. A siding runs off from a straight main track, using a No. 8.5 frog. The distance between track centers is 18 feet. What is the radius of the con- necting curve and its length ? 2. A siding using a No. 9 frog runs off from the outside of a 4° 30' curve. What is the radius and length of the connecting curve? In all of these problems, consider the distance between track centers to be 13 feet. 3. Using the same frog, a siding is to run to the inside of the same track. What will be the radius and length of the con- necting curve ? Until "^ is computed, it is impossible to say which of the three possible cases w^ill be used, but the solution of equation 80 immediately decides that point, which will show that ^ is slightly greater than F, but that the difference is so little that the resulting value r is very great. -^ ("^ - F) is such a small angle that Table VI* must be used to determine its sine. 4. If a crossover is to be ran between two straight parallel main tracks 13 feet between centers, using No. 8 frogs, how much will be saved in distance measured along the main track by using a reversed curve rather than a straight track ? Since the dlffererK^e in*distance is called for, we may ignore in this solution the abso- lute length of the switch rails and consider that they would be the same in either case. 5. Required the dimensions for a cross-over between two main tracks which are on a 4° 30' curve; the distance between track centers thirteen feet, the frog for the outer main track (Fj in Fig. 132) is No. 9; Fg is No. 7; the connecting curve is to be a reversed curve. When the radius of a double main track is given, it means the radius of the center line between the two tracks. We must, therefore (as indicated in Fig. 133), add and subtract 6.5 to the radius of a 4° 30' curve (1273.6) to obtain the radii of the centers of the two main tracks. The figure and formulae allow for this. Since point switches would unquestionably be used, we must determine 7\ and n by the method outlined in §121; Rj the radius of the outer main track = 1280.1 (which means that D, = 4° 29'), while R-g ^^^ radius of the inner track = 1267.1 and D2 = 4° 31'. Then by the rule of §121, r, = radius of ((I, + D,) ° curve *See Webb's "Trigonometric Tables," pubUshed by American School of Correspond- ence, Chicago. 111. Price, 50c. RAILRAOD ENGINEERING 1.55 = radius of (7° 3X' + 4° 29') curve = 478.34; r^ = radius of [d^ - D^)" curve = radius of (12° 26' - 4° 31') curve = 724.31. ' ~ \ III /^^ ^•^ thus obtain /',, y\„ r.^, and /'^, as indicated \i/ ^--'''* in "Fimirfi 140 T^pfprrinor in thp frianorlp Fig. 140. vers F, in Figure 140. Referring to the triangle F1C1C2, and calling s^ = ~^{c ^ r^-\- rj, we may write : 2 (^i-^'OG'^i -^4) Similarly in the triangle Ffifi^^ let s.^ = -^ (c -{- r^ -\- r^ and in the triangle FgCjCg, let ^g = -^ (8«ih It is an independent road 371 miles long, with a capitMl- Bt6ck of $1,114,400 and a funded debt of $9,415,000, which is madfe up of bonds to the amount of $8,555,000 and "equipment trust ^bli- 220 RAILROAD ENGINEERING 209 gations" to the amount of S860,000. This is evidently a case of a road built chiefly on the proceeds of the bonds, the issue of stock being quite small. The gross fevenue for 1901-1902 was SI ,708,937. Of this, $1,101,884 or 64.5 per cent was spent in operating expenses. Of the remainder, $552,821 or 32.4 per cent was needed for the ''fixed charges". This left only $54,232 available for anything else. Although this amounted to nearly 5 per cent on the rather small issue of capital stock, no dividend was declared. It was evidently preferred to add this amount to their working capital or perhaps to use it in improvements. Such an action is virtually the reinvestment of profits for the improvement of the road. The complication, due to the corporate ownership of railroad stocks and bonds, as well as other income-bearing property, by railroad corporations, makes it impossible to analyze the financial statements of most railroad companies as easily as has been done above. A disbursement item by one corporation is an income item for another corporation. The Interstate Commerce Commis- sion publishes each year a statement which analyzes the reports of all the roads of the country and considers them as one system, which is done by eliminating all but the net balance of all inter- corporate payments. Some of the items of the statement for the year ending June 30, 1912, are as follows: (Millions) Operat ing revenues (rail operations) $2,842, Operating expenses (rail operations) 1,972, Total net revenue (adding a million from "outside operations") 871, Taxes accrued 120, Operating income 751, Other income (chiefly dividends and interest on stocks and securities owned) 89, Gross income 840, Deductions from gross income (chiefly interest on funded debt and net intercorporate balances) 488, Net corporate income for year 352, Adding balance of profit and loss, June 30, 1911 1>124, Gross surplus, June 30, 1912 1,477, Net loss during year (from "adjustments, through profit and loss") .... 30, Surplus available for appropriation 1,447, Net dividends declared during year $299, Appropriations for extensions and betterments $ 53, 352, Balance, carried to general balance sheet $1,095, 221 210 RAILROAD ENGINEERING Although it may appear ultraconservative to have allowed dividends of only 299 millions when the "surplus available for appropriation" was nearly five times that amount, it should also be noted that the net balance carried over was but little over one- half of the annual operating expenses. The balance, after paying interest charges for the year, would not run the roads four months if all income were cut off. While this is an inconceivable contin- gency, the margin for working capital is none too large. Even this margin was reduced 30 millions during the year. 164. Fixed Charges. The fixed charges of a simple railway corporation which operates only the line which it owns will consist chiefly of the interest on its bonds. Besides this there may be the interest on "equipment trust obligations" which are merely a particular form of bond issued to pay for equipment needed by the road. Another item will be the interest on sundry interest- bearing current habihties; this is generally but a small percentage of the fixed charges, but the current liabilities are often made to disappear by a new issue of bonds which take up an old issue and at the same time cover all floating liabilities. The complicated financial relations existing between operating roads and their leased lines introduces some other items which are entered under fixed charges. One of these items, which is always less than 1 per cent of the total fixed charges, is called "salaries and maintenance of organization". These refer to the salaries which are paid to a few of the general officers of a leased road who are retained to continue such work. Another item is placed, when it occurs, among the fixed charges; this is the rental paid for a leased road. As this is an "intercorporate" payment, it did not appear in the above general summary for the roads of the United States, nor did it appear in the detailed statement of the road previously described, since that road had no leased lines. 165. Net Revenue. The net revenue is that which remains after the operating expenses and fixed charges have been paid. In general it is available for dividends, but practically a very consid- erable proportion of it will be devoted to improvements or to the accumulation of a surplus which will serve as "working capital". During the year 1911-12, 34.57 per cent of railroad stock paid no dividends, although the case quoted above is but one of many in 222 RAILROAD ENGINEERING 211 which there was a considerable surpkis after paying the operating expenses and fixed charges. Dividends of less than 4 per cent were paid on 2.67 per cent of stock. This small proportion shows the tendency to pass the dividend unless it may be made larger. About 49 per cent of the stock paid dividends varying from 4 to 8 per cent. This represents the bulk of the stock paying normal dividends. Smaller percentages of the stock paid higher rates. On 8.43 per cent of stock, dividends of 10 per cent and over were paid. Of course this last represents roads which are short and very exceptional in character. It should also be kept in mind that the percentages of dividend-paying stock quoted above are almost the highest of any in the history of railroading. If general railroad conditions should ever return to those existing in 1896, when over 70 per cent of all the stocks paid no dividends, railroad stock would be less attractive for investment than now in spite of the abnormal profits which are occasionally realized. 166. Operating Expenses. Uniformity per Train-Mile. The classification of operating expenses here adopted will follow, both in general and in detail, the classification used by the Interstate Com- merce Commission. The figures given will, in general, be averages. This is further justified by the very remarkable fact that the expenses per tram-mile are nearly constant, whether the trains be few or many, heavy or light. Of course there are very numerous excep- tions to this rule, but it will generally be found that the marked exceptions apply to very short roads which either have abnormal traffic or have peculiar financial relations with a parent company which is operating it. The report for 1901-2 shows that the ten greatest railroads of the country, each operating more than 4000 miles of road, spent SI. 167 per train-mile. The average for the whole United States was $1.1796. It should also be noted that the ratio of total operating expenses to total receipts from operations was 59.78 per cent for the ten roads and 64.66 per cent for the whole United States. To judge of the operating expenses of smaller roads, the figures for No. 10, Table XIV, were taken from the report, the selections being made at random except that the lengths were all less than 100 miles and all of the roads were "operating roads independent". 223 212 RAILROAD ENGINEERING TABLE XIV Operating Expenses Ratio of Total Operating Expenses No. Length Operating Expenses TO Total Receipts from Operation (miles) PER Train-Mile (per cent) 1 21.25 $0.70621 71.62 2 32.60 0.47828 64.21 3 31.00 0.60649 96.12 4 64.10 0.90588 43.41. 5 42.00 0.54323 63.07 6 61.00 0.75357 81.05 7 50.00 0.87456 90.32 8 50.39 2.07044 97.58 9 70.78 1.02854 53.46 10 52.20 1.74952 62.15 Average $0.97167 72.30 10 longest roads 1.167 59.78 Whole U. S. 1 . 17960 64.66 A little study of the above figures will show, as might be expected, that local conditions will so affect a very small road that its operating expenses per train-mile may be considerably more or considerably less than the average. The average value for the ten short roads here chosen is less than the average for the United States, and although two of the ten are much greater than the average, it is found that the average value for short roads is a little less rather than more. The reasons for the uniformity are not difficult to understand. Although the gross expense of any one item (such as rail renewals) for a large road is enormously greater than the same item for a small road, the divisor (the number of trains) is correspondingly greater and the quotient, which is the expense for that item per train-mile, is substantially uniform. Average Cost of a Train^Mile. The increase in the average cost of a train-mile is shown in Table XV, which gives the average cost of operating a train 1 mile during 23 consecutive years. The nearly uniform growth of over 73 per cent between 1895 and 1912 is very significant. While predictions of future cost are necessarily guesswork, estimators in railroad economics must make the best possible predictions for five or ten years ahead. There seems to be no 224 RAILROAD ENGINEERING TABLE XV Average Cost of Operating a Train 1 Mile (All roads in U. S.) 213 Year Cents Year Cents Year Cents Year Cents 1890 96.006 1896 93 . 838 1902 117.960 1908 147.340 1891 95.707 1897 92.918 1903 126.604 1909 143 . 370 1892 96.580 . 1898 95.635 1904 131.375 1910 148.865 1893 97 . 272 1899 98.390 1905 132.140 1911 154.338 1894 93.478 1900 107.288 1906 137.060 1912 159.077 1895 91.829 1901 112.292 1907 146.993 reason to hope for a decrease in the rate or to expect anything else than a continued increase, even though it may prove less rapid than heretofore. 167. Classification of Operating Expenses. In Table XVI is shown the classification adopted by the Interstate Commerce Com- mission — the total cost for each item, each item's per cent part of the total, and the cost in cents per train-mile, which is found by multiplying each percentage by the average cost per train-mile for that year ($1.59077, or 159.077 cents). While these averages are very instructive in giving a broad view of the subject, they must be used cautiously. For example, the fuel required per mile for loco- motives is a very variable quantity, depending on the size of the locomotive and the amount of work done, and it would be very foolish to make any calculations on the basis that the cost of fuel per locomotive-mile would be exactly 16.27 cents. 168. Maintenance of Way and Structures. The cost of ties is the largest single item for track material; the cost per train-mile has nearly doubled since 1895. This has been due to a combination, in varying proportions, of three causes — (a) increased cost of ties; (b) lowering of quahty to pass inspection, due to growing scarcity; and (c) increase in train load and concentrated wheel load, resulting in more rapid deterioration. There seems to be no chance of decrease in cost in the future unless possibly by more effective preservative processes or by the invention of a metal or a steel-concrete tie which shall be so durable that, in spite of increased first cost, it is cheaper per train-mile. The cost of roadway and track (item 6) is the labor of track 225 214 RAILROAD ENGINEERING TABLE XVI Analysis of Operating Expenses of all Railroads in the United States for Year Ending June 30, 1912, Showing Percentage of Each Item to Total and Cost in Cents per Train=Mile Total Per Cent Cents per Item Account Amount OF Total Train- No. (thousands) Expenses Mile MAINTENANCE OF WAY AND STRUCTURES 1 Superintendence Ballast $18,789, 0.990 1.58 2 7,157, 0.377 .60 3 Ties 55,463, 2.921 4.65 4 Rails 16,438, .866 1.38 5 Other track material 17,346, .914 1.45 6 Roadway and track 129,397, 6.815 10.84 7 Removal of snow, sand, and ice 6,920, .364 .58 8 Tunnels 1,141, .060 .10 9 Bridges, trestles, and culverts 27,712, 1.460 2.32 10-12 Crossings, all; fences; snow structured 8,066, .425 .68 13-15 Signals, telegraph, electrical power trans- mission 13,681, .720 1.14 16,17 Buildings, grounds, docks, wharves 35,389, 1.864 2.96 18 Roadway tools and supplies 4,480, .236 .38 19 Injuries to persons 1,989, .105 .17 20,21 Stationery, printing, and other expenses 1,038, .054 .09 22,23 Joint tracks, etc. (net balance) 3,463, .182 .29 348,471, 18.353 29.20 MAINTENANCE OF EQUIPMENT 24 Superintendence Repairs, renewals, and depreciation: Locomotives, steam and electric 13,175, .694 1.10 25-30 175,889, 9.263 14.74 31-33 Cars, passenger Cars, freight 38,968, 2.052 3.26 34-36 183,968, 9.690 15.41 37-39 Equipment, electrical, car 318, .017 .03 40-42 Equipment, floating 1,333, .071 .11 43-45 Equipment, work 6,128, .322 .51 46 Equipment, shop (machinery and tools) 10,418, .548 .87 47 Equipment, power plant 268, .014 .02 48 Injuries to persons 1,818, .096 .15 49,50 Stationery, printing, and other expenses 4,036, .213 .34 51,52 Joint equipment, at terminals (net bal- ance) 676, .036 .06 436,995, 23.016 36.61 TRAFFIC EXPENSES 53-60 Agencies; advertising; fast freight lines; etc. 59,047, 3.110 4.95 226 RAILROAD ENGINEERING TABLE XVI (Continued) 215 Analysis of Operating Expenses of all Railroads in the United States for Year Ending June 30, 1912, Showing Percentage of Each Item to Total and Cost in Cents per Train=Mile Total Per Cent Cents per Item Account Amount OF Total Train- No. (thousands) Expenses Mile TRANSPORTATION EXPENSES 61,62 Superintendence and train dispatching $40,743, 2.146 3.41 63 Station employes 133,877, 7.051 11.22 64-66 Weighing; car service association; coal and ore docks 15,949, .839 1.33 67-72 Yards (wages, expenses, supplies) 116,781, 6.151 9.79 73-76 Yard locomotives (fuel, water, lubricants, supplies) 33,658, 1.773 2.82 77, 78 \Operating joint tracks, terminals, yards, / and facilities (net balance) 104, 105 10,430, .550 .88 79,80 Motormen and road enginemen 120,966, 6.371 10.14 81 Road locomotives, engine-house expenses 33,951, 1.788 2.84 82 Road locomotives, fuel 194,142, 10.225 16.27 83 Road locomotives, water 12,482, .657 1.04 84,85 Road locomotives, lubricants, and other supplies 7,430, .392 .62 86,87 Operating power plants, purchased power 1,797, .095 .15 88 Road trainmen 128,339, 6.759 10.75 89 Train supplies and expenses 34,462, 1.815 2.89 90-92 Interlockers, signals, flagmen, draw- bridges 17,831, .939 1.49 93 Clearing wrecks 5,167, .272 .43 94-98 Telegraph, floating equipment, station- ery, miscellaneous 20,009, 1.054 1.68 99-103 Loss and damage to property, personal injuries 56,838, 2.994 4.76 984,852, 51.871 82.51 GENERAL EXPENSES 106-116 Salaries of general officers, clerks, etc.; law, insurance, pensions, miscella- neous 69,297, 3.650 5.81 Total Operating Expenses $1,898,662, 100.000 159.08 maintenance. The average daily wages of trackmen have increased almost uniformly from $1.22 in 1900 to $1.50 in 1912;. the wages of section foremen are quite uniformly about 30 per cent above those of trackmen. The number of trackmen per 100 miles of Hne has also increased from 118 to 143 in this same period, but there have 227 216 RAILROAD ENGINEERING been greater fluctuations. The increased number and increased wages have combined to increase very greatly the cost of track maintenance. 169. Maintenance of Equipment. The cost of this group of items has been, increasing very greatly in recent years, not only in gross amount but also in percentage to total cost of a train-mile and in cents per train-mile. This increased cost is due to higher labor costs in the shops and higher costs for materials. While a change of alinement, involving increase or decrease in length of road, or ^'distance", will affect these items, the cost is not directly proportional to distance and the same remark applies to many other items. Curvature afl'ects the cost of repairing very greatly — chiefly in wheel wear, and the engineer must consider this in estimat- ing the value of a saving in curvature. The rate of grade also has an effect on this item. During the first years of the life of a locomotive, the repairs (barring accidents) will be small, but as the locomotive grows older they increase in a growing ratio. When the annual repair charge becomes one-fourth (or in exceptional cases one-third) of its first cost,%the locomotive should be sent to the scrap pile, for in such eases the cost per train-mile becomes larger than a reasonable annual charge, allowing for all depreciation, on the cost of a new locomotive. When an old locomotive is replaced by one of a better and more costly type, the excess cost should be charged to '' betterments' ^ or ''permanent additions to equipment". 170. Transportation Expenses. There are five items in this group which amount to more than 5 cents per train-mile. The largest is that for fuel. The cost of this (for both yard and road locomotives) has nearly doubled since 1895. This is due partly to increase in cost of coal per ton and partly to the great increase in the power of the average locomotive and therefore in the amount of coal burned per mile. The other four of the five large items are made up almost exclusively of wages, which have increased very greatly in the past twenty years. Any economic calculation, which requires a prediction of the future cost of operation, must include the proba- bility that the cost of conducting transportation will probably not decrease and may increase very materially even during the next five or ten years. 228 RAILROAD ENGINEERING 217 ECONOMIC LOCATION 171. General Principles Involved. A hasty mental review of the previous discussion, as well as a few considerations of common sense, v^iW show the truth of the following statements : (1) Disregarding the comparatively rare cases in this country where a practicable location of any kind is a creditable engineering feat, it may be said that a comparatively low order of engineering talent will suffice to lay out a line along any general route over which it is physically possible to run trains, and that there are usually several such possible^routes. The route selected may not be favor- ably located for obtaining business, its alinement may be such that its operating expenses are high, and the ruling grades may be so high that only light trains can be run, but the road can be operated even with these handicaps. (2) Among the many possible routes which may be selected for a road, there is one which is superior to any other from an operat- ing or business standpoint, and it is the province and test of the engineer to select that best route. (3) There are several more or less conflicting interests which must be studied — (a) the maximum of business must be obtained, but this is sometimes only obtainable at great initial cost; (b) the ruling grades must be made as low as possible, which is generally costly, and it inay require a location which will sacrifice some busi- ness; (c) the alinement must be kept easy so as to reduce operating expenses, but this usually is very costly; (d) the total cost must be kept within a figure which will be justified by the future earnings and also leave enough margin as working capital out of the total funds which are raised, so that the road may continue to operate during the five or ten years which are required to build up the ^'normal" traffic. (4) Each new route suggested forms a new combination of the above conflicting elements, and the business of the engineer is to estimate and compare these elements, selecting the combination which will give the largest return for the least outlay, considering both initial cost and future operating expenses as elements of the outlay. 172. Reliability and Value of Economic Calculations. The student should not form the idea that the following calculations 229 218 RAILROAD ENGINEERING will enable one to compute with mathematical precision the effect of changes of alinement. There are far too many elements involved, and the effect of certain influences is variable. But although a precise solution is unobtainable, a solution which is sufficiently accurate for practical purposes may be made, and this is infinitely better than no solution at all. For example, suppose that a very crooked stretch of road may be changed to comparatively easy alinement which saves considerable curvature by an additional expenditure of say $20,000. Assume that it has been computed (by methods developed later) that the operating expenses would be reduced $3500 per year by the reduction of that curvature. As $3500 per year, capitalized at 5 per cent, is equivalent to an investment of $70,000, and as the improvement may be made for $20,000, the improvement is evidently justifiable. Such is the bare outline of the method. The estimate of the cost of the improvement may be accurately made, but it is not claimed that the estimate of the saving per year is precise. It may, however, be shown that, even with ample allowances for the uncertain items, it is practicable to assign upper and lower limits between which the truth must lie. A greater knowledge of the subject and greater experience on the part of the engineer will enable him to narrow those limits so that the error is immaterial. And frequently even this is unnecessary. The real question is not whether the capitaHzed value of the improve- ment is $70,000, or $50,000, or $90,000. It may be that an improve- ment which would make possible that saving may be made for a few thousand dollars, or it might require $200,000. In either case, the true answer is unquestionable. If the cost of the improvement is very nearly equal to its computed capitalized value, then no great harm can come from either decision, for the decision would then be based on the willing- ness of the company to spend additional money. The method furnishes a criterion, which even in the hands of an inexperienced engineer has some value, and which alone gives value to his opinion. But the method enables the experienced engineer to give the best opinion which is obtainable, for it enables him to apply his experience to a method of computation which approaches accuracy as nearly as may be. 230 RAILROAD ENGINEERING 219 It must not be supposed that the numerical values worked out in the following pages are necessarily applicable to any assumed case. They are gi\'en to show the method of their derivation, and should be modified to fit local conditions according to the best judgment of the engineer. DISTANCE 173. Relation of Distance to Rates and Expenses. Rates are usually based on distance traveled on the apparent assumption that the value of the service rendered and the cost to the company are directly proportional to the number of miles traveled. The assumption in either connection is not true. If a passenger or a load of freight is to be transported from one city to another city 100 miles away, the service rendered is to accomplish the transfer as easily and quickly as possible. If another road were constructed, perhaps at extravagant cost, by which the distance were cut dowTi to 90 miles, that road would render a greater and better service, because it would reduce the necessary travel, and yet on the mileage basis the shorter road would be entitled to less than the other in spite of the fact that it renders a better service. The assumption that the cost is proportional to the distance is more nearly correct, although, as will be shown later, even this is far from accurate. It is not difficult to compute an average cost for a large number of passenger trains and, by dividing it by the total passenger mileage, to obtain a value of the cost of a "passenger- mile". But the additional cost of transporting one additional passenger on a i«egular train is hardly more than the cost of print- ing his ticket. Even if it were practicable to compute the extra consumption of coal and the infinitesimal addition to other oper- ating expenses due to his being on the train, the added cost would evidently be but an insignificant fraction of the average cost of a passenger-train-mile. The same argument holds, but not to the same extent, if we consider the additional cost of an extra ton of freight. By the same line of argument it will be shown that a change in distance will not affect the cost of running trains in proportion to the change. It is easy to see that general expenses will be abso- lutely unaffected by an alteration of alinement which saves a mile 231 220 RAILROAD ENGINEERING in distance, and it will be shown that even the consumption of fuel does not vary in i)roportion to the distance. If it were practicable to construct a tariff of rates which should consider excessive curva- ture and grades on the various parts of the line and make the rates dependent on them as well as on many other constructive features which add to the cost of operation, the rates would be more nearly proportional to the cost, but the public would not appreciate it and it would be useless work. And when it is further shown that it is sometimes justifiable for a road to haul competitive business at a rate actually less than the average cost of their traffic, it will be seen that the relation of distance to rates and expenses cannot be expressed by any simple proportion. 174. Effect on Receipts. Among all the details of alinement, distance is the one for which there is some compensation in an increase, and that is because rates are based on distance rather than on curvature or grades. Although it is unquestionably con- trary to public policy to burden traffic unnecessarily by an increase in distance, yet it may be demonstrated that the added receipts from non-competitive traffic due to such increased distance will amount to more than their added cost. But in order to study this feature properly the distinction between competitive and non-competitive rates must be noted. For our purposes traffic may be classified as "through" and as *iocal", in which through traffic refers to that which passes over tivo or more roads, no matter how long or short any section of the trip may be, and in which local traffic refers to that which is confined to one railroad system, though it may run from one end to the other. Further subdivision is necessary as follows : (1) Non-competitive local — on one road with no choice of routes. (2) Non-competitive through— on two (or more) roads but with no choice. (3) Competitive local — a choice of two or more routes, but the entire run may be made on the home road. (4) Competitive through — direct competition between two or more routes, each passing over two or more lines. (5) Semi-competitive through — a lion-competitive haul on the home road and a competitive haul on foreign roads. 232 RAILROAD ENGINEERING 221 Receipts for traffic passing over two or more lines are divided between the lines in proportion to mileage. "Terminal charges" are sometimes subtracted from the amount before the division is made and sometimes a strong road forces a weaker road to submit to some other exaction before the division is made, but the final , division is made in proportion to the mileage for each passenger ticket or each freight bill. It may be shown that the cost of oper- ating an additional mile is about 58 per cent of^the average cost. This means that on all non-competitive business (class 1) there is an actual profit in this added distance. On the other hand, com- petitive rates are made with small regard to distance, are generally equal, and therefore any added distance results in a sheer loss with- out any compensation. This applies to all the traffic of class 3. Illustrative Example. The other classes of traffic are affected by distance in various degrees between these two extremes. Suppose that the distance on the home road for any given shipment is 100 miles, and the distance on the foreign road for that shipment is 150 miles; suppose that the freight charge is $10; then the home road will receive X $10 = $4.00. This means 4 cents per mile for 100+150 that particular class and weight of freight. Suppose that the distance is increased 5 miles on the home road, but assume that the traffic is wholly competitive and therefore that the total rate received will be $10, regardless of the added distance. Then the home road will receive ——^X$10 = $4.1176. If we allow to lOo+loO the original 100 miles its full previous allowance of 4 cents per mile, we have left 11.76 cents to pay for the extra 5 miles. This is at the rate of 2.352 cents per mile, which is 58.8 per cent of the 4-cent rate. This nearly equals the computed percentage of added cost for additional distance computed in miles. Therefore, if the original 4-cent rate is profitable, the added receipts due to the added distance will be sufficient to operate the added distance profitably, or without loss. Incidentally, the foreign road suffers, for it will receive less for precisely the same service. The above numerical case is very nearly at the dividing line between profitable and unprofitable additition to distance. If the length of the home road 233 222 RAILROAD ENGINEERING is but a small proportion of the total distance, then it may be simi- larly computed that an addition to distance is distinctly profitable. On the other hand, if the length of the home road is a large pro- portion of the total distance, an addition to distance is distinctly unprofitable, and when the length of the foreign road is zero (which means that the competitive haul is entirely on the home road) then any addition to distance is sheer loss without any compensation, even partial. The above numerical case represents but one of an almost infinite number. Each station along the line has possible traffic connection with almost every other railroad station in the country. The route from each station to every other station represents a new combination, and the net effect of the added distance is the com- bined effect of all the separate cases. This instantly shows that a precise mathematical solution is impossible, but the above solution has value in pointing out some general truths as follows : In all non-competitive business, whether through or local, the added receipts due to added distance will be profitable, and if the business of a road is almost entirely non-competitive there is little or no disadvantage in added distance, especially if the construc- tion is cheapened in spite of the added distance. For example, a road which follows the banks of a very crooked river may cost less to build, even though much longer and more crooked, than the road which tunnels through the horseshoe bends. When roads handle a very large amount of competitive busi- ness any additional distance may be a source of loss on that class of business, and the loss may be so serious as to justify a considerable expenditure to reduce it. Another reason for the subsequent expenditure of money to reduce distance is that, after freight rates are once established between roads on through business, they are not apt to be disturbed to make them conform to the slight fluc- tuations of distance caused by changes in the alinement. The above statements can be reduced to the general conclusion that since every road handles a considerable proportion of non- competitive business, there is always some compensation for the added expenses of operating additional distance. The majority of small roads do a business which is almost wholly non-competitive, and to them the added receipts will usually pay for the added dis- 234 RAILROAD ENGINEERING 223 tance, even if it is not an actual source of profit. Finally, it may be said that a road is not usually justified in making an additional expenditure to shorten distance (i.e., adopt a route which will have a greater gross cost in spite of the shortened distance) unless it handles a very large amount of highly competitive business. There are some other considerations which must not be ignored in considering this question. One of them is the question of the additional time required to make the trip. This may be important in two ways. (1) The competition for passenger business between two cities, such as New York and Philadelphia, or Philadelphia and Atlantic City, might be so keen that a difference in length of line which would affect the running time by even 10 minutes would have great financial importance. (2) A very considerable change in distance may have a serious effect on the operation of the heavy through-freight trains, although it would not ordinarily increase the total cost of operating those trains over that division more than the extra number of train-miles times the reduced train- mile cost. But in any case, this phase of the question should not be ignored. Another consideration is the possible effect on the business done. "A short straight line" is the popular description of a well- designed road. If the engineer's aim for a short road leads him to pass by sources of income and thus lose them, his road will have little business and the receipts will be reduced because it is short. As a gen- eral rule ''adopt that route which will give the greatest traffic per mile of road". On the one hand, this avoids the error of running a line which is excessively crooked in the effort to secure every possible element of traffic and thus burdening the whole traffic with an excessive haul, and on the other hand, avoids running a line which misses important sources of traffic in the effort to have a straight fine. CURVATURE 175. Operating Disadvantages of Curvature. The non-tech- nical mind appreciates, even too readily, the disadvantages of curvature. But it is generally true that the ones which are most thoroughly appreciated by the pubfic are of least economic value to the engineer. The several disadvantages ^\^ll be classified 224 RAILROAD ENGINEERING and discussed in an order which is perhaps the inverse order of their importance, as follows: (1) It increases the danger of collision and derailment and aggravates the damages of a derailment when it occurs. The appli- cation to be made to this statement of undoubted fact is — how much is a road justified in expending in order to reduce or elimi- nate any given curve? Since the entire elimination of curves is a physical as well as a financial impossibility, the question reduces to the lessening of danger from accidents that would result from such reductions as are possible. The Interstate Commerce Com- mission report on railroad accidents for the year ending June 30, 1902, showed that the number of passengers carried 1 mile for one killed was 57,022,283. This means that the chances are even that a passenger could ride 57,000,000 miles before he would be killed. If he were to ride continuously at the rate of 60 miles per hour, it would require over 9,500,000 hours, or nearly 400,000 days, which is considerably over 1000 years. But how many of such casualties are due to curvature, and how many million miles must be traveled by the average passenger before, according to the law of probabilities, he would be killed by an accident which should not only be directly charged to cur- vature, but also to curvature w^hich is physically or financially avoidable. If we estimate the number of curves on all the railroads of the country as 250,000, what is the probability of a fatal accident happening on any one curve and how much may be spent on that curve to reduce the danger? Even if it were spent, would there remain no danger of an accident there? A thorough logical analysis of this question shows that although it is always proper to take reason- able precautions to avoid accident at an especially dangerous curve (such as maintaining a flagman there), it is impossible to assign any financial value to the mere danger of accident which would accomplish anything toward modifying construction. (2) Curvature may affect traffic (a) by reducing the possible speed of fast trains. There is some force to this objection as it applies to sharply competitive traffic between two cities — a traffic of which most roads have not a trace. The extent to which the passenger traffic might be increased by the minute or two which might be saved is, however, so uncertain that it defies analysis. 236 RAILROAD ENGINEERING 225 (b) It may produce rough riding, and (c) it may create an apprehen- sion of danger which may of itself deter travel. The disadvantages resulting from all three of these sub-causes are greatly reduced by good roadbeds and transition curves. Freight traffic, which com- prises about two-thirds of the total, is unaffected by it unless the curvature is extreme, and the passenger traffic of most roads will not be influenced by it; and therefore an engineer is not ordinarily justified in giving it any financial weight. (3) It may affect the operation of trains (a) by limiting their length and (b) by limiting the type and weight of engines. There are a few instances known where roads which run along a river bank have very easy ruling grades and on which the curvature is perhaps very sharp on account of sharp bends in the river. On such roads the curvature may be the feature which limits the length of trains, but such cases are rare and even when they occur a com- putation similar to that later developed will show how much may profitably be spent to reduce the rate of curvature. If a long grade up a mountain were kept uniform, regardless of curves, the curves would add such resistance that they would limit the length of trains, but good practice requires that the grades shall be "compensated for curvature", as explained later. The excessively sharp curvature which has been used on some mountain roads may preclude the use of some of the largest types of locomotives. But such roads ordinarily do not have a traflSc which justifies the use of the heaviest locomotives. And when it is considered that a Mallet locomotive, having sixteen drivers and a weight on the drivers of over 400,000 pounds, can be operated on a 20-degree curve, any limitation in the use of engines may be ignored for all ordinary railroad work. (4) Curvature increases operating expenses. This disadvan- tage is definite, positive, and approximately computable, and since a reduction in expenses may be made by reducing curvature, we must calculate the effect of curvature on operating expenses. . 176. Compensation for Curvature. Curvature makes a very definite increase in train resistance, and such increased resistance is readily equated to its equivalent in added grade. Assuming that the curve resistance on a 6-degree curve is 4 pounds per ton, which is the grade resistance of a 0.2-per-cent grade, if there should be 237 226 'RAILROAD ENGINEERING a 6-degree curve on a 1 .0-per-cent grade, the resistance on that grade would be the same as on a straight track having a 1.2-per-cent grade. On this basis, if 1.2 per cent were selected as the ruling grade and it became necessary to introduce a 6-degree curve, the grade should be reduced on that curve to 1 per cent so that the total resistance on that curve shall be no greater than on the tangent. This is the fundamental idea of curve compensation. On grades which are so low that they will never be ruling grades even if the rate of ruling grade is reduced by reconstruction, there is no neces- sity for curve compensation, but the neglect of it on ruling grades means that the ruling grade is practically increased to the grade which is the equivalent of the combined grade and curve resistance. Rate of Compensation. This term means such a reduction in the grade that the saving in grade resistance equals the curve resistance. But curve resistance varies somew^hat as the velocity, the condition of the rails, and even the type of the wheel base. For simplicity of calculation the curve resistance is usually assumed to vary as the degree of curvature. While this is nearly true for low degrees of curvature, it becomes grossly inaccurate for excessively sharp curva- ture, on which the resistance is fortunately much less than its pro- portionate amount. This is probably due to the fact that a large part of the resistance from curvature is due to causes which are independent of the degree of curve. The resistance will amount to about 2 pounds per ton per degree of curve (equivalent to a 0.1- per-cent grade) when the velocity is very low — as when starting a train. It is less for fast trains than for slow trains, but considering that it is the slow and heavy freight trains w^hich must be chiefly considered, the larger values for compensation which are needed for the slower velocities must be used. Compensation results in a loss of elevation for a given horizontal distance and when money has been spent in "development" in order to reduce the grade to some desired limit, any useless compensation is a waste and should be avoided. If a curve occurs on a grade immediately below a stopping place for all trains (or at least all trains which are so heavy that they will be affected by the ruling grade), the compensation may be reduced or omitted altogether on the ground that the curve resistance would simply use up the energy which might otherwise be used up by brakes in stopping the train. If 238 RAILROAD ENGINEERING 227 that heavy grade should continue on above that stopping place, then the compensation should be made even greater than the aver- age to allow for the increased resistance while starting. Since the curve resistance merely adds to the virtual grade, and the object of compensation is to prevent such additions from increasing the ruling grade, there is no object in using compensation on a grade, which is already so low that the added resistance will not make it virtually equal to the ruling grade. An exception to this lies in the danger that it may some time prove desirable to make such changes of alinement that the ruling grade is very materially cut down, and it might happen that neglect to compensate would add that much to the revised ruling grade. The above discussion may therefore be reduced to the following rules: (1) On the upper side of a stopping place for all heavy trains compensate 0.10 per cent per degree of curve. (2) On the lower side of such a stopping place do not com- pensate at all — but this rule should be applied cautiously. (3) Ordinarily compensate about 0.035 per cent per degree of curve. (4) Increase this rate to 0.04 per cent when the curve is habit- ually operated at slow speed, or when the super-elevation is excessive for freight trains, unless it is found that the higher rate of com- pensation causes such a loss of height that the grade on the tangent must be increased. (5) Curves which are so much less than the ruling grade, that they will always be minor grades need not be compensated, but the possfbilities of a future reduction in the rate of ruling grade should be considered. 177. Limitations of Curvature. Surveys for railroads are frequently made under instructions that curves (and also grades) shall not exceed some chosen limitations. What should be the limitation, if any, of the degree of curvature? Probably no definite answer is correct unless it be said that there should be no limita- tion. It has been shown that all ordinary degrees of curvature even up to 20 degrees will still permit the use of heavy engines, and there are numerous instances where a heavy railroad traffic has been hauled for many years around excessively sharp curves without any serious difficulty — as, for instance, the traffic on the Baltimore & Ohio 239 228 RAILROAD ENGINEERING Railroad at Harper's Ferry, which for many years was hauled around a 19-degree 10-minute curve (radius 300 feet). This curve was changed some years ago. Of course the young engineer should not conclude from this that curvature is of no consequence, and that he may recklessly put in as much and as sharp curvature as might seem at first the easiest plan to adopt. It may be shown that there is a definite money value in reducing every possible degree of central angle and also that the radius of curvature should be made as large as pos- sible without a serious sacrifice of other interests or extravagant expenditure. It generally happens, when running a road through a mountainous country, and when a high summit must be crossed, that the grades can only be reduced by the adoption of very sharp curvature or by a large expenditure in construction. Since the expenditure is usually limited by financial considerations, the error of adopting a high ruling grade is usually made and the degree of curvature is limited to a low figure which is ridiculously out of proportion to the general condition of the road. Sometimes the limited money at the disposal of the company is wasted on a route which gives easy curves when the money could have been spent advantageously in other ways. The most com- mon error is the needless increase in the ruling grade. Many rail- roads have been laid out under the instructions that the maximum grade may be 60 feet per mile and the minimum curve 6 degrees. These limits have been used separately, or in combination, with the result that when a 6-degree curve occurred on a 60-foot grade, the virtual grade was thereby increased (on a 0.035-per-cent basis) to over 71 feet per mile. While a grade of 60 feet per mile might be la very proper ruling grade under certain conditions, it might readily happen that the option of using a lO-degr^e curve (properly compensated) would permit adopting a line with a ruling grade so much less than 60 feet that the advantages of the reduction of grade would far out- weigh the comparatively insignificant disadvantages of the sharp curvature. Therefore, as a general answer it may be said that the limits, if any, should conform to the general character of the country, and that when it appears possible to obtain a great advantage, such as the reduction of the ruling grade, by an increase in the degree of curvature and even in the degrees of central angle, such increase should be made unless it may be definitely computed 240 RAILROAD ENGINEERING 229 that the disadvantages of the increased curvature would outweigh the advantages of the reduced grade. GRADE 178. Distinction between Minor and Ruling Grades. The distinction between minor and ruUng grades must be very clearly understood before their operating disadvantages may be computed. The cost of running a train one mile is largely independent of whether the train is long or short, heavy or light. The receipts for transport- ing so many tons of freight is a definite quantity and is unaffected whether it is transported in one train load or two. If it is possible by a reduction in grade to haul in a single train load as much freight as would require two train loads by the old plan, then, since the receipts are constant and the cost of the two light trains will be nearly double that of the one heavy train, it is evident that the low-grade plan will be very profitable and the other plan corre- spondingly costly and financially ruinous. Although it is not often practicable to double the weight of the train behind a freight engine, a very material increase in the train load can generally be made by such reduction of the ruling grade as is practicable, and such increase in train load frequently makes all the difference between large dividends and an actual deficit. The ruling grade definitely limits the load that can be hauled by an engine with a given weight on the drivers and its financial effect is very great. On the other hand, a minor grade does not limit the number of cars and its effect on operating expenses is confined chiefly to an increase in the consumption of fuel and other locomotive supplies. While this increase in expense has an importance which is worth computing, it is insignificant compared with the cost of running additional trains to handle a given traffic. The real cost of minor grades is also less than it might other- wise be considered owing to the fact that each rise has its corre- sponding fall. Even though several high summits may be crossed, the difference in elevation of the terminals, say 200 feet, or even 500 feet, is insignificant from the standpoint of grade when the distance is perhaps as many miles. And even in the extreme case when the grade is all in one direction, the additional energy required to climb the grades is partly returned in the assistance the grade 241 230 RAILROAD ENGINEERING gives to trains on the return trip and the consequent saving in motive power. 179. Laws of Accelerated Motion. Application to Movement of Trains. When a train starts from rest and acquires its normal velocity, say 30 miles per hour, the engine must develop not only the power required for all the ordinary tangent and perhaps curve and grade resistances, but also the "kinetic energy" corresponding to the velocity which has been acquired. This kinetic energy is not wasted; all of it is transformed back into work of some kind. The energy may be consumed and wasted in the brakes, but it may also be spent (and is so spent) in overcoming resistances when- ever the velocity of the train is reduced. The amount of this kinetic energy is a definite mathematical quantity. The laws of Mechanics tell us that this energy equals W (v'^-T-2g), in which W is the weight of the train, v is its velocity in feet per second, and g is the acceleration of the force of gravity, which equals 32.16 feet per second in a second. A better appreciation of this force may be obtained by con- sidering for a moment that if the train could move along the track without any resistance, then, when running at a velocity of v feet per second, it possesses a kinetic energy which would raise it to a height of h feet, where h = v^-i-2g. If we consider that the engine is furnishing exactly the power required to overcome the tractive resistances, then the train would run until it had climbed a grade to a height of h feet, no matter whether it was accomplished in 100 feet, or a mile. By an expansion of the theory it is also shown that when the train has climbed a vertical height of h^ feet (less than h)j it will have left a velocity v' =y2g {h — W). Illmtrative Example. Assume that the velocity of a train is 30 miles per hour, or 44 feet per second. It then has a kinetic energy 442 which would raise it a height h = - — ^1777. = '^^^-1 ^^'^t. If the engine furnished just enough energy to overcome the tractive resistances, the kinetic energy would carry the train up a grade of 15 feet per mile for a distance of about 2 miles, or up a grade of 60 feet per mile for a distance of about | mile. If the train were moving up a grade of 20 feet per mile and had proceeded half a mile, it would have climbed 10 feet and would still have a kinetic 242 RAILROAD ENGINEERING 231 energ y correspondin g to 20.1 feet, and its velocity would then be / = V2X32.16X20.1=35.9 feet per second, or 24.5 miles per hour. If the train were a solid mass the above figures would be abso- lutely correct, but the solution is a little complicated by the fact that an appreciable part of the weight of the train consists of revolving wheels, to w^hich must be imparted the kinetic energy of rotation, in addition to the kinetic energy of translation. The ratio of this rotative kinetic energy to that of translation depends chiefly on the ratio of the weights of the wheels and of the whole car or engine. Evidently this ratio depends on the detailed design of the rolling stock, and more especially on whether the cars are loaded or empty. This consideration shows that no one value will be accurate for all cases, but there will be little error in adopting 5 per cent as an average value for the increase in the kinetic energy. Table XVII, which will be found very useful in these com- putations, has therefore been compiled on the following basis: .t^j 1 .^ , i„ ^^ in ft. per sec. 1.4667 V^ in m. per h. Velocity head =-^-^^^^= ^4.32 = 0.03344 F2 and, adding 5 per cent for rotative kinetic energy of the wheels, = 0.00167 F^ Therefore, corrected velocity head = 0.0351 IF^ Part of the figures of Table XVII were obtained by interpola- tion, and, therefore, there may be an error of a single unit in the hun- dredths place in some of the figures, but considering the uncertainties in the problem, the exact value to hundredths is of no prac- tical importance. Examples of the application of this table will be given later. The tractive force required to produce this acceleration in a given distance may be stated as W 2gs in which Vi and Vz are the lower and higher velocities in feet per second, s is the distance in feet, g is the acceleration of gravity (32.16), and W is the weight in pounds. If we substitute 1^ = 2000 (or one ton), gf = 32.16, Vi= Vi — — , and2?2= V2 7——, to reduce the 3600 3600 243 TABLE XVII Velocity Head (Proportional to Kinetic Energy) of Trains Moving at Various Velocities Velocity Velocity Head (miles per F2X0. 03511 hour) 0.0 ■ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 5 0.88 0.91 0.95 0.99 1.02 1.06 1.10 1.14 1.18 1.22 6 1.26 1.31 1.35 1.40 1.44 1.48 1.53 1.58 1.62 1.67 7 1.72 1.77 1.82 1.87 1.92 1.97 2.03 2.08 2.14 2.19 8 2.25 2.30 2.36 2.42 2.48 2.54 2.60 2.66 2.72 2.78 9 2.85 2.91 2.97 3.04 3.10 3.17 3.24 3.30 3.37 3.44 10 3.51 3.58 3.65 3.72 3.79 3.87 3.95 4.02 4.10 4.17 11 4.25 4.33 4.41 4.49 4.57 4.65 4.73 4.81 4.89 4.97 12 ^5.06 5.15 5.23 5.32 5.41 5.50 5.58 5.67 5.75 5.84 13 5.93 6.02 6.12 6.21 6.31 6.40 6.50 6.59 6.69 6.78 14 6.88 6.98 7.08 7.19 7.29 7.39 7.49 7.60 7.70 7.80 15 7.90 8.00 8.11 8.22 8.33 8.44 8.55 8.66 8.77 8.88 16 8.99 9.10 9.21 9.32 9.43 9.55 9.67 9.79 9.91 10.03 17 10.15 10.27 10.39 10.51 10.63 10.75 10.87 10.99 11.12 11.25 18 11.38 11.50 11.63 11.76 11.89 12.02 12.15 12.28 12.41 12.55 19 12.68 12.81 12.95 13.08 13.22 13.35 13.49 13.63 13.77 13.91 20 14.05 14.19 14.33 14.47 14.61 14.75 14.89 15.04 15.19 15.34 21 15.49 15.64 15.79 15.94 16.09 16.24 16.39 16.54 16.69 16.84 22 17.00 17.15 17.30 17.46 17.62 17.78 17.94 18.10 18.26 18.42 23 18.58 18.74 18.90 19.06 19.22 19.38 19.55 19.72 19.89 20.06 24 20.23 20.40 20.57 20.74 20.91 21.08 21.25 21.42 21.59 21.77 25 21.95 22.12 22.30 22.48 22.66 22.84 23.02 23.20 23.38 23.56 26 23.74 23.92 24.10 24.28 24.46 24.65 24.84 25.03 25.22 25.41 27 25.60 25.79 25.98 26.17 26.36 26.55 26.74 26.93 27.13 27.33 28 27.53 27.73 27.93 28.13 28.33 28.53 28.73 28.93 29.13 29.33 29 29.53 29.73 29.93 30.13 30.34 30.55 30.76 30.97 31.18 31.39 30 31.60 31.81 32.02 32.23 32.44 32.65 32.86 33.08 33.30 33.52 31 33.74 33.96 34.18 34.40 34.62 34.84 35.06 35.28 35.50 35.72 32 35.95 36.17 36.39 36.62 36.85 37.08 37.31 37.54 37.77 38.00 33 38.23 38.46 38.69 38.92 39.15 39.38 39.62 39.86 40.10 40.34 34 40.58 40.82 41.06 41.30 41.54 41.78 42.02 42.26 42.51 42.76 35 43.01 43.26 43.51 43.76 44.01 44.26 44.51 44.76 45.01 45.26 36 45.51 45.76 46.01 46.26 46.52 46.78 47.04 47.30 47.56 47.82 37 48.08 48.34 48.60 48.86 49.12 49.38 49.64 49.91 50.18 50.45 38 50.72 50.99 51.26 51.53 51.80 52.07 52.34 52.61 52.88 53.15 39 53.42 53.69 53.96 54.23 54.51 54.79 55.07 55.35 55.63 55.91 40 56.19 56.47 56.75 57.03 57.31 57.59 57.87 58.16 58.45 58.74 41 59.03 59.32 59.61 59.90 60.19 60.48 60.77 61.06 61.35 61.64 42 61.94 62.23 62.52 62.82 63.12 63.42 63.72 64.02 64.32 64.62 43 64.92 65.22 65.52 65.82 66.12 66.43 66.74 67.05 67.36 67.67 44 67.98 68.29 68.60 68.91 69.22 69.53 69.84 70.15 70.46 70.78 244 RAILROAD ENGINEERING 233 velocities Vi and V2 (which are in feet per second) to Vi and V2, the velocities in miles per hour, the equation becomes Adding 5 per cent for the kinetic energy of rotation, the coefficient 66.89 becomes 70.23, but, considering that the 5 per cent correction is somewhat approximate and variable, the coefficient is taken at the even figure of 70 and the equation becomes 70 . p = ^ (Fa^-Fi^) (104) s in which P is the force in pounds per ton to accelerate a train from a velocity of Vi miles per hour to V2 miles per hour in a distance of s feet. Conversely, P is the force in pounds per ton which can be utilized in overcoming tractive or grade resistance when the velocity is reduced from ]\ m.p.h. to W m.p.h. in a distance of s feet. 180. Virtual Profile. The following demonstrations are made on- the basis that the ordinary tractive resistances and also the tractive force of the locomotive are independent of velocity. Neither of these assumptions is strictly true, especially the latter. The variation of tractive power with velocity will be considered later (article 191). But the approximate results obtained on the basis of these two assumptions are so instructive and useful that the demonstration is given. Assume that Fig. 157 shows the profile of a section of road and that the grade of ^ E is 0.40 per cent, which is 21.12 feet per mile. Assume also that a freight engine which is climbing up the grade has been so loaded that when the engine is working uniformly at its normal maximum the velocity up such a grade would be uniformly 20 miles per hour. But since the train is moving at 20 miles per hour it has akinetic energy corresponding to a velocity of 14.05 feet (see Table XVII). At A it encounters a downgrade of 0.20 per cent, which is 1500 feet long. Although A B has a dowTigrade of only 0.2 per cent, its grade with respect to the upgrade oi A E (0.40 per cent) is 0.60 per cent. There- fore B is 9.00 feet below B'. Since the work done by the engine would have carried the train up to the point 5' with a velocity of 20 miles per hour, the virtual drop of 9 feet will increase the 234 RAILROAD ENGINEERING 50-I7I u s '^^\ \ (V ^"p-b>7 velocity head from 14.05 feet to 23.05 feet, which corresponds to the velocity of 25.6 miles per hour, and this will actually be the velocity of the train at the point B. At B the grade changes to a 1 .0-per-cent upgrade for a distance of 2300 feet. The approach of the grade B C to the grade B' C is at the rate of 1.0-0.4, or 0.6 per cent and tlierefore the point C will be reached in 1500 feet. In the re- maining 800 feet the line will cHmb to 7), which is 4.8 feet above D'. Although at B the train is moving at the rate of 25.6 miles per hour and the engine is working at such a rate that it will carry the train up a 0.4-per-cent grade, yet when climbing up a 1. 0-per-cent grade it consumes its kinetic energy in over- coming the additional grade. When it reaches C, it has lost the additional kinetic energy which it gained from A to B, and as it continues it loses even more. When it reaches Z), it has lost 4.8 feet more and its velocity head is reduced to 14.05-4.8 = 9.25 feet, which corresponds to a velocity of 16.2 miles per hour. At D the grade changes to +0.1 per cent. Here we have the rather surprising condition that, although the grade is actually rising, it is virtually a down- grade under the given conditions, for the engine is working harder than is required to run up merely a 0.1-per-cent grade and hence will gain in velocity. At E, a dis- tance of 1600 feet from D, it reaches what would have been a uniform 0.4-per- 246 RAILROAD ENGINEERING 235 cent grade from A to E and the grade continues at that rate. Although the train has actually climbed 1 .6 feet from D to E, it has virtually fallen the 4.8 feet between D and D', and the velocity head has increased from its value of 9.25 feet at D to 14.05 feet, and its velocity is again 20 miles per hour. The upper line repre- sents the 'Virtual profile", which may always be drawn by measur- ing off to the proper scale at every point an ordinate which is the velocity head at that point. Since the engine is working uniformly, the virtual profile is in this case a straight line. Although the variation of resistance and tractive effort with velocity will have some effect on the precision of the above figures, as discussed later, yet the demonstration must not be considered as fanciful and impractical. Under the given conditions it is sub- stantially what would take place. If the grade B D were continued to Fj or until the actual grade intersected the virtual profile, the train would become stalled, for when the engine is loaded for an indefinite haul up a 0.4-per-cent grade, it cannot haul a train indefi- nitely up a higher grade. Practically the train would stall some- what short of F, since the tractive resistance increases as the velocity drops to nearly zero. Under such conditions, B D is sl ''momentum grade", which may be higher than the ruling grade, and yet it is practically harmless under these conditions, provided that a train is never required to stop on that grade. A B C is technically a "sag" in the grade A C and would be considered such even ii A B were an upgrade (although less than the grade A C). Such a sag is usually harmless unless it is so deep that the train would acquire a dangerously high velocity at the bottom of the sag B. In the above numerical case the velocity is only 25.6 miles per hour, w^hich is not at all dangerous even for freight trains in these days of air brakes and automatic couplers. But a much deeper sag might require the use of brakes, which not only consumes some of the energy stored in the train, but also wears out the wheel treads and brake shoes. Another phase of the question is developed when we consider the action of a train stopping on a grade. Assume, as in Fig. 158, that a train is climbing up the grade A B at sl uniform velocity whose velocity head is measured by A A' = B B' . At B it com- mences to slow up for a stop at C. Since it is stationary at C, the 247 236 RAILROAD ENGINEERING velocity head is zero and the virtual profile A' B' runs from B' to C by a line which may or may not be straight. Assume that the train starts up and. the engine exerts such force that at J) it has regained the velocity it had dit A ov B. The ordinate D D' must equal A A' and the virtual profile must run from C to D' . C D' therefore represents the virtual grade up which the train must climb. To put it in figures: Ass-ume that C D = 1300 feet; the required velocity at D is 20 miles per hour, and therefore D D' = 14.05; the grade of C i) is 1.0 per cent and therefore DD" = \Z feet, and D'' D' = 27.05 feet; the virtual grade CD' is therefore 2.08 per cent instead of the actual 1.0 per cent and these figures represent the actual ratio of the drawbar pulls at the engine. Fig. 158. Diagram Showing Action -of Forces on Train Stopping on Grade To be more precise, the virtual grade C D' will not be a uniform grade as shown in the figure but will be a curved line wh;ch will be steeper at the beginning of the grade on account of the increased resistance to traction when starting. This is somewhat compen- sated by the fact that the tractive force of the engine is greater at the very low velocities. It requires, however, a little margin for safety. The fact that the engine can increase its velocity from zero to 20 miles per hour in that distance and on that grade shows that it is capable of doing much more than rini its train up the 1.0-per- cent grade at a speed of 20 miles per hour. In fact, unless the power is reduced when the train reaches D, the train will continue to gain velocity. If resistance and tractive power were independent of velocity, the train would continue to gain indefinitely, assuming 248 RAILROAD ENGINEERING 237 that the grade continued uniformly. But practically, when the veloc- ity had increased to a much higher figure, the resistances would increase and the tractive power decrease until there could be no further incre^e in velocity. From all the above it may be inferred that (1) When the velocity is uniform, the virtual profile is parallel with the actual profile. (2) When the velocity is increasing, the profiles are separat- ing; when it is decreasing, they are approaching each other. (3) When the velocity is zero the profiles coincide. (4) The virtual grade at any place is a measure of the work required of the engine beyond that required to overcome merely the tractive resistances. If it is horizontal it shows that the engine is doing nothing besides overcoming the tractive resistances. If it is upward and is uniform, as in Fig. 157, it shows that it is work- ing uniformly and is storing in the train "potential" energy which may be utilized on the return trip if it is not utilized in moving down a succeeding downgrade. If it is downward, as from B' to C, Fig. 158, it shows that the train is giving up kinetic energy, probably consuming most of it in brakes, but utilizing some of it to furnish the tractive power to run from B to C and also to overcome the grade from B to C. 181. Use, Value, and Possible Misuse of Virtual Profiles. It has been previously shown that, aside from securing the maxi- mum traffic, the most important accomplishment for the locating engineer is to obtain low ruling grades. At the same time the cost for grading must be kept as low as possible without sacrificing the more important elements. The grade B D in Fig. 157 is an example of the possibility of introducing a grade which is much steeper than the ruling grade, providing it is not so long that the kinetic energy of the train at the bottom of the grade is exhausted before it reaches an easier grade, and also provided that no heavy trains are ever compelled to stop on that grade. Herein lies the danger and the possible misuse of this method. A grade might be laid out substantially as shown in Fig. 157, with the intention of running all heavy trains up that grade with- out stopping. Later, another railroad might require and make a grade crossing at or near C, which would occasionally require that 249 238 RAILROAD ENGINEERING trains shall stop at the crossing, and such loaded trains would be unable to start against such a grade, especially since the tractive resistance to starting is so much greater than the resistance at ordinary speeds. The chief value of such a method lies in the fact that it enables the engineer to determine the actual demand on the locomotive, as it is affected by the velocity of the train. The ''undulatory" profile shown in Fig. 157 will probably be much cheaper to construct than the uniform grade A E which would involve a fill at B and a cut at D. The method of a virtual profile will show at once whether ^uch a profile at that place will be a permissible way of economizing in spite of the fact that it intro- duces a 1-per-cent grade which is perhaps higher than the ruling grade. Many of the "improvements of old lines" depend on this process for their solution. For example, a grade which always may have been harm- less and unnoticed suddenly becomes important when it becomes desirable or necessary to require all heavy trains to stop at some point on it; such a ease is sketched in Fig. 158. The above method indicates how such a problem may be investigated. The grade C D' of course becomes the critical grade, but under given con- ditions the virtual profile will show the demand on the locomotive. Examples of this w^ill be given later. Undulatory grades have the advantage of decreasing the cost of construction and of being harmless under given conditions, but there are some dangers. C D Em Fig. 157 is called a "hump" in the grade. In the numer- ical case given it is only 4.8 feet and would be harmless under almost any conditions, but if it were considerably more, and if a train when passing C had a velocity much less than 20 miles per hour, it might become stalled before reaching the summit of the hump. Slippery rails or a strong head wind may so increase the resistances against which a train works that if the computed margin of velocity head at the top of a hump is made too small it may be entirely overcome and the train may be stalled before it is safely over the hump. A velocity of 5 miles per hour, which corresponds to a velocity head of only 0.88 feet is the least margin that should be safely allowed. This is also partly due to the fact that when the velocity becomes less than 5 miles per hour the resistances per ton increase, and as the velocity drops very low they increase 250 RAILROAD ENGINEERING ^39 very rapidly and the law on which the above calculations are based becomes inoperative. Another danger is that a sag may be so deep that trains will acquire an excessive velocity when passing through it unless brakes are applied. This of course does not mean that the sag must not be used. It simply means that the sag will cause a waste of energy in brakes, a waste which must afterward be made up by increased work from the locomotive. This, consequently, is one of the cases which requires computation, by methods which follow, to determine whether or to what extent the sag is justifiable so that the two items of increased first cost and increased operating expenses shall be made a minimum. For example, a freight train may approach a sag with a velocity of 20 miles per hour. Its velocity head is therefore 14.05 feet. If the -sag at its lowest point is 40 feet lower than the imaginary grade line on which the train could have run without changing its velocity (the grade ^ J5' in Fig. 157), then the velocity head of the train at the bottom of the sag would be 54.05 feet, which corresponds to a speed of 39.2 miles per hour. Although this is a permissible speed with freight trains which are equipped with air brakes and automatic couplers, it is approaching the limit, and there might be some local conditions which would render even this speed through the sag inadvisable. 182. Problems. 1. If a train is running uniformly along a level grade at a speed of 35 miles per hour and reaches a 1.2-per- cent upgrade, how far up the grade could it run before its speed is reduced to 10 miles per hour? Velocity head for 35 miles per hour = 43.01 feet Velocity head for 10 miles per hour= 3.51 feet Permissible increase in elevation = 39.50 feet Distance from bottom of grade = 39.50 ^.01 2 = 3292. feet 2. At what speed may a train approach a sag 28 feet below the normal grade line so that its maximum speed at the bottom of the sag shall not exceed 36 miles per hour? At 36 miles per hour the velocity head = 45.51 feet Subtracting the depth of the sag = 28.00 feet The permissible velocity is that due to 17.51 feet or 22.3 miles per hour. 251 240 RAILROAD ENGINEERING RESISTANCES 183. Train Resistance. The energy of the steam in the loco- motive boiler is spent first in overcoming the various internal resist- ances between the boiler and the rims of the driving wheels. This engine resistance is computed later. Then the resistance due to the truck wheels of engine and tender and the atmospheric resist- ance together make up the difference (on a level track and at uni- form velocity) between the adhesion at the drivers and the draw- bar pull. The draw-bar pull is spent, as discussed herewith, in overcoming the effect of (1) grade, (2) curvature, (3) the normal track resistance on a straight-level track at uniform velocity, (4) the force required to accelerate and (5) the starting resistance. (1) Grade Resistance. Grade resistance is readily determin- able with mathematical accuracy and equals 20 pounds per ton (of 2000 pounds) for each per cent of grade. For example, the grade resistance on a 1.2-per-cent grade is 20X1.2 = 24 pounds per ton. (2) Curvature Resistance. Curvature resistance is usually con- sidered to be the equivalent of a .035-per-cent grade for each degree of curvature, although the resistance varies somewhat, depending on the velocity, and on the superelevation of the outer rail, the resistance being greater if the velocity is much less than that for which the superelevation was designed. This is the value usually taken in computing the compensation for curvatures (see article 176). Then the resistance in pounds per ton equals 20 X. 035 = 0.7 pound for each degree of curvature. • Examples. 1 . What is the curvature resistance per ton on a 4-degree curve? Solution. 4 X 0.7 = 2.8 pounds per ton '2. What is the combined curvature and grade resistance on a 6-degree curve, located on a 2.2-per-cent grade? Solution. The grade equivalent to the curve = 6X -035 = 0.21, which added to 2.2=2.41 per cent, the equivalent grade. 20X2.41=48.2 pounds per ton, the resistance. (3) Normal Track Resistance. Normal track resistance is a combination of several resistances which are variously affected by changes in conditions. The resistance to the rolling of wheels on the rails is a very small part of the total resistance. Accurate tests of journal friction show that the friction of axles in their bearings is actually less at higher velocities, probably because the resulting higher 252 RAILROAD ENGINEERING 241 temperature reduces the friction. The total varies with the number of cars in the train. The resistance per ton is much lower as the load per wheel increases. The atmospheric resistance of freight trains evidently depends on whether the train is made up of only one type of car (box, flat, or gondola), or of a combination of types, which would increase that resistance. Numerous experiments have been made, by placing a dynamometer between the locomotive and first car, to determine the amount of the tractive force and to dis- cover its variation with velocity and its other laws. Of course it was necessary, when analyzing the results of these tests, to deduct first the effect of grade, curvature, and acceleration or retardation; but even then the results are so far from uniform that no set of numerical values can be uniformly applied to all grades of track. This variation is due to the very evident fact that the resistance would be less on a high-grade, well-kept track, with heavy rails than on a cheap, rough track, with light rails. But there is one very significant and surprising result which may be deduced from each series of tests, and that is, that a formula which makes the resistance equal a constant times the number of tons plus another constant times the number of cars, but with no variation depending on veloc- ity, will satisfy the dynamometer results as closely as any other equally simple law. This statement applies to freight trains between the velocities of 5 miles and 35 miles per hour. When starting the resistance is greater. At higher velocities than 35 m.p.h. the resist- ance is also greater, but since the economies of reduced resistance apply chiefly to freight trains at usual working velocities, the sim- plicity of the above law is important. Each set of tests on any given piece of track will give a new pair of constants for the resist- ance formula. A compilation of the results of many tests gave the following, issued by the American Railway Engineers Association, as an average formula: R = 2.2 r+121.6C (105) in which R is total resistance at uniform velocity on a level tangent; T is total weight of cars and contents, in tons; and C is number of freight cars in train. It should be clearly understood that the formula does not necessarily give the actual resistance for any given case, since the 253 242 RAILROAD ENGINEERING resistance will depend on the actual condition of the track, but the result will be a good average result and for comparative purposes the formula is useful. The resistance of trains at higher velocities than 35 miles per hour must be considered as depending on velocity. The formula used by the Baldwin Locomotive Works is 7^ = 4.3+0.0017 V (106) in which R is the resistance per ton, and V is the velocity in miles per hour. The formula is particularly applicable to passenger trains having cars weighing 45 tons and over. For lighter cars, the freight-train formula should be used. The formula should not be used for low velocities, especially those below 10 miles per hour, nor for light-weight cars. Example. Assume that there are 33 freight cars weighing, with con- tents, 2200 tons. What is the total resistance behind the engine? Applying equation (105) /2 = 2.2 X 2200 + 121 .6 X 33 = 8853 pounds As an illustration of variations in results, depending on varia- tions in track condition, some tests on the Baltimore & Ohio Railroad were reduced to a formula similar to equation (105) but with the constants, 2.78 and 113.9. Using these constants and applying the formula to the above numerical case, the computed value of R would be 9875, an increase of nearly 12 per cent. This variation shows the uselessness of attempting to apply any definite numerical values and to expect accuracy unless the resistance of the particular track in question has been determined by actual test. (4) Accelerative Force. Accelerative force has been computed theoretically in article 179. The formula for acceleration may also be applied to determine how far the kinetic energy in a train will help to force it up a grade which is greater than that up which the locomotive could haul such a train indefinitely. (5) Starting Resistance. As previously stated, the resistance per ton when starting a train is considerably in excess of the ordinary resistance. When cars have been left standing for several hours, or even days, especially in winter weather, it may take a force of 40 pounds per ton to produce motion. The bearings become "frozen". But such resistance is only momentary and may be 264 RAILROAD ENGINEERING 243 partly overcome by the impact of moving cars or engine striking against the stalled cars. When an engineer reverses his engine, backs it against the cars, and then immediately reverses again so as to go forward, he accomplishes three things: (1) the journals become loosened from the comparatively rigid condition they will assume even during a short stop; (2) the springs of the couplers w ill become compressed during the small backward motion and their expansion during forward motion wdll materially assist the forward motion; (3) if the train is very long, the total slack in the couplers is very considerable and the locomotive will have moved several feet before the last car begins to move and the cars are started one by one. Such devices in operation reduce to a variable extent the resistance which would be encountered if all cars were started at the same instant. A series of tests on the Rock Island system gave results with an ordinary range from 10 to 18 pounds per ton and averaging 14.1 pounds. An extreme value of 30 pounds was noted for ''frozen bearings" and a low extreme of only 6 pounds extra when the stop was only momentary. Since a juggling of the train can produce virtually the same result as a mere momen- tary stop, the necessary extra starting resistance for a limiting case will be considered as only 6 pounds per ton in solving some numerical problems in a later article. Example. How much draw-bar pull wiU be required to haul a freight train of 10 cars, each weighing 70 tons, and a caboose weighing lo tons, at a uniform velocity of 15 miles per hour up a 0.9-per-cent grade? Solution. The only significance of the 15 m.p.h. in the solution is the fact that it is between 5 and 35 and that equation (105) is applicable. The grade resistance per ton is 20X0.9 = 18 pounds, and for the 11 cars weighing 715 tons it is 715X18 = 12,870 pounds. The tractive resistance, by equation (105), is 72 = 2.2X715 + 121.6X11=2911 pounds Adding the gi-ade resistance, the total resistance would be 15,781 pounds. The above problem assumed- gondola cars weighing 40,000 pounds and- each carrying 100,000 pounds and a 15-ton caboose. Suppose that the train consisted of empties, say 35 empties at 20 tons each, or 700 tons, and the 15-ton caboose. The total weight being the same, the grade resistance is the same. But the number of cars being greater, the tractive resistance is greater and 7^ = 2.2X715+121.6X36 = 5951 pounds 255 244 RAILROAD ENGINEERING which is an increase of 3040 pounds, and the tractive resistance is more than doubled. It should be noted that if there were no grade, the tractive resistance would be only 2911 pounds for the loaded train and 5951 pounds (over twice as much) for the empty train of the same gross weight. On the other hand, on the 0.9-per- cent grade the resistance of the loaded train would be 15,781 pounds and that of the train of empties 5951 + 12,870 = 18,821 pounds, which is only 19 per cent greater. The average tractive resistance per ton of the loaded train is 2911-^-715 = 4.07 pounds, while that of the empty train is 5951 -r- 715 = 8.32 pounds. The grade resistance is constant in either case at 18 pounds per ton. The character of the train load, whether loaded or consisting of a long train of empties of the same gross weight, is thus a matter of great impor- tance on a level or nearly level road and becomes of much less impor- tance on a grade of even 0.9 per cent. On a 2-per-cent grade the tractive resistance is comparatively small and variation in the character of the loading is of still less importance. Example. How much tractive force will be required, using the data of the previous example, to increase the velocity from 15 m.p.h. to 20 m.p.h. in a distance of 500 feet? Solution. Applying equation (104) we have Fi = 15, ¥.^ = 20, and s= 500. Then 70 P = ^(20^-15^) =24.5 pounds per ton For the 715-ton train, this will require an extra pull of 17,518 pounds. This is the equivalent of a 24.5-^20=1.225-per-cent grade. Whether the locomotive has sufficient tractive force to pull 15,781 pounds of tractive force and grade resistance and 17,518 pounds more for acceleration, or a total of 33,299 pounds, is a matter to be studied under "power of the locomotive", article 189. The further question would arise, could the locomotive make steam fast enough to produce this energy? This will be considered in article 189. Example. What is the tractive resistance behind a passenger engine of a load of 4 cars, each weighing 52 tons and traveling at a velocity of 60 miles per hour? Solution. Substituting in equation (106) the value of F = 60, we obtain R = 10.42 pounds per ton, and for the 208 tons the draw-bar pull would be 2167 pounds. 256 RAILROAD ENGINEERING 245 Irrespective of the resistance of the locomotive itself, considered later, this pull of 2167 pounds at a velocity of 60 m. p. h., or 88 feet per second, is the equivalent of 88X2167 = 190,696 foot-pounds per second, or, dividing by 550, equal to 346 horsepower. PULLEY POWER OF LOCOMOTIVES 184. Rating of Locomotives. Since it is very important for the economical operation of roads that each locomotive should be loaded to the limit of what it can efficiently haul, and since, as shown in article 183, the hauling power of a locomotive, especially on a flat grade, depends on the number of cars as well as on their gross weight, it is important to determine for each locomotive a loading which will measure its power and which is independent of the number of cars or of the rate of grade. This loading is called its ''rating" and by applying to the rating a proper correction, depending on the number of cars and grade, the hauling power or the proper loading of that locomotive for any grade may be readily determined. Let P be pulling powder of the locomotive, or the tractive power as measured at the rim of the drivers; E weight of engine and tender, in pounds; W weight of cars behind tender, in pounds; R rate of grade, or ratio of vertical to horizontal; K a constant which, as determined by tests, is the factor 2.2 pounds per ton, in equation (105); C a constant which, as determined by tests, is the factor 121.6 pounds per ton, in equation (105); N number of cars in the train; and A the desired rating. Then P={E+W) {R+K)^NC transforming. R+K ' R-\-K The right-hand side of this equation is the weight of the train behind the tender plus the number of cars times a quantity made up of two constants and the rate of grade. This right-hand side of the equation is called the rating, or A. Values of the fraction C-i-{R-\-K), in tons per car, which are independent of engine or train characteristics, are tabulated for various rates of grade, as given in Table XVIII. In computing these values, since C and A' are resistances per ton, R must be the resistance Der ton for the rate of grade considered. 246 RAILROAD ENGINEERING TABLE XVI H Values of C-7-(R-\-K) for Various Grades (In tons per car) Grade R (per cent) Tons Grade R (per cent) Tons Grade Tons Grade Tons Grade Tons PER Car PER Car R PER C.\.R R per Car R per Car (R+K) (R+K) (per cent) C-r iR+K) (per cent) C^ iR+K) (per cent) (R+K) Level 55 0.5 10.0 1.0 5.5 1.5 3.8 2.0 2.88 0.1 29 0.6 8.5 1.1 5.0 1.6 3.6 2.1 2.75 0.2 20 0.7 7.5 1.2 4.6 1.7 3.4 2.2 2.63 0.3 14 0.8 6.7 1.3 4.3 1.8 3.2 2.3 2.52 0.4 12 0.9 6.0 1.4 4.0 1.9 3.0 2.4 2.42 Examples. 1. Assume that the pulling power P of a locomotive, or the power at the rim of the drivers, computed as in article 190, was estimated to be 33,742 pounds and that the weight E of the engine and tender was 315,000 pounds. On a 0.5-per-cent grade R = .005 and K = 2.2 pounds per ton or .0011 pound per pound. Solution. P ^^ 74-9 A=^^^-E= ^^:\;^,, -315,000 = 5,216,000 pounds = 2608 tons il-f-zl .OUo + .LMJll which is the rating for a 0.5-per-cent grade. Similar ratings for that locomotive may be easily computed for all rates of grade. Such a locomotive may haul on any grade a load W such that A=W+N C-=-(fl+K). From Table XVIII we find that, for a 0.5-per-cent grade, C-^{R+K) = 10. If there are 40 cars in the train, then 2608 = TF-f- (40X10) W = 2608 - 400 = 2208 tons which is an average of 55 tons per car. If the cars are of uniform weight (such as empties, weighing say 18 tons) then W = 1S N, and the equation becomes 2608 = 18 iV + 10 AT = 28 AT and iV=93 which means that such an engine can haul a load of 93 empties, each averaging 18 tons, up a 0.5-per-cent grade at a uniform velocity. Note that this ignores curvature resistance, which if it exists is assumed to be provided by a com- pensation of the grade. 2. What would be the rating for the same locomotive on a long 1.6-per- cent grade? Solution. 33,742 A = 315,000 = 1,658,000 pounds = 829 tons Again considering .016 + .0011 By Table XVIII, the "adjustment" in tons per car is 3.6 empties weighing 18 tons, we would have 829 = 18 A^+3.6iV = 21.6 AT and N = SS 258 RAILROAD ENGINEERING 247 If all cars were loaded and had an average weight of 56 tons, we would have 829 = 56 Ar+3.6 i\r = 59.6 N A'' = nearly 14, or say 13 loaded cars and the caboose In the above examples the pulUng power P is determined on the basis of the locomotive working at the maximum velocity M at which it can maintain full stroke. See article 190. This represents practically the maximum power of the locomotive. The velocity M is usually from 4 to 7 miles per hour and is as low as should be allowed on maximum grades, since an attempt to utilize a slightly higher tractive force at a somewhat lower velocity would probably result in stalling the train if an unexpected resistance in the track slightly increased the normal resistance. 185. Units of Operation. A large part of the calculations in railroad economics consists of a valuation of changes in alinement or the financial value of a reduction of distance, curvature, rise and fall, and ruling grade. Formerly such calculations were made exclusively on the basis of the cost of an average train-mile^ especially as this is shown to be surprisingly constant for roads of all charac- ters, long and short, heavy traffic and light traffic. The general method was to take up each item in turn of the average cost of operating trains and to estimate the effect of a change in alinement on the normal average percentage of each item. Some of the items are affected very materially; others are affected very little or not at all. The normal average for each item was then multiplied by the percentage by which that item was estimated to be affected by that unit change in alinement conditions, and then the sum of these prod- ucts would be the computed percentage by which that unit change of alinement would affect the average cost of a train-mile. Further study has shown that the cost of fuel, for example, for freight trains is disproportionately high. Therefore, when comparing the rela- tive costs of operating freight locomotives on two different grades, it will not do to base the estimate of increased fuel demand on the average cost of fuel for locomotives of all kinds. But it has become increasingly apparent that the effect of grade, for example, on the cost of operating a train is largely dependent on the weight of the train, on the character of the locomotive and its rating. Therefore the effect of grade cannot be measured by any one factor times the number of train miles involved. 259 248 RAILROAD ENGINEERING Some of the elements of variation of operating expenses are more accurately measured by the number of ton-miles. A study of the effect of rolling stock on track maintenance shows that it is largely dependent on train velocity and also on intensity of axle loading. Although exact ratios are not computable, it has been broadly estimated that passenger trains, having a much higher average velocity, are responsible for twice as much track damage as the same tonnage of freight trains; also that locomotives, having heavier axle loads and not being truly counterbalanced, are respon- sible for twice as much track damage as the cars of the same train, which w^ould mean that the locomotive of a high-speed passenger train would do four times as much damage as the car axles of a slow freight. The passenger-mile, although frequently used in statistics of service rendered by railroads, has little or no relation to the cost of service and therefore is not used in problems of changes in alinement and grade. The car-mile is a useful unit for some special purposes. If a steel passenger car weighs 100,000 pounds and carries even its maximum load of 80 passengers with an average weight of 125 pounds, the total live load (10,000 pounds) is only 10 per cent of the dead load. And when, as is usual, the actual live load is only a part, and perhaps a small part, of the possible load, then it makes but little difference in the tractive force required for hauling, espe- cially on low grades, whether the car is loaded or empty. Other items of expense vary almost directly as the number of car-miles. The engine-mile is similarly a useful unit in estimates in which certain costs vary as the number of engine-miles and nearly or quite regardless of variations in other factors. Another element of practical cost in the operation of trains over a division is the total time required for a run by the slow freight trains. The old methods would invariably indicate that the- most economical grades, using locomotives of a certain power, were those which would permit the maximum train load, even at the slowest velocity. But it was later developed that it is actually more econom- ical to run somewhat lighter trains at a higher velocity; and that there is a certain combination of train load and velocity beyond which, if the train load is increased and the time of run increased. 260 RAILROAD ENGINEERING 249 the extra fuel burned, the extra time of the train crews, and the extra blocking of the tracks (especially on a single-track road) more than offset the economy of increased tonnage in one train. A con- sideration of these various elements and units of operation shows the impracticability of adopting any uniform unit values for one foot (or mile) of distance saved, or of one degree of curvature saved, or for each fV per cent of grade lowered, which would be sufficiently accurate for universal applicability, and that the only accurate method of studying the value of a proposed change of alinement for handling an assumed amount of business, with an assumed type of locomotive, is to estimate the power of that locomotive on each of the two grades (or other variations of alinement) and the relative number of trains, with their cost of operation, in order to handle that business. If the problem is a suggested change in an existing road, the investigator has the advantage of an opportunity to study what the locomotive in use can do on the existing alinement and grades, and he has only to compute the effect of the changes. If the problem is a suggested change in a proposed new line, the cost of operation under both conditions must be estimated. 186. Types of Locomotives. The variations in locomotive service have developed all conceivable types as to total weight, ratio of total weight to weight on drivers, types of running gear, relation of steaming capacity to tractive power, etc. The method of classification on the basis of the running gear is very simple. The number of wheels on both rails of the pilot truck, if any, is placed as the first of three numbers. If there is no pilot truck, the character is used. This is followed by the number of drivers and then by the number of trailing wheels, if any. For example, a Pacific-type engine has four wheels on the pilot truck, six driving wheels, and two trailing wheels under the rear of the boiler. The wheel base is symbolized as 4-6-2. The most common types of locomotives, with their popular names and wheel-base symbols, are 2-8-0 2-8-2 4-8-0 2-10-2 A-B-B-A 1, usually 2 or Six-wheel switcher 0-6-0 B= drivers, varying from 4 to 10 261 American 4-4-0 Consolidation Columbia 2-4-2 Mikado Atlantic 4-4-2 Mastodon Mogul 2-6-0 Santa Fe Ten-wheel 4-6-0 Mallet Pacific 4-6-2 A = truck w. 250 RAILROAD ENGINEERING The Interstate Commerce Commission report for 1912 showed 534 locomotives of the *'Mallet" type, out of a total of 62,262 in the U. S. This is less than 1 per cent but, considering that the growth in numbers of this type in one year was nearly 23 per cent while the increase in all classes was about IJ per cent, or that more than 10 per cent of the net increase was of this type, it deserves special men- tion. Excluding freak variations, they are always "four-cylinder compounds", one pair of cylinders discharging into the other pair and then exhausting. They have from five to ten driving axles, and have a length of engine wheel-base up to nearly 60 feet. Some- times the boiler is made ''flexible" by a set of accordion-shaped steel rings forming a joint in the boiler shell. The boiler proper is on one side of the joint and the feed-water heater, the reheater, and perhaps the superheater are on the other side. Or, the boiler shell is made rigid, one end is rigidly attached to the frame carrying the high-pressure cylinders and the other end is supported on a bearing on the truck frame which carries the low-pressure cylinders and the drivers operated by them. The low-pressure truck frame swings around a pivot in the fixed frame and this so cuts down the length of rigid wheel-base that these engines are operated successfully on 20-degree curves, and are therefore practicable on any road having reasonable alinement. These locomotives are chiefly used by roads handling large quantities of heavy freight, such as coal, up long stretches of heavy grades, where the demand for tractive power is very great. The tractive power of some of these locomotives is over 110,000 pounds, which is nearly four times as great as that of the average locomotive in the United States. 187. Oil=Burning Locomotives. In 1912 over one-sixth of all the locomotives west of the Mississippi River used oil as fuel. Some of the advantages in using oil are as follows: (1) the British thermal units in one pound of oil vary from about 19,000 to 21,000; those in a pound of coal vary from perhaps 14,000 down to 5000 for the poorer grades of lignite found in the western part of the United States and this means a great reduction in the cost of carrying and storing fuel, measured in heat units; (2) the cost of handling fuel is reduced and that of disposing of ashes is eliminated; (3) engine repairs are reduced in many respects although it is said that the increased cost of fire-box repairs, due to the intense heat of the oil 262 RAILROAD ENGINEERING 251 flame, offsets any reduction in other items; (4) the fires can be more easily controlled and waste of heat reduced during stoppages or when drifting down grade; (5) wayside fires due to sparks are alto- gether eliminated; (6) there is a practical limitation (see article 189) to the amount of coal that one fireman can feed to a fire, but there is no such limitation when using oil; (7) there is an equality in cost of heat units when a 42-gallon barrel of oil, weighing 7.3 pounds per gallon, costs 60 cents and a ton (2000 pounds) of coal, having two-thirds as many heat units per pound, costs $2.61, or 4.35 times as much. The other items of difference almost invariably favor the oil and might make it more desirable even when the ratio of cost seemed to favor the coal. Oil is used very extensively west of the Mississippi River, where in many places oil is plentiful and cheap and coal is poor in quality and high in price. 188. Relation of Type to Service and to Track Conditions. Economy in operating conditions requires a thorough co-ordination between the characteristics of the locomotive, the fuel it is to burn, the roadbed and track it is to run on, and the character of service it is to render. It may not even be the best economy to use the same type of locomotive, for a given kind of service, on consecutive divisions of the same road. IV heel- Load to Rail-Weight. Since the support w^hich the rail receives from the ties and ballast is uncertain and variable, any rule for the relation must be empirical and approximate. The rule adopted by the Baldwin Locomotive Works ("300 pounds of wheel per pound of rail per yard") may be used in making a diagram from which the relation between total weight on driving wheels, number of drivers, and weight of rail, may be readily observed. Fig. 159. For example, if it is desired to use a type of locomotive with 170,000 pounds on the drivers and also 75-pound rails, four pairs of drivers will be needed. By using 95-pound rails the same weight on drivers could be placed on three axles. As another example, a Pacific-type locomotive, with 150,000 pounds on its six drivers, should have a rail with a minimum weight of 83 pounds, or say an 85-pound rail. 189. Power of Locomotives. The tractive power of a loco- motive, or its *'draw-bar pull" is limited by the adhesion of the drivers, and by the capacity of the boiler to make steam. The 263 252 RAILROAD ENGINEERING adhesion of the drivers is a fairly definite ratio of the weight on the drivers. Under very favorable conditions, with a dry rail and using sand, a ratio of one-third and over can be obtained. As 500,000 : 7 J / T z / z z / z yicn nnn / 7 z ^50,000 - J 7 ~ : ^/' -A"^- z y w 7 7 7 <\^ r/ / ^ z ^ r\n nnn /^ 1 \A r 7 ^00,000 - 7r^ -Ja -. y ~ ~ >^ A^- /r 7 : ^^ -/m-7 W ^ y ^. ^^v/-. ^^ ./r, / / ncrn nnn i\ y^^ 1 7" : y' . 350,000 ^1 ,/$x)V .y^ /^ -S / ?^?)Y X y g 7 / ^ v^ > ^ ~y 7 /_ ^0 /^ •>L r^nr) nnn t 7 7 ^ Zjiv y , JUO, 000 - - 7 /. V y ^"^ : : ^=^ <0 "Z ^ ^ <<-v - _ .^ '^ ^ I /. z ^ ^^ 1 ^ z ^^ t- - .^ »v. ocn nnn /_ 7 y ^^ ^ CD0,000 - / r 7" ^^ - ^ / y^ ^^ - - ^^^ i /^ .^ .^^ fiL _ _ ^x=" '^ t ^ ^ ^^ ^^ C^ {9/0/0 nr\ n y ^^ t ^'^'' ^ COO.OOO \.^ .-^ ^ •*>, tt / ^'^ ^^ oWC^ ' •^ y >■ ^^ "^ 4^ ' ^-^ -^ _ .^ ^'^ ^ ^^-^ *^ linn nnn t ^^ ^^: "■^ ^ ^ •nr^'^ ^^^ -^'^'^ Soil ' ^ .^ ^ r ^^ ^^X-"^" inn nnn - . iu^efs lUU, 00 U _^— ■ Si?^"^- ^ ^ ^ ^ —"^ 50,000 . 50 60 70 60 90 100 Weight of Rail -Pounds per Yard Fig. 159. Curves for Finding the Number of Drivers Needed for Given Weight on Driving Wheels and Weight of Rails an ordinary value one-fourth {\%), or perhaps nine-fortieths is more usual. Under unfavorable conditions, the ratio reduces to one-fifth (j^), or less. The capacity of the boiler to make steam depends on the grate area, the heating surface, and (in the case of 264 RAILROAD ENGINEERING 253 modern heavy freight locomotives) the capacity of the fireman to shovel coal. Experience shows that an average fireman, when he must maintain the full power of the locomotive for long periods of time, can handle about 4000 pounds of coal per hour, although individual performances, in special test cases and for short periods of time, have given much higher values. It may occasionally be admissible to estimate on extra work up to 5000 pounds per hour for a short period, provided it is preceded or followed by easier work. The use of automatic stokers can raise this hourly consumption very considerably (say up to 7000 pounds) or up to the capacity of the locomotive to burn coal properly, whatever it may be for the par- ticular type. There is of course no such limitation in the use of oil-burning locomotives, which now include about 7 per cent of the total number in the United States. These are the exceptional cases. The power developed by any given type of locomotive depends largely on the characteristics of the coal used. A British thermal unit (symbolized as B.t.u.) is the quantity of heat required to raise the temperature of 1 pound of pure water 1° Fahrenheit, when the water is at or near its maximum density at 39.1° Fah- renheit. When it is said that a certain grade of coal has 14,000 B.t.u. it means that the heat in 1 pound of that coal will raise the temperature of 14,000 pounds of water 1°, or, approximately, 100 pounds of water 140°. But although it only requires 180.9 heat units to heat water from 32° to 212°, it requires 965.7 more heat units to change it from water at 212° to steam at 212°. It requires only 53.6 more heat units to change it from steam at 212° to steam at 387.6° or with a pressure of 200 pounds per square inch. A study of locomotive tests made at the St. Louis Exposition resulted in the compilation of Table XIX, which is copied from the Proceedings of the American Railway Engineering Association, and is now included as Table 1, in the Economics section of their Manual. It was found that the steam produced per square foot of heating surface is very nearly proportional to the coal burned per square foot of heating surface. The results are purposely made about 5 per cent below the results obtained in the St. Louis tests to allow for ordinary working conditions. 265 254 RAILROAD ENGINEERING TABLE XIX Average Evaporation in Locomotive Boilers Burning Bituminous and Similar Coals of Various Qualities, and for Various Quantities Consumed per Square Foot of Heating Surface per Hour (Based on feed water at 60° Fahrenheit, and boiler pressure 200 pounds) Steam per Pound of Coal OF Given Thermal Value Coal per Square (lb.) . Foot of Heating Surface per Hour (lb.) 15,000 14,000 13,000 12,000 11,000 10,000 B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. B.t.u. 0.8 7.86 7.34 6.81 6.29 5.76 5.24 0.9 7.58 7.07 6.57 6.06 5.56 5.05 1.0 7.31 6.82 6.34 5.85 5.36 4.87 1.1 7.06 6.59 6.12 5.65 5.18 4.71 1.2 6.82 6.37 5.91 5.46 5.00 4.55 1.3 6.59 6.15 5.71 5.27 4.83 4.39 1.4 6.37 5.95 5.52 5.10 4.67 4.25 1.5 6.17 5.76 5.35 4.94 4.52 4.11 1.6 5.97 5.57 5.18 4.78 4.38 3.98 1.7 5.79 5.40 5.02 4.63 4.25 3.86 1.8 5.61 5.24 4.86 4.49 4.12 3.74 1.9 5.44 5.08 4.71 4.35 3.99 3.63 2.0 5.27 4.92 4.57 4.22 3.86 3.51 2.1 5.12 4.78 4.44 4.10 3.75 3.41 2.2 4.97 4.64 4.31 3.98 3.64 3.31 2.3 4.83 4.51 4.19 3.86 3.54 3.22 2.4 4.69 4.38 4.07 3.75 3.44 3.13 2.5 4.56 4.26 3.95 3.65 3.34 3.04 2.6 4.44 4.14 3.84 3.55 3.25 2.96 2.7 4.32 4.03 3.74 3.46 3.17 2.88 2.8 4.21 3.93 3.64 3.37 3.09 2.80 2.9 4.10 3.83 3.55 3.28 3.01 2.73 3.0 3.99 3.73 3.46 3.19 2.93 2.66 The quantity of steam evaporated for intermediate quantities or qualities of coal can be found by interpolation. On bad-water districts deduct the following from tabular quantities: For each ye inch of accumulated scale 10 per cent For each grain per U. S. gallon of foaming salts in the average feed water 1 per cent 190. Power Calculations. Illustrative Example. Assume that a Mikado locomotive, having a total heating surface of 2565 square feet is fired with coal whose samples test 13,000 B.t.u. On the basis that a fireman can handle 4000 pounds of coal per hour and main- tain such work throughout his run, the coal may be fed at the rate 266 RAILROAD ENGINEERING 255 of --— = 1 .56 pounds per hour per square foot of heating surface. ZODO If the air-dried mine samples of the coal tested 13,000 B.t.u., the average run-of-car coal would have about 90 per cent of this, or 11,700 B.t.u. Interpolating in Table XIX for 1.56 and 11,700 we find that the pounds of steam per pound of coal would be 4.72. But since the locomotive is designed for use at 175 pounds gage pressure, instead of 200, as in Table XIX, the amount of steam produced will be about 0.3 per cent more, or say 4.73. The uncer- tainties of firing are so great that such small corrections may be ignored. But considering that a superheater is used in this loco- motive, and that, with the usual superheater proportions and efficiency, 0.85 pound of superheated steam may be considered as having the same volume and pressure as 1 pound of saturated steam, the amount of steam developed by 1 pound of coal is equivalent to 4.73 -^ 0.85 = 5.56 pounds. Then the equivalent amount of steam developed per hour equals 5.56X4000 = 22,240 pounds. The weight of steam used per stroke may be computed most easily by utilizing Table XX, which is also taken (but somewhat amplified) from the Proceedings of the American Railway Engineering Association, and now included as Table 2 in the Economics section of their Manual. The weight of steam per foot of stroke for 22 inches diameter and 175 pounds gage pressure is 1.106 pounds and for a stroke of 28 inches (2 J feet) it is 2.581 pounds. For a complete revolution of the drivers it is 4X2.581 = 10.324 pounds. Since the engine can develop the equivalent of 22,240 pounds of steam per hour and will use 10.324 pounds at one revolution, it can run at a speed of 22,240 -^ 10.324 = 2154 revolutions per hour, or 35.9 revolutions per minute, at full stroke and maintain full boiler pressure. The drivers are 57 inches in diameter and there- fore have a circumference of (57-^ 12) X3.1416 = 14.923 feet. The maximum engine speed for full stroke is 35.9X14.923 = 535.7 feet per minute. Multiplying by 60 and dividing by 5280, or dividing by 88, we have 6.087 miles per hour as the maximum speed at which full stroke can be maintained. In Table XXI, also taken from the proceedings of the American Railway Engineering Association and now included as Table 4 in the Economics section of the Manual, are given the pounds of steam 267 256 RAILROAD ENGINEERING TABLE XX Weight of Steam Used in One Foot of Stroke in Locomotive Cylinders (Cylinder diameter is for high-pressure cylinders in compound locomotives) Diameter Weight op Steam per Foot of Stroke for Various Gage Pressures Cylinder (inches) 220 Pounds per Square Inch (lb.) 210 Pounds per Square Inch (lb.) 200 Pounds per Square Inch (lb.) 190 Pounds per Square Inch ' (lb.) 180 Pounds per Square Inch (lb.) 170 Pounds per Square Inch (lb.) 160 Pounds per Square Inch (lb.) 12 13 14 15 15^ 0.405 0.475 0.551 0.633 0.675 0.389 0.456 0.529 0.607 0.649 0.370 0.435 0.504 0.579 0.618 0.354 0.415 0.482 0.553 0.590 0.337 0.396 0.459 0.527 0.562 0.321 0.376 0.436 0.501 0.535 0.304 0.357 0.414 0.476 0.508 16 17 18 18^ 19 0.720 0.812 0.911 0.962 1.015 0.691 0.780 0.875 0.924 0.975 0.658 0.744 0.834 0.881 0.928 0.629 0.710 0.796 0.841 0.887 0.599 0.676 0.759 0.801 0.845 0.570 0.643 0.722 0.762 0.804 0.541 0.611 0.685 0.724 0.763 191 20 20^ 21 22 1.069 1.125 1.181 1.240 1.361 1.027 1.080 1.134 1.191 1.307 0.978 1.029 1.081 1.134 1.245 0.934 0.983 1.032 1.083 1.189 0.890 /0.936 0.984 1.032 1.133 0.847 0.891 0.936 0.982 1.078 0.804 0.846 0.888 0.932 1.023 23 24 25 26 27 1.487 1.620 1.758 1.901 2.050 1.428 1.555 1.688 1.825 1.968 1.361 1.482 1.608 1.739 1.875 1.300 1.416 1.536 1.661 1.792 1.238 1.348 1.462 1.582 1.706 1.178 1.283 1.392 1.506 1.624 1.118 1.218 1.322 1.430 1.542 28 2.204 2.117 2.017 1.926 1.835 1.745 1.657 For weight of steam used per revolution of drivers at full cut-off: Multiply the tabular quantity by four times the length of stroke in feet for simple and four-cylinder compounds. For two-cylinder compounds multiply by two times the length of stroke. per indicated-horsepower hour for simple and for compound locomotives for various velocities, which are multiples of M, the maximum velocity at which the boiler can maintain steam at full pressure. The table is computed on the basis of 200 pounds gage pressure, but factors are given for other pressures. For example, continuing the above numerical problem, the pounds of steam per i.h.p.-hour, for a simple locomotive, at M velocity, and at 200 pounds pressure, taken from Table XXI, is 38.30; for 175 pounds pressure we must multiply by the factor 101.7, which makes 268 RAILROAD ENGINEERING 257 TABLE XXI Maximum Cut-Off and Pounds of Steam per I.H.P.-Hour for Various Multiples of M {M is maximum velocity in m ilea per hour at full cut-oflf, with boiler presaure at 200 pounds per square inch) Pounds -Steam per Pounds Steam per 1 I.H.P.-Hour I.H.P. -Hour Velocity Cui^Ofp (per cent) Velocity Cut-Opp (per cent) Simple Compound Simple Compound l.OM Full 38.30 25.80 2.9 M 38.5 24.37 21.04 1.1 " 94.4 36.46 24.36 3.0 " 37.0 24.22 21.21 1.2 " 89.1 34.89 23.24 3.2 " 34.2 24.00 21.57 1.3 " 84.3 33.56 22.35 3.4 " 31.8 23.85 21.93 1.4 " 79.7 32.41 21.65 3.6 " 29.8 23.8 22.27 1.5 " 75.4 31.40 21.14 3.8 " 28.0 23.8 22.57 1.6 '• 71.4 30.49 20.77 4.0 " 26.4 23.87 22.85 1.7 " 67.7 29.67 20.52 4.25 " 24.7 24.05 23.22 1.8 " 64.3 28.93 20.40 4.50 " 23.3 24.24 23.56 1.9 " 61.0 28.25 20.40 4.75 " 22.1 24.44 23.85 2.0 " ' 58.0 27.62 20.40 5.00 " 21.1 24.64 24.15 2.1 " 55.2 27.05 20.40 5.5 " 19.5 24.98 24.70 2.2 " 52.6 26.52 20.40 6.0 " 18.4 25.20 2.3 " 50.1 26.06 20.40 6.5 " 17.6 25.45 2.4 " 47.8 25.67 20.40 7.0 " 17.1 25.60 2.5 " 45.7 25.32 20.47 7.5 " 16.7 25.70 2.6 " 43.7 25.02 20.60 8.0 " 16.4 25.80 2.7 " 41.8 24.76 20.73 9.0 " 16.1 25.90 2.8 " 40.1 24.54 20.88 For steam per i.h.p.-hour for ot! aer boiler pressures take the following percental ges of values given in table: 160 lb., 103 per cent 180 lb., 10] . 3 per cent 210 lb., 99.5 I 3er cent 170 lb., 102 . 1 per cent 190 lb., 10( ) . 6 per cent 200 lb., 99.2 1 3er cent the quantity 38.95. Dividing this into 22,240, the steam produced per hour, we have 571.0, the i.h.p. at M velocity. Multiplying this by 33,000, the foot-pounds per minute in one horsepower, and dividing by 535.7 the velocity in feet per minute, we have 35,174, the cylinder tractive power in pounds, when burning 4000 pounds of coal per hour and running at 6.087 m.p.h. To obtain the draw-bar pull, we must deduct the engine resist- ances which may be computed as given in Table XXII, also taken from the Proceedings of the American Railway Engineering Association and now included as Table 7 in the Economics section of the Manual. 269 258 RAILROAD ENGINEERING TABLE XXII Locomotive Resistances Total Locomotive Resistance is A-\-B+C, in which A = resistance between cylinders and rims of drivers, and in pounds = 18.7 T-\-80 N in which T = tons weight on drivers and iV = number of driving axles. .6 = resistance of engine and tender trucks, and in pounds = 2 . 6 jr+20 iV in which T = tons weight on engine and tender trucks and N = number of truck axles. C = head-end or "air" resistance, and in pounds = .002 V^A in which 7 = velocity in miles per hour, and A =end area of locomotive. On the basis that the end area averages 125 square feet, the last formula becomes C = 0.25 V^. The number of pounds air resistance for various velocities is as given below. Ve- LOC- Resist- Veloc- Resist- Veloc- Resist- Veloc- Resist- Veloc- Resist- Veloc- Resist- ance ity ance ity ance ity ance ity ance ity ance ITY V C V C V C V c V c V C 1 0.25 8 16.00 15 56 22 121 29 210 36 324 2 1.00 9 20.25 16 64 23 132 30 225 37 342 3 2.25 10 25.00 17 72 24 144 31 240 38 361 4 4.00 11 30 18 81 25 156 32 256 39 380 5 6.25 12 36 19 90 26 169 33 272 40 ' 400 6 9.00 13 42 20 100 27 182 34 289 50 625 7 12.25 14 49 21 110 28 196 35 306 60 900 Draw-bar pull on level tangent equals the cylinder tractive power less the sum of the engine resistances. At low speeds, the adhesion of the drivers should be considered and available draw-bar pull should never be estimated greater than 30 per cent of weight on drivers at starting with use of sand, or 25 per cent of weight on drivers at running speeds. Applying Table XXII to the numerical problem, item A=(18.7X 76.6) + (80X4) = 1432 lb. The total weight of engine and tender is 315,000 pounds; subtracting 153,200, the weight on the drivers, we have 161,800, or 80.9 tons, the weight carried by the engine and tender trucks. Item B = (2.6X80.9) + (20X6) =330. Item C for velocity ikf is almost insignificant, say 9 pounds. The sum of A, B, and C is 1771 pounds; subtracting this from 35,174 we have 33,403 pounds, the estimated draw-bar pull for that speed and coal consumption. To note the effect of increasing the rate of coal consumption, the problem may be again worked through on the basis that the rate of coal consumption is increased, even temporarily, from 4000 270 RAILROAD ENGINEERING 259 pounds to 5000 pounds per hour. The steam developed per pound of coal is reduced from 5.56 to 4.93, but the total steam produced per hour is increased from 22,240 to 24,650. The increased capacity comes through a loss in efficiency. The increased steam production raises the velocity at which full stroke may be maintained from 6.087 m.p.h. to 6.746 m.p.h. and the i.h.p. from 571.0 to 632.8. But the computed cylinder tractive power is practically identical, the numerical computation of 35,174 being only changed to 35,175. But these cylinder tractive powers are each computed for the "if" velocities, the maximum velocities at which full stroke can be maintained, and M is higher with increased coal consumption. For a real comparison, the figures must be reduced to the same velocity, e.g., the working velocity of 10 m.p.h. 10-^-6.087 = 1.643, the multiple for the original problem. For 5000 pounds of coal per hour, M velocity is 6.746 m.p.h., and the multiple is 1.482. From Table XXIII we find that the percentages of cylinder tractive power for simple engines for these two multiples of M are 77.44 and 81.93, respectively. The higher value is 105.7 per cent of the lower, which shows that, in this case, adding 25 per cent to the rate of coal consumption adds only 5.7 per cent to the cylinder tractive power at 10 m.p.h. As another instructive variation of the same problem, assume that the coal has effective B.t.u. of 13,000, instead of only 11,700. It will be found that steam will be produced more rapidly, the M velocity is 6.777 m.p.h. and the horsepower at that velocity is 635.7, but the cylinder power is computed to be 35,177 pounds, which is again almost identical with the previous values although the M velocity is still higher. The multiple for 10 m.p.h. is 1.476 and by Table XXIII the per cent of cylinder tractive power is 82.11, which is an increase of 6 per cent over 74.44 per cent, showing that the increase in effective B.t.u. from 11,700 to 13,000 adds 6 per cent to the cylinder tractive power at 10 m.p.h. These values for cylinder power may again be checked by the simple rule that m , . e (piston diameter)^ X effective steam pressure X stroke Tractive force = — —. j-r-. diameter oi driver The "effective steam pressure" is generally considered as 85 per cent of the gage pressure, and for the above case would be 271 260 RAILROAD ENGINEERING TABLE XXIII* Per Cent Cylinder Tractive Power for Various Multiples of M {M is maximum velocity in miles per hour at which boiler pressure can . be mamtamed with full cut-off) Veloc- ity Per Cent (Com- pound) Per Cent (Simple) Veloc- ity Per Cent (Com- pound) Per ■ Cent (Simple) Veloc- ity Per Cent (Com- pound) Per Cent (Simple) Start 135.00 106.00 3.6 M 32.40 44.75 6.4 M 23.59 0.5 ilf 103.00 103.00 3.7 " 31.25 43.56 6.5 " 23.18 1.0 " 100.00 100.00 3.8 " 30.10 42.39 6.6 " 22.79 1.1 " 96.28 95.57 3.9 " 29.14 41.24 6.7 *' 22.42 1.2 " 92.55 91.53 4.0 " 28.24 40.10 6.8 " 22.06 1.3 " 88.83 87.83 4.1 " 27.38 39.00 6.9 " 21.71 1.4 " 85.12 84.46 4.2 " 26.56 37.96 7.0 " 21.38 1.5 " 81.40 81.37 4.3 " 25.77 36.97 7.1 " 21.06 1.6 " 77.68 78.55 4.4 " 25.03 36.03 7.2 " 20.75 1.7 " 73.96 75.97 4.5 " 24.34 35.13 7.3 " 20.45 1.8 " 70.25 73.60 4.6 " 23.69 34.26 7.4 " 20.16 1.9 " 66.54 71.41 4.7 " 23.07 33.41 7.5 " 19.88 2.0 " 63.21 69.37 4.8 " 22.48 32.59 7.6 " 19.61 2.1 " 60.20 67.47 4.9 " 21.92 31.82 7.7 " 19.34 2.2 " 57.48 65.67 5.0 " 21.38 31.11 7.8 " 19.08 2.3 " 54.97 63.94 5.1 " 20.87 30.42 7.9 " 18.82 2.4 " 52.68 62.22 5.2 " 20.37 29.75 8.0 " 18.57 2.5 " 50.42 60.55 5.3 " 19.89 29.10 8.1 " 18.33 2.6 " 48.16 58.92 5.4 " 19.43 28.48 8.2 " 18.09 2.7 " 46.08 57.33 5.5 " 18.99 27.87 8.3 " 17.86 2.8 " 44.10 55.78 5.6 " 27.33 8.4 " 17.64 2.9 " 42.29 54.26 5.7 " 26.81 8.5 " 17.43 3.0 " 40.57 52.78 5.8 " 26.30 8.6 " 17.22 3.1 " 38.95 51.33 5.9 " 25.81 8.7 " 17.01 3.2 " 37.42 49.91 6.0 " 25.34 8.8 " 16.82 3.3 " 35.98 48.55 6.1 " 24.88 8.9 " 16.63 3.4 " 34.66 47.24 6.2 " 24.44 9.0 " 16.45 3.5 " 33.53 45.97 6.3 " 24.01 ♦Table 5 in Economics Section of Manual of American Railway Engineering Association. .85X175 = 149 pounds; diameter piston = 22 inches; stroke = 28 inches; diameter of driver = 57 inches. Then the tractive force = 35,425 pounds, which is less than 1 per cent in excess of the other values. This rule is more simple as a method of obtaining merely the maximum tractive power at slow velocities, but the previous method, although longer, is preferable, since it computes the critical velocity M, and also the tractive force at higher velocities. 191. Tractive Force at Higher Velocities. At higher velocities than My the cylinder power falls off quite rapidly, since the steam 272 RAILROAD ENGINEERING 261 is cut off at part stroke and is used expansively. The proper per cent of cut-off and the number of pounds of steam per i.h.p. are shown in Table XXI. In Table XXI is given the per cent of cylinder tractive power for multiples of M, The table shows, for example, that, for simple engines, the cylinder tractive power is 69.37 per cent of its value for full stroke when the velocity is 2M and that when the velocity is increased to 5M the tractive power is reduced to 31.11 per cent. Applying this to the above numerical problem, when M = 6.087 m.p.h., the cylinder tractive power is reduced to 31.11 per cent of 35,174, or 10,943 pounds, but, since the velocity is five times as great, the horsepower developed is 31.11 per centX5 = 1.55 times as great. It should be noted that Table XXIII shows a slight excess of tractive power (6 per cent when starting) for the simple engine. This is due to the fact that with very low velocities the cylinder pressure more nearly equals the full boiler pressure and there is not the usual reduction of about 15 per cent. Also, compound locomotives are operated with all the cylinders using full-pressure steam, which increases their effectiveness at starting about 35 per cent, although at some loss in economy of steam due to compounding. But since the starting resistances are so much greater than the resist- ances above 5 miles per hour, the extra assistance is very timely. 192. Further Power Calculations. Illustrative Exainple. Con- tinuing the investigation of the Mikado locomotive (see article 190), draw a curve representing its cylinder tractive power for all Velocity Cylinder Tractive Power Locomotive Resistance Draw-Bab Pull (multiples of M) (miles per hour) (per cent) (pounds) (pounds) (pounds) 0.0 0.000 106.00 37,284 1762 35,322 1.0 6.087 100.00 32,174 1771 33,403 1.2 7.304 91.53 32,195 1775 30,420 1.5 9.131 81.37 28,621 1783 26,838 2.0 12.174 69.37 24,400 1799 22,601 3.0 19.261 52.78 18,565 1854 16,711 4.0 24.348 40.10 14,105 1910 12,195 5.0 30.435 31.11 10,943 1993 8,950 6.0 36.522 25.34 8,913 2095 6,828 velocities from to 35 miles per hour. From the numerical example worked out in article 190, we found that the cylinder tractive power for M velocity (6.087 m.p.h.) was 35,174 pounds. From Table XXIII, 273 262 RAILROAD ENGINEERING the power at starting is 106 per cent of this, or 37,284 pounds, and the change in power is assumed to vary uniformly in that range. By muhiplying 35,174 by the various percentages for the various multiples of M, we have the tractive power at the several velocities. These values are plotted in Fig. 160. From Table XXII we find that the locomotive resistance is 1762 pounds for the A and B resistance at all velocities and that the C resistance varies from about 9 pounds at M velocity (6.087 m.p.h.) to about 333 pounds at 6 if velocity. Subtracting these resistances from the computed values of cylinder tractive power, we have the "draw-bar pull" for the various veloc- ities, all as shown in the tabular form. These several values for cylinder power and of draw-bar pull are plotted for the correspond- ■40,000 30.000 £0,000 S 10,000 5 < 10 15 £0 S5 30 35 Fig. IGO, Tractive Power of Mikado Locomotive at Varying Velocities ing velocities in Fig. 160, giving the two curves as shown. The rapid decrease in possible draw-bar pull for increase in velocity is well shown. But the student should carefully note that this curve represents the limitation of draw-bar pull and not the actual, which may be considerably less and which is measured by the resistance. 193. Relation of Boiler Power to Tractive Power. The power at high velocities depends on the rapid production of steam, as has been shown, and this depends on the area of the fire box. All of the older styles of locomotives have fire boxes limited to the width which can be properly placed between the drivers. The Wootten fire box was placed over the drivers, which made it incon- 274 RAILROAD ENGINEERING 263 Mogul Prairie Cylinders, diam.X stroke 20 in.X26 in. 20 in. X 24 in. Boiler pressure 200 pounds 200 pounds Fire box, length X width 108 in. X 33 in. 74 in.X66 in. Grate area, square feet 24.70 34.000 Heating surface, sq. ft., fire box and tubes 1952.00 2135.000 Driving wheels, diameter, inches 51.00 51.000 Weight on driving wheels, pounds 137,300.00 122,100.000 Weight of engine alone, pounds 154,000.00 153,300 . 000 Weight of engine and tender, pounds 254,000.00 253,000.000 Assumed B.t.u. in coal used, 4000 lb. per hr. 12,000.00 12,000.000 Coal per sq. ft. of heating surface per hour Pounds steam per pound coal (Table XIX) Pounds steam per hour (multiply by 4000) 2.05 1.873 4.16 4.390 16,640.00 17,560.000 Pounds steam per stroke (Table XX) 2.230 2.058 Pounds steam per revolution (multiply by 4) 8.920 8.232 Revolutions per hour, at M velocity 1865 . 50 2133.500 Revolutions per minute, at M velocity 31.09 35 . 560 Circumference of drivers, linear feet 13.35 13.350 Velocity (v), feet per minute, M velocity 415.05 474.730 Velocity (F), miles per hour, M velocity 4.716 5.394 Horsepower at M velocity (Table XXI) Cylinder tractive power, pounds, at M velocity 434.40 458.400 31,400.00 31,865.000 veniently high, unless the drivers were objectionably small. Then the plan was devised of placing the fire box over a low pair of trailing wheels and behind the rear pair of drivers. This plan made it possible to double the net width of the fire box. In order to get essential fire-box area in the older styles of locomotives, it is neces- sary to lengthen the fire box until it is difficult for the fireman to reach and properly clean and tend the fire at the forward end. But by doubling the width, the fire box may be made as large as desired and even shorter than some of the older designs. The ^ Mogul Locomotive Prairie Locomotive Multiples OF M Velocity Cylinder Tractive Velocity Cylinder Tractive (m.p.h.) Power (m.p.h.) Power 0.0 0.000 33,284 0.000 33,778 1.0 4.716 31,400 5.394 31,865 1.2 5.659 28,740 6.473 29,166 1.5 7.074 25,550 8.091 25,929 2.0 9.432 21,782 10.788 22,105 3.0 14.148 16,573 16.182 16,818 4.0 18.864 12,591 21.576 12,778 5.0 23.580 9,769 26.970 9,913 6.0 28.296 7,957 32.364 8,075 7.0 33.012 6,713 275 264 RAILROAD ENGINEERING increased fire-box area justifies a greater heating surface and results in a greater production of steam per pound of coal and a more rapid production of steam, and hence greater power. The value of this change is best shown by a comparison of two locomotives which are very similar in many respects except those due to the difference in fire boxes, etc. The two locomotives are a "Mogul" (2-6-0) and a "Prairie" (2-6-2). The several characteristics, some of which are computed as in article 192, are best shown by tabulating them. (See top of p. 263.) Knowing the cylinder tractive power at M velocity {M being somewhat different for the two locomotives), we can determine the 30,000 Z 0,000 10.000 5 10 15 £0 £5 30 35 Fig. 161. Comparative Cylinder Tractive Power of Prairie and Mogul Types of Locomotive cylinder tractive power for various multiples of M, by means of Table XXIII, by the method already given in detail. The results are tabulated at bottom of p. 263 and are plotted in Fig. 161. The student should note that the two locomotives are of almost the same weight, have the same driving-wheel diameter, same cylinder diameter, same boiler pressure, and are compared on the basis of using the same quality of coal. The Mogul has 15,200 pounds extra on the drivers, which should apparently give it advan- tage, but Fig. 161 shows that, even at the start, the Mogul has slightly less tractive power. But the Prairie fire box is wider, although shorter, and has 38 per cent more area. This permits more rapid production of steam. By scaling the vertical intervals between the two curves at all points, it is found that for any veloc- 276 RAILROAD ENGINEERING 265 ities between 5.5 and 25 miles per hour the Prairie has about 2000 pounds more cyHnder tractive power. Of course, the comparison should be made on the basis of their relative draw-bar pulls, which would be obtained by subtracting the engine resistances, as given in Table XXII. But this shows that the engine resistance of the Mogul is greater than that of the Prairie, which leaves an even greater difference in favor of the Prairie. The trailing wheels under the fire box also serve the purpose of guiding the driving wheels around curves when the locomotive is running backward and in this respect accomplish what the pilot truck does for forw^ard running. The comparative power of these two locomotives may be shown by a numerical example. Assume that a train of 16 coal cars, each weighing when fully loaded 70 tons, and a caboose weighing 15 tons, is being hauled up a 0.3-per-cent grade at a uniform velocity of about 20 miles per hour. The resistance, by equation (105), is i? = 2.2X(16x70+15) + 121.6Xl7 = 4565lb. The grade resistance of the cars is 20X0.3X1135 = 6810 pounds. It is assumed that all curve resistance is eliminated by a sufficient reduction of grade w^here it occurs so that it may be included with the grade resistance. The velocity being assumed uniform, there is no requirement for energy for acceleration. The total car resist- ance is therefore 11,375 pounds. The engine resistance is a function of the velocity, but considering that the element depending on velocity is relatively small, we will consider it at its average value for 20 miles per hour. The resistances may be computed as 1876 and 1532 for the Mogul and Prairie engines, respectively, which gives 13,251 and 12,907 pounds, respectively, for the total demands on cylinder tractive power. These resistances, being practically independent of velocity, are horizontal lihes and are drawn as shown in Fig. 161. This indicates that the limit of velocity of the Mogul locomotive with that train on a 0.3-per-cent grade is less than 18 miles per hour, while the Prairie engine could haul the train at over 21 miles per hour. This gain of 3 miles per hour would have considerable value in the economy of train operation. Or, it may be showTi that the Prairie engine could haul 19 loaded cars (an increase of over 18 per cent in revenue load) and a caboose, and 277 266 RAILROAD ENGINEERING could haul them on the 0.3-per-cent grade at a velocity of 18 miles per hour, the limiting velocity for the Mogul. The student should remember that, as before intimated, there are several elements of uncertainty (such as the strength and abihty of the fireman, and the condition of the track) which might modify the above figures and make them unreliable as a precise measure of the real power of either locomotive, but, on the basis of average conditions, the figures are a measure of the comparative value of the two locomotives. 194. Effect of Grade on Tractive Power. The effect of grade on tractive power is best shown by some numerical computations whose results are plotted in Fig. 162, The cylinder tractive power was computed for three engines of greatly different total w^eight and power, but which had driving-axle loads nearly identical (about 50,750 pounds) and therefore, by the rule given in article 188, could all be operated on the same kind of track. Using the Baldwin Locomotive Works rule, as given in article 188, J X 50,750 ^300 = 84.5, which means that the rails should weigh at least 85 pounds per yard. Making computations for these locomotives, using 12,000 B.t.u. coal, similar to those already detailed in articles 190 to 193, it was found that, on a level, the cylinder tractive powers of the Pacific, Mikado, and IVIallet loco- motives were 29,718, 33,575, 49,095 pounds, respectively, when the velocity was uniformly 10 m.p.h. and the locomotives each burned 4000 pounds of coal per hour. The several engine resistances at 10 m.p.h. are easily computed from Table XXII and are tabulated below. The net values, or the draw-bar pulls, are plotted Engine Characteristics (At velocity V = 10 m.p.h.) Pacific 4-6-2 (lb.) Mikado 2-8-2 (lb.) Mallet 2-8-8-2 (lb.) Cylinder tractive power on level Engine resistance on level Draw-bar pull on level Draw-bar pull on 3-per-cent grade 29,718 2,205 27,513 15,213 33,575 2,648 30,927 18,207 49,095 4,864 44,231 25,631 on the left-hand vertical line of Fig. 162, and in each case are the left-hand ends of the solid lines which show the tractive powers of the locomotives. On a 3-per-cent grade the grade resistances for the locomotives equal 60 pounds per ton, and are 12,300, 12,720, and 18,600 pounds, respectively. This reduces the effective draw- 278 RAILROAD ENGINEERING 267 bar pull approximately 40 per cent in each case. Since this reduc- tion varies uniformly with the grade, we may plot the three values, 15,213, 18,207, and 25,631, on the 3 per cent vertical line and draw straight lines which represent in each case the tractive power of the locomotive at 10 m.p.h. and on any grade within that range. Assume trains of cars, all averaging 50 tons per car and varying from 10 cars weighing 500 tons to 50 cars w^eighing 2500 tons. The resistances at 10 m.p.h. on a level grade are given by equation (105), and may be plotted on the left-hand vertical line of Fig. 162. Grade adds resistance proportional to the grade. For example, on a 0.7-per-cent grade the grade resistance per ton is 14 pounds and for 2500 tons is 35,000 pounds. Adding this to 11,580, the tractive resistance, we have 46,580 which we plot on the 0.7 per cent ver- tical line. It is indicated by a small circle. Joining the two points gives the resistance line for 2500 tons hauled at 10 m.p.h. The circles on the other lines indicate similar com- putations. The intersec- tions of these resistance lines with the lines of tractive power indicate the relative power of each locomotive. For example, the 1000-ton train can be hauled by the Pacific locomotive at 10 m.p.h. up a 0.96-per-cent grade, but a Mikado can do the same on a 1.1-per-cent grade, while the Mallet can do it on a 1.52-per- cent grade. All of these calculations were made on the basis of burning 4000 pounds of coal per hour, which, as before stated, is the 50,000 - 1 r '■" 7 Z r ^ 2 7 2 L J < (I ^ 1 f ^ L di2 1 > i I -,t -> 7 i jTx ^^ 1 . 1 i^j / / -i - 1 40,000 , -^i J -} 1 4 ,LLu^l ' 7 '«-^ ^sIZ f J. 4-jlC^ h- ts^ ^ n^nnn X -^4 ■ ^/- ^ vZ 35,000^ ^^1 ^f$L^ Z^ ^ 1 % ^^L ^-tt^J- t 5s ^" 'l"^h~B"^T^> p "^i^ J' t- T^^/^/W"W 7>?0^ .^ pi ^^ ^^_ W ^^^^ ' J I^^F C ^'% - >r:-^z: 2 t^^. :^ r xS__ v^ r (nv^ s5,oDo •§-] "-3 -^- \% 5:^^ ■# \ll 1 ^^^^ z± r^cTni^ A.-' '^ _,' ^^^ 1 1 IT'^^^^^ A_ 1 >Tf>^ 1 '" ^^'V ' 1 L ■^ cO.OOO ■ -" -h-i -J -p- ^^=^^ "^^^- tt-i"''-. -, " I ->^ - ^ u / . / / ^ ^">^ }l\ J ' / >«s. if^ nnn \\, 1 1 l\ / ^ "^ V, T-JT-l-A > - TP-, / ^ '^lZ I V Itri 7 i: 2Z/%- : 'l ^ .nnn'l'l'X - '- 5JJ00 ^ r- i^'^ J a^ 1.0 1.5 z.o S.5 3.0 Fig. 162. Curves Showing Effect of Grade on Tractive Power 279 268 RAILROAD ENGINEERING practical limit of what an ordinary fireman can be expected to do for an extended run. The description of the Mallet locomotive (built by the Baldwin Locomotive Works) stated that its tractive power is 91,000 pounds. A computation of its cylinder tractive power at M velocity, using 12,000 B.t.u. coal, shows it to be 95,389 pounds. Subtracting the engine resistance (4843 pounds) we would have 90,546 pounds, which is a very fair check, especially as the Baldwin Locomotive Works method of calculation is different. 195. Acceleration — Speed Curves. The time required for an engine of given weight and power to haul a train of known weight and resistance over a track with known grades and curvature is an important and necessary matter for an engineer to compute, since the saving in time has such a value as to justify constructive or operating changes which will reduce that time. Fig. 160 shows that the draw-bar pull is very much greater at very low velocities than at the moderate speed of even 15 m.p.h. In spite of the increased resistance at these low velocities the margin of power left for acceleration is also greater and the "speed curve" is really '^ curve and not a straight line. Its general form may be most easily developed by a numerical example, especially as each case has its own special curve. Illustrative Example, The Mikado locomotive, whose char- acteristics have already been investigated in article 190 et seq., has draw-bar pulls at various velocities as shown in the tabular form in article 192, to which frequent reference must be made in this demonstration. Assume that this locomotive starts from rest on a 0.4-per-cent upgrade, hauling a train of 14 cars, each weighing 50 tons, and a caboose weighing 10 tons. Then the normal level tractive resistance, by equation (105), equals i? = (2.2x710) + (121.6Xl5) = 33861b. The grade resistance of the cars will be 20X0.4x710 = 5680 pounds. The extra starting resistance will be considered as 6 pounds per ton, or 4260 pounds. These three items total 13,326 pounds. The average draw-bar pull of the locomotive at velocities between zero and M velocity, which is 6.087 m.p.h., is 34,362 pounds, but this must be diminished in this case by 20X0.4X157.5 = 1260 280 RAILROAD ENGINEERING 269 pounds for grade and by 157.5X6 = 945 pounds for starting resist- ance, leaving a net draw-bar pull of 32,157 pounds, excluding the force required for the acceleration of the locomotive. The net force available for acceleration of both the locomotive and the train is 32,157-13,326 = 18,831 pounds, or prorated, is 18,831^ (157.5-f-710)=21'.71 pounds per ton. Transposing equation (104), with Fi = 0, F2 = 6.087, and P = 21.71 pounds, we have * = (37.05-0) 70-^21.71 = 119 feet, the distance required to attain a velocity of 6.087 m.p.h. While the velocity is increasing from 1.0 if to 1.2 ilf, the mean draw-bar pull is 31,912 — 1260 = 30,652 pounds, less the accelerative resistance of the locomotive. Subtracting the tractive and grade resistances of the cars, we have 30,652 — 3386 — 5680 = 21,586 pounds. Note that there is no longer any starting resistance. The accelerative force in pounds per ton is 21,586 -i- 867.5 = 24.88. The distance s required to increase the velocity from 6.087 m.p.h. to 7.304 m.p.h., is (53.35 -37.05)70 -^ 24.88 = 46 feet. Similarly the distances required to increase the velocity from 1.2 M to 1.5 M, from 1.5 If to 2 M, etc., are computed as in the accompanying tabular form, p. 270. The corresponding distances and velocities have been plotted in Fig. 163. The velocity of 10 m.p.h. is acquired in a little over 300 feet, but it requires nearly 1000 feet to acquire a velocity of 15 m.p.h. and about 2400 feet to raise it to 20 m.p.h. The force, in pounds per ton, available for acceleration is maximum at low velocities, after the extra starting resistance is overcome. As the margin per ton for acceleration becomes less and less, the greater is the distance required to increase the velocity 1 mile per hour — especially through the last increments — up to the velocity at which the net draw-bar pull exactly equals the total car resistance and the velocity becomes uniform. There is an approximation in using average draw-bar pulls between the different velocities at which the draw-bar pull has been definitely computed, but the computed distances are practically correct up to 4 if velocity or 24.35 m.p.h. But the computation for the distance required to increase the velocity from 4 M up to 4.58 M is far less accurate if the average draw-bar pull is used. The effective pull at 4 if velocity equals 12,195 — 1260 = 10,935, less the accelerative resist- 28X 270 RAILROAD ENGINEERING I >o 00 00 1—1 2 1 H CO Oi lO »o Oi ^ CO Tt< Ills CO CO CO Oi to CO rH 1—1 (N lO Oi^ c^ (N^ OD H 1— < to t^" o s cb 05 CO 8 ■^ oq (N 1—1 Q 01 as ^~^ rti t^ lO CO 00 •| > 00 +i tH 1— 1 (M ■Tt^^ (M Oi^ g +j — ' y—t co" 1-^ < 1— 1 . c 1— 1 §8 O Oi CO CO rH 1—1 lO d d ^a (N (N (N t— I is ^ ^ CO CO "* ^ 1^ to 5^ <5 CO 00 o Oi CO (N CO 00 oo" u oo" CO Oi'^ TlT Oi T-( (N 1-1 1—1 CO CO CO CO CO CO S ?:? o o o 8 o s CO rH * Oi oT Oi" Oi"" Oi" H r* g _ 03 a? l> (N Oi o CO CO o3CQ_ M^ lO lO CO CO Oi d (N CO t^-" co" oo" 1—1 co" CO CO (N c^ 1—1 1—1 Is to o O o o ^ 11-1 St^ Q CO CO CO CO CO (N i-T (N (N^ rH i-T ssr 'N' (N (N Oi o CO CO CO T— 1 f\j (N to to CO 05^ CO t^ CO ■^ TtT T-T oo" Ttn" oT Tj^" Q CO CO c^ (N rH 111 lO 8 2 ^ 8 ^ ^ oi (N i6 CO (N 00 (N CO CO j^ Tf ^ 00 O CO t^ CO to 00 Q CO tH (M CO 00 H s^-^ CO t^ d (M d TJH t^ £ 1— I (N (N M) tH > ja <^.^ t^ '^ ,_( 1 8 = ^ CO 1—1 tH ^ to CO d d t^ d (N d rH ^ 1^ 8 Tt< t^ 1—1 to to CO Oi to '* 00 i 00 to & rH r-i tH (M CO RAILROAD ENGINEERING 27i ance of the locomotive. The tractive and grade resistance of the cars at this velocity is 3386+5680 = 9066. This leaves 10,935- 9066 = 1865 pounds available for acceleration of both locomotive and cars. The reduction in tractive force between 4 If velocity and 5M velocity (see article 192) is 12,195-8950 = 3245 pounds. By proportionate interpolation we w^ould then say that the excess force available for acceleration would be exhausted at (1869-^3245) = .58 of the interval, or at a velocity of 4.58 M, or 27.88 m.p.h. The mean accelerative force is one-half of 1869, or 935 pounds, which is 1.077 pounds per ton of train. The distance, by an inver- ^00 1000 ZOOO * 3000. 'lOOO • 5000 Fig. 163. Time Curves for Mikado Locomotive and Train 6000 sion of equation (104), is computed to be 11,981 feet. Owing to the approximate equality of w^orking force and resistance and the momentary variations in both, the precise point where the accel- eration would cease and the velocity would actually become uniform would be very uncertain. Fortunately the inaccuracy is of little or no practical importance and for the purposes of our calculations we may call this last interval 11,981 feet, assuming that the grade is as long as 17,234 feet or 3.2 miles. If the 0.4-per-cent grade continued indefinitely the train would travel at this uniform velocity as long as the locomotive operated on the basis assumed for this problem. Note that Fig. 163 would have to be extended to nearly three times its present length before the time curve would reach and become tangent to the *^line of uniform velocity". 272 RAILROAD ENGINEERING 1 a a 1 CO Oi CO (N t^ t>- 1 2|o . CO iO ^ CD CO ■^ OQ CO o £5£ 00 (N C^ ^ i \r^^m^ (N 10 co" '^ t m Q 2 CO (M 10 CO OJ ® O 00 r^ •^ ^ > «,:i 00 CO (M^ -< T-T of i-T r^ (M Tfl -^ 05 (N (N 10 ■^ i-H 10 ^ h. I— 1 « , |-^ i.'S ao CO CO Q CO Tt^ 10 ^O (>f [2 oT ""i^" co^ oa tf 1—1 i gS o CO CO CO § (N 0" C^ (N (M fM H > ?2 CO « ■^ CO 00 H t^ (S 10 1—1 >% S|g£ i 1 CO CO CO" J« s § s? s (N Ttt CO yX "^f oT Q 1—1 1-H 1— 1 ?? 8 9 8 00 (N CO r^ CO CO (N »— 1 10 CO t>. rH CO "i 95 10 CO t^ 00 CO (N 1-1 Ni Tji oi - C^ 00- -tj Si d 10 06 !>. fe ""^ CO <» el •D « C3 CO I s a P "I 822 EARTHWORK 23 swinging circle which is pivoted to the front end of the platform. The boom revolves with the swinging circle. The upper and outer end of the crane is connected to the top of the A-frame mth rods, and has a sheave over which the hoisting cable passes on its course from hoisting drum to dipper handle. The latter carries the dipper at its lower end and moves through the crane and over a pinion which engages a toothed rack on its under side. The dipper handle is usually a single timber of hardwood, reinforced mth steel plates or angles. The dipper is made in the form of a scoop with closed sides, open top, and a hinged and latched door at the bottom. It is made of heavy steel plates reinforced at top and bottom with steel bars. The top or front edge is provided with a sharp, heavy- steel cutting edge, or manganese-steel teeth. The bottom of the bucket is of heavy steel, hinged to the rear side and closed by a spring latch on the front side. The operation of the bottom door is controlled by a small line which leads from the door to the side of the boom, where the cranesman stands. Other types of buckets or dippers may be used wdth the steam shovel, for various classes of excavation, but, as they are largely used for dredging, their con- struction and use will be described under the section on "Floating Excavators". Method of Operation. A steam shovel of the first class is gen- erally operated by a crew of 7 men; an engineer, a cranesman, a fireman, and 4 laborers. The engineer and cranesman directly con- trol the movements of the machine. The fireman keeps the boiler supplied with fuel and water and sees that the machinery is in good running order. The laborers are generally under the direct control of the cranesman and their duties consist in the breaking down of high banks, assisting in the loading of the dipper, leveling the surface in front of the machine, laying the new track, operating the jack braces, and for general service about the shovel. In rock excava- tion, from 2 to 6 extra laborers are required for breaking up the rock, mud-capping, etc. The engineer stands at the set of levers and brakes which are located in front of the machinery. The cranesman stands on a small platform on the right side and near the lower end of the crane. The former controls and directs the raising and lowering of the dipper, the swinging of the crane, and the traction of the whole machine. 323 24 EARTHWORK The cranesman controls the operation of the dipper, and of the dipper handle, regulating the depth of cut, releasing the dipper from the bank and emptying it into the car, wagon, or spoil bank. The process of excavation commences with the dipper handle nearly vertical and the dipper resting on the floor of the pit with the cutting edge directed toward the bank. The engineer then moves a lever throwing the hoisting drum into gear and starting the engine. The revolution of the hoisting drum winds up the hoisting hne and pulls the dipper upward. Simultaneously, the cranesman starts the thrusting engine and moves the dipper handle forward as the dipper rises. These two motions must be made smoothly and coordinately or the hoisting engine will be stalled and the whole machine tipped suddenly forward. When the shovel has reached the top of the cut or its highest practicable position, the engineer throws the hoisting drum out of gear and sets the friction clutch with a foot brake, thus bringing the dipper to a stop. Immediately, the cranesman releases his brake and slightly reverses the thrusting engine which thus draws back the dipper handle and withdraws the dipper from the face of the excavation. When the dipper digs clear of the excavation it is unnecessary to release it as described for the last motion. The engineer then starts the swinging engine into operation and moves the crane to the side until the dipper is over the dumping place. With a foot brake he sets the friction clutch controlling the swinging drums and stops the side wise motion of the crane. The cranesman then pulls the latch rope, which opens the latch and allows the door at the bottom of the dipper to drop and to release the contents. The engineer then releases the friction clutch by the foot brakes and reverses the swinging engine, pulling the crane and dipper back to position for the next cut. As the boom is swung around, the engineer gradually releases the friction clutch of the hoisting drum and allows the dipper to slowly drop toward the bottom of the cut. When near the point of commencing the new cut and as the dipper handle approaches a vertical position, the cranesman releases the friction clutch on the hoisting engine with his foot brake. Thus, as the last part of the drop is made by the dipper, it is also brought into proper position and the length of the dipper arm regulated for the commencement of the new cut. As the dipper drops into place* 324 EARTHWORK 25 = -2 & & & »o t>~ CO CO CO CO 00 t^ ^ •* CO ^ X CO 00 T-l rH T-l CO T-H CO «o O fc (4 o l5 C0 lO CO CO CO 1-4 CO CO CO ooo O-^co OiOt^ (M T-i 00 1-hOOO Oi Oi Oi 05 05 05 00OTt<(M iO»Ot>- COtH 05 OOOO 00 (N (N (M r-H OOQOOO C.cO CO 6^^< fl a; > O^S<5 •Baa Sh.S § CS IIP I OS^^ ■5 s a ^ 2 =3 Si. >• S fl ^ Mm ID c3 a 'b 'ert ra O JH 5=! a EARTHWORK 29 dipper. In making a cut for a railroad or large canal, or in opening up a gravel pit, mine, or quarry, the shovel ordinarily makes a through cut and then returns on a parallel cut, dumping into wagons or cars which move along the previous grade at a higher level. A typical Train of Pump Cars Tram of Pump cars Fig. 17. Diagram of Shovel Operation arrangement would be as shown in Fig. 17. Under such conditions the cost of operation of a 2J-yard steam shovel in the excavation of clay and gravel, for a 10-hour day, would be as follows: Cost of Excavating Clay and Gravel Labor: 1 engineer $5.00 1 cranesman 3.50 1 fireman 2.50 \ watchman, @ $50 per month 1.00 4 pitmen, @ $1 . 75 each 7.00 1 team and driver (hauling coal, water, etc.) 3.50 Total labor, per day $22.50 Fuel and Supplies: 2h tons of coal, @, $4.00 $10.00 Oil, and waste 1.50 Water .50 Total fuel cost, etc. $12.00 General and Overhead Expenses: Repairs $5.00 Incidental expenses 2.00 Depreciation (5% of $12,000)* 3.00 Interest (6% of $12,000)* 3.60 Total general cost $13.60 Total Cost of Operation per 10-hour Day $48. 10 Average Daily Excavation (cu. yd.) 1600 Unit Cost of Excavating clay and gravel per cu. yd., $48.10 -r- 1600 = 00 . 03 The same steam shovel used in the excavation of a stiff clay or shale would probably require the services of 2 extra laborers at ♦Based on a 20-year life and 200 working days per year. 329 30 EARTHWORK $1.75 per day each. The average daily excavation would be 1000 cubic yards, and the cost of operation would be about $0.05 per cubic yard. For the excavation of rock which requires blasting, the addi- tional labor and expense would be as follows: Labor: Additional Cost of Excavating Rock 4 pitmen, 2 laborers, $1 . 75 each ^ $1 . 50 each $7.00 3.00 $10.00 $4.00 Fuel: 1 ton of coal, @ $4.00 Loosening Materials: Dynamite, caps, fuse, powder, etc. $1 . 50 Total Additional Cost of Excavating rock $15 . 50 Total Cost of Operating Shovel in SoHd Rock per 10-hour Day $63 . 60 Average Daily Excavation (cu. yd.) 900 Unit Cost of Operation, per cu. yd., $63,604-900= 00.07 The above statement does not include the cost of transporting the shovel to and from the job, the cost of living and camp expenses, or office and other fixed charges. Fig. 18. Bucyrus Shovel Filling Dump Cars with Clay The cost of the disposal of the excavated material varies from nothing when the material is dumped upon the sides of the excava- tion (highway or canal construction on a side hill) to 15 or 20 cents 330 EARTHWORK 31 331 32 EARTHWORK per cubic yard when the material must be hauled for a long distance and spread. The disposal consists of two operations: the hauling; and the dumping. The cost of hauling depends on the type of conveyance used, number of cars in train, length of haul, etc. The cost varies from 3 to 12 cents per cubic yard. The cost of dumping varies from J cent per cubic yard for wagons to IJ cents per cubic yard for cars. Fig. 18 shows a shovel loading a train of side-dump cars with clay. Fig. 19 shows a large size steam shovel loading a train of box cars mth limestone in a cement quarry. REVOLVINQ=PLATFORM TYPES Arrangement. There are several makes of revolving shovel which are alike in general arrangement and construction. The Fig. 20. Type 1 Thew Shovel Mounted upon Car Wheeld Courtesy of The Thew Automatic Shovel Company, Lorain, Ohio essential features of the revolving shovel are a lower or trUck plat- form and an upper or revolving platform on which are located the operating and excavating equipments. A typical make of revolving shovel is shown in Fig. 20. Platforms. The lower or truck platform is composed of a rectangular structural-steel framework which is strongly braced and riveted. This platform rests on 2 steel axles, the front one pivoted and the rear one fixed *in position. On the rear axle is located a 332 EARTHWORK 33 sprocket wheel, which is chain-connected to the engine and thus provides for the traction of the machine under its own power. The turning of the front axle governs the direction of the tractive move- ment of the shovel. The wheels may be either wide-tired wood or Fig. 21. Details of Thew Hoistinjr Engine — Horizontal Double Reversing Type steel, or flanged railroad wheels when the shovel is to operate on a track. Upon the top of the platform is located a large casting which comprises a circular gear, the roller track and the central journal or gudgeon, which supports the upper platform and works. The upper or revolving frame carries the machinery and lower end of boom and corresponds to the car body of the fixed-platform class of shovel. This platform is a rigid framework of structural- steel members which are strongly braced and riveted. A heavy cast- steel socket is located on the lower side of the platform and rests on the journal of the lower frame. The whole operating mechanism can revolve in a complete circle about the stationary lower frame. Power Equipment. The power equipment of a revolving steam shovel consists of a vertical boiler and independent engines for hoisting, swinging, and thrusting. The boiler is of the vertical, submerged multi-tubular type, and made to operate under a working pressure of from 100 pounds to 125 pounds. The boiler feed consists of an ejector and a pump, 333 34 EARTHWORK which can supply water to the boiler while the shovel is in operation. The boiler is located on the rear end of the upper platform. The engines are all double-cylinder, horizontal, and reversible. The swinging and hoisting engines are located in front of the boiler near the front end of the upper platform. The thrusting engine is located on the upper side of th^ crane or boom. The hoisting drum is controlled by a friction band which is operated by a foot lever. Fig. 21 shows the swinging and hoisting engines of a well-known make of revolving shovel. The thrusting engine in several makes is of the double, horizontal, reversible type which is used on shovels of the fixed-platform class. One make, the Thew Automatic Shovel, uses a very unique and efficient method of thrusting or crowding the dipper. A carriage or trolley to which is hinged the upper end of the dipper arm, moves horizontally along a track. As the carriage moves forward, the center of rotation of the dipper is changed and produces a prying action. The crowding motion is always in a horizontal direction. The movement of the carriage is. controlled by the cranesman, who operates the throttle lever of the crowding engine. The throttle is also connected to a "trip", which auto- matically shuts off the steam when the carriage reaches either end of the trackway. Fig. 20. (jrasoline power can be used to great economic advantage when coal is high in price and inaccessible. The prime mover is then a gasoline engine which is mounted on the rear of the platform and belt-connected to the operating units. The upper platform is provided with a housing of wood or cor- rugated steel for the enclosure and protection of the machinery. Excavating Equipment. The crane or boom is a structural frame of steel, or of steel and w^ood. The lower end is hinged to the turntable and the upper end is supported by guy rods which extend to the rear corners of the upper frame. The boom is made in two sections and so arranged that the dipper handle may move between them. Upon the upper side of the boom is located the thrusting mechanism. The dipper handle is of steel, or hardwood reinforced with steel plates. The lower end of the handle is attached to the dipper. Upon the under side of the handle is the steel-toothed rack which engages the pinion of the shipper shaft, which is the gear-operating 334 EARTHWORK 35 mechanism of the thrusting engine. In the Thew shovel, the dipper handle is made of steel and in two sections; the lower member tele- scopes into the upper section, and the two may be clamped in any position. The dipper is usually constructed of steel plates and forgings. The cutting edge is usually made of manganese steel and for hard soils is provided with tool-steel teeth which can be removed and replaced when worn out or broken. Method of Operation. A revolving steam shovel is generally operated by a crew of 3 to 5 men; an engineer, a fireman, and 1 to 3 laborers. The engineer controls the operation of the machine. The fireman feeds the boiler with fuel and water and keeps the machinery oiled and greased. The laborers haul coal, assist in the loading of the shovel in hard material, break down the bank, plank the floor of the excavation for the support of the shovel, etc. The engineer stands at the set of levers and brakes which are located near the front end of the upper platform. The method of operation of this type of shovel is similar to that of the fixed-platform class, and the student is referred to the detailed description given under that section. Note, however, that in the case of the revolving shovel, there is no cranesman, and the engineer directly controls the three operating motions of hoisting, swinging, and thrusting. The revolving shovel will excavate any class of material, except solid rock, which must first be blasted down and broken into pieces of a size which can be handled by the dipper. The excavated material may be dumped into spoil banks along the side of the excavation, or into wagons hauled by horses or traction engines, or into dump cars hauled by dinkey locomotives over a narrow-gage track. The dimensions and working limitations of an efficient make of revolving steam shovel of the revolving-platform class are given in Fig. 22. In column 1 of the table the class numbers correspond to dipper capacities of |, |, 1| or If , J or 1 (for shale excavation), and If o*ibic yards, respectively. The actual working capacities of revolving shovels depend upon the nature of the material, depth of cut, efficiency of hauling equipment, efficiency of engineer, size, capacity, and efficiency of shovel, etc. In ordinary clay, under average working conditions, 335 336 EARTHWORK 37 with a cut of from 5 feet to 10 feet, the output for a 10-hour day should average from about 500 cubic yards, for a f -cubic yard machine, to 1000 cubic yards for a If -cubic yard machine. OPERATING COSTS OF POWER SHOVELS Revolving Shovels. The revolving shovel is one of the most satisfactory and efficient machines for the excavation of dry soils when the required output does not exceed about 1000 cubic yards per day. For light earthwork, where the excavation is widely dis- tributed over a wide area or within narrow boundaries for long Qrant Sfreet Fig. 23. Excavation Diagram for Reinforced-Concrete Building Showing Location and Path of Shovel distances, this type of shovel is much more economical than its larger and heavier prototypes of the fixed-platform class. This character of work comprises allotment grading, highway and street grading, railroad construction, cellar and reservoir excavation, sewer trench work, reclamation projects, stripping of quarries, operation of gravel pits, brick yards, etc. The size of revolving shovel in general use is the |-yard dipper machine equipped with traction wheels. The shovel begins at the surface and works its way down on an easy slope to the final grade. 337 38 EARTHWORK Then the path of the shovel may be varied to suit the requirements of the job, but usually it assumes the form of a series of parallel lines. At the completion of the work the shovel can pull itself up a tem- porary incline by means of a cable attached to a "deadman" or anchorage located in the original surface above. The path of a revolving shovel in excavating a cellar for a large reinforced-con- erete building is shown in Fig. 23. Illustrative Example. The following example is a typical case of the use of a revolving shovel in quarry, gravel pit, or similar work, where the magnitude of the excavation warrants the installation of a transportation equipment of track and trains of dump cars. The shovel is a |-cubic yard dipper machine mounted on broad-tired wheels which move over heavy planking. The material is a glacial clay fairly free from rock and boulders and varying in depth from nothing to 6 feet. The material is dumped into 6-cubic yard side- dump cars which are hauled by a dinkey engine in trains of 4 cars each. The following cost schedule is based on a 10-hour working day. Cost of Operating a Revolving Shovel Labor: 1 engineer 1 fireman 1 laborer $4.00 2.50 2.00 Total labor cost, per day Fuel and Supplies: 1 ton coal, @ $4.00 I gal. cylinder oil,. @ 40c -^ gallon engine oil, @ 36c Waste, packing, etc. $2.00 .07 .04 .19 $8.50 Total cost of fuel and supplies General and Overhead Charges: Depreciation (based on 20-year life) Interest, @ 6% Repairs, and incidentals $0.70 .84 1.00 $2.30 Total fixed charges $2.54 Total Cost for 10-hour Day $13.34 Average Daily Output (cu. yd.) 300 Unit Cost of Revolving Shovel Operation, per cu. yd., $13,344-300= 00.045 338 EARTHWORK 39 In cellar and reservoir excavation, where the average cut would be 10 feet and the material loam, clay, and sand, the daily output might be increased to a daily average of 500 cubic yards by the use of sufficient cars or dump wagons to keep the shovel busy during 60 to 70 per cent of its working time. This would make the average operating cost about 3 cents per cubic yard. In street gradings, where the material is dense and compacted by traffic and the cut shallow or an average of 1 foot, the conditions of successful operation would be more difficult than usual. If the shovel were properly supplied with l|-cubic yard dump wagons, and efficiently operated, the average output for a 10-hour day should be 250 cubic yards. This output would incur an operating cost of about 8 cents per cubic yard. Electrically Operated Shovels. Where electric power is avail- able in large quantities and at a low cost, recent experience has shown the economy of this type of power for the operation of power shovels. Advantages of Electric Power. Where electric power is inex- pensive, the cost of operation of an electric ^^hovel is less than that of a steam shovel; with electric power at 3 cents per kilowatt hour, the cost of operation is about one-half that of steam-power machines. Under favorable supply conditions, the use of electric power is desir- able and economical for the following reasons : (1) less labor required for operation; eliminates the fireman and the shovel becomes a one- man machine; (2) eliminates the hauling and expense of coal and water; (3) greater economy of power; as power is used only when operating, and steam must be kept up continuously in case of the steam shovel; (4) operation is quieter, steadier, and quicker than that of the steam shovel; (5) eliminates the discomfort of freezing pipes in cold weather and of boiler temperature in hot weather; and (6) eliminates the trouble of banking fires at night and the delay in getting up steam at the commencement of work. Electrical Equipment, The prime mover is the electric motor which may be operated by either direct or alternating-current service. The wound-rotor type of motor is used for direct-current service and the compound-wound motor for alternating-current service. The various sizes of motors for the various capacities of shovels are given in Table IV. 339 40 EARTHWORK TABLE IV Sizes of Motors for Various Shovel Capacities Weight of Shovel (tons) Size of Dipper (cu. yd.) Power ob Motors Hoist (h. p.) Swing (h. p.) Thrust (h. p.) 30 35 , 35 35 42 65 95 100 1 u u 11 2 3i 4 50 50 60 75 75 100 150 200 30 30 30 35 30 35 50 80 30 30 30 35 30 35 50 80 The hoist and swing motors are mounted behind their respective engines and are geared to them through reducing gears. The thrust motor is mounted on the upper side of the boom, and geared to the pinions through proper reducing gears. Shovel service is particularly severe on electric equipment on account of the high power at low speed and the quick starting, stopping, and reversing of the machinery. The sudden stopping of the dipper in the bank, due to cutting too deep, or striking an obstruc- tion, or the sudden stopping of the boom in the act of swinging to one side, tends to stall the motor and burn it out. The use of auto- matic magnetic controllers and magnet switches has resulted in the efficient control and protection of the motor against such overloads. On revolving shovels, a single-motor drive has been found to be the more satisfactory on account of the economy in initial cost and the simplicity and flexibility of operation. The current is taken from trolley wires, or a transformer on a high-power line, and is received through the truck by wire cables. In the case of revolving shovels the current is transmitted to the motor above through copper rings on the truck frame and carbon brushes suspended from the rotating turntable. Field of Usefulness. The electric-power shovel is especially adapted for underground service in mines and tunnels, for plant service in the handhng of ores, coal, fertilizers, etc., for excavation in large cities, for electric street-railway construction, and for brick yards, gravel pits, etc. Probably the best field of service for the electric-power shovel at the present time is the use of the electri- cally operated revolving shovel in the construction of city and inter- 340 EARTHWORK 41 urban electric lines. The track trenching usually requires the shallow excavation of dense, hard material to a uniform grade, and the revolving shovel is the most efficient excavator for this class of work. An electrically operated revolving shovel is shown in Fig. 24. Efficiency and Economy of Power Shovels. The steam shovel is one of the most universally serviceable and efficient of modern excavators. When the soil is sufficiently dry and firm to support Fig. 24. Electrically Operated Power Shovel Courtesy of Westinghouse Electric and Manufacturing Company, Pittsburgh, Pennsylvania its weight and the work is of sufficient magnitude to warrant its use, it can be used economically for all classes of earthwork. Hand shoveling has been almost entirely superseded by power-machine shoveling on work where the amount of w^ork will justify the cost of installation of the plant. The relative economy of the two methods may be determined approximately by estimating the cost per cubic yard by hand labor and the same cost by power machine. 341 42 - EARTHWORK including in the total cost by the latter method the items of plant installation, depreciation, interest, and repairs. A comparison can be made for the excavation of ordinary soil of loam, clay, and sand, under average working conditions, between power-shovel and hand labor. This discussion cannot be exact as there are many indeterminate and variable conditions of soil, labor efficiency, etc., which will affect the results for the peculiar condi- tions of each case. However, the student is urged to study the method of analysis, as it can easily be applied to the investigation of other methods and of other types of machinery. Illustrative Example. Let us assume a loam and clay soil with few boulders or obstructions; the hauling to be done by 2-yard dump wagons of sufficient number to keep the hand shovelers or power shovel busy; the cut to average 8 feet, and runways to be arranged for the incoming and outgoing teams; the material first to be loosened in the case of hand shoveling. Cost of Shoveling by Hand Loosening: 1 plow team, with driver and plow holder; Team, plow, and driver $3 . 50 Plow holder 1.50 Total labor cost, per day $5 . 00 Repairs, depreciation, etc. 1 . 00 Total Cost of Loosening $6 . 00 Total Amount of Loosened Material (cu. yd.) 400 Unit Cost of Loosening Material, per cu. yd., $6.00-v-400= 00.015 Shoveling and Loading: One man can shovel and load about 20 cubic yards per 10-hour day. Hence the plow should loosen enough material to keep 20 men busy. Load- ing dump wagons, these men can work efficiently in 4 groups of 5 men each. Each group of 5 men can load on an average 6 wagons per hour or 50 wagons per 10-hour day, allowing for delays. 1 foreman $ 3.00 20 laborers, @ $1 .50 each 30 . 00 Total labor cost, per day $33 . 00 Repairs, incidentals, etc. 1 . 00 Total Cost of Shoveling and Loading $34.00 Total Amount of Earth Handled (cu. yd.) 400 Unit Cost of ShoveUng and Loading, per cu. yd., $34.00-^400 = 00 . 085 Total Cost of Hand ShoveUng 400 cubic yards 40 . 00 Unit Cost of Hand Shoveling, per cu. yd., $40.00^400 = 00 . 10 342 EARTHWORK 43 Assume also a revolving steam shovel equipped with a |-yard dipper and operated by an engineer, fireman, and 2 pitmen. With good wagon service, the average output will be 500 cubic yards per 10-hour day. The shovel will load on an average 30 wagons per hour. Cost of Power Shoveling Labor: 1 engineer $5.00 1 fireman 2.50 2 pitmen, @ $1.50 each 3.00 Total labor cost, per day $10.50 Fuel and Supplies: f ton coal, @ $4.00 $3.00 Oil and supplies 1.00 Total fuel and supplies $4.00 General and Overhead Charges: Depreciation* $1.00 Interest t 1.20 Repairs and Incidentals 1.80 Total fixed charge $4.00 Total Cost of Operation per 10-hour Day $18 . 50 Average Daily Output (cu. yd.) 500 Unit Cost of Power Shovel Operation, per cu. yd., $18,504-500= 00.037 The above data show that the output is increased by 25 per cent at a reduction in cost of 65 per cent by the use of the steam shovel. The average loading time by hand shoveling was assumed as 10 minutes and for the steam shovel as 2 minutes. This means a saving of about 4 minutes per cubic yard by the use of the steam shovel. If the teams are paid at the rate of 50 cents per hour for a 10-hour day, the economy in the value of the team time saved, for different shovel outputs, will be as follows: Economy in Team Cost 300 cu. yd. per 10-hr. day, at 3t min. 900 min. or 15 hrs. @ 50c $7.50 400 cu. yd. per 10-hr. day, at 3t min. 1200 min. or 20 hrs. @ 50c 10.00 500 cu. yd. per 10-hr. day, at 3^ min. 1500 min. or 25 hrs. @ 50c 12 . 50 600 cu. yd. per 10-hr. day, at 3$ min. 1800 min. or 30 hrs. @ 50c 15.00 * Based on 5 per cent and 20-year life. t Based on 6 per cent and 20-year life. t Value of 3 minutes is used as being conservative. 343 44 EARTHWORK Thus it will be noted that the saving in team time per 10-hour day, on the basis of an efficient shovel operation of 600 cubic yards, is nearly enough to pay for the operating cost of the shovel. Hence it is likewise true that the economy resulting from the efficient use of a power shovel is often equal to the entire cost of shoveling and loading by hand methods. If the job comprised the removal of 45,000 cubic yards and hand shoveling cost 10 cents per cubic yard, the use of a steam revolving shovel would effect a saving sufficient to pay for the cost of the machine. DREDGES DRY=LAND EXCAVATORS Preliminary Discussion. The steam shovel is not well adapted to earthwork operations on wet or soft soils on account of the con- centration of the heavy load of the machine and loaded dipper over a long, narrow area. The crane or boom of the power shovel is short, of heavy construction, and produces great pressure over a small area of base. Hence, for the excavation of soft and wet soils, especially on reclamation projects, it became necessary to devise a machine, similar in construction and operation to the power shovel, but with the load distributed over a wide base and with a long boom for the direct removal of the excavated material to spoil banks adjacent to the excavation. Thus was developed the dredge. Classification. Dredges may be divided into two different classes: dry-land excavators, and floating excavators. The different types of dry-land excavators will be considered in this section and the different types of floating excavators in the following section. Dry-land excavators are those which move over and operate from the surface of the land. They may be classified as to their construction and method of operation as follows : scraper excavators, templet excavators, wheel excavators, tower excavators, and walk- ing excavators. Scraper excavators may be subdivided into two general classes, as to their method of operation : the stationary dredge with pivoted boom, and the revolving dredge or excavator. STATIONARY SCRAPER EXCAVATOR During the past decade, the reclamation of thousands of acres of wet land in the Middle West and South, has required the con- 344 EARTHWORK 45 struction of drainage ditches. For this work the stationary dredge, a light portable type of excavator, has been designed particularly for the economical excavation of the smaller sized channels. This machine is stationary only as regards its position during excavation, as it is a traction machine. Construction. The machine consists of a framework of stand- ard structural-steel shapes, supported on two trucks. Each truck comprises a heavy steel axle with two broad-tired steel wheels of 5-foot to 6-foot diameter. Some makes of excavator are supported on cateroillar tractors so as to distribute the load more uniformly Fig. 25. Caterpillar Tractor over a larger area of wet soil. As in the view of one of these tractors in Fig. 25, the framework supports the operating and excavating equipment. An excavator loading cars is shown in Fig. 26. Operating Equipment. Near the front end of the platform are placed the operating drums and gears which are belt-connected to a kerosene or gasoline engine mounted near the rear end of the plat- form. The hoisting and drag-line drums are controlled by friction clutches operated by levers. These light excavators are operated almost entirely by internal- combustion engines as they are clean, compact, easy to operate, and economical. A 25- to 50-horsepowei: kerosene or gasoline engine is 345 46 EARTHWORK s ^ 1^ ;!! 346 EARTHWORK 47 used, depending on size and capacity of machine. With a |-yard bucket and 50-foot boom, a 40-horsepower engine is of sufficient size to furnish the power for the excavation of all classes of soils. The engine is equipped with forced-oil feeder, gear-driven magneto, car- bureter, throttle, governor, large oil tank, etc. Excavating Equipment. The excavating equipment consists of the boom, and bucket or scoop. The boom is made of steel channels latticed and braced with truss rods. The lower end rests in a uni- versal joint at the front end of the platform, and the upper end is supported from the A-frame by cables and carries the sheave over which the hoisting cable passes. The bucket is a steel scoop pro- vided with tool-steel teeth for the excavation of dense and hard soils. Method of Operation. One man is required to operate the machine and he stands at the front and controls the machine by a set of levers. The bucket is lowered to the surface by releasing the hoisting line. Then the drag line is hauled in and this pulls the bucket toward the machine, SQOoping up a thin slice of earth during its progress. When the bucket is near the machine and filled, the boom is swung to one side until the bucket is over the spoil bank, when it is inverted and dumped. Field of Usefulness. The stationary dredge of the light, port- able type of construction is rapidly developing a wide field of eco- nomic service in earthwork. Being simple and light in construction, the machine can be set up in a short time and can move readily over fairly level ground. In reclamation work, this excavator is efficient in the excava- tion of open ditches up to about 40 feet in width. It can be used advantageously for the cleaning out of old ditches which have become silted up. For the excavation and back filling of trenches for drain tile from 24 inches to 42 inches in diameter, the scraper excavator is very efficient. When highway and railroad work are in wet soils, the light scraper excavator has" proved its adaptability in the construction of cuts and embankments. The cuts can be made to any desired side slope and to any depth or width by making one or more trips on the same or different levels. The machine can borrow the material from one or both sides and construct the side ditches in the making of embankments. 347 48 EARTHWORK The cost of operation will vary from 4 cents to 10 cents per cubic yard for an output of from 1000 to 500 cubic yards per 10- hour day, depending on soil conditions, efficiency of the operator, etc. The machine is generally operated by one man and one or more men are necessary for general service in the pit and about the work. REVOLVING EXCAVATOR Methods of Mounting. The most generally used type of dry- land scraper-bucket excavator is the revolving type. These machines may be mounted in three different ways as follows: (1) On skids and rollers, when the machine travels over the planks laid on the surface. The machine moves ahead by pulling itself up to its bucket, which acts as an anchor. (2) On trucks, when the machine is mounted on small, steel, 4-wheel trucks. The machine moves ahead as in the case of skids and rollers. (3) On caterpillar tractors, when the machine is supported on 4 moving platforms which are especially adapted for soft soil condi- tions and allow the machine to move ahead without the use of planking, tracks, etc. Construction. The essential parts of a scraper-bucket excava- tor are the substructure, consisting of the upper and lower platforms and turntable; the power equipment; and the excavating equipment. These essential parts are practically the same, as regards their method of operation, for all makes of drag-line excavator. These parts are shown in Fig. 27. The substructure consists of a lower platform, an intermediate turntable and an upper platform. The lower frame consists of a rectangular framework of structural-steel shapes. The frame is mounted in one of three ways stated above. Upon the upper sur- face of the lower platform is fastened the track upon which runs the moving circle. In the center is located the lower section of the central pivot. The turntable consists of a swinging circle, which is a steel frame carrying a series of flanged wheels. The upper framework or platform consists of steel shapes framed rigidly together. Upon the lower surface of its frame is placed the upper section of the central pivot. 348 *^ \ 349 50 EARTHWORK Power Equipment. Scraper-bucket or drag-line excavators may be operated by steam, electric, or gasoline power. The steam equip- ment is the one generally used and will be discussed first. Steam Poiver. The power equipment of a steam-power exca- vator consists of the boiler, steam pump, injector, feed- water heater, main, and swing engines. The boiler may be either of the horizontal, locomotive type or of the vertical, submerged-tube type. The former is the more efficient for hard usage and the latter the more economical of space. A steam pressure of about 125 pounds is ordi- narily maintained under average conditions. A steam pump of the Fig. 28. Interior View of Scraper Bucket Excavator. A, A-Frame; B, Boiler; C, Hoisting Engine; D, Feed-Water Heater; E, Deck Winch; F, Swinging Engine; G, Feed-Water Pump Courtesy of Lidgerwood Manufacturing Company, New York City standard duplex type is generally connected to a water supply from which the boiler is furnished by an injector. A feed-water heater is often necessary to purify alkali waters before they are admitted to the boiler. The main or hoisting engines are of the horizontal, double- cylinder, friction-drum type. The swinging engine may be a part of the main engine or a separate mechanism. The latter method is the more satisfactory. The hoisting engine in this case has two drums, one for the hoisting cable and the other for the drag line. These drums are often controlled by double-band outside friction 350 EARTHWORK 51 clutches operated by auxiliary steam rams. The swinging engine is of the steam, reverse type and drives, through a chain of gears, a pinion which operates the large circular rack on the lower frame. The power equipment of a typical drag-line excavator is shown in Fig. 28. Electric Power. Where electric power is available and reason- able in cost, it is advisable to use electric motors, in place of the steam-boiler equipment. Either alternating or direct current may be used. The motors may be gear or belt-connected to the shafts of the hoisting and swinging engines. The drums of these engines are controlled by outside-band friction clutches, which are actuated by pneumatic-thrust cylinders. A small belt-connected air com- pressor with receiving tank supplies the compressed air for the rams. On a 120-ton machine equipped -mth a 2|-yard dipper, a 115-horse- power, 60-cycle, 3-phase motor for the hoisting engine, and a 50- horsepower, 60-cycle, 3-phase motor for the swinging engine are suitable for the power equipment. The cost of current will vary from i to 1 cent per cubic yard, depending on the market price. The reliability, cleanliness, and economy of this form of power are strong factors in favor of its use. It has proved very advanta- geous in reclamation work in the arid regions of the West, where coal and water are scarce and expensive, and electric power is available from near-by transmission lines of water-power plants. Gasoline Power, Gasoline and kerosene engines have been successfully used in the operation of the machinery of the smaller sizes of scraper-bucket excavators. The engine is mounted on a base just to the rear of. the drum mechanism to which it is belt- connected. A 50- to 80-horsepower engine is necessary for the efficient operation of hoist and swinging engines. The drums of the hoisting mechanism are provided with outside-band friction clutches, which are controlled by pneumatic-thrust cylinders. Double-cone friction clutches are used to operate the drums of the swinging mechanism. A small air compressor actuated by a belt connection with the engine furnishes compressed air to a receiving tank. The air is supplied to the thrust cylinders, which operate the band friction clutches on the drums. A water tank for supplying water to cool the engine cylinder and a gasoline supply tank are also placed on the upper platform near the engine. 351 52 EARTHWORK The gasoline engine is the most economical*" type of prime mover or power producer in locaUties where coal and water are scarce and expensive, and electric power is not available. Excavating Equipment. The excavating equipment consists of the A-frame, boom, and bucket. The A-frame is generally a framework, shaped like the letter A, composed of wooden or steel members. This frame is located near the front end of the platform. The top of the boom is* connected by cable with the top of the frame which is also guyed back to the two rear corners of the platform. The top of the boom may be raised and lowered by means of a wire cable, which passes from the Fig. 29. Page Scraper Bucket end of the boom over a sheave at the top of the A-frame and thence down to the deck winch. The boom is generally a steel framework which is pivoted to the front end of the platform. The upper end of the boom is framed so as to form a boxing for one or more sheaves over which the hoist- ing cable passes. The bucket may be one of three types: the scraper bucket, the clam-shell bucket, and the orange-peel bucket. The last two types will be discussed in the section under "Floating Dipper Dredges", Part II. The scraper bucket is the type generally used with a drag-line excavator. It consists of a box-shaped scoop made of heavily reinforced, shaped steel plates. The lower front edge is the cutting edge and is made of manganese steel and for hard material 352 EARTHWORK 53 is provided with teeth. There are several makes of these buckets, which differ only in their details of construction. The Page bucket is shown in Fig. 29. Method of Operation. A steam-operated machine requires the services of four men : an engineer, a fireman, and two laborers. The engineer stands at the front end of the platform and by means of the levers and brakes controls the entire operation. The fireman keeps the boiler fed with fuel and water and has general supervision of the machinery. The laborers act as pitmen and are of general serv- ice about the machine. The fireman can be eliminated in the case of the excavators operated by electric motors or internal-combus- tion engines. The operation of excavation commences with the bucket in the first position shown in Fig. 27. The engineer releases the hoisting- line and drag-line drums and allows the bucket to drop to the surface, where it will be in the second position showTi in Fig. 27. In descend- ing, the weight of the bucket maintains its vertical position and forces the cutting edge into the soil, giving it an initial bite. With the hoist- ing line still released, the operator starts up the drag-line drum and pulls the bucket toward the machine. The first pull on the drag line tilts the bucket to the proper position for the penetration of the soil. By a slight manipulation of the hoisting line, the proper angle of the bucket may be kept for a deep cut in soft soils or for a thin cut in hard soils. When the bucket is filled, the drag-line drum is set and the hoisting drum is started, and this automatically raises the front end of the bucket and thereby prevents the spilling of the contents during the swing to the spoil bank. The front end of the bucket is held up by means of the tension of the dumping line which is the upper branch of the drag line. See third position of the bucket in Fig. 27. When the dumping position is reached, the operator releases the drag line and the bucket revolves into a vertical position and dumps. The tension is applied or released by pressure on the brake lever actuating the drag line and hence the operation of dumping is always under the control of the operator. Cost of Operation. The cost of operation of a scraper-bucket excavator depends on the class of work, the kind of material to be handled, the size of the machine, the efficiency of the operator, the character and cost of the power used, etc. 353 54 EARTHWOEK Illustrative Example. The type of machine in general use is a steam-power excavator, equipped with a 2|-yard bucket. Such a machine, on ditch or railroad construction should excavate about 1200 cubic yards of loam and clay during a 10-hour working day. The following is a typical case of the cost of operation, under such conditions, for a 10-hour day : Operating Cost of Steam-Power Scraper-Bucket Excavator Labor: 1 engineer $5.00 1 fireman 3.00 2 laborers, @ $1 .75 each 3 . 50 1 team and driver (hauling coal, etc.) 3.50 Total labor cost, per day Fuel and Supplies: 2 tons of coal, @ $4.00 $8.00 Oil, and waste 1.75 Water 0.35 Total fuel and supplies General and Overhead Expenses: Repairs $4.00 Incidental expenses 2.00 Depreciation (10% of $10,000)* 5.00 Interest (6% of $10,000)* 3.00 Total general and overhead expense $15.00 $10.10 $14.00 $39.10 Total Cost of Operation for 10-hr. Day Average Daily Excavation (cu. yd.) 1200 Unit Cost of Scraper-Bucket Excavating, cu. yd., $39.10-M200 = 00.033 Fig. 30. Diagram of Limitations of Drag- Line Excavators on a life of 10 years and 200 working days per year. 354 EARTHWORK 55 Field of Usefulness. The field of work of the drag-line exca- vator has become a wide one since 1910. Its early use was largely in reclamation work, the construction of ditches and dikes on irriga- tion and drainage projects. Its great length of boom gives this excavator a wide radius of operation and permits of the deposition of material in spoil banks at a sufficient distance from the sides of the cut to prevent caving of the banks. The drag-line principle permits the excavation of material at a considerable depth below the surface and its elevation to a correspondingly high elevation Fig. 31. Revolving Excavator on Caterpillar Tractor Operating on Drainage Work above the surface. The limitations of the drag-line excavator are shown in Fig. 30. The use of the caterpillar tractor allows a heavy machine to move over soft, wet soils on drainage work. The machine starts at the lower end of the canal and excavates as it moves upstream, thus allowing the surplus soil water to drain off through the new channel. The careful operation of the bucket will result in the construction of a canal with smooth and uniform bottom and side slopes. An example of this class of earthwork is shown in Fig. 31. Recent experience in the South and West has proved the efficiency of this type of excavator in the construction of dikes and earthen dams on 355 56 EARTHWORK reclamation projects and embankments on railroad work. The machine moves parallel to the work and borrows the material from one side, or moves ahead of the work and borrows the material from both sides. Earthen dams and dikes, if of large size, should be made in layers of about 6- to 8-inch depth, and each layer wetted and rolled by a heavy steam roller before the deposition of the material for the next layer. Small dikes and railroad fills can be satisfactorily built without wetting and rolling. The drag-line excavator saves Fig. 32. Drag-Line Excavator Operating on Placer Mine in Siberia the haulage equipment necessary in this class of earthwork where either an elevating grader or a power shovel is used. The scraper-bucket excavator is very efficient in the excavation of gravel pits and in stripping soil from quarries and mines. When the power shovel has become drowned out of a pit which has been Hooded, the drag-line machine can work from a higher level and excavate for a considerable distance below the water. Fig. 32 shows a drag-line excavator, equipped with a l|-yard bucket and a 65-foot boom, which operated successfully in 1915 on a large placer mine in eastern Siberia. Such a machine has proved to be very 356 EARTHWORK 57 la > s il II CO ^ S '5' 05 o O 357 58 EARTHWORK economical where conditions do not warrant or permit the use of a large hydraulic dredge. TEMPLET EXCAVATOR Considerable difficulty has been experienced in the maintenance of drainage and irrigation channels. This has been caused by their rapid filHng up with silt, debris, and vegetable growth. Many forms of dredges construct the channels with rough bottoms, uneven sides^ and steep banks, which are subject to subsequent caving. These irregularities in the surfaces of the channels retard the flow of the water and augment the deposition of silt, debris, and other heavy materials carried by the water in suspension. During the decade P^ ■: '^t9f^KKK^^i^^^W^. . :mmmmm'. . 5^H |BI -*■'— • J^r- .. — — 1 Fig. 34. Narrow-Bottom Templet Excavator Courtesy of F. C. Austin Drainage Excavator Company, Chicago 1905-1915, a unique type of excavator, called the templet excavator, came into use for the construction of open ditches with true and smooth side slopes and grades. Construction. A double-faced, reversible, positive-cleaning bucket moves along a guide frame, which is shaped at its lower section to the desired cross-section of the ditch. The guide frame is supported on a platform or framework composed of structural-steel members, strongly braced and bolted together. This platform is supported on wheel trucks or caterpillar tractors, which are neces- sary for soft, wet soils. Templet excavators with wide and with narrow frames are shown in Figs. 33 and 34, respectively. Power Equipment. Power for the operation of the machine may be furnished by a steam-power equipment or by an intemal- 358 EARTHWORK 59 combustion engine. The latter type of power equipment has gener- ally been found to give very satisfactory results and to be cleaner, cheaper, and simpler in operation than the ordinary steam plant. If a steam engine and boiler are used, a 25-horsepower to 40-horse- power engine will be required, while a gas engine for the same machine should have from 50 horsepower to 80 horsepower. The power plant is mounted on the central part of the platform and is operated with a set of levers by one man. Excavating Equipment. The excavating equipment consists of the guide frame and the bucket. The guide frame is made up of 2 -66'-0" Fig. 35. Limitations of Templet Excavator with Narrow-Bottom Frame Courtesy of F. C. Austin Drainage Excavator Company, Chicago steel members which are placed parallel and form a track over which the bucket moves. This frame is made in two shapes at its bottom section to provide for the excavation of narrow and of wide ditches; the side slopes are nearly 1:1. The frame is well braced by steel- frame members and can be raised and lowered through the platform. The bucket is a rectangular-shaped box with 2 open ends and cutting edges. A plunger head fits inside the box section. Method of Operation. The guide frame is lowered to the ground surface and the bucket drawn down and along the bottom of the frame. As it moves along it cuts a thin slice of earth which is 359 60 EARTHWORK carried on to the upper section of the frame. Here trips are located and they push the plunger head through the bucket and thus the contents are discharged into either wagons or cars or upon a spoil bank below. As the bucket moves back and forth along the frame, the latter is lowered so as to gradually feed the bucket into the earth and increase the depth of cut. Thus a section of ditch prism about 3J feet in length is made with one position of the machine. The machine then moves ahead and cuts another section of ditch, Fig. 36. Limitations of Templet Excavator with Wide-Bottom Frame Courtesy of F. C, Austin Drainage Excavator Company, Chicago and so on. The limitations of the two types of templets — narrow and broad bottoms — are given in Figs. 35 and 36. Cost of Operation, The gasoline-power machine equipped with caterpillar tractors is the type of templet excavator, which is most generally used in the excavation of channels in loose and soft soils. For the operation of this machine a crew of 3 to 4 men would be required; an engineer, an assistant, a laborer, and a teamster. A steam-operated machine, run on a track would require the services of one or two extra men to haul fuel, move track, etc. The engineer operates the bank of levers which control the movement of the 360 EARTHWORK 61 bucket, the raising and lowering of the frame, and the tractive move- ment of the machine along the surface. The assistant keeps the machinery oiled and in good working order. The laborer provides planking or tracking w^here necessary, and does general service about the machine. The teamster hauls the gasoline, water, and supplies necessary for the work. Illustrative Example. The cost of operation of a typical machine in the construction of a drainage channel through alluvial soil under favorable conditions would average about as follows for a 10-hour day: Operating Cost of Templet Excavator Labor: 1 engineer $4.00 1 assistant 2.50 1 laborer ' 2.00 1 team and driver 3 . 50 Total labor cost, per day $12 . 00 Fuel and Supplies: 35 gallons of gasoline, @ 20c Oil, waste, etc. Total fuel and supplies $8.00 General and Overhead Expenses: Depreciation (12 1% of $12,000)* Interest (6% of $12,000)* Repairs and incidentals Total general and overhead expense $19.00 Total Cost of Operation for 10-hour Day $39.00 Total Excavation (cu. yd.) 700 Unit Cost of Templet Excavating, per cu. yd., $39.00-5-700= 00.055 Field of Usefulness. A water channel, to secure highest effi- ciency of operation, should have a true grade and uniform and smooth side slopes. On irrigation and drainage projects, the dis- tribution canals and open ditches are peculiarly susceptible to filling up with silt, debris, and vegetable matter during seasons of low flow. In the case of small ditches, this filling up may become so great in a few years as to render the channel practically useless. This means that these artificial waterways must be cleaned out every few years in order to maintain their efficiency and capacity. In order to * Based on 150 working days a year and an 8-year life. 361 $7.00 1.00 $10.00 4.80 4.20 62 EARTHWORK reduce this maintenance expense to a minimum, it is advisable to construct the channels as nearly mechanically perfect as possible. The templet excavator is the best form of excavator for the construction of an open channel, where the soil conditions are favor- able. In alluvial soils, such as loam, clay, sandy loam, and marl, the machine does very satisfactory work. But in hard soils, such as hard pan or indurated gravel, and in lands where many obstruc- tions such as stumps, boulders, and roots occur, the progress is slow and difficult and the work expensive. WHEEL EXCAVATOR The wheel excavator is a machine which has been devised to excavate small open ditches on reclamation work. Most types of Fig. 37. Wheel Excavator Constructing Small Drainage Ditch excavators are unfitted on account of size and method of operation to construct the smaller lateral ditches of drainage and irrigation systems, and there has been a great demand, beginning in the decade of 1905-1915, for a small, hght, portable machine, which can excavate to a true and uniform cross-section. Construction. The ditcher consists of a frame which supports the power equipment on the front end, and a pivoted framework containing the excavating wheel on the rear end. The platform is supported at the front on an axle which has 2 broad-tired steel wheels, and at the rear by 2 caterpillar tractors, which allow the machine to operate in wet, soft soils. A view of a wheel excavator con- structing a small drainage channel is shown in Fig. 37. 362 EARTHWORK 63 Power Equipment. The power may be supplied either by a steam or internal-combustion engine. The earlier machines were supplied with the former type of engine but the more recent machines are nearly all equipped with gasoline engines. These gasoline engines are generally of the marine type and made with 4-cycle multiple cylinders, ranging from 20 horsepower to 90 horsepower. They are provided with high-tension magneto and dual ignition. The motive power is transmitted to the wheels either by sprocket chain or bevel-gear drive. Excavating Equipment. The excavating equipment consists of the excavating wheel and belt conveyor. The wheel is an open steel frame, around the periphery of which are attached from 8 to 12 Fig. 38. Diagram of General Dimensions and Specifications of Wheel Excavators buckets of scoop shape. At the rear and near the upper part of the wheel is placed the belt conveyor, which projects out a considerable distance either side of the machine. Method of Operation. The excavating wheel revolves either on a central axle or anti-friction wheels placed along its rim and each bucket cuts out a thin slice of earth which is deposited on the machine end of the belt conveyor, when the bucket reaches the top of the wheel. The operator gradually feeds the wheel into the ground as the wheel revolves. After one section has been dug to the required depth, the machine moves ahead several feet under its own power and another section is dug, and so on. The sizes, limita- tions, and capacities of the various sizes of a well-known make of wheel excavator are given in Fig. 38 and Table V, 363 64 EARTHWORK 05 to 00 CO CO 1—1 X ^ b 05 (N (N 1—1 1—1 CO b CO ,—1 t- CO (N (M (N '"' iHiN 05 Ot-4 CO m !>. CO 00 OS Th 1—1 X CO ^ b b CO b CO § 88 i 8 lO ^ 1—1 i >i rfi c^ 00 1—1 (N ?5 1— 1 CO 04 CO g t^i-i t^ 1-1 T-l g Tt^ s 00 1—1 CO 00 1—t T— 1 X l5 1—1 ^ b 1—1 o CO s^ ^^ 1-4" i cc CO 00 1—1 b 1—1 X 1-4 ?* b b b b o CO d' ccoo s i-T t^'^ . c »o to lO m (N CO 00 1— H CO 1—1 b 1— 1 X CO • lb b t^ b CO (of b't''^ i-M~ 1 s 5 O o 1— 1 fc & ^ 88 g g , »o ■^ CO y b rj< ^ CO Tt< l_) rt^ tJ^ Oi (M CO 1—1 1—1 CO i-M i-H (N Th (M S (M CO ^ c O -^ CQ o Q &q n1 Ci x: -u a ^ ^ :B:B T3 4) (V >i ^ ^ i 4h « > j3 <^ m b O W § 13 S o ■i3 3 :z; 2§ w-S 3 ::3 , S CO a 2 < o 1 Q g 03 ^ Xi faC 1 OH oS fe 1 a 2 < 1 < 1 ■*^ <5 1 1 1 1 1 bC O bC 5 o O 6 1 -4-3 PQ o § -4-3 so d 364 EARTHWORK 65 Cost of Operation. The cost of operation depends on the size of the job, the size and make of excavator, the character and condi- tion of the soil, the efficiency of the operator, etc. Ilhistratire Example. With a machine which digs a ditch with a top width of 4 feet 6 inches, an average depth of 3 feet 6 inches, bottom width rounded to 12 inches, and side slopes of about ^il, the average cost of operation for a 10-hour day would be about as follows : Operating Cost of Wheel Excavator Labor: 1 operator, @ $125 per month $4.00 1 assistant 2.50 1 laborer, @ $2.00 2.00 1 team and driver 3.50 Total labor cost, per day $12.00 Fuel and Supplies: 30 gallons gasoline, @ 20c $6.00 Oil, waste, and supplies 1.00 Total fuel and supplies $7.00 General and Overhead Charges: Depreciation (12|% of $6000)* $5.00 Interest (6% of $6000)* 2.40 Repairs and incidentals 4.60 Total general and overhead expense $12.00 Total Operating Cost per 10-hour Day $31.00 Average Progress per Day (ft.) 2000 Average Daily Excavation (cu. yd.) 700 Unit Cost of Wheel Excavating, per cu. yd., $31.00^700= 00.044 Field of Usefulness. The wheel excavator is the most practical form of excavator for small ditches where the soil conditions are favorable. This machine cannot excavate economically very hard, dense soils, or where large quantities of stumps, boulders, and other obstructions are present. In glacial clay, alluvium, marl, and similar soils, this excavator operates very smoothly and satisfactorily. In irrigation and drainage systems, where the smaller ditches run full only a small part of each year, a large amount of silt, debris, and vegetation gradually accumulates. These obstructions in the course of a few years will gradually fill up and greatly reduce the * Based on 150 working days a year and an 8-year life. 365 66 EARTHWORK carrying capacity of the channels. Hence it is necessary to con- struct the smaller channels to as near true grade and cross-section as is practicable. In open, porous soils, such as occur often on irriga- tion projects, it becomes necessary to line the ditches with some Fig. 39. Tower Excavator Operating on New York State Barge Canal impervious material such as concrete to prevent large seepage losses. In such cases it is a great advantage to excavate a channel, which is to be subsequently lined, with a true grade and smooth side slopes, so that the form work for the concrete may be set without the extra labor and expense of trimming and shaping the excavation. EARTHWORK 67 TOWER EXCAVATOR The tower excavator is a unique type of machine which was developed and used with success several years ago on the Chicago Drainage Canal and recently on the construction of the New York State Barge Canal. As will be seen from Fig. 39, this excavator derives its name from its principal part, which is a movable tower. Construction. The tower is a framed, timber structure, the height of which is determined by the width of the area to be exca- vated. The tower rests on a platform or car, which is braced by overhead, horizontal-chord, combination trusses. This car is mounted on 4 solid, double-flanged cast-steel wheels generally about 14 inches to 16 inches in diameter and with 4-inch treads. The wheels run on a track, which consists of 80-pound to 90-pound rails, spiked to cross ties, w^hich are bolted to 30-foot planks. The car and tower are moved ahead by a cable which passes over a sheave on the car and thence to a "deadman" or anchorage placed at a suit- able point ahead of the car, and then back to a drum on the engine. The tower is braced to the car by cables which extend from the top of the tower to the rear corners of the car. Power Equipment. The power equipment is placed on the rear of the car and consists of a vertical boiler and a double-drum hoist- ing engine. The engine is usually of the vertical, reversible type, with double, 40-inch by 12-inch cylinders, and equipped with friction-clutch control for the drums. Excavating Equipment. The excavating equipment consists essentially of a 2-line scraper bucket. At the rear of the bucket is a frame carrying 2 sheaves at right angles to the cutting edge, which is strongly reinforced and provided mth teeth for the excavation of hard material. On the bottom of the bucket are attached 2 curved shims, or shoes. The front of the bucket is connected to the drag- line drum of the engine by a cable which passes over a sheave sus~ pended on the front side of the tower about J of its height from the base. Another cable extends from the hoisting drum of the engine over a sheave at the top of the tower, then between the sheaves on the bail of the bucket and then to an anchorage at the far side of the excavation. Method of Operation. The bucket is lowered over the hoist line by allowing it to slide down the cable by its own weight, to the 367 68 EARTHWORK far side of the cut. Then the bucket is loaded by pulHng it toward the tower by winding up the drag-hne cable. When the spoil bank is reached, the hoisting cable is raised and the bucket is overturned and dumped. The bucket is returned to the excavation by still further tightening the hoisting cable and releasing the drag-line cable, whereby the bucket rises and slides back to the starting point. Where a tower 65 feet in height has been used, a reach of 210 feet from the far side of the excavation to the near side of the spoil bank was attained with efficiency of operation. A bucket, of Tower lio.S ELEV/iTIOti Fig. 40. Diagram of Double-Tower Excavator 2-cubic yard capacity, made an average output of 3 cubic yards and was operated at the rate of 4 cubic yards per minute. A crew of from 5 to 9 men is required to operate a tower exca- vator, depending on the magnitude of the job, the character of the material to be excavated, etc. Under average conditions, there will be required an operator, a fireman, a team and driver, and 3 laborers. The operator is stationed on a platform on the rear side of the tower and at about \ its height. He controls the machinery by a set of levers and brakes and has an unobstructed view of the work. The fireman keeps the boiler and machinery supplied with fuel, water, and oil, and in proper working condition. The team and 368 EARTHWORK 69 driver haul fuel, water, and supplies to the work. The laborers move the track and perform general service about the work. DoubIe=Tower Excavator. A double-tower excavator was used some years ago on a section of the Chicago Drainage Canal. A diagrammatic view of this excavator is shown in Fig. 40. As will be noted from the plan, the inclined booms were so designed that a straight line from the apex of either tower to the point of the oppo- site boom, clears the side of the tower. This allowed each bucket to clear the tower and empty directly on the adjacent spoil bank. A double-drum hoisting engine was located on the side of the platform of each tower. Each bucket was operated by a drag line and a hoisting line. The buckets were loaded, dumped, and returned to the excavation as is described above for the single tower excavator. By changing the location of the suspended sheaves, the position of the bucket in digging was altered so as to reach the entire half width of the canal prism. This machine, in the excavation of a canal section having a bottom width of 26 feet, side slopes of 2:1, and an average depth of 27 feet, through a clay soil, did very satisfactory work. Cost of Operation. Illustrative Example, The following may be taken as an estimate of the cost of operation of a single-tower excavator, equipped with a 75-foot tower, controlHng a 250-foot width of excavation, a 2-yard scraper bucket, and a 10 X 12-inch double-drum, vertical hoisting engine. The excavated material would be dumped upon a spoil bank at the tower side of the excavation and into wagons or dump cars by means of a loading platform. A train of four 5-yard dump cars would be loaded in about 15 minutes. An average output of 600 cubic yards would be attained in the excavation of a glacial clay under average working conditions during a 10-hour working day: Labor: Operating Cost of Single-Tower Excavator 1 engineer $4.00 1 fireman 2.50 1 team and driver 3 . 50 3 laborers, @ $2.00 each 6 . 00 Total labor cost, per day $16.00 .S6» 70 EARTHWORK Fuel and Supplies: I ton of coal, @ $4.00 $3.50 Oil, and waste 0.50 Total fuel and supplies $4.00 General and Overhead Expenses: Depreciation, (10% on $2000)* $1.40 Interest (6% of $2000)* 0.80 Repairs, and incidentals 5.50 Total general expense $7.70 Total Cost of Operation for 10-hr. Day $27 . 70 Average Excavation per 10-hr. Day (cu. yd.) 600 Unit Cost of Single-Tower Excavating, per cu. yd., $27.70 -J- 600 = 00 . 046 Field of Usefulness. The tower excavator was originally used in canal excavation where the cross-section was very wide with a comparatively shallow depth. When the top width of a channel is over 80 feet, it becomes necessary to use drag-line excavators in pairs, one along each bank, or a floating dipper dredge which shifts from one side of the channel to the other. The tower excavator can cut the full width of the channel at one set-up and complete the section as it moves along. This type of excavator could not be used satisfactorily in very wet soils, or where rock occurred in great quantity. The tower excavator is especially efficient in the excavation of large, shallow areas such as reservoirs, athletic fields, and the base- ments of large buildings. In such cases, it might be advisable to have the tower or towers move over curved tracks; the center of curvature being the point of anchorage of the hoist cable. Quarries, surface mines, and gravel pits can be economically stripped with a tower excavator, when the area covered is sufficient to warrant the installation of the plant and the soil conditions are favorable to uniform scraper-bucket operation. WALKING SCOOP DREDGES The walking dredge is rather a novelty in the field of excavating machinery and derives its name from its ability to move over the ground under its own power and to turn short angles or curves with- out sliding or skidding. The walking scoop type was devised about 1905, and is similar in general construction and operation to the ♦Based on a 10-year life and 150 working days per year. 870 EARTHWORK 71 floating dipper dredge. Another type, placed on the market in 1914, is an adaptation of the "walking" principle to the drag-Hne excavator and will be discussed later. Construction. The walking scoop dredge consists essentially of a wooden hull supported on 6 legs or feet and supporting the operating machinery and excavating equipment. The hull is con- structed of heavy timbers and is braced longitudinally by large, overhead, wooden trusses. It is usually made of sufficient width to straddle the ditch which it is excavating. On the front of the hull is placed the A-frame, which consists of two heavy timbers, bolted to the sides of the hull at their lower ends and joined at the upper ends to a "head" casting. The A-frame sets in nearly a vertical Fig. 41. General View of Walking Scoop Dredge plane and is braced to the rear corners of the hull by wire cables which extend to the top of the frame. Operating Equipment. The operating equipment for steam power is similar to that used for a floating dipper dredge. The boiler is placed at the rear of the hull, and in front of it are the hoisting and swinging engines. These will be fully discussed in the section entitled "Floating Dipper Dredges". On several jobs, it has been found to be more economical to use a gasoline engine instead of the steam equipment. Engines of the multiple-cylinder marine type are generally used and vary from 16 horsepower to 50 horsepower, depending on the capacity of the exca- vator, the size of the ditch, and the character of the soil. A machine 371 72 EARTHWORK with a 40-foot boom and a f-yard dipper has been satisfactorily operated by a 50-horsepower engine. Walking Equipment. The hull is supported at each of its cor- ners by a timber platform shaped like a large stone boat. Each "foot" is about 6 feet wide, 8 feet long, and 4 inches thick, and has an iron rod bolted across the bottom near the front edge to prevent slipping. Each pair of feet is connected by a timber so that the two feet will move conjointly. Each foot is pivoted to the hull and connected to a drum of the swinging engine by a chain, so that the feet may be turned by the revolution of the drum. In the center of each side or midway between the corner feet is a center foot similar in construction to the corner feet. On the under side of each center foot, a transverse 6-inch by 6-inch timber is bolted to prevent sliding or slewing. A large timber extends from the top of each center foot, between each pair of trusses, where it is pivoted. A chain, one end of which is fastened to the side timbers of the hull, passes over two pulleys attached to the frame on which the foot support is pivoted, and then passes along the hull to the rear corner and across the back end to a drum near the center of the hull. The movement of the excavator is effected as follows: The drum is revolved and the chain pulls the foot support gradually to a vertical position. This raises the dredge from its corner feet and shoves it ahead about 6 feet. The rear chain is then released and the weight taken off the center feet, which are pulled ahead by a chain attached to a drum, located near the front part of the hull. A general view of a walking scoop dredge is shown in Fig. 41. Excavating Equipment. The excavating equipment consists of the boom, dipper handle, and dipper, all of which are of unusual design in this machine. The boom is made up of two parts; the upper part is supported Fig. 42. Dipper and Dipper Handle of Walking Scoop Dredge 372 EARTHWORK 73 at its lower end on a turntable, similar to those used on a floating dipper dredge. The upper end is supported by a cable from the peak of the A-frame. The lower part of the boom is pivoted at one end to the lower end of the upper section and on its outer end is pivoted an iron-trussed framework shaped like a walking beam. This framework is the dipper handle, to the lower end of which is attached the dipper which is shaped like a slip scraper. The dipper and dipper handle are shown in Fig. 42. A chain or cable passes from the upper end of the handle to a drum on the hull. By winding up this chain or cable, the top of the frame is pulled back. A chain or cable is also fastened to the lower end of the handle at the back of the scoop. This line passes over sheaves in the outer ends of the booms and thence to a drum on the hull. The method of excavation is as follows: The lower section of the boom is lowered until the tip of the scoop is at the required elevation; the Hue attached to the upper end of the dipper handle is drawn in by revolving the drum, and the scoop is thus forced into the earth. After the scoop is filled, the lower section of the boom is raised and simultaneously the whole boom is swung to one side until the scoop is over the spoil bank, when the upper line is released and the lower line is drawn in until the scoop is pulled back to the boom and the contents of the scoop are dumped. The walking scoop dredge can move across fairly level land at the rate of about 1 mile in a 10-hour day. It can make a quarter turn in about 50 feet. It may be operated as a rear or head-on excavator. In the first case, the machine starts at the outlet and works upstream, backing away from the excavation similar to the drag-line excavator, w^hile in the latter case, the machine starts at the upper end of the channel and straddles it as it works downstream. WALKING DRAQ=LINE EXCAVATOR This machine is an adaptation of a walking traction device to the drag-line excavator. The advantages of this method of traction over the ordinary ones of rollers, wheels, or caterpillars, are the pro- duction of a direct bearing pressure on the soil and the elimination of track, plankways, skids, and the labor necessary for their manipu- lation. 373 74 EARTHWORK Construction. The walking drag-line excavator differs from the ordinary drag-line machine principally in its substructure construc- tion. The customary lower frame and truck rollers or caterpillar tractors are replaced by the w^alking device, which is quite different in design and operation from that described above for the walking scoop dredge. The superstructure of this excavator is very similar in design and construction to the ordinary drag-line excavator. Three sizes of machine are in regular use : the smallest, equipped with a 40-foot boom, a 1-yard bucket, and operated by a 45-horsepower kerosene Fig. 43. Walking Drag-Line Excavator Courtesy of Monighan Machine Company engine; the medium, equipped with a 50-foot boom, a 2-yard bucket, and operated by a steam plant; and the largest, provided with a 60-foot boom, a 2J-yard or 3-yard bucket, and operated by a steam plant. Walking Equipment. The walking device consists of two large shoes or platforms, one on each side of the central circular support, and two wheel segments or cams, each of which is keyed to the end of a heavy shaft extending across the machine. On the lower end of each cam is pivoted a beam whose ends are chain-connected to the ends of each platform. A view of this mechanism is shown in 374 EARTHWORK 75 Fig. 43. A large gear wheel on the shaft meshes with a pinion on the loading-drum shaft of the main engine. The pinion is controlled by a jaw clutch and brake. To move the machine, the pinion clutch is thrown in and the engine started. As the shaft revolves, the cams and pivoted beams lift the platforms and swing them forward to a resting place on the ground. As the shaft revolves, the cams move over the upper sur- faces of the platforms until they come into contact with the stop blocks, when the motion is stopped, and the machine is moved for- ward and downward to the surface. When further movement is not desired, the cams are revolved until the beams and platforms are elevated above the ground, and the machine then rests entirely on its circular base, about which it may revolve as a pivot for the pur- pose of excavating. The pinion is now locked by a brake and the drum clutch released to commence digging. Field of Usefulness. The walking excavator is especially adapted to use oh drainage and irrigation projects, where several ditches are to be built in one locality. Ordinarily, when an excavator is through with one job and is ready to commence another channel, it is generally necessary to dismantle the machine, transport the parts to the new site, and reassemble them. This involves a con- siderable expenditure of time, labor, and money. The walking machine can move over soft, wet, and rough ground and can make sharp turns by revolving about the central support. The machine can be erected at the transportation point where it is unloaded from cars or boats and can walk to the job at the rate of about 3 miles per 10-hour day. This excavator can be efficiently used in the excavation of wide ditches by moving along the center of the channel and working alternately on opposite sides. The walking scoop dredge operates at about the same cost as the floating dipper dredge. A machine equipped with a l|-cubic yard dipper, and operated by a 40-horsepower gasoline engine, can handle about 1500 cubic yards of loam and clay per 10-hour day, at an average cost of about 4 cents per cubic yard. 375 < < < Ji < ^ w = to X O 2 H c O ^ ft -a O ^ W ;g X a W o H S w ft 2 w o 2 1 n c o EARTHWORK PART II DRE DQ ES— (Continued) FLOATING EXCAVATORS Classification. The excavators of this division, as the name indicates, move over the water Hke a boat. They may be classified as to the method of operation as follows: the dipper dredge, the ladder dredge, and the hydraulic dredge. DIPPER DREDGE Dipper dredges may be classified as to the field of operation 3B follows: dredges for the excavation of drainage and irrigation channels, dredges with narrow hulls and side floats for digging and maintaining canals, and marine dredges for river and harbor improvements. These three classes comprise many types and sizes of dredges depending upon the service for which the machines are intended. The general arrangement and method of operation of all the types are very similar. Construction. The principal parts of a dipper dredge a^e the hull, the power equipment, and the excavating equipment. The chief differences in the construction of the different types of dredge are in the design of the machinery, boom operation, and kind of spuds used. Detailed views of dipper dredges equipped with bank spuds and with vertical spuds are shown in Figs. 44 and 45, respectively. Hull. The hull or boat may be constructed of either w^ood or steel. For marine dredges, where the machine is to be kept in use over long periods of time and where the cost of maintenance is an important item, steel hulls are desirable. For inland operation, as on reclamation work, wooden hulls are preferable on account of availability and economy of material and the ease of assembly and dismantling. 377 78 EARTHWORK 378 EARTHWORK 79 The dimensions of the hull depend upon the size of the machinery, length of boom, capacity of dipper, and width of channel. In the construction of small-sized channels, the width of the hull should be nearly the width of the channel so as to secure the increased stability afforded by the use of bank spuds. The width of the hull should bear some relation to the length of the boom, as the tendency of the dredge to tip sidewise will depend upon the distance of the dipper from the center of the hull. The length of the hull must be sufficient to provide adequate space for the housing of the operat- ing equipment* but principally must be proportioned to balance the weight of the excavating equipment in its various positions. The depth of the hull is governed by the necessary displacement, Fig. 45. Ditching Dredge with Vertical Spuds. Letters Have Same Significance as in Fig. 44 but ordinarily should be made with as light draft as possible to provide for shallow excavation. The wooden hull is generally made up of heavy timbers, strongly braced transversely and longitudinally to form a rigid and strong box. All the outside joints are calked with oakum and tar to make the hull water-tight. Operating Equipment. The operating equipment is of the same general design in all types of dipper dredges. The essential parts are the boiler, the hoisting and backing machinery, the swinging machinery, and the spud machinery. An interior view of a dipper dredge, showing the operating equipment, is given in Fig. 46. The locomotive type of boiler is generally used on account of its adaptability to various kinds and grades of fuel and its ease 379 80 EARTHWORK of cleaning. The Scotch marine type is used on the smaller sizes of dredge and under favorable working conditions is perhaps more economical of fuel, more durable, and safer than the locomotive type, but under the usual conditions of poor fuel, hard water, and severe loading, the latter generally renders the more efficient and economical service. A working pressure of 125 pounds is generally used for the operation of the dredge. A feed-water heater should be used to soften and purify the boiler water in localities where hard or alkali water exists. A duplex pump and injector supply Fig. 46. Interior of Dipper Dredge Showing Operating Equipment the feed water to the boiler. The water may be pumped directly from the channel or from neighboring wells. The hoisting and backing machinery are of three different types, depending on the method of transmitting the power: single, double, and triple hitch. These three classes are provided for by the use of a single, a two-part, or a three-part hoisting line. In the first class, the power developed by the engine is compounded through gears, the hoisting rope being connected directly to the dipper handle. In the two latter classes, the power is compounded by means of a sheave attached to the bail of the dipper. The main engine is of the double-cylinder, horizontal, nonreversible type, mounted on a braced structural-steel bed. There are two 380 EARTHWORK 81 drums, one for the hoisting cable and the other for the backing cable. The drums are generally grooved to hold the first layer of cable in place and are controlled by outside friction bands, which are operated by steam-actuated rams attached to the spokes of the large gearwheel. The swinging machinery usually consists of an independent, double-cylinder, horizontal, reversible engine, which is geared to a shaft carrying a drum at each end for direct leads to the swinging circle. The engine is controlled by a single, balanced throttle Fig. 47. Dipper Dredge in Operation valve. On the smaller size dredges, the swinging mechanism consists of friction drums, gear-driven from the main engine. The spuds are leg braces which are used to provide stability for the dredge during its operation. One is located in the center of the rear end and one on each side near the front of the hull. Inclined bank spuds are used when the channel is narrow and the hull is nearly the full width of the excavation. As will be seen from an inspection of Fig. 47, the upper ends of the spuds are attached to the head block of the A-frame and the lower ends sustain large timber platforms which transmit the pressure directly to the soil. 381 82 EARTHWORK Short braces connect the lower ends of the spud timbers with the sides of the hull, near the feet of the A-frame. Vertical side spuds are used on the larger sizes of dredge for wide channel and harbor work. In this case, the lower ends of the spuds bear directly on the bed of the stream. The rear spud is always vertical and is used to prevent the hull from swinging about during the operation of the excavating equipment. Each spud is a single, solid timber which moves up and down in an iron or timber box, or guide frame. Teeth on a rack fastened to the lower side of the spud, engage a pinion on the lower side and at the end of the guide frame. The spuds are raised and lowered by means of cables passing over sheaves and thence to special drums. These drums are gen- erally mounted on a separate base, and their shaft is connected to the end of the backing-drum shaft by a jaw clutch, which is disengaged when the spuds are not being operated. In the larger size dredges an independent engine is placed near each spud and operates the spud by a direct gear connection. Excavating Equipment. The excavating equipment consists of the boom, dipper handle, and dipper. The boom is generally shaped like a fish-beUied beam and may be made of either steel or wood. It is made in two sections so spaced that the dipper handle may move between them. For long booms, a trussed type is used to secure lightness with the requisite strength. For long booms and dippers of large capacity, a trussed- steel beam is preferable. The boom at its center should have a depth equal to about ^ o of its length. The length of the boom should be about 1| times the width of the hull with vertical spuds, and up to about twice the hull width when bank spuds are used. The upper end of the boom is connected to the yoke at the top of the A-frame by wire cables. At the outer end also is the sheave over which the hoisting cable passes on its way from the dipper to the fair-lead sheaves, at the lower end of the boom, and thence to the hoisting drum. The lower end of the boom is pivoted to the swing- ing circle or upper sections of the base casting. The swinging circle is a steel circular framework which is located just above the deck or several feet above the deck when it is necessary to secure sufficient swinging power for long booms. The diameter of the circle should be sufficient to give a direct pull from the drums 382 EARTHWORK 83 of the swinging engine and should not be less than j of the hori- zontal reach of the boom. The dipper handle is universally made up of a solid timber reinforced with steel plates. Upon the lower side of the handle is placed the steel racking which meshes with the pinion of the ship- per shaft located on the upper side of the boom, near its center. The length of the handle should be made about f that of the boom. The dipper is attached to the lower end of the handle by means of a pin connection, so that the pitch of the cutting edge may be changed to suit different classes of materials. The dipper which is used for the dredging of ordinary soils is of the same type as that used on steam shovels. A reference to Fig. 47 will show the general shape and construction. The front is made of a heavy manganese-steel plate which is riveted to the side plates. The back is a single steel casting which is also riveted to the side plates. The bottom or door is hinged to the back and is provided with a latch which is tripped by a rope extending to the cranesman's platform at the right side of the boom. The size or capacity of the dipper varies from | to 15 cubic yards; but IJ yards is the size generally used in work of average magnitude, and 3J yards for large channels and work of great magnitude. Large sea-going dredges equipped with dippers of from 5- to 10-yard capacity have been used for several years on harbor improvements, and in 1914 two mammoth dredges, each equipped with 15-yard dippers, were put into operation on the Panama Canal for the removal of the slides. For the excavation of loose sand and gravel, the clam-shell and orange-peel buckets are very efficient. These are single-line buckets, and the backing cable would not be used. The details and dimensions of a standard make of clam-shell and orange-peel buckets are given in Figs. 48 and 49, respectively. Method of Operation. The method of operation of a dipper dredge is very similar to that of a steam shovel, which has been previously described in the section on Power Shovels. The crew of a dipper dredge consists of an engineer, a cranesman, a fireman, and from 2 to 4 laborers, for each shift. A dipper dredge is ordi- narily run on two 11-hour shifts, and hence two complete crews are necessary. The engineer operates the levers and brakes which 383 84 EARTHWORK control the motions of hoisting, backing, swinging, and moving the dredge. The cranesman stands on a Httle platform just above the sv/inging circle on the right side of the boom, and controls the operation of the dipper as to loading and dumping. The fireman supplies the boiler with fuel and has general charge of the oiling and care of the machinery. The laborers supply the dredge with fuel, oil, and supplies, and perform the necessary general work around the machine. As the dipper and dipper handle slide downward toward the face of the excavation, the bottom of the dipper closes of its own weight and latches. When the dipper reaches the bottom of the channel, the engineer appHes the friction clutch to the hoisting drum and throws a lever, starting the drum to wind up the hoist line. This pulls the dipper upward, and the forward motion is regulated by the tension on the backing line. As soon as the dipper is clear of the surface and has completed the cut, the engineer throws the hoisting drum out of gear and sets the friction clutch, thus bringing the dipper to a stop. Then the swinging engine is started and the boom is swung around to one side until the dipper is over the dumping place. With a foot brake, the engineer sets the friction clutch and stops the revolution of the swinging drums. The cranesman then pulls the latch rope, and this opens the latch, releasing the bottom which drops and allows, the dipper contents to slide out. The engineer then releases the friction clutch and reverses the swinging engines, pulling the boom and dipper back into position for the next cut. As the boom swings around, the engineer slowly releases the friction clutch of the hoisting and backing drums and simultaneously slightly pulls in the dipper toward the dredge and lowers it into the cut, so as to produce a prying action. As the latter part of the drop is reached, the backing cable is released gradually and the dipper allowed to move forward toward the face of the cut. The time required for a complete cycle of operations depends upon the skill of the operator and the nature of the material excavated. The average time for a complete swing should be about 40 seconds. The most efficient results are secured when the opera- tions are made smoothly and uniformly so as to cause the least amount of lost motion and wear and tear on the machinery. After the entire face of the cut has been removed within reach 384 EARTHWORK 35 of the dipper, the dipper is raised and the boom slowly swung irom side to side to relieve the pressure on the spuds. With the boom remaining in a central position, the spud hoists are put in operation and the spuds raised from their resting places, thus allowing the hull to float ahead toward the face of the cut. With each move, Fig. 48. Typical Clam-Shell Bucket Courtesy of The Hayward Company, New York City CLOsrn Open Approx. Weight Capacity (lb.) Height Length Width Height Length Ft. In. Ft. In. Ft. In. Ft. In. Ft. In. 1| cu. yd. 4400 7 8 6 2 4 2 8 8 9 If cu. yd. 4800 7 8 6 2 4 6 8 8 9 2 cu. yd. 6800 8 6 6 11 4 10 9 6 9 9 2i cu. yd. 7800 8 9 7 5 3 9 9 10 3 cu. yd. 9000 8 9 7 6 2 9 9 10 the dredge makes an advance of about 6 feet. The spuds are then lowered by releasing the drums, or by reversing gears, and the dredge is ready f«r the next cut. Gjst of Operation. The cost of operation of a dipper dredge will depend on the size and type of dredge used, the character and 385 86 EARTHWORK magnitude of the work, the kind of material to be excavated, the efficiency of the operator, etc. Illustratke Example. As a typical case, the following is a detailed statement of the expense connected with the operation Fig. 49. Typical Orange-Peel Bucket Courtesy of The Hayward Company, New York City Closed Open Capacity Approx. Weight (lb.) (Cu. Ft. and Diameter Height Diameter Height Cu. Yd.) Ft. In. Ft. In. Ft. In. Ft. In. 4 CU. ft. 950 3 4 8 3 9 5 1 5 CU. ft. 1000 3 2 4 9 3 11 5 3 7 cu. ft. 1100 3 6 5 4 3 5 7 9 cu. ft. 1200 3 10 5 2 4 7 5 10 12 cu. ft. 2200 4 3 6 2 5 2 6 10 15 cu. ft. 2350 4 7 . 6 6 5 6 7 2 21 cu. ft. 3800 5 1 7 6 6 3 8 4 1 cu. yd. 4200 5 8 7 10 6 10 8 9 l\ cu. yd. 4600 6 8 7 3 9 S 1^ cu. yd. 5350 6 4 ■8 2 7 8 9 4 \\ cu. yd. 7750 6 4 9 4 7 10 10 4 2 cu. yd. 8500 7 9 10 8 6 11 2| cu. yd. 9500 7 8 10 2 9 3 11 6 3 cu. yd. 10500 8 10 4 9 7 11 10 S 4 cu. yd. 12500 8 10 10 10 10 6 12 6 386 EARTHWORK 87 of a dipper dredge, equipped with a If -yard dipper and a 70-foot boom, on the construction of a drainage channel along the bottom lands of a central western river. The soil is loam and clay with no stone and a small amount of stumps to be removed. The channel will be assumed to contain about 2500 cubic yards per station of 100 feet. Two crews work on 11-hour shifts and live on a houseboat, which floats along behind the dredge. The following statement is based on the average output for an 11-hour shift. Operating Cost of Dipper Dredge Labor: 1 engineer, @ $100 per month $4 . 00 1 fireman, @ $60 per month 2 . 40 1 cranesman, @> $75 per month 3.00 2 laborers, @ $50 each per month 4.00 1 cook, @ $40 per month 1.60 Total labor cost, per day $15.00 Fiiel and Supplies: 2 tons coal, @ $6 . 00 $12.00 Oil, waste, grease, etc. . 2.00 Total cost of fuel and supplies $14 . 00 General and Overhead Expenses: Board and lodging for crew of 10 men, per day $3 . 50 Repairs and incidentals 4 . 00 Interest on investment (6% of $10,000)* 1 .50 Depreciation (10% of $10,000)* 5.00 Total general expense $14 . 00 Total Cost of Operation for 11-hour Shift $43 . 00 Average Output (cu. yd.) 1200 Unit Cost of Dipper Dredging, per cu. yd., $43 . 00^ 1200 = 00 .036 Field of Usefulness. The dipper dredge is the best known and most popular type of excavator used in the construction of drainage channels. Most of this class of work must be done on low, swampy land, where it is difficult for anything but a boat to move about. The dipper dredge with its large bearing area and shallow draft is especially adapted to operating under these con- ditions. Where the soil is too soft to support the smaller types of dry-land excavators, and a considerable number of large stumps must be removed, the smaller lateral ditches of a drainage system * Based on 200 days in a yega: and a 10-year life. 387 88 EARTHWORK can be excavated more economically with a small dipper dredge than with any other type of excavator. In many cases it is cheaper to use one of the smaller sizes of dipper dredge (having a 16-foot width of hull, a 40-foot boom, and a 1-yard dipper), and to excavate a ditch twice the necessary size, than to use a smaller machine of another type to dig a channel the size required. The most economical size of channel for the operation of a dipper dredge is one with a bottom width of 40 feet and an average depth of 10 feet. When the cross-section of the channel becomes greater than this, the cost increases until a channel having a cross-sectional area of about 1200 square feet is reached, when the use of the dipper dredge is no longer efficient or practicable. The channel which a dipper dredge excavates is rather uneven in cross-section and does not have smooth side slopes and true Fig. 50. Section of Ditch Constructed by Floating Dipper Dredge bottom grades. The form of ditch excavated by this machine is shown in Fig. 50. After several years' use the channel will assume a general semicircular section. In shallow channels, or those where the stream flow is small during a large part of the year, considerable reduction of the cross-section may be caused by the deposition of silt and debris and the growth of vegetation. The dipper dredge is one of the most versatile of modern excavators as it can excavate all kinds of soil from silt to loose rock, pull stumps, remove boulders, bridges, and other obstructions, drive piling, build earthen dams, and perform many other duties which may arise during the course of operation. LADDER DREDGE General Characteristics. The elevator or ladder dredge has been little used in this country, except in the West and in Alaska for placer mining, but which is very popular and of nearly universal 388 EARTHWORK 89 use in Great Britain and on the continent. Since 1900 the ladder dredge has been used on large waterway construction; notably the Chicago Drainage Canal, the New York State Barge Canal, and the Panama Canal. Construction. The ladder dredge consists of a hull on which is placed the operating machinery and the excavating equipment. The operating machinery includes engines for the operation of the elevator, the belt conveyors, the hydraulic monitor, the spuds, etc. The excavating equipment comprises the ladder frame and ladder, and the means of disposal of the excavated material, con- "Fig. 51. Elevator Dredge Excavating Large Drainage Ditch sisting either of a hopper and a discharge channel, or of belt convey- ors. The placer dredge is provided with a revolving screen and dis- tributing channels for the separation of the gold from the gravel. A general view of a ladder dredge excavating a large drainage channel is shown in Fig. 51. A detailed view of an electrically operated placer dredge is shown in Fig. 52, and detailed views of a ladder dredge especially designed for canal excavation are given in Fig. 53. The hull or barge is shaped like a rectangular box and is generally built of heavy timbers. The hull may be built as one structure with a well through the bow for the passage of the ladder, 389 m EARTHWORK ^^ > IT a a> o IS 1^ "833 390 EARTHWORK 91 391 92 EARTHWORK or as two members with a space between. The latter type is some- times used so that the excavator may be passed in sections through narrow structures such as canal locks. The size of the hull depends upon the capacity of the dredge. The length, which varies from 50 feet to 125 feet, is generally about five times the width, which varies from 30 feet to 50 feet. The draft of a ladder dredge in working condition is from 4 feet to 6 feet and the depth of hull should be from 6 feet to 10 feet. The hull should be strongly braced both transversely and longitudinally and made watertight by well-calked joints of the outer planking. A few hulls have been made up of 2 steel-framed pontoons connected by steel cross-frames. For permanent work this type of hull is better than the wooden structure, as it is more rigid and durable. Operating Equipment. The power for the operation of a ladder dredge may be either steam or electricity. Several independent engines are required for the different performances of operating the ladder, the belt conveyors, the revolving screen, the spuds, swinging the hull, etc. These separate engines are uneconomical in the use of steam and hence it is often advisable to generate electric power by a steam plant and operate each engine by an individual electric motor. When several dredges are working in the same locality, it is most economical to locate a power plant on shore and to transmit the electric current by wires to the motors on the machines. An economy in the use of electric power is the saving of hull room by the elimination of the boiler and steam engines. The operating equipment for a steam-operated dredge con- sists of the boiler and engines for the various motions. The boiler is generally of the Scotch marine type and is mounted on the floor of the hull in the rear of the dredge. It should be of more than the theoretical estimated capacity to supply the engines and be operated at a working pressure of about 125 pounds. The engines are of the horizontal, double-cylinder type, which have been described in detail for steam shovels and dipper dredges. These engines are gear-connected to the drum or winch machinery. The drums are controlled by outside friction clutches actuated by small rams. Independent gear drives for the revolving screen and ladder are often operated from the main engine by belt and pulley EARTHWORK 93 393 94 EARTHWORK connections. However, separate engines are generally used for the operation of the spoil conveyors and spuds. A centrifugal pump, driven by a separate engine, is generally used to furnish water for a hydraulic monitor, for the hoppers and revolving screen, and for the perforated pipes which extend along the sides of the belt conveyor for cleansing purposes. Steam pumps of standard type are used to supply the condensers, feed-water heaters, and boilers with necessary water. When electric power is used, individual motors are generally mounted on the winch drum or drive frame and gear-connected by a pinion. These motors may receive current from a generator operated by a steam plant on the dredge or from a steam or water power plant located on the shore. Excavating Equipment. The excavating equipment consists of the gantry, ladder frame, and chain and buckets. The gantry is an inclined framework composed of timber or structural-steel members strongly framed together. The frame is placed at the bow of the hull and is held in position by braces extending to the front end of the hull. Sheaves at the top of the frame carry the cables which support the outer and lower end of the ladder frame. The gantry has a height of from 15 feet to 30 feet. Fig. 54. The ladder frame is generally a structural-steel framework shaped like the boom of a dipper dredge. The length of the frame varies with the size and capacity of the dredge and the depth of the proposed excavation. The upper end of the ladder frame is hinged to the upper tumbler shaft, while the lower end is suspended by heavy tackle from the gantry. The frame carries tumblers or large, hexagonal, steel barrels at its ends. The upper tumbler is revolved by power supplied from the main engine through a shaft, while the lower tumbler is revolved by the friction of the bucket chain. The chain is composed of a continuous series of buckets, links, and connecting pins. The buckets are cup-shaped and made of three sections, strongly riveted together. They have capacities varying from 3 cubic feet to 13 cubic feet. They are placed in *'open" or "close" order — that is, consecutively, or with open links between adjacent buckets — depending upon whether the soil is soft or hard. 394 EARTHWORK 95 The movement of the bucket chains is slow and uniform and is such as to feed from 15 to 20 buckets per minute into the bed of the stream. Fig. 55 shows a section of a chain with ''close" order and Fig. 54 shows the buckets provided with teeth for the excava- tion of dense, hard materials. One or two spuds are generally placed at the stern of the hull to provide for the stability of the dredge and for its lateral movement. They are usually composed of a single timber with a pointed shoe at the lower end and are operated by separate engines of the type used on the floating dipper dredge. Fig. 55. Section of Chain Used on Ladder Dredge Material Distributing Machinery. The disposition of the excavated material depends upon the character of the work. In placer-mining operations, the dredge is provided with a hopper into which the material falls. Then the material passes through a revolving screen and upon a screen trough where the gold is collected by amalgam plates. In the excavation of canals or stream beds the materials pass from the hopper into a chute or trough which discharges into barges, as shown in Fig. 56, or directly from the bucket chain to belt conveyors which carry it to the spoil banks along either side of the channel, Fig. 51. In some cases, when the material is to be conveyed for some distance, the con- 395 96 EARTHWORK veyor is placed at the stern of the hull and discharges into a series of other conveyors supported on pontoons. Method of Operation. The outer end of the ladder is lowered until the bucket chain is in contact with the bed of the stream. Each bucket in the revolution of the chain, removes a slice of material as it comes into contact with the soil. At the top of the ladder, the buckets in turning over the upper tumbler, dump their contents into a hopper which discharges into a screen or directly Fig. 56. Ladder Dredge Provided with Trough for Discharging Excavatiou into Barges upon a belt conveyor. The ladder is gradually lowered as the excavation proceeds. The dredge is swung from side to side across the channel by wire cables attached to trees along the shore and to winch drums on the hull. To move the dredge ahead the spuds are alternately raised and lowered as the dredge is swung from one side to the other. When high banks are to be removed it is customary to use a large hydraulic monitor, which is placed near the ladder frame 396 EARTHWORK 97 397 98 EARTHWORK i and above the deck of the hull at the bow. Fig. 57 shows an ele- vator dredge, equipped with a monitor, excavating a large irri- gation canal in the West. The machinery of the dredge is usually controlled by an operator, who is located in a small cabin placed near the bow and above the machinery house. Besides the operator there are required an engineer, who has general charge of the machinery, a fireman who runs the boiler of the steam equipment, an oiler, a deck hand for general service on the dredge, a man who has charge of the opera- tion and control of the conveyors, and one or more men who have charge of the shore conveyors or barges. Each dredge requires the service of 1 tug and from 4 to 8 scows, depending upon capacity of the dredge, size of channel, character of materials, etc. The scows may be of steel or timber and are generally of the bottom-dumping type with several independent compartments. Cost of Operation. As elevator dredges are generally built to meet special conditions of service, it is difficult to give any accurate statement of the average cost of operation. However, in order to suggest the cost of operation in canal excavation, the following statement of the use of ladder dredges in the construction of an irrigation canal on a Reclamation Service project is given. Illustrative Example, The channel had a total length of about 20 miles and in many places the banks were high on one or both sides. On fills and shallow cuts, bulkheads were built along the right of way on the lower bank to keep the wet material from flowing on to adjacent fields. The material excavated varied from a loose gravel to hard pan, which in places had to be blasted. The dredge used was a Bucyrus ladder dredge, equipped with steam power and a 3|-cubic-foot continuous bucket chain. The hull was built of timber, with a length of 82 feet, a width of 30 feet, a depth of 6 feet 6 inches, and drew 5 feet of water. Steam was furnished by 2 locomotive-type boilers, 44 inches in diameter and 18 feet long, and having a rated capacity of 80 horsepower. The main drive and ladder hoist were driven by an 8 X 12-inch double horizontal engine of 70 horsepower. The winch machinery for operating the spuds and swinging the dredge was driven by a 2-cylinder, 6 X 6-inch, double horizontal engine of 20 horsepower. 398 EARTHWORK 99 The belt conveyors were operated by two 7 X 10-inch, single-cylinder, center-crank, horizontal engines of 18 horsepower. A No. 1 Hendy hydraulic giant was mounted on the bow of the dredge and water was forced through it by a 2-stage, 6-inch, centrifugal pump, belted to a 10 X 12-inch, single-cylinder, upright engine of 80 horsepower. The giant was used to remove banks above the water level and beyond the reach of the bucket chain. Two belt conveyors, one on each side of the dredge, were used for the disposal of the excavated material. Each conve^^or was 72 feet long and consisted of a steel framework supporting a 7-ply, 32-inch, rubber conveying belt. Fig. 57 shows the dredge in operation. The operating force consisted of 8 men and 4 horses. Follow- ing is a schedule of the labor expense per day. Expense Schedule of Daily Labor Labor Day Rate Superintendent $7.50 Operator 5.00 Engineer 4.67 Spudman 3.83 Fireman 3.33 Oiler 3.00 Deckman 2.50 Man-and-team 4.50 The following tabulation gives the total and unit cost of the work. Cost of Work by Ladder Dredge (Excavation of 929,723 cu. yd.) Cost Division Total Unit (per cu. yd.) Labor (dredge) Labor (spoil bank) Fuel Plant Maintenance Plant Depreciation $29,960.63 31,159.06 33,043.07 52,327.40 41,432.53 $0,030 0.034 0.036 0.057 0.045 Total Engineering and Administration $187,922.69 28,154.41 $0,202 0.031 Grand Total $216,077.10 $0,233 Field of Usefulness. The elevator dredge has Been universally used in Europe for harbor and canal excavation and notably on 399 100 EARTHWORK 400 EARTHWORK 101 the construction of the Suez Canal, the Panama Canal, and the New York State Barge Canal. In this country the ladder dredge has not come into general use on account of the high initial cost of the plant. The average American contractor prefers to use a dipper dredge costing about $40,000, rather than a ladder dredge requiring an investment of about $100,000, in order that he may secure immediate results on a less capital charge. The elevator dredge is efficient in the excavation of all classes of material from silt to hard pan and the softer stratified rocks. This dredge cannot work to advantage in narrow channels, and hence is not adapted to the excava- tion of small canals and ditches or the dredging out of narrow rivers. In such cases the dipper dredge should be used. When the banks are high, difficulty is experienced in depositing the excavated material. When the banks are low, dikes or bulkheads must be erected to prevent the soft material from flowing back into the channel or over adjacent land. When the sides of the channel are to be sloped, the bucket chain must be gradually raised and lowered as the dredge is swung over to the side. Trouble is often experienced in the operation of the spoil conveyors and water jets are required to keep them clean. The excavated material is gen- erally so wet that the deposition of the material in uniform spoil banks along the shore is a difficult matter. The proper sphere of usefulness of the ladder dredge is in large canal, river, 401 102 EARTHWORK and harbor work, where there are wide, long reaches and a large amount of dense material to be removed. In such cases, the scow method of removal should generally be used. HYDRAULIC DREDGE During the last twenty years, the great improvements in the rivers, lakes, and harbors of this country have made a demand for an excavating machine of great power, capacity, and efficiency in the removal of large quantities of the looser soils. The reclamation of the great tidal marshes along the Atlantic and Pacific coasts and the cleaning out of the channels of the larger rivers, canals, and harbors are being continually carried on by the Government. The most efficient and economical excavator for this class of work is the hydraulic or suction dredge. Construction. The essential parts of a hydraulic dredge are a revolving cutter, a centrifugal pump, and the machinery to drive it, and the barge or hull. Detailed views of a hydraulic dredge are shown in Figs. 58 and 59. The hull is usually rectangular in shape and has a length of about 3| times its width. The size of the hull depends on the capacity of the dredge. The depth varies from 6 feet to 15 feet, providing a draft of from 3 feet to 9 feet. Hulls are constructed of wood or steel, but the latter material is the preferable on account of its greater strength, durability, and rigidity. Cross-frames of steel or wood are placed on about 2-foot centers and connect the keelsons and deck beams. This framework is covered with steel plates or heavy wooden planking. The winch machinery is placed on an upper deck while the pumping machinery is placed on a lower deck. A superstructure houses the machinery and con- tains the operating room and usually living quarters for the crew. At the stern of the hull is located a vertical frame from which are suspended two spuds by means of sheaves and cables leading to the winch drums. The spuds are generally single timbers of fir, pine, or oak, and are of sufficient length to reach the bottom of the excavation at high water. Operating Equipment. The operating equipment of a hydraulic dredge consists of the winch or hoisting engine and the pumping equipment. 402 EARTHWORK 103 The hoisting engine controls the movement of the barge, the operation of the ladder and of the spuds. It generally consists of 5 drums which are mounted on a single base and operated by a double-cylinder engine. Upon the forward shaft, the drums on each side swing the dredge and the center drum is used for the raising and lowering of the outer end of the ladder. The two rear drums operate the two spuds at the stern of the barge. In some cases a separate engine is used to operate the spuds. The pumping machinery consists of a centrifugal pump and the engine to operate it. The pump is the most important element in the construction and operation of a hydraulic dredge. The excavated material is drawn up through the suction pipe and dis- charged through the discharge pipe to scows or to spoil banks on shore. The pump consists of a shell or casing of circular form with two apertures, one on the periphery and the other at the center of one side. Inside this shell revolves a set of vanes mounted on a shaft which extends through the center of the casing and is usually direct-connected to the engine. The vanes are generally made in two sections; the inner section, which is made as a part of the shaft; and the outer sections which are separate pieces bolted to the inner section. The abrasion by the material passing through the pump is largely on the outer sections of the vanes, which can be easily unbolted and replaced. The opening in the center of the side is the admission orifice to which the suction pipe is attached and through which the material enters the casing. The steel suction pipe is ordinarily from 15 to 30 inches in diameter and varies in length from 10 feet to 60 feet. To the periphery of the casing is attached the discharge pipe, which varies in diameter from 6 inches to 48 inches. A 20-inch centrifugal pump is shown in Fig. 60. The pump is usually direct-connected to a steam engine of the vertical, marine type. For the small sizes and capacities, compound engines are used, but for large capacities, hard service, and high heads, triple-expansion engines are used. Excavating Equipment. The excavating equipment of a hydraulic dredge consists of the gantry, ladder, and cutter. The excavating equipment of a small dredge is shown in Fig. 61. The gantry is a double, inclined, timber frame which carries 403 104 EARTHWORK the sheaves over which pass the cables for raising and lowering the outer end of the ladder. The ladder is a steel-framed girder which is hinged to the bow of the hull at its inner end and suspended by cables at its outer end. On the upper side of the ladder is placed a gear-operated shaft which drives the cutter and the suction pipe. The cutter is a series of knives which revolve about the hood or circular mouthpiece of the suction pipe. The type of cutter used depends upon the character of the material to be excavated; a heavy, chrome-steel head being used for hard materials and where Fig. 60. Centrifugal Pump of Hydraulic Dredge boulders are prevalent, while a light, open construction is used for soft materials and in places where brush and roots occur. Electric Power for Operation. Dating from about 1910, the prevalence of cheap water power has led to the use of electric power for the operation of hydraulic dredges in several cases. The elec- trical equipment includes the wound-rotor type of motor to operate the cutter, the hoisting engine, the pump, and the spuds. On isolated work, where fuel would be expensive on account of high transportation costs, but where water power is available, or in the proximity of large cities where electric power from large 404 EARTHWORK 105 steam plants is obtainable at low rates, it will be found more econom- ical to carry a branch transmission line to the dredge and use an electrical equipment. The advantages of compactness, cleanliness, and efficiency, which have been previously discussed for the ladder dredge, are as appUcable in this case. Fig. 61. Typical Hydraulic Dredge on Canal Con.structioa Courtesy of Great Lakes Dredge end Dock Company, Chicago Method of Operation. The dredge is held in position by cables which extend from the main or hoisting engine to anchorages on either side of the bow, and by the two spuds in the stern of the hull. By alternately raising a spud and winding up and unwinding the cables, the dredge may be swung from side to side so as to cover a wide area. The revolving cutter excavates the material, which may vary 405 106 EARTHWORK from silt to hard pan. The disintegrated material, diluted by water, is sucked up through the suction pipe into the pump and then forced out through the discharge pipe which is carried by pontoons, and discharges into scows or out upon an area which is to be filled in. Cost of Operation. It is impossible to give any accurate statement as to the average cost of excavation with a hydraulic dredge. Such a dredge on work of any magnitude is usually made especially for the particular conditions at hand and the cost of operation may vary within rather wide limits. Illustrative Example. Following is a t^^pical labor schedule for the operation during an 8-hour shift of a hydrauhc dredge equipped with a 20-inch centrifugal pump. Labor Expense Schedule Labor M( JNTHLY Rate 1 operator $100.00 1 engineer 100.00 1 engineer 80.00 3 firemen, @ $70.00 each 210.00 1 spudman 60.00 1 oiler 50.00 4 deck hands, @ $50.00 each 200.00 The average cost of operation would depend upon the size and capacity of the dredge, the character of the material, efficiency of operation, kind of power used, etc. Records of recent work show a range of from 4 cents to 15 cents per cubic yard for materials varying from sand to indurated gravel. Field of Usefulness. Hydraulic dredges have been in use for the last half century, but their greatest development has been during the last two decades, since 1895. In Europe their use has been largely in the maintenance of channels in the large rivers and in the construction of great canals. In this country they have been used principally in the reclamation of low, wet lands, along rivers, lakes, and harbors, the construction of great artificial water- ways, such as the New York State Barge Canal and the Panama Canal, and the maintenance of channels in large inland waterways, such as the Mississippi River. The earlier types of hydraulic dredge were provided with an agitator and water jets at the mouthpiece end of the suction pipe, and hence they could handle only the softer soils, such as silt, sand, 406 EARTHWORK 107 f 1 r I 407 108 EARTHWORK and clay. In recent years, however, the cutter head has been developed in different forms, and very hard dense soils can be loosened and broken up sufficiently to be discharged through the pump. ! The hydraulic dredge is not an' economical type of machine to use in the construction of levees or in canal excavation where the disposition of the excavated material must be madd within a confined space. The material as it emerges from the discharge pipe is [in such a [high state of dilution that it will not remain in place unless confined within banks or bulkheads. Some method of removing the sur- plus water in the discharge pipe may be used effectively; one such method being the installation of overflow strainers placed at intervals in the upper sections of the pipe. This type of dredge is unique among excavators in its abihty to discharge the excavated material in any direction and at a considerable distance from the site of the excava- tion. This wide range of disposal is of especial value in the filling in of waste lands along waterways. SUBAQUEOUS ROCK BREAKERS LOBNITZ ROCK CUTTER For use in connection with the beds of channels through very indu- rated materials or rock which must be broken up before the removal by dredge, there are two radically differ- ent types of rock breakers : the Lob- nitz rock cutter; and the drill boat. t- Ql__. 408 EARTHWORK 109 The Lobnitz rock cutter consists of a heavy chisel of steel, weighing from 4 tons to 15 tons, and equipped with a hardened- steel cutting point. The chisel is raised to a height of from 5 to 10 feet and then dropped upon the surface of the hard material. The impact of the falling point serves to splinter and fracture the material so that it can be removed by the dipper of a floating dipper dredge, or by the buckets of a ladder dredge. The cutter is capable of breaking up the hardest rock, in layers 3 feet thick at a time. The cutter is mounted on a hull composed of two barges, rigidly connected by cress-frames. The details of a Lobnitz rock cutter are shown in Figs. 62 and 63. In Europe, where this form of rock breaker is in general use, the ladder dredges are often provided with several picks or chisels, located in a well alongside of the ladder. These chisels are placed about 2 feet apart and are operated singly or in unison. The picks are generally made of heavy timbers which are provided with hard- ened-steel points. The buckets of the ladder dredge are made especially heavy and provided with teeth on the cutting edges. With a 10-pick ladder dredge, an excavation of 43 tons of hard rock per hour has been made. \ THE DRILL BOAT Speed a Characteristic. The Lobnitz rock cutter has not found favor in this country on account of its slow speed and cumbersome method of operation. Hence, a drill boat has been devised and this machine uses the standard steam-actuated percussion drills, which provide great lifting and striking power combined with a larger number of blows per minute. The drill boat consists ^f a barge equipped with a spud at each corner to support it upon the bed of the stream during the drilling. Each of the four spuds is operated by a pair of independent engines geared to a rack on the side of the timber. When the drills are in operation, the spuds are forced down until the boat is raised above the height of normal flotation. The constant elevation of the boat is maintained by the automatic regulation of the steam pressure in the spud engines. The drills are steam-operated percussion drills, similar in design and operation to the ordinary steam drills used in drilling 409 no EARTHWORK 410 EARTHWORK ' 111 on land. The piston diameter is from 5 J inches to 0§ inches, and the drills are mounted on movable steel towers, which run on a track along the side of the barge. The drills may be raised or lowered along vertical guides 15 feet to 30 feet in length. The feed of the drill is controlled by hydraulic plungers having a stroke equaling the length of the guides and moved by long screws which arc operated by small engines. The towers are moved along the track by steam or by hydraulic power. A view of the drill side of a drill boat drilling and blasting bed rock in Boston Harbor channel, is shown in Fig. 64. Cost of Operation. The output and cost of operation of a drill boat depends upon the number and size of drills, the character of the rock, the depth of excavation, etc. It is impossible to state any general rules which may be used in this class of work. The following statement is given as a typical case of the use of a drill boat in channel excavation. Illustrative Example. The work consisted in the excavation of a ship channel, 200 feet wide and 17 feet deep, in a large river. The material was a very hard limestone rock occurring in strata from 20 inches to 30 inches thick. The work was carried on in a stream having a current of from 8 miles to 12 miles an hour, in an area of turbulent water. The drill boat was equipped with four 5-inch drills, which operated through four slots, each 20 feet long and 18 inches wide, and located in the forward part of the barge. The drill frames carried steel drill spuds with pipe guides for the drill bars, and were arranged to move along tracks the length of the wells. Thus each drill made several holes at each set-up of the barge. Holes were drilled and blasted in groups of four. The rock was drilled below grade to a depth equal to half the hole spacing, which was about 6 feet. The dynamite used was proportioned on a basis of about 1 pound to a cubic yard of rock. The barge was supported on four 20 X 20-inch power-controlled spuds. Gear drums operated five IJ-inch breasting chains, one leading upstream, and two over each side. Each chain was attached to an anchor weighing about 1 ton. The monthly cost of operation is as follows: 411 112 EARTHWORK Labor: Operating Cost of Drill Boat 1 captain $100.00 4 drillers, @ $75 . 00 each 300 . 00 4 helpers, @ $30 . 00 each 1 20 . 00 1 fireman 30.00 1 machinist 65.00 1 blacksmith 70.00 1 helper 30.00 1 blaster 60.00 1 helper 35.00 1 cook 30.00 Total labor expense, per month Board and Lodging: 16 men, @ $12.00 each, per month Fuel and Supplies: $840.00 $192.00 60 tons coal, @ $4 . 00 $240 . 00 Oil, and waste 40 .00 Blacksmith's coal 15, .00 Steel, iron, and suppUes 52.00 $347.00 Total fuel and supplies Grand total, per month $1,379.00 Cost of Drilling, per drill hour 1.105 Cost of Drilling, per foot drilled 0.049 Average Depth of Drilling, per hour (ft.) 21 Depth of Drilling (ft.) to 11 Field of Usefulness. The two types of rock breakers are very efficient for subaqueous rock drilling and give results which compare favorably with drilling on land. The Lobnitz rock cutter works most efficiently in shallow cuttings of stratified rock, which is easily shattered. The drill boat, of the American type, does its most efficient work in hard rock of depths of over 3 feet. TRENCH EXCAVATORS • Classification. The great amount of trenching necessitated by the construction of sewer, water-supply, and drainage systems has led, in recent years, to the development and use of excavators especially adapted to this class of work. These trench machines are more efficient and economical than hand labor on work of any magnitude. 412 EARTHWORK 113 Trench excavators may be divided into two general classes as follows: (1) Sewer and water-pipe trench excavators. (2) Drainage-tile trench excavators. Fig. 65. Traveling Derrick on Trench Excavation Work Courtesy of Brown Hoisting Machinery Company, Cleveland, Ohio 413 114 EARTHWORK PIPE=TRENCH TYPES This class of excavators embraces five distinct types as follows : the traveling derrick or locomotive crane, the continuous bucket excavator, the trestle-cable excavator, the trestle-track excavator, and the tower cable way. TRAVELING DERRICK The traveling derrick or locomotive crane is a very useful and adaptable type of excavating, hoisting, and conveying machine. It has been serviceable in many lines of construction work as the machine may be used for excavation, transportation of various kinds of materials, loading and unloading wagons, cars, barges, etc. In this discussion, we will consider the machine only as a trench excavator. Construction. The essential parts of a traveling derrick are the car, the hoisting engine, and the derrick. The machines are made in capacities varying from 3 tons to 20 tons. A machine on trench excavation is shown in Fig. 65. The car is a steel-frame platform which supports directly the cast-iron turntable bed and the counterweights. The platform is mounted on a 4-wheel truck, equipped either with broad-tired w^heels for road traction, or with standard railroad wheels for the smaller sizes of crane. The larger sizes, generally above 10-ton capacity, are mounted on two 4-wheel trucks, equipped w^ith stand- ard railroad wheels. The car is provided with drawbars for the 4-wheel type, and couplers, steam brake, grab handles, steps, etc., for the 8- wheel type. Operating Equipment. The power for the cranes may be steam, electric, or that furnished by an internal-combustion engine. Ordinarily steam power is used, but the other kinds would be more economical when the cost of coal or wood is high compared with electric power and gasoline. The steam equipment consists of a boiler, engine, hoisting mechanism, rotating mechanism, and traveling mechanism. The boiler is of the vertical, tubular type, and should be capable of work- ing at a pressure of 100 pounds with quick-steaming qualities and large steam capacity. The engine is usually of the vertical, double- cylinder type, provided with link-motion reversing gear, wide- 414 EARTHWORK 115 g ;5 H| 415 116 EARTHWORK ported slide valves, etc. The hoisting mechanism consists of a double-drum winch. The hoist drum is driven from a friction clutch on the main engine shaft. The shell drum is operated from the hoist drum by a slip friction. Both drums are controlled by friction-clutch brakes, lever-operated by one man. The rotating mechanism consists of 2 friction clutches driving a chain of gears. The upper platform, which supports the operating and excavating equipments, can be revolved in either direction through a complete circle. The traveling mechanism consists of a set of gears driven by a friction clutch on a shaft geared to the crank shaft of the engine. The machine may be moved in either direction. Excavating Equipment. The excavating equipment consists of the boom or crane, and the dipper or bucket. The boom is a steel-frame structure, hinged at its lower end to the front of the upper platform, and supported at its outer and upper end by guys extending to the rear corners of the platform. At the outer end of the crane is the sheave over which the hoist line passes on its path from the drum to the bucket. The bucket or dipper may be a grab bucket, of the orange- peel or clam-shell type, or a drag-line dipper. The former is used for the excavation of softer soils while the latter is more serviceable in the removal of the denser and harder soils. In the latter case, a separate drag-line drum must be provided in the hoisting mechanism. A traveling derrick using a drag-line bucket in canal construction is shown in Fig. 66. Method of Operation. A traveling derrick is operated by a crew of three to ten men, depending on the amount of extra labor necessary. An engineer controls all the operations of excavating, rotating, and traveling, a fireman operates the boiler, a signalman is often necessary for deep-trench work, and one or more laborers are used for general service about the machine and in the excava- tion. When a skip is used, shovelers are required. The method of operation is very vsimilar to that of a revolving shovel and the student is referred to that section of the text for a complete discussion of this subject. On trench excavation, one machine may be used for excavation only, or may excavate and later return to back fill. On large works, it has been found advantageous to use two or more machines 416 EARTHWORK 117 coordinately; one for the rough excavation, one for the finished excavation and for handUng pipe and materials, and one for the back fining. Cost of Operation. The cost of operation would vary greath* with the size of the machine, the efficiency of its operation, the character of the material, etc. Thejollowing statement is given as an approximate idea of the cost of operation under average con- ditions. Illustrative Example. A 10-ton machine, equipped with an automatic clam-sheU bucket of 1-yard capacity, and moving on a track along the side of the trench, will be considered. The material is clay for a depth of 8 feet, and is underlaid by a substratum of gravel. Following is an estimate of the cost of operation for a 10-hour working day: Operating Cost of Traveling Derrick Labor: 1 engineer 1 fireman 3 laborers, @ $2 . 00 each Total labor cost, per daj' Fuel and Supplies: 1 ton coal Oil, waste, and repairs $5.00 2.50 6.00 $4.00 1.50 $13.5© Total fuel and supplies General and Overhead Expenses: Depreciation (5% of $5000)* Interest (6% of $5000)* Incidental expenses $1.25 1.50 2.25 $5.50 Total general expense $5.00 Total Cost of Work for 10-hour Day $24 . 00 Total Excavation for 10-hour Day (cu. yd.) 400 Unit Cost of Traveling Derrick Excavation, per cu. yd., $24.00^400= 00.06 Field of Usefulness. The traveling derrick is economical for trench excavation when the soil is loam, clay, sand, or gravel, and can be easily handled by a grab bucket, or a drag or scoop bucket. This type is especially adapted for wide trenches, over 5 feet in width, which cannot be readily excavated by other t>T>es. * Based upon 200 working days in a year and a 20-year life. 417 118 EARTHWORK This type of excavator is very efficient with good management, as it may be used for excavation, back fiUing, and pulhng sheeting. CONTINUOUS BUCKET EXCAVATOR Construction. There are several makes of machine, which are especially devised for the digging of trenches with vertical sides. This type of excavator has been developed in recent years to meet the demand for a machine for municipal work under favorable conditions of soil and for large work. An analysis of continuous bucket excavators shows the following essential parts: a frame supported on wheel trucks, the operating 67. Diagram of Parsons Trench Excavator Courtesy of G. W. Parsons Company mechanism, and the excavating mechanism. All makes are built on the principle of the continuous excavator or ladder dredge, and differ only in details of construction. The platform is built of steel members strongly braced and framed together. It may be supported on 2 trucks equipped with broad-tired wheels, or made in two sections and supported on 3 trucks. In the latter case, the rear section which carries the exca- vating chain is hinged to the main section and is supported on 1 truck. Fig. 67 shows a diagrammatic view of this type, and Fig. 68 shows a view of the single-platform machine. Operating Equipment. A steam or internal-combustion engine may be used. The latter is more economical in sections of the 418 EARTHWORK 119 West where coal is expensive, and is cleaner, more compact, and does away with the use of a fireman and the discomfort of a boiler in warm weather. A steam-power equipment consists of a boiler, an engine, and the transmission mechanism. The boiler is of the vertical, tubular type and is placed near the front end of the platform. The engine is placed behind the boiler and is of the single-cylinder, vertical type. Power is transmitted to the bucket chain, the dis- posal conveyor, and the central axle, for traction through gears and sprocket chains. Fig. 68. Chicago Trench Excavator Courtesy of F. C. Austin Drainage Excavator Company, Chicago Excavating Equipment. The excavating equipment consists of the bucket chain, and the disposal conveyor. The bucket chain in one type of machine comprises an endless chain moving over sprocket wheels on the ends of an arm, which is suspended from the rear end of the platform and is adjusted to permit of the exca- vation to the proper grade regardless of inequalities of the surface over which the machine passes. In the other type of trench machine, a circular wheel is suspended from the rear of the platform and revolves on a central axle. The buckets are attached to the sprocket chain or to the periphery of the wheel. They are scoop-shaped and provided with cutting edges or teeth, depending upon the nature of the material to be excavated. The width of the trench is governed by the 419 120 EARTHWORK width of the buckets, which are made in several widths and can be easily removed and changed. In one make of machine, an increased wddth of trench can be secured by moving the whole bucket chain sideways along the supporting frame. This arrangement provides for the excavation of a trench up to 6 feet in width without changing the buckets and also the excavation of a manhole at any point without delay. Fig. 69 shows a sectional bucket used on the Parsons Trench Excavator. Fig. 69. Sectional Buckets Used on Parsons Trench Excavator The disposal conveyor consists of a belt conveyor placed at the rear of and transversely to the platform. Its elevation is below the top of the bucket chain. At the top sprocket, the buckets turn over and deposit the material on this moving belt, which conveys it to one side of the trench and deposits it in a spoil' bank. Method of Operation. The labor crew necessary to operate a trench excavator depends on the character and magnitude of the work and the kind of power used. With a steam-power equip- ment, an engineer or operator, a fireman, and one or more helpers 420 EARTHWORK 121 > a U CO •o N g«« • S.S.S.S 'S'o'o "o S oooo^ OOOi-tO go - ^ a: a > .StJ ^J g^ g^ Ih Sh O S-i o s- o; 0) o) o o Q^ ^ o3 K ^ K^ c3 v.- ^■^ :2 fl J3 il -^ -t-3 .B.B cc CO 2? 02 OOO' • LO LO O t^ 00 ^S ^ 888888 (M lO t^ >OCO O Tfi -^ Tti lo t^ 00 :2 S.J- fl 111; ^^ V o 00 00 00'^'' (N (M (N cvfccr CO TtTrtTrtr^^ CO CO ^'^'^'oo'^oo'^oo- lOO t^ t^O (N a s s s s s ^ ^ ^ ^ ^ ^ O CJ o o o o ,>j ^j -ij -^J -kj ,tj OOOOOO iC CO t^OO OiO 421 122 EARTHWORK will be required. The operator has direct charge of the operations of excavation and traction. The fireman operates the boiler and has general supervision of the engine. The helpers are of general service in furnishing the machine with fuel, w\ater, and supplies, in bracing the trench when necessary, and in general service about the work. The bucket chain moves downward and inward and removes a thin slice of material as each bucket comes in contact with the soil. The .depth of cut is regulated by raising and lowering the free end of the frame. When obstructions, such as cross pipes, large boulders, etc., occur, the chain may be raised over them and fed down into the earth on the other side. The material, from the top of the revolving chain or wheel, falls upon the belt conveyor and is carried to either side of the trench, making a continuous spoil bank. When one section has been excavated, the machine moves ahead and starts another slice. The excavating chain or wheel can be raised clear of the surface and the machine moved over ordi- nary roads at a speed of about 1 mile per hour. Table VI gives the dimens'ions, weights, capacities, and costs of three different makes of trench excavator. Cost of Operation. The following comparison of the cost of excavation of a trench by hand and by machine labor will be of interest to the student, who is urged to make a close study of the method of analysis. Illustrative Example. The soil is clay and loam and the ground surface fairly level and solid enough to support a trench machine. The trench has a width of 28 inches and an average depth of 12 feet. Each laborer will excavate 7 cubic yards per 10-hour day and as the material must be rehandled for the last 3 feet of depth of cut, we will assume 5 extra men for the work and not include their output. A crew of 45 men will dig 350 feet of trench during a 10-hour day and the total excavation will be about 315 cubic yards. The same crew will back fill at a cost of 7 cents per cubic yard. The machine will excavate 250 feet of trench per 10-hour day. The back fiUing will be done by teams and scrapers. Following is a detailed statement of the cost of the work for the two methods, based on a 10-hour day. 422 EARTHWORK 123 Cost of Trench Excavation by Hand Labor: 1 foreman 1 timberman , 1 helper 1 pipe layer 1 helper 50 laborers, @ $2 . 00 each Total labor cost for excavation Back filling 315 cubic yards, @ 7c Total cost of Hand Work for a 10-hour Day % 4.00 3.00 2.50 3.00 2.50 100.00 $115.00 22.00 $137.00 Cost of Trench Excavation by Machine Labor: 1 foreman $ 4.00 1 timberman 3.00 1 helper 2.50 1 pipe layer • 3 . 00 1 helper 2.50 1 engineer 4.00 1 fireman 2 . 50 3 teams, (c 2 laborers, $4.00each| hauling for excavator 2 back filling trench $2.00 each 12.00 4.00 Total labor cost, per day Fuel and Supplies: 1 ton coal Oil, and waste Water Total fuel and supplies Overhead and General Expenses: Interest (6% of $6000)* Depreciation (10% of $6000)* Repairs Incidentals Total general and overhead expenses Total Cost of Operation for a 10-hour Day $5.00 1.00 1.00 $1.80 3.00 2.70 4.50 $37.50 $7.00 $12.00 $56.50 Total cost of excavation of 315 feet of trench, pipe laying, and back filling by hand work, for a 10-hour day, is $137.00. Total cost of excavation by machine of 225 feet of trench, pipe laying by hand work, and back filling by scrapers is $56.50. *Based upon 200 working days in a year and a 10-year life. 423 124 EARTHWORK A comparison of the above results shows that during a 10-hour day, a trench excavator will do about 70 per cent of the amount of trench excavation that can be done by hand labor and at 40 per cent of the cost. Field of Usefulness. The continuous bucket excavator is especially adapted for trench excavation, where the width does not exceed 72 inches and the depth 20 feet, and the soil conditions are favorable. This is especially true through the IVIiddle West, where clay and loam with few obstructions such as boulders, roots, etc., predominate up to shallow depths. On account of the great weight of the machines, they are not practicable for use in soft, wet soils, unless mounted on caterpillar tractors. For the excavation of hard soils, considerable trouble is often experienced on account of the breaking of the bucket chain. Hence it is desirable to use a machine with a strong, heavy chain for the digging of hardpan, blue clay, and other hard, tough materials. The trench excavator is efficient and economical for the exca- vation of trenches 24 inches and over in width and over 6 feet in depth, and one machine can do the work of from 80 to 200 men. TRESTLE CABLE EXCAVATOR Construction. The trestle cable excavator has been in general use, especially in the eastern section of this country, during the past 30 years, for the excavation and back filling of large trenches for waterworks and sewer systems. It has many admirable features and is especially well-adapted to large sewer trench work in hard soils. A trestle cable excavator on sewer-trench construction is shown in Fig. 70. This type of excavating machine consists of a series of trestles supporting an overhead track. The trestles or bents are connected by rods at the bottom and by the beam track at the top and rest upon a plank or rail track. The operating machinery is carried by a platform located at one end of the structure. The overhead track supports several carriers which carry the buckets or tubs. The whole framework is self-contained and can be moved ahead as a unit from one section of the work to another. The trestles are made of timber framed together to form square or A-shaped bents. They are from 15 feet to 20 feet in height 424 EARTHWORK 125 and are equipped with castor frames, wheels, etc. These bents are connected together at the bottom by bars of tubular steel of from 1 inch to 2§ inches in diameter. The bents rest on T-rails which are spiked to sections of planking, and enough track is provided to move the whole machine ahead 100 feet at a time. The track or support for the travelers or carriers is made up of sections of I-beams or channels which are bolted to or hung from the head blocks of the bents. iJlj^ J^^ 1| ■ MTli^i } am" ^H — — -^^^1 ^ ^ s^-:^^§im^ IPi^Hgp: vf^!f?S«^^ .:-- Fig. 70. Trestle Cable Excavator ou 8ewer Treuch Construction Courtesy of Carson Trench Machine Company, Boston, Massachusetts Operating Equipment. The operating equipment consists of the boiler, engine, and car upon which the machinery is placed. The boiler is of the vertical, tubular t\T)e, and is equipped with all appliances for efficient operation and control. It is usually operated at a steam pressure of about 100 pounds. The engine is a 2-drum, double-cylinder, hoisting machine with reversible link motion. The drums are controlled by friction-clutch brakes; one carries the hoisting rope, and the other carries the endless rope which 425 126 EARTHWORK operates the carriers and buckets. The drums are independent, and so arranged that they may be operated in unison or separately. The boiler and engine are generally mounted on the same bed plate which is supported by a platform mounted on rollers or wheel trucks. The front end of the car supports the head trestle. A suitable house is usually built, in sections, over the platform and may be used completely or partly, depending on climatic conditions. Excavating Equipment. The excavating equipment consists of the tubs, the carriers, and the cables. Upon the overhead track run several carriages, travelers, or carriers, which are provided with wheels made to fit the flanges of the structural sections. From each carrier is suspended a tub which is equipped with an automatic catch and is self-dumping and self- righting. The carriers are connected by a continuous rope which is operated by a drum on the engine, and are raised and lowered by hoisting ropes controlled by a rope operated by another drum on the engine. Method of Operation. The labor crew necessary to operate a trestle cable excavator consists of an engineer, a fireman, a latch- man, and a tubman. The engineer operates the engine and has general charge of the work. The fireman supplies the boiler with fuel, and oils the machinery. The latchman operates the latches, which release and grip the tub lines for raising and lowering the buckets. The tubman hooks and unhooks the tubs, and has gen- eral charge of their filling and emptying. The machine being set up in position, the engineet* operates the hoisting line and releases the jaw clutches on the tub ropes, thus allowing the tubs or buckets to drop into the excavation. The tubs are unhooked and another set of filled tubs hooked on. The loaded tubs are then hoisted up to the locks on the carriers, and the whole set is moved to the disposal place by the operation of the continuous traversing line. Usually one section of the trench is being excavated while another section is being back filled, so that the material removed at the former place can be utilized directly in the latter. It may be necessary at the beginning of the work, or in special cases of crossings, etc., to dump the material into temporary spoil banks, or into carts for removal from the site. As soon as one section is completed, the machine pulls itself ahead 426 EARTHWORK 127 by means of a winch on the engine and a rope passing through a snatch block attached to a deadman set ahead. Machines may be had with double and single upper tracks. The nominal capacity of a double-track machine is 50 per cent greater than that of a single-track machine, as one set of buckets is being raised loaded, while the other set is being lowered empty. Thus 3 sets of buckets are continually in use, one set being filled, one hoisted and carried to the dump, and the other dumped and returned to be loaded. A double-track machine is more economical for trenches over 5 feet in width. The average output for a 6-bucket, single-track machine is about 125 cubic yards for a 10-hour day. Cost of Operation. The rental charge of a 6-bucket, single- track machine is about $200 per month. The cost of transportation, setting up, and dismantling will vary with the distance, length of haul, experience of men, etc., and will range from $100 to $500. About I ton of coal per day will be used, and the cost of oil, waste, supplies, etc., will vary from $1 to $5 per day. The net cost of operation of the machine would be about $25 per day. Assuming an average output of 100 cubic yards, the cost of the work exclusive of sheeting, pumping, loosening of material in trench, etc., would be about 25 cents per cubic yard. Field of Usefulness. The trestle cable excavator is especially adapted to the excavation of trenches for large sewers and water mains in hard soils, and in city streets. The work is restricted to the immediate area of the trench, leaving part of the street unob- structed for traffic. The method of operation is efficient, as the excavated material is generally used directly in back filling. The method of operation is also easy, simple, and safe. TRESTLE TRACK EXCAVATOR Construction. The trestle track excavator is very similar in its method of operation to the trestle cable excavator. The principal difference is the suspension of the carriers from a car or carriage which moves along a track supported on the tops of the trestles. The construction consists of a series of light, steel-frame trestles, of trapezoidal shape and 6 feet in height, spaced about 10 feet on centers. These trestles are mounted on double-flanged wheels, which 427 128 EARTHWORK run on rails. The tops of the trestles are connected by steel channels which form a continuous track on which the carriage runs. Operating Equipment. The operating equipment consists of a vertical, tubular boiler, and a double-drum hoisting engine, carried on a car at the forward end of the machine. Excavating Equipment. The excavating equipment consists of a steel-frame car supported on four wheels which run upon the trestle Fig. 71. Trestle Track Excavator Courtesy of Potter Manufacturing Company track. The car is operated by cables which connect to the hoisting engine. On the car is a hoist which raises and lowers two steel buckets. The buckets are made in three sizes: J-, §-, and 1-cubic yard capacities. A view of a car in operation is shown in Fig. 71. Method of Operation. The machine requires a crew of 3 men; one to operate the hoisting engine, and two to operate the bucket hoists on the carriage. 428 EARTHWORK 129 The carriage is moved by a cable from the hoisting engine to the place of excavation, where either one or both buckets are lowered into the trench, filled by the laborers in the trench, and raised above the floor of the car. The car is then moved to the place of back fill or dump, where the buckets are lowered and dumped. Cost of Operation. The following statement is given as a typical case of the cost of excavation with a trestle track machine. niustrative Example. The trench had a width of 21 feet and an average depth of 30 feet. The material excavated consisted of a shallow top la\'er of loam, then 15 feet of soft blue clay, 6 to 8 feet of stiff blue clay, 1 foot of sandy loam, and then about 2 feet of hard blue clay. The trench machine was equipped with 6 buckets of J-cubie yard capacity, and 4 were filled while the remaining 2 were being removed and dumped. The excavator removed the lower 12 or 14 feet of the trench. The following gives the cost of operation based on an 8-hour day. Operating Cost of Trestle Track Excavator Labor: 1 foreman $ 4.00 1 engineer 5.00 1 fireman 2.50 1 car operator 3.50 1 car helper 2.00 20 laborers in trench, @ $2.00 each 40.00 1 laborer on dump 2.00 Total labor cost, per day $59 . 00 and Supplies: \ ton coal, @ $5.00 $2.50 OU, waste, etc. 1.00 Repairs 1.50 Total fuel and supplies $5.00 rat. Rent of machine, @ $125 per month $5.00 Total Cost of Operation for an 8-hour Day $69 . 00 Average Daily Excavation (cu. yd.) 175 Unit Cost of Trestle Track Excavating, per cu. yd., $69.00^175= 00.39 Field of Usefulness. The trestle track excavator has the same scope and advantages as the trestle cable excavator. It is especially efficient in trench excavation in congested city streets where the 429 130 EARTHWORK demands of keeping at least part of the street open to public traffic requires the restriction of the work to as limited an area as possible. On very wide trenches, it is advisable to use a machine equipped with a double track and 2 cars in order to facilitate the work. TOWER CABLEWAY Development. The tower cableway is an excavating, hoisting, and conveying device devised about 1875 for slate quarries in eastern Pennsylvania. Then for a period of years the cableway was used largely in quarry work and logging operations. In more recent times, this machine has been adapted to the conveying of materials on construction work, the excavation of the hghter and softer soils, the hoisting and conveying of the harder soils excavated by other machinery, etc. This article will deal with the use of the cableway in trench construction only. A double cableway on trench excavation is shown in Fig. 72. Construction. The essential parts of a tower cableway are the towers, the cable, bucket or dipper, carrier, and the power equipment. The towers are framed timber structures varying in height with the location and character of the work. They are either fixed or anchored in position, or mounted on wheel trucks which run on tracks, thus providing for the movement of one or both ends of the cableway. The tops of the towers are provided with saddles and sheaves for the cables. Operating Equipment. The operating equipment of a tower cableway consists of a boiler and an engine. The boiler is generally of the vertical, tubular type, and equipped with the necessary accessories for operation at a pressure of 100 pounds. The engine is a 2-drum, double-cylinder machine, fitted with reversible link motion. The drums are of the friction-brake type; one for the hoisting rope, and the other for the endless, traversing rope or cable. The drums are so arranged as to be operated together or independently. The machinery is placed on a housed-in plat- form built of timber and supported on 4 car wheels which run on short sections of the track. Excavating Equipment. The excavating equipment comprises a traveler, the tubs, buckets or skips, and the cables. 430 EARTHWORK 131 The main cable is made of crucible steel and of a diameter depending upon the span, load, elevation, etc. It passes over the tops of the towers, is anchored behind them, and is the track over which the carrier passes. The hoisting and traversing ropes 431 132 EARTHWORK are crucible-steel cables of from | inch to | inch in diameter and extend from their respective drums on the engine over the sheaves at the tops of the towers and thence to the carrier. The traveler or carrier is a wrought-iron frame which carries the sheaves over which pass the hoisting and traversing cables and the fall block which supports the tub, skip, or bucket. The carrier is provided with 2 or more flanged wheels which run on the main cable. One or more carriers may be used on the same cable- way. The fall block of the carrier supports the tub or skip which is of steel or w^ood and of widely varying capacity. For trench work tubs are generally used and are made of steel and provided with double bottoms and automatic catches. When the cableway is used for direct excavation, grab buckets or drag-line buckets are used and require special operating equipment. Method of Operation. For trench excavation, a cableway having a length or span of from 200 feet to 400 feet is generally used. The length of excavation will be about 50 feet shorter than the distance between towers. The labor crew required consists of an engineer, a fireman, a signalnian and two or more laborei's. The engineer operates the engine and has general charge of the work. The fireman provides the boiler with fuel and water, and looks after the oiling of the machinery. The signalman signals to the engineer for the raising and lowering of the bucket or tub. The laborers are used in filling and in dumping the tub, and in general service about the job. The bucket is lowered into the trench, filled by the shovelers, and then raised above the excavation by the operating of the hoist- ing drum, which is thrown out of gear and held by a brake. The traversing line is then operated and the carrier moved in either direction until the bucket is over the place for dumping. Then the bucket is lowered by means of the brake band on the hoisting drum. The material may be used for back fill in a section of trench where the pipe is laid or dumped into a spoil bank or into wagons for removal to a distant place of disposal. A small crane or derrick may be used to advantage, adjacent to the excavation, for the transfer of the buckets from the cableway to the dumping board or hopper. 432 EARTHWORK 133 Cost of Operation. A typical case of sewer trench construc- tion will be considered in the following statement of the cost of excavation with a cableway. Illustrative Examyle. The trench is 12 feet wide and with an average depth of 20 feet. The soil varies from a surface layer of loam of 2-foot depth, through a clay substratum of 8 feet, to a hard gravel deposit. The machine has two 30-foot towers placed 300 feet apart and is equipped with 1-yard tubs or buckets. Bracing and sheeting were carried on at the same time as the excavation, and the sewer construction followed closely to allow for back filling at one end of the section with the material from the other end. Following is an estimate of the cost of excavation under average working conditions, during a 10-hour day. A crew of 30 men are required to pick and shovel the material into the buckets and the average daily output will be taken as 300 cubic yards. Operating Cost of Tower Cableway Labor: 1 foreman $ 4.00 1 engineer 5.00 1 fireman 2.50 1 signalman 2.50 . 2 dumpers, @ $2 . 00 each 4.00 30 laborers, @ $2 . 00 each 60.00 Total labor expense, per day $78.00 Fuel and Supplies: i ton coal, @ $5 . 00 $2.50 Oil, waste, etc. 1.00 Repairs 1.50 Total Fuel and Supplies $5.00 General and Overhead Expenses: Interest (6% of $8000)* $2.40 Depreciation (10% of $8000)* 4.00 Incidental expenses 2.60 Total general expense $9.00 Total Cost of Operation for a 10-hour Day $92 . 00 Total Output for a 10-hour Day (cu. yd.) 300 Unit Cost of Tower Cableway Excavating, per cu. yd. of material handled, $92.00^300= 00.030 Unit Cost of Hoisting, Conveying, and Dumping (excluding pick and shovel labor), per cu. yd. of material handled, $29 .00-^300 = 00 . 097 ♦Based upon 200 working days in a year and a 10-year life. 433 134 ^ EARTHWORK Field of Usefulness. The cableway excavator has a wide and important field of usefulness. It is especially efficient in the handling of materials across large waterways, valleys, quarries, pits, etc., where surface transportation would be difficult and very expensive. In the excavation of large quarries, gravel pits, surface mines, dam foundations, reservoirs, etc., the cableway can be used as a tower excavator directly or to convey skips, tubs, or buckets which con- tain the material previously excavated by other machines. The same cableway can of course be used for the transportation of concrete, stone, timber, and other building materials, as well as tools, men, etc., during the construction work which follows the excavation. The cableway can be satisfactorily used in trench excavation when the excavation is of large extent, generally over 6 feet in width and 10 feet in depth. With the use of this type of excavator, the weight of the machinery is largely concentrated at the ends of the trench, the cable is at a considerable height above the work and allows space for storage, handling of materials, etc. The principal objection to the use of the cableway on trench work is its lack of lateral control. It is almost impossible to avoid the swinging of the buckets during the raising and lowering, and this is liable to result in some displacement of and damage to the sheeting, forms, etc. TILE=TRENCH TYPES General Features. Preceding the year 1900, trench excavation for drain tile was made largely by hand. With the rapid and extensive development of agricultural drainage through the South and Middle West, came the use of machinery to economically and expeditiously perform the great amount of excavation work required by the construction of drainage systems. At the present time, there are several makes of trench excavators, which are especially adapted to tile-trench excavation. The essential parts of tile-trench excavators are practically the same as for the water and sewer-pipe trench machines, described under Pipe-Trench Types. There is one make of machine which has been specially devised for the laying of the tile as well as for the excavation of the trench. A description of this machine will follow. 434 EARTHWORK 135 HOVLAND TILE DITCHER Power Equipment. The Hovland tile ditcher is made in two sections : a front platform w^hich carries the power equipment, and a rear platform which carries the excavating chain. Both platforms are made of a steel framework supported on two large caterpillar tractors. Fig. 73 shows a general view of the Hovland tile ditcher. It \Aill be noticed that the forward tractor carries the power equipment which consists of a vertical, 3-cylinder gasoline engine. The main shaft of the engine is connected by sprocket chains to the driving shafts of the excavating belt of the tractions, and of the belt conveyor. Fig. 73. View of Hovland Tile Ditcher Courtesy of St. Paul Machinery Manufacturing Company, St. Paul, Minrtesota Excavating Equipment. The excavating equipment is carried on the rear platform and consists of an excavating chain and its supporting framework. The excavating chain is made up of two continuous chains which carry an endless set of hinged links. To the vertical sections of these links are bolted the knives or cutters of any width from 5 inches to 30 inches. The links are hinged in such a way that when a cutter strikes a stone or other obstruction in a trench, the chain gives, and the cutter slides over the obstruction without injury. An automatic cleaning device consisting of a projecting arm, is placed above the upper end of the chain and scrapes over 435 136 EARTHWORK the surface of each bucket as it passes. The excavated material is thus removed from the buckets and falls upon a moving belt con- veyor which is located under the excavating chain at its upper end. The framework which supports the excavating chain is shown in Fig. 74. It comprises a small, upper wheel and a large, lower wheel, or drum, about which the chain revolves. The lower wheel is suspended by chains from the rear of the frame and can be raised and lowered by a gear-operated shaft. The upper wheel is on a shaft which is chain-driven from the engine located on the forward platform. An adjustable steel-frame curbing can be fastened to the rear of the excavating tractor and drawn along the completed trench. Fig. 74. Excavating Wheel and Frame of Hovland Tile Ditcher Courtesy of St. Paul Machinery Manufacturing Company, St. Paul, Minnesota This curbing can be adjusted to the width of the trench and made high enough to project above the ground surface. A steel spout is placed on the inner and curved portion and as the machine pro- gresses, a man places a tile in at the top of the spout, which is curved so as to allow the tile to slide out in place along the bottom of the finished trench. Method of Operation. A crew of 3 or more men are necessary to properly operate a tile-trench excavator: an engineer who has charge of the operating equipment, an operator who manipulates the excavating wheel, a tile layer and one or more laborers to supply 436 EARTHWORK 137 fuel, water, and supplies for the machine and for general service about the work. The revolution of the excavating chain or wheel brings a series of knives or buckets into contact with the soil and each bucket removes a slice of earth, which is dumped upon the belt conveyor and carried to the spoil bank, at the sides of the trench. The operator lowers the wheel or chain into the soil as the excavation proceeds and governs the depth by a sight rod, placed on the machine. As soon as the required depth is reached the engineer sets the tractor chain in motion and the machine moves ahead to the next position. With the Hovland tile ditcher the drain tile can be laid as the excavation is completed, by placing the tile in the curb which follows directly behind the excavating chain. Fig. 74. It is often necessary to reset the tile after it leaves the curb in order to secure proper alinement and close-fitting joints. One manufacturer has devised a longitudinal belt conveyor, which carries the excavated material to a point behind the machine and dumps it back into the trench. This device has not been satisfactory because it does not allow enough time after the exca- vation for the placing of the tile. Cost of Operation. An approximate estimate of the capacity and cost of operation of a tile ditcher will be given in the following statement. Illustrative Example. A trench machine has a gasoline power equipment and an excavating chain or wheel capable of digging a trench 14| inches wide and 4J feet deep. The soil is loam and clay with gumbo in places. The average depth of cut is 4 J feet, and the average progress is 1300 feet per 10-hour day. Operating Cost of Tile Ditcher Labor: $14.00 Total fuel and supply cost $2 . 50 437 1 operator, @ $125 per month 1 fireman 1 helper 1 team and driver $5.00 2.00 2.00 5.00 Total labor cost, per day Fml and Supplies: 10 gallons gasoline, @ 20c Oil, waste, etc. $2.00 .50 138 EARTHWORK General and Overhead Expenses: Interest (6 % of $5200) * $2 . 00 Depreciation (12^ % of $5200) * 4 . 25 Repairs and incidentals 2 . 75 Total general expense $9.00 Total Operating Cost per 10-hour Day $25 . 50 Average Progress per Day (ft.) 1300 Average Daily Excavation (cu. yd.) 260 TT -^ r^ ^ <• rr-i rp uTT 4.- fper f t. $25.50"^ 1300 00.019 Unit Cost of Tile-Trench Excavating <^ jd^occn o^^ n/^ «r.o ^ (per cu. yd. $25.50-^260 00.098 Field of Usefulness. The tile-trench excavator is a very efficient and practicable machine for ordinary soil conditions in fairly level land with few obstructions. Where the soil is low and wet, the machine must be supported on caterpillar tractors to distribute the weight over the soft soil. Where obstructions such as large stones, roots, etc., abound, a large amount of extra hand labor is required. For work of considerable magnitude, the tile ditcher can exca- * Based on 150 days per year and an 8-year life. 438 REVIEW QUESTIONS 439 REVIEW QUESTIONS ON THE SUBJECT OF RAILROAD ENGINEERING PART I 1. What are the elements of railroad location which are in general antagoni.^tic? Deduce from the above the chief duties of the locating engineer. 2. What is the chief object to be accomplished by a recon- noissance survey? 3. What are the three elements involved in the survey of any line and what are the methods of determining these elements in reconnoissance surveys? 4. What is the practical value and what are the limitations of barometric leveling? 5. What is the general object to be accomplished by means of a preliminary survey? 6. To what extent should the compass needle be used dur- ing preliminary surveys? 7. Why is it that a Locke level with its limited accuracy is a proper instrument for cross-section work? 8. Under what circumstances is the stadia method advan- tageous for preliminary surveys? 9. What is the justification of making two or more pre- hminary surveys through difficult portions of the route? 10. How are the tangents and curves for the "location" determined? How is the location survey ''tied" to the prelim- inary survey? 11. How would you select a low-grade line through a difficult piece of mountainous country? 12. How are transit stations and bench marks secured against disturbance during construction of the road? 441 RAILROAD ENGINEERING 13. Define the degree of a curve. What is the approximate rule for the radius of a curve of a given degree 'i What is the percentage of error of this rule for a 10° curve ? 14. What is a sub-chord ? What will be the excess length of a sub-chord with a nominal length of 45' on a S'^ curve? 15. What is the difference between the nominal length of a railroad curve and its true length measured on the arc ? What will this amount to in the case of a 6° curve subtending a central angle of 34° 30'? 16. If two adjacent tangents which make an angle of 24° 16, are connected by a 3° 30' curve, what will be the distance from the vertex to the point of the curve ? 17. In the case given above, how far will the curve pass from the vertex ? 18. A 3° 30' curve is to begin at Sta. 142 + 65 and is to have a total central angle of 28° 30' ; compute the deflections from the tangent at the P.C. to each station and to the P.T. 19. In the above case assume that on account of obstructions to sighting it was necessary to set up the instrument at Sta. 147 and sight back to Sta. 144. Applying the rule of section 25, what should be the reading of the horizontal plate when the instrument is sighted at Sta. 144, and what should be the reading when it is sighted ahead at Sta. 148 ? 20. Assume that a 3° curve having a central angle of 14° 30 is to be located by tangential offsets; make a sketch of this case and compute and mark on the sketch the deflections and distances. 21. After running a 4° curve to some point n as in Figure 16, the curve is found to be obstructed. It is estimated that the curve would again be clear about 400 fett further on. Compute the long chord nvi and the angle which 7i?7i would make with a tangent to the curve at n. What would be the offset from this long chord to the second station beyond n'^ 22. Give detailed solutions of the problems stated in sec- tion 30 ? 23. Give detailed solutions of the problems stated in sec- tion 34 ? 24. What is the essential character of a transition curve and why it is necessary ? 442 REVIEW QUESTIONS ON THE SUBJECT OF RAILROAD ENGINEERING PART II 1 . What is the chief cause of the deterioration of locomotive boilers due to impure water supply? 2. What are the chief difficulties encountered in the construc- tion of engine houses and how are the difficulties met? 3. What elements must be considered in computing the total cost of any kind of railroad tie? 4. What is the preferable method of locating ties with refer- ence to rail joints? 5. Assuming that an 85-pound rail and a 70-pound rail have similar cross-sections, what is the relative stiffness? 6. What are the elements of a perfect rail joint and why is it impossible to produce a perfect rail joint for steam railroad work? 7. Why are plain smooth spikes preferable to spikes wkich are jagged? 8. What are the three principles which form the basis of the design of nut locks? 9. Give a brief statement of the general methods of obtaining a pure water supply. 10. What are the elements of an ideal form of ballast? What the disadvantages of *'mud" ballast? What are the advantages of stone ballast? 11. What are the causes, other .than mere decay of the wood, which require that ties should be renewed? 12 What are the features of the A. S. C. E. rail section which are constant for all weights of rails and what are the proportions which are constant or nearly constant? 13. What are the advantages and disadvantages in using very long rails? 443 RAILROAD ENGINEERING 14. What are the advantages obtained by the use of tie plates? 15. How many track bolts in a mile of single track using six- bolt splice bars and 30-foot rails? 16. How much is allowed for rail expansion and how is this practically provided for? 17. How much gap would you allow at a rail joint when the temperature of the rail at the time of laying is 45° F? 18. What should be the middle ordinate of a 30-foot rail bent to a 40° curve? 19. What would be the superelevation of the outer rail for a 60° curve when the maximum speed is 45 miles per hour? 20. If the maximum speed for trains is assumed at 60 miles per hour, what will be the length of a string or tape which, when stretched as a chord inside the rail, will give a middle ordinate equal to the required superelevation? 21. What is the fundamental advantage of a point switch over a stub switch? 22. Suppose it were required to make to order a frog having a frog angle of 6° 30'; what would be the frog number? 23. Verify the calculations for the length of the lead of a switch from a straight track using a No. 8 frog on the basis, first, of circular lead rails, and second, of straight point rails and straight frog rails, using the values given in Table III. 24. If a No. 8 frog has been used in switching from a straight track, what will be the radius of the connecting curve when the distance between track centers is 13 ft.? 25. What will be the length and radius of the connecting curve running from a switch on the outside of a main track, which is a 4° 30' curve, the frog used being No. 9 and the distance between the track centers 13 ft.? 26. Make all the computations for the location of a turnout to the inside of a 4° curve using a No. 8 frog. 27. What are the different kinds of tracks making up a freight yard? 28. By what device is engine service economized in planning a freight yard? 444 REVIEW QUESTIONS ON THE SUBJECT OF RAILROAD ENGINEERING PART III 1. Discuss the two classes of financial interests in the ownership of railroads — the security and profits of each. 2. Describe methods of estimating the probable volume of traffic on a proposed road. 3. Discuss the division of the gross revenue and the per- centages spent in operating expenses, fixed charges, and dividends. 4. Discuss operating expenses per train-mile; their uni- formity for heavy and light traffic roads; the tendency toward variation of the chief items. 5. Discuss the relation of railroad rates to railroad expenses. 6. Explain why a reduction in distance is profitable when handling competitive business, but unprofitable when handling non-competitive business. 7. Discuss curve compensation; the reasons for its use: the values which should be employed. 8. Explain the distinction between minor and ruling grades. 9. What is the meaning of 'Velocity head"? What is the velocity head of a train when moving at the following velocities in miles per hour: 21; 27.4; 32.25? What velocities correspond to velocity heads of 18.58; 38.92; 49.25? 10. Explain the fundamental principle of a virtual profile, and describe its use and possible misuse. 11. Classify train resistances, with a brief discussion of each class or kind, 12. How much additional tractive force per ton will be necessary to increase the velocity of a train from 8 m.p.h. to 22 m.p.h. in a distance of 800 feet? 445 RAILROAD ENGINEERING 13. Assume that an engine weighs * 253,000 pounds and that its cylinder tractive power at M velocity is 33,778 pounds, what is its rating for a 1.1 per cent grade? 14. How many cars (empties) each weighing 17 tons, could be hauled up that grade? 15. On the basis of a Mikado locomotive, with 220,000 pounds on the drivers, weighing 435,000 pounds, including tender, total heating surface 4720 square feet, besides a superheater, boiler pressure 170 pounds, using 4000 pounds of coal per hour, whose effective B.t.u. is 11,500, cylinders 28 inches in diameter and 32 inches stroke, drivers 63 inches diameter: (a) What is the maximum velocity (M) at which full pres- sure of steam may be maintained? , (b) What will be the cylinder tractive power and the draw- bar pull at M velocity? (c) What willbe the cylinder tractive power at a velocity of 20 m.p.h.? (d) Draw the curves for cylinder tractive power and draw- bar pull for all velocities up to 35 miles per hour. (e) Assuming a train of 20 freight cars averaging 68 tons and a caboose weighing 12 tons, what is the maximum rate of speed which could be maintained on a 0.7 per cent grade? (f) Draw the speed curve for acceleration from starting to maximum speed for this train and grade. 16. Demonstrate the fundamental principle in the economy of pusher grades. 17. Given a maximum grade of 2.10 per cent, what would be the corresponding through grade if one pusher engine is used — the engine being of the type described in Question 15? If two pushers were used on the 2.10 per cent grade, what would be the corresponding one-pusher and through grades? 18. Discuss the elements of the cost of the operation of pusher engines. 19. Discuss the fundamental principles of the ''balance of grades for unequal traffic". 20. Assume that an investigation showed a 3:1 ratio in east-bound and west-bound traffic. On the basis of a 0.7 per cent grade against east-bound traffic and the use for both through and pusher work of engines of the type described in Question 15, what would be the corresponding grade against west-bound traffic? 446 REVIEW QUESTIONS ON THE SUBJECT OF EARTHWORK PART I 1. State the different classes of power shovels. 2. How would you excavate a canal 200 feet wide and 15 feet deep? 3. Compute the time and cost of excavation with a |-yard revolving shovel of a basement excavation, 200 feet long, 60 feet wide, and 10 feet deep, in a sandy clay soil. 4. How many cubic yards of loam and clay can one laborer loosen from a pit 5 feet deep and shovel into 1 J-yard dump wagons in a 9-hour day? 5. Compute the cost of operation of a 2-yard drag-line excavator on an irrigation can^l in glacial clay and requiring the removal of about 2500 cubic yards per 100 feet. 6. What is the most efficient method of supporting an excavator on soft wet soils? 7. Describe the method of operation of an elevating grader. 8. Give an analytical statement showing the relative economy of hand- and power-shovel excavation. 9. Discuss the factors which determine the method to be used in excavation. 10. Discuss the relative efficiencies of four types of scrapers. 11. State the advantages of electric operation of a power shovel. 12. What is the drag-line principle? 13. Describe a machine which can excavate a canal to a true grade and with smooth side slopes. 14. Describe and illustrate by a diagram the operation of a double-tower excavator. 447 EARTHWORK 15. Describe the different tools and methods of loosening earth. 16. Describe the method of grading up an earth road with a blade grader. 17. What are the relative advantages of blade and elevating graders in earth-road construction? 18. Describe the method of operation of a steam shovel of the fixed-platform type. 19. Describe the most economical power equipment to use on a drag-hne excavator operating on a canal in the Middle West, twenty miles from a railroad. 20. What are the special fields of usefulness of the small revolving shovels? 21. Describe the various types of hand shovels. 22. What type of dredge would you use on a job where there were several canals to be dug in the same locality? 23. Describe the machine which can be most economically used for the excavation of small ditches in favorable soils. 24. Describe the walking equipment of a walking drag-line excavator. 25. Discuss the relative efficiency of different types of excavators in shallow earth excavation. 448 REVIEW QUESTIONS ON THE SUBJECT OF EARTHWORK PART II 1. What are the principal fields of usefulness of a hydraulic dredge? 2. Compute the cost per foot of trench excavation and tile laying for 12-inch tile at a depth of 5 feet. 3. Can a hydraulic dredge excavate hard materials? 4. What are the different classes of dipper dredges? 5. Describe a ditcher which can excavate a trench and lay tile. 6. Describe the operation of a Lobnitz rock cutter. 7. Describe the most efficient operating equipment of a dipper dredge. 8. Why has the ladder dredge not become a more generally used excavator in this country? 9. Discuss the relative merits of three different makes of continuous bucket excavators. 10. What are the fields of usefulness of the tower cableway? 11. Describe the method of operation of a ladder dredge. 12. What kind of side spuds are the most satisfactory for dredge operation in narrow canals? 13. Describe the continuous bucket excavator. 14. How are high banks excavated with a ladder dredge? 15. Illustrate and describe the section of a ditch which a dipper dredge can excavate. 16. What is the best form of excavator to use in the excavation of large trenches in narrow city streets? Why? 17. Describe three types of buckets. 18. Describe the operating equipment of a hydraulic dredge. 449 EARTHWORK 19. What method of subaqueous rock excavation is used in this country? 20. When should electric operation be used on a hydraulic dredge? 21. How would you operate traveling derricks on trench excavation? 22. Describe the method of operation of the trestle track excavator. 23. Compare the relative efficiency and scope of work of the Lobnitz rock cutter and the drill boat. 24. State the different classes of trench excavators. 25. Discuss the field of usefulness of the dipper dredge. 450 INDEX 451 INDEX The page numbers of this volume will he found at the bottom of the jtages; the numbers at the top refer only to the section. Page Page A Curves (continued) Abutments 103 simple transition 26 43 B vertical 57 Ballast 124 amount 126 D broken stone 125 Dipper dredge 377 cinders 125 Distance 231 cost 126 effect on receipts 232 gravel 125 relation to rates and expenses 231 laying 126 Ditches 61 mud 124 Dredges 344 shells, fine coals, etc. 125 excavators, dry-land 344 slag 125 excavators, floating rock breakers, subaqueous 377 408 C Dry-land excavators 344 Cattle guards 121 drag-line, walking 373 Cattle passes 112 revolving 348 Coaling stations 120 scoop, walking 370 Compound curves 39 scraper, stationary 344 definition 3^ templet 358 location, modifications of 41 tower 367 two branches, mutual relations of 40 wheel 362 Construction, earthwork 59 Constructive earthwork 83 E Continuous bucket excavator 418 Earthwork 301 Corbels 104 excavations, methods of 301 Crossings 170, 171 principle 301 Culverts 110 scope 301 cattle passes 112 Earthwork construction 59 old-rail 112 details, constructive 61 pipe 110 roadbed, width of 61 Curvature 235 slopes and cross-sections 59 compensation 236 Earthwork, constructive 83 limitations 239 blasting 83 operating disadvantages 235 classification 87 Curves embankments, formation of 86 compound 39 excavating 83 Note. — For page numbers see fool of pages. 453 INDEX Page Page Earthwork — surveys 63 Fresno grader 305 problem, nature of 63 Frogs 149 slope stakes, position of 63 volume, computing the 66 G Economics of railroad engineering 213 Grade 241 curvature 235 accelerated motion, laws of 242 distances 231 minor and ruling, distinction be- finances, railroad 213 tween 241 grade 241 profile, virtual 245 location 229 use, value, and possible resistances 252 misuse of 249 Economic location 229 Graders 310 economic calculations, reliability elevating 314 and value of 229 four-wheel blade 310 general principles 229 reclamation 311 Electric shovels 339 two-wheel blade 310 advantages 339 equipment 339 H usefulness 340 Engine houses 120 Hovland tile ditcher 435 Engine yards 178 Hydraulic dredge 402 Excavations in earthwork, methods of 301 electric power 404 dredges 344 I excavators, trench 412 graders 310 Interlocking 195 hand, details of 302 scrapers, drag and wheel 304 L shovels, power 318 Ladder dredge 388 Lobnitz rock cutter 408 F Location surveys 24 Floating excavators 377 methods 25 dredge, dipper 377 route, selecting a 24 dredge, hydraulic 402 Locomotives dredge, ladder 388 acceleration, speed curves 280 Framed trestles 100 drifting 285 abutments 103 oil-burning 262 form, general 100 power calculations 266, 273, ,287 foundations 101 rating of 257 multiple-story 101 relation of type to service and Freight yards 174 to track conditions 263 accessories 177 retardation, speed curves 284 cranes 178 route, selection of 288 scales, track 177 tractive force at higher velocities 272 connection with main tracks 176 tractive power, effect of grade on 278 engine yards 178 tractive power, relation of boiler minor 177 power to 274 principles, general 174 types of 261 Note. — For page numbers see foot of pages. 454 INDEX Page Page N Railroad finances 213 Nut locks 138 capitalization 213 O charges, fixed 222 Old-rail culverts 112 equipment, maintenance of 228 expenses, operating 223 P classification 225 Pile driving 98 expenses, transportation 228 Pile trestles 98 monopoly 219 Pipe culverts 110 revenue, gross 216 Pipe-trench excavators 414 diversion 220 bucket, continuous 418 revenue, net 222 cable, trestle 424 stocks and bonds 214 cable way, tower 430 ways and structures, maintenance derrick, traveling 414 of 225 track, trestle 427 Railroad surveys 11 Power shovels 317 interests, conflicting 11 classification 317 principles, general 11 cost, operating 337 Reconnoissance surveys 12 electric 339 elements 13 steam, revolving 337 existing maps, utilization of 13 efficiency and economy 34] L-344 grades, low ruling 17 fixed-platform 318 methods 13 revolving-platform 332 problem, essential 12 Preliminary surveys 19 Resistances 252 cross-section method 19 grades for unequal traffic, 1 bal- object, general 19 ance of 296 party required 22 principles 296 re-surveys 23 relative traffic, estimation of 298 stadia method 21 theoretical balance, computa- Pusher grades 289 tion of 297 economy, general principles of 289 grades, pusher 289 engines, operation of 291 train 252 length of 292 locomotives, rating of 257-289 pusher-engine service, cost of 293 locomotives, types of 261 services, balance of grades for 290 operation, units of 259 tractive power, effect of R grade on 278 Rails 130 Revolving excavator 348 length 133 weight 131 Rail braces 136 S Rail joints 133 insulated 135 Scrapers, drag and wheel 304 Railroad engineering 11 drag 304 construction and maintenance, four-wheel 308 work of 11 Fresno 305 economics 213 two-wheel 306 Note. — For page numbers see foot of pages. 455 INDEX Page Page Signaling 179 Switches 146 systems 179 construction 146 automatic 184 frogs 149 controlled manual 183 guard rails 148 details, mechanical 186 switch stands 148 electro-pneumatic crossings 170-172 semophores, electric 194 crossovers 162, 163 simple manual 180 curve connections 159, 160 wires and pipes 191 laying, rules for 167 Simple curves 26 slip 168 deflections, computing 31 turnouts 155, 157 deflections, location of points by 30 Switch stands 148 elements 28 instrumental work 32 T length 28 Tables location, modifications of 38 Austin trench excavators, sizes location, obstacles to 35 and capacities of 421 location, special methods of 33 cut-off and pounds of steam per measurement, method of 26 1 h.p.-hour for various 1° curve, elements of 29 multiples of M 269 sub-chords 27 evaporation in locomotive boil- Slip switches 168 ers, average 266 Spikes 136 expenses, operating 224 Stationary scraper excavator 344 expenses of railroads in U. S., Steam shovels operating 226, 227 fixed-platform 318 fixed-platform shovel, working arrangement 318 hmits of 325 body, car 321 head velocity of trains 244 equipment, excavating 321 motors for shovel capacities, equipment, power 321 sizes of 340 operation, cost of 327 operating a train 1 mile, average operation, method of 323 cost of 225 revolving-platform 332 resistance, locomotive 270 arrangement 332 standard steam shovel, sizes of 320 equipment, excavating 334 steam shovel service 328 equipment, power 333 steam used locomotive cylinders, operation, method of 335 weight of 268 platforms 332 various grades, values of C-^ (72+ Stringers 103 K) 258 Subaqueous rock breakers 408 various multiples of M, cylinder boat, drill 409 tractive power of 272 Lobnitz 408 wheel excavators, dimensions of 364 Surveys Templet excavator 358 location 24 Ties 127 preliminary 19 cost 129 railroad 11 cutting 129 reconnoissance 12 dimensions 128 Note. — For page numbers »ee foot of pages. 456 INDEX Page Page 'lies (continued) Trench excavators (continued) laying and reviewing 129 pipe-trench 414 spacing 128 tile-trench 434 wood 127 Trestles 97 Tile-trench excavators 434 floor systems 103 ditcher, Hoveland tile 435 framed 100 Tower cableway excavator 430 pile 97 Tower excavator 367 Trestle cable excavator 424 Track and track work materials 124 Trestle floor systems 103 ballast 124 corbels 104 bolts, track 138 fire, protection against 108 braces, rail 136 guard rails 105 joints, rail 133 stringers 103 nut locks 138 super-elevation of outer rail on rails 130 curves 106 spikes 136 ties, trestle 106 ties 127 timber, choice of 109 tie plates 135 Tunnel construction 95 Track bolts 138 general principles 95 Track laying 140 methods 96 ballast 140 Tunnel design 92 outer rail on curves, super-eleva- cross-sections 92 tion of 144 grade 92 practical rules 145 lining 93 rails 141 portals 94 surfacing 144 Tunnels, surveying 88 surveying 140 character of 88 ties 140 distance 89 Track maintenance 197 down shafts 91 ballast 205 levels 89 ditching 202 underground 90 labor, or organization of 209 surface 89 rails, distributing 204 Turnouts 155, 157 ties, distributing 203 Turntables 118 tools 197 trestle filling 207 V work trains 201 Vertical curves 57 Track trestle excavator 427 geometrical form 58 Transition curves 43 use 57 compound curves, use with 53 Volume of earthwork, computing 66 deflections 46 borrow pits 77 field work 56 center of gravity, eccentricity of 79 spirals in old track, inspection of 50 correction, prismoidal 75 symbols 46 curvature, correction for 78 systems 43 irregular ground, volume in 75 Traveling derrick excavator 414 methods, common 66 Trench excavators 412 prismoid, volume of 68 Note. — For page numbers see foot of pages. 457 INDEX Volume of earthwork, computing (continued) products, computation of sections, equivalent sections, irregular sections, level sections, three-level side-hill section, eccentricity of center of gravity of side-hill work W Walking drag-line excavator Walking scoop dredges Note. — For -page numbers see foot of pages. Page Page Water-supply 115 pumping 116 72 tanks 117 67 track tanks 117 73 Wheel excavator 362 66 69 Y 82 Yards and terminals 173 77 freight-yard with main tracks, connection of 176 proper design, value of 146 573 yards, engine 178 J70 yards, freight 174 458 i RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY BIdg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS • 2-month loans may be renewed by calling (510)642-6753 • 1 -year loans may be recharged by bringing books to NRLF • Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW FEB 1 9 2009 f DD20 15M 4-02 /V