CfnrneU UttioetaUg Siihrarg 3t((8ta, Hew fork ALEXANDER GRAY MEMORIAL LIBRARY ELECTRICAL ENGINEERING THE GIFT OF Cornell University Library TF 855.S54 1920 Electric traction and transmission engin 3 1924 004 603 290 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004603290 f C I- 'I 111 5 t MIf ( HI im [■■jU^uomiw I il=-.l Electric Traction and Transmission Engineering BY SAMUEL SHELDON, A.M., Ph.D., D.Sc. PROFESSOR OP PHYSICS AND BLECTRICAL e'nGINEERING AT THE POLYTECHNIC INSTITUTE OF BROOKLYN AND PAST-PRESIDENT OF THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS AND ERICH HAUSMANN, E.E., Sc.D. PROFESSOR OF PHYSICS AT THE POLYTECHNIC INSTITUTE OF BROOKLYN, AND FELLOW OF THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS SECOND EDITION, REVISED X27 Illustrations NEW YORK D. VAN NOSTRAND COMPANY Eight Warren Street LONDON CROSBY LOCKWOOD & SON 7 Stationers' Hall Court, Ludgate Hill 1920 Copyright, 191 1 and 1920, by D. Van Nostrand Company OTHER WORKS BY THE SAME AUTHORS DYNAMO ELECTRIC MACHINERY ITS CONSTRUCTION, DESIGN AND OPERATION A consolidation of the author*' former volume*. "Direct Current Machine*" and "Alternating Current Machine*." About 500 Pages. Illustrated. In Press PHYSICAL LABORATORY EXPERIMENTS for Engineering Student* PART I, MECHANICS, SOUND. HEAT AND LIGHT 134 Pages. 40 Illustrations. Postpaid, $1.25 TELEGRAPH ENGINEERING By PROFESSOR HAUSMANN 416 Pages. 192 Illustrations. Postpaid, $3.00 PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA, PREFACE TO SECOND EDITION. The favorable reception accorded to this book upon its original appearance and its extensive use for nine years in many colleges has demonstrated that the original plan was well-suited for student use. That plan has been adhered to in preparing the present edition. The chaotic condition of the world as a consequence of the war reflects itself in the traction enterprises at present, but it is safe to say that they will persist and that the problems of their reconstruc- tion will fall upon the engineers. As a fundamental prep- aration for this kind of work it is believed the present edition will prove serviceable. Polytechnic Institute, Brooklyn, N. Y., February i, 1920. PREFACE TO FIRST EDITION. The ultimate purpose of nearly all the professional efforts of an engineer is the attainment of efficiency in the utilization of labor, capital, and energy. To attain the highest efficiency in the construction and the subsequent operation of a complete installation requires a knowledge of the facts and a familiarity with the laws pertaining to these three factors. Decisions as to the selection of the type and the dimensions of an element, often attributed to the exercise of good judgment, are generally the specific results of the correct application of laws to all pertinent facts. The number of facts to be considered in determining the final elements of a complete electric traction system is enormous. As a consequence students and young engineers become bewildered and are unable to discriminate as to the pertinency or necessity of specific details. To meet this condition the present text has been prepared, it being believed that no other single published book meets it. The book attempts to present a perspective view of the design of a complete railway installation, from the cars to the power-station, to indicate the nature and sequence of the various entailed problems, and to suggest or illustrate methods for their solution. In preparing the text the determination of what to omit has involved nearly as much effort as of what to include. vii viii PREFACE A descriptive treatment of specific forms of structures has been avoided. On the other hand, a number of numerical illustrations of the calculation of economic magnitudes has been given. Again, the inevitable future extensive use of hyperbolic functions has claimed for them a brief but comprehensive exposition and their utiUty is demonstrated in connection with calculations relating to electric-wave propagation. Appreciation is hereby expressed of the services of Mr. G. I. Rhodes in making helpful suggestions and in reading the proofs of the sections on economic determinations. Polytechnic Institute, Brooklyn, N.Y. May I, igii. CONTENTS. CHAPTER I. Determination of the Number and Size of Cars for an Urban Road. ART. PAGE 1. The Engineer's Problem i 2. Tjrpes of Service i 3. Length of Track 2 4. Receipts 4 S- Number of Cars 4 6. Size of Cars , 8 7. Trains 12 Problems 14 CHAPTER II. Tractive Efport Required for Gar Propulsion. 8. Train Resistance 15 9. Grades 19 10. Curves 20 11. Acceleration 22 12. Braking 23 Problems 25 CHAPTER III. Types and Performance Curves of Motors. 13. Traction Motors 26 14. Direct-current Motors 27 15. Alternating-current Motors 28 16. Methods of Drive 41 17. Motor Curves 44 Problems 49 ix X CONTENTS. CHAPTER IV. Speed Curves. AKT. PAGE i8. Motor Limitations 50 19. Motor Capacity S^ 20. Speed , 51 21. Tjqjical Speed Curves 52 22. Data for Plotting Speed Curves. S3 23. Plotting Speed Curves S^ 24. Numerical Example S9 25. Distance Curves 66 26. Speed Curve Plotting with Grades and Curves 67 Problems 73 CHAPTER V. Railway Motor Control. 27. Direct-current Control 74 28. Rheostatic, Method 74 29. Series-parallel Method 7S 30. Starting Resistances 78 31. Numerical Example 87 32. Field Control 89 33. Alternating-current Control 90 34. Compensators 93 . 35. Induction Motor Control 96 36. Controllers 103 Problems : . . . no CHAPTER VI. Energy Consumption. 37. Current Curves in 38. Average and Effective Currents 112 39. Numerical Example 113 40. Effective Motor Current for a Trip ri6 41. Voltage Curve 118 42. Motor Heating 118 43. Energy for Direct-current Propulsion "120 44. Energy for Alternating-Current Propulsion 121 CONTENTS. xi ART. PAGE 45. Effect of Operating Conditions on Energy Consumption.. V -124 46. Gear .Ratio 130 Problems 132 CHAPTER VII. The Distributing System. 47. Classification of Conductors 133 48. Contact Conductors 134 49. Branches 135 50. Collecting Devices 140 51. Supplementary Conductors 142 52. Graphic Time-table , 147 53. Feeders 151 S4- Track Rails iSS 55. Negative Track Feeders . . . ; 1S7 56. Electrolytic Surveys 161 57. Alternating-current Distribution • • • • • 164 Problerfls 164 CHAPTER VIII. Substations. $8. Types of Substations 166 Sg. Direct Currents Received and Delivered . . 166 60. Alternating Currents Received and Delivered. ■ 168 61. Alternating Currents Received and Direct Currents Delivered . . . 169 62. Location of Substations ./...;. 17s 63. Numerical Illustration ;.........' 186 64. Auxiliary Storage Batteries .' 188 6s. Arrangement of Apparatus i8g 66. Portable Substations .■ :...'. ? 193 Problems ..../....' 197 ■CHAPTER- IX. Transmission Lines. 67.. Location of the Transmission Line 199 68.. Number of Phases :...... 201 69. Frequency 203 70. Economic Voltage r.. .,. 205 71. Numerical Illustration 2U xii CONTENTS. AKT. PAGE 72. Separation of Conductors , 213 73. Resistance of Conductors 220 74. Line Inductance 222 75. Hyperbolic Functions 224 76. Line Capacity 230 77. Equations of Wave Propagation along Wires 23S 78. Attenuation and Wave-length Coefficients 238 79. Current and Voltage Distribution on Lines 240 80. Regulation 243 8r. Numerical Illustration 244 82. Corona Loss 247 83. Lightning 251 84. Protection from Lightning 254 Problems 258 CHAPTER X. Power Stations. 85. Station Load Curves 259 86. Selection of Generators 261 87. Types of Prime Movers 263 88. Power Station Costs 264 Steam Stations. 8g. Engines and Turbines 265 go. Condensers 267 91. Boilers 270 92. Feed-water Heaters 272 93. Chimneys or Stacks 272 94. Buildings 274 95. Arrangement of Apparatus 275 96. Cost of Steam Stations 280 97. Operating Expenses 280 Hydraulic Stations. 98. Turbines 281 99. Water-power Development 288 100. Cost of Development 293 loi. Depreciation and Obsolescence 297 102. Relative Operating Expenses 299 103. Costs per Kilowatt-hour 299 Problems 301 ELECTRIC TRACTION AND TRANSMISSION ENGINEERING. CHAPTER I. DETERMINATION OF THE NUMBER AND SIZE OF CARS FOR AN URBAN ROAD. 1. The Engineer's Problem. — The problem of the electric railway engineer is the determination of the car equipment required to yield a proposed service, the char- acteristics of the low-potential distribution system, the location and capacity of the substation equipment, the characteristics of the high-tension transmission line, and finally the capacity of the main generating station. His report should include cost estimates of the various items of the electric railway system, probable operating expenses and approximate gross income on the investment. 2. Types of Service. — The object of a railway is the transportation of passengers or freight between any points on the road in accordance with a schedule which is pre- pared to accommodate the trafi&c most economically and to lead to a sufi&cient income on the original investment to the operating company. The probable location of a proposed electric railway is governed by purely local con- ditions, such as density of population, future growth of the community, and topography of the land. An approxi- 2 TRACTION AND TRANSMISSION. mate estimate of the length of a proposed railway and its subsequent income, as well as the determination of the nimiber and size of the cars or trains, may be obtained from government reports and other statistical sources. Electric railway undertakings are of three kinds, — new roads, extensions to existing railways, and electrifications of present steam railroads. Of these, the former will first be considered. A new electric railway undertaking may relate to an urban, suburban, or interurban installation. Frequently a single system will include all of these types of service. 3. Length of Track. — For a new urban street railway the economically feasible length of road will depend largely upon the population. Thus, curve i of Fig. i shows the number of miles of track per 1000 of population for various population Centers. This curve represents the data of the following table showing the relation of trackage and trafiic to population in groups of urban centers; it is taken from the Census Report on Electric Railways for 1902. The figures refer to single track, and for a double-track road the length of track is twice the length of the road. All centers over soo-,000 population. All centers between 100,000 and 500,000 population. TWenty-nine • selected centers between 25^000 and 100.000 population. Forty-six seleotted centers of less than 25,000 population. Total population ' served 10,274,470 4,998.89 •49 2.4S6.'542|27o 239-1 \, 5,380,647 3.SS9-82 - .66 994.327.8s3 184.7- 1,258,615 9SI-93 '. -76 I35i842,3i2 107.9 718,254 485 ,-93 , r . .. .68 49.179.49s Number of miles of ' track Miles of track per 1000 of population Number of passen- ' gers Number of rides . "per inhabitant... . NUMBER AND SIZE OF CARS FOR URBAN ROAD. The present population is, however, not the value to be, considered in determining the track factor, t> from this curve, but instead the population at some future time, this time depending upon the probable duration of the p ■(- < a. . o a. o • o o < \- 0.4 r<=,^ ^^ FiSi II p \ y 9j^ 1 > / / \ '. / 'V ^^C ^ / »£ic 22^ T / 1 240 200 I- z < m < X z 160 = 120 z 80 40 0.25 0.50 1.00 0.75, MILLIONS AVERAGE POPULATION. Fig. 1. 1.25 1.50 period of construction, the depreciation, and later pro- spective developments in electric traction. The popula- tion, N, at some future time may be estimated from the past -growth of the community. Thus, a curve of popula-. tion for, the last ooe hiindred years might be drawn and 4 TRACTION AND TRANSMISSION. extended, or a percentage increase of population may be assumed. A population value corresponding to a time ten years later offers a reasonable working basis. Then the number of miles of track, Z,, to be installed can be expressed as L = miles. lOOO 4. Receipts. — In the foregoing table is also given the annual number of rides per inhabitant for various popu- lation centers, the data showing that passenger traffic is comparatively greater in the larger cities. The riding habit of people increases from year to year as the com- munity grows, as its business, family and social life be- comes more complex, and as its facilities for intercommun- ication improve. Curve 2, Fig. i, shows the number of yearly passengers per inhabitant, or what may be termed the passenger factor, 7. Then the number of passengers per year can be written as Yearly passengers = Ny. The annual receipts, in dollars, R, of a traction company are evidently the product of the total yearly passengers into the fare, /, in dollars, or R =^"7/ dollars. In this country the usual urban fare prior to the war was five cents regardless of the distance traveled. For inter- urban roads the fare depends upon the distance traveled, varying from one to three cents per mile. 5. Number of Cars. — The determination of the num- ber of cars to install may be made by the aid of tables which show the income and operating expenses per car NUMBER AND SIZE OF CARS FOR URBAN ROAD. mile of a number of electric railways. The following table compiled by H. M. Beardsley gives such data for some electric railways in New York State for 1905. Herefrom the average income per car mile is 21.56 cents. Company. Albany & Hudson United Traction Co. of Albany . . . . Auburn and Syracuse Co Binghamton Ry. Co International Tr. Co. of Buffalo . . . Rochester & Eastern Cortland Traction Co E. W., L. & R.R. Co., Elmira City Ry., L. & R. Co., Fishkill. . . . Dunkirk & Fredonia Hudson Valley Ry. Co., Glens Palls Hornell Elec. Ry., Hornellsville . . . Ithaca St. Ry. Co., Ithaca King. Consol. R.R. Co., Kingston.. Orange County Trac. Co., New- burgh Ogdensburg St. Ry. Co I. C. & R. S. Ry. Co., Oneonta Income from operation. $200,671.65 1,714,848.82 268,507.78 258,819.85 3.694,339 01 212,668.51 49,139.86 192,921.47 41,474.56 44,457.88 499,148.09 16,919.70 91,817.90 123,632.92 119,270.85 27,240.09 103,862.05 Income per car mile. Cents. 28.50 22-35 25.12 20.14 25.16 27.88 22.95 16.06 24.17 2,6.92 25.89 9-3° 23.21 23.08 20.04 9.78 iS-97 Total expense per car mile. Cents. 24-30 IS-3S 16.24 11.23 14.90 21.36 16.06 11. 61 16.34 22.57 18.13 9.06 17.87 I4-S7 15-39 7.86 13-82 The following table presents information compiled by G. H. Davis and furnished by sixteen electric railway companies which represent both geographically and politi- cally nearly all sections of the United States and all con- ditions of operation. The values given are for the year 1910; the average passenger earnings per car mile being 27.31 cents. The growth of traction earnings in the larger American cities, together with the corresponding operating expenses on a car mileage basis are shown in Fig. 2, which was pre- pared by B. J. Arnold. It will be noted, for instance, that in Brooklyn the earnings per car mile (average for street TRACTION AND TRANSMISSION. a 11 ill 1 •SI •is 0.2 P •s u I'- ll Average revenue per passenger, including trans- fer, in cents. -1' III I 485.2 585.0 208.2 136.0 101.7 306.6 139 -7 no. 4 86.8 186.0 129.4 58.0 1330 41.6 627.6 330 53.362,500 37.537.433 27.80 28.77 *3-x 4-34 *3-3 3.12 3-62 3-89 *3-3 4.09 4.10 4.09 4-90 4-94 4.08 *4-2 4-15 4.07 20.0 2 3 4 S 6 7 8 9 10 S33.90S 465.786 373.740 347.469 516,152 233.65° 131,105 129,867 155.000 88,926 51,521 132,685 36,346 1,549,008 46,000 1,018,463 14.4 13.5 403,740 512,886 516,152 234,650 151,10s 216,867 185,000 13,812,813 *i5,377.ooo 24,229,010 9.346,183 6,895,421 4,068,502 9,538,867 27.42 31-50 30.75 28.86 26.14 28.70 23.84 26.14 12. 1 14.6 17.7 12.6 16. 1 8.3 18.0 14.0 12 60,521 140,000 71,346 1,993,400 46,500 7-8 13 14 IS i6 6,194,583 2,045,703 70,943,404 1,790,722 26.32 23.29 25-34 27.42 13-6 9-S 19-5 8.8 * Estimated. and elevated railway service) increased from 24 cents in 1902 to 29 cents in 1906 and then decreased to 26.8 cents in 1910. The total number of annual car miles to be operated is equal to the annual receipts divided by the annual income per car mile i?c„; this result, when divided by 365 days and the daily number of hours of operation, k, gives the number of car miles to be operated per hour. If this be divided by the schedule speed, V, in miles per hour includ- ing stops, there results the number of cars required for the service. The schedule speed is limited by city ordinance in many cities to 12 miles per hour or less. The smallest number, v, of cars required then, may be expressed as R ^ Nyf 565hVK„ 365 hVR,,^' NUMBER AND SIZE OF CARS FOR URBAN ROAD. •SONINaVB SSOMO S3SN3dy3 DN1iVy3dO U3M0d OKV NOiiviaodSNvai ^ .\ \ \ \ \ \ I \ \ A- \ \ \ \ \ \ \ \ \ 1 \ "'\ V \ \ \ \ °\ \ \ \ °'\ \ \ w \ \ \, \ , \ \ \ \ 1 I o \ t i \ \ '.?, > " t ?\ IT ° \ » " V \ IS\ \ \ V^^ .'(\ \l \ TT i \ \ \ V N . \ \i \ \ t "\ \ il:**\ \ s \ \ A^ R \-^ \ \ \ \ \ v^ \ 5\ r \\ p r ^ \ \° ^ \ \ \ \ %_ \ Vs r \ \ \^ \ \ \ ',\ \ h \ 'JX \ \ ^ \ \"^ \ s \ \ \ \ \ ^ \ \ «\ \ A \ VA^ \ \ \ \ , \% \\ \ t \ '$ \ \ \ \ \ ..1,1 \ V 9>. N^ l1 \ h i\ %- 't i '"' \ ^ A 9 U ^ q 'X \;\ \ \ \ \ \ \ \\ ml ['A s \ \ \ \ \ ks\ \s si '-\ ^ A \ \ \ \ S" \ \ d \ x' s^ ¥ \ \ ^V %)tf ,\ 4 \ ffl % i^ ■tV, r\ \ \ k ■\ \ m V- \ \'A', \ >-/»' \ Vi 1 y \ \ \ \ \ \ s \ \ v^ \ ^ \ \ CO \ \ \ \ \ \ '' \ CD \ \ \^ A \ \ \ , 1 lij Y<=> \ \ \ \ ?-%■? Ifl X 1— \ .y '\ ^\ \ \ X'"! n CO O) \.^ 1A \ ,# *°\ -ftr'l z en < CO f^-- \\ \ vV v^ L®t en ■o- < \iKS \ \\ \' ^A V^ °v 1 1 \1 A ^\ w \ si L 3 — z cr- < -i < \ °^'^\ A \ \^\ '« < \ pAW Ai-i s\j UJ z < m w^ %°\ b ir — > o q: ^M ,¥, w < o: ••s*- r \\ '^Ap^l < y \ \Vi ] \ 5 \i\ o o \\\^ m\\ ^ M\\\\ L llj _l , s ice «' < e4c^c^c-4c^— _ — — — ______ •savnoa Nomm ni s3SN3dX3 DNiivd3doaNvsoNiNav3 ssoao 8 TRACTION AND TRANSMISSION. 6. Size of Cars. — The number of passengers carried per year divided by 365 and the number of cars in service gives the average number of passengers conveyed by each car per day. The number of trips per day made by each car is found by multiplying the schedule speed by the number of hours the car operates daily and dividing by the length of the hne. The average number of passengers per trip is therefore ^ ^ NjL ^ NtR„, _ 365 vVh 1000/ When several lines are operated in the same district or city, the second member of this equation applies to each line of track-length L miles. With a single line the last member is applicable. The number of passengers riding in a car at different times varies widely, and it would be poor economy to em- ploy cars or trains of such size as to permit the average num- ber of passengers per trip, as obtained from the foregoing expression, to be seated at one time. Not all of these passen- gers ride the full length of the road, and again, others may stand. In a specific case information should be obtained, from records concerning similar cases, as to the average length of rides by passengers. Available data indicate that the average passenger ride, r, is from 2 miles to 4.5 miles. The length of track divided by the average length of ride determines the number of times that the car is refilled each trip. The average number of passengers per trip divided by this number gives the passenger capacity of a car as C = — = ^^"^ L ~ 365 vVh an expression which assumes uniform trafl&c conditions. With due consideration for the provision of additional NUMBER AND SIZE OF CARS FOR URBAN ROAD. 9 Fig. 3. Fig. 4. seats for the accommodation of passengers during the rush hours, the seating capacity of the car is thus determined. Climatic conditions and limitations as to the total amount of rolling stock determine the characteristics of car-body 10 TRACTION AXD TRANSMISSION. construction as to whether it shall be open, closed, con- vertible, semiconvertible, double-decked, or combination open and closed. Figs. 3, 4 and 5 show the character- istic forms of construction of convertible, " Narragansett " open, and scmicon\ertible interurban cars respectively. Fig. 6 (top) shows a pay-as-you-enter car which is being extensi\-ely adopted for congested urban traffic because it facilitates comfort, ingress and egress of passengers, and collection and conservation of fares. In non-congested traffic districts "one-man" cars. Fig. 6 (bottom), are being used, wherewith the motorman is the only attendant; naturally the cost of operation is reduced. The arrangement of seats, as to whether they shall be transverse, longitudinal, or partly both, is dictated by the type of serx'ice to be rendered. Transverse seats are far more comfortable for seated passengers and are essential in long-haul service. Longitudinal seats greatly facilitate ingress and egress of passengers, give greater comfort to standing passengers, and as a rule permit of a greater ratio of standing to seated passengers. In urban and frequent- NUMBER AND SIZE OF CARS FOR URBAN ROAD. 1 1 stop service facility of ingress and egress is of paramount importance in order that a high schedule speed may be mamtained. During the morning and evening rush hours the number of standing passengers frequently equals that of those seated. "■"/■t:;^"'^ .!ii i ) iii .....,,.4j.jUi. Fig. 6. 12 TRACTION AND TRANSMISSION. The weights of car bodies are always much greater than might be desired, but are necessitated in order to give adequate strength to withstand the rough usage of ordi- nary service and to give some insurance against collapse in case of collision. As will appear later, the first cost and expense of operation are dependent upon the total weight. The weight of passengers seldom reaches one-quarter the total weight. It is evidently desirable to reduce the weight of cars to a minimum consistent with adequate strength. The total weights of closed and semiconvertible cars of re- cent design are usually between 90 and 130 poundsper square foot of floor area, considering the floor area as the product of the length over bumpers by the width over belt rails. An analysis of the possible saving incident to the use of light cars in a group of street railway properties, having for 1 9 10 gross earnings of approximately $5,700,000, shows that of the 92.33 per cent of such earnings expended for all purposes, excluding dividends, including operating ex- penses 54.47 per cent, interest 24.74 per cent, taxes 7.12 per cent, depreciation 6 per cent, only 53.08 per cent is influenced by car weight or live weight transported. Of this the items particularly affected are cost of power, car and track repairs, interest and depreciation, which in the aggregate do not generally exceed 15 per cent of the gross earnings. Having decided upon the seating capacity of the car, its size and weight may be determined from the following table. The average weight of a passenger may be taken as 140 pounds. The weights of trucks as given include the weights of motors except where starred. NUMBER AND SIZE OF CARS FOR URBAN ROAD. 13 7. Trains. — In most of the large cities in the United States the traffic is so dense that the capacity of the largest car which it is practicable to employ is inadequate to meet conditions. It is customary therefore to operate trains of two or more cars. On surface roads a motor car connected with a trailer is often used and in southern cities it becomes possible to thus separate the colored and white people by assigning the trailer to the former passengers. In subways and on elevated roads lo-car trains are often operated. On the New York Municipal Railway each car accommodates 78 seated and 72 standing passengers, allow- ing 5 square feet of floor space to each standing individual. With cars of such size a number of doors should be provided so that the duration of stops will not be excessive. The cost of operation per car mile with trains is materially reduced by the use of side doors having remote-control CAR DATA. Type. Closed cars: Single truck Single truck Single truck Single motor Double truck Manhattan Elev I. R. T. Co. (steel).. N.Y. C. (steel) Open cars: 8-bench lo-bench i2-bench i4-bench-. Semiconvertible cars: Single truck Single truck Double truck Double truck Length of body. . Seating capacity. 16' 22 18' 20' 8" 24 32 28' 30' 8" 42' 44' 38 44 S8 60 so' 70 15' 8" 32 21' SO 60 30' 2" 70 18' 24 20' 8" 32 28' 30' 8" 40 44 Weight of body, pounds. 6,000 6.S7S i3,7So 11,310 26,725 22,000 56,300 85,100 6,37S 13.340 IS.2SO 20,300 6,640 10,240 15,120 19,500 Weight of trucks, pounds. 4,600* 4,825 S,I2S 7.050 14,500 15,000* 21,000* 21,000* S.iSo S.92S 11,250 7.SSO 4.900 5,100 10,450 10,800 14 TRACTION AND TRANSMISSION. automatic door-opening devices, which practice reduces the number of employees to one attendant per car. On suburban sections of electric railways the schedule speed is most frequently from 15 to 20 miles per hour and on interurban sections from 25 to 3,5 miles per hour. The highest schedule speed at present for limited interurban service is 55 miles per hour on a 36-mile run. At high speeds the energy consumption per mile per ton of car weight is much greater for a single car than for a train of several cars, and consequently economical interurban opera- tion dictates the employment of trains of several units in- stead of single cars. It is interesting to note that the traffic on an interurban railway is furnished principally by the inhabitants of the towns, the rural districts supplying only from about 20 to 30% of the total traffic. PROBLEMS. 1. How many cars, accommodating at a maximum 80 passengers each, should be used for a proposed electric railway for a city of the size indicated below.' The schedule speed is specified at 10 miles per hour over three parallel lines of equal length, the period of opermion to extend over the entire day. Take 4 miles as the average passenger ride, and assume the traffic at rush-hours to be five times the average traffic and to endure for about two hours morning and evening. The past growth of this city is indicated below: 1850 2,000 inhabitants i860 4,000 1870 8,000 1880 17,000 1890 42,000 1900 90,000 1910 200,000 1920 350,000 2. Plot a curve showing the relation which should exist between the population of the city just referred to in former years, and the number of cars necessary at those times. TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 15 CHAPTER II. TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 8. Train Resistance. — The determination of motor capacity for a proposed service involves a knowledge of the tractive effort to be exerted to produce the specified or assumed acceleration against the resistances offered by- windage, friction, grades and curves, and also information about the performance of various sized motors such as is usually embodied in motor characteristic curves supplied by the manufacturers. The tractive effort, or force exerted at the rim of the car wheels, required to propel a car at constant speed on a straight level track is only that neces- sary to neutralize at that speed the resistance offered to car movement by bearing friction, rolling friction and flange friction on the track, and wind pressure; these resistances are considered under the single term train resistance. Many empirical formulae based upon experi- mental data have been proposed for use in estimating train resistance. A consideration of the various components of train resistance mentioned above will lead to the formu- lation of a fairly reliable expression therefor. Bearing friction, resulting from the sliding of the sur- faces of the axles over those of the journals, follows the ordinary laws of sliding friction. It . depends upon the pressure between the surfaces, and increases slightly with speed. Rolling friction is due to deformation of the rails and wheel rims where they come in contact, and to un- l6 TRACTION AND TRANSMISSION. evennesses in the surface of the track. The energy con- sumed in overcoming rolling friction is theoretically pro- portional to the weight on the track and to the distance covered. The force required to overcome it should there- fore be constant. It is, however, generally assumed to increase slightly with the velocity of the train. Experi- mental data thus far obtained warrant the following expression for the tractive effort necessary to overcome bearing and rolling friction: R' = k^- KV, where R' is expressed in pounds tractive effort per ton of car weight, V is the speed in miles per hour, and k and K are constants. The value of k, since it depends upon the weight concentrated on the bearings, may be expressed in terms of train weight, W, in tons, and the expression k = ^^ VW gives results agreeing well with experimental values, the minimum value of k being limited to 3.5. Values of K obtained experimentally vary from 0.03 to 0.07 depending upon track conditions and type of equipment, the lower values being the more representative. For light equipment and poor conditions of track the use of higher values is desirable. The resulting expression for bearing and roll- ing friction may then be written simply as 50 V R' = -j= -\ pounds per ton. The principal component of train resistance at high speeds is the wind pressure on the moving car. Wind pressure varies approximately as the square of the car TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 17 velocity, as shown by numerous experiments. Therefore an expression for head-end wind resistance takes the form R" = k'SV- pounds, where S is the car cross section in square feet and k' is a constant denoting the wind pressure per square foot at unit speed, the value of which depends upon the shape of the car end. For cars with perfectly flat ends its value would be about 0.004 t^nd for cars of the pointed-nose design k' is as low as 0.0015, whereas for city and suburban cars of the usual types and for the modern electric locomo- tives a value of 0.0025 ma-y be taken with propriety. The wind pressure thus far considered is that on the car end, but there is also air resistance at the sides of the car or cars, which effect is particularly prominent in trains of several cars. There it becomes necessary to introduce a factor which takes care of this skin friction along the surface of succeeding cars, and it is usual to add 10 % of the head-end resistance as just obtained for each car follow- ing the first. Then, if n be the number of cars in the train, the tractive effort in pounds per ton of train weight is 50 V SV [ , n - il , p, = — \- h TT.; I + pounds per ton, a formula which combines the various expressions of the components of train resistance. Car cross sections may be taken as follows: 90 sq. ft. for 20- ton cars, 100 sq. ft. for 30-ton cars, no sq. ft. for 40-ton cars, and 120 sq. ft. _, for heavier cars. *A. H. Armstrong uses 33 and 500 as average values of the respective constants of the second and third terms in his formula. i8 TRACTION AND TRANSMISSION. Fig. 7 shows by curves the dependence of train resistance of single cars upon speed and weight of car as determined by the foregoing formula. As an illustration, determine the tractive effort per ton exerted by an electric train of one or more cars when run- / 1 // -i 50 1 7 / o K a. bJ a. i/i/ / 7 ' f Ay 7 o z / / / ' o 0. bl O Z /j h / / /: // < 03 m 20 / / '// / a. y V Y/ / < l_ 10 <^. <^ / ■i^ 20 40 60 MILES PER HOUR. Fig. "7. 80 100 ning at 6o miles per hour on a straight level track, assum- ing the weight of each car to be 50 tons and the cross- sectional area as 120 square feet. The tractive effort for a 50 , 60 , 120(60)^ . . ^- 60 single-car tram is — p= + — + ,„„ ^ ,^ Vso 25 400 X 50 per ton; and for a three-car train is = 31.1 pounds TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 1 9 V50X3 25"^400X50X3\^"^ 10 / ^^'^ pounds per ton. The formula for i?i is not suitable for car or train speeds less than about 5 miles per hour, for tests at speeds lower than this value have shown that the train resistance per ton is greater than the formula indicates. For example, tests by D. D. Ewing on a 27-ton interurban car showed that under varying track conditions a tractive effort of from 25 to 54 pounds per ton were required to start the car on a straight level roadway, the average being 40. To keep this car just perceptibly moving required 22 pounds per ton, which is about double the tractive effort needed at 5 miles per hour. The train resistance in tunnel and subway operation exceeds the value for trains run in the open because of increased windage. Various tests indicate that if the values derived from the preceding equation be increased by about 20 per cent., they will be found suitable for sub- way operation. 9. Grades. — If grades be encountered additional trac- tive effort must be exerted. If a car be on a grade of inclination a to the hori- zontal plane, Fig. 8, the com- ponent of its weight along the direction of motion is W sin a, the other compon- ent being balanced by the reaction of the rails. To maintain uniform motion up the grade a force equal and opposite to W sin a. must be exerted. For small values 20 TRACTION AND TRANSMISSION. of a, such as are met with in railway work, sin a = tan a approximately, whence grades may be expressed as the ratio of the vertical rise to the horizontal length of grade. It is customary, therefore, to consider that a grade of g per cent means a rise of g feet in a hundred feet. The tractive effort necessary to propel each ton of car weight up a one per cent grade is therefore X 2000, or 20 pounds, and to draw a car of W tons up a grade of g per cent with uniform speed requires G = 20 qW pounds tractive effort. For a down grade G is considered negative. For routes having numerous grades, g should be taken as the equivalent percentage grade. On the assumption that only half of the kinetic energy acquired by a car or train in descending a grade is utilized in ascending the next up-grade because of stops on grades, non-alternate distri- bution of up- and down-grades, and the necessity of braking to avoid excessive speeds, the equivalent up-grade may be expressed as 100/ hiX where hi and h^ are the respective sums of all the rises on up-grades and the drops on down-grades in feet, and L is the length of the route in feet. In building a roadway, grades should be made as small as is economical, so that the cost of operation over the grades will be less than the interest on the amount necessary to reduce the grades. 10. Curves. — Curvature of track presents additional resistance to the motion of a car because of increased flange friction. To neutralize this effect a larger tractive effort must be exerted, but since curves are usually of short length, this does not present a serious factor. Indeed TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 21 track curvature may be ignored in calculations of required torque unless such curves are numerous and very sharp. Sharp curves, such as occur with city traction systems, are generally rated by radius, but long curves are expressed in degrees, a one-degree curve being conventionally defined as one in which a chord loo feet long will subtend an angle of one degree at the center. Thus the radius of a 1 • -i i 1 ^6o X loo , ^ one-degree curve is qmte accurately "^ > or 5730 feet, 2 IT and consequently the number of degrees of curvature, c, of a curve, specified according to con- vention by radius R, Fig. 9, is c = ^^^ degrees. K Curve resistance is usually taken as from 0.4 to i.o pound per ton of train weight per degree of curvature, and ^8- 9- depends upon the speed of the train. Prof. E. C. Schmidt gives the following formula for curve resistance as a result of tests on a 28-ton car: C = 0.058 cV pounds per ton, where V is the velocity in miles per hour. When a car moves around a curve it experiences a cen- trifugal force which depends in magnitude upon the speed and mass of the car, and the degree of curvature. This force tends to derail the car by rotating its center of mass outwardly around the outer rail. To neutralize this ten- dency the outer rail is raised above the inner rail to such an extent that the plane of the track is perpendicular to the resultant of the centrifugal and gravitational forces acting on the car. 3 22 TRACTION AND TRANSMISSION. Let m = mass of car in pounds, v = speed in feet. per second, g = acceleration of gravity in ft./sec.^, and R — radius of curve in feet. Then —^ = horizontal centrifugal force, and mg = vertical gravitational force. An inspection of Fig. lo shows that the resultant of these forces will be perpendicular to the plane of the track when that plane makes an angle B with the horizontal such that 8 = tan~':=--- A road section devoid of curves is said to have a tan- gent track. 1 1 . Acceleration. — In the foregoing paragraphs only ^'*^' "" the torque to be exerted at the rim of the car wheels for uniform speed was determined. But in railway operation a number of stops must be made to allow passengers" to board or alight from the cars, or to take on or unload freight, and further, between these stops the velocity of the car must be such as to maintain the specified schedule. Thus the car must be accelerated, and later brought to rest. To accelerate a car requires considerable tractive effort. The force in pounds acting on a body weighing w pounds which produces a change of velocity of a feet per second . . . wa w , ^ m one second is f = — ■ = a pounds. Representing the weight of the car in tons by W, and the rate of accelera- tion in miles per hour per second by A, then the tractive effort required for acceleration alone is TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 23 „ 2000 PF 52804 „,. F = • 2 — ZTT' = 91-3 WA pounds. 32.2 60 X 60 To allow for the energy of rotation of armatures, wheels, etc., which is difficult of exact determination and which depends upon the construction of these parts, the constant 91.3 is replaced by 100. Acceleration rates of from | mile to 2 miles per hour per second are usual for cars and rapid- transit trains, while lower rates apply to locomotive-hauled trains. The greater the acceleration rate of a given equip- ment, the higher will be the schedule speed which can be maintained thereby. Limitations are imposed upon the maximum acceleration rate attainable by considerations of comfort to passengers, permissible starting current, and slipping of wheels on the rails. Thus the total tractive effort required at any instant for the propulsion of a car or train of total weight W tons may be expressed by the complete general equation l^ 25 400 L 10 J ' ^ + 0.058 F PFc I -f 100 WA pounds. Representing the expression in braces, which includes the effects of train resistance, grades, and curves, by Tj, pounds, and rearranging, the acceleration becomes A= '^-^^^ 100 W 12. Braking. — The kinetic energy represented by a moving car at any instant must be dissipated in some manner if the car is to be brought to a standstill at some later time. A force must in some manner be exerted between the roadway and the car, and must be in such a direction as to oppose and retard the latter's motion. The to static friction between 24 TRACTION AND TRANSMISSION. the wheel rims and the track rails where they are in con- tact. Two bodies with surfaces held in contact with each other by transverse pressure are capable of exerting forces upon each other along the direction of their plane of separation, which forces may be varied in magnitude from zero to such a maximum as will initiate slid- ing of the surfaces with respect to each other. This maximum usually bears a fairly constant ratio to the trans- verse force which presses the surfaces together, and is the coefficient of friction for the given materials of which the bodies are constituted. This coefficient for moving steel wheel rims on steel rails is, however, not constant because of the small areas in contact and the consequent enormous normal pressures, and because fresh surfaces are continu- ally becoming effective. This variable coefficient is also called the coefficient of adhesion, and, while it_may amount to 0.3 for clean dry rails, frequently sinks to|ai5 fpr wet rails, and may be subsequently raised tofo.25 byT;he application of sand. If the maximum retardation^ o^i: negative acceler- ation, which this coefficient 0.25 will permit, be represented by ^B, then the maximum retarding force or braking effort W Fb = 0.25 W = — Ab tons, g and consequently the retardation rate Ab = 0.25 g = 8.04 — ^ = 5.5 miles per hour per second. To bring this frictional force into existence the kinetic energy of the car must be gradually dissipated. This is usually accomplished by pressing brake shoes upon the rims of the wheels so that the energy is consumed in attri- tion and heating of the shoes. The pressure on the brake TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 25 shoes is attained through levers actuated by hand, by pneumatic pressure, or by electromagnetic forces. The energy is sometimes allowed to expend itself in rotating the motor shaft against an electromagnetic counter-torque, a portion of the energy being thus returned to the line. The coeflScient of friction between brake shoes and wheel rims decreases with increase of speed, of pressure, and of duration of application. The last is doubtless occasioned by the local elevation of temperature. To use the brake- shoe friction most effectually the pressure should, there- fore, be a maximum at high speed and be reduced with decreasing speed. This friction should never be so great as to cause slipping of wheels on the track, for the adhesion is thereby reduced and flat wheels may also result. PROBLEMS. 3. Calculate the total train resistance of a New York Central locomotive weighing 220,000 pounds when it runs alone at a uniform velocity of a mile per minute. Cross section of locomotive is 120 square feet. 4. Determine the tractive effort required to enable a train consisting of 5 motor cars and 3 trailers to climb a 3.1 % grade with a uniform speed of IS miles per hour. The weight of the trucks per car is 9 tons; the weight of motors and control equipment per motor car is 7K tons; and the weight of a car body is 21 tons. Each car can accommodate 80 passengers (aver- age weight = 140 pounds). 5. If a curve having a radius of 1500 feet existed on this section of the road, how much additional tractive effort must be exerted to maintain the same velocity? 6. Calculate the total tractive effort required to accelerate a car weigh- ing 30 tons, carrying s° passengers, at the rate of 1.3 miles per hour per second on a tangent level track. Take 140 pounds as the average weight of a passenger. Neglect train resistance. 7. Assimie a train to be running on a straight level track at 60 miles per hour and an adhesion of 0.25 to be available for making an emergency stop. Find the elapsed time and distance covered in making the stop. 8. Determine the proper elevation of the outer rail of a track for train speeds of 25 miles per hour, a curvature of 6 degrees, and a track gauge of 4 ft. 8}^ inches. 26 TRACTION AND TRANSMISSION." CHAPTER III. TYPES AND PERFORMANCE CURVES OF MOTORS. 13. Traction Motors. — An electric motor suitable for traction purposes must exert the necessary torque for accelerating the car at the predetermined rate, or to pro- pel the car up a grade, without causing excessive energy demands from the central station. This is possible only when large tractive efforts are exerted at low speeds, which follows from the fact that the power output of a motor is equal to the product of torque and, speed. Torque depends upon the field flux and the current in the armature of the motor. The former varies with the field current, and, in an unsaturated motor, would be directly proportional to that current, but in practice it is less because of magnetic saturation. The speed of any motor depends upon the field flux, number of armature conductors, number of pairs of poles, and the counter electromotive force generated in the armature; thus (E - 7J?) 60 X 10' ^"^ = ^^*5 '■^''- P^"" ""'"•' where E is the impressed E.M.F., la is the armature current in amperes, R is the motor resistance in ohms, in- cluding armature and all series coils, p is the p^irs of field poles, $ is the flux per pole in maxwells, and 5 is the number of armature conductors in series between brushes. TYPES AND PERFORMANCE CURVES OF MOTORS. 27 14. Direct-current Motors. — In a series direct-current motor the armature and field windings are connected in series and are traversed by the same current; therefore the torque exerted is roughly proportional to the square of that current. If a small current flows, the field strength will be low, and from the foregoing expression for speed it is seen that the speed will be high. Again, if the motor takes a large current, the field strength will be intense and consequently the speed will be low. Thus, a series motor exerting large torque runs at low speed, and when exerting little torque operates at high speed. It follows that the power consumption of a series motor does not fluctuate violently, and therefore is well suited for rail- way work. In the shunt direct-current motor the field strength is approximately constant, and therefore the torque is directly proportional to the current and the speed is practically constant. When a large torque is required from such a motor its power consumption is enormous, since the speed is not materially lowered. Consequently the central station supplying equipment of this kind would be subject to great load variations. For this reason shunt motors are not used on railways. The direct-current series motor operating at 500 or 600 volts has been in use since the advent of the electric railway. The commutating-pole series motor is now the standard for direct-current railways. Their use improves com- mutation, and permits the use of field control and high voltages. ■ Fig. 1 1 shows the circuital relations of this motor. The tendency being to reduce the initial investment of a railway system, its operation, particularly over long dis- tances, must be effected at high voltages, since the principal 28 TRACTION AND TRANSMISSION. item of expense is the distributing system itself. But com- mutation difficulties limit the voltage of direct-current railway motors. Therefore it is usual to generate a high alternating electromotive force, preferably three-phase, at the power house, and to supply alternating current at this high voltage to a number of substations where, by means of transformers and converters, this current is changed to ■ TROLLEY p. A- RAILS Fig. n. direct current, which is then supplied to the railway motors over the low-tension distribution system. Such genera- tion and transformation entail large initial investment and operating expenses, and also considerable energy loss. These items may be greatly reduced by employing alter- nating-current motors, which can be operated at a potential of several thousand volts. IS- Alternating-current Motors. — The advantages in- cident to the use of the alternating-current motor are the lower first cost of the low-tension distribution system, TYPES AND PERFORMANCE CURVES OF MOTORS. 29 the substitution of the simple and efficient transformer substation for the converter substation, and the reduction of the cost of operation. It is not advisable to employ high trolley potentials in cities or densely populated sub- urban districts, but for trunk line operation, requiring an infrequent service, economical operation dictates high trolley potentials; in many cases transformation to a lower motor voltage is effected by transformers on the cars or locomotives. In alternating-current traction, controller sys- tems may be utilized which do not entail the large energy losses incident* to starting direct-current motors. Three-phase generation is more economical than single- phase generation of E.M.F. The current from the former system may be converted into a two-phase current by means TROLLEYS Fig. 12. of a Scott transformer, each phase of which supplies single- phase current to the motors on one side of the station. Fig. 12 shows the scheme of connections. A single-phase load drawn from one phase of a large polyphase system unbalances the system for use otherwise. Phase converters or modifiers are used to restore this balance. There are several types of alternating-current single- phase railway motors at present in operation, but of these the compensated series motor is the only one used in this country. 30 TRACTION AND TRANSMISSION. Series Motors. — Consider a direct-current armature mounted within a single-phase alternating magnetic fields as in Fig. 13. When the armature is stationary an electro^ motive force will be induced in the armature turns, due to the alternating flux which passes between the field poles. The greatest E.M.F.'s will be induced in the turns perpendicular to the field axis, since these turns link with Fig. 13. the greatest number of lines of force; and no E.M.F.'s will be induced in the turns in line with the field axis. The directions of the E.M.F.'s induced in the armature turns by the change in -field flux are indicated in the figure by the full arrows, and it is seen that the maximum value of this E.M.F. is across BC. As in transformers, the effec- tive value of this electromotive force is „ 2 irf^„N Kt = — = — -' V 2 10* where $„ is the maximum value of the flux entering the (i) TYPES AND PERFORMANCE CURVES OF MOTORS. 3 1 armature and N is the equivalent number of armature turns. The maximum number of lines of force linked with a single turn depends upon the position of this turn in the magnetic field, and is proportional to the greatest value of $m times the cosine of the angle of displacement of the turn from the position AD. Assuming the turns to be evenly distributed over the periphery of the armature, the average value of the maximum flux linked with the arma- 2 ture turns will be - $„. If there be Na conductors on the armature, the number of turns connected in continuous N senes will be — -• The electromotive forces induced in 2 the upper and lower groups of armature turns are added in parallel, consequently the effective number of turns in I Na Na series between brushes is - — - = — . Therefore the 22 4 equivalent number of armature turns may be expressed as TT 4 2 TT Substituting this value of N in equation (i), the E.M.F. induced in the armature winding by the change in value of the field flux is Er = ^' ■ (3) and it lags 90° behind the field flux in time. If the brushes of the motor, A and D, are placed at the points shown in Fig. 13, this electromotive force will not manifest itself externally, since it consists of two equal and opposite components directed toward these brushes. This E.M.F. appears, however, in the coils short-circuited 32 TRACTION AND TRANSMISSION. by the brushes, as will be shown later. The current, which enters the armature by way of the brush and which traverses the two halves of its windings in parallel, pro- duces an armature flux of maximum value #„,„. This sets up a reactance E.M.F. in the armature which in the case of uniform gap reluctance can be similarly expressed as £. =%^' (4) V2 10* and lags 90° behind the current. When the armature revolves, there are, in addition, electromotive forces induced in the armature conductors as a result of their cutting the field flux. The directions of these E.M.F.'s are indicated by the dotted arrows, and it is seen that these E.M.F.'s, generated by the rotation of the armature, add to each other and appear on the com- mutator as a maximum across AD. The average value of the electromotive force due to the rotation of the armature in a bipolar field is V Erotav = ^/Na — lO ^ 00 where V is the armature speed in rev. per min. and $/ is the field flux; and the effective value of this E.M.F. is Ero. = ^^3 • ^' (S) and is in time phase with the field flux, but appears as a counter E.M.F. at the brushes AD. When an alternating current is passed through the field coils, the alternating field flux is set up, and this flux pro- duces a reactive E.M.F. in the field winding lagging 90° behind the flux in phase, exactly as in a choke coil. The magnitude of this E.M.F. is TYPES AND PERFORMANCE CURVES OF MOTORS. 33 Ef = 2 irf^tJJf (6) where */„ is the maximum value of the field flux, and Nj is the number of field turns. The electromotive force, E, which is impressed upon the motor terminals, is equal and opposite to the vectorial sum of Ea, E„t, Ej, and the IR drop of the armature and field windings, as shown in Fig. 14, where / is the current Fig. 14. flowing through the field and armature, and # represents the phase of the flux. In this diagram, eddy current and hysteresi% losses are ignored. The impressed electromotive force is therefore E = V(£„, + /^)2 + (£„ + £/^ (7) In the series motor, the same current passes through field and armature windings, and, if uniform reluctance around the air gap be assumed, then the armature and field fluxes will be proportional to the equivalent armature turns and field turns respectively. Representing by t the ratio 34 TRACTION AND TRANSMISSION. of field turns to effective armature turns ^am _ N Nj2T _ I $/m ~ Nf~ Nf ~ T (8) whence $/m = r^am. Substituting this value in (5), together with the equivalent of Ealf to be derived from (4), there results _ r F I V and Erot = ~r-^f'ZZ- fr •'60 Neglecting the armature and field resistance drop, the impressed E.M.F. shown in (7) reduces to ^=^V(^/+(^^+^)^ (9) which is the fundamental E.M.F. equation of the plain series motor. The power factor of the motor is cos = — = , ' (10) and the current supplied to the motor is equal to the arma- ture voltage Ea divided by its reactance, still neglecting motor resistance. Solving (9) for £„ there results , Ea E -A^il-^^^ + 1? TYPES AND PERFORMANCE CURVES OF MOTORS. 35 When V = 60/, the motor is said to run at synchronous speed (bipolar field). The power factor of a plain series motor, having t = i, when running at this speed, is — => or 0.446, and for values of r other than unity the power factor is Jess than 0.446. It is true that if the resistance of the motor be considered, the power factor will exceed this value, but nevertheless it remains extremely low. The current intake under these same conditions is — =r— • ■When the motor is at standstill, V = o, and the power p factor is zero. The current intake at standstill is -— r- 2 X„ Hence the ratio of the current at synchronism to the cur- rent at standstill is —= -f- - = 0.894. The ratio of the vs 2 torque at synchronous speed to the torque at standstill, since it varies as the square of the current, is (—7=-) -^ (-j = 0.80, which shows that the starting torque is but little greater than the torque at synchronous speed. Since for railway service motors are required having large start- ing torque and which torque rapidly decreases as the speed of the motor increases, it is seen that independent of its low power factor, the plain series motor, having uniform magnetic reluctance around the air gap, is unsuitable for traction and for similar purposes. If, however, the reluctance of the air gap in the direction AD, Fig. 13, be increased, the power factor and speed- torque characteristics will be improved, and these will depend largely upon the ratio of field turns to effective armature turns, as will be seen by considering the construe- 36 TRACTION AND TRANSMISSION. tion of the motor to be such that the proportion, equation (8), must be modified by introducing into its antecedents a constant considerably greater than unity. A motor of this kind, with few field turns compared to arma- ture turns, might be suitable for traction, but more important improvements have been made, which will now be discussed. It appears from Fig. 14 that the power factor of series motors may be increased by increasing IR and £„<, or by decreasing Ef and £„. It is obvious that increasing IR signifies an increase in losses, thus resulting in a lower efl&ciency. £„< can be increased by increasing the number of armature turns. Both Ef and £» can be decreased by lowering the frequency without affecting £„(, hence low frequencies are desirable. To decrease the reactive elec- tromotive force of the field, it is necessary that the reluc- tance of the magnetic circmt be low, i.e., small air gap and low flux densities in the iron, in order that the required flux can be produced by a minimum number of ampere- turns. The armature reactive E.M.F., Ea, is not essential to the operation of the motor, and can be neutralized by the use of compensating windings, and this feature of alternating-current series motors is a very important one. The compensating winding is embedded in slots in the pole faces, as shown in Fig. 15, which represents a West- inghouse four-pole compensated single-phase railway motor with its armature and field windings removed. The num- ber of turns of the compensating winding is adjusted so as to set up a magnetomotive force equal and opposite to that due to the current in the armature coils. The com- pensating winding may be energized either by the main current, by placing this winding in series with field and TYPES AND PERFORMANCE CURVES OF MOTORS. 37 armature, or by an induced current, which is obtained by short-circuiting the compensating winding upon itself, thus utilizing the principle of the transformer in that the main and induced currents are opposite in phase. The Fig. 15. former method of neutralizing E„ is known as conductive or forced compensation, and may be used with both alter- nating and direct currents, and the latter method is known Fig. 16. Fig. 17. as inductive compensation, and may be used only with alter- nating current. Figs. 16 and 17 show schematically the connections of the conductively and inductively compensated alternating- current series motors respectively. The compensating winding is preferably distributed so that the armature 4 38 TRACTION AND TRANSMISSION. reactance is neutralized as completely as possible. The current flows in the same direction in all of the conductors of the compensating winding embedded in one field pole, and flows in the opposite direction in the conductors em- l?edded in the adjacent poles. When the compensating winding completely neutralizes the armature reactance, the impressed electromotive force from equation (7) is E = V(£„, + IRy + £/, (12) where R is the resistance of the motor including that of the compensating winding. If R be neglected, then, since ^ro, = ^£/ and E = Ef^[ -'- ) + i, the power factor is -^A^.)' £.„, V cos (^ = —=- = , (11.) E VF2 + (6o/r)2 ^ -^^ The motor current is At synchronous speed V = 60/, and therefore the power factor at this speed becomes , Still neglecting the motor resistance, the current intake Et at synchronous speed is — — ' and at standstill it ■^f VI + T^ p is — ' consequently the ratio of the current at synchronous X; TYPES AND PERFORMANCE CURVES OF MOTORS. 39 speed to the current at standstill is Since torque varies as the square of the current, the ratio of the torque ,-2 at synchronous speed to the starting torque is -• Hence it follows that the speed-torque characteristics of a compensated series motor may be adjusted to the re- quired conditions by properly proportioning the number of armature and field turns. Repulsion Motors. — The repulsion motor, Fig. 18, has a field resembling the stator of the single-phase induction motor, and an armature which is similar to the armatures of direct-current and alternating-current series motors. The armature winding always remains short-circuited in a line incUned at a definite angle with the field axis, this being accomplished by means of brushes, bearing on the commutator, which are joined together by a conductor of low resistance. The field winding is supplied with single- phase alternating current. The fact that the armature and field windings are electrically distinct makes it pos- sible to operate the motor on high- voltage systems, the armature winding being so adjusted that the currents therein can be commutated satisfac- torily. The inclination of the short-circuit axis is essential to start the motor, for if perpendicular to the field axis the induced E.M.F.'s in the armature coils neutralize each other and there is no current, whereas if parallel with the field axis the torques on both sides of this axis are equal and Fig. 18. 40 TRACTION AND TRANSMISSION. opposed. Modified forms of this motor by Atkinson have two field coils displaced in space by 90 electrical degrees, that of La Tour, Winter and Eichberg omits the field coil, its function being performed by the armature winding, and that of Deri has an additional pair of short-circuited brushes which alter the speed when shifted. Induction Motors. — The three-phase induction motor may be used for traction purposes where the service require- Fig. 19, mcnts are of a constant nature, such as on long mountain grades. The induction motor is practically a constant- speed motor, the speed variation being less than about ten per cent of the no-load value, and therefore causes large energy demands on the central station. On the other hand, energy may be returned to the system when trains operated by them descend grades. This type of motor is adapted for heavy traction with infrequent stops. Two or three separate trolleys are necessary for such oper- ation. Fig. 19 shows the motors and the method of their mountings on the trucks on the locomotives used in the TYPES AND PERFORMANCE CURVES OF MOTORS. 41 Cascade tunnel of the Great Northern Railroad. Six thousand six hundred volts are dehvered to the locomotives from two trolley wires and the track rails, and are stepped down by transformers in the cab to 500 volts, which are impressed upon the motor terminals. 16. Methods of Drive. — Traction motors may drive the car wheels by means of gears, connecting rods, or driving pins. The first method is universally employed Fig 20 on street railways, the speed being reduced by a pinion on the motor shaft meshing with a gear wheel on the wheel shaft. Fig. 20 shows two geared G. E.-69, 200 horse- power direct-current motors mounted upon a truck, as used on the West Jersey and Seashore Railroad. The latter methods of drive are used in high-speed locomotive service. In the Pennsylvania electric locomotives the motors are mounted upon the frame and side-connected to driving wheels by a system of cranks and parallel connecting rods, TRACTION AND TRANSMISSION. TYPES AND PERFORMANCE CURVES OF MOTORS. 43 44 TRACTION AND TRANSMISSION. similar to steam practice. Fig. 21 shows a truck of one of these locomotives with the cabs removed so as to show the method of mounting the motors. The connecting rods and all reciprocating parts are counterbalanced so as to eUmin- ate pounding on the track. ■ In the New Haven locomotives the motors are mounted upon a quill surrounding the driv- ing axle, the torque being transmitted to the wheels directly by projecting pins on the armature structure engaging in sockets in the spokes of the driving wheels. Fig. 22 gives, at the top, two views of a quill, and at the bottom, two views of the quill in place upon the axle before the motor is mounted. In some installations, notably in the New York Central locomotives, the motor armatures are mounted di- rectly on the driving axle, being rigidly connected thereto. 17. Motor Curves. — The characteristic curves of a motor include curves of speed, torque, and efficiency in terms of the current flowing through the motor. Instead of using the speed- of the motor in revolutions per minute and the torque in pounds at one foot radius, it is usual in railway practice, to plot the speed of the car in miles per hour and tractive effort or the force exerted at the rim of the car wheels in pounds. The relations between these quantities are given by the following equations, where Vm = motor r.p.m., T = pounds tractive effort, iig and ftp are the respective numbers of teeth on gear and pinion, D = diameter of wheel in inches, T' = motor torque in lb. -ft., V = car speed in m.p.h. and eg = gear efficiency. The work performed by the motor while its armature makes one revolution is 2 irT'. When multiplied by the gear efficiency it also represents the work done by the trac- tive effort in turning the car wheel through the correspond- ing portion, fip/ug, of a revolution. Therefore, TYPES AND PERFORMANCE CURVES OF MOTORS. 45 2000 Fig. 23. 46 TRACTION AND TRANSMISSION. / / / / % E ^FICIENCY / / / ^ "^ /■ ■48 — \ / / / / •40 4 / \ f 1- ■32-^ -4000- i\ V / o DC UJ \ 'f Q. Q- > \ \ / 24 _j < 1- X >^ / m / / ' SP £E0_ / x' / 200 5 H.P. 50 V MO OLTS TOR X 3 GEAF 3"W ? RA1 1EEL 10 2 3, D-63 225 300 AMPERES Fig. 24- 450 TYPES AND PERFORMANCE CURVES OF MOTORS. 47 \ -80 — \ / -70 \ ~~^ t^ liVfg ^^10 trir. / / \ \ £ EFF,f / \ -60 / /■ \ y y ^ ^^ f- \ / / a. -50^ L- li- \b / z UJ tiJ > \ / UJ 0- 4 2 -2000- < ■> / ^ _J 7 ^^ ^/ A / / / 250 H.P !5 C-\ . MC CLES TOF / 2 6 25 \ 2"W OLTS -lEEL !. 2S0 750 1000 AMPERES Fig. 25- 1.250 1750 48 TRACTION AND TRANSMISSION. / -240 / leiE- / -21 Q ) — / ^ — ^ <^ ^ ' / y w ff.^ / / ' /' 1/ / / / 8G +&e( M / / _i / ( R-7-0 -1-20C LiJ [ 9 UJ Q-6-e- o / 25 H 300 P. MOT D Vo'lTS DR -90 e / / 2 3 CY 3 PH 3LES ASE / -60< / __^ / i ^ ^ ■^ -30( 1 / 0- ^ "" / / / 10 20 30 40 50 AMPERES PER PHASE Fig. 26. 60 70 TYPES AND PERFORMANCE CUR^'^ES OF MOTORS. 49 2 -KigV = 2 vDnj,T/2^ng foot-pounds. • '• T = 2^ngigT'lnpD pounds. Equating the effective power exerted by the motor to the power exerted by the tractive effort, 2 7rFmeBr'/33,ooo = 5280 Fr/6o- 33,000 horsepower. .'. V = o'.07i4 -~- Vm miles per hour. Figs. 23 to 26 show respectively the characteristics of G.E. 216A motor, of the motor used by the I.R.T.Co. of N.Y.C., of the Westinghouse compensated single-phase motors used by the N.Y., N.H. & H.R.R., and of an induction motor. PROBLEMS. g. Plot a curve showing the ratio of the current talcen by a compensated series motor at synchronous speed to that taken at standstill, cocJrdinated to the ratio of the number of field turns to the effective armature turns. ( io.~; The motor of an electric car having 33-inch wheels, when traveling at 25 miles per hour, exerts a torque of 550 pounds at one foot radius from the center of the armature shaft. If the gear ratio be 26 to 60, and the effi- ciency of the gears be 97 %, determine the tractive effort at the base of the car wheels, the horsepower, and the number of revolutions of the motor per minute. 11. Determine the horsepower output and speed of the induction motor whose characteristic curves are given in Fig. 26, when taking 50 amperes at 2850 volts. How many stator poles has the motor? 12. The gearless 2S-cycle, single-phase motors used on the New Haven locomotives have 12 poles. Determine the velocity of the locomotives, which have drivers 62 inches in diameter, when the motors run at synchron- ous speed. ( 13^ -The total weight of a Pennsylvania electric locomotive is 166 tons, of which 104 tons are carried by the drivers, and the trailing load is 550 tons. What is the maximum grade this train can ascend with uniform velocity without slipping the wheels on clean dry rails? Neglect train resistance. 50 TRACTION AND TRANSMISSION. CHAPTER IV. SPEED CURVES. i8. Motor Limitations. — The size of the motors to be installed on cars so that they may perform a proposed service must be such that the motors will exert the necessary tractive effort for the prescribed acceleration and operate without overheating. As the tractive effort exerted by a motor depends upon its current intake, and the maximum current which may be supplied to the motor depends upon commutation, it is seen that the rate at which a car -may be accelerated is dependent upon the allowable current input. Another limitation to the rate of acceleration, besides the consideration of comfort to passengers, is ex- pressed by the coefhcient of friction or adhesion, that is, the ratio of the tractive effort necessary to cause slipping of the wheels on the rails to the total weight on the drivers. This coefi&cient depends upon the condition of the track. The following values are approximate and are based upon a uniform torque exertion: Clean dryrails 0.30 Wet rails 0.18 (with sand 0.25) Sleet-covered rails 0.15 (with sand o . 20) Snow-covered rails o. 10 (with sand o. 15) It is seldoin necessary to apply motors to every axle, economy dictating that the number of axles equipped be as small as possible and as permitted by the coefficient of adhesion. In train operation some cars are equipped with motors while others are mere trailers without motors. SPEED CURVES. Si The heating of motors in service is determined by the square root of the mean square current supplied to the motor and the average voltage across the motor terminals. ^ This mean square current is obtained from a series of in- stantaneous current values taken over a considerable time interval, as shown later. Thus, a motor should be selected which will commutate the abnormal current taken during the period of acceleration without excessive sparking at the brushes and also perform the required service without excessive temperature rise. 19. Motor Capacity. — To determine the motor capac- ity for a proposed service, a knowledge of the load under which the motor must operate is essential. This load is of an exceedingly variable nature, fluctuating between no load at stopping points and a maximum load, which occurs during starting of the car. The method of procedure is as follows: a trial equipment is assumed (a guide to its selection may be obtained from a comparison of the equip- ments of similar existing installations), and from the motor performance curves there are plotted curves of speed of the car in traversing the entire roadway and of motor current. The former curve enables one to foretell if the prescribed schedule speed can be maintained, allowing a reasonable margin for making up delays, and the latter curve serves as the basis for determining whether the assumed motor can perform the required service without such extreme heating as to endanger the insulation. 20. Speed. — The velocity of a car in operation varies widely from time to time. Starting from standstill, the car is accelerated, rapidly at first, then more and more slowly until a uniform speed is attained. After running at this speed for a definite time, the current is turned oU 52 TRACTION AND TRANSMISSION. and the car is allowed to coast, the velocity meanwhile gradually decreasing. Finally the brakes are applied in order to bring the car rapidly to rest at the next stopping Fig. 27. point. Here freight or passengers are taken on or dis- charged; thereafter similar runs are performed. 21. Typical Speed Curves. — The velocity of a car at successive instants of time may be graphically portrayed by a speed curve, in which the instantaneous speeds are plotted in terms of time. Such a curve takes the form of a series of lobes, each one representing a run and one of which is shown in Fig. 27. The slope of the curve at any point indicates the time rate of change of speed. This slope may be positive, zero, or negative, corresponding respectively to acceleration, uniform speed, or retardation. The speed curve may be considered as made up of four parts as follows: starting, motor, coasting, and braking. The starting part corresponds to the period of manipula- tion of the controller, the acceleration of the car and the current in the motor being kept constant, while the voltage impressed upon the motor is gradually increased from zero to its normal value. The motor part corresponds to a SPEED CURVES. 53 gradual decrement of acceleration of the car and of motor current, normal voltage being impressed upon the motor. The coasting part corresponds to the movement of the car under its own momentum, no current passing through the motor. The braking part corresponds to the period during which the car is being quickly brought to rest by the absorption of energy at the brake shoes. The starting and motor parts are often considered together as constitut- ing the acceleration part of a speed curve. The ordinate B of the speed curve represents the max- imum velocity of the car during the particular run, and the horizontal line DE shows the duration of standstill at the subsequent stop. The schedule speed of the car is obtained by finding the area of the speed curve over the entire road- way and dividing by the total time taken therefor inclusive of stops. This time is the interval between A of the first run and E of the last one. The shorter the time of stops the greater will be the schedule speed, other conditions remaining unaltered. The greater the rates of acceleration and retardation the greater will be the schedule speed pro- vided the same maximum speed is attained. If the rate of braking be too high the car wheels will slide on the rails, and there will be a tendency for the car body to move ahead over the trucks. The maximum practicable braking rate is considered to be 2.5 miles per hour per second, t 22. Data for Plotting Speed Curves. — The plotting of a speed curve for a proposed equipment over a typical run requires a knowledge of the following conditions: Type of motor. Number of motors per car or train, Motor performance curves at full line voltage and at a definite gear ratio, 5 54 TRACTION AND TRANSMISSION. Total weight of the car with live load, Plan and profile of the roadbed, Schedule speed required, Rates of acceleration and braking, and Duration of stops. For single-car operation (double-truck cars) a four- motor equipment is preferable, whereas for train operation two-motor equipments are generally used, and sometimes both rhotors are placed on one truck. The performance curves of a railway motor show its characteristics at normal voltage under any load. When starting the series motor, the voltage impressed upon its terminals is low at first, and is gradually increased by means of a controller, which cuts out resistance or, with single- phase motors, decreases the ratio of transformation of a compensator. With suitably designed controllers properly operated the current supplied to the motors will be roughly uniform until the full line voltage is impressed upon the terminals of each motor. The torque exerted, being pro- portional to the current intake, will also be uniform. After the line voltage is applied to the motors, their performances are entirely dependent upon their characteristics. It is essential to have a reliable estimate of the weight of the tentative car for a proposed service, this weight to include live load, electrical equipment, and brake apparatus. Weights of car bodies and trucks are given in Chapter L The average weight of passengers may be taken as 140 pounds per individual. The weights in pounds of some standard 6oo-volt electrical equipments having commu- tating-pole railway motors, made by the General Electric Co. and the Westinghouse Electric & Manufacturing Co., for direct-current railways follow: SPEED CURVES. 55 Weight of Each No. of Type of 1 i-inl-ml Weight of Total Trade Name. H. P. Motor Including Control Weight of Gears and Case. v^oniroii Apparatus. Equipment. 2S8 25 88s 2 K-63 7SO 2520 4 ^■As 1285 482s 4 IS^ 133s 487s o 247 ... . 40 1740 2 K-63 755 423s CJ 4 ^■AS 1490 8450 o 4 PCt 1490 8450 S 2i6A* . . SO 288s 2 K-ii lois 678s jj 4 K-I4 2250 13790 u 4 t 2070 13610 "s 203 SO 2280 2 K-36 IICX) s66o c 4 K-3S 1520 10640 4 PCt 1600 10720 201 .... 65 284s 2 K-36 131S 700s 4 K-3S 1690 13070 4 PCt 1650 13030 .240 105 3840 4 K-64 2820 18180 4 PCt 1710 17070 ■ S06A . . . 25 913 2 K-63-B 750 2576 c3 4 K-3S-G-2 1228 4880 4 HLt 1610 5262 _ti S14C . . . 40 179s 2 K-63-B 822 4412 1 4 K-3S-G-2 1550 8730 ^ 4 HLt 1610 8790 S32B . . . SO 2340 • 2 K-3^J 1156 S836 4 K-3S-G-2 1654 11014 M ' 4 HLt 1769 1 1 129 ^ 306CV4. 6S 267s 2 ,?-3y 1191 6541 3 O 4 K-3S-G-2 1894 I2S94 J3 bo 4 HLt 2032 12732 .C S48C . . . 100 319s 2 K-35-G-2 ~ 1642 8032 S 2 HLt 164s 803s 1 4 HL- 2654 «S434 SS7A8 . . 140 4050 2 HL- 2105 1020S * Without commutating poles. t Multiple unit. The weights of single-phase motors somewhat exceed the foregoing values for the same capacity, but owing to their limited adoption up to the present time, the design of this type of motor has not yet become standardized. The dimensions of the car chosen for the proposed rail- way should be known, particularly those dimensions which limit the minimum permissible radius of track curvature, 56 TRACTION AND TRANSMISSION. the clearances on each side of the track at curves, and the maximum possible size of motor which can be installed on the truck. The physical characteristics of a roadway are usually embodied in a map and profile of the route showing the length of line, proposed regular stations, junctions and crossings with existing roads, switches and branch lines, and the location and extent of grades and curves. A subdivision of the total length of the road into city, suburban, and interurban sections can usually be effected. Different operating conditions obtain in these sections, because the schedule speeds and length and frequency of stops are not the same for all. Representative values for these factors follow. Service. Interurban express Interurban local City rapid-transit express Suburban City elevated or subway (local) City surface lines Schedule speeds in miles per hour. 35 to 60 25 to 40 20 to 30 15 to 20 15 to 20 8 to 12 Average dura- tion of stops in seconds. 60 30 2S IS 12 7 Number of stops per mile. o . 05 to o . 2 0.3 to o . 7 0.4 to I . o I t0 2.S to 3 to 10 The choice of gear ratio for the trial equipment should be such that' the peripheral velocity of the motor armature when the car is running at its highest speed will not be excessive. The ratio of the maximum speed to the schedule speed varies between 1.2 and 1.8, this ratio increasing as the runs become shorter and the duration of stops becomes longer. This enables the selection of the proper gear ratio. 23. Plotting Speed Curves. — To understand the method commonly used in plotting speed curves consider the dif- SPEED CURVES. 57 ferent portions of the curve in Fig. 28 and the following formula for the car acceleration (see § 11): A = ^^^ „„ , (i) 100 W where Tm is the tractive effort exerted by a motor, Tt is the train resistance per motor, and W is the weight of the car or train per motor. Then ^U-y^^ T^ = Tt + 100 W'A. (2) The starting part of a speed curve is taken as a straight line, and it passes through 0, the origin of time, at an angle Ba. with the horizontal such that 6 a = ta.rx'^A, where Fig. 98. A is the assumed constant rate of acceleration at starting. It terminates at the point A having a speed ordinate taken from the motor characteristic curves for full voltage cor- responding to the tractive effort T^ calculated from equa- tion (2), in which Tt is based on half schedule speed. The motor part of the speed curve is considered as made up of a series of elements which are themselves straight. The speed ordinate of the upper end of any element is 58 TRACTION AND TRANSMISSION. assumed, while that of its lower end is the same as for the upper end of the preceding element. This element makes with the horizontal an angle 6n = tan~'.4,., where A^ is the average of the accelerations corresponding to the speeds at the terminals of the element and each calculated by means of formula (i). The calculation of these ele- ments is greatly facilitated by two auxiliary curves, one showing the relation between motor tractive effort and speed and the other between train resistance and speed. The coasting part is generally assumed to be straight, although it really is concave towards the time axis. It is drawn from an assumed point B and makes with the hori- zontal an angle dc = tan~^ Ac, where .4c is calculated from formula (i), whose terms are based upon the speed V which is the ordinate of the point B. The other end, C, of this part of the curve is determined by the intersection with the remaining part. The braking part of the speed curve is also assumed to be straight, passes through the time axis at D corresponding to the specified expiration of the run, and makes with the horizontal an angle Bb = tan~*.4B, where ^b is the assumed rate of braking. The method just outlined assumes that equal distances along the two axes have the same numerical value; for example, if one inch along the horizontal axis of Fig. 28 represents 50 seconds, then one inch along the vertical axis must correspond to 50 miles per hour. If, for convenience, other than equal value scales are used, the parts of the speed curve cannot be constructed by laying off the angles as described, but instead, by measuring the horizontal and vertical components on cross-section paper according to their individual scales. Thus, in laying out the motor part of a speed curve, the abscissa increment, in seconds, for an SPEED CURVES. 59 element may be determined by dividing the speed incre- ment in miles per hour by the average acceleration in miles per hour per second, or symbolically At = AV/A. 24. Numerical Example. — The process of plotting a speed curve is best illustrated by considering a specific case, as follows: (o) Data. Car, single car to seat 40 passengers and to accommodate an equal number standing, weighing with trucks 23,650 pounds. Cross section, 5 = 95 square feet. 900 : 800 3 700 O a. z 600 : 500 '400 ■300 ■200 100 :^ V \ ^ \ \ X \^ ^^ 10 20 30 SPEED IN MILES PER HOUR. Fig. 29. 40 Trial equipment: four direct-current 50-horsepower, 600-volt G.E. 216A motors with Type K-14 control; total weight is 13,790 pounds, § 22. Characteristic curves of motors are shown in Fig. 23 for a gear ratio of 17 to 69. From these curves a new curve. Fig. 29, of tractive effort per motor and speed is plotted for convenience. 6o TRACTION AND TRANSMISSION Run, 0.8 mile run on a straight level track. Schedule speed = 20 miles per hour. Length of stop = 20 seconds. Initial acceleration rate = 1.5 miles per hour per second. Braking rate = 2 miles per hour per second. The total weight of the car with live load is W = 23,650 + 13,790 + (80 X 140) = 48,640 pounds f ,<.' ,K|/-^ = 24.32 tons, .i, ]fj The total tra& resistance fer ^' r- WV SW T-p = 50 VPF + —- + -— = 246 + 0.97 V + 0.238 W. Fig. 30 shows the relation which exists between the train resistance per motor Tt = T^./^ pounds and the speed V miles per hoi^r. C fj ^ J l//;y.[ru^' ^^- 160 CO a ,y ^ ^ Z3 0-120 z ^ y^ ^ V^ z H 80 CO -^ ■-^ ^^ z 5 40 a: H 10 20 30 SPEED IN MILES PER HOUR, 40 Fig. 30. SPEED CURVES. 6 1 (b) Acceleration at Subnormal Voltages. To produce an acceleration of i .5 miles per hour per second requires a net tractive effort of , , VV A 100 WA = 100 X 24.32 X 1.5 = 3648 pounds, or a net tractive effort of 3648 -r- 4 = 912 pounds per motor. To neutralize train resistance during the period of initial acceleration additional tractive effort must be exerted. The amount may be taken equal to the train resistance at half schedule speed, that is, at 10 miles per hour. Its value is found from Fig. 30 to be 70 pounds per motor. There- fore the total tractive effort to be exerted by each motor in starting is 7"™ = 912 + 70 = 982 pounds. This tractive effort is produced when each motor takes 64 amperes at 600 volts, as shown by the motor performance curves, Fig. 23 ; and the corresponding speed of the car is 16.9 miles per hour. Thus, the current consumed as the car is accelerated uniformly at the prescribed rate from standstill to a speed of 16.9 miles per hour is maintained roughly constant by the controller at a mean value of 64 amperes. The time required to attain this speed is — = — — =11.3 seconds. This represents the first point of the speed curve, and is shown at A in Fig. 31. Since the acceleration during the first 11.3 seconds of the run was approximately uniform, the speed curve over this interval may be drawn as a straight line, as OA . (c) Acceleration at Normal Voltage. The full line volt- age is applied to each motor when the speed of 16.9 miles per hour is reached, and thereafter the acceleration be- 62 TRACTION AND TRANSMISSION. comes less and less because the current decreases as the car speeds up and this results in a lower available tractive effort. Increased train resistance at higher speeds is also instrumental in lowering the acceleration rate. To obtain other points of the speed curve, the car is supposed to be running at some higher speed, say 20 miles per hour. At this speed the motor current will be 48.2 amperes, the total tractive effort will be 660 pounds per motor, and the train resistance will be 90 pounds per motor. The net tractive effort producing acceleration is 660 — 90 = 570 pounds; whence the rate of acceleration at a speed of 20 miles per hour is J- m -1 t A, = - „-7 = S7o-;-(iooX ) = 0.94 mile per hr. per sec. 100 W \ 4 / The average acceleration during the period in which the velocity of the car increased from 16.9 to 20 miles per hour may be taken without serious error as the mean of the initial and final acceleration rates of the period. The time required to gain this velocity increment is, of course, the increment divided by the average acceleration, which in this case is 20 — 16. Q ^.i , At = ; ^ = -^ — = 2.54 seconds. 1.5 + 0.94 1.22 2 Thus, the second point of the speed curve shows a veloc- ity of 20 miles per hour at 11.3 + 2.54, or 13.84 seconds (^ Fig- 31)- This process is continued with small velocity increments until the speed of the car becomes constant. A tabula- tion of the values so obtained follows; the various points are indicated on the curve. SPEED CURVES. 63 vnoH u3dS3iin 64 TRACTION AND TRANSMISSION. Speed. Tractive Train Net trac- Accelera- Total time. Point. effort, resistance, Ti. tive effort. tion rate, A. A 16.9 20 912 S70 I -50 0.94 11.30 b 660 90 13-84 c 22 S30 96 434 0.714 16.26 d 24 430 102 328 0.540 19 -45 e 26 360 108 252 0.4IS 23.6s f 28 300 "S i8s 0.304 29.22 e 30 2SS 122 133 0.219 36.88 h 32 220 130 90 0.148 47-78 t 35 170 I4S 25 0.041 79.6 J 36.8 152 152 177.0 {d) Braking. After plotting the entire acceleration curve of a car with an assumed electrical equipment for a partic- ular run, the speed curve is completed by drawing the coasting and braking curves. Since the time of passage over a se|ction of the road is specified by the schedule speed and the average duration of a stop, it is necessary to construct the braking curve first so as to determine how much coasting may be permitted and still bring the car to the next station in the required time. In the numerical illustration the car is to travel 0.8 mile at a schedule speed of 20 miles per hour, which means that the time required for this run is ^ = 144 seconds. 20 But this time includes a stop of 20 seconds; therefore the actual running time is 124 seconds. The braking curve may now be drawn through this point on the time axis at a slope corresponding to the braking rate and .extending to its intersection with the acceleration curve at F. It should be drawn as a straight line, and, since the braking rate is specified at 2 miles per hour per second, the line will pass through the point which indicates that the veloc- SPEED CURVES. 65 ity of the car is 2 X 10 = 20 miles per hour at a time of 124 — 10 = 114 seconds from the beginning of the run. (e) Coasting. Since the ordinates of a speed curve are velocities and the abscissae are times, the area of such a curve will be expressed in units of velocity X time, or — -; X time, or simply in units of distance. Thus, time in Fig. 31, the area of a large square is 10 miles per hour X 20 seconds = 200 mile-seconds per hour = ^Vt/V or ^» mile. The area enclosed by a speed curve is therefore a measure of the distance traversed by the car. The speed curve drawn thus far allows for no coasting, and the area enclosed thereby may be less than, but in general will exceed, that representing a run of 0.8 mile. For a run of this length the speed curve must enclose exactly 0.8 ^ tV = 14.4 large squares. In order to obtain just this area, the position of the coasting curve BC is varied until properly located; its slope, however, cannot be taken at random. When the current supply to the motors is discontinued the car tends to run at constant speed, but train resistance retards the motion and produces a negative acceleration. As train resistance depends upon the speed, the coasting curve will not be strictly a straight line, but will have a slight curvature tending to become more nearly horizontal at lower speeds. It is usual to draw the coasting line straight and at a slope corresponding to the train resistance value at the speed at which the car is running when the power is cut off. The coasting curve is drawn at the proper inclination in a trial position and the resulting area of the speed curve is determined. If the area be different from the proper 66 TRACTION AND TRANSMISSION. value the line is shifted parallel to itself up or down as the case may be, until the enclosed area is found to be correct. Should the coasting curve require considerable shifting so that it commences at a somewhat different speed value, then its inclination must be redetermined on this basis. The area of the curve AFD of Fig. 31 is 16.8 large squares, and the position of the coasting curve was adjusted so that the enclosed area ABCD is equal to 14.4 squares; thus the speed curve truly depicts a 0.8 mile run. The train resistance at the speed where coasting begins is 130 pounds per motor. The negative acceleration produced thereby is -r^ r = 0.21 mile per hour per 100 X (.24.32 -T- 4) second, a value giving the proper slope of the coasting line. Had the area of AFD been less than 14.4 squares, the curve would have indicated that the chosen equipment is incapable of maintaining the specified schedule speed under the given conditions. In such cases other curves should be drawn for the same equipment with lower gear ratios, or for other equipments comprising larger motors. On the other hand, if the excess area be unduly large, other speed curves corresponding to higher gear ratios or smaller motors should be constructed. A reasonable margin should, however, be allowed for making up for delays. The equipment ultimately selected for the given service should be able under emergency conditions to make a complete trip in 5 to 15 % less running time than that allowed for regular service. 25. Distance Curves. — Speed curves of cars over runs having grades or curves are more difficult to construct than those over a tangent level roadway. Here the addi- tional tractive effort required for propelling a car or train SPEED CURVES. 67 up a grade or around a curve must be considered, and indeed, these additional forces are applied at definite places on the run. This implies a knowledge of the exact location of the car at every instant of time, so that these influences may be properly represented on the speed curve. The instanta'neous positions of a car are shown most con- veniently by a distance curve plotted in terms of time. The distance curve for the run mentioned in the fore- going is plotted as follows: The average velocity over the first 1 1.3 seconds of the run is i (o -f- 16.9) = 8.45 miles per hour, and therefore the space traversed during this . J. II. 3 X 8.4s .■, 05.4X5280 ^ _ ,^ period IS — =^- ^ mile, or ^^ ^ -^ = 95.4 X 1.467 3000 3000 = 140 feet. The average velocity over the next 2.54 seconds is i (16.9 + 20.0) = 18.45 miles per hour, and the dis- tance traveled during this time interval is 18.45 X 2.54 X 1.467 = 68.6 feet. This process is continued over the entire running time, and the final sum should be equal to 0.8 X 5280 = 4224 feet. The speed and distance curves are generally plotted si- multaneously, using for ^ L isso- -i "^ convenience the same time i;;;^"^^-;; ^ increment values. 26. Speed Curve Plot- ting with Grades and Curves. — As an illustra- tion of the method of plotting speed curves over runs having grades and curves, consider the same car and equipment making a 0.9 mile run over a roadway the plan of which is shown in Fig. 32 ; all other conditions to remain imaltered. Fig. 32. 68 TRACTION AND TRANSMISSION. As before, to produce an acceleration of 1.5 miles per hour per second on a level track requires 1.5 X 100 X =912 pounds per motor, 4 and to overcome train resistance 70 pounds additional must be exerted. But as the car must be accelerated on a 2.3 % up grade, a further tractive effort must be exerted amounting to 20 X 2.3 X 6.08 = 280 pounds per motor. This total force of 1262 pounds is produced when each motor takes 77 amperes, as obtained from Fig. 23, and this current value is maintained moderately uniform until the motors operate on the full line voltage of 600 volts, which occurs when the car has attained a speed of 15.3 miles per hour. The time required therefor is -^^ = 10.2 seconds, .1-5 and the distance traversed during this interval with uni- formly accelerated motion is -^^^ X 10.2 X 1.467 = 114 feet. 2 These values constitute the first points respectively of the speed and distance curves for this particular run, and are shown at A and a' on the curves of Fig. 33. When the speed of the car has reached 18 miles per hour the total tractive effort exerted by each motor is 840 pounds. The grade resistance is still 280 pounds, but the train resistance at this speed is now 84 pounds per motor. There- fore the net tractive effort producing acceleration is 840 — (280 + 84) = 476 pounds; whence the rate of acceleration at the instant the velocity of the car is 18 miles per hour is 476 100 X 6.08 = 0.78 mile per hour per second. SPEED CURVES. 69 o o o ±33J O o o o o o o CO o o o o o o ? ^-" Y _^--'' \ ' -2-'"' ^54-""^ J. _I^ ' -l5^ / -d^ -J \ \ 2 I V -.^ \ ^ 2 i s^^ 2 t \ -f\ M z ^v -4 ^%^ V t ^% \4 Z$S. XL \ 3^ HX C \ ^ ^^ A ~f«^. ^-^ ^^ ^^ 35 - - . - ^. , -\ ^ V 1b- X I "S -^ \ t^il >>!, ^V ^ ^^ ^i- <^^ \ ~-~-n o o CO rf o CO o CM CO unoH a3d S3nm 00 7° TRACTION AND TRANSMISSION. The time required for the car to gain this velocity incre- ment of 2.7 miles per hour is 2.7 -j- i (1.5 + 0.78) = 2.36 seconds, and the space traversed during this interval is 2.36 X i (15.3 + 18.0) X 1.467 = 57-5 feet. Thus, 12.56 seconds after the car started from rest it acquired a speed of 18 miles per hour and covered a dis- tance of 1 7 1. 5 feet. These values constitute second points respectively on the speed and distance curves, and are indicated at b and b' iri Fig. 33. Other points are similarly determined, as noted in the following table, the process being continued until a distance of 800 feet has been passed over by the car. At this place the grade ceases and the remainder of the run is on a level track. 1 ^^1 > ■8" f 'P P i "73 |s CO A 15-3 18 1262 1-50 0.78 10.2 10. z 1 14.0 1 14.0 171-S b 840 84 476 2.36 12.56 S7-S c 20 660 90 290 0.48 318 IS -74 88.6 260.1 d 22 530 96 1 54 0.25 S-48 21. 22 168.9 429 e 24 430 102 48 0.079 12. IS 33-37 409 838 Cl 239 43S 102 S3 0.088 II. 21 32-43 376 80s It is seen in the table that point e was corrected in order to approximate the distance of 800 feet more closely. Beyond the grade the net tractive effort for producing acceleration becomes larger by the amount of 280 pounds per motor, and thus the speed of the car increases more rapidly than before. Continuing the tabulation until the SPEED CURVES. 71 car strikes the curve, there obtains (compare with points e to hoi table of § 24) the following: 4 ii (0 CO II "^1 Si II ■8" II 1 ■3 C/3 '•3 gj / 26 360 108 252 0.41S 8.3s 40.78 30s IIIO s 28 300 "S !«.■; 0.304 5-57 46.3s 220 1330 h 30 2SS 122 133 0.219 7.6s 54. 326 1656 » 32 220 130 90 0.148 10.90 64.9 495 2151 J 34 i»S 139 46 0.072 18.20 83.1 880 3031 Ji 33-3 198 135 03 0.104 10.30 7S-2 493 2644 Since the car encounters a curve after running 2650 feet, a readjustment of point j of the speed curve was neces- sary, because after passing this place the rate of accele- ration of the car decreases since some tractive effort is required to neutralize the increased flange friction. Taking this as 0.5 pound per degree per ton for simplicity, the additional tractive effort is -^V/X 6.08 X 0.5, or 36 pounds. The length of the curve is 480 x -f- 2 = 754 feet; that is, the curve ends at a distance of 3404 feet from the starting point. The figures in the following table refer to the car movement on the curve of 480 feet radius. ^1 i p. CO ^1 1 II )f 1 •3 to .a k 34 34-2 i8s 181 139 145 10 0.0165 11.62 24.22 86.82 III. 04 573 1212 3217 4429 Had the curve extended over a greater distance the ulti- mate velocity of the car thereon would have been 34.2 miles 72 TRACTION AND TRANSMISSION. per hour; but the curve ends before this velocity is acquired and thereafter the car runs on a tangent level track. The time when the car emerges from the curve is shown by the distance curve of Fig. 33, and the. acceleration curve from this time on may now be completed along the lines previ- ously outlined. The braking and coasting curves are then drawn in their proper positions, so that the enclosed area truly represents a 0.9 mile run. The completed speed curve is shown as ABODE in Fig. 33. By reference to this curve it is seen that the power is cut ofE from the car when its velocity is 32.1 miles per hour and when it has been running for 65.6 seconds. Dur- ing this time the car traveled 2175 feet, as indicated by the distance curve. While the car is coasting for 67.4 seconds it passes over 67.4 X i (32.1 -h 17.9) X 1.467 = 2465 feet. Thus the brakes are applied when the car is distant 4640 feet from the starting point. The time required to bring the car to rest from a velocity of 17.9 miles per hour at the prescribed rate of braking is 8.95 seconds, and the distance traveled during this period is 8.95 X -^ X 1.467 = 117 ft. 2 , . Thus the total length of the run as determined by summa- tion of the separate distances is 4757 feet, a value which exceeds the true length of run by but 5 feet. Distance curves therefore serve as admirable checks in the plotting of speed curves. SPEED CURVES. 73 PROBLEMS. 14. Plot a complete acceleration curve of a car weighing 20 tons with live load and equipped with two so-horsepower, direct-current motors whose characteristic curves are given in Fig. 23. TJie initial acceleration rate is to be 1.3 miles per hour per second and the schedule speed is specified at IS miles per hour on a tangent level track. What is the maximum possi- ble velocity of this car on such a roadway? 15. Complete the speed curve of the equipment mentioned in problem 14 over a |-mile level roadway, allowing a 15-second stop at the following sta- tion. The braking rate is specified at 1.5 miles per hour per second. 16. What is the shortest running time that a motor car weighing 43 tons total with passengers and equipped with two 200-horsepower, 550-volt, direct-current motors whose characteristic curves are shown in Fig. 24, can complete a one-mile run up a uniform grade of 1.5 %? The acceleration and braking rates are 2 miles per hour per second. (^17]? An 8-car New York Subway train having five motor cars each equipped with two 200-horsepower, 550-volt motors, weighs 320 tons in- cluding live load. The characteristic curves of the motors are shown in Fig. 24. Plot the acceleration portion of the speed curve for an initial accekration of two miles per hour per second on a tangent level track. /l8A If the schedule speed of the train in the foregoing problem is 25 miles pet-hour and the rate of braking is 2ljniles per hour per second, com- plete the speed time curve of problem 17 for a run of i^ miles, allowing a ten-second stop. 74 TRACTION AND TRANSMISSION. CHAPTER V. RAILWAY MOTOR CONTROL. 27. Direct-current Control. — The motor-control equip- ment of an electric car or train serves to regulate the speed and direction of rotation of the motors and to govern their action during periods of initial acceleration. The most important function of a railway motor controller is to maintain a sufficiently uniform change of velocity during initial acceleration, due consideration being given to the durability of the apparatus and to the comfort of passengers. Thus the variations in the starting current from the aver- age value necessary to produce the required tractive effort for the specified rate of acceleration must be so restricted that the accompanying fluctuations in torque will not be injurious to the equipment or unpleasant for the passengers, and the maximum current attained will not give rise to commutation difficulties. With direct-current series motors two general methods of control are in use: i, rheostatic control, and 2, series- parallel control. 28. Rheostatic Method. — In the rheostatic method, for use with one or more motors, resistance is connected in series with the motor circuits, which is varied so as to regulate the voltage impressed upon the motors. A scheme of connection for a rheostatic railway controller is indicated in Fig. 34. Successive portions of this resist- ance are short-circuited by closing switches i, 2, 3, and 4. RAILWAY MOTOR CONTROL. 75 in the order named, thus gradually increasing the pressure applied to the motor terminals. This method, although sim- ple, is infrequently employed because the loss in the regulat- ing resistance is not conducive to economical operation. /. -O O-pO O-r-O O-T-O 0-1 m^ — I Fig- 34- 29. Series-parallel Method. — The series-parallel method of railway motor control is extensively used for equipments with two (or any multiple of two) motors. The car is started from rest and accelerated by first placing the two motors and a resistance in series and then cutting out the resistance step by step until the motors are operating in series on full voltage. Since with all the resistance cut out there is no unnecessary V-R loss, this is called a running connection, and the controlling mechanism is said to be on a running point. To increase the speed further, the motors are placed in parallel, with a resistance in series with both. This resistance is then cut out step by step until the motors are each operating on the full line voltage. This also constitutes a running connection. The circuits of a series-parallel controller are more com- plex than those of the rheostatic type, since additional con- nections are required to effect the transition from the series to the parallel position. For accomplishing this change three different methods may be used. Their distinctive features are respectively (i) the shunting or short-circuit- ing of one of the motors; (2) the opening of the power 76 TRACTION AND TRANSMISSION. circuit; (3) the maintenance of full current through all motors during transition. Most of the so-called Type K controllers, ordinarily used with single-car equipments, operate according to the first method, the successive steps of which are essentially as follows : the starting resistance is gradually cut out until the motors operate in series on full line voltage ; thereafter a portion of the total starting resistance is reinserted in series with the two motors, one of which is then shunted or short-circuited, thus connecting the other motor across full voltage but with a protective resistance in circuit. The short-circuited motor is thereafter connected in paral- lel with the other, the resistance now being in series with both motors; this resistance is subsequently cut out in suc- cessive steps. The second method of series-parallel control, that of opening the power circuit during transition, exemplified by Type L controllers, is merely an extension of the first, intended for use with motors of very large capacity. This method is now rarely employed because of its inferiority to the third method, which has been developed to meet the same requirements more effectively. The third method of transfer from the series to the parallel position is used with multiple-unit control, and also appUed to a few Type K controllers designed to meet the exacting conditions associated with large motor capacity and high voltage. During transition, full current is main- tained through all the motors by means of a "bridge" connection. A scheme of connections illustrating th's type of series-parallel control is shown in Fig. 35. The controller performs the following operations: switches A and B are closed, thus placing both motors and all the RAILWAY MOTOR CONTROL. 77 resistance in series between the trolley or third rail and ground. This connection, which corresponds to a slow speed that is suitable for switching in terminal yards, is passed over quickly when accelerating at the usual rate. The first movement of the controller handle accomplishes the simultaneous closing of switches s, 6, and 7. Switches i to 4 are then closed consecutively, followed by the closing of switch C and the subsequent opening of switches 2 to 7 and B, thus connecting the motors in series across the line 4§i: 1 2 3 4 1-00— I ^-^ 1-0 O-p-O O-pO 0-1 -J-WNAMzf M jZl— vAilib WV-^AAaJ-^WVA -O Fig. 35. through the "bridging" switch C. Thereafter switches a and b are closed. Thus two currents will flow through switch C in opposite directions, one from the trolley through the motors to ground and the other through the resistance to ground. With properly proportioned resistances prac- tically no current will pass through C, and consequently this "bridging" switch may be opened, thereby placing the motors in parallel, with resistance in series with each. After this, switches 2 and 5, 3 and 6, and 4 and 7 are closed progressively, thus finally placing each motor on full volt- age. This method is desirable in that no motor is sub- jected to a sudden increase in voltage nor is the circuit opened at any time. Unnecessary variations in torque are therefore avoided. 78 TRACTION AND TRANSMISSION. When four motors are installed on a car, they may first be connected in series, then each pair in parallel with the two groups in series, and finally all connected in parallel; this is known as the series, series-parallel, parallel method. Usually, however, the motors are arranged in two groups, each con- sisting of two motors permanently connected in parallel and treated as a single unit in so far as their control is concerned. 30. Starting Resistances. — The design of starting re- sistances for use with railway controllers requires a knowl- edge of the allowable variation in torque during accelera- tion. When a motor is started from rest with resistance in series, the current gradually decreases with increase in speed because of the generation of more and more counter E.M.F., until a portion of the resistance is cut out, caus- ing a sudden increase in current. Thereafter the current gradually decreases again with further increase in speed until another portion of the resistance is cut out, which causes a sudden rise in current as before. This current fluctuation continues until full line voltage is applied to the motor terminals. These current variations produce corresponding variations in torque, which, if violent, cause unevenness in the velocity increase of the car, resulting in discomfort to passengers and in severe mechanical stresses on the apparatus. Experience shows that, in general, the maximum and minimum values of torque should not differ from the average value required to produce the prescribed acceleration by more than ten per cent of such average value. Since the iron of a direct-current series motor ap- proaches saturation when taking the large current required for starting, the torque exerted is approximately proportional to the current. Hence the current is restricted to a similar range of variation. RAILWAY MOTOR CONTROL. 79 Fluctuations in the current supplied to a series motor affect its field strength and thus produce changes in the counter electromotive force generated, which must be considered in designing the controller resistances. The necessary information relative to these changes of counter E.M.F. is obtained from the saturation curve of the motor, a curve which shows the electromotive force generated in the armature as a function of the field (or armature) current when the machine is driven at constant speed. This curve is readily computed from the resistance of the motor and its characteristic curves. The electromotive forces corresponding to any given values of current evi- dently bear the same relation to each other whatever that constant speed may be. Rheostatic Controllers. The proper resistance units for a rheostatic railway controller may be determined as follows: ' Let E = line voltage, i2„ = resistance of motor, ri, r-i, rs, . . . , r„ = the respective controller resistances in series with the motor when the controller arm is on contact studs I, 2, 3, . . . , «, Fig. 36. £2, E3, . . . , En = the respective counter electromotive forces generated at the instants when the arm makes contact with studs 2, 3, 4, . . . , w, El, E2, . . .,£„'= the respective counter electromotive forces generated at the instants when the arm breaks contact with studs I, 2, 3, . . . , », 8o TRACTION AND TRANSMISSION. I = average current necessary to produce the required tractive effort for the prescribed rate of accel- eration, /max = maximum current value and /min = minimum cur- rent value as dictated by the allowable range of current variation, Fig. 36. £n = the electromotive force corresponding to the cur- rent /max as determined from the saturation curve. Fig. 37, Ejnm = the electromotive force corresponding to the cur- rent /mil, Fig. 37, and for convenience let ■*-'min and K = -'mm At the instant when the arm touches stud i, the resist- ance ri should be such that the current flowing through the motor will not exceed /max; then RAILWAY MOTOR CONTROL. 8i / ^ (l) ■'™« ~ „ 1 D ' whence the total resistance of the rheostat is Fig. 37. (2) As the motor starts from rest and accelerates, the current gradually decreases, and at the instant when it reaches the value 7min the arm should leave stud i ; then £-£,' ■'min . J-, Dividing (3) by (i) there results £-£1' (3) K = E which when solved for £1' gives 82 TRACTION AND TRANSMISSION. E^'=E{l-K). (4) At the instant when the arm touches stud 2 the motor current should again be /max, which is now equal to J _ E — E2 /A '-•^^-r. + Rj ^^^ r. = ^-R^-^- (6) i max -^ max whence Since E2 and £1' are generated at the same speed and with the respective field currents /max and /min, reference to the saturation curve shows that E2 _ -Emax _ •El -Emin and therefore E2 = qEi', which, by substitution from (4), becomes E2 = Eq{i-K). (7) At the instant when the current has again decreased to /min the arm leaves stud 2 and /min = , ^ ' (8) Dividing (8) by (5), ^ ^ E — E2 ^ E — £2 from which £2' = E{z-K)+ KEi, whence by substitution from (7) £2' = £ (i - ii:) + EqK (i - K). (9) Proceeding in a similar manner there results £ T> £3 / \ n = -j. Rm — J — ' (10) ■* max ■* max RAILWAY MOTOR CONTROL. 83 E3 = qE2' = Eq{i-K) +Eq^Kii-K), (11) Ez'=E{i - K) + KEi = E{i - K) + EqK{i - K) + Eq^K^{i-K), (12) and so on. The resistance of each of the various steps may now be determined; thus, subtracting (6) from (2) and substitut- ing from (7), the portion between studs i and 2 is r,-r, = f^=^q{^-K). (13) ^ max ^ max Similarly, r2-H = Y-{E,-E,) = ^{i-K)=qK{n-n), (14) -' max -^ max r,-n=^{E,-E,) = ^^{i-K)=qK{H-n),{^i) -t max -* max and so on. An expression for the total number of steps required may be derived, but it is more convenient to proceed by first determining the total resistance by equation (2), then computing successive steps by equations (13), (14), etc., until the sum of the resistance steps thus obtained is approx- imately equal to (preferably equal to or greater than) the total resistance. This determines the number of steps into which the total resistance is to be divided. The foregoing equations may be used in designing the starting resistances of rheostatic controllers for any num- ber of motors, connected in any way, provided appro- priate values are substituted for /max and Rn- The same expressions may also be employed for calculating the series resistance steps of series-parallel controllers. Series-Parallel Controllers. The design of the parallel resistance steps for series-parallel controllers involves a de- 84 TRACTION AND TRANSMISSION. termination of the proper resistances to be connected in series with a motor (or motors) already in operation and therefore generating a definite counter electromotive force. This is a more general problem of which the preceding deri- vation is a particular case. Thus, if the controller shown in Fig. 36 is to be placed in series with a motor that has already attained some definite speed because of its previ- ous operation in series with another motor, the equations governing the design of the rheostat must be modified as follows. At the instant when the lever arm touches stud i the current flowing is ri + Km where Ei is the counter electromotive force that is being generated at this instant. The other symbols retain their former significance. Herefrom E „ -El / \ ''I = 7 Rm- J (17) ■* max ^ max At the instant when the arm leaves stud i the current flowing should be as before, /min=fff'- (18) Dividing (18) by (16) and solving for Ei there results El' = Eii-K)+ KEi. (19) , Again, at the instant when the arm touches stud 2 the current should again be J E — E2 , ^ consequently RAILWAY MOTOR CONTROL. 85 ^l - 7 K-m— 7 (21) ■* max -/ max As before, £2 = 5'£i', whence by substitution from (19) £2 = £g (i - ii:) + qKEr. (22) The instant the arm leaves stud 2 the current diminishes to J E-E2' , . Dividing (23) by (20) and solving for £2',, £2' = £ (i - ii:) + EqK {i-K)+ qK'Ei. (24) Herefrom n = ^-R^-f^ (25) -^ max ^ max and £3 = ^£2' = £? (i - x) + £?2ii: (i _ ii:) + j2ii:2£i, (26) and so on. Proceeding exactly as in the foregoing derivation there are obtained the following expressions for the resistances of the various steps of the controller: ^i-r2 = T^(£2-£i)=^(i-X)-^(i-gii:),(27) ■^ max ■* max -* max ri-rz=Y— (£3 - £2) = qK {n - n), • (28) ■^ max r3-r4,-=rj. — {Ei- E^ = qK{ri-ri), -.- (29) -* max and so on. If the controller having the resistance steps under con- sideration is to be used in starting a motor (or motors) from rest, £1 is equal to zero and the equations reduce to the forms previously derived. If, however, the motor is already in operation, Ei will have some value greater than 7 86 TRACTION AND TRANSMISSION. zero. In calculating the parallel resistance steps of a series-parallel controller, this value may be determined from the fact that the total resistance for parallel operation should be of such magnitude as to allow the current to increase from 7mjn to /max when the motors are transferred from the series to the parallel connection. Herefrom it follows that „ „ -El = ?-E„ where E^ is the counter E.M.F. per motoi: at the instant when the series connection is interrupted. Since the total counter E.M.F. generated when the motors are running in series without resistance is equal to the line voltage minus the total resistance drop, the value of E^ may readily be obtained in any given case. Thus, for a two-motor equipment £i = g£, = g ^^-^^J^-) . (30) 2 A definite knowledge of the resistance of the motor con- nections and car wiring is conducive to even greater accu- Fjg a8. racy in the determination of the controller resistaiice units. A three-point grid resistance manufactured by the Westinghouse Electric Company is shown in Fig. 38. RAILWAY MOTOR CONTROL. 87 31. Numerical Example. — As an illustration of the method of applying the foregoing equations to the calcu-. lation of resistance steps, consider the design of a series- parallel drum-type controller for use on a car equipped with two 35-horsepower, 500- volt motors. The saturation curve of the motors is shown in Fig. 39, and the resistance 30 20 : 10 ^^^ ^ /^ ^v^ / f / / 10 30 40 50 AMPERES Fig. 39. 60 70 80 of each motor is 1.18 ohms. The operating conditions are such that an average starting current of 60 amperes per motor is necessary to produce the prescribed initial acceleration rate, and the controller specifications require that the limiting values of current shall not differ from this average value of 60 amperes by more than 10 %. In this problem /max = 60 X I • I = 66 amperes, /min = 60 X 0.9 = 54 amperes, and therefore 88 TRACTION AND TRANSMISSION. "54 2.92 Z=g =0.818, 2= — =1.10, and aK = i.i X 0.818 = 0.90. The total starting resistance required for the operation of the two motors in series is ri = ^—T — 2 X 1. 18 = 7.58 — 2.36 = 5.22 ohms, 00 and the various series resistance steps into which it is divided are: ri — r2 = - — — — ^(i — 0.818) = 1.52 ohms, 06 r2 — r3 = 0.9 X 1.52 = 1.37 ohms, rz — ri = o.g X 1.37 = 1.23 ohms, and ri — r^ = 0.9 X 1.23 = I. II ohms, making a total of 5.23 ohnis. The counter E.M.F. generated at the instant when the motors are placed in parallel is P I.I (500 - 2 X 1. 18 X 54) , u ^1 = " = 205 volts. Hence the total resistance required for parallel operation is 500 1. 18 205 , , \ ^ , '■^=66^-~-6'^=^-79-(°-S9+-5S) = i.6sohms. and the various parallel resistance steps into which it should be divided are: 50 X I.I / o o^ 205 , s and = 0.758 - 0.155 = 0.603 ohms, rt — ri = 0.9 X 0,603 =^ 0.543 ohms, RAILWAY MOTOR CONTROL. 89 Ta — n = 0.9 X 0.543 =^ 0489 ohms, constituting a total of i .635 ohms. 32. Field Control. — With commutating-pole direct-cur- rent railway motors additional running speeds may be obtained by varying the number of turns on the main field without introducing commutation difficulties. Motors utilizing this method, called field-control motors, have more field turns than they would otherwise and have their field windings divided into two parts, so that both parts may be connected in series to secure high torque during starting and only one part is used during operation at high speed. The benefits derived in using such motors are the lowering of the starting current and the reduction of energy loss during the starting period. 40 \ No. 307-04 MOTOR \ \ CEAR RATIO 15:69 33"V(HEE1.3 A 30 \ \ F ^ y \*3 ,S.F. J V k^p. 20 ^<5N V A %y / V "x w 10 A . . - — ■ — ^ -^ y x< ^ 2400 O 1600§ 60 75 AMPERES Fig. 40. 125 Fig. 40 shows the tractive effort and speed curves of a 50-horsepower, 600-volt Westinghouse field-control motor go TRACTION AND TRANSMISSION. for full field (F.F.) and short field (S.F.) conditions. If a car requires each motor to exert a tractive effort of 1 600 pounds at starting, the motor will take 81 amperes on full field until a speed of 12.4 miles per hour is reached. Then if the short-field connection is made this same tractive effort would demand 90 amperes until a speed of 14. 2 miles per hour is attained. Thus the motor without field control (that is, the equivalent of short-field connection) would take 90 amperes for the starting time from o to 14.2 miles per hour, whereas the field-control motor would only take 81 amperes for 7/8 of that starting time. In consequence less energy is taken with such motors than with others of equivalent rating, the saving in energy having been found to be from 5 to 15 per cent in various service tests. 33. Alternating-current Control. — Single-phase series motors in railway service are controlled, like direct-current motors of the series type, by varying the pressure applied to their terminals. This variation may be effected by the standard direct-current method previously described. More efficient means of potential regulation are, however, avail- able with alternating current, so that the large PR loss incident to the use of starting resistances may be avoided and a greater number of running points obtained. Two general methods of control peculiar to alternating currents are at present employed with single-phase equipments : i, the induction regulator, and 2, the compensator method. Induction Regulators. — In starting a car or train by the former method the voltage impressed upon the motor terminals is gradually increased by means of a single-phase induction regulator. This device is essentially a trans- former of which one coil is movable with respect to the other, the windings being arranged in a manner similar RAILWAY MOTOR CONTROL 91 to those of a coil-wound induction motor. The primary coil is usually connected to suitable taps on an autotrans- former or compensator, used to step down the voltage. The secondary coil is placed in series with the motor cir- cuit, which is likewise connected to transformer taps of suitable potential. By changing the relative position of the regulator coils the effective E.M.F. induced in the secondary winding of the regulator may be varied from zero to a definite maximum value in either direction, that is, in phase with or in phase opposition to the E.M.F. impressed upon the motor circuit by means of the trans- former. Thus, if Et is the E.M.F. between the transformer GROUND Fig. 41. taps to which the motor circuit is connected, and E, is the maximum E.M.F. induced in the secondary coil of the regulator, then, neglecting the impedance drop in the wiring, the pressure applied to the motors may be varied 92 TRACTION AND TRANSMISSION. through all values from Et — E; to £, + E^ according to the cosine of the angle of displacement between the axes of the two windings. This method of control is illustrated by the scheme of connections shown in Fig. 41, where C is the autotransformer which is connected across the line, 5 is the secondary coil of the induction regulator and is in series with the motor circuit, and P is the primary coil thereof, which in this case is the movable element of the regulator. Evidently every possible position of the control- ler will result in a definite voltage upon the motors, so this 12 o — ^wr^ p 11 o TO MOTORS •^:=-GROUND Fig. 42. method of control yields a multiplicity of running positions. The large weight and low power factor of the regulators, and RAILWAY MOTOR CONTROL. 93 the complicated mechanism required for their operation are, however, serious objections which tend to retard the further adoption of this type of control. 34. Compensators. — In the compensator method of control the voltage at the motors is regulated by varying the ratio of transformation of a compensator, which serves also as a step-down transformer in those installations where high trolley potentials are used. One terminal of the motor circuit is connected to ground. The other terminal may be successively connected to a series of compensator taps so arranged that during initial acceleration the E.M.F. applied to the motor circuit may be increased in suitable steps until each motor operates on rated voltage. The connections of a compensator-type controller should be such that the transition from one compensator tap to another may be effected without interrupting the motor current or short-circuiting any portion of the compensator winding. For example, in transferring the motor connec- tion from tap i to tap 2 of the compensator C, shown in Fig. 42, an uninterrupted flow of current through the motors is maintained by closing switch 2 before switch i is opened. In order that this procedure may not short- circuit the portion of the compensator winding included between taps i and 2, a preventive coil P is connected in series with switch 2 as shown. The resistance R and the reactance X of this preventive coil are so proportioned that the impedance drop ZI, resulting from the passage of the motor current /, is equal in magnitude and opposite in phase to the voltage E existing between taps i and 2 of the compensator winding. This relation is indicated by the vector diagram in Fig. 42, where 4> is the angle by which 94 TRACTION AND TRANSMISSION. the motor current lags behind the pressure E, which is of course in phase with the voltage impressed upon the motor circuit by means of the compensator. It is evident from this figure that the values of resistance and reactance required depend on the power factor, cos , of the motor circuit. Since the power factor varies through a consider- able range during the period of uniform acceleration, it is desirable to connect in series with each compensator switch a preventive coil designed to meet the particular conditions obtaining at the instant when that switch is closed. This method of control has, however, the disadvantage of requir- ing a relatively large number of preventive coils no two of which have the same constants, yet each must be designed to carry the full motor current. In the so-called multiple-switch method of compensator control, now extensively employed, the preventive coils are used as auto-transformers to divide the motor current between two or more compensator switches. Thus, at each running point of the controller the motor circuit is connected to a set of two or more successive compensator taps, each of which supplies a definite fractional part of the motor current. The essential features of this method are illustrated in Fig. 43. In the particular scheme of connec- tions there depicted, three preventive coils are used to divide the motor current into four approximately equal parts. The first running position of the controller is at- tained by closing switches i, 2, 3, and 4. The voltage applied to the motor circuit when the controller is in this position is evidently equal to the potential relative to ground of a point on the compensator winding midway between taps i and 4. When the controller handle is moved to the second running position switch i is opened, RAILWAY MOTOR CONTROL. 95 followed by the closing of switch 5. Similarly, to pass to the third running point, switch 2 is opened and then switch 6 is closed; and so on until the motors are supplied with current at rated voltage through switches 5, 6, 7, and 8. It is obvious that during transition from one running point GROUND Fig. 43- to another the full motor current is maintained without short-circuiting any portion of the compensator winding. Since each switch is required to handle only a fractional part of the total current suppHed to the motor circuit, this method is well suited for use with railway equipments of large capacity. In cases where single-phase series motors are required to 96 TRACTION AND TRANSMISSION. operate on direct current over a portion of the roadway, some form of rheostatic or series-parallel control must be installed for use during the periods of direct-current oper- ation. The losses that would result from the use of start- ing resistances during the intervals of alternating-current operation are, however, in general sufficient to justify the installation of compensator control for use on the sec- tions where alternating current is employed. This com- pensator may constitute a part of the autotransformer which is used to step down the high trolley voltage asso- ciated with alternating-current traction to a lower value which is suitable for motor operation. The use of com- pensator control on road sections supplied with alternating current therefore involves little additional expense. . 3S. Induction Motor Control. — The methods of control required with three-phase induction motors are essentially different from those employed with alternating-current rail- way motors of the series type. The latter methods are not applicable to induction motors in railway service, since the reduction in impressed voltage necessary in starting by any of these methods causes a prohibitive decrease in the capacity of such machines. The following methods are, however, available for the control of three-phase induction motor equipments: (a) variable resistances in the second- ary circuits of the motors; (b) changing the number of poles of the motors; (c) cascade operation of the motors. (a) Variable Resistance Method. The insertion of vari- able external resistances in series with each phase of the secondary windings of the motors by means of suitable slip rings constitutes the principal method of maintaining an approximately uniform torque during the periods of initial acceleration. These resistances are so proportioned RAILWAY MOTOR CONTROL. 97 that the motor exerts at starting a torque sufficient for the prescribed acceleration rate. As the speed of the motor increases, causing a decrease in the E.M.F. induced in the rotor windings, the external resistances are cut out successively, thereby maintaining a moderately constant secondary current and thus uniformly increasing the speed at which the motor exerts the definite torque required. While this method possesses the advantage of simplicity, it does not permit of efficient acceleration because of the PR losses in the rotor resistances. It also provides for only one efficient running speed, since the induction motor is practically a constant-speed machine, the slip rarely exceeding 10 % of the synchronous speed which the motor closely approaches when the car runs at its ultimate veloc- ity on a level roadway. It is therefore desirable to employ in connection with this resistance method of control some means of changing the synchronous speed of the motors, thereby reducing the PR losses during acceleration and providing for one or more additional running speeds. {b) Variable MuUipolarity Method. In the second method of control the synchronous speed of the motors is varied by changing the number of motor field poles. If the frequency of the voltage be/ cycles per second, the synchronous speed in revolutions per minute is V =^. P where p is the number of pairs of poles on the induction motor. In order to change the number of poles of a given induc- tion motor it is necessary either to provide two or more separate windings, each of which is designed to yield a 98 TRACTION AND TRANSMISSION. different number of. poles, or to employ a single winding so arranged that the number of poles which it produces may be altered by a suitable change in the connections between the various parts of the winding and the three-phase line. The latter method is the more desirable since no inductors are idle during operation. A simple arrangement of windings for carrying out this method is illustrated in Fig. 44, which shows the stator winding of one phase of an 8-pole — 4-pole, three-phase in- duction motor. The complete phase winding 1-3 is divided N A s N A s N A S N A s [8 POLES] [4 poles! 1 2 3 4 5 6 7 8 1 \ C c ^ Sh v_ ^ / \ ) 1 c Fig 1 > 44 into the two parts 1-2 and 2-3 by a tap 2 at the middle point of the winding. Terminals i and 3 connect with the windings of the two other phases, which for clearness are not shown in this figure. The winding shown in Fig. 44 differs from the usual induction motor winding in that only alternate poles are wound. To produce an 8-pole magnetic field the windings 2-1 and 2-3 are placed in parallel with each other by connecting tap 2 to one of the line wires and taps I and 3 to the neutral point of the phase windings. The coils are so arranged that when tliu§ connected they prg- RAILWAY MOTOR CONTROL. 99 duce poles which are all of the same polarity. Interme- diate poles of opposite polarity will therefore be formed between them, thus producing an 8-pole field as indicated. If, however, a 4-pole field is desired, windings 1-2 and 2-3 are placed in series by connecting terminals i and 3 to POLES POLES Lj: o- -GROUND Fig. 45. line wires of the three-phase supply. One of the windings is thereby reversed with respect to the other and conse- quently the poles pertaining thereto will be of opposite polarity. The intermediate poles will then disappear, re- sulting in a 4-pole field. Fig. 45 shows the schematic ar- rangement and the controller connections for simultaneously changing the number of poles of all three stator phases. lOO TRACTION AND TRANSMISSION. (c) Cascade Method. The third method of three-phase induction motor control consists in operating two motors in cascade. In the cascade connection, or concatenation, of two induction motors, the rotors of both machines are mounted on the same shaft or otherwise mechanically coupled as by gears or connecting rods. The primary of the first motor is connected to the line and its secondary is connected to the primary of the second motor. The secondary windings of the latter machine are short-cir- cuited through suitable starting resistances. When two induction motors are started in cascade con- nection, the power output of the first machine consists in part of mechanical power delivered to the rotor shaft and in part of electrical power supplied to the primary of the second machine. During initial acceleration, the torque exerted by such a cascade set is maintained approximately constant by progressively cutting out the starting resist- ances. Thereafter the torque decreases with further in- crease in speed, approaching zero as the slip of the second motor decreases toward zero. Thus two motors connected in cascade approach, when operating under light loads, a definite limiting speed, which may be determined as follows: Let / = the frequency of the line E.M.F., V\ = the synchronous speed of the first motor in rev. per min., Vi= the synchronous speed of the second motor in rev. per min., V = speed of rotor shaft in rev. per min., pi = number of pairs of poles of the first motor, pi — number of pairs of poles of the second motor, S\ = slip of the first motor, ^2 = slip of the second motor. RAILWAY MOTOR CONTROL. lOI Then F. = ^ (x) and V _6o5i/_6o// Fi-F\ 6o/-/ _V_\ ' ^ ^ V Fi y p^ V fJ' which by substitution from equation (i) becomes pi Since F2- F therefore F = F2 (i - 52). (3) Substituting in equation (3) the value of F2 given in equa- tion (2), there results F = ^5=^^(1-..), (4) pi which shows that as Si approaches zero F approaches the limiting speed, 60/ pi + pi Hence the synchronous speed of the two motors connected in direct concatenation is the same as that of a single motor having pi + pi pairs of poles. Two similar induction motors connected in cascade share the load with approximate equality; thus the second motor utilizes a considerable portion of the energy that would otherwise be consumed in the starting resistances when operating at speeds below the synchronous speed of the combination. At the latter speed, however, the torque exerted is zero, and with further increase in speed, such as 102 TRACTION AND TRANSMISSION. occasioned by running down grades, the torque becomes negative and the cascade set operates as a generator, return- ing energy to the line. In most cases of cascade control the motors are divided into groups, each of which consists of a main motor and an auxiUary motor, the latter being employed during cascade 7 TROLLED Fig. 46. operation only. In starting, each auxiliary motor is con- nected in cascade with the corresponding main motor, and the starting resistances in the secondary circuits of the former are cut out in successive steps. The cascade connection is then broken by short-circuiting the second- ary windings of the main motor through the starting resistances, which are thereafter cut out progressively as before. Thus the auxiliary motors are required to operate only intermittently on a low voltage, and the full-speed power factor of the main motors is higher than would be the case if their load were shared with the auxiliary motors by connecting the latter across the line. Fig. 46 shows a scheme of connections for this method of control. RAILWAY MOTOR CONTROL. 1 03 36. Controllers. — All types of railway motor control must include means for changing the direction of rotation of the motors. A series motor is reversed by interchang- ing the connections of either its field or its armature wind- ings. The standard method of reversing series motors which have no commutating poles is to reverse the arma- ture, while that of commutating-pole motors is to reverse the main field so that the relative directions of current through the armature and commutating-pole windings will be unchanged. With a three-phase induction motor reversal of direction is obtained by exchanging the con- nections of any two of the three leads that supply the motor with current. Hand Control. — The manipulation of the switches is ac- complished directly by hand or through the- intervention of an auxiliary control. In the former system a motorman makes the necessary electrical connections by moving a handle at the top of a controller on the car platform. The movement of this handle causes the rotation of a vertical cylinder and thus permits of the successive connection of various contact studs thereon with stationary fingers, which, by means of suitable car wiring, are properly con- nected to the trolley or third rail, to the motors, and to the different rheostat terminals or compensator taps. Fig. 47 shows a Westinghouse controller, for series-parallel operation, with the cover removed. It has seven control- Kng points in the series position and six in the parallel position, and the motors are short-circuited during the transition period. The direction of rotation of the motors is changed by moving a reversing lever and thus actuating a smaller cylinder which is mounted beside the main cylin- 104 TRACTIOxN AND TRANSMISSION. der of the controller and is provided with suitable contact pieces for effecting the necessary change in connections. In- terlocking devices are supplied, so that the reversing handle cannot be moved unless the controlling handle is in such a position that connection with the trolley or third rail is Fig. 47- broken. The controlling handle also cannot be moved if the reversing handle is not properly set cither for forward or backward motion of the car. The reversing handle can be removed from the controller only when in its neutral or "off" position, to which it cannot be turned unless the controlling handle is also in its "off" position, thus entirely disconnecting the motor circuits from the trolley or third RAILWAY MOTOR CONTROL. 105 rail. Cut-out switches are provided, so that a defective motor or group of motors may be disconnected without interfering with the operation of the remaining motor or motors. As serious arcs are liable to ensue upon breaking a circuit of 500 volts, the contact pieces and fingers are separated from adjacent ones by strips of insulating mate- rials, which are usually fastened to the inside of a separate cover. Such arcs are effectively disrupted by the field of an electromagnet, which is an essential part of controllers used with motors of large capacity. Multiple-Unit Control. — -The system of motor control in which the switches are operated electrically or pneumatically through the intervention of an auxiliary circuit is called the multiple-unit system, since it is designed for the operation of several motor cars coupled together in a train, all the motors being controlled simultaneously from any master controller on the train. This system is now extensively employed not only for the operation of trains made up of motor cars and trailers but also for the control of electric locomotives and single-car equipments of large capacity. The control apparatus for each motor car or locomotive consists of a motor controller and two master controllers. The motor controller is composed of a number of switches or contactors, which close and open the various motor, resistance, or compensator circuits, and in general effect the changes in connection necessary in controlling the particular tj^je of motor employed. Each of these con- tactors opens in a strong magnetic field, so that all arcs are immediately disrupted. A separate reversing switch gov- erns the direction of rotation of the motors. On motor cars all this apparatus is usually placed underneath the car, but on locomotives it is located in the cab. The contac- I06 TRACTION AND TRANSMISSION. tors and reverser may be operated by solenoids or by the use of compressed air controlled by electrically operated valves. In either case the solenoids or other electromag- nets that govern the movement of the switches are connected to the wires of the auxiliary circuit and are supplied with current in proper sequence by the hand-operated master controller. The master controller is considerably smaller than the ordinary street-car controller, but is similar in appearance and method of operation. The contact fingers of each master controller are connected to the wires of the auxiliary or control circuit, which usually consists of a multiple- conductor cable. By means of suitable couplers this con- trol cable is made continuous throughout any number of motor cars or locomotives operated together in a train. Current for the master control is taken from the line, or from a storage battery, through whichever master controller the motorman operates. Since this current is used solely for energizing the operating coils of the motor contactors, its value is comparatively small, usually not exceeding 2.5 amperes for each car equipment. As the operating coils of each motor controller are connected to the wires of the control cable, any master controller on the train will simultaneously operate corresponding contactors on all the motor cars and thus establish similar motor con- nections on them. To avoid accidents which may occur through the physical disability of a motorman, the operat- ing handle of the master controller is sometimes provided with a button which must be held down in order to keep the auxiliary control circuit closed. In some cases the con- nections are so arranged that releasing this button applies the air brakes as well as opens the control circuits. RAILWAY MOTOR CONTROL. 107 The essential features of the multiple-unit system of control as applied to direct-current equipments are illus- trated in Fig. 48, which shows the principal motor and control circuits for one motor car. For clearness the re- verser is omitted, as are also the circuits necessary for its control. Assuming therefore that the reverser is properly set, the subsequent operation of the control system during initial acceleration is as follows : turning one of the master controllers to the first notch results in the closing of contac- l?^ppj^^=f Fig. 48. ^ tors a, b, and h, due to current received from train wires i, 2, and 8, thus establishing connection with the line and placing the two motors and a protecting resistance in series. Turning the master-controller handle successively to notches 2, 3, and 4 closes contactors c, d, and e, respectively, thereby progressively reducing the resistance by placing additional resistance units in parallel. When the controller handle is moved to the fifth notch, contactor / is closed, lo8 TRACTION AND TRANSMISSION. short-circuiting the resistances and connecting the motors in series across the line. In passing over the sixth or tran- sition notch contactors c to / and h are opened, followed by the closing of contactors g and i. This places the motors in parallel, with resistance in series with both. Turning the master-controller handle successively to notches 7, 8, 9, and 10 progressively reduces the resistance as before until each motor is operating on full line voltage. The operation of the switches of a multiple-unit equip- ment in other than their proper sequence is prevented by various interlocking devices. For example, the connec- tions are so arranged that the reverser on a car cannot be actuated save when the contactors on that car are open, nor can the operating coils of the contactors be energized unless the reverser is properly set for the direction of motion indi- cated by the master controller. By means of a suitable cut-out switch the operating coils of the motor controller on any car can be disconnected from the control circuit without interfering with the operation of the train from either of the master controllers on that car. In multiple-unit equipments similar to that illustrated in Fig. 48 the progressive closing of the contactors is accomplished by turning the master-controller handle to successive notches. The maintenance of an approximately constant current during initial acceleration is therefore entirely dependent on the motorman's care and skill. It is often desirable to have the progressive operation of the contactors regulated by the motor current itself, in order that the variations in this current from the average value required during acceleration may be automatically re- stricted to the prescribed range, thereby insuring a uniform rate of acceleration and permitting the motorman to con- RAILWAY MOTOR CONTROL. 109 fine his attention to the track and signals. This auto- matic acceleration is effected by means of current-limit relays having coils connected in series with the motor cir- cuit. Such relays may be arranged to regulate the pro- gressive closing of the motor-controller switches in either of two ways: i, by governing the movement of the master- controller contact cylinder, or 2, by governing the supply of current to the operating coils of the individual contactors. In the former method the contact cylinder of each master controller is connected to its operating handle through a helical spring. The cylinder is restrained by a magnetic clutch actuated by a current relay in series with the motor circuit. This relay is so adjusted as to release the clutch and allow the contact cylinder to advance one step whenever the motor current falls to its minimum limiting value. The master-controller handle may therefore be turned at once to any desired position, and the contact cyhnder will follow in successive steps automatically governed by the motor current of the car on which the motorman is stationed. Evidently this method cannot be expected to give satis- factory results in cases where there is a material difference in the motor characteristics or the current requirements of the various cars composing a train. In the second method of automatic acceleration each motor car is provided with a current-limit relay that is designed and adjusted with reference to the reqmrements of that particular car equipment. The motor connection ultimately established on all the motor cars in a train is determined by the position to which the handle of the master controller is turned; but the successive steps neces- sary to attain this connection are governed independently for each car by the motor current of that car. The connec- no TRACTION AND TRANSMISSION. tions between the operating coils of the contactors and the control circuit are made automatically through auxiliary contacts on the contactors themselves; and the control current for closing these switches passes through the con- tacts of the current-limit relay. PROBLEMS. 19. Determine the resistance units of a rheostatic railway controller for use with one 3S-horsepower, 500-volt, direct-current motor having a resist- ance of 1. 18 ohms. The saturation curve of the motor is shown in Fig. 39. The average current required during initial acceleration is 50 amperes; and the maximum and minimum values of the current must not differ from this average value by more than 9 %. 20. Determine the parallel resistance steps of a series-parallel railway controller for use with two 35-horsepower, soo-volt, direct-current motors, the saturation curves of which are shown in Fig. 39, the resistance of each motor being 1.18 ohms. An average current of 50 amperes per motor is required during uniform acceleration, and the limiting values of current are specified at 45 and 55 amperes. 21. A 220-volt, single-phase motor is to be started by means of an induc- tion regulator with an initial voltage of 150. What are the angular dis- placements between the two regulator coils if 7 steps were required which yield equal voltage increments on the motor ? 22. Determine the resistance and the inductance of a preventive coil to be connected in series with a certain compensator switch in order to effect sparkless transition by the method of control illustrated in Fig. 41. At the instant during acceleration when this particular switch is to be closed the 25-cycle motors have attained a speed such that the power factor of the motor circuit is S3 %. The motor current during the period of initial acceleration is approximately constant at 100 amperes and the E.M.F. between adjacent compensator taps is 25 volts. 23. A motor car is equipped with four three-phaSe, four-pole induction motors arranged in pairs for cascade control. Each main motor has 5 stator slots per pole per phase and 18 conductors per primary slot. Each auxiliary motor has 4 stator slots per pole per phase and 4 conductors per primary slot. Determine the equivalent number of stator conductors per pole when the motors are operating in cascade. ENERGY CONSUMPTION. Ill CHAPTER VI. ENERGY CONSUMPTION. 37. Current Curves. — During the period of initial accel- eration of a car the current taken by the direct-current motors is maintained roughly constant by the control equipment, provided no changes of grade or curvature occur during this interval. Thereafter, until the car attains its ultimate uniform velocity on the particular roadway under consideration, the motor current decreases, at first rapidly and later more slowly. The instantaneous values of current from the time all the controller resistance is cut out until the power is shut off may be read directly from the performance curves of the motor, since each motor takes a definite current at the various speed values of the car during this period. A curve showing these instantane- ous current values in terms of time over a run is called a current curve of the railway motor, and serves as the basis for determining whether the assumed motor for a proposed installation can perform the prescribed service without overheating. It is usual to construct the curve of current per car rather than the current per motor in determining the energy consumption of a tentative equipment. When starting the car the two motors of a two-motor direct- current equipment are connected in series, or the four motors of a four-motor equipment, arranged for the usual series-parallel control, are connected in two groups joined 112 TRACTION AND TRANSMISSION. in series, each group consisting of two motors connected in parallel. Four-motor equipments adapted for series, series-parallel, parallel control are not frequently employed. Hence from the instant of starting until the controller leaves the series position and connects all the motors in parallel with resistance across line voltage the current per car is equal to the current per motor times one-half the number of motors comprising the car equipment. At the end of this period, that is, when the motors are operating on the series position without resistance, the speed of the car is E-IR ^' where E is the line voltage, / is the current traversing the motor and R is its resistance, and Fi is the car speed when the controller is full "on." It is at this speed that the current per car increases from its former value to the product of the current per motor times the number of motors on the car. While the motors operate on reduced voltage in the parallel position their current intake is con- stant, but thereafter the current per motor and that per car decrease as dictated by the motor performance curves on full line voltage. When coasting begins the current intake ceases and the current curve drops to zero. 38. Average and Effective Currents. — The average cur- rent taken by the car over a complete run is based not merely upon the time during which the car receives power for propulsion nor upon the running time, but upon the time of the entire run including stops. This average current is determined by finding the area of the current ENERGY CONSUMPTION. 1 13 curve and dividing it by the time of the run as given by the specified schedule speed. The current per motor which when flowing continuously will yield the same average copper loss in the windings is called the effective motor current and is equal to the square root of the average of the squares of the instantaneous current values. The effective current may be found by squaring a suitable number of values of the motor current and plotting these squared values on the time axis. The square root of the average ordinate of the curve drawn through these points and taken over the total time of run represents the equivalent motor current to which the heat- ing of the machine is proportional. 39. Numerical Example. — As an illustration, consider a car equipped with four 50-horsepower, 600-volt, G.E. 2 16- A direct-current motors whose characteristic curves are shown in Fig. 23. The speed curve of this car over an 0.8 mile run on a straight level track at a schedule speed of 20 miles per hour is shown in Fig. 31, which permits of a 20-second stop. Determine (i) the average current intake for the -car and (2) the effective current per motor. The current consumed by the motor as the car is accel- erated uniformly at 1.5 miles per hour per second from standstill to a speed of 16.9 miles per hour (see page 61) is maintained roughly constant at a mean value of 64 amperes, the time necessary for the acquirement of this speed being 11. 3 seconds. The current curve over this period will have a series of peaks occasioned by the vari- ations in voltage which is impressed upon the motors by the controller, but the exact shape of this part of the curve is of no particular consequence, and it may be drawn straight through the mean current value. Taking the 114 TRACTION AND TRANSMISSION. resistance of each motor as 0.30 ohm, the resistance drop thereof is 19.2 volts. Therefore the speed of the car at the instant when the transition from the series to the parallel position is made is 600 — 19.2 600 — 19.2 X 16.9 = 8.2 miles per hour. 8.2 This speed is attained in -^ = 5.46 seconds from the instant of starting. Thus, when the car is in motion for 5.46 seconds the current per car increases from 64 X t or 128 amperes to 64 X 4 or 256 amperes. The latter current value per- sists for 1 1. 3 — 5.46 or 5.84 seconds. The current curve for the car before the motors operate on full line voltage is shown by OABCD in Fig. 49. Beyond the point D the current curve is entirely depen- dent upon the motor performance curves, since the current intake per motor at different car speeds is directly obtain- able therefrom. The times at which these speeds obtain are given by the speed curve for the run under consider- ation. Thus the curve of current per car may be plotted in terms of time, as done herewith from the following com- putations : Speed of car Current per motor Current per car Time of speed acquire- ment (seconds). See table, page 64. (miles per hour). (amperes). (amperes). 20 48.2 192.8 13.84 22 42.1 168.4 16.26 24 37-4 149.6 19 -45 26 33-9 I3S-6 23-65 28 31.0 124.0 29.22 30 28.4 113. 6 36.88 32 26.3 105.2 47.78 ENERGY CONSUMPTION. "S o o ■ o CO . Q ot CO O bs LxJ PEI CO O CO O o o o n n o < O o o lO O lO CM S3a3dWV ^* o o CO o o CD snoA o 8 (N Il6 TRACTION AND TRANSMISSION. After so seconds coasting begins and the current curve is completed by drawing the vertical hne EF. The area of the current curve per car is 7350 ampere- seconds, which when divided by the time of the run, namely 144 seconds, gives the average current per car over the given run as 51.0 amperes. The curve of current per motor is shown in Fig. 50, as OABCD, the portion BC being also plotted from the values recorded in the foregoing table. The ordinates of this curve when squared yield the curve OEFGD, the area of which is 90,930 amperes-seconds. The mean square current over the given run which requires 144 seconds for its completion is 631 (amperes)^- Therefore the effective heating current of the motor is 25.1 amperes. 40. Efifective Motor Current for a Trip. — The effective motor current for a trip over an entire roadway which is divided into a number of individual runs distributed over several territorial sections on which different service condi- tions exist is obtained by averaging the squared current values over all the runs and extracting the square root of this average. Thus, for example, if the effective motor current values on typical runs on the city, suburban, and interurban sections of a certain railway are respectively 40 amperes for 25 minutes, 35 amperes for 20 minutes, and 28 amperes for 15 minutes, then the effective current for the entire trip is / (45^ X 25) + (35' X 20) + (28' X is) 25 -f- 20-1- IS , / 40,ooo 4- 24,500 + 11,760 _ f- V 60 ^^ ' ENERGY CONSUMPTION. 117 < ( ( D p ( t ( c 3 C 3 C ? C > C (S3a3dWV) 3 < 3 < ! 3 2 • 1 1 1 10 > 111 lu. lu. |L1I ( > 01 CT D H / )LTS ON MC /Or 1 li.. > 1 1 < ( in . a o oz ■" (D O M as o o o CO o o CO o o (D < / / 'oive 5 con: UMP "ION / / 0.5 1.0 1.5 MILES RUN Fig. 53- 2.0 2.5 3.0 20-second stops but no coasting, is shown in Fig. 53. This curve is based on data obtained from Fig. 31, on which a number of braking curves may be drawn corresponding to runs of various lengths. Proportionately less of the energy taken from the supply circuit is used to overcome the losses in other than train resistance for long runs than in short runs, and therefore the power consumption per mile is decreased by increasing the lengths of runs. This is also shown in Fig. 53 for the particular car under consideration; the curve of power con- sumption per car mile without coasting was computed in 128 50 40 H30 z Ul o q: u 0.20 10 TRACTION AND TRANSMISSION. ^ -^ 6-CARTRAlN,-4 MOTOR CARS.-154 .<^^ ^ — ^ TONS. AVQ. BRAKING RATE1.75 .Jy ^/ <<^ " /fi z 1 1 1 ul 0.1 ' 0.5 1.0 1.5 2.0 RATE OF ACCELERATION IN MILES PER HOUR PER SECOND. Fig. 54- 0.5 1.0 1.6 2.0 RATE OF BRAKING IN MILES PER HOUR PER SECOND Fig. 55: connection with Fig. 49. The effect on schedule speed and on energy consumption of changes in the rates of accelera- tion and braking is not as conspicuous on long runs as on short ones. ENERGY CONSUMPTION. 129 The schedule speed of railway cars depends to a great extent upon the duration of the stops for the purpose of taking on or discharging passengers or freight. Obviously, the longer the period of standstill the lower will be the maximum schedule speed attainable by a given equipment. An increase in the time of coasting results in a reduction of the power consumption. The results of a series of tests on a 6-car train of the elevated railway in New York City 50 40 1-30 z o DC 120 10 6-CAR TRAlN,-4 MOTOR CARS, -154 TONS. \VQ. BRAKING RATE1.75 MILES PER HR. PER SEC STATION STOP-14 SECONDS. PERC ^^77-52 ^srTTvS- PERC ENT SA VING iN~-p7^ N \ 2 3 4 5 6 TIME IN SERIES POSITION, SECONDS. Fig. 56. made by H. S. Putnam are embodied in the curves of Figs. 54, 55 and 56, which show for a given schedule speed the influence on the percentage of coasting and per- centage saving in electrical energy, of acceleration and braking rates, and of running time in series position. The motor performance curves and the speed and power curves derived from them refer to a definite and constant trolley voltage. In practice this voltage has not the same value at different points on the roadway, owing to the drop I30 TRACTION AND TRANSMISSION. of potential along the trolleys, on third rail, and on feeders from the substations. The minimum voltage at the car should not be less than 350 volts for the usual 600-volt equipment. Consequently in selecting the car equipment for a proposed railway service due attention must be given to the voltage regulation on various parts of the road. Speed curves of cars operating on road sections on which the voltage is lower than normal must be based upon the average voltage existing at the definite locality. With series motors the speed at constant load varies almost directly with the impressed voltage, and hence the speed of the car at the instant full line voltage is applied to the motors is lower when the line voltage is below normal. Thus to maintain the same services under reduced voltage requires that the motor receive power for a longer time, and this frequently implies a greater power consumption. Sufficient trolley voltage all along the car route is impor- tant, particularly so on grades. 46. Gear Ratio. — When a railway motor takes a cer- tain current at constant voltage a definite torque is devel- oped, and the corresponding tractive effort produced by the motor at the base of the car wheels depends entirely upon the gear ratio, that is, the ratio of the number of gear teeth to motor-pinion teeth. The resulting speed of the car for this motor current is inversely proportional to the tractive effort, and consequently the smaller the gear ratio the higher will be the speed of the car and the lower will be the tractive effort available for acceleration. There- fore, to maintain a specified initial rate of acceleration requires a larger current through the motors when geared for high car speed than when provided with a large gear ratio (i.e., low car speed). On the other hand, the time ENERGY CONSUMPTION. 131 that power is on the motors of a car when operating over a given run is longer with high gear ratios than with low ratios. The effect of change in gear ratio on the rate of acceleration with a definite accelerating current and on the magnitude of this current with a definite acceleration rate, is indicated respectively in the two following tables which refer to the 24.32-ton car equipped with four 50-horse- power, 600-volt, direct-current motors whose characteris- tic curves are shown in Fig. 23 for a gear ratio of 17,^0 69 (or 4.06). Gear ratio. Rate of acceleration. IS 2.0 3° 4.06 S-o 0.48 0.68 1.08 I SO 1.87 Accelerating Gear ratio. - current per motor. i-S 142 2.0 IIO 3° 80 4.06 64 S-° SS (Accelerating current =64 amperes per motor.) (Acceleration rate = 1.5 miles per hour per second.) By constructing speed and power curves over a t3^ical run for a given equipment when supplied with different gears, and subsequently plotting curves of power consump- tion and of effective heating current in terms of gear ratio, that gear ratio for the equipment can be determined which is conducive to a minimum expenditure of energy and least heating of the motors. In general, it develops that the most suitable gear ratio for motors of proper capacity for a specified service is that which will yield the lowest car speed consistent with the prescribed schedule speed, due allowance being made for delays. A gear ratio so chosen will result in a low energy consumption by the motors and a smajl temperature elevation. 132 TRACTION AND TRANSMISSION. PROBLEMS. (^^^^ Upon the speed curve of Problems 17 and 18 plot the curve of current andpower input per motor car. In determining the speed of the car at which the transition from the series to the parallel connection of the motors is made neglect the motor voltage drop. Compute the average current and power input per motor car over the time of the complete run. A 2S?\CalcuIate the energy consumption, in kilowatt-hours per train-mile ahd-i«r watt-hours per ton-mile, of the train considered in Problems 17, 18, and 24. 26. How much energy in liilowatt-hours is consumed by the equipment of the 20-ton car mentioned in Problems 14 and 15 over the run for which the service conditions are there specified? What is the equivalent heating current on this particular run? 27. Determine from the curves of Fig. 51 the energy consumption in watt-hours per ton-mile of the so-ton car equipped with four 75-horsepower, single-phase motors. Add 8 % of the power taken by the motors to allow for other losses in the car equipment. 28. Plot curves of initial current, full voltage speed with initial accelerat- ing current, and time of running on reduced voltage, all in terms of the rate of acceleration, for a 100-ton New Haven electric locomotive equipped with four 2So-horsepower, single-phase motors whose characteristic curves are shown in Fig. 25. Assume train resistance uniform at a. value of 15 pounds per ton. 2g. Construct a curve showing the maximum schedule speed possible, in terms of the duration of a stop, for the car whose typical speed curve on a level track is shown in Fig. 31. 30. A motor car, weighing 43 tons, equipped with two 200-horsepower motors (gear ratio 20 : 63), whose characteristic curves are shown in Fig. 24, gains velocity at the rate of 2 miles per hour every second on a tangent level track. Assuming train resistance as 15 pounds per ton, plot a curve of the accelerating current required per motor when the equipment is pro- vided with different gear ratios, in terms of gear ratio. THE DISTRIBUTING SYSTEM. 133 CHAPTER VII. THE DISTRIBUTING SYSTEM. 47. Classification of Conductors. — It is common to divide the conductors of the distributing system into two parts, the ones which convey current from the station to the cars being termed positive and those which return it being termed negative. The positive conductors may be divided into three classes as follows: (i) bare contact conductors, such as trolley wires, third rails, and T conductors in slot systems, from which the current for propulsion is taken by means of collecting devices; (2) supplementary conductors, which are parallel to the contact conductors, are connected with them at frequent or infrequent intervals, and which are designed to increase or supplement their conductivity; and (3) feeder s~ which extend from the station to a feeding point on the contact or supplementary conductors, and which supply current to them. The negative conductors may be similarly classified, although the bare conductor which receives current from the car is not usually termed a contact conductor. It usually consists of the connected track rails, although it may be a second trolley wire or T conductor in a slot system. Negative feeders and supplementary conductors are also common. The contact conductors are usually divided into successive sections each one of which is insulated from adjacent sec-, 10 134 TRACTION AND TRANSMISSION. tions. Their lengths vary from a few hundred feet to sev- eral miles. 48. Contact Conductors. — To determine the drop as- sume a contact conductor BD, Fig. 57, fed at 5 with / Fig. 57- amperes, /i and h amperes being drained from it at dis- tances from B of h and h feet respectively. If the specific resistance of the conductor be p ohms per mil-foot and its cross section be A circular mils, then the drop from B to Dis e = j[k{h + h)+h{k-h)], or e = 7 (/i/i -I- ^2/2) volts. Similarly in general, if any number, n, of currents of dif- ferent magnitudes /,„ be drained off at different distances, l^ from B, the total drop from B to the most distant point of drainage may be expressed as where /o = },Z ? is such a distance from B that if the total current / were carried that far the resultant drop THE DISTRIBUTING SYSTEM 13S would be e volts. The relations which exist between the currents, the distances, and h are so similar to those which exist between the elementary and total masses of a body, the respective distances of the former from a plane, and the distance of the center of gravity from the plane, that the point which is h feet from B is termed the center of gravity of the combined drainage load. The total drop in a section of contact conductor is almost always assumed. Taken together with the drop in the negative part of the system it must not be so great as to hinder the proper starting and operation of the motors and the proper functioning of the lamps. The maximum drop in the negative conductors is usually made small, with a view to meeting municipal ordinances or to preventing electrolytic corrosion. In England it is limited to seven volts. The total drop varies from 10 % to 50 % of the nor- mal voltage, the smaller value ruling in all alternating-cur- rent and in urban direct-current systems, while the larger is found in direct-current interurban systems. Knowing, therefore, the value of e, if the length of conductor and the distribution of the load be given, the proper cross section may be determined from (i) as A = -IfJ circular mils. (2) e The minimum cross section of the contact conductor is dictated by mechanical considerations in the case of trolley wires, and by manufacturing standards in the case of third rails. The size of trolley wires is usually Nos. 000 or 0000 B. &. S., although No. o has been used. With double- track roads and those single-track roads which employ twin trolley wires the sum of the cross sections of the two wires should be taken. If, therefore, the cross section, the 136 TRACTION AND TRANSMISSION. drop, and the load distribution be known, the limiting length of contact conductor which can be fed from a single feeding point may be determined by means of formula (i). The specific resistance of third rails varies with their chemical composition. Armstrong recommends the follow- ing limitations as to ingredients: Carbon not to exceed 0.12 per cent Manganese not to exceed 0.40 " " Sulphur not to exceed 0.05 " " Phosphorus not to exceed o.io " " Such compositions result in a resistivity of approximately 14 microhms per centimeter cube at 20° C, a value which is seven and three-quarters that of commercial copper. The following table of rail resistances is based upon this value: RESISTANCE OF THIRD RAILS INCLUDING BONDS Rail weight in pounds per yard. Resistance in ohms per mile. 40 0.093 SO 60 0.074 0.062 70 80 0-0S3 0.046 90 100 0.042 0.038 no 0.034 Inasmuch as the current taken by a car varies with the time and location of the car and, in congested districts, is subject to further variations due to traffic conditions and the idiosyncrasies of the motorman, it is customary to assume a uniform drainage of /q amperes per foot from the contact conductor when treating urban or suburban problems where several cars are taking current at the same time from the same section. The value of 7o changes THE DISTRIBUTING SYSTEM. 137 during the day, and for calculating limiting conditions the rush-hour value should be taken. Its average value may be determined by multiplying the average current taken by each car in passing over the section by the num- ber of cars on the section at one time and dividing this product by the length of the section. The ratio of its \ "i \ \ 2.0 \ S, \ \ 1.5 s. \ ^ 1,0 ■ 10 20 30 NUMBER OF CARS. Fig. 58. 40 50 maximum to its average value may be determined by reference to Fig. 58, which is based upon experience. End Feeding. Consider a section of length L feet, fed at one end as in Fig. 57, and let it be uniformly loaded. Since the current density /o = I/L, and the distance of the center of gravity of tlie aggregate load /o = L/2, the total drop over the section is whence V 2Ae feet. (4) 138 TRACTION AND TRANSMISSION. The total drop is therefore proportional to the square of the length of the section, and the maximum permissible length of section is to be obtained by use of equation (4). Center Feeding. If the section be fed at its middle point instead of at the end, the permissible length of contact conductor section is twice that indicated by equation (4). Such a system is schematically represented in Fig. 59, and is considered ideal from an operating viewpoint, for each section may be controlled by a circuit breaker at the station in the feeder supplying that section. This gives complete . .BREAK ERS ^^^^^^3 -BUS Fig- 59- control of each and every section in case of overload, short circuit, accident, or repairment. It is the system most frequently used for urban roads. It may be desirable to connect the adjacent ends of the sections of the contact conductor through a section breaker which may be located on a near-by pole. When these circuit breakers are closed there results an equalization of the current distribution and the conductivity of the whole positive system becomes available. The remoteness of these breakers from the station, however, is objectionable as lacking accessibility. Watts Lost in Conductor. While the cross section of the contact conductor is usually prescribed by the maximum permissible drop or by mechanical considerations, cases may arise where a larger cross section will prove more THE DISTRIBUTING SYSTEM. 139 economical. In such cases the power lost in the contact conductor may be found as follows: Let le = effective current per foot in amperes, R = resistance per foot in ohms, L = total length of conductor from feeding point in feet. Then the power lost in an elementary length dl of the conductor at a distance I feet from the feeding point is dP = [/, (L - l)f- Rdl and the total power lost is or P = -//i? watts. (S) 3 For a section fed at one end, L represents the length of the section. If the section be fed at the middle and be 2 Z feet long, the loss will be twice that given by equation (5). The proper cross section is then determined by Kelvin's law as in §62. I, G^ h A FEEDING POINT Fig. 60. iD 49. Branches. — When a contact conductor section is bifurcated because of a branch in the roadway as shown in Fig. 60, and when it is fed at the point of bifurcation, the drainage current on each part may be found as follows: I40 TRACTION AND TRANSMISSION. Let m = number of cars operating between A and B, n = number of cars operating between A and D. Then at any time: number of cars between A and C — ni = m - — ^ + n — number of cars between C and B = n2 = in: ^ k + k and number of cars between C and D =ni= n- — ^• k -rk The drainage current per unit length, /o„, for any part of the section may be expressed in terms of the average current per car, /„, as lon = ~j — amperes. 50. Collecting Devices. — The conduction pf current to the motors on the cars from the contact conductor is accomplished by means of wheels, rollers, or sliding bows for trolley wires, of shoes for third rails, and of plows for slot systems. Trolley wheels are grooved wheels of from 3.5 to 6 inches in diameter and are mounted in self-lubricating bearings at the end of a trolley pole. The other end of the pole is movably mounted in a trolley table upon the top of the car and is controlled in a vertical plane by springs and levers so as to exert a fairly uniform pressure between the wheel and the trolley wire, irrespective of the angle of elevation of the pole. This pressure varies from 15 to 40 pounds. The maximum current which can be collected by this means decreases with the speed and is represented in the curve of Fig. 61. If it be necessary to collect more current than that indicated by this curve, either a plurality of THE DISTRIBUTING SYSTEM. 141 trolley wheels or some other form of collecting device must be used. When the direction of car movement is reversed, it is necessary to turn the trolley pole through 180° in a horizontal plane so that it may incline to the rear of the car. To avoid this shifting, use is sometimes made of cylindrical rollers mounted in pantograph frames on top of 1000 .800 S Ui 600 D. s <400 200 • V V "\ ^ ■ ^ 10 20 30 40 MILES PER HOUR. Fig. 61. 50 60 the cars. The contact is not as good as in the case of a grooved wheel, and the inertia of the heavy frame tends to produce arcing at the contact with high speeds. The sliding-bow collector, mounted upon a spring-con- trolled pole or pantograph frame, is rapidly coming into use, especially in connection with alternating-current systems. This form of collector is more common in Europe than in this country. The construction and principle of operation of shoes depend upon the chara,cter of the third-rail mounting with which they are to be used. With an overrunning third rail, as used on the Manhattan Elevated Railroad in New York, and mounted as shown in Fig. 62, the pressure between the shoe and the rail surface is due to the weight 142 TRACTION AND TRANSMISSION. of the shoe. The construction of a shoe adapted to such conditions is shown in the figure. In case the third rail is protected against sleet and ac- cidental contact by an insulating barrier at one side and over its top, or is of the underrunning type, the shoe is generally hinged and the contact pressure is controlled by springs. The construction of such a shoe for use with the latter type of third rail is shown in Fig. 63. The current-collecting capacity of shoes is very large, 2000 amperes per shoe for speeds up to 35 miles per hour being attainable. Since the plows used with slot systems must conduct current to and from the car motors, their circuits must be carefully insu- lated from each other, and, as the slot aperture is of necessity nar- row, they usually assume a thin, flat form. Spring-controlled wings at their lower ends serve to form the circuit with the con- tact conductors on either side in the conduit underneath the slot. 51. Supplementary Conductors. — When a supplementary con- ductor is of uniform cross section throughout its length and is connected with the contact conductor at successive THE DISTRIBUTING SYSTEM. 143 points near to each other, the two may be considered as a single composite contact conductor of cross section equal to the sum of the two. The economic use of copper requires, however, that the cross section of the supplementary conductor be not uni- V^'WV Cor c/eoronce Center O/ie m'raf/r'o// form. Consider such a composite contact conductor sec- tion to be fed with / amperes at one end and to be divided into m short elements, each of length / feet, and of different cross sections, that of the wth element from the remote end being y^ circular mils. For a uniform drain of current /q 144 TRACTION AND TRANSMISSION. amperes per foot, the current in the wth element is nlj,, the volume of the element is yj, circular mil-feet, its resist- ance is pl/jn ohms, and the drop over it is npIiPlyn volts. If T) be the total volume of copper and e be the total drop, then z) =X^3'" = ^'%y^ circular mil-feet (i) and e = plip'%n/y„ volts. \ (2) Therefore substituting the value of I from (2) in (i), m j 1) =\ — ^ circular mil-feet. (3) In order that the copper volume v may be a minimum dv/dy must be a minimum, which involves the conditions that Vjn be a minimum while Vw/y„, or the total drop, remain constant. If, each term of the latter be multiplied by an unknown constant C, to be determined later, the result will still be a^constant. Further, if 6ach term of the result be added to the corresponding term of the series Vy„, a y "* [Cn \ new series will be formed, of the form z = 2)( +3'»)> which also must be a minimum. Therefore dZn _ _ On _ syn yn :. y„ = VCm, THE DISTRIBUTING SYSTEM. 145 and since nl = x, the distance in feet of any chosen point from the remote end, substituting the value of n fCx yx = Y — circular mils. (4) To determine the value of C, consider that the drop in an element of length dx at a distance x from the remote end is de^el^^^plJIVxdx; therefore the total voltage drop is e = pU sj^j\hx = ph \/^ - L^ volts. (s) Since the total entering current, /, is equal to the product of /o and the total length of the section, L, the value of v/f y from equation (5) becomes consequently ./C 2pTVl. y^ = V^ circular mils. (6) This equation shows that the curve which relates total cross section of supplementary and contact conductor with distance from the remote end is a parabola with its vertex at the remote end. Of course it is not practicable to con- struct a conductor with such a varying cross section, but it is common to reduce the cross section by steps as the remote end is approached. The connection of the supplementary to the contact con- ductor at many points involves considerable expense espe- cially when made through contact switches. It is therefore 146 TRACTION AND TRANSMISSION. common practice to employ a moderate number of connec- tions and to feed sections at each end and often from separate substations. In many instances this arrangement is used when the load is concentrated rather than uniformly distributed. In such cases the determination of the proper SUPP. COND. CONTACT \ SUBSTATION CONDUCTOR SUBSTATION/ TWT ■7^ Fig. 64. disposition of copper is involved and is best arrived at by trials based upon assumed distributions of copper and of load. Assume a system connected as in Fig. 64 which is elec- trically equivalent to the arrangement shown in Fig. 65, 1' y Fig. 65. where the resistances of the various branches and the voltage at the substations are known and the equivalent resistances R of the load and x of the rest of the conducting system, out and back from both substations and considered as connected in parallel, are to be found. The problem is solved by applying Kirchhoff's laws, which result in the following equations, where the resistances THE DISTRIBUTING SYSTEM. 147 A = ffl + 6 + c B = d+J + g ohms. C=b+d+h Ah -biz +IR = E Bh -dh -IR =-E -bh -dh +Ch = h -h = I (7) (8) Solving for R by means of determinants R = A -b E B -d-E —b —d C 1 —I / A -b I B -d -I —b—d C 1 —I = A -b {E-AI)fI B -d -Ell -Q}+d) C b A B -{b+d) -b -d c I —I ohms. (9) RI -volts. (10) Whence the voltage impressed upon the load is _ E{b+dY-E{A+B)C-{Ad^+Bb-'-ABC)I , {b + dy -{A+ B)C The drop e between either substation and the load is e = xl = E-RI volts, (11) where x is the equivalent resistance in ohms of the con- ducting system between the substations and the load. The drop between a substation and any point with a plurality of variously located loads is equal to the sum of the drops produced by each load. 52. Graphic Time-table. — Since the reason for the employment of supplementary conductors is the preven- tion of an excessive drop of voltage between the substa- tions and the cars, the conductors must be of adequate t4& TRACTION AND TRANSMISSION. cross section to cope with the worst condition likely to arise in the operation of the electric railway. As the voltage drop varies with the current and with the resist- ance, and the latter is proportional to the length of the conductors, the worst condition will be when a maximum total current is taken by cars at a maximum distance from both substations. To determine this condition use is made of graphic time-tables or train-sheets for the proposed service; such a curve is shown in Fig. 66. It consists of a set of intersecting curves, each one constituting the locus of the correlated time and place relations of a car or train. The ordinates may represent the hours of the day, while the abscissae represent distances from the road terminus in miles. The curves are usually considered as made up of straight-line elements. With equal scales for ordinates and abscijssae the cotangent of the angle between a por- tion of the curve and a parallel to the axis of abscissae represents the corresponding speed in miles per hour. If the elements be straight the speed is constant, and in plotting these curves the average running speed is assumed to be maintained throughout. The perpendicular elements represent stops of durations proportional to the lengths of the elements. The ordinate of a point where two curves cross each other gives the time when the corresponding cars meet each other, while its abscissa determines the neces- sary location of a turnout, if the road have but a single track. For a specific problem the time-table should have indicated upon it also the distribution of copper and the location of towns, villages, and substations. Confining the attention to a single section of the road, and assuming an average value of current taken by a car when running and another greater value when starting, the THE DISTRIBUTING SYSTEM. 149 3WIX II 150 TRACTION AND TRANSMISSION. magnitudes of the currents and the distances from the sub- stations of their points of drainage, corresponding to any chosen time, can be readily obtained. A comparison of the results for different times readily reveals the worst condi- tion likely to arise. With single-track interurban roads giving infrequent train service such condition is likely to occur when and where two trains pass each other. Having determined the worst condition, the adequacy of the assumed distribution of copper can be. determined by the method outlined in the preceding section. The mini- mum voltage permissible at the car on 600-volt systems is 300 volts, or with high-class service 350 volts. In the case of a supplementary conductor with numerous connections with a contact conductor which extends between f 1 j I I I I I I 11 I I I I I I I I I I I r 2 j Fig. 67. two substations and is fed by both, the drop produced by a concentrated load is proportional to the current and to the distance from the nearer substation. Consider the conditions as represented in Fig. 67. If i? be the resistance in ohms per foot of combined conductor, the drop is e = Rhh = Rl2(L - h) volts. (i) But I = I1 + I2 amperes; (2) hence e = RI (i — jj h volts. (3) Therefore, for a given current /, the drop increases with increase of h from h = o to h = — . These equations also THE DISTRIBUTING SYSTEM. 151 show that the portions of the current supplied to a car by the two substations vary inversely as their respective dis- tances from the car. 53. Feeders. — Although supplementary conductors are often termed "auxiliary feeders" or simply "feeders," the latter term is used in this text to represent conductors which extend from the station to a single feeding point and which carry the same current at the same time through every cross section. The cross section of a feeder is often determined from economical considerations and by the use of Kelvin's law as modified by Kapp: The most economical area is that for which the annual cost of energy wasted is equal to the annual interest on that portion of the capital outlay which can be considered proportional to the weight of metal used. Let / = maximum current in amperes carried by the feeder, L = length of feeder in feet, A = its cross-section in circular mils, h = effective annual hours of operation at maximum current, p = resistance of feeder in ohms per mil-foot, and ■w = weight of a mil-foot in pounds. Then the resistance of the feeder is ^ ohms, and, if the cost per kilowatt-hour delivered to the feeder be C3 dollars, the annual expense for energy lost in the feeder is C/ = '-^ dollars. (i) 1000 A At a cost of d dollars per pound of feeder conductor and 152 TRACTION AND TRANSMISSION. at a rate for interest and depreciation of p2, the annual charge against capital outlay for feeder conductor is Cf" = piCiwLA dollars. (2) With overhead construction the cost of insulators and of installing the feeder will be independent of the cross-section for a specific case. Therefore the most economic cross- section is that which will make C/ -\- C/' a minimum, in which case C/ = C/' and the economic cross-section is =v: 1000 piCiW Hence the maximum economic drop is ^^ — circular mils. (3) The reciprocal of the radical in equation (3) may be termed the economic current density. Often the maintenance of a suitable operating voltage or the inevitable heating of a feeder precludes the use of the economic cross section. Long feeders may be fed from a special bus at the station at a potential somewhat in excess of the normal station voltage. In case the feeders are to be placed underground, an expression must be obtained for the annual expense charge- able against the cost or rental of conduit ducts in terms of the feeder cross-section. This expression must then be added to equations (i) and (2) before differentiating in order to obtain a minimum. Boosters. ■ — In the case of feeding points remote from the station the cross section of feeders as prescribed by the permissible drop may be very large and may entail an almost prohibitive first cost. The cross section may be materi- ally reduced if a booster be inserted in the feeder circuit. THE DISTRIBUTING SYSTEM. 153 Whether or, not a booster should be used depends upon its cost and the expense of its operation and maintenance as compared with the saving resulting from the reduced feeder cross section. The determination of the advisabil- ity of its use and of its voltage may be made as follows, neglecting the losses in the booster: Let X = maximum voltage of booster, Cf = maximum total drop in boosted feeder, / = maximiun amperes in feeder, pi= interest, depreciation, etc., on cost of booster, / and g = cost constants. Then Ix Capacity of booster = K.W. 1000 Ix Cost of booster = / + g dollars. 1000 Hence the annual interest and depreciation on the booster is Ci = Pilf + g-^) dollars. \-^ 1000/ If h be the yearly effective hours of feeder operation and C3 be the cost in dollars of generating a K.W.-hour, the annual cost of energy lost in the feeder is C2 = -^^^^i^ hca dollars. (5) 1000 If the length of the feeder be L feet, and its weight be w pounds per mil-foot, its cross section is A = — circular nails, (6) x + ef and its weight is W = — — pounds. (7) X + Cf 154 TRACTION AND TRANSMISSION. At a cost of Ci dollars per pound and a rate of interest, etc., of pi per cent, the annual feeder expense is C3 = ^?^^^^^' dollars. (8) x-\-et The total annual feeder and booster expense therefore is C = Ci + C2 + C3, or \ 1000/ 1000 X, -\- 6; In order that this expression may be a minimum its differ- ential coefficient with respect to x must equal zero, or dC _ gl Ihcs _ CipjivpIU _ dx 1000 1000 {x + CfY therefore . .2 _ c-ipi^wpU 1000 and ^=i>^2^£?te_ olts. (10) Since x must be a positive quantity, that value of L which makes it equal to zero is the minimum length of feeder with which the use of a booster is advisable. It should be noted that this minimum length increases as the yearly hours of boosted-feeder operation increase. Boosters are therefore to be especially recommended for intermittently operated feeders. If the average efficiency of the booster set be «, multiplication of the term Czh in (10) by (2 — e) will include the losses of the set. With the following values for the constants — those in brackets being suggestive of the order of magnitude — equation (10) may be simplified for use with copper feeders: THE DISTRIBUTING SYSTEM. 155 P = 10.5. C3= [0.006]. w = 0.00000303. pi= [o.io]. C2= [0.17]. / = [300]. . p2= [0.06]. g = [28]. X = 0.018 L \/-r~ — —, -e,. (11) * 2.8 + 0.000 « For a total boosted-feeder drop of 50 volts and continuous operation of A = 24 X 365 = 8760 hours, the minimum length of feeder to be boosted is found by making x = o. It is L = 20,650 feet. An infrequent operation would indicate a poorer load factor and accordingly higher cost per kilowatt-hour cz. Assum- ing h == 1000 hours and Cz = o.oi the minimum length becomes L = 10,000 feet. S4. Track Rails. — The size of track rails is determined by consideration of the mechanical requirements of the rolUng stock, the schedule speed, and the character of ballast. The common sizes weigh from 60 to 100 pounds per yard of length. The specific resistance varies with the chemical constitution and, as carbon and manganese are usually present to the extent of about one-half per cent, amounts to about 20 microhms per cubic centimeter, while that for standard . copper at 0° C. is 1.594. It is convenient to assume that for average temperatures it is ten times that of commercial copper. The usual length of a rail is 30 feet, although twice this length is sometimes used. In order satisfactorily to return the current to the station from the car, the rail sections must be conductively connected with each other by means IS6 TRACTION AND TRANSMISSION. of bonds. These bonds are often made of copper, which has a much larger temperature coefficient of expansion than steel. As a consequence, it is not easy to maintain a good electrical contact between a copper bond terminal and the rail, under varying temperatures and the displace- ments caused by trafiic. Many forms of these bonds have therefore been devised. The most satisfactory forms have their terminals either brazed to the rail or mechanically expanded in a hole in the web or flange of the rail. When heavy current-carrying capacity is desirable and the den- sity of traffic warrants the expense the rail sections may be welded to each other. It is desirable to use a pair of bonds for each joint, when they are of copper, to insure continuity of the circuit in case one bond should fail. With such bonding the resist- ance per mile of 30-foot rails may be assumed as 10 % larger than if the rail were continuous. For convenience in calculating the voltage drop in tracks the following values for the resistance of two track rails in parallel including that of 9-inch bonds of half the carrying capacity of the rail are given: RESISTANCE OP TRACK RAILS INCLUDING BONDS. Weight of rail. Resistance per mile, pounds per yard. ohms. 40 0.066 S° OOS3 60 0.044 70 0.038 80 0.033 90 0.030 100 0.027 no 0.024 THE DISTRIBUTING SYSTEM. 157 55. Negative Track Feeders. — In those systems which make use of the earthed track rails for returning current from the car motors to the generating station, differences of potential exist between different points along the rails; as a consequence, the neighboring soil takes a part in the conduction of the return current owing to the presence in it of moisture, of dissolved substances, and of pipes or other metallic subsurface structures. At the points where the current leaves the last to enter the connection from the negative bus at the station, electrolytic corrosion occurs to an extent dependent upon the ampere-hours conducted. It is therefore desirable that this leakage current from the rails should be made as small as possible. Its magnitude is dependent upon that of the potential differences along the rails, and varies inversely as the resistance offered by the earth. It is not often that the engineer can alter the earth resistance, but he can materially vary the poten- tial distributions along the rails by using negative sup- plementary conductors or feeders, connected to the track at predetermined points, which serve as auxihary return conductors. Owing to the large cross section offered to the current by the earth, its chief resistance, outside of that existing at the ground plate for the negative bus at the station, is that due to the layers of soil in the immediate vicinity of the rails, and this may be, and hereinafter is, considered as a transition resistance of a ohms per foot length of track (two or four rails) and varying inversely as the length. In the case of a track whose rails are connected to the ground and to the negative bus at the power house, if the excesses of potential, e, of the various points in the track above that of the negative bus be represented by the ordinates of the curve of Fig. 68, while the abscissae repre- 158. TRACTION AND TRANSMISSION. sent distances in feet from the power house, then the leakage current die, escaping at the point / to the soil from an elementary length, dl, of track, is represented by the proportionality dUo.^-^, (i) and the total leakage current is proportional to the area 30 lU > < to CO p o > . — • ^ ^ .'' ^ y 1 / ^ r I /■ / -! '-dl ^ .1 200 400 600 800 1000 DISTANCE FROM POWER HOUSE, i, IN FEET. Fig. 68. included between the potential curve and the axis of abscissae, or /eoc - I edl. (2) a Jo In order to compare the relative merits for the reduction of leakage current of various proposed dispositions of the same amount of return copper, it is desirable that analyti- cal expressions be obtained for e in terms of the distances, I, from the power house for each proposed disposition. Substitution can then be made in (2) and that disposition which yields the minimum value of the integral may be adopted. As an illustration, consider a single generator supplying THE DISTRIBUTING SYSTEM. 159 I amperes to trolley feeders for a single-track road extend- ing L feet in only one direction from a station, the load being uniformly distributed along the line. Assume that the negative terminal of the generator is grounded at the station and that one negative supplementary conductor of uniform cross section, and bonded to the rails at short intervals, extends from the station to the end of the hne. Let / = distance in feet of any point on the line from the station, i = current at this point in amperes, e = voltage of track at this point above negative terminal of generator, r = resistance in ohms per foot of return, including rails and negative supplementary conductor, p = ohms per mil-foot of copper, Ai= copper cross section in circular mils equivalent in conductivity to the track rails, Ac= cross section of negative supplementary conduc- tor in circular mils. Then i = I (i — j] amperes, (3) "-/.'•""-ITTxi'-Ti)™"'- « The curve coordinating voltage to distance is therefore a parabola, and the area contained between it and the I axis, that is, the value of the integral in equation (2), is Jo Ai + A,T, i6o TRACTION AND TRANSMISSION. George I. Rhodes has compared various dispositions of return copper and concludes that a maximum reduction of leakage current can be obtained by the use of several insulated negative feeders of such cross section that the average potentials at their feeding points are maintained CO 1 a: iij a u 16 Ll ii. o z |,a liJ O 3 2 8 -1 o 1- lu 4- o DC U V \ n "~^ — . 12 3 4 5 NUMBER OF NEGATIVE FEEDERS Fig. 69. equal, the negative bus bar being insulated from the ground at the station. If, in addition, use be made of negative boosters in the feeders, the potentials at the feeding points can be rnain- tained uniform with that of the negative bus-bar even with widely fluctuating loads. The amount to which the original leakage current is reduced by various numbers of such negative feeders and boosters as a percentage of what would exist in the case of no feeders, is shown in Fig. 69. THE DISTRIBUTING SYSTEM. l6l If the contact-conductor sections be supplied by individ- ual feeders and the current of each be passed through the field exciting coil of the booster which is connected to the track feeder for the corresponding section, as indicated in Fig. 70, the potential of the track feeding points can be kept practically equal to that of the negative bus at the station. It should be noted that the track rails are insu- lated from the negative bus. This arrangement of connec- NEGATIVE TRACK FEEDERS Fig. 70. tions is the most effective one for minimizing electrolytic corrosion in those systems which return current through the grounded track rails. 56. Electrolytic Surveys. — The determination as to whether and to what extent track feeders shall be installed depends upon the conditions which result from the opera- tion of a road. These conditions are usually found by mak- ing an electrolytic survey and stud3dng the results thereby attained. The difference of potential between the tracks and the various pipe systems is measured at many points throughout the roadway. Care must be taken that good terminal contacts be secured, for these differences seldom amount to more than a few volts. Upon a map, which clearly shows all the tracks, the potential differences are plotted as ordinates with respect to the track as abscissae, and a curve is drawn through their ends. Wherever the l62 TRACTION AND TRANSMISSION. track is positive with respect to the pipe the area included between the curve and the track is generally colored blue. In case it be negative the area is colored red, indicating that the potential conditions at such places are favorable to corrosion of the pipes. Another map is prepared from which the tracks are omitted but upon which the pipe system under investi- gation is indicated. The magnitude and direction of the currents flowing in the pipes at various points, especially in the red districts, are obtained and are indicated on this map by arrows of proportionate length and direction. Currents may be measured by the drop-of-potential method, using a low-reading millivoltmeter. The portion of the pipe over which the drop is to be obtained must be insulated from the earth and therefore excavations are generally necessary. A study of this map is likely to reveal the location of points where electrolytic corrosion is likely to take place. Thus, if at two points on an unbranched pipe currents be simul- taneously flowing towards each other, the conclusion is inevitable that they both leave the pipe at an intermediate point. Again, if a large current flow towards a point where a smaller one is flowing in the same direction, the excess of the former must leave the pipe at intermediate points. A relatively high potential difference between a track and pipe does not necessarily indicate that a large current is flowing between them, for such would not be the case if the resistance offered by the soil were large. It may be desirable to know whether the current be large or not, and this can be determined by the use of Haber's earth ampere- meter. It consists of a wooden frame in which is mounted a plate of glass with a copper plate on each side of it. The free surfaces of the latter are covered with a thin layer of THE DISTRIBUTING SYSTEM. 163 paste, made of copper sulphate and 20 % sulphuric acid, and held in place by parchment. This frame is buried in the soil transverse to the supposed path of current flow. Leads from the copper plates are connected with a milli- amperemeter which will indicate the flow of current through the soil. The device is non-polarizable, and experience shows that its presence in the soil does not distort the current flow-lines. In order to make the current measurements it is neces- sary to know the resistance per unit length of the pipe. This may be obtained from the following table published by Prof. A. F. Ganz, based upon a specific resistance of 0.00144 ohm per pound-foot of cast iron and 0.000181 ohm per pound-foot of wrought-iron pipe. WEIGHT AND RESISTANCES OF CAST- AND WROUGHT-IRON PIPE. Standard cast iron. Standard wrought iron. Extra heavy wrought iron. diameter of pipe, inches. Weight per foot without hub pounds. Resistance per foot, ohms. Weight per foot without hub pounds. Resistance per foot, ohms. Weight per foot without hub pounds. Resistance ] per foot, ohms. i I 2 3 4 6 8 10 12 16 18 20 24 30 36 48 II. 18. 31- 42. SS- 70. 109. 130. 151- 205. 294. 408. 604. .000131 .000080 .0000465 .0000343 .0000262 .0000206 .0000132 . OOOOI I I .0000095s .00000702 . 00000490 .00000353 .00000238 .84 1-7 2.7 3.6 7-S 10.6 18.8 28. 40. 49- .000215 . 000106 .000067 . 0000502 .0000241 .0000171 . 00000963 . 00000647 .00000452 .00000369 I.I 2.2 3-6 S- 10. IS- 29. 43- S4- 6S. .000164 .000082 .0000502 .0000362 .0000181 .0000121 .00000623 .00000421 .00000335 .00000278 164 TRACTION AND TRANSMISSION. 57. Alternating-current Distribution. — The voltage drops which occur with alternating-current systems are dependent not only upon the resistances of the conductors but also upon their reactances and the phases of the components of current. An adequate general treatment of the subject is out of place in this text. The methods of determin- ing line reactances will be given in a later chapter. The flexibility and cheapness of transformers permit of their extensive use for the equalization of potentials, whereas excessive copper or boosters are essential in direct-current systems. The high permeability and the hysteresis characteristics of steel track and third rails involve large drops when they carry alternating currents. Skin resistance becomes an important factor and it has been estimated that at frequen- cies of 15 and 25 the current confines itself to a peripheral depth of but 4 and 3 millimeters respectively. Disregarding any drop due to flux set up outside the rail, its impedance, according to Armstrong, is 8 times the ohmic resistance at 25 cycles and 6.2 times at 15 cycles. PROBLEMS 31. Calculate the resistance at 20° Centigrade of a 30-foot length of track rail weighing 700 pounds. Take 7.7 as the specific gravity of steel rail. 32. How far from the terminus of a road is the last feeding point to a No. 0000 copper contact conductor supplying o.oi ampere per foot, if the potential at the feeding point is maintained at 550 volts and the drop in the contact conductor must not exceed 20 per cent? 33. The two cross-bonded contact conductors of the Manhattan Ele- vated Railroad consist of third rails weighing 100 lbs. per yard. They are fed at both ends from substations which maintain a constant potential of 625 volts. If the distance between substations be one mile and the current drainage from both tracks at maximum load be 0.3 ampere per foot, what is the maximum percentage drop in the contact conductors? 34. Determine the economic cross-section of a copper feeder to carry THE DISTRIBUTING SYSTEM. 165 350 amperes for 2500 effective hours per year. Assume the cost of a kilo- watt-hour as one cent,, the cost of a poimd of copper 18 cents, and the rate of interest and depreciation as 6 per cent. 35. If the feeder of problem 34 be supplied with current at 550 volts, what is the greatest length which may be used without producing a drop exceeding ten per cent? 36. Plot a curve, based upon the constants given in § 53, which shows the dependence of equivalent hours of operation upon the iniTiiTniim feeder length for economic installation of a booster assuming an average booster eflSciency of 85 per cent. 12 1 66 TRACTION AND TRANSMISSION. CHAPTER VIII. SUBSTATIONS. 58. Types of Substations. — A substation is a station which contains devices which serve to alter the voltage or character of the current received from the transmission line and thereafter deliver it to the distributing system'. Sub- stations are of three types, depending upon the character of the received and delivered currents as to whether they are direct or alternating. 59. Direct Currents Received and Delivered. — With the Thury system, which is employed to some extent in Europe but which is not looked upon with favor by Amer- ican engineers, direct current is generated at the power house, transmitted and received at the substation and direct current is sent out from the substation. A typical example of this system is the plant which transmits power from Moutiers in Savoy to Lyons for the operation of the street railways in the latter city. Sixteen water-turbine- driven direct-current generators, consisting of four sets of four each, are connected in series with each other and can, at full load, generate 3500 volts each or 56,000 volts in all. They supply a constant current of 75 amperes to the line, and their voltage is varied with the load by means of electrically operated regulators connected in series with the line. The sets may be operated singly or together accord- ing to the load reqiurements, a single movement of a controller handle on a simple switchboard serving to cut in SUBSTATIONS. 167 or out a set. The transmission line is no miles long, con- sists of two copper wires 0.354 inch in diameter, and entails a constant loss of 535 kilowatts. It has been found necessary to keep the line connected to the earth through high resistances and to provide numerous lightning arresters. At the substation the received current is used to operate motors each of 540 horsepower capacity. The speed of the motors is maintained constant by centrifugal regula- tors which shift the brushes when the load changes. These regulators are criticized as being an inherent defect of the system, for they are complicated and frequently require adjustment and repairs. Each motor is used to drive a 600-volt direct-current generator which is connected with the distributing system. Special precautions are taken to insulate the motors from each other, from the earth, and from the generators which they drive. Tests have shown that the power output of the substation is 0.705 that of the intake of the turbines which drive the generators at the power house. As a precaution against breakdown of the line or power station, the substation is amphfied by an auxiliary transformer station in which direct-current motors are direct connected to 10,000-volt three-phase generators, the latter being adapted for connection with the lines of another operating company. These sets are reversible and by means of them energy may be supplied to or received from the other system. The power stations and the substations in this direct-current system cost more than those which use alternating currents for transmission. The cost of the transmission line is less and the maximum voltage, as limited by the appearance of corona, § 72, is greater. The system is lacking in that flexibility which characterizes the use of transformers. i68 TRACTION AND TRANSMISSION. 60. Alternating Currents Received and Delivered. — In those systems which employ induction motors on the cars or locomotives, three-phase currents are generated at the power station, and, if the length of the transmission line requires more than an impressed voltage of 12,000 — the upper voltage limit of generators — at least three single- phase step-up transformers or one three-phase transformer must be used. At the substation three step-down trans- formers must be located, and usually a fourth one is in- stalled as a spare unit. Such substations are designed to 1.00 >-0.99 o z uiO.98 0.97 FU Oj^ SS~- ^ 250 500 CAPACITY IN KILOWATTS. Fig. 71. 750 operate without an attendant and therefore the transformers are self-cooling and both the primary and secondary circuits are supplied with automatic oil switches adjusted to open on short circuits but not on overloads. Fig. 71 shows the full-load efficiencies of a Hne of 25-cycle, 11, 000- volt air- blast transformers of capacities from 100 K.W. to 750 K.W. The buildings are of fireproof construction, and permanently installed ammeters and voltmeters facilitate the location of possible faults on the system. In those systems which employ single-phase commutator SUBSTATIONS. 1 69 motors, if the transmission line be single phase and be long, and consequently the voltage be high, but one step- up and one^step-down transformer are necessary. Since, however, it is cheaper to use a three-phase transmission line it is advisable to use a three-phase generator and three step-up transformers at the power station and two step- down transformers at the substation, the latter being con- nected according to Scott's method for transformation from three-phase to two-phase with connections as shown in Fig. 12. Furthermore, the cost per kilowatt of three- phase genetators is but about three-quarters that of single- phase generators, because in the former a single magnetic circuit is used in common by all phases. Experience has shown that it is practicable to use alternating-current pressures as high as 20,000 volts on overhead contact conductors. In such cases stationary substations may be dispensed with, and voltage reduction, suitable to the requirements of the motors, can be attained by the use of transformers located on the cars or locomo- tives. In some respects this arrangement is ideal, each motor having a substation and carrying it with it. There are no substations on the electrically equipped portion of the N. Y. N. H. & H. R.R., 11,000 volts being generated and impressed directly upon the contact conductors of the system. Each motor, however, is provided with a trans- forming device. The locomotives used in the Berlin- Zossen tests were equipped with polyphase motors wound for an impressed pressure of 10,000 volts taken direct from the contact conductors without the intervention of voltage transforming devices. 61. Alternating Currents Received and Direct Cur- rents Delivered. — Substations which convert alternating I70 TRACTION AND TRANSMISSION. current into direct current are the type most frequently used. By means of transformers the voltage of the currents received from the transmission line is stepped down and the secondary currents are supplied to converters or motor- generators which deliver direct currents to the distribut- ing system. The motor element of the motor generators may be either a synchronous motor or an induction motor. The proper selection of the conversion apparatus involves a number of considerations. Floor Space. — In all cases it is customary to install three single-phase transformers or one three-phase trans- former for each converter. Since both induction and syn- chronous motors are wound for an impressed E.M.F. up to 12,000 volts, step-down transformers can usually be dispensed with. Even then the floor space occupied by converters and transformers is less than that required for equivalent motor-generators. Wilson and Lydall give the following values for units of about 750 K.W. capacity: Converters and transformers, 0.21 sq. ft. per K.W. Induction motor-generators, 0.31 sq. ft. per K.W. The possible separate location of converters and trans- formers, for instance the placing of transformers on a gallery, gives a flexibility of arrangement of apparatus not possessed by motor-generators. With urban substations and expensive real estate the occupied floor space becomes an important factor. Efficiency. — The efficiency of synchronous converters is greater than that of motor-generators. Even if to the losses of the converters be added the losses in transformers and regulating devices, which are not involved in the use of motor-generators, the efficiency of the combined converter SUBSTATIONS. 171 installation excels. W. R. C. Corson gives the average operating efficiencies from this point of view as follows: Synchronous converters 91% Synchronous motor-generators 85% Induction motor-generators 84% Figs. 72 and 73 contain curves showing the operating characteristics of a shunt- wound, 25-cycle, 600-K. W. conver- 25 50 75 100 125 150 175 200 PER CENT, OF FULL LOAD CURRENT FROM COMMUTATOR Fig. 72. ter, and of a 50-cycle, 230-K.W. induction motor-generator respectively. ■ Regulation. — Since the ratio between the commutator and slip-ring voltages of a converter is practically constant, irrespective of the field excitation, except in the case of split-pole converters, it is customary to insert a reactance coil in the circuit between the low-tension terminal of a 1/2 TRACTION AND TRANSMISSION. transformer and the converter slip ring which it supplies with current, and to provide the converter with a series magnetizing coil which is traversed by the direct current from the commutator before it enters the feeders of the distribution circuit. The field excitation is thereby caused to increase with load, and the alternating current which enters the slip rings is therefore made to lead the impressed voltage. The passage of the leading current through the reactance coil establishes such phase relation that the vector <0.6 0.5 ■ 0.4 ^ f^c^ OP' ~~~ ^ / ^ k^ / / f 100 200 LOAD IN KILOWATTS, Fig. 73. 300 400 sum of the transformer and reactance voltages is greater than the former and therefore the slip-ring voltage is raised with load. The converter with such an arrangement is said to be compounded, and may maintain a constant direct- current voltage under wide variations of load. It is usual to provide for each phase a reactance coil of a combined kilovolt-ampere capacity equal to 15 % of the rated kilowatt capacity of the corresponding converter. Fig. 74 shows a General Electric Company air-blast reac- tance set and starting switches for a looo-K.W., six-phase converter. The operating characteristics of the 600-K.W. SUBSTATIONS. 173 converter previously mentioned, with added series ampere- turns at full load amounting to 64 % of the shunt ampere- turns, are shown in Fig. 75. With proper adjustments of the series and shunt field coils it is possible to make the converter take a lagging current on light loads and a leading current on heavy loads. It therefore increases the power Fig. 74- factor of the transmission circuit on heavy loads. This method of regulation, however, fails to give satisfactory results when the line resistance drop exceeds 10 % of the impressed line voltage or even less; and yet on large trans- mission systems and with long transmission lines it is desir- able and often economical to have a drop greater than this. With motor-generators, however, the direct-current volt- age can be as easily and satisfactorily regulated as with 174 TRACTION AND TRANSMISSION. plain generators, and the regulation is in nowise dependent upon the drop in the transmission line. Furthermore, by the use of series coils on a synchronous motor field the motor-generator set may be adapted for power factor correc- tion to the same extent as with converters. Cost. — The cost of converters per se is less than that of motor-generators of the same capacity. Compound con- 25 50 75 100 125 150 175 200 PER CENT, OF FULL LOAD CURRENT FROM COMMUTATOR Fig. 75. verters cost more than shunt converters because of the lower flux density in the iron. To make a proper comparison of the costs of the two types of installation one should consider the whole system and compare the total cost of converters, regulating devices, transformers, switch gear, ventilation apparatus, and trans- mission cables with that of equivalent motor-generators, switch gear, and cables. Parshall and Hobart make such a SUBSTATIONS. 175 comparison for a plant supplying three substations each having a rated output of 1800 K.W., the most remote being 6 miles from the power house. The results are given in the following table. RELATIVE COSTS OF CONVERSION INSTALLATIONS High-tension cables Converters (6-900 K.W.) Motor generators Transformers and ventilating sets (21-300 K.W.) Substation switchboards and gear Total Converters. SSOjOOO 67,500 3I.S°° 27,000 $206,000 Motor generators. 118,000 $191,000 The smaller cable expenditure with motor-generators results from their ability to operate satisfactorily with a greater line drop than is allowable with converters. Whether the interest on the 7 % less outlay with motor-generators would offset the increased operating cost resulting from the smaller efficiency of the motor-generators would require a careful study of the substation load diagrams. The pre- ceding table is based upon the following costs per rated kilowatt: Converters $12.50 Transformers and ventilation apparatus 5.00 Converter switch apparatus 5.00 Motor-generators 2i.go Motor-generator switch apparatus 3.33 The data concerning the converter equipment relate to an existing substation. 62. Locatioa of Substations. — There are certain points on the roadway of a traction system which may be con- sidered as natural points for the location of a substation. 176 TRACTION AND TRANSMISSION. These are the centroids of load in urban networks, the power house when it is located on the line, and the middle or a point near the remote ends of the terminal sections of the lines. It is also often desirable to have the substation located at a passenger station, thus making it possible for the ticket agent to serve as a substation attendant. If it be assumed that there is a uniform drainage of cur- rent throughout the length of the road and that the con- tact conductor has numerous connections with the supple- mentary conductor, the composite conductor, of uniform cross section, extending from one substation to each adja- cent substation, then the economic distance between sub- stations can be determined by mathematical treatment. ^-a i:::I ^ COMPOSITE CONTACT CONDUCTOR j L -, Fig. 76. Furthermore, if the profile of the road be such that along certain portions the drainage of current is greater than along the rest of the line, each portion by itself can be treated mathematically. Assume a road of length L feet to be supplied with cur- rent from n substations, equally spaced from each other by a distance X = L/n feet, and arranged as in Fig. 76, whfere the substations are represented by 5. The annual mean effective current per foot of contact conductor can be determined from a study of the train diagrams and from the instantaneous currents per car. The maximum drop, which will occur at a point midway SUBSTATIONS. 1/7 between substations and at the terminals of the line, is limited to such a value as will permit satisfactory operation of the motors and lighting of the lamps, is known, and must be used as a check on the economic drop about to be determined. See problem No. 37. For a fixed distance between substations, the economic cross section, A, for the composite contact conductor is such that the annual charge for interest and depreciation on its cost is equal to the annual charge for the energy lost in it. To prove this, consider that the former charge is dependent on the weight of the conductor, that is its cross section, and may be placed equal to KiA, and the latter on the resistance, which may be placed equal to K2/A, where Ki and K2 are constants. The sum of these two charges, X, must be a minimum, hence the differential of x, with respect to A, must equal zero. Therefore dx „ K-i -=ii:i-- = o and KxA = K2/A dollars. (i) If now, with a conductor of constant cross section, the distance between the substations be increased, which is equivalent to reducing the number of substations for a road of given length, the resistance and weight of the con- 'ductor between stations will be increased proportionately. The interest charge will likewise increase, while the energy charge will increase to a greater extent, because the current entering the section of conductor from the substation has also been increased. Therefore K2/A is, in this case, larger than KiA, and to maintain the equality of equation (i) the value of A must be increased. 178 TRACTION AND TRANSMISSION. The increase of distance between substations, or reduc- tion in their number, furthermore affects the charges for interest, maintenance, and operation of all the substations. The wages for fewer attendants and the costs and losses per kilowatt of the larger units installed are thereby de- creased. The economic cross section of contact conductor and economic distance between substations, therefore, in- volves a minimum annual charge for wages, for interest on total cost of copper and equipment, and for cost of total energy lost in copper and equipment. Expressions for each of these items of annual charge must be found in terms of the distance, X, between substations, and the differential coefficient of their sum, with respect to X, must be equated to zero in order to determine the economic separation of substations. It will be assumed that the annual charges against the transmission line, the energy lost in the track, and the cost of substation buildings are not affected by changes in X. The last two charges can be introduced without difficulty, if desired. The first charge materially alters with X only in the case of very short lines and very heavy trafl&c. Wages. — For a given type of substation, length of line and density of traffic, the necessary number of attendants in each substation and their average wages will not vary with the size of the units, so far as these sizes are dependent upon X. For all substations, however, they will vary directly with the number of substations, n = L/\, and if there be n' attendants per substation, receiving on an average w' dollars per year, the total annual charge for attendants C„ = nn'w' = [n'w'L] - • (2) SUBSTATIONS. 179 With transformer substations there are no attendants and therefore C„ becomes, in this case, zero. Charges against Contact Conductor. — Consider that part of the contact conductor of cross section A circular mils which is fed from one substation. Under the assumption of a uniform drainage of /o mean effective amperes per foot, the watts lost in each half of the conductor, or X/2 feet, are, according to equation (5), § 48, pi (?\^/ 24 A. There being 8760 hours in a year, at a cost of C3 dollars per kilowatt- hour delivered from the substation, the_annual_cliarge for the-energy lost in_XJe£t_of the conductor is C/= ^262 _P£3^ ^^2^3 dollars. (3) 1000 12.4 If the cost of conductor be C2 dolla rs per pound and j£_be the weigMo f a mil-foot in po unds, at an interest rat e of P2 the annual capital_diarge~aga-inst^rhe-T0ntact conductor is Cc" = piCiwAX dollars. (4) Since C/ must equal CJ' when the cross section A is most economical, equations (3) and (4) may be equated and solved for A as follows: ^ = 0.8 •; =; 7oX v/ ^ ^ circular mils. (5) Substituting the value of A in (4), multiplying by 2 so as to include CJ and by L/\ = n to cover the whole length of line, the totaJjjinualxhargeagainsLiontact conductor is c. = hc/+cn = '-^c/', or Cc= [1.71 LIq Vpfwp^CiCslx dollars. (6) Annual Charge against Substations. — If the total max- imum output of all substations be P kilowatts and if the l8o TRACTION AND TRANSMISSION. overload coefficient or ratio of maximum output to rated installed capacity be 5, then the rated capacity of the appa- ratus installed in each substation is P/Sn K.W. The over- load coefificient is determined from a study of the nature of the load diagram for each substation and from the over- load guarantees as to the apparatus. In determining the number of units to be installed in each substation the fol- lowing points must be considered: (a) It is desirable and good practice to have the same sized units throughout the system whenever possible. (b) There are limits as to the maximum size of units to be found among manufacturers' standard lines. (c) The daily load curve is often of such a character that one unit and several units can be operated for pro- tracted intervals at nearly maximum efficiency. (d) The maintenance of the continuity of service requires that either a spare unit be installed in each substation or that there should be a portable substation which can be placed on a siding as needs may require. (e) The peak of the load may be taken by a storage battery installed in each substation. (/) Provision must be made for increased output with growth of traffic. Fig. 77 shows the load curve on No. 2 substation of the Manhattan Division of the Interborough Rapid Transit Company on a particular day. This substation was then equipped with six 1500-K.W. converters each having effi- ciencies of 93.5, 95.751 and 96.0 per cent at half, full, and five-quarters load respectively. They were supplied with alternating current from eighteen 550-K.W. transformers, three for each converter, each having efficiencies of 97, 97.75, and 97.7 per cent respectively at the corresponding loads. SUBSTATIONS. i8r 2: 1- < a: UJ 0- z CO H z CO m < q C I] r 1 c =d ID d q q 1 1 1 L 1 n u < 1= J 1 1 CO CC =) i: <: CD C31 ID II H => D- H =) H l±j z < 1 n 1 n pj J < o > r 3 1 < Q q 6 ■^ 1 — a 1- 1 H 1 ((I m r _J 1 1 L 1 1 L n _i LO CM 6 ID (3 ' L -2 l_ _ u 1 1 IMS I- 10 ID (0 ■* •SJ.XVMOTI>l 13 IS2 TRACTION AND TRANSMISSION. Assuming that the overload capacities are as recommended in the Standardization Rules of the A. I.E. E., that is, that they can each carry an overload of 25 % for two hours and 50 % for one-half hour, the load diagram shows the prob- able operating conditions of these units on this day to be as in the accompanying table, the numbers in the third column indicating the equivalent number of hours that a unit must be operated at full load in order that its losses may be the same hypothetically as they are in fact. To determine the equivalent hours, if the ef&ciency at any load be e, let the expression (i — e) be termed the deficiency at that load; then the equivalent hours are equal to the pro- duct of the number of hours at any load by the ratio of that load times its deficiency to full load times its deficiency. CONDITIONS OF OPERATION OF UNITS Unit. Hours per day. Equivalent hours per day. No. I 24 21.4 No. 2 ISS 15.0 No. 3 8.8 7-S No. 4 2.0 2.0 No. s No. 6 Total daily equivalent unit, hours, 45.9 The equivalent annual hours of operation of all units in this substation at full load are therefore ^ = 365 '^ = 2792 hours. 6 The load on this substation was about 20 % greater in winter than as shown in Fig. 77, due partly to the current required for car heaters. Instantaneous fluctuations of SUBSTATIONS. 183 current above and below those shown in the figure amounted in some cases to 40 %. In calculating losses in a proposed substation a mean effective load diagram should be used. To obtain an expression for the annual charge for energy lost in the substation in terms of \, it is necessary to plot deficiency curves in terms of the rated capacity of units. There should be say three curves, for half, full, and three- halves load respectively. The points on these curves can y.04 Q iitv -^ Mo_ "~~~ iHf fee 2iM JT| --- --. 3 L L ^ 24C -o.c 100^ ^ ~ ~~~- ^ CONVERTER -TRANSFORMER UNITS. 500 CAPACITY. P. 1000 ' 1500 IN KILOWATTS. Fig. 78. be obtained readily from manufacturers' efficiency curves of units for say three rated capacities, as 500, 1000, and 1500 kilowatts. Three such curves for combined transformer- reactance-converter units, at unity power factor, are shown in Fig. 78. The full-load curve is practically straight over the portion covered by the capacities entering into the problem, and the deficiency, s, may be expressed analyti- cally as »=/3-^3Po, (7) where Pq is the rated capacity in kilowatts. i84 TRACTION AND TRANSMISSION. The following values are suggestive of the order of magni- tude of the constants /s and gs for conversion at 25 cycles from 11,000 volts to 6oo~volts: DEFICIENCY CONSTANTS Units. K.W. h- «.!• Transformer-reactance-converter Transformer-reactance-converter Transformers. 500 to 2000 200 to 500 100 to 750 0.072 0.087 0.024 0.000012 . 000060 0.000014 The converters of larger capacity listed in the table are wound six-phase, while those of smaller capacity are three- phase. If there be u units of capacity Pq kilowatts in- stalled in each substation, including spare units, and h be the equivalent annual hours of operation of all units at full load, then, since Po = P/5nu, the annual loss of energy in all substations is Pouuih Phh P%h S^nu kilowatt-hours. (8) Since nj= L/SK, if the cost per kilowatt-hour of energy delivered to the substation be Cz dollars, the annual charge against the substations for energy lost in them is C ' = ' Pc,%h - . 5 . -PWM X dollars. (9) The cost of one unit of capacity Pq kilowatts can be expressed analytically as /s' -|- gs'Po dollars, where fi and ga' are constants determined by the manufacturer. The cost of all units to be installed in all substations is therefore nuifz + Pgi'/dnu), and, if pz be the annual rate covering interest, depreciation, and oBsblescence, the annual charge against cost of substation equipments is ' SUBSTATIONS. 185 C/' = p^nuf^' + Pp,g,'/5, or, since n = L/\, C/' = [^^] + [Lp,fM i dollars. (10) The following values are suggestive of the order of magni- tude of the constants /s' and g^ . COST CONSTANTS Units. K.W. U- S3'. Transformer-reactance-converter. . . Transformer-reactance-converter. . . Transformers 500 to 2000 200 to 500 250 to 750 3200 2000 240 9-4 II. 2.66 The total annual charge against the substation equip- ments is equal to the sum of C/ and C," as given in equa- tions (9) and (10), or is The Economic Spacing of Substations. — The economic value of \ is such that the total annual charges or the sum of C„, Cc, and C,, as given in equations (2), (6), and (11), shall be a minimumi To avoid needless repetition of the letters entering into the bracketed coefficients of these equations, these coefficients may be represented as follows: Cc = Kc\, Cs = ifj -|- Kg /X -{- Kg X, and their sum as C = Kg+{K„ + Kj)/\ + (K^ + Kg") X. To determine the minimum value of X, the differential l86 TRACTION AND TRANSMISSION. coefScient of C, with respect to X, must be placed equal to zero, or dC K^ + K', dX X^ .K.+Kj'^o. Solving, and substituting the values of the coefScients, X= / '''''' ^ ^ - ^'H""^ feet. (13) SJ i.7iLIoVpwp,c,c,-^^(^-^) The economic cross section, A, for the composite contact conductor can now be obtained by inserting the value of X in equation (5). 63. Numerical Illustration. — For the purpose of more clearly understanding the influence of the factors entering into the economic spacing of substations, assume a road 200,000 feet long with converter substations that are to be cared for by two attendants, each receiving $720 per annum, and each on duty 12 hours each day, every station to be equipped with two converter units of equal size. The cost and deficiency constants will be those applying to units under 500 K.W. capacity. Let the following be the values of the characteristic constants: P/5 = 2500 K.W., 5 = 1.25, /o = 0.00875 ampere per foot, p2 = c.o6, h = 5000 hours, p3 = o.ic, p = 10 ohms, Ci = C.18 dollar, w = o.ooogo3o^ound, cs = c/ =0.01. SUBSTATIONS. 187 Then X = ([2 X 720 X 200,000 +0.10 X 2000 X 2 X 200,000] -^ 1. 71 X 0.00875 X 200,000 X V 10 X 0.00000303 X 0.06 X 0.18 X o.oi — / ,, ,^ o.oi X 0.00006 X sooo1\^ (2500)2 X — — ^ — 200,000 X 2 J/ = ([288,000,000 + 80,000,000] -W. H- [2990 V 0.000000003 2 7 — 0.0469])! ^68,000,000 r, J- ^ -1 '^ — = 54,800 feet = 10.4 miles. 0.169 — 0.0469 Thus, the economic separation of converter substations on this 37.8-mile electric railway is 10.4 miles; consequently \ UAL COSTS IN I^NDS OF DOLLAR CO ^ ^ JLES 10 1000 2000 CAPACITY IN KILOWATTS. Fig. 8S. 3000 transformers are less than those for 25 cycles and the oper- ating efi&ciencies of the former are greater than those of the latter. The differences are not very great, as will be seen from the curves in Figs. 88 and 89, which refer to 1000 2000 CAPACITY IN KILOWATTS. Fig. 89. 3000 33,000-volt, plain steel, air-blast transformers. Induction motors for higher frequencies are also cheaper, but operate at lower power factors. At the lower frequency it is less difl&cult to operate generators and other synchronous appa- 204 TRACTION AND TRANSMISSION. ratus in parallel, because the unavoidable variations in speed are smaller in proportion to the angular velocity. The charging current of the line and the inductive drop are less with low frequencies, and may give a better regulation. For lines of moderate length it might prove desirable to use 60 cycles, but the general tendency is to use 25 cycles. For lines of great length, however, it is usually undesir- able to use 60 cycles for the following reasons. In all large systems odd harmonic frequencies of voltage and current, of which the third and fifth may predominate, are likely to be present and be superposed upon the fundamental frequency. Electromotive-force harmonics may be due to armature reaction, to pulsation of inductance, to the distribution of armature windings, or to non-uniform distribution of mag- netic flux in the air gaps of the generators. Current har- monics may result from similar causes associated with the structures forming the receiving apparatus. Every trans- mission line, because of its inductance and capacity, has a resonant frequency. The magnetic field of the former and the electric field of the latter serve for the storage of energy in kinetic and potential forms respectively. Such capacities for the storage of the two forms of energy are characteristic of every medium for wave propagation, and their magni- tudes determine the velocity of the propagation. As will be shown later, the velocity with which an impressed differ- ence of potential travels away from a generator along a line of usual construction is but slightly less than the velocity of light, that is, in the neighborhood of 186,000 miles per second. Now a transmission line with both ends open or both ends short-circuited has a resonant frequency which corresponds to a wave length equal to twice the length of the line, as is the case with an organ pipe open at both ends. TRANSMISSION LINES. 205 On the other hand its length is but a quarter wave length when one end is open and the other short-circuited, as is the case with a closed organ pipe. In the latter condition a line 155 miles long would correspond to a wave length of 4 X 15s = 620 miles and the corresponding resonant fre- quency would be 186,000 miles per second divided by 620 miles, or 300 per second, which is the frequency of the fifth harmonic, when the fundamental is 60 cycles per second. The use of 60 cycles on a line of such length is therefore likely to result in resonant oscillations of current and electro- motive force which may prove disastrous. For the operation of single-phase railroads a frequency of less than twenty-five permits of a marked reduction in the size of a motor for a given output; and yet almost all such iroads have adopted 25 cycles. The New York, New Haven & Hartford Railroad is an instance. The Midi Railway of France, among others, has adopted 15 cycles. A deter- mination of the most suitable frequency for such installations is desirable, involves extensive knowledge as to costs and peculiarities in operation, and must be considered as to its bearing on the general question of the standardization of practice. 70. Economic Voltage. — The economic voltage between the wires of a transmission line depends upon the amount of power and the distance over which it is to be transmitted as well as upon the various cost factors of equipment and energy. To understand the method for its determination and to avoid complexity, assume a single three-phase Hne of equivalent length S feet supplying at a maximum P kilo- watts, divided equally among n substations, each of which contains two <:onverter units of rated capacity P/2 n kilo- watts. Assume further that the rated capacity of each of 2o6 TRACTION AND TRANSMISSION. the three single-phase step-up transformers at the power station is P/3 kilowatts. Conductor Expense. — If the yearly mean effective power factor be cos and the voltage between wires be E kilovolts, the full load current per wire will be r P I = — = amperes. V 3 E cos If the resistance of a mil-foot of conductor be p ohms, the resistance of each wire will be pS/A ohms, and if the equivalent effective yearly hours of operation on full load current be h, the annual loss of energy in all three wires will be = r-ri^. r— kilowatt hours. 1000 1000 ^A'' COS'' <^ If the mean annual cost of delivering a kilowatt hour to the middle of the line be C3 dollars, the annual expense for energy lost in the line conductors will be C:= ^5^1^^- dollars. ' (i) 1000 y4£'' cos'' ^ If w be the weight of a mil-foot in pounds, Ca be the cost per pound, and pi be the rate of interest and depreciation on the cost of conductors, the annual charge on the capital outlay for all three conductors is C<," = 3 piCiwSA dollars. (2) Since equations (i) and (2) must be equal to each other for a minimum annual cost, they may be equated and solved for A, giving A = — \ — circular mils. (3) E cos 4> V 3000 piCiW TRANSMISSION LINES. 207 Substituting this value of A in (2) and multiplying by 2 so as to include (i), the total annual charge against the conductors will be C. = C/+ C/' = r^il^QfiP^ Vcsphp,c,w] i dollars, (4) L cos <^ J £ and representing the bracketed expression by Kc, C, = KJE dollars. (5) Pole and Insulator Expense. — There are several stand- ard forms of construction of towers or poles. Many rigid steel towers have been installed and recently flexible steel structures costing materially less than those of the rigid type have been used with success. The determination of the type to be employed can best be made in connection with a specific problem, which determination will also give the economic distance, \' feet, between poles. With poles of the flexible type the cost, Cp, does not materially vary with the voltage between the line wires. Furthermore, if insulators of the suspension type be employed, the cost of each one per kilovolt, Cj, is practically constant. Since the number of poles to be used on a line of real length S' equals S'/\' and the number of insulators is three times this, if the annual interest and depreciation on these items be pp and pi respectively, the annual pole and insulator expense is Cp = [PpCpS'/\'] + [3 PiCtS'/\'] E dollars, (6) and, representing the bracketed expressions by Kp and Kp' respectively, Cp = Kp + Kp'E dollars. (7) Pin-type insulators cost more per kilovolt as the oper- ating voltage increases. It is assumed by some that the cost thereof increases as the cube of the voltage. 2o8 TRACTION AND TRANSMISSION. Transformer Expense. The costs of transformers depend not only upon their rated capacity but also upon the volt- age at the high-tension terminals. The insulation expense increases with voltage. For the same capacity and voltage water-cooled transformers are cheaper than air-cooled ones. Power-station facilities are generally such as to permit the use of water-cooled step-up transformers, while air-blast transformers are common in substations. A study of the prices for transformers shows that the cost of each, c,, can be expressed by the following formula, where E represents the high-tension kilovoltage, Pi the rated capacity in kilo- watts, and K and K' are constants: Ct = {KE + K') VPi dollars. (8) This formula applied to transformers where Pi varies from 500 to 4000 and E from 22 to 66, gives results within the variations between the quotations from different manufac- turing companies. It is approximately true also for higher voltages. In a particular problem with many substations it would be wise to make use of two sets of values for the constants applying respectively to the power and sub- station transformers. The number of transformers in the power station is three; each of capacity P/3 kilowatts. There are 6 » in the n substations; each of capacity P/6n kilowatts. If pt be the rate of interest and depreciation on this apparatus, the annual expense for transformers in dollars is C, = iPt {KE + K') VP/3 + 6 p,n {KE + K') Vp/6 n, which by combining and transposing becomes Ct = [3 p,K'yf'¥h{T- + ^'^)\ + [3 PtKVpJl{i + V^)] E (9) TRANSMISSION LINES. 209 and, if Kt and K/ represent the bracketed expressions, the annual transformer expense may be represented as Ct = Kt + Kt'E dollars. (10) Auxiliary Expense. — The costs of aluminum lightning arresters, choke coils, and oil switches increase with the voltage of the circuits with which they are to be connected. The first mentioned increase more rapidly than the voltage, the second nearly directly, and the last less rapidly. If their combined costs for different voltages be determined, it will be found that the cost per three-phase unit may be expressed, with sufficient accuracy, as a linear function of the voltage. Considering a unit to consist of a four-tank arrester, three choke coils, and a triple-pole oil switch, and one unit to be installed in each substation and in the power station, if Ca be the cost per unit per kilovolt and p^ be the rate of interest and depreciation, the annual expense charge- able to these auxiliaries will be C, = [paCa{n + i)\E, (11) and representing the bracketed expression by Ka, Ca = KaE dollars. (12) Solution. The economic voltage is now determined by adding the expressions for the annual expenses for con- ductors, poles, insulators, transformers, and auxiliaries, differentiating the sum with respect to E, equating to zero and then solving for E as follows : C = {K^ + Kt) + KJE + {K^ -I- K:^- Ka)E dollars, (13) ^ = -KJE^ -f {KJ + K: + iTj = o. all, 2IO TRACTION AND TRANSMISSION. Therefore the economic voltage between wires is Substituting the values of the constants from equations (4), (6), (9), and (11), _ / (0.1096 PS/cos (j)) Vczphp2C2W ~ V 3 piCiS'/\'+3 p,K Vp/^ (i + VTn) + p^c, (n + i) kilovolts, (15) and the economic cross section of the conductors is found by inserting this value in equation (3). In the above derivation the total transformer capacity at the power station has been assumed equal to that in all substations. In existing plants the latter exceeds the former by from 40 per cent to 60 per cent. This is feasible when the load peaks of the different substations are not simultaneous. The ratio of the maximum load supplied at one time to all substations to the sum of the maximum loads on each substation is termed the diversity factor. Further- more, it has been assumed that the power factor at maxi- mum load is unity. This can be realized as resulting from the phase of the currents taken by converters at maximum load when the voltage regulation is that produced by reactances. The converters then tend to correct the power factor of the line. The energy given to the line at the power station must, however, exceed that which is deliv- ered to the substations by the amount which is lost in the transmission line. Generally a transmission line extends from the power station to one of several substations, then divides, and con- tinues to the other substations. The currents in the branch TRANSMISSION LINES. 211 conductors are less than in the conductors of the main line and the cross section is accordingly reduced. The eco- nomic cross section of a conductor of a branch, of length Sb feet between substations, is determined by equation (3) and the total annual charge against the conductors by equation (4). If the mean annual effective power factor on the branch be the same as on the main hne, then the main line may be considered as having added to it a length Se such that the annual conductor expense for the branch is included in that for the main line. Remembering that / = P/ v3 E cos 0, and equating two expressions hke equa- tion (4), applied to lengths Sb and Sjs and to currents Is and / respectively, IbSb — ISe, whence Se = SbIb/I- (16) If the distance from the power station to the first sub- station be So feet, then the equivalent length to be used in calculating the annual expense of conductors is S = So-\- -^Se, (17) the last term including the extension of length due to all branches. In calculating the annual expense against insulators and poles, however, the real length of the complete line must be taken. 71. Numerical Illustration. — Assume a single three- phase 25-cycle Hne having an equivalent length oi S = 350,000 feet and a real length of S' = 450,000 feet, trans- mitting, at maximum rated load, P = 3000 kilowatts divided equally among n = $ substations at the receiving end of the line. Let the annual effective power factor be cos ((> = 0.90, the equivalent annual hours of operation be 212 TRACTION AND TRANSMISSION. h = 3500, and let the constants have the following values — the bracketed values being suggestive of the proper order of magnitude : p = 10. •w = 0.00000303. pi = [0.06]. d = [0.18]. C3 = [o.oi]. Pi = Pp = Pt ^ Pa = [0.12]. Substituting these values, K^ = (0.1096 X 3000 X 350,000/0.9), V.oi X 10 X 3500 X .06 X .18 X 0.00000303 = 432,0,00, Kp'= 3X0.12X0.2X 450,000/600 = 54, K,' = sX 0.12 X0.5 Viooo (i + Vio) = 23.75, K, = 0.12 X 50 X 6 = 36. Substituting these values in equation (14), the economic voltage is Cp = [80]. X' = [600]. Ci = [0.20], K = [o-So] K' = [65]. Ca = [50]. E = 1/ 43^,°°° = 61.7 kilovolts. V 54 + 23.75 +36 The American Institute of Electrical Engineers recom- mends as standard voltages for transmission circuits 6.6, II, 22, 33, 44, 66, or 88 kilovolts. Furthermore, 55-kilo- volt apparatus is listed by manufacturers. The problem in hand requires for greatest economy 61.7 kilovolts, a value which falls between two of those recommended. It is instructive to find what additional annual expense would be entailed in following the recommendations. The annual expense items for different voltages are therefore given in the following table. TRANSMISSION LINES. ANNUAL EXPENSES AT DIFFERENT VOLTAGES. 213 Items of Annual Expense. Conductors : KclE Poles and insulators: JCp Kf'E Transformers: Kt Kt'E Auxiliaries: K^E Total annual expense Kilovolts between Wires. 9,010 7,200 2.378 4,050 1,044 1,582 $25,094 7,860 7,200 2,970 4,050 1,314 1, 980 $24,404 61.7 7,010 7,200 3,330 4,050 1,467 2,220 $24,307 6,55° 7,200 3,560 4,050 1, 568 2,376 $24,334 These results show that the additional annual expense would be but $97 at 55 kilovolts or $27 at 66 kilovolts, and therefore either standard voltage should be adopted. The use of the higher voltage requires a somewhat smaller initial investment. It may be desirable in some cases materially to increase the operating voltage above that determined in this manner, in order to limit the first cJDst. 72. Separation of Conductors. — The proper separation of the conductors of a transmission line depends largely upon the insulating properties of the atmosphere. If the voltage between two aerial conductors be gradually in- creased a critical voltage is reached at which a discharge of electricity from the conductors into the air is initiated. This critical voltage depends upon the sizes of the con- ductors and the distance between them, and upon the temperature and pressure of the air. When this voltage is exceeded, the conductors when seen at night are sur- rounded by a luminous envelope of red-violet color. The ' 'phenomenon is termed corona. A considerable loss of ^ T5 214 TRACTION AND TRANSMISSION. energy results from the employment of transmission voltages above the critical value, this loss being termed corona loss. At normal pressure and temperature, the air breaks down and becomes convec'tively conductive when subjected to a uniform electric field strength of 78 kilovolts per inch or 3 1 kilovolts per centimeter. For alternating currents these values apply to the maximum value of the voltage wave, therefore, if a sine wave is assumed the strength of air is 31 -T- ■\2 or 21.9 effective kilovolts per centimeter. The electric fields in the vicinity of the conductors of an ordinary aerial line are not uniform, for the lines of electrostatic flux diverge in leaving the conductors. The amount of diverg- ence depends upon the sizes "•"V of the conductors and the distance between them. The distribution of potential between two wires, A and B, is typified by Fig. 90. The strength of the electric field at any point between the , conductors is measured by the slope of the curve at that point, and is termed the volt- age gradient. This gradient, expressed in volts (or kilo- volts) per centimeter, is seen to be greatest at the wire surface and least midway between the wires. In conse- quence, it is at the surface of the wires where the break- down of the air must first occur, and therefore the electrical conditions for the starting of corona may be determined from the critical field intensity at the surface of the conductor. The physical process underlying the initiation of corona is termed ionization by collision. Due primarily to the DISTANCE BETWEEN WIRES Fig. 90. TRANSMISSION LINES. 215 presence of radioactive substances on the earth, there are always present in the atmosphere positive and negative ions, each carrying a charge of 4.6 X lO"'" abstat coulombs or multiples thereof. Under ordinary conditions the num- ber present per cubic centimeter is of the order of 1000, and this number is inadequate to permit of appreciable convective conduction by the air of the problem under consideration. Each of these ions however, if subjected to an electric field intensity of sufficient magnitude, will acquire adequate kinetic energy in traversing a free path, to ionize a neutral air molecule with which it collides. The energy required to ionize a gas particle, as determined by various methods, is of the order 4 X io~" ergs. Since the free path of a gas particle increases directly with decrease of pressure at constant temperature and with increase of temperature at constant pressure, the value of the critical voltage will accordingly decrease with like proportionality. Numerous experiments show that the voltage gradient (mciximum value in the case of alternating currents) at the surface of the wire when corona appears on a round wire located in air depends upon the diameter of the wire and the density of the air in a manner given by Peek's equation '4'^ g = A8 + B .tj — kilovolts per cm., (i) where D is the diameter of the wire in cm., A and B are constants, and 5 is a density factor. The value of this density factor is unity at a barometric pressure of 76 cm. of Hg. and a temperature of 25° C, while for any other pressure p cm. and other temperature t° C. its value is f. ^PL 273 + 25 ^ 3.92 p 76' 273 + t 273 + t' ^ ' 2l6 TRACTION AND TRANSMISSION. The values of the constants A and B in equation (i) obtained by various observers are somewhat at variance with each other, due probably to difficulties in measuring the ratio of the maximum to the effective values of the high alternating voltages and to the dissimilar surface con- ditions of the wires tested. Recent tests by Prof. J. B. Whitehead on wires ranging from 0.074 to 0.231 cm. diameter yield the following values for A and B : A B Alternating current 33.7 12.6 wire positive 33.7 11.5 Continuous current , wire negative 31.02 13.5 F. W. Peek uses as his most recent coefficients corresponding to A and B for alternating currents the following: A = 31.0 and B = 13.5. The usual experimental method for ascertaining the value of the critical surface gradient g is to apply a high voltage between a wire and a metal tube, which tube is placed coaxially around the wire. If the wire has a diam- eter D cm. and the tube a radius of b cm., and corona appears when the applied voltage has reached a maximum value of V kilovolts, then the critical voltage gradient at the wire surface is given by 2V g = T kilovolts per cm. (3) ^log.^ Prof. Bennett calls this the hypothetical gradient because it holds for pure dielectrics permitting of elastic displace- ment only, but does not necessarily hold for dielectrics at potentials causing corona around the wire. Corona pro- duced by alternating currents may be detected by visibility TRANSMISSION LINES. 217 or by an electroscope, while for direct-current corona a galvanometer may be used as an additional method. In a particular experiment by Whitehead, a wire of 0.231 cm. diameter within a tube 6.109 cm. in diameter required 22,500 volts (maximum value of alternating voltage) for S 60 < a < <3 ul §20 \ \ V. \ *^ Pi Eir~ LEAD ■ • 0.4 0.8 1.2 WIRE DIAMETER IN CM. Fig. 91. the appearance of corona; the critical surface intensity from equation (3) is therefore g = 2 X 22.5 0.231 X 2.3026 logio 6.109 0.231 59.6 kilovolts per cm. Having experimentally determined the values of g in this way for various values of wire diameter D and of density factor 5, the numerical magnitudes of the constants A and B of equation (i) are then ascertained. 2l8 TRACTION AND TRANSMISSION. The critical surface gradients for various sized conductors are given in Fig. 91 as calculated from equation (i), using the alternating-current constants A and B as given by Peek and Whitehead and taking S = i. The curves are prac- tically coincident over the range of Whitehead's experi- ments, but separate beyond a conductor diameter of 0.2 cm. The gradient at the surface of a wire of diameter D cm. within a conducting cylinder of radius b cm. with a voltage V across the wire and cylinder is the same as the surface gradient of the same wire when used as one of parallel wires if the voltage from wires to neutral is equal to V and the distance d from center to center of the wires is equal to b. Then, from equation (3), the gradient for the appearance of corona on parallel wires is 2V g = — "vkilovolts per cm., (4) D log. ^ where V is the voltage from a wire to neutral in kilovolts^ (maximum value) and d is the conductor sejiaration in cm. Solving this expression for V and using equation (i) there results as the visual critical voltage to neutral: V = ) 2d D f Is \ 2d ■ log, ■^ = -\^AS + ByJ~j log, -^ kilovolts. (5) To take care of the condition of the conductor surface, an irregularity factor m should be inserted in the foregoing equation. Its value is given by Peek as follows: Polished solid conductors i.oo Roughened or weathered wires 0.98 to 0.93 Cables (seven strand) 0.82 to 0.72 Converting equation (5) to effective voltage to neutral by dividing by V2, reducing the logarithm to base 10, and TRANSMISSION LINES. 219 using A =31.0 and B = 13.5, there results as the effective voltage at which corona becomes visible: i V = mD I 25.2 5 + ii.o 5 A 2d ■^ j logio -^ kilovolts. (6) CORONA LIMITING VOLTAGES ON THREE-PHASE TRANSMISSION LINES Effective Kilovolts Between Wires for VarioosSpaclngs In Feet (Conductors Equidistant) WIRES CABLES / s i m Y f '/ f mo = 0.95 d==1.0 0.1 0.3 WIRE DIAMETER (Inches) Fig. 92. / 4" Y/, A ^ ^ V\ y / ^ ^ / /4 ^ / /A V/ / A r / A W f m„ = 0.85 ,5 = 1.0 KV. 260 140 0.3 0.5 0.7 0.9 CONDUCTOR DIAMETER (Inches) Fig- 93- A loss of power from transmission lines occurs at a voltage lower than that at which corona appears, the difference being considerable with small wires. This voltage, termed the disruptive critical voltage, is expressed by the following equation given by Peek and similar in form to equation (5) : E„ = goOTo— 5 log, 2d 'd kilovolts to neutral. (7) where go is the disruptive voltage gradient at the conductor surface and may be taken as 21.9 kilovolts (effective value) 220 TRACTION AND TRANSMISSION. per centimeter, and mo is the irregularity factor which is the same as m for wires but has values between 0.87 and 0.83 for cables. The critical voltage between conductors is V3 times the value of E„ for three-phase lines and twice E„ for single-phase lines. The critical voltage is lowered by smoke, fog, sleet, rain and snow, but is not appreciably affected by humidity, air velocity or wire material. The disruptive critical voltages between conductors (triangularly spaced) on three-phase lines are shown by the curves in Fig. 92 for solid wires and in Fig. 93 for cabled conductors, plotted from equation (7). When the three wires lie symmetrically in one plane the critical voltage for the center wire will be about 4 per cent lower, and for the outer wires 6 per cent higher than shown. 73. Resistance of Conductors. — The resistance per mile of length of a conductor in which the current density is uniform throughout the cross section, A circular mils, at any temperature t degrees centigrade is 2?, =5280^(1+ a/), where p is the resistivity in ohms per circular mil-foot at o degrees centigrade, and a is the mean temperature coefi&cient of electrical resistance; accepted values of which for the usual line materials being pa w Copper (hard drawn) 9.54 0.00415 0.00000303 Aluminum (hard drawn) 15.8 0.0039 0.00000091 The weights per circular mil-foot in pounds of copper and aluminum are given in the last column. Uniform distribution of current in conductors is realized in the transmission of continuous currents. In conductors TRANSMISSION LINES. 221 carrying alternating currents, the current density at the surface is greater than at the axis of the conductors; this unequal distribution of current increases with the fre- quency of the impressed electromotive force and manifests itself as an increase in resistance by rendering part of the conductor cross section ineffective. Fig. 94 shows the per- kj CO §30 2 / / / llj < 20 1- cn / / / / Id cc CJ 10 < h- z / ^ ^ iij ^ ^ 1.0 1.5 2.0 Z Fig. 94- 3.0 3.5 4.0 centage increase of resistance of conductors when traversed by alternating currents over that when traversed by contin- uous currents in terms of a function z, which is defined as -'4h- where r is the radius of the wire in inches and / is the fre- quency in cycles per second. The resistances per unit length of cables are somewhat greater than those of sohd conductors of like cross-sectional areas. If there be A'^ strands in a cable having a lay of i in n (i.e., the pitch of the strand helices is n times their diameter measured along the central wire), the total re- 222 TRACTION AND TRANSMISSION. sistance of the cable, assuming no current flow between strands, will be N R = R. , n{N -i) I + ■ - Thus, the resistance of a 19-strand cable having a lay of i in 15 is 2.05 per cent greater than the resistance of a solid conductor of equal cross-sectional area. 74. Line Inductance. — Conductors carrying a varying current are surrounded by a magnetic field of varying in- tensity. A change in the magnetic flux which encircles a conductor develops in it an electromotive force of self- induction. If the conductors carry an alternating current an alternating electromotive force will be induced in them, the magnitude of which depends upon the time rate of change of current, that is, its value at the instant tis L-j-, at where L represents the inductance of the circuit and I' is the instantaneous current value. Fig- 95. To determine the inductance L per unit length of single wire, consider a two-wire line carrying an alternating cur- rent, the conductors being of radius r and separated be- tween centers by a distance d, as shown in Fig. 95. The TRANSMISSION LINES. 223 magnetic flux which passes through an element outside of the conductor of width dx and of unit axial length is equal to the magnetomotive force divided by the reluctance, or J - 4 iri . dx a5>i = — — = 2t — I 2 irx X dx where i is the instantaneous value of the current flowing in the conductors. The total magnetic flux which passes be- tween the wires due to the current in one of them is obtained by integration for values of x between d — r and r, as *l = 2tl — = 2t log. d X r d and r being both expressed in terms of the same unit. The magnetic flux which passes through the conductor material is of appreciable magnitude owing to the greater flux density near the wires. Assuming for simplicity that the current is uniformly distributed over the cross sections of the cylindrical conductors, then the current inside the x^ circle of radius a; is — i, and the magnetomotive force which it produces is 4 7r — i. The magnetic flux per unit length of the element dx is 2 i/x — - > and since this flux is associ- ated with but — ths of the wire, the equivalent elementary magnetic flux which may be considered as linking the entire conductor is ,^ . x^dx d#2 = 2i/t— T" r Integrating for values of x between o and r, there results ^2 = h h- 224 TRACTION AND TRANSMISSION. Hence the total magnetic flux linked with each, conductor of the two-wire line is [d — r , fi~\ 2 log. — h - J . and therefore the inductance per centimeter length of the straight conductors, being the flux per unit current, in abso- lute units is d — r , IX 1 = 2 log, h - centimeters. r 2 By reduction, the inductance per mile for a single copper or aluminum wire becomes I, = 741 logio 1- 80.5 IQ-' henries. For 19-strand and 7-strand cables the constant 80.5 should be replaced by 89 and 102 respectively. 75. Hyperbolic Functions. — Many numerical calcula- tions in Electrical Engineering are greatly facilitated by the use of hyperbolic functions, just as are calculations in mechanics by the use of circular functions. The use of the former is as simple as that of the latter and the rela- tions which exist between the functions of each type are almost identical, the transformation formulae seldom differ- ing from each other in more than sign. Hyperbolic func- tions are especially useful in treating the problems arising in connection with transmission lines. In Fig. 96 consider the rectangular hyperbola HH and the circle CC concentric with O as a center. Since OA equals the radius, r, of the circle, yjOA is the circular sine of the angle B by conventional definition. Similarly yu/OA is, by definition, the hyperbolic sine, or, as it is commonly expressed, the sink of the corresponding magnitude. Al- though the circular functions are usually specified in terms TRANSMISSION LINES. 225 of the angle, 6, included between the axis of abscissae and the radius vector through any point, P^, of the circle, they might equally as well be specified by twice the area AOP^ of the circular sector which corresponds with this angle, if the Fig. 96. radius were unity. This will become evident if it be con- sidered that the circular sectorial area m„ = — irr"^, whence 2 X 2 . d = —u- that is, 6 varies directly with u^. The hyperboUc functions are not specified by the angle d but by twice the hyperbolic sectorial area AOPh = Uk. Referring to a circle of unit radius, by definition xJOA = cos d = cos 2 «<. and yjxc = tan 2 m^; similarly Xh/OA = cosh 2 w* and yh/xh = tanh 2 Uh, the final h signifying hyperbolic functions. The relations which exist between the coordinates of any 226 TRACTION AND TRANSMISSION. point, Ph, on the hyperbola and the corresponding sectorial area Uu may be derived from the equation of the equilateral h)^erbola, x^ — y^ = r^. The area of the sector OAPh is Ma = area of triangle OQP* — area of segment AQPu or u^ = '^^- T'ydx 2 *} r 2 Xhjh -fv.- r"^ dx 2 = L^og,?^+i^ 2 r Therefore x^^yu _ ^ ^ _ ,. r Since the equation of the hyperbola may be written as r^ = (a; + y) {x - y), x + y r whence = > r X — y ^^LJZJ!.* = ,-^ (2) By adding (i) and (2) In general, dropping the subscript of x, making the radius r = I, and letting u = — t^j X = ^ {e" + r") = cosh u. (4) By subtracting (2) from (i) and expressing in general form y = !(;«-,-«) =sinhM, (s) and dividing (5) by (4), y sinhM . , ,^. •^ = — ; — = tanhM. (6) X cosh M TRANSMISSION LINES. 227 The ratio of the areas, m = 2 Uhjr'', is termed the argument, which specifies the functions. For large values of u the second exponential terms in equations (4) and (5) vanish and sinh u = cosh u while tanh M = I. Relations between the Functions. — The following useful formulas, showing some of the relations existing between the hyperbolic functions, may be derived readily from the properties of the hyperbola or by substitution or transfor- mation. cosh^M — sinh^M = 1. (7) sinh (u dzv) = sinh u cosh v ± cosh u sinh v. (8) cosh {u ±v) = cosh u cosh v ± sinh u sinh v. (9) sinh 2 M = 2 sinh u cosh u. (10) cosh 2 M = cosh^ u + sinh^ u. (i i) cosh u ± sinh m = £=*="- (12) Differential Coefficients. — By successively differentiating equations (4) and (5) there results ^sinhM £" + €"■" , dP' sinh u . , , . — ; = — ' = cosh m; — 3-^— = smh u, (13) du 2 CM dcoshM «"-«"" . , L)I„ (i) and ^ = {g+j<.C)E^, (2) where E^ and 7„ represent the maximum (or effective) values of electromotive force and current at any point on the circuit, {R + jiaV) is the conductor impedance, and (g + joiC) is the dielectric admittance. Differentiating either of these expressions and substituting the other in the result yields respectively ^=(R +Jo>L) (g +jo£) £„. = 7^£„ (3) d^T and ^ = (^ + >i) is + J'^C) K = 7''/™, (4) • See p. 74, Alternating Current Machines (1908) by Sheldon, Mason, and Hausmann. TRANSMISSION LINES. 239 where y^ ={R + jwL) (g + jwC) for convenience. Equa- tions (3) and (4) are identical equations as to £„ and /„ and differ only in the terminal conditions, consequently the solution of one will suffice. Considering equation (4) and multiplying through by 2 —r^ ' there results as ds ds^ *" ds which when integrated becomes f^X- . ^5 / Replacing the constant of integration Ci by 7W, where C2 is also a constant, and separating the variables, there results dL = yds. Integration yields log€ [C3 (/„ + V/J + c^)] = ys, where Cz is another constant of integration. Writing in exponential form, this equation becomes Squaring, I J + c^' = -^ ■\- im - 2l„,—> Cz Cz ,27s ,7» or — r — Of = 2 1^ — , Cz^ Cz whence 7^ = Jl! - ^^^5£!! ^A,-" -Be--', (s) 2C3 2 where the two constants are A = and B= 2C3 2 Since the exponential coefficient 7 is the square root of 240 TRACTION AND TRANSMISSION. the product of two complex numbers, it also is a complex quantity, and may be written 7 = ;8 +ja, (6) where /3 and a are its two rectangular components. Then iS^ + 2ja0 +jV = (R +jo^L) (g +ycoC), or ifi^ -a^) + 2 jaP = {Rg - cc'^CL) +j (ga,i +wRC). This equation can be true only if „2 _ ^2 = ^2CL - Rg, and if 2 a^ = co {RC + gL). These are simultaneous equations which can be solved for a and /3. Thus, substituting the value of a from the latter in the former gives the biquadratic ^ + {2iC-i?g)^ + 0,2 (iJC + giy 2 2 and ■ - ^ =\/i [VCco^C^ + g2) (i?2 + ^2^2) _ ^i^c + Rg]; (7) similarly a =N/i [V(;7C2 + g2) (^2 + ^2£2) + ^2ic - Rg]. (8) The constant /3 is called the attenuation coefficient, and a is called the wave-length constant. These constants give the value of 7 in equation (5) for the current at any point of the line. 79. Current and Voltage Distribution on Lines. — Ap- plying hyperbolic functions to equation (5) of the fore- going paragraph for the current on a line at a point distant s from the receiving end, there results Im = A (cosh 75 -I- sinh ys) — B (cosh 75 — sinh 75). - ' ={A-B) cosh ys+{A-\- B) sinh 7s. (i) TRANSMISSION LINES. 241 The voltage at the same point is found by differentiating (i) with respect to distance and substituting -7^ in equa- tion (2) of § 78. Since ^-cosh 75 = 7 sinh ys and -r sinh 75 = 7 cosh js, as as there results £™ = ^ /"/" [{A - B) sinh 75 + (4 + B) cosh ys]. (2) The constants A and B of equations (i) and (2) may be determined from the conditions at the receiving end of the line. Let E^ and 7^ be the maximum (or effective) values of the voltage and current at this terminal. Then for 5 = 0, since cosh (o) = i, and sinh (o) = o, Ir = A-B and E. = ^^{A+B). Substituting these values in (i) and (2) and remembering that the complex quantity 72 = (,3 +jay = iR+jwL)ig+jo,C), there results: 7„ = Ir cosh ys + E,^— ^^sinh ys (3) and Em = -Er cosh ys + Ir , ■ 7^ sinh 75. (4) g -\- JUL, When s is reckoned from the generator toward the receiving end of the line, these equations become ^ -\- ja /„, = Ig cosh ys - Eg -^, ■j £;sinh 75 (5) 242 TRACTION AND TRANSMISSION. and Em = Eg cosh 75 — I„ — ; — :-7,sinh ys. (6) g + jut The hyperbolic functions of the quantity y may be expanded by using cosh ju = cos u and sinh ju = j sin u ; thus cosh ys = cosh (/8j +jas) = cosh ^s • cos as+J sinh j85 • sin as and sinh ys = sinh /3s • cos as +j cosh j8s • sin as. The terminal conditions in any special problem are usu- ally specified, the voltage being considered the reference phase. In the present notation for vector rotation a cur- rent leading the voltage is written ii + JH and a lagging current is represented by ii — jii. From equation (5) it is seen that for an infinitely long line, 5 = 00, on which the current at the inaccessible end is zero, Im = o, which, when substituted in the same equation, gives the current, at a point distant s from the generator end of such a line, as Im = Ig (cosh 75 — sinh ys) = Igt"^'. Similarly E^ = Egt-^' = EgC^'C'"'. The exponential function with the imaginary exponent may be written in the trigonometric form by means of the expression j*y« = cos as ± 3 sin as, whence — = — = e~^' (cos as — j sin as), (7) wherein a is the delay in phase in radians per unit length of line (mile). If a length of line r miles be chosen so as to TRANSMISSION LINES. 243 contain exactly n wave-lengths, then 2irn = ar, and the wave length is \ = - = — miles. n a As the frequency / of the impressed electromotive force is 03 - — cycles per second, the velocity of wave propagation ^^11 be w 2 7r oj . V = fk = — • — = — miles per sec. 2 IT a a The expression for a in terms of the line constants is given in § 78. For a perfectly insulated resistanceless line g = o, R = o, a = u yLC, and the velocity of wave propagation _ I ^ ~ rjTp , is that of light, namely 3 X 10^" centimeters per second, or 186,000 miles per second. 8o. Regulation. — The voltage regulation of a trans- mission line is the ratio of the voltage variation at the receiving end between no load and full non-inductive load to the full-load voltage at the same end of the line for constant impressed voltage at the other end. When the transmission line is open-circuited at the re- ceiving end, the current, /„„, entering it at the generator, called the charging current, is obtained from equation (5) of the preceding article ior s = S = total length of the line, by placing Im = o. ° R+jo)L cosh 75 Since — r~^ = tanh yS, cosh 70 this becomes Ig^= Eg . tanh75. (i) 244 TRACTION AND TRANSMISSION. Substituting this value for Ig in equation (6) of § 79, there results the voltage at any point distant 5 from the gen- erating end of the line as £„ = Eg (cosh 75 — sinh ys • tanh 75), (2) and the voltage at the receiving end for 5 = 5 as £r„ = E,g (cosh yS — sinh yS • tanh 75), or, since cosh^75 — sinh^75' = i, The regulation of the transmission line is then expressed as Tj , , . £,„ — Er Eg sech yS — Er , . Regulation = -^ = -^ ^ '• (4) 81. Numerical Illustration. — Let it be required to trans- mit 10,000 kilowatts at 60 cycles over a three-phase aerial transmission hne 300 miles long, employing stranded alu- minum conductors 0.63 inch in diameter of area 0.236 square inch, triangularly spaced with 9 feet interaxial dis- tance. The voltage at the receiving end of the line is to be 100,000 volts between conductors, and the power factor of the load is 85 per cent lagging. Determine the voltage to be impressed on the line, the entering current, the effi- ciency of transmission, the voltage regulation of the line, and the charging current. The constants per mile of a representative single circuit with a perfectly conducting ground return path and carry- ing one-third of the total energy, are R = 0.30 ohm, L = 0.00196 henry, C = 0.0153 X io~* farad, g = practically zero. TRANSMISSION LINES. 245 The current per single circuit (or per wire) at the load end is J 10,000,000 Ir = = 08.0 amperes, 3X^^X0.85 V3 or Ir = 68.0 [0.85 -j sin (cos-^ 0.85)] = 57.8 - 35.8^; the voltage at the receiving end, namely '--^— or 57,700 volts per phase, being considered the datum phase. The attenuation and wave-length constants per mile for a frequency of 60 cycles (whence w = 377) are respectively ;8 = v 2.88(Vo.090 + o.5476 — 0.74) X 10"' =0.000412 and a = \/2.88 (0.799 + o-74o) X io~' = 0.00210. The hyperbolic and circular functions respectively of ^s and as for the total length of the transmission line are cosh (0.1236) = 1.00765 cos (0.630) = cos 36° 6' = 0.8080 sinh (0.1236) = 0.1239 sin (0.630) = 0.5892. The current at the generator end of the line may then be obtained from equation (3) of § 79 as ■f» = (S7-8-3S-8i)(i-oo765Xo.8o8o-|-o.i239Xo.5892j") • + 57-7f °"'^^ , ^"^•^• )(P-i239Xo.8o8o+i.oo765Xo.5892y), \o.30+o.74^/ or I« = (57-8 - 35-8 j) (0.8142 + 0.0730;) + 90.5 (1.678 + o.325i) (o.iooi + 0.5937 j) = 49.67 - 24.93 J + 90.5 (- 0.0249 + i.027i) = 47.42 + 68.01 j amperes, and the current from the generator per wire is 82.9 amperes. 17 246 TRACTION AND TRANSMISSION. Similarly the voltage at the generator end of the trans- mission line is £. = (57-8 - 3S.8j)^^^y^"(o.iooi +0.5937^) + 57.700 (0.8142 + 0.0730 j) = (57-8-35-8-7) (0.364-0.0715^) (o.iooi +0.5937 j) 10' + (46.95 + 4-2ii) 10' = (12.04 + 9-23 J + 46.95 + 4-21 i) 10' = 58,990 + i3.44oi, and the voltage per single circuit to be impressed on the line in order to have 57,700 volts per phase at the receiving end is 60,490 volts. vlag \ Fig. zoi. The vector diagram, Fig. loi, exhibits the phase rela- tions of the voltages and currents at the ends of the line. It is seen herefrom that the current at the generator end leads the voltage at the same place by the angle 55" 7' — 12" 50', or 42° 17'. The efficiency of transmission at full load is 57,700 X 57-8 60,490 X 82.9 cos (42° if) y-. = 0.899, or 89.9 per cent. [^0 TRANSMISSION LINES. 247 Since cosh 7^ = 0.8142 + 0.0730 j, the voltage at the receiving end on open circuit for the same impressed E.M.F. at the generator end is P 58,990 + 13.4407 „ , ^^» = 0.8142 + 0.0730i = 73.350 + 9.930 J. and the absolute value is 74,900 volts. Consequently the voltage regulation of the transmission line for 85 per cent power factor is 73.900 - 57.700 = 0.281, or 28.1 per cent. 57,700 The charging current per single circuit or per wire is obtained from equation (i) of § 80 as /o4i2-|-2^"\/o.iooi +0.5937 A = (58.990+13.440.) (^„ 3^+^ ^^.j(„ 3^^^^^ ^^3^. j = (i38.5+3i-5i) (i. 678+0.325 j) (0.1248 +0.476 j) = - 18.8 + 1 18.0 j, and the absolute value is 119.5 amperes, and leads the volt- age Er by 99° 3'. Therefore the charging current at the generating end of the line leads the voltage at the same place by the angle 99° 3' — 12° 50', or by 86° 13'. 82. Corona Loss. — It is found by experiment that the corona lose on a transmission line is proportional to the square of the excess voltage over the critical disruptive value, and is dependent upon the frequency, the size of the conductors, the distance between them, and the density of the air. The loss per mile in watts on a single conductor under fair weather conditions is given by Peek as P = 3.9-^-^ -\^ {E^ - E^rY, (I) 248 TRACTION AND TRANSMISSION. where £„ is the voltage (effective value in kilovolts) from conductor to neutral, E„ is the effective value of the critical disruptive voltage in kilovolts to neutral (§ 72), / is the frequency in cycles per second, S is the air density factor (§ 72), D is the conductor diameter in inches, and d is the distance between centers of conductors in inches. This expression shows that the corona loss increases very rapidly as the voltage is raised beyond the critical voltage Ecr. It is not desirable nor economical to operate trans- mission lines above the disruptive critical voltage because of the. production of noise and luminous discharge and of chemical action at the conductor surface. The corona loss is increased by smoke, fog, rain, sleet and snow; in order to approximate the loss during storms consider Ecr as 80 per cent of its fair-weather value as given by equation (i). The method of measuring corona loss is by means of a wattmeter, the current coil of which is connected directly in the transmission line at the neutral, which is grounded, and the potential coil of the wattmeter is connected to the high-potential transformer coil. An important consideration arises when the distant end of a long transmission line is open-circuited, for the voltage at every point on the line increases, and the potential over a considerable portion of the circuit exceeds the critical voltage, and consequently a loss of energy ensues. This loss begins at that point where the voltage £0 is just equal to the critical value E^r, and becomes greater and greater as the far end is approached. The voltage at any point on an open-circuited line is given by equation {i) of § 80. By substituting various values of 5 therein, and plotting the corresponding values of Eo in terms of distance, a voltage-distribution curve for the particular line will result. TRANSMISSION LINES. 249 From this voltage-distance curve can be seen the distance, 5o, from the generator end of the transmission line at which corona loss begins. Of course, this equation might be solved for Sq, but not knowing the phase of voltage Eo at the end of this part of the circuit, this plan leads to diffi- culty in the solution of actual problems. In order to determine the total corona loss on an open- circuited single conductor of length S, consider an element ds of the circuit, distant ^ miles from the point So where corona loss begins, for which the ex- cess voltage is E^, — E„ kilovolts; Fig. 102. The ^'e- '"• power loss over this elementary line section in watts is dP = K (£„ - EcrY ds, where K replaces the terms of equation (i) not included in the parenthesis; and over the entire distance I = S — Sa the loss is P = K f (£™ - EcrY ds. Jo Applying equation (2) of § 80, Em = E„ (cosh 7^ — sinh 75 tanh 7O ; therefore P = KEJ = KEc (cosh 75 — sinh 75 tanh 7Z — lY ds, r 2 I cosh 75 ds -f- tanh^ yl | sinh^ 75 ds cosh^ ys ds — 2 tanh yl ( sinh 75 cosh 75 ds f Jo f Jo 250 TRACTION AND TRANSMISSION. + 2 tanh yl I sinh ys ds -\- \ ds \. Upon integration this equation becomes P = Ecr^ [sinh yl cosh -yl + yl — tanh yl (cosh 2 yl — l) 2 y — 4 sinh yl + tanh^ 7Z (sinh yl cosh 7Z — yl) + 4 tanh 7? (cosh 7Z — i) + 2 yl], and when simplified reduces to P=fE.^z[3-^^^^'-tanh^7/] (2) as the expression for the total corona loss in watts on an open-circuited single conductor. As an illustration consider a 6o-cycIe, three-phase trans- mission line with No. 0000 stranded aluminum conductors (0.53 inch diameter) placed triangularly 15 feet apart. The line constants per mile on a representative single-wire circuit which transmits one-third of the total energy, are R = 0.463 ohm (includes resistance increase due to skin effect and stranding), L = 0.00218 henry, C = 0.0137 microfarad, and g is negligibly small = o. The disruptive critical voltage of this line is given by equation (7) of § 72 as 77 sy n^ w O-53 X 2.54 , 2 X 15 X 12 Eor = 21.9 X 0.85 X log, = 82 00 kilovolts to neutral for 5 = i (see also Fig. 93). The attenuation and wave-lengths constants per mile are respectively ^ = 0.000563 and ' oL = 0.00214; whence 7 = 0.000563 + 0.00214J. TRANSMISSION LINES. 25 1 If a length of 100 miles (Z = 100) at the open-circuited end of the line has a voltage greater than E^r, then yl = 0.0563 + 0.2140 J, sinh ■yl — 0.0550 + 0.2123 j, cosh -yl = 0.9788 + 0.0120 J, tanh 7Z = 0.0589 + 0.2161 j, 3 tan yl 1 = 3-0308 - 0.0264 j, tanh^ 'yl = — 0.0432 + 0.0255 J, ir . ^ 60 + 25 / 0.53 and 12.7 P = ^- (82)2 100 [3 - (3.0308 - 0.0264 j) - (- 0.0432 + 0.0255 j)l = 53.000 watts, or 53 kilowatts. Whence the corona loss on the three wires would be 3 X 53 = 159 kilowatts. 83. Lightning. — The physical processes, accompanying the establishment of atmospheric differences of potential, resultant discharges from which are known as lightning, are not well understood. Closely related to the phenomenon are two facts established by somewhat recent experiments. As the result of the presence in the earth of radioactive substances and the characteristics of their decay, the lower strata of the atmosphere are partially ionized. The num- ber of positive ions per unit volume usually exceeds the number of negative ions. This excess seems to disap- pear at an elevation of about 10 miles. The resultant posi- tive volume electrification establishes a positive potential 252 TRACTION AND TRANSMISSION. in the various strata with respect to the' surface of the earth. Fig. 103, due to Liebenon, shows the calculated potential differences for strata of various altitudes, and is based upon experimental evidence. Air saturated with water vapor requires the presence of 2Q0 150 CO ^ ^ > 100 3 J / / 50 / / / / 10 20 30 40 ELEVATION IN THOUSAND FEET Fig. 103. 50 60 solid nuclei in order that the vapor may condense to form the globules which constitute a cloud. Frequently these nuclei consist of dust particles. Kelvin showed that the necessity of a nucleus was due to the influence of curvature of surface upon the vapor tension, because the greater the curvature of a liquid surface the more it tends to evaporate. J. J. Thomson showed that electrification would partially neutralize the effect of curvature; and C. T. R. Wilson showed that ionized air required less supersaturation to effect cloud formation than non-ionized air and that nega- tive ions were more effective than positive ions. Since uncharged globules of a cloud continually move under the TRANSMISSION LINES. 253 influence of the excess of gravitational force above the force of air resistance, and since charged globules move as the result of an additional force due to the presence of the electric field, — positive or negative according to the sign of the charge, — it is reasonable to believe that these forces contribute towards the establishment of potential differences between different parts of a cloud, between clouds, and between a cloud and the earth. Under poten- tial differences of sufficient magnitude the intervening air breaks down accompanied by a discharge. The gradual formation of a cloud over a transmission line electrostatically induces a charge in the line wires and holds it bound. Upon the neutrahzation of the cloud potential by discharge, the energy of the charge on the lines is delivered to the line, and tends to dissipate itself under conditions prescribed by the constants of the line and its environment. Current surges may be set up in the line circuit and be superposed upon the normal currents, which surges will cease when the energy has been expended in heating the conductors, or an arc may be initiated between a wire and ground over an insulator or between two wires. The subsequent maintenance of the arc will be due to energy supphed by the generator. The current in an arc to ground is generally intermittent and, if main- tained, may set up resonant currents in apparatus con- nected with the Une, since each piece of apparatus has a natural frequency of its own. These resonant currents are likely to be accompanied by voltages of magnitude suffi- cient to destroy insulation and cause short circuits. The energy of the magnetic field associated with a short circuit between line wires is delivered to the line when the short circuit ceases, and may cause surges similar to those 2£^,S TRACTION AND TRANSMISSION. which result from lightning. Some writers have therefore extended the meaning of the term " lightning" to include such phenomena. Fig. 104. 84. Protection from Lightning. — In order to protect apparatus from the high voltages due to lightning it is common to insert choke coils, Fig. 104, in series between the apparatus terminals and the line wires so that the incoming high-voltage wave front may be retarded thereby for a short interval of time. On the line side of the choke coil is installed a grounded device which conductively connects the line with the ground whenever the voltage of the line exceeds a predetermined value. This device is termed a lightning arrester, and its operation, in connection with the choke coil, quickly relieves the line of excessive potentials. Some means must be employed, however, to prevent the maintenance of a discharge at normal voltage from the line to ground over the path rendered conductive by the initial discharge under excessive potentials. In nearly all types of arresters the circuit from the line wire to the ground is TRANSMISSION LINES. 255 normally interrupted by a short dielectric gap which will break down under a slight excess over normal voltage. The various arresters differ from each other in the means employed to suppress the subsequent flow of current at normal voltage. In one type this is accomplished by separating the spark-gap electrodes by means of a plunger Fig. 105. solenoid; in another there is an electromagnetic blow-out; and in another, for use on alternating circuits, there is a series of gaps between electrodes which will not permit the maintenance of an arc at normal potentials. Two types of lightning arresters have proved particularly effective in the protection of station apparatus, namely the aluminum-cell and the oxide-film arresters. The former 256 TRACTION AND TRANSMISSION. consists of a series of aluminum cup-shaped electrodes upon whose surfaces are formed films of aluminum hydroxide, immersed at short distances from each other in a suitable electrolyte. The cross section of such an arrester is shown at the left in Fig. 105. It is characterized by the conduc- tion of minute currents at normal voltage and of very large currents, without much elevation of temperature, at volt- ages slightly in excess of normal. The number of electrodes or cells depends on the operating voltage, each cell with- standing permanently about 300 volts. To avoid loss of energy under normal potentials these arresters are con- nected in series with a horn gap. This practice necessitates ; daily charging of the arrester, as the film dissolves rapidly. The oxide-film lightning arrester consists of a series of circular sherardized iron electrodes separated by porcelain rings, the space between the electrodes being filled with lead peroxide, a good conductor, applied under moderate pres- , sure. When a current is passed through the arrester heat ; is developed at the contacts of the peroxide and metal because of the contact resistance, and when the temperature reaches about 150 deg. cent, the peroxide at the metal surfaces is reduced to a lower oxide, red lead, an insulator; consequently obstructing the current flow. The number of peroxide layers or cells in the arrester., depends upon the ' operating voltage, allowing about 250-400 volts per cell. When subjected to an over voltage the insulating films are punctured and the discharge takes place through the lead peroxide, but the dynamic current following this discharge converts the surfaces of the peroxide into the lower non- conducting oxide, and thus seals the punctures in the films. Commercially, the films are put on initially by dipping the plates in a suitable insulating varnish, and after assembly TRANSMISSION LINES. 257 the passage of a current seals any openings that may exist in the varnish film. The arrester is used with a spark gap in series, and is depicted at the right of Fig. 105, the metal housing being shown removed at one side. The fact that this arrester need not be charged extends its use to localities where there are no attendants. No effective means has been found for the protection of a transmission line from a direct stroke of lightning. Such strokes usually result in short circuits and shuttered insu- lators. The damage is usually confined to one tower on metal tower lines, but extends over several poles when the cross arms and poles are of wood. When the stroke is not direct but in the vicinity of the line, a common result is a spill-over or arc to ground over SELECTIVE RELAY iin OIL SWITCH Fig. 106. an insulator. The maintenance of the arc after the stroke by energy from the generator is likely to destroy the insu- lator, to set up surges, and to interrupt the service. To interrupt such arcs, E. E. F. Creighton has devised a sup- pressor, which automatically grounds the affected line at the station for a short interval of time, sufficient to allow the conducting vapors to escape and the insulator to cool off. This time is not so great as to interrupt the service because of the slowing down of synchronous apparatus. 258 TRACTION AND TRANSMISSION. The arc ceases because the ground at the station robs it of its potential. Fig. io6 is a diagram of the circuit connec- tions. The selective relay, which controls the operation of the grounding oil switch, is itself controlled by electro- static forces on high-voltage lines and by electromagnetic forces on moderate-voltage lines. The relay contact is normally held open by these balanced forces, but is closed when the balance is destroyed. Success has been attained in protecting lines by ground wires erected above the line and connected with ground at every fifth pole or so. The use of such wires has resulted in a reduction of 50 per cent in insulator failures. PROBLEMS. 42. Plot a curve showing the resonant frequency of open-circuited trans- mission lines of various lengths when connected to impedanceless generating units. What length of line corresponds in periodicity with the fifth har- monic of a wave whose fundamental frequency is 25 cycles? 43. Determine the economic voltage to be employed in transmitting 15,000 kilowatts at 25 cycles to a single substation over a 120-mile three- phase aerial transmission line using aluminum conductors. Take the equiv- alent annual hours of operation as 4000, the mean annual power factor as 0.8s, the cost of line material as 0.24 dollars per pound, and all other factors as suggested in § 71. 44. Calculate the critical disruptive voltage for the transmission line discussed in § 81 in a region where the atmospheric pressure is 70 cm. of mercury and the temperature averages 20 deg. cent. 45. Determine the line constants per mile per phase at 15° C. of a three- phase 60-cycle aerial power transmission line using solid hard-drawn copper conductors 0.8 inch in diameter spaced triangularly 6 feet apart. 46. Calculate the voltage and current at the generator end of the line, the efiiciency of transmission, the voltage regulation, and the charging current of the transmission line of § 81 when the frequency is 25 cycles, all other conditions remaining unaltered. 47. Plot a curve showing the corona loss per mile of the transmission line of § 81 for various operating voltages up to 200 effective kilovolts be- tween conductors. Take the density factor as unity. POWER STATIONS. 259 CHAPTER X. POWER STATIONS. 85. Station Load Curves. — The proper design of a power station depends to a large extent upon the characteristics of its output. A curve with ordinates representing the output of a station in kilowatts and with corresponding r\ f \ CO l- 1- <30 I \ / \ \ \ 1 / \ ii. 020 en a \ J \ 1 \ < CO 10 X H N 1 v ^_ \ ^^ J 12 A.M. 2 4 6 8 10 12 2 4 TIME IN HOURS 6 8 10 12 P.M Fig. 107. abscissae representing the time of day is termed a load curve of the station. Fig. 107 represents a typical load curve for a power station supplying energy for traction purposes. It is characterized by two peaks, which occur at about 8.30 in the morning and 6.00 in the evening respectively, and which last for two or three hours, and by 26o TRACTION AND TRANSMISSION. a very low value during the early morning hours. The peaks are due to the demands of traffic in carrying pas- sengers to business in the morning and returning them to their residences at night. The maximum value of the peak at the power station is less than the sum of the peaks at the different substations; because the latter occur at different times, that is, because of the diversity factor. In the morning, the peaks at the substations in the residential districts occur prior to those in the business and manu- facturing districts, while the reverse is true in the evening. Furthermore, the average duration of the power-station peaks is greater than characterizes the substation peaks for the same reason. The ordinates of the load curve are greater in winter than in summer because of the necessity for heating and lighting the cars, and often because of the presence and removal of snow. The energy required for heating may be 20 per cent of that required for car propul- sion. The shape of the load curve is likely to be entirely different on Sundays and holidays from its shape on week days and may be materially modified by the maintenance of seasonal amusement or recreation resorts. Instantaneous fluctuations 'va. the power output, not shown in the load curve and due to the abnormal currents necessary in the starting of trains, are always present. With few cars in operation the relative magnitude of these fluctuations is greater than when there are many. The amount of fluc- tuation can be determined with sufficient exactitude from the curve of Fig. 58, which shows the dependence of the ratio of maximum to average current upon the number of cars in operation. The power-station load curve for a proposed installation can be predetermined with considerable accuracy from the POWER STATIONS. 261 train-sheet, § 52, of the tentative service to be maintained and the curves of power input to the car, § 43, for different times. The ordinate of a point on the power-station load curve for a given instant is equal to the sum of the inputs to all cars in operation at that instant, divided by the product of the efi&ciencies of transmission, of conversion, and of distribution, which product usually' ranges from 70 per cent to 75 per cent. With urban systems, where congestion of street traffic constantly interferes with regu- larity of schedules, this method is inapplicable. In such cases a fair estimate of the power-station output in kilo- watts at any instant is, however, numerically one-half the rated horsepower of all the motors on cars in service at that instant. This method of estimation is based upon the fact that the continuous current capacity of a railway motor is about one-half its capacity when nominally rated in ac- cordance with the Standardization Rules of A.I.E.E. The average power supplied to a certain number of cars is there- fore one-half the rated horsepower of the corresponding motors, and with an efficiency of 75 per cent in transmission from the power station to the cars a kilowatt at the station corresponds to a horsepower at the car. 86. Selection of Generators. — For stations of small capacity supplying energy for short roads it is often eco- nomical to use 2 200- volt generators, as the cost of wiring is less than for lower voltages and the cost of insulation is less than for higher voltages. Furthermore, this being a stand- ard voltage for lighting generators, there is a complete line of these generators available. For systems where the economic voltage for transmission, calculated under the assumed use of step-up transformers, is of the order 20 kilovolts, standard generators wound for 12 kilovolts and 18 262 TRACTION AND TRANSMISSION. connected directly to the transmission line will generally prove more economical. For transmitting large amounts of power at higher voltages step-up transformers must be used while the generator voltage should conform with stand- ards such as 6.6 or ii kilovolts. The size of a imit, including generator and prime mover, should be such as to entail a minimum annual charge against it, arising from its cost and operation. To reduce the relative losses in a unit it should be operated as nearly as possible at that load which gives a maximum efi&ciency. Because the designed operating efhciency is generally great- est at about rated load and, because of the characteristics of the load curve, the losses would be least with units of minimum rated capacity. The efficient use of such small units, however, would necessitate irequent starting and stopping of the different units corresponding to the fluctu- ations of load, and this would require a large force of attendants. Furthermore, the cost, the deficiency, and the required floor space per kilowatt is greater for small units than for large ones, and therefore the proper selection is, by nature, a compromise. Very small stations are generally located upon cheap land and space economy is of no great importance, whereas the number of attendants must be reduced to a minimum. Furthermore, the cost per kilowatt varies so greatly with the capacity of small units that, if capital is limited, it may be necessary to install but a single unit. For the sake of reliability of service, however, it is undesirable to use less than two units. For the average station of moderate capacity four units, one of which serves as a reserve unit, to be used in case of failure of another, will generally prove most economical. POWER STATIONS. 263 The relative values of the early morning and noonday loads, which endure for protracted periods, may, however, make it desirable to use a larger number of units so as to operate at good efficiency during these hours. Very large stations have been installed in the past with the number of units prescribed by the maximum capacity available. Steam-turbine units are now constructed which have a rated capacity of over 45,000 kilowatts. According to the standardization rules of A.I.E.E. gen- erators should be able to carry a 25 per cent overload for two hours. If a railway power station were to be equipped with five units, each of rated capacity equal to one-fifth the maximum station load, then in case one should fail the whole load could safely be carried by the remaining four. This is possible because the fiith unit is seldom in service for more than two hours during the peak loads. A reserve unit may thus be dispensed with. If the power factor of the load on the generators be less than unity, the overload capacity may not be sufficient as a substitute for the reserve unit. 87. Types of Prime Movers. — The types of prime movers at present available for electric power stations are steam engines, internal combustion engines, and water wheels. As a rule that type should be employed which will result in a minimum average cost of reliably delivering a kilowatt-hour of energy. To make an equable com- parison the point of delivery should be the same in all cases. This will generally require for hydraulic plants that a part or the whole of the expense of the transmission sys- tem shall be considered as chargeable to the power station. If the financial hazard associated with the undertaking be large or if capital be limited, it may be necessary to reduce 264 TRACTION AND TRANSMISSION. the first cost, the plant thereafter being burdened with an excess cost of energy production. Internal combustion engines burning gas or liquid fuel in their cyHnders have a high thermodynamic efficiency. The high pressures developed require heavy construction, the high temperatures require cooling systems, and the intermittent release of energy requires heavy flywheels. They therefore cost more than other forms of prime movers, and depreciate in value faster. Furthermore, gas engines have a very limited overload capacity. Reliability in their operation has not been sufficiently established to warrant the recommendation of their adoption as a sole source of power in a station for supplying energy for railways. Yet the Milwaukee and Northern road as well as the Warren and Jamestown road are operated solely from generators driven by gas engines. 88. Power Station Costs. — The annual cost of operat- ing a station is conveniently divided into two parts, namely, fixed charges which do not vary with or depend upon the output of the station after it is built and equipped, and operating expenses which vary with the output. The fixed charges usually comprise interest, taxes, insurance, rental, depreciation, and obsolescence. Sometimes there is apportioned to the power station a part of the annual administration costs, including office rentals, salaries, and legal expenses. The operating expenses comprise labor or attendance, repairs and maintenance, fuel, water, oil, waste, and other supplies. STEAM STATIONS. 265 STEAM STATIONS. 89. Engines and Turbines. — Steam-driven prime movers may consist of reciprocating engines or turbines, operated with or without exhaust steam condensers. The former are usually either simple or compound and are sometimes clas- sified as high-speed or low-speed, although there is no sharp dividing line in this respect. A speed of 150 revolu- tions per minute may be assumed as the usual line of division. The proper selection of a prime mover of this type is based upon the first cost of the prime mover and of the rest of the equipment entailed by its use, as well as upon the expenses of maintenance and operation. Data concerning steam prime movers generally iaclude pounds of steam consumed per indicated horsepower-hour or per kilowatt-hour of output, initial and back pressures of the steam, and the mechanical efficiency of the mover. The steam consumption and efficiency vary with the load, as does the efficiency of a generator. With assumed con- ditions as to pressures and load, the pounds of steam per kilowatt-hour of generator output is to be found by dividing the pounds of steam consumed per indicated horsepower- hour by 0.746 times the product of the generator and prime-mover efiiciencies. The steam consumption of re- ciprocating engines increases somewhat with use, whereas that of turbines remains fairly constant. The steam con- sumption of Curtis turbines decreases about one percent for each increment of 10 pounds in gauge pressure and one pound per kilowatt-hour per inch of vacuum. At a given pressure, steam having the minimum tempera- ture consistent with its remaining in the form of a vapor is termed saturated steam, and a reduction of its tempera- 266 TRACTION AND TRANSMISSION. ture causes condensation. If saturated steam be removed from contact with water, its temperature may be raised above that of the water from which it was produced. It then acts like an imperfect gas and is termed superheated stedm. The rise of temperature in degrees Fahrenheit is a measure of the amount of superheat. If steam rises from a surface of water faster than about three feet per second, it carries water with it in the form of spray, and when fine spray is once formed in steam it does not readily settle. The resultant mixed steam is termed wet steam. Superheated steam, if homogeneous, cannot be wet, be- cause water particles would of necessity be evaporated under the influence of heat derived from the surrounding steam. The cyclical changes in the temperature of cylinder walls, accompanying the operation of reciprocating engines, causes cylinder condensation losses of heat when it is fed with saturated steam. Such losses are seldom less than lo per cent and often amount to 40 per cent of the supplied energy, and may be materially reduced by the use of superheated steam. The presence of moisture in the steam passing through a turbine occasions a wear of the turbine blades as the result of impact. It is therefore desirable to supply superheated steam to reciprocating engines on the ground of economy and to turbines on the ground of maintenance. A device used to elevate the temperature of steam above its saturation temperature is termed a superheater and may consist of a set of tubes connected in the steam line and subjected to the heat from the fire of the main boiler or from an auxiliary source. The data contained in the following table give an idea of what may be expected as to the performance of these STEAM STATIONS. 267 types of prime movers. The efHciency of reciprocating engines and of generators has been assumed as 92 per cent and 97 per cent respectively. STEAM CONSUMPTION. Type of engine. Pounds of steam per K.W.H. Saturated Steam: Simple noncondensing SS 3S 33 27 20 14 IS Simple condensing Compound condensing Turbines Superheated Steam: Compound condensing 90. Condensers. — Consider a simple engine run so that the steam after expansion exhausts into the atmosphere; that is, run noncondensing. The effective force per unit area of piston, available at any instant for performing work, is the difference between the pressure of the steam on one of its surfaces and the back pressure exerted by the atmosphere at that instant on the other surface. Since the mean effective value of the former may be of the order 50 Ib./in.^ and the latter is 14.7 Ib./in.^, a reduction of the latter to 1.7 would theoretically increase the power out- put 13/50 or 26 per cent. An enclosed device which is adapted to receive the exhaust steam, lower its tempera- ture, and thereby condense it, is termed a condenser. Its use materially reduces the back pressure because steam, after condensation, occupies an insignificant portion (ttVt) of the space filled by it prior to condensation. In order to cool and condense the steam it must be deprived of 268 TRACTION AND TRANSMISSION. some of the heat associated with it. This may be done by passing it along one surface of a thin metal which is kept cool by water circulated in contact with the other surface or by mixing the steam with a spray of cooling water. A device using the first method is termed a sur- face condenser, and one using the latter is termed a jet condenser. The condensing water used with the jet con- denser is variously termed, as injection, cooling, or circulat- ing water. To maintain the condenser in operation the condensed water, which has collected in a hot well, must be removed by a wet-vacuum pump, which may also serve to remove the air which is invariably present as the result of leakage, or absorption in the injection water. To main- tain a high vacuum an additional dry-vacuum pump is often used for removing the air. The amount of cooling water required per pound of condensed steam depends upon the vacuum and upon the initial and final temperatures of the cooling water. Let X = total heat of the exhaust steam above 32° F., To = initial temperature of the cooling water, „ ^ ( temperature of the condensed steam (surface), f temperature of the discharge water (jet), Ti = temperature of the discharge water. Then the weight of cooling water, W, necessary to con- dense one pound of saturated steam, is TT7 "K — Tl-\- X2 , W = _. 'T,-^ pounds. ■ii — J^ Surface condensers cost more than jet condensers, but permit the use of the condensed steam as feed water for the boilers after any oil, which became mixed with it in the engine, has been removed from it. They are there- STEAM STATIONS. 269 «W^ fore adapted for use where there is a hmited supply of suitable feed water but a superabundance of cooling water, such as results from a location near salt waterways. When the supply of cooling water is limited the use of cooling ponds or cooling lowers permits of the repeated use of the same water, but these arrangements are expensive. The advisability of installing condensers depends upon whether the annual saving of energy is greater or less than the annual expense entailed by their cost, maintenance, and operation. A jet condenser is shown in Fig. 108 with parts cut away so as to indicate the in- terior construction. The ex- haust steam enters through the large pipe at the left and the cooling water through the large pipe at the right. The latter is sprayed through the valve in the center, mixes with the steam, con- denses it, and both fall into the pipe below. The air- pump is connected with the small pipe at the left. With the surface condenser shown in Fig. log, the cooling water is passed through the interior of the small tubes and ab- stracts heat from the exhaust steam, which surrounds the tubes, thereby condensing it. The circulating pump to the right and the vacuum pump to the left are operated by an intermediate auxiliary engine. Fig. 108. 270 TRACTION AND TRANSMISSION. 91. Boilers. — An essential element in a steam plant is the boiler equipment, and its size and cost depend upon the amount of steam which is to be supplied to the prime movers and to the auxiliaries. A typical form of boiler for use in power stations is shown in Fig. no, wherein the water to be heated circulates as the result of localized tempera- ture differences, moving to the right iii the cylindrical Fig. log. drum at the top, and to the left in the water tubes, which are enveloped in the hot gases resulting from the combustion of the fuel. These gases ultimately pass through the dam pcr-controWed opening near the top of the right-hand enclosing brick wall, and through a breeching to the chimney or stack. Steam is generated and confined under pressure in the upper part of the drum, and is fed through the nozde on top to a header, whence it is conducted direct to the prime mover. The capacity of a boiler is rated in horsepower STEAM STATIONS. 271 and the builder's rating is based upon a heating surface of 10 to 12 square feet per horsepower. A boiler of one horsepower capacity is considered to be capable of allowing an evaporation of 34.5 pounds per hour of water at 212° F. into steam at atmospheric pressure, and to have an over- load capacity of 33^ per cent. If the temperature, t, of the feed water be less than 212°, the steam be x part dry, or the steam be superheated /,° F., the delivery of 34.5 Fig. no. pounds of steam per hour under such conditions will re- quire a boiler of more than unit capacity, and to deliver Q pounds of steam per hour the horsepower capacity of the boiler should be Q / xr + q + Ct,-t + y. 34.5 V 970-4 where r = latent heat of evaporation at the resultant pressure, q = heat in liquid at this pressure, and C = mean specific heat of the superheated steam. horsepower, 272 TRACTION AND TRANSMISSION. The values of the various constants may be found in Engineering handbooks. The steam consumed in operating aiixiliaries such as feed pumps, vacuum pumps, and circulating pumps, ranges from 6 per cent to 15 per cent of that taken by the prime movers. Available boilers are limited in capacity to about 2250 horsepower, and it is common to install smaller ones in batteries of two or more. 92. Feed-water Heaters. — It is undesirable to pump cold water into a hot boiler because of excessive stresses which may result from wide differences in the temperature of adjacent parts of the metal of the boiler. Furthermore, there is a saving of about one per cent in fuel for every II degrees elevation in the temperature of the feed water, provided such elevation is produced by heat that would otherwise be lost. The temperature of the feed water may be raised by heat taken from the exhaust steam through the aid of a vacuum heater or an atmospheric heater, and by heat from the hot flue gases, using an economizer. 93. Chimneys or Stacks. — A chimney serves two pur- poses, namely, to carry off the obnoxious gases resulting from combustion, and to produce a draft which will give a sufficient supply of oxygen for combustion. The former requires an adequate cross section and the latter an ade- quate height of chimney. Experience shows that the draft pressure, measured in inches of water as compared with atmospheric pressure, should be from 0.5 to 1.5 inches, de- pending upon the character and size of the fuel to be used, and upon the quantity to be burned per square foot of grate surface. Heights above the grate, which have given satis- factory results in practice with plants of moderate capacity emplojdng different fuels, are given in the following table: STEAM STATIONS. HEIGHTS OF CHIMNEYS. 273 Fuel. Height in feet. Free-burning bituminous 80 100 120 ISO 1 75 Anthracite, large sizes . Anthracite buckwheat Anthracite slack The ascending gases in a chimney are retarded by fric- tion in the vicinity of the walls, and the equivalent cross section A oi a, round chimney is therefore generally taken as that corresponding to a diameter four inches less than the real internal diameter of the chimney. Assuming a coal consumption of five pounds per horsepower-hour, a chimney of height k feet, properly to carry off the gases from boilers of P horsepower, should have an equivalent cross section of . o.zP J. . A = ,- square feet. Vh Chimneys are constructed of steel, reenforced concrete, or masonry. Steel chimneys weigh less, cost less, require less space, expose less surface to the wind than other forms, and are more efficient because they are air-tight. They, however, depreciate more rapidly because of rust and be- cause of the corrosive influence of the flue gases. Sometimes short chimneys are used in connection with mechanical draft apparatus, consisting of either an exhaust fan in the smoke flue or a mechanical or steam-jet blower underneath the grate bars. An induced draft is produced by the former and a forced draft by the latter. The advis- ability of installing mechanical draft apparatus is depend- ent upon the results of an economical comparison with 274 TRACTION AND TRANSMISSION. the saving resulting from the lessened necessary height of chimney. 94. Buildings. — Power-station buildings may be con- structed of wood, brick, reenforced concrete, or stone. Wood is used only for very small stations and stone only for elaborate stations. If a single building is used for housing the boiler plant as well as the generating plant, the ^■3 UJ DC < 0-1 CO 10 20 30 40 50 60 70 00 90 100 THOUSANDS OF KILOWATTS Fig. III. two should be separated by a brick wall with no openings in it which will allow dirt to pass through from the boiler room to the engine room. The boilers and the units which are supplied with steam from them should be on opposite sides of the dividing wall and so placed as to reduce the length of steam piping to a minimum. The height of both rooms should be ample, to permit the use Of hfting machinery and the replacing and repairing of boilers. The building should be well Ughted, well ventilated, of fire-proof con- struction, and arranged with a view to extension in case of growth of demanded output. I \. \ A \ • c • X • < --- X .PA cu iSONS ixrs TL URBINI RBINE! S. X RE IIPROW TING E 4GINE8 STEAM STATIONS. 275 The floor space required for turbines is materially less than that for reciprocating engines of the same capacity and the foundations can be much lighter. Where the cost of land is great a considerable saving may be effected by placing turbines on a floor above the boiler room. The station is then termed a double-deck station. The space required for passageway around units is greater per kilowatt for small units than for large ones. The curve of Fig. 1 1 1 is based upon existing plants, and shows the average floor space allowed per rated kilowatt in terms of the total capacity of a plant. 9S. Arrangement of Apparatus. — It is customary to arrange the apparatus in a steam-power station so that the path of energy is as short as possible. The coal is there- fore received and delivered to the boilers at one end of the station and the electrical energy is delivered to the line from the generators at the other end. Figs. 112 and 113 show an elevation and floor plan of the Winona Interurban Railway Power House which has a capacity of 1200 K.W. The output is supplied at 33,000 volts from two banks of three transformers, each of 200 K.W. capacity and stepping the voltage up from 2300 volts. There are two 600-K.W. 25-cycle, 2300-volt generators, each directly connected to a cross-compound engine guaranteed to have a full-load steam consumption not to exceed 14. i pounds per indicated horsepower-hour at 140 pounds pressure and 26 inches of vacuum. Each engine is supplied with a jet condenser. Steam is supplied by four boilers, arranged in batteries of two each, there being 3000 square feet of heating surface provided in each unit. It will be noted that a transformer- converter substation, for suppl3ang 600-volt direct current to the distribution circuits in the immediate vicinity is housed under the same roof. 276 TRACTION AND TRANSMISSION. STEAM STATIONS. 277 Fig. 114 shows a cross section of the Port Morris Power House of the New York Central Railroad, which is equipped with Curtis steam-turbine units and surface condensers. Fig. 113- The very complete system of labor-saving apparatus for conveying coal and removing ashes and its method of operation is clearly shown. 278 TRACTION AND TRANSMISSION. STEAM STATIONS. 279 POWER-PLANT COSTS PER KILOWATT. Min. Max. I . Real estate i! . Excavation 3. Foundations, reciprocating engines 4. Foundations, turbines 5. Iron and steel structure . 6. Building (roof and main floor) 7. Galleries, floors, and platforms 8. Tunnels, intake and discharge 9. Ash storage pocket 10. Coal hoisting tower 1 1 . Cranes 12. Coal and ash conveyors 13. Ash cars, locomotives, and tracks 14. Coal and ash chutes 15. Water meters, storage tanks, and mains 16. Stacks 17. Boilers 18. Boiler setting ■19. Stokers . : 20. Economizers .,,... 21.' Flues, dampers, and regulators '. . . 22. Forced draft blowers, air ducts 23. Boiler, feed,'and other pumps . . . 24. Feed-water heaters 25. Piping, traps, and separators .- .' 26. Pipe covering 27. Valves 28 Main engines, reciprocating 29. Exciter engines, reciprocating 30. Condensers, barometric or jet 31 . Condensers, surface .- 32. Electric generators 33. Exciters 34. Steam-turbine units, complete 35. Converters, transformers, blowers 36; Switchboards, complete 37. Wiring for lights, motors, etc 38. Oiling system 39., Compressed air system and other small aux- iliaries 40. Painting, labor, etc 41 . Extras 42. Engineering expenses and inspection $3.00 $7.00 •75 I.2S 2.00 3.00 ■SO ■7S 8.00 10.00 8,00 10.00 1-5° 2.50 1.40 2.80 .70 i.So 1 .20 2 .00 .40 .60 2.00 2-7S 15 ■30 - ..40- 1 .00 ■50 1 .00 I-2S 2.00 9 • SO ^- 11 .50 1-25 I -75 1.30 2 .20 1.30 2.25 .50 .90 I-2S I -65 .40 ■75 . 20 ■35 3.00 5, 00 .60 , I '. 00 .60 i 1. 00 22.00 - 30.00 .40 ■ ■70 1 ,00 2.50 6.00 7 50 16.00 22.00 .60 .80 22.00 32.00 .60 1 .00 3.00 3.90 .20 ■30 ■IS ■35 .20 ■30 I^2S 1^75 2.00 2.00 4.00 6.00 28o TRACTION AND TRANSMISSION. 96. Cost of Steam Stations. — The table on the preced- ing page, due to H. G. Stott, includes the approximate cost per kilowatt of the various elements entering into the cost of a steam plant. A fair average cost per kilowatt is ?ioo for plants using reciprocating engines and ?8o for those using steam-turbine units. 97. Operating Expenses. — Data concerning twenty- three stations of moderate capacity, using mostly bitu- minous coal ranging in price from ^2.75 to ^5 per gross ton, and all operated condensing, has been published re- cently by E. F. Tweedy. Fig. 115 shows the operating costs OuJ OUJ _j > 3 X RECIPROCATING STEAM ENGINES. • STEAM TURBINES. XMIXEO EQUIPMENT-ENGINES & TURBINES, EQUATION OF HYPERBOLIC CURVE Y- 1 -1- BOO, 000 \ \ \ n 2 in \ Z C *-.. ,^ 1 ^ ■-J*^ — s P-°-« "-- — - e 3 _1. h 4ILL ION 2 SOf ■KIL 3 OW HO JRS 3 GEr f JER 3 ME DPE R Y EAR 3 9 Fig. 115. per kilowatt-hour in terms of total annual outputs. The highest load factor based upon rated capacity was 0.23, the lowest o.ii, and the average 0.17. The coal consumed per kilowatt-hour ranged from a little over 3 pounds for the larger plants to about 5 pounds for the smaller ones. The station rating in kilowatts per man employed in operating the station, ranged from about 100 K.W. for the HYDRAULIC STATIONS. 281 smallest stations to 250 K.W. for the largest. Fig. 116 shows the percentage distribution of operating costs among fuel, labor, and miscellaneous items. MISOELLANEollS COSTS AVEfi^bE ie.48i« ■? \ <; / /*r-' \ c _,o» .--* V— L— ■**--. **-.. -i V CO ST ■ LA^OR -■ -•X ^ -s / A AVERAGE 27.82^ 4 -80 o 160 '40 20 / 'A Vs 3/4 GATE OPENING Fig. 119. unit time, upon the available head of water, and upon the turbine efficiency, e, and is r, 62.4 OfH OeH , F = ^ — = ^--— horsepower, 550 8.81 ^ where q is the discharge in cubic feet per second and which may be expressed empirically as q = KD'' VJl, wherein D is the diameter of the runner in feet, and K is an experimental constant of discharge dependent upon the design of the turbine. Therefore P = — — - — horsepower, 0.81 n^^ HYDRAULIC STATIONS. 287 tience the proper wheel diameter for a given head is '^feet. (X) [le values of K vary widely among the different designs of irious manufacturers, but most values thereof lie between 3 and 3.5 for reaction turbines, and between 0.015 and 324 for impulse wheels. For a given turbine the speed of the rimner varies with e square root of the head. Let t be the rario of the iripheral velocity of the buckets to the theoretical velocity at water would acquire in falling freely a hei<5ht equal to e head of water. Then the speed of the wheel in revolu- )ns per minute is le values of t range from 0.65 to 0.93 with different signs of reaction turbines and between 0.43 to 0.51 with ipulse wheels. Having determined the turbine speed for ^iven head of water, the multipolarity of the alternators : the generation of electromotive forces of definite fre- ency becomes known. As an illustration of the foregoing, determine the proper mber of poles for a 2000 K.W., 60-cycle, three-phase ;ernator which is to be driven by a Pelton water wheel a head of 970 feet, the constants of the wheel being = 0.019, T = 0.505, and e = 0.83. Taking the alternator iciency as 92 per cent, the rating of the prime mover is 2000 _ ^^^^ horsepower and the diameter of '46 X 0.83 X 0.92 ; water wheel is \J — "^J"" =8.0 feet. Therefore * 0.019 (970)^ o 84 288 TRACTION AND TRANSMISSION. its speed is -1^- 0.505 ^970 = 300 revolutions per minute. At this speed there must be 24 poles for the production of 60-cycle currents. 99. Water-power Development. — In any hydraulic de- velopment the water must be conducted from some source to the wheels by means of a head-race, and discharged from the turbines into the tail-race at a lower level. Two general types of water-power development are discernible which usually characterize respectively low-head and high- head developments; namely, (i) where the entire head is utilized at the dam, the power station being located at one end thereof; (2) where long pipe lines, canals, ox flumes are required to transfer the water from the intake at the keadworks to the station, this distance being only suffi- ciently long to secure for a given amount of water a head which will enable the generation of the required power. (i) The object of a dam is to concentrate the fall of a stream so that the water power becomes available by the elevation of the water surface. That portion of a dam over which excess water pours is called the spillway, and this must be sufficiently long to allow escape of the water in times of heavy flood without undue rise in level of the water in the reservoir above the dam. It is essential that the dam have a solid foundation, that it be stable against overturning and be water-tight, and that it be so con- structed as to prevent washing out of the river bed and banks below it and erosion of the dam itself. Dams may be constructed of timber, masonry, or reenforced concrete. They must be equipped with drain or sluice gates for the purpose of draining the reservoir above them as well as for assisting in the discharge of water during the heaviest floods. The surface of the reservoir may be raised at HYDRAULIC STATIONS. 289 times by means oiflashboards, which collapse automatically upon excessive rise of water. A plan of a typical low-head hydraulic development is illustrated in Fig. 120, which shows the Johnsonville de- velopment of the Schenectady Power Company. This dam causes the flooding of 850 acres, thereby giving a. storage DEFLECTING WALL SPILLWAY 530 FT. SLUICE GATL3 Fig. 120. capacity or pondage of about 350 million cubic feet. Fig. 121 shows the power house and sluice-gate masonry of this development, looking upstream. The power furnished by a given stream may be increased by a suitable reservoir, for the water impounded during the rainy seasons may be partially drawn off during time of low water. The water available for pondage is limited, how- ever, since the level of head water can only be lowered a comparatively small amount without impairing the output and efi&ciency of the plant. Water is led from the head-race or the reservoir through 290 TRACTION AND TRANSMISSION. suitable hand- or motor-operated head gates to the forebay and from there to the wheel pits. The water in entering the wheel pit from the head-race usually passes through a trash rack consisting of narrow iron bars, the function of which is to prevent large floating objects from entering the turbines. Open wheel pits are usual for heads up to 30 feet, whereas closed flumes or penstocks leading from the Fjg. 121. head-race to the wheel pits are utilized for higher heads. It is desirable to set the turbines in separate pits so that one or more may be temporarily shut down without inter- fering with the operation of the station. A cross-sectional view of the Rocky Creek Power House of the Southern Power Company is shown in Fig. 122, which also illustrates the construction of the penstock and draft tube for each turbine, and the water-tight stuffing box between the wheel pit and the generator room. HYDRAULIC STATIONS. 291 Fig. 122. 292 TRACTION AND TRANSMISSION. Fig. 123 shows the interior of the Rainbow Station of the Great Falls Power Company, Montana. Each of the six 3500 K.W. alternators is driven by a 6000 H.P. reaction turbine with two runners, each runner being enclosed in a separate spiral casing fed by a separate 8-foot steel Fig. 123. penstock from a balancing reservoir and discharging into a common draft tube. (2) High-head developments require long canals or pipe lines for conveying water from the intake to the power house. Level canals may be constructed along the hillside to a point above the power station, and from there the water can be passed down to the water wheels through a HYDRAULIC STATIONS. 293 instock. It is usually cheaper, however, to use a pipe le which need not be level but can follow the contour of e land. Wood, cast-iron, or riveted wrought-iron pipe is ed for such purposes. The transmission of water through pes or canals is accompanied by a reduction in the avail- ile head, the extent of which depends upon the size of the pe or canal. This loss of head can be computed from pressions given in most books on HydrauHcs. Provision must be made to prevent injury to penstocks pipe lines which might occur when the turbine gates or iter-wheel nozzles are regulated too quickly. Automatic 'ief valves of sufficient area may be employed at the lower d of the pipe, or either standpipes or surge tanks may be ed to alter the velocity of the water in the pipes. Fig. 124 gives a sectional view of a typical power house in lich impulse wheels are installed. Speed regulation of e prime movers is accomplished by deflecting the nozzles st the buckets and allowing part of the water to impinge lon heavy metal deflector plates. Frequently hydraulic developments have auxiHary steam gas engine plants to supplement the water power during e dry seasons or during periods of peak loads. 100. Cost of Development. — The cost of a proposed drauUc development depends largely upon the extent to lich the stream flow is to be developed, upon the nature d remoteness of the power market, as well as upon rious topographical, geological, and meteorological con- ions of the locality. The decision as to the commercial Lsibility of a proposed water-power development must ibrace a careful study of all such factors which influence ,ter supply, of the available head and its variations, of ; power available with and without pondage, of the 20 294 TRACTION AND TRANSMISSION. HYDRAULIC STATIONS. 29s tion and extent of the hydraulic construction and 'er house, of the probable market for the power gener- I and its load factor, and the desirability of auxiliary er. ough estimates in terms of generator capacity of the of turbine equipments may be derived from Figs. 125 126, which embody data from existing installations. v \ \ \ V \, \ \ s N \ \ ■^-10 22_J: :VV\_ ^ ^ fio^ ivv. 20 40 60 80 100 120 HEAD IN FEET. Fie. 135- figures refer to reaction turbines and impulse wheels ectively, and include extra movers for exciter units, jrnors, and cost of erection. he following table, given by 0. S. Lyford, gives the item- cost (estimated or actual) per kilowatt of generator icity of seven separate water-power developments in same general district in our southeastern states, these ers being developed with heads varying from 30 to 1 20 , and with generator capacity varying from 10,000 to 296 TRACTION AND TRANSMISSION. o < Pi o H < Hi O Q s O s W 03 Eh W s c< o P-) (I) Q Pi E- O C4 ►J o Bi Q >< a O to to O O ¥00 r^ M H 100 ^ ^ CO t^MOOcO civOvO'O t^ m r^oo -^o ^ t^ ^^ ■^ O vO looo t^ 10 Oi fO 0\ t^ ^ ^^O "^ CO OvOO 0\ ^ iJTO O CO c^ O vO 'O t>- "4-1 .„ ° a 3 lU ^11 to ^ MB c +^ g „ O 0) cfl „„ ^ g u S (U D^aj ^ .S a " s o g O 3 03 tS-^a-^ a =i " S S-° g'l M-d O 3 "i S g ^ § i I rt:9 g I jS S^t§ lUS S.Q-S^ MQ HYDRAULIC STATIONS. 297 30,000 K.W. The appended column gives the average of the proportional costs of the general groups for the seven plants. 16 \ \ \ 1- < 5 12 -1 :«: 0: 0. 8 \, \ \ \ ■^'Oo N X s Jn ^ ^ K CO < ^v. ^ [Jl^^ ^ "~-~ -1 _l ' — 400 800 1200 HEAD IN FEET. Fig. 196. 1600 loi. Depreciation and Obsolescence. — It is difficult to predetermine with accuracy the cost of repairs essential to maintain the various parts of an installation in operating condition, the time that these parts will endure before it becomes unwise to repair them, and the time which will elapse before it will prove more economical to substitute for them more efficient parts. It is necessary, however, to attempt to make such predeterminations in order to carry out an economic design. The following values in reference to hydraulic plants are those given by Dr. Gary T. Hutch- inson. He also states that the general consensus of opinion as to the depreciation of steam generating plants is that it amounts to from 5 per cent to 7.5 per cent, with an addi- tional like value for obsolescence. The basis of the follow- 298 TRACTION AND TRANSMISSION. ing table is the assumed life and annual charges compounded at the rate of 4.5 per cent. The depreciation in terms of the total cost assumes that the cost of the power house, the transmission line, and the substation amounts to but S7 per cent of the total cost. DEPRECIATION RATES. Item. Power Hoitse: 1. Stop logs, gates, and other wood exposed to air and water 2. Flooring, roofing and hardware, and miscellaneous fixtures .... 3. Tile wainscoting, sewage, plumb- ing system, and metal window frames, etc 4. Electric light and telephone. , 5. Switchboard equipment 6. Cables and heavy wiring 7. Cranes 8. Water wheels 9. Water-wheel governors 10. Generators and transformers. Transmission Line: I. Right of way ■i. Towers 3. Special structures. 4. Insulators 5. Copper 6. Installation Substation : 1. Land 2. Buildings 3. Transformers. 4. Switches, etc.. 5. Installation. . . Propor- tional cost. 0.80 9.80 2-4S 0.80 4-3S 3-90 I-2S 33-75 2.90 40.00 100.00 45- 18.4 S-i 2.1 23-7 S-7 100. o 6.0 30. 40. 16. 8. 100. Life years. [19] IS IS 10 10 10 IS 2S 10 25 [26] 15 10 10 25 Annual amount for depreciation in per cent of total cost. 0.146 0.472 O.I18 0.065 0-35S 0.318 0.060 0.757 0.23s 0.898 3 423 0.88s 0.415 0.170 0.530 [20] 2.000 25 20 10 0.67 1.28 1.29 3-24 HYDRAULIC STATIONS. 299 M. Relative Operating Expenses. — The following ^e, due to H. G. Stott, is applicable to plants having a dmum load of over 30,000 K.W., and gives operating jnses and probable fixed charges based upon 5 per cent rest, I per cent for taxes and general administrative ;nses, and 5 per cent amortization or obsolescence in steam and hydraulic plants. RELATIVE COSTS PER KILOWATT-HOUR. Items. Maintenance ;ine room, mechanical. . . . ler or producer room 1-and ash-handling apparatus :;trical apparatus Operation .1 ter ;ine-room labor [er- or producer-room labor, 1- and ash-handling labor . removal :trical labor ine-room lubrication ine-room waste, etc er-room lubrication, etc ; operating cost, per cent. . . ! investment, per cent e average cost, per K.W.($) e fixed charges 2s Pi 2-59 4.65 0.58 i.i3 61.70 7.20 6.7s 7.20 2.28 1.07 2. 54 1.78 0.30 0.1 100,00 100 . 00 125.00 11% ffi 0.51 4.33 054 1 .13 5S-53 0.65 1.36 6.74 2.13 0-9S 2.S4 0.35 0.30 0.17 77.23 7S.OO 93-75 11% ci E rt bo "u ■u fl lis « .as tm p. 1-55 3.55 0.44 1 .13 52.44 0.61 4.06 5.5° 1.7s 0.81 2.54 1.02 0.30 0.17 75-87 80.00 100.00 11% 5.1 1. 16 o.2g 1.13 26.52 3.60 6.76 1. 81 1. 14 0.54 2.54 1.80 0.30 0.17 52.94 110.00 137.50 12% 2.84 1.97 0.29 1 .13 25.97 2.16 47.23 96.20 120.00 11.5% ■s I 0.51 I-I3 1.36 2-54 0.20 0.20 5.94 100.00 125.00 11% 13. Costs per Kilowatt-hour. — The average annual per kilowatt-hour of output depends upon the annual 300 TRACTION AND TRANSMISSION. load factor and upon the type of an installation. The annual load factor is the ratio of the annual output in kilowatt- hours to 8760 times the maximum power of the installed apparatus in kilowatts. Since the fixed charges are de- pendent upon the rated capacity but independent of the 60 2 50 >• a: UJ a. H40 o I 30 -20 10 / / y .ti-^ ^X .^ ty ^ ■^ r ^ ^ y y ^ %^ ^ ^ y^ ^•, 3^ ^ ^ ^ ^ W HYDBA JLIC 0.2 0.4 0.6 LOAD FACTOR. Fig. M7. 1.0 output, whereas the operating expenses are dependent upon the latter and independent of the former, the cost per kilo- watt-hour of output will be a minimum for a load factor of unity. Furthermore, for a typical railway load of a given maximum demand the rating of the power-station equip- ment necessarily installed to meet this demand differs with the type of the installation. This is due to differences in HYDRAULIC STATIONS. 301 overload capacity. The necessary capacity progressively increases as the type changes from steam to gas and steam again to hydraulic or to gas alone. For a complete discussion of this subject the reader is referred to Mr. Stott's paper (Trans. A. I. E. E., xxviii, p. 1479), from which Fig. 127 is taken. This figure shows the dependence of the total annual cost per installed kilowatt upon the load factor and the type of plant. The titles associated with the various lines refer to the col- umns in the table of the preceding article, each of which represents a definite t3^e of installation. A low grade of coal, costing ^1.50 per ton and giving 11,000 B.t.u. per pound, has been assumed. The average cost per kilowatt- hour may be determined by dividing the value of any ordinate by 8760 times the corresponding load-factor. PROBLEMS. 48. Determine the proper size and number of steam turbo-generator units for a power station having a load curve of the form indicated in Fig. 107 but with ordinates of half the value. What would be the probable number of daily hours of operation of each unit ? 49. If the turbines of problem 48 consume 17 pounds of dry saturated steam at 175 pounds gauge pressure per kilowatt-hour and if the auxiliaries use 10 per cent of the total steam generated, how many boilers should be installed per unit and what should be the horsepower of each ? Assume the temperature of feed water to be 80° F. 50. Determine the diameter of the runners for a twin reaction turbine to operate on a 100-foot head for a 5000-kilowatt, zs-cycle, three-phase alter- nator, whose efficiency is 96 per cent. The constants of the turbine ate K = 3.o T = 0.74 6 = 0.8s INDEX. leration, 22. tomatic, lo8. rve. S3, S7- . :es, changes in, 126. [uacy of copper distribution, ISO. ;sion, coefficient of, JO. stment of speed curves, 66. nating-current control, 90. distribution, 164. motors, 28. substations, 166. linum-cell arrester, 256. lal car-miles operated, 5. iratus, arrangement of station, 189, 275. suppressor, 257. sters, lightning, 209, 254. Dspheric heaters, 272. tential differences, 252. nuation constant, 238. imatic acceleration, 108. bstations, 188. liary feeders, iji. )rage batteries, 188. age current per car, 112. eries, storage, 188. ing friction, IJ. ;rs, 270. is, track, 156. Iters, 152. :ing, 23. rve, 52, S8. ergy lost in, 126. iches in roadway, 1 39. es, resistance of, 221. icity of lines, 230. motors, 51. body, types of, 9. ass sections, 17. uipments, weights of, 55. Car-mile, earnings per, 6. -miles, annual, J- number of, for urban road, 4. propulsion, tractive effort for, 15. size of, 8. types of, 9. Cascade control, 100. Center feeding of sections, 138. of distribution, 199. Charging current of line, 247. Chimneys, 272. Choke coils, 209, 254. Classification of conductors, 133. Closed cars, 9. Coasting curve, J2, 58. effect of changes in, 129. Coefficient of adhesion, 24, 50. Collecting devices, 140. Commutating-pole motors, 27, 55. Compensated series motors, 36. Compensators, 90, 93. multiple-switch, 94. Compounded converters, 172. Condensers, 267. Conductive compensation, 37. Conductor separation, 213. Conductors, resistance of, 220. weights of, 202, 220. Connecting-rod drive, 41. Contact conductors, 134. Continuous rating of motors, 1 19. Control, alternating-current, 90. apparatus, weights of, 55. cascade, 100. compensator, 93. direct-current, 74. field excitation, 89. hand, 103. induction motor, 96. regulator, 90. methods of, 74. multiple-unit, 105. rheostatic, 74. series-parallel, 75. 303 304 INDEX. Controllers, 103. Converter, characteristics of, 171. substations, 169. -transformer deficiences, 183. Convertible cars, 9. Cooling towers, 269. Copper loss of motor, 118. Corona, 213. loss, 214, 247. Corrosion, electrolytic, 157. Cost constants, 185. of electrical energy, 299. of hydraulic development, 293. movers, 295. of steam stations, 279. of substation units, 174. of transformers, 208. Critical line voltage, 213. Cross section of contact conductor, I3S- of feeder, IJI. of line conductor, 206. of supplementary conductor, 143- Current, average, per car, 112. curves, iii. density, economic, 152. distribution on lines, 240. effective, motor, 113. -limit relay, 109. Curves in roadway, 20. Daily load diagrams, 180. Dams, 288. Data for plotting speed curves, 53. Deficiency constants, 184. Degree of track curvature, 21. Density factor of air, 215. Depreciation of generating plants, . ^97- Design of controller units, 79. Developments, hydraulic, 288. cost of, 293. Direct-current control, 74. motors, 27. transmission, 166. Disruptive critical voltage, 219. Distance curves, 66. Distributing system, 133. Distribution of current on lines, 240. Diversity factor, 210, 260. Double-decked cars, 9. stations, 275. Drive, methods of, 41. Duration of stops, 56. Earnings per car-mile, 5. Economic current density, 152. section of contact conductor, 135, spacing of substations, 176. transmission voltage, 205. Economizers, 272. Effective motor current, 113. per trip, 116. Effect of operating conditions on energy consumption, 124. Efficiency of hydraulic movers, 285. of substation apparatus, 170. of transformers, 168, 203. of transmission, 246. Electrical energy, cost of, 299. Electric field intensity near con- ductors, 214. Electrolytic corrosion, 157. surveys, 161. E.M.F. equation of single-phase motors, 32, 38. Elevation of outer rail, 22. End feeding of sections, 137. Energy consumption, iii. effect of operation on, 124. for car propulsion, 120. Engineer's problem, i. Engines, steam, 265. Equations of wave propagation, Equivalent grade, 20. hours of operation, 182. line length, 211. Expenses per car-mile, 6. Feeders, IJI. negative, 157. Feed-water heaters, 272. Field control, 89. Fixed charges of power station, 264. Floor space in power stations, 274. in substations, 170. Forced compensation, 37. Frequency, 203. resonant, of line, 204. INDEX. 305 on, coefficient of, 24. ngines, 264. for turbines, 282. drive, 41. o, choice of, 56. ifect on acceleration rate, 131. "ators for power station, 261. mors for hydraulic movers, 284. ;s, 20. lie time-tables, 147. resistances, 80. id wires, 258. control, 103. ng of motors, Jl, 118. Its of chimneys, 273. ipower rating of motors, 1 19. aulic construction, 288. rer stations, 281. rbolic functions, 224. dance of rails, 164. Ise wheels, 281. le of electric railways, 5. ;tance of lines, 222. :tion motor, 40. ontrol of, 96. ulators, 90. ;tive compensation, 37. dients of third rails, 130. nations, substation, cost of, itors, 207. lal combustion engines, 264. 3ole motors, 27, 55. ition of air, 215. OSS of motor, 118. es, resistance of, 163. )ndensers, 268. ige current, 157. ince, line, 237. ;h of average passenger ride, 8. ;rack for urban road, 2. ning, 251. ;sters, 209, 254. tection, 254. ations of motors, Jo. Line capacity, 230. inductance, 222. leakance, 237. resistance, 220. Load curves, 180, 259. Location of substations, 175. of transmission line, 199. Locomotives, electric, 40. Losses in motors, 118. in substations, 184. Master controllers, 106. Mechanical draft apparatus, 273. Mixed-flow turbine, 281. Motor capacity, 51. characteristic curves, 44. control, 74. effective current, 113. -generator substations, 170. heating, 51, 118. limitations, 50. output, 49. saturation curve, 79, 87. Motors, alternating-current, 26. compensated series, 36. direct-current, 27. field-control, 89. induction, 40. railway, 26. repulsion, 39. series, 27, 30. weights of, 55. Moutiers-Lyons transmission, 166. Multiple-switch compensator, 94. -unit control, 105. Narragansett type of car, 10. Negative conductors, 133. track feeders, 157. Nominal rating of motors, no. Number of cars for urban road, 4. of units in substations, 180. Numerical examples, 18, 59, 67, 87, 113, 127, 186, 205, 211, 218, 244, 250, 287. Obsolescence of generating plants, 297. Oil switches, cost of, 2og. One-man cars, 10. Or»pn ram n 3o6 INDEX. Operating characteristics of con- verters, 171. of motor-generators, 172. conditions, changes in, 124. expenses of power stations, 264, 280, 299. of railways, 6. Output of power stations, 261. Overload capacity of generators, 182, 263. coefficient, 180. Overrunning third rail, 141. Oxide-film arrester, 256. Pantograph frames, 141. Passenger factor, 3. Pay-as-you-enter cars, 10. Performance curves of motors, 44. Phase converters, 29. Phases, number of, 201. Pipes, resistances of, 163. Plotting speed curves, 56. with grades and curves, d'j. Polarity induction motor control, 97. Poles, transmission, 207. trolley, 140. Population served by railway, 4. Portable substations, 193. Positive conductors, 133. Power factor curves, 122. of single-phase motors, 34, 38. lost in conductors, 138. -station buildings, 274. costs, 264, 279. location of, 200. output, 261. Preventive coils, 93. Prime movers, types of, 263. Problems, 14, 25, 49, 73, no, 132, 164, 197, 258, 301. Propagation of electric waves, 235. Protection from lightning, 254. Pumps for steam stations, 268. Quill drive, 43. Rails, 155. impedance of, 164. Rates of acceleration, 23. of braking, 53. Reactance set, 172. Receipts of electric railway, 4. Regeneration of energy with induc- tion motors, 40. Regulation of converters, 171. of transmission line, 243. Regulators, induction, 90. Relative operating expenses of gen- erating plants, 299. weights of conductors, 202. Relay, current-limit, 109. Repulsion motors, 39. Resistance of conductors, 220. offered to car movement, I J. of iron pipes, 163. of third rails, 136. of track rails, 156. to alternating currents, 221. Resistances, motor starting, 78. Resonant currents, 253. frequency of line, 204. Retardation, 24. Reversing motors, 103. Rheostatic control, 74. Ride, average passenger, 8. Rights of way, 200. Roadway, characteristics of, 56. Rolling friction, 15. Saturation curve of motors, 79, 87. Schedule speeds, 13, 56. Scott transformer connection, 29, 169. Seating capacity of cars, 9. Seats, arrangement of, 10. Sectional contact conductors, 138. Selection of gear ratio, 56. of generator units, 261. Semiconvertible cars, 9. Separation of line conductors, 213. Series-parallel control, 75. -wound motors, 27, 30. Service, railway, types of, i. Single-phase railway motors, 30. Skin effect, 221. resistance of rails, 164. Speed curves, 50. of car, SI. of hydraulic movers, 287. of motor, 26, 49. INDEX. 307 Stacks, 272. Standard transmission voltages, 212. Starting resistances, 78. energy lost in, 125. Station load curves, 259. Steam power stations, 265. Stops, duration of, 56. Storage batteries, 188. Substations, 166. arrangement of apparatus in, 189. automatic, 188. cost of, 175. efficiency of apparatus in, 170. floor space in, 170. location of, 175. number of units in, 180. portable, 193. connections of, 197. Superheaters, 266. Supplementary conductors, 142. Surface condensers, 268. Surges from lightning, 253. Surveys, electrolytic, 161. Synchronous speed of induction motors, 97. Table of hyperbolic functions, 228. Temperature elevation of motors, "9- Third rails, composition of, 136. resistance of, 136. Three-phase railway motors, 40. -point grid resistance, 80. Thury transmission system, 166. Time-tables, graphic, 148. Total drop in conductor, 135. Towers, transmission, 207. Track factor, 3. feeders, 157. length of, for urban road, 2. rails, ISS- Traction motors, 26. Tractive effort, 15, 49. -speed curve, 60. Train resistance, IJ. -sheetSj 148. Trains, 13. Transformer efficiencies, 168, 203. Transformers, costs of, 208. weights of, 203. Transmission lines, igg. Trolley wheels, 140. wires, 135. Turbines, hydraulic, 281. steam, 265. Typical speed curves, 52. Underrunning third rail, 142. Units, controller resistance, 79. generator, 262. Urban road, cars for, i. Vacuum heaters, 272. pumps, 268. Velocity of car, 51. of wave propagation, 243. Voltage along roadway, 129. critical, 213. curves, 118. distribution on lines, 240. gradient, 214. of boosters, 154. regulation, 243. transmission, economic, 205. Wages of substation attendants, 178. Water-power development, 288. wheels, 284. Watts lost in conductor, 138. Wave-length coefficient, 238. propagation along wires, 235. Weights of car equipments, 54. of cars, 13. of conductors, relative, 202. of iron pipe, 163. of transformers, 203. Wheels, trolley, 140. Wind resistance, 16. '■?i:»*-'^.».i«lLH»l