Class Book Copyright N° COPYRIGHT DEPOSIT. The D. Van Nostrand Company intend this book to be sold to the Public at the advertised price, and supply it to the Trade on terms which will not allow of discount. OTHER WORKS BY THE SAME AUTHORS DYNAMO ELECTRIC MACHINERY; ITS CONSTRUCTION, DESIGN, AND OPERATION Vol. I. Direct Current Machines, Eighth Edition, Completely Rewritten, 8vo. Cloth, Illustrated. 338 pp. Net, $2.50. VOL. II. ALTERNATING CURRENT MACHINES, Eighth Edition, Completely Rewritten, 8vo. Cloth, Illustrated. 366 pp. Net, $2.50. Electric Traction and Transmission Engineering BY SAMUEL SHELDON, A.M., Ph.D., D.Sc. PROFESSOR OF PHYSICS AND ELECTRICAL ENGINEERING AT THE POLYTECHNIC INSTITUTE OF BROOKLYN, AND PAST-PRESIDENT OF THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS AND ERICH HAUSMANN, E.E., M.S. INSTRUCTOR IN PHYSICS AND ELECTRICAL ENGINEERING AT THE POLYTECHNIC INSTITUTE OF BROOKLYN, AND ASSOCIATE OF THE AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS With 127 Illustrations NEW YORK: D. VAN NOSTRAND COMPANY 23 Murray and 27 Warren Sts. 1911 s* ^ Copyright, 191 i, by D. VAN NOSTRAND COMPANY S*~\ P~ Stanbope iprcs& F. H.GILSON COMPANY BOSTON. U.S.A. ©CU29237 6 PREFACE. 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. VI 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 utility 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, Brooexyn, N. Y. May i, 1911. CONTENTS. CHAPTER I. Determination of the Number and Size of Cars for an Urban Road. ART. PAGE i. The Engineer's Problem i 2. Types of Service i 3. Length of Track 2 4. Receipts 4 5. Number of Cars 4 6. Size of Cars 8 7. Numerical Example 12 Problems 14 CHAPTER II. Tractive Effort Required for Car Propulsion. 8. Train Resistance 15 9. Grades 19 10. Curves 19 n. Acceleration 21 12. Braking 22 Problems . . . : 24 CHAPTER III. Types and Performance Curves of Motors. 13. Traction Motors 25 14. Direct-current Motors 26 15. Alternating-current Motors 27 16. Methods of Drive 40 17. Motor Curves 43 Problems 49 vii van CONTENTS. CHAPTER IV. Speed Curves. ART. PAGE 18. Motor Limitations 50 19. Motor Capacity 51 20. Speed 51 21. Typical Speed Curves 52 22. Data for Plotting Speed Curves 53 23. Plotting Speed Curves 56 24. Numerical Example 59 25. Distance Curves 66 26. Speed Curve Plotting with Grades and Curves 67 Problems 72 CHAPTER V. Railway Motor Control. 27. Direct-current Control 74 28. Rheostatic Method 74 29. Series-parallel Method 75 30. Starting Resistances 78 31. Numerical Example 87 32. Alternating-current Control 89 33. Induction Regulators 89 34. Compensators 91 35. Induction Motor Control 95 36. Controllers 102 Problems 109 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 116 41. Voltage Curve 118 42. Motor Heating 118 43. Energy for Direct-current Propulsion 120 44. Energy for Alternating-Current Propulsion 121 CONTENTS. IX ART. PAGE 45. Effect of Operating Conditions on Energy Consumption 124 46. Gear Ratio 130 Problems 132 CHAPTER VII. The Distributing System. 47. Classification of Conductors 133 48. Contact Conductors 134 49. Branches 139 50. Collecting Devices 140 51. Supplementary Conductors 142 52. Graphic Time-table 147 53. Feeders 151 54. Track Rails 155 55. Negative Track Feeders 157 56. Electrolytic Surveys 161 57. Alternating-current Distribution 164 Problems 164 CHAPTER VIII. Substations. 58. Types of Substations 166 59. 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 175 63. Numerical Illustration 186 64. Auxiliary Storage Batteries 188 65. Arrangement of Apparatus 189 66. Portable Substations 194 Problems 197 CHAPTER IX. Transmission Lines. Location of the Transmission Line 199 Number of Phases 201 Frequency 203 Economic Voltage 205 Numerical Illustration 211 X CONTENTS. ART. 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 235 78. Attenuation and Wave-length Coefficients 238 79. Current and Voltage Distribution on Lines 240 80. Regulation 243 81. Numerical Illustration 244 82. Corona Loss 247 83. Lightning 252 84. Protection from Lightning 254 Problems 257 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. 89. Engines and Turbines 265 90. 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 293 101. Depreciation and Obsolescence 297 102. Relative Operating Expenses 299 103. Costs per Kilowatt-hour 299 Problems 3 ox ELECTRIC TRACTION AND TRANSMISSION ENGINEERING. CHAPTER I. DETERMINATION OF THE NUMBER AND SIZE OF CARS FOR AN URBAN ROAD. i. 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 traffic most economically and to lead to a sufficient 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- TRACTION AND TRANSMISSION. mate estimate of the length of a proposed railway and its subsequent income, as well as the determination of the number 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 1 of Fig. 1 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 traffic 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. Total population served Number of miles of track Miles of track per 1000 of population Number of passen- gers Number of rides per inhabitant . . . All centers over 500,000 population. 10,274,470 4,998.89 •49 2,456,542,270 239.1 All centers between 100,000 and 500,000 population. 5,380,647 3,559-82 .66 994,327,853 184.7 Twenty-nine selected centers between 25,000 and 100,000 population. 1,258,615 951-93 .76 135,842,312 107.9 Forty-six selected centers of less than 25,000 population. 718,254 485-95 .68 49,179,495 68.5 NUMBER AND SIZE OF CARS FOR URBAN ROAD. ,3 The present population is, however, not the value to be considered in determining the track factor, r, from this curve, but instead the population at some future time, this time depending upon the probable duration of the .9 .2 7 r< ,*Gg 1 .— fm^l II y£" / N\ ^c \ / ^^ jog. 7" / 1 300 240 I- ■z. 200 ? CD < 160 fC 120 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 one hundred years might be drawn and 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, L, to be installed can be expressed as Nr miles. iooo 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. 1, shows the number of yearly passengers per inhabitant, or what may be termed the passenger factor, y. 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 = Nyf dollars. In this country the usual urban fare is five cents regardless of the distance traveled. For interurban 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. 5 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 Falls 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 Income per operation. car mile. Cents. $200,671.65 28.50 1,714,848.82 22-35 268,507.78 25.12 258,819.85 20. 14 3,694,339.01 25.16 212,668.51 27.88 49,139.86 22.95 192,921.47 16.06 41,474.56 24.17 44,457-88 26.92 499,148.09 25-89 16,919.70 9-30 91,817.90 23.21 123,632.92 23.08 119,270.85 20.04 27,240.09 9.78 103,862.05 15-97 Total expense per car mile. Cents. 24.30 15-35 16. 24 11.23 14.90 21.36 16.06 11 .61 16.34 22.57 18.13 9.06 17.87 14-57 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 19 10; 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. T0 V •a & a a & 6 o §8 +3.S °5 1 P. .5 .. . W- 1 U o p — IS w « is 6 § u c S g'C fin H J O Oh < ►J I 485.2 585.0 53,362,500 37,537,433 27.80 28.77 *2 T 2 533.905 1,018,463 4 34 14 4 3 4 465,786 373.740 208.2 *3 3 3 12 13 12 5 1 403,740 I36.O 13,812,813 27.42 5 347.469 512,886 IOI.7 *i5,377,ooo 3I-50 3 62 14 6 6 516,152 516,152 306.6 24,229,010 30.75 3 89 17 7 7 233.650 234,650 139-7 9,346,183 28.86 *3 3 12 6 8 131. 105 151,105 no. 4 6,895,421 26.14 4 09 ib 1 9 129,867 216,867 86.8 4,068,502 28.70 4 10 8 3 IO 155.000 185,000 186.0 9,538,867 23.84 4 09 18 ii 88,926 5i.5 2 i 132,685 129.4 58.0 i33-o 26.14 4 4 4 90 94 08 14 7 13 12 60,521 140,000 8 13 6,194,583 26.32 6 14 36,346 71,346 41.6 2,045,703 23.29 *4 2 9 5 15 1,549,008 1,993,400 627.6 70,943,404 25-34 4 15 19 5 16 46,000 46,500 33-o 1,790,722 27.42 4 07 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 R cm ; this result, when divided by 365 days and the daily number of hours of operation, h, 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 V ^ S hVR cm ^ShVR cm NUMBER AND SIZE OF CARS FOR URBAN ROAD. •SONINHV3 ssoao S3SN3dX3 3NllVa3dO i 83M0d awt JOIXVlHOdSN*ai zs i \ \ _ \ \ V \ s s V \' \ ' . A \ \ \ \ \ \ \ \ \ \ *\ \ \ \ \ si \ \ \ !i \ \ "1 \ \ . \ fc \ \\ \ n \ \ \ \ y n* A \ \o \ I- o yr°1. . \ \ > « h \ > \ \ % \ *wB o\ I A 1 \ T \l\ k \ t \ (2 \ lf\ \\ s \ * \ \ \ \ il* \ j 1 F t\ Uii \ \ ^ \ \ I \ £*s ? ' 1* \ \ \ \W v v_ \ \ \ \ ■fc U \ \ V \ \ \ \^ • \U \ ■ V \ ^ \ \ \ \ •^ \ T i \i \ \ \ \ ^ \ s \; A \ 1p) . '*' S\ A \ \ \ \ .v \ \ r V ^ v : - * 4 % L. ft % I \- CO) V V \ • \ ■- \ v l \ • \\ » Jl -% ,v \ \ \ \ \ A ) L \ s\ %- ^ xA \ \ \ \ s \ ctj A i \ °-| % k \ . \ \ v.* '\ - *\ °° \ 7 ''■-A \ \^v \ V W \ is \ ,N -\ \ \ \ 1 \ \ \ \ . - > \ \ \ \ \ \ \' \ \ \ \ x A \ \ \ ,\ I \ L j CO 2_ y; $ \ \ \ y W^v- \:lf\ > < \ % \\ \ \4j r 3 E9 co > \a^\ i \ , f* °Wl < CO vT Vb.», - v\ \ V"! 5 m < "^rs A \\ \'° = -\ Xvh I -J _l V \ \\ w v \kl ; 2 < \ * A a, »ura 1 < ■z. V u J Z < CO ^Kl ? \W \ l\ - ► o cc VI \4\\ < ( or V % -•,\i\i < c \ WMM % A W\\ c > \ ^ w \ mm 2 < C-l C>4 04 CM CS — •saviioa Nom oor-.toin'a-cocM — onoorocaLn^cocM — IW Nl S3SN3dX3 ONUVa3dO a NV SDNINHV3 SSOHO 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 line. The average number of passengers per trip is therefore = NyL NrR cm 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 = — = Nyr L 365 vVh an expression which assumes uniform traffic 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 IO TRACTION AND TRANSMISSION. construction as to whether it shall be open, closed, con- vertible, semiconvertible, double-decked, or combination open and closed. Figs. 3, 4, 5' and 6 show the CharaCter- Fig. 5- Jft Fig. 6. istic forms of construction of convertible, " Narragansett " open, semiconvertible interurban, and pay-as-you-enter closed cars respectively. The last is being extensively adopted for congested urban traffic because it facilitates NUMBER AND SIZE OF CARS FOR URBAN ROAD. II comfort, ingress and egress of passengers, and collection and conservation of fares. The arrangement of seats, as to whether they shall be transverse, longitudinal, or partly both, is dictated by the type of service 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- stop service facility of ingress and egress is of paramount importance in order that a high schedule speed may be maintained. During the morning and evening rush hours the number of standing passengers frequently equals that of those seated. 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 12 TRACTION AND TRANSMISSION. 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. CAR DATA. Type. Length of body. Seating capacity. Weight of body, pounds. Weight of trucks, pounds. 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 16' 18' 20' 8" 28' 30' 8" 42' 44' 5o' 15' 8" 21' 3o' 2" 30' 2" 18' 20' 8" 28' 30' 8" 22 24 32 38 44 58 60 7o 32 5o 60 7o 24 32 40 44 6,000 6,575 i3,75o 11,310 26,725 22,000 56,300 85,100 6,375 i3,34o 15,250 20,300 6,640 10,240 15,120 19,500 4,600* 4,825 5,125 7,050 14,500 15,000* 21,000* 21,000* 5,150 5,925 11,250 7,550 4,900 5,IOO 10,450 IO,8oo 10-bench 12-bench 14-bench Semiconvertible cars: Single truck Single truck Double truck Double truck 7. Numerical Example. — As a numerical example of the foregoing method of estimating the number and size NUMBER AND SIZE OF CARS FOR URBAN ROAD. 13 of cars on a proposed electric railway consider the case of a city of 60,000 inhabitants and not having any street rail- way service. Allow a 25% increase in population for the subsequent 10 years. The economically feasible length of track is 0.76 X 60 X 1.25 = 57 miles. The annual re- ceipts of the operating company would be 60,000 X 1.25 X 132 X .05 = $495,000. The number of cars required is 4^ = 24, which assumes continuous oper- .24 X 365 X 24 X 10 ation at a schedule speed of 10 miles per hour and an income of 24 cents per car mile. The number of passengers per 4 . . 60,000 X 1.25 X 132 X 57 , rp. 1 • -1 trip is — a — = 268. Taking 4.5 miles F 365 X 24 X 10 X 24 as the average passenger ride, the capacity of the car with uniform traffic should be — = 21 passengers. A car 57 having a seating capacity of 1^ times this number of pas- sengers, say 32, would be appropriate for the service. According to the foregoing table such cars would weigh with live load 23,355 pounds or 11.68 tons. For an interurban road the procedure just outlined would be modified by other conditions, such as the dis- tance between terminals, the ability to compete with existing steam roads in regard to service, the schedule speed, and the headway. On suburban sections the sched- ule speed is most frequently from 15 to 20 miles per hour and on interurban sections from 25 to 35 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- 14 TRACTION AND TRANSMISSION. 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 and what sized cars should be used for a proposed elec- tric railway for a city of the size of Portland, Ore.? The schedule speed- is specified at 10 miles per hour over three parallel lines of equal length, the period of operation to extend over the entire day. Take 4 miles as the average passenger ride in determining car capacity for uniform traffic, and provide 50% additional seats for the accommodation of rush-hour crowds. 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 2. Plot a curve showing the relation which should exist between the population of the city just referred to in former years, and the seating capacity serving it 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 f 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 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 Vw 25 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\ where S is the car cross section in square feet and k r 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 an d 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 may 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 t.j^+L+sv 1 H pounds per ton, VpF 2 5 400 W[_ 10 a formula which combines the various expressions of the components of train resistance. Car cross sections may be taken as follows: Total car weight. 5. 20 tons 90 sq. ft. 30 100 40 no 50 120 60 " 120 " i8 TRACTION AND TRANSMISSION. Fig. 7 shows by curves the dependence of train resis- tance upon speed and weight of car as determined by the foregoing formula. As an illustration, determine the total tractive effort exerted by an electric car (Berlin-Zossen type) when run- 1 1 // , ..... ■£ 50 / o Or/ * / Ul 0. o 1 V 3 Q Z 3 // ' O / // 1/ Ul o z / < co ™ 20 // LJ DC < DC |_ -JO 20 40 60 MILES PER HOUR. Fig. 7- 80 100 ning at ioo miles per hour on a straight level track, assum- ing the weight of the car to be 104 tons and the cross- sectional area as 120 square feet. The tractive effort per _, qo . 100 . 120 (ioo) 2 , , ton is R = -7= + + 3 — - = 34-7 pounds, and V104 2 5 4oo X 104 the total tractive effort required is 104X34-7 = 3 6l ° pounds. TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 19 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 of a, such as are met with in railway work, sin a = tan a approximately, and therefore grades may be expressed as the ratio of the vertical rise to the horizontal length of grade. It is cus- tomary, therefore, to consider that a grade of q per cent means a rise of q 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 100 draw a car of W tons up a grade of q per cent with uniform speed requires G = 20 qW pounds tractive effort. For a down grade G is considered negative. 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 20 TRACTION AND TRANSMISSION. 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 ioo feet long will subtend an angle of one degree at the center. Thus the radius of a one-degree curve is quite accurately * > or 5730 feet, 2 7T 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 0.7 pound per ton of train weight per degree of curvature, a value Fig- 9. f 0.5 being representative. 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. Let m = mass of car in pounds, v = speed in feet per second, g = acceleration of gravity in ft. /sec. 2 , and R = radius of curve in feet. TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 21 Fig. io. Then — - = horizontal centrifugal force, and K mg = vertical gravitational force. An inspection of Fig. io shows that the resultant of these forces will be perpendicular to the plane of the track when that plane makes an angle with the horizontal such that = tan- 1 — • Rg 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 in one second is / = — = a pounds. g 3 2 - 2 Representing the weight of the car in tons by W, and the rate of acceleration in miles per hour per second by A, then the tractive effort required for acceleration alone is 22 TRACTION AND TRANSMISSION. „ 2000 PT 5280^4 ,, 7 . , F = • 7 -~ = 01. 3 PM pounds. 32.2 60 X 60 y ° ^ 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 the conservative value 100. Acceler- ation rates of from \ mile to 2 miles per hour per second are usual. The greater the rate of acceleration of a given equipment, the higher will be the schedule speed which can be maintained thereby. Limitations are imposed upon the maximum acceleration rate attainable by con- siderations 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 pro- pulsion of a car of weight W tons may be expressed by the complete general equation T m = )5 oV ^+ H 1 + \+2oqW + — I ( 25 400 L 10 J 2 ) + 100 WA pounds. Representing the expression in braces, which includes the effects of train resistance, curves, and grades, by T t pounds, and rearranging, the acceleration T — T A ■*- m ±_t m 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 force generally utilized is that due to static friction between TRACTIVE EFFORT REQUIRED FOR CAR PROPULSION. 23 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 0.15 for wet rails, and may be subsequently raised to 0.25 by the application of sand. If the maximum retardation, or negative acceler- ation, which this coefficient 0.25 will permit, be represented by Ab, then the maximum retarding force or braking effort W F B = 0.25 W = — A B tons, g and consequently the retardation rate A B = 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 24 TRACTION AND TRANSMISSION. 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 coefficient 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 15 miles per hour. The weight of the trucks per car is 9 tons; the weight of motors and control equipment per motor car is 7^ 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 50 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. Assume 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 and a curvature of 6 degrees. TYPES AND PERFORMANCE CURVES OF MOTORS. 25 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 somewhat less than this proportion indicates. The speed of any motor depends upon the field flux, number of armature conductors, num- ber of pairs of poles, and the counter electromotive force generated in the armature; thus T/ (E - I a R a ) 60. 10 8 V m = * ^— ^ rev. per mm., where E is the impressed E.M.F., I a is the armature current in amperes, R a is the armature resistance in ohms, p is the number of pairs of field poles, <£ is the magnetic flux per pole in maxwells, and 5 is the number of arm- ature conductors in series between brushes. 26 TRACTION AND TRANSMISSION. 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. At present a few roads employ direct-current series motors operating at pressures up to 1400 volts. Fig. 11 shows one of the G. E.-205, 1200-volt commutating-pole railway motors used on the Pittsburg-Newcastle railway. 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 TYPES AND PERFORMANCE CURVES OF MOTORS. 27 item of expense is the distributing system itself. But com- mutation difficulties limit the voltage of direct-current railway motors to about 1400 volts. 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 cur- rent is changed to direct current, which is then supplied Fig. 11. to the railway motors over the low-tension distribution system. Such generation and transformation entail large initial investment and operating expenses, and also con- siderable energy loss. These items may be greatly reduced by employing alternating-current motors, which can be oper- ated at a potential of several thousand volts. 15. 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, 28 TRACTION AND TRANSMISSION. 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 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. 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. Repulsion motors are used abroad to a consid- erable extent; single-phase induction motors starting as repulsion motors have not been seriously considered from the railway viewpoint. TYPES AND PERFORMANCE CURVES OF MOTORS. 29 Series Motors. — Consider a direct-current armature mounted within a single-phase alternating magnetic field, 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*f* m N E T - — p — -> (1) V2 IO 8 where <£ m is the maximum value of the flux entering the 30 TRACTION AND TRANSMISSION. 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 - <£ m . If there be N a conductors on the 7T armature, the number of turns connected in continuous N series 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 N N series is - • — - = — - • Therefore the equivalent number of 2 2 4 armature turns may be expressed as iV = 2.^ = ^- ( 2 ) 7T 4 2 7T 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 E T = &&-, (3) V 2 IO 8 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 (4) TYPES AND PERFORMANCE CURVES OF MOTORS. 3 1 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 $ am . This sets up a reactance E.M.F. in the armature which in the case of uniform gap reluctance can be similarly expressed as T? J ^ r am J - }l a V2 IO 8 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 arejndicated 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 E rotav = <$> f N a — io 8 , 00 where V is the armature speed in rev. per min. and $ f is the field flux; and the effective value of this E.M.F. is _ $> fm N a V { . E rot = -7= " J" > (5) V 2 IO 8 DO and is in time phase with the field flux, but appears as a counter E.M.F. at the brushes AD. When an alternating current is passed through the field coils, the alternating field flux is set up, and this flux pro- duces a reactive E.M.F. in the field winding lagging 90 behind the flux in phase, exactly as in a choke coil. The magnitude of this E.M.F. is 32 TRACTION AND TRANSMISSION. V 2 IO WY,, (6) where /m is the maximum value of the field flux, and Nj is the number of field turns. The electromotive force, E, which is impressed upon the motor terminals, is equal and opposite to the vectorial sum of E aj E rot , E f , and the IR drop of the armature and field windings, as shown in Fig. 14, where / is the current flowing through the field and armature, and represents the phase of the flux. In this diagram, eddy current and hysteresis losses are ignored. The impressed electromotive force is therefore e = V(E rot + my + (E a + E f y. ( 7 ) In the series motor, the same current passes through field and armature windings, and, if uniform reluctance around the air gap be assumed, then the armature and field fluxes will be proportional to the equivalent armature turns and field turns respectively. Therefore TYPES AND PERFORMANCE CURVES OF MOTORS. 33 * am :$, m = N:N f = ^:N,. (8) 2 7T Representing the ratio of the field turns to the effective N armature turns by r, then 3> /m = r$ am , and N f = t — -' 2 7T Therefore expressions (4) and (6) become respectively $, N f ^« ~7= — I ~ V 2 IO 8 T and E / = -^^-/r. v 2 io 8 Equation (5) then reduces to t V 1 V E rot = -£ a -' and E rot = -£,—• f 60 fr 60 Therefore E f = r 2 E a . Neglecting the armature and field resistance drop, the impressed E.M.F. becomes £ = £ V(J / J + ^ + 1 ) 2 - (9) which is the fundamental E.M.F. equation of the plain series motor. The power factor of the motor is COS = — = r^=> (10) and the current supplied to the motor is ^ghv+v still neglecting the motor resistance. 34 TRACTION AND TRANSMISSION. When V = 60 /, the motor is said to run at synchronous speed (bipolar field). The power factor of a plain series motor, having r = 1, when running at this speed, is — => or 0.446, and for values of r other than unity the power factor is less 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 — — V 5 X a When the motor is at standstill, V = o, and the power factor is zero. The current intake at standstill is Hence the ratio of the current at synchronism to the cur- rent at standstill is — = ■*- - = 0.894. The ratio of the V5 2 torque at synchronous speed to the torque at standstill, since it varies as the square of the current, is (- 7=-) + = 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- TYPES AND PERFORMANCE CURVES OF MOTORS. 35 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 E rot , or by decreasing E f and E a . It is obvious that increasing IR signifies an increase in losses, thus resulting in a lower efficiency. E rot can be increased by increasing the number of armature turns. Both E f and E a can be decreased by lowering the frequency without affecting E rot , 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 circuit 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., E a , 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 36 TRACTION AND TRANSMISSION 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 a 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 TYPES AND PERFORMANCE CURVES OF MOTORS. 37 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- bedded in the adjacent poles. When the compensating winding completely neutralizes the armature reactance, the impressed electromotive force from equation (7) is E = V(E rot + IRY + £/, (12) where R is the resistance of the motor including that of the compensating winding. If the resistance, R, be neglected, then, since V E rot = — — E f , OOJT the impressed electromotive force becomes and therefore the power factor is CQ S0= g^ = r V (13) E VV 2 + (6o/r) 2 The motor current is 1 = > E y . • (I4) At synchronous speed V = 60/, and therefore the power factor at this speed becomes , Vi + r 2 Still neglecting the motor resistance, the current intake Et at synchronous speed is — — > and at standstill it X f Vi + r 2 ^ 38 TRACTION AND TRANSMISSION. is — > consequently the ratio of the current at synchronous speed to the current at standstill is Since torque Vl+T 2 varies as the square of the current, the ratio of the torque T 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 consists of 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 inclined 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 pulsating flux through the armature, produced by the alternating current in the field winding, may be re- Fig. 18. TYPES AND PERFORMANCE CURVES OF MOTORS. 39 solved into two components, one in the direction of the brush axis and the other perpendicular thereto; these being represented in Fig. 18 respectively by OA and OB. The component OA produces an E.M.F. in the armature conductors and causes a current to flow through them. The other component, OB, reacts upon this armature current, thereby developing torque. Induction Motors. — The three-phase induction motor may be used for traction purposes where the service require- Fig. 19. ments 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 40 TRACTION AND TRANSMISSION. Cascade tunnel of the Great Northern Railroad. Six thousand six hundred volts are delivered 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, TYPES AxND PERFORMANCE CURVES OF MOTORS. 41 42 TRACTION AND TRANSMISSION- TYPES AND PERFORMANCE CURVES OF MOTORS. 43 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 elimin- 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 V m = motor speed in revolutions per minute, T = tractive effort in pounds, n g = number of teeth on gear, n p = number of teeth on pinion, D = diameter of car wheel in inches, T' = motor torque in pound-feet, V = speed of car in miles per hour, and e g = gear efficiency. 44 TRACTION AND TRANSMISSION. / 2000 / / f / % FFr / 1500 Q.Q £^cy / I \ O U. / \ J 7 Ul 1x1 > X DC \ o. H O irlOOO 05 D. O) .9-Q.UJ. 2 . / 7 _l / si ^ 500 10 / 5 50 e H.P. 00 V MO OLTS for 3 GEA 3"W R RA HEEL no 1 3, ^-69 100 80 70 20 40 60 AMPERES. Fig. 23. 80 100 120 TYPES AND PERFORMANCE CURVES OF MOTORS 45 / J / / % E r FICIENCY / / -7000- / _ 90- "48 — \ / 6000T - / 80 -40 -5000- \ 4 '/ < DC co GO _1 . SP £JD_ 10 200 5 H.P. 50 V MOTOR OLTS, X 3 GEAF 3"WI * RA1 iEEL ■10 2 3, 0-63 150 225 300 AMPERES Fig. 24. 375 450 525 46 TRACTION AND TRANSMISSION. \ -80— -4000- / -TO -3500- £^Pc !£!£» ^c>«. / / r, . £ FFI( / 90 -60 -3000- / s y <\ \ H / «^80 -50-©- cc —2500- O Li_ Ll. X s / H z UJ °7fl Ld > / cc' UJ Q. CO -40-3- i -2000- 1- o < ^ / CO 4 60 -30 CO _1 &/ V / -20 -1000- ^ -io — 250 H.P >5 C\ . MOTOR 'CLES, 225 \ 62"WI 'OLTS, HEELS. 250 500 750 1000 AMPERES Fig. 25. 1.250 1500 1750 TYPES AND PERFORMANCE CURVES OF MOTORS. 47 -240 $ E"FF tClEi vie/ r^T" w \\& -1-80C , j /<{ / -1-5-0 ( » e / = / F-7-0 Z UJ -1-2-0 G UJ I ' y DC UJ 0-60- l- / 25 H 300 p. r vo AOT LTS DR -9-0 <: A / 2 5 CY 3 PH CLES ASE / / / / -96 < / 5^ / / / ^ *^~^ 10 20 30 40 AMPERES PER PHASE Fig. 26. 50 60 70 48 TRACTION AND TRANSMISSION. The work performed by the motor while its armature makes one revolution is 2 -kT '. 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, n p /n g , of a revolution. Therefore, the wheel radius being D/24. feet, 2 7re a T ; = 2 7r T foot-pounds. ... T = tbL2k T > pounds. n p D Equating the effective power exerted by the motor to the power exerted by the tractive effort, 2 irV m e g T' 5280 jrrrx. — — = — — VT horsepower. 33,000 60.33,000 Solving this equation for the car speed, T' V = 0.0714 JL — V m miles per hour. The characteristic curves of a 50-horsepower, 600-volt General Electric Company direct-current railway motor (G.E. No. 216A) are shown in Fig. 23. They are based upon 33-inch car wheels and a gear ratio of 17 to 69, i.e., 4.06. Fig. 24 shows the performance curves of the 200- horsepower, 5 50- volt, direct-current motors used by the Interborough Rapid Transit Company of New York City. These curves are for a gear ratio of 20 to 63, with 33-inch car wheels. The characteristic curves of the 2 50-horse- power, 25-cycle, 225-volt, gearless Westinghouse conduc- tively compensated single-phase motors used on the elec- tric locomotives of the New York, New Haven and Hartford TYPES AND PERFORMANCE CURVES OF MOTORS. 49 Railroad are shown in Fig. 25. The performance curves of a 2 50-horsepower, three-phase, 2850-volt, 2 5-cycle induction motor for railway service are given in Fig. 26. PROBLEMS. 9. Plot a curve showing the ratio of the current taken by a compensated series motor at synchronous speed to that taken at standstill, coordinated to the ratio of the number of field turns to the effective armature turns. 10. 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 25-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. 1 8. 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 coefficient 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 coefficient depends upon the condition of the track. The following values are approximate and are based upon a uniform torque exertion: Clean dry rails o . 30 Wet rails 0.18 (with sand o. 25) Sleet-covered rails 0.15 (with sand o . 20) Snow-covered rails o. 10 (with sand o. 15) It is seldom 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. 5 1 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 off 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. 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, 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 motors 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 approximately uniform. After the line voltage is applied to the motors, their performances are entirely dependent upon their char- acteristics. 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 I. The average weight of passengers may be taken as 140 pounds per individual. The weights of some standard 500 to 600- volt electrical equipments,that is, railway motors and the accessory controllers and resistances, made by SPEED CURVES. 55 the General Electric and the Westinghouse Manufacturing Companies for direct-current railways are given below. Trade Name. GE-54... W-12-A. . W-69 .... GE-78. . . W-92-A. . GE-70. . . W-101 . . . GE-216-A W-93-A.. GE-87. . . W-85 .... GE-66 . . . W-134... GE-69 . . . H.P. Number of Motors. 25 2 4 25 2 4 30 2 4 35 2 4 35 2 4 40 2 4 40 2 4 50 2 4 4 50 2 60 4 2 4 75 2 4 125 2 160 4 2 4 200 2 4 Type of control. K-io K-12 K-10 K-12 K-10 K-12 K-10 K-28 K-10 K-28 K-10 K-28 K-10 K-28 K-11 K-14 Mult. Unit K-11 K-14 Mult. Unit Weight of each Weight tff motor including control gears and case, apparatus in pounds. in pounds. 1830 940 "75 2 200 940 ii75 1950 940 ii75 2560 940 1350 2265 940 1350 2745 940 1350 2645 940 ' 1350 2885 1015 . 2250 2070 3355 1015 2250 35io 1765 2670 4500 1770 3640 4375 2715 375o 6230 3380 577o Total weight of equipment. ,600 .495 ,34o ,975 ,840 ,975 ,060 p59Q ,47o 10,410 6,430 12,330 6,230 11,930 6,785 i3,79o 13,610 7,725 15,670 8,785 16,710 10,770 21,640 11,465 21,250 12,200 26,800 15,840 30,690 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 25 15 12 7 Number of stops per mile. 0.05 to 0.2 0.3 to o. 7 0.4 to 1.0 1 to 2.5 2 to 3 5 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 developed in §11: T m -T t A = Then (1) (2) 100 W = T t + 100 WA. The starting part of a speed curve is taken as a straight line, and it passes through O, the origin of time, at an angle B A with the horizontal such that d A = tan -1 ^4, where Fig. 28. 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 m calculated from equa- tion (2), in which T t 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 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 6 n = tan~M n , where A n 58 TRACTION AND TRANSMISSION. 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 Be = tan -1 Ac, where Ac 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 6 b = tan - 1 Ab, where Ab is the assumed rate of braking. Its upper terminus is determined by the point of intersection, C, with the coasting part. In plotting the different parts of the curve on coordinate paper it is inconvenient to lay off the angle by means of a protractor. Since A=AV/At, therefore At = AV/A. The abscissa increment, in seconds, for an element may be determined by dividing the speed increment in miles per hour by the average acceleration in miles per hour per second. In making calculations both T, and W should be based upon the total weight of car or train divided by the number of motors. SPEED CURVES. 59 24. Numerical Example. — The process of plotting a speed curve is best illustrated by considering a specific case, as follows: (a) 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. Fig. 29 shows the relations which exist between train 160 CO Q S O °- 120 z ESISTANC cc z < 40 tr l- 10 20 30 SPEED IN MILES PER HOUR. Fig. 29. 40 resistance per motor, T t , and speed calculated from the formula given in § n. Trial equipment: four direct-current 50-horsepower, 600- volt G.E. 216A motors with Type K-14 control. Characteristic curves of motors are shown in Fig. 23 for a gear ratio of 17 to 69. From these curves a new curve, Fig. 30, 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. TRACTIVE EFFORT IN POUNDS. OOOOOOOOO 00 00000000 \ \ 10 20 30 SPEED IN MILES PER HOUR. Fig. 30. 40 The total weight of the car with live load is 23,650 + 13,790 + (80 X 140)= 48,640 pounds = 24.32 tons. (b) Acceleration at Subnormal Voltages. To produce an acceleration of 1.5 miles per hour per second requires a net tractive effort of T = 100WA = 100 • 24.32 • 1.5 = 3648 pounds. To neutralize train resistance during the period of initial acceleration additional tractive effort must be exerted. SPEED CURVES. 6 1 The amount may be taken equal to the train resistance at half schedule speed. In this problem the train resistance is R = 50 VW + 1 25 400 / . 10X24.32 95 X 10 X 10 1 = 50 V 24.3 2 + =L ^ L - + — = 280 pounds. Therefore the total tractive effort divided by the number of motors gives the effort to be exerted by each motor in starting, as 3648 + 280 , * 2 - 3 = 982 pounds. 4 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 A 1.5 of the speed curve, and is shown at A in Fig. 3 1 . 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- comes less and less because the current decreases as the car speeds up and this results in a lower available tractive 62 TRACTION AND TRANSMISSION. 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 A b =— m — =77= S7o-7-(iooX ) = 0.04 mile per hr. per sec. i 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 — 16.9 3.1 , 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 (b, 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. The values of T t in the fourth column represent the total train resistance divided by the number of motors. SPEED CURVES. 63 w 1 1 1 LJ Q. -— ^ — — ' 1 ^-^**"'^ - -\ <&'"' H ^-'-" £ _e=:r / - - t JZ 1 L 3 l i jz t -/ t 7 3t I ! _T -\ / H c 1 / W _\r IS.* n L_ I -fc V 41 St K-» \a Y^ < "^^is^ ^"^.^ "^^ o CM anoH a3d S3"im 6 4 TRACTION AND TRANSMISSION. Point. Speed, V. Tractive effort, T Train resistance, Tt. Net trac- tive effort, T m ~T t . Accelera- tion rate, A. 16.9 20 22 24 26 28 30 32 35 36.8 912 570 434 328 252 185 133 90 25 1.50 O.94 0.714 0.540 0.415 0.304 0. 219 0. 148 0.041 O 660 530 430 360 3OO 255 220 I70 152 90 96 102 108 115 122 130 145 152 Total time. 13 16 19 23 29 36 47 79 177 (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 section 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 = ^°o°o or rV 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 -5- T V = 144 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 7^ r = 0.21 mile per hour per 100 X (24.32 + 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 instantaneous 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 \ (o + 16.9) = 8.45 miles per hour, and therefore the space traversed during this . , . n. 3 X 8.45 ., 95.4 X 5280 vy , period is — ^— — mile, or yo ^ = 95.4 x 1.407 360a 3600 = 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 ; j^ [mL ^l ^ convenience the same time T" " 8 °° 1 — v+ + 2.35? GRADE ^^j 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 unaltered. 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, and the distance traversed during this interval with uni- formly accelerated motion is -^^ X 10.2 X 1467 = 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 133J l i- ---' 1 1 ^S-qr" \l , __--- — / - 44-:t^ 7 .3 / -i-V 7 ^ v 'T\ 7- } V -/ M- ^ 2 it XV 2 X 41 -J V -3 t \- " \ / ^\ -U £ 5^ ■*s / -\ T / lV~ ■ ^ftCQ ~"-^i ^ S*_ \ >. j\ ^^\ \ \ £\ A """""S V \ \ °r~ « \ ^ ^ _ . *A> "faV \ ^\ N= -^ -± ^ ---^ ifi UJO CD 8* an oh U3d sanm 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 4- J (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' in 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. to 0) CO u 05 ^ 8 > it, S3 SB "a3 o . si .IN | & .S "B CO _. A 15-3 18 20 22 24 2 3-9 1262 476 290 154 48 53 1-50 0.78 0.48 0.25 0.079 0.088 10. 2 2.36 3.18 5- 48 12.15 11 . 21 10. 2 12.56 15-74 21.22 33-37 32.43 114. 57-5 88.6 168.9 409 376 114. b c d e ei 840 660 530 430 435 84 90 96 102 102 171. 5 260.1 429 838 805 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 h of table of § 24) the following: 6 £ +i 2 > *a3 . •S a .1 •S a .52 ^ '3 U co 5 0) > O H CO / 26 360 108 252 0.415 8-35 40.78 305 IIIO g 28 300 us 185 0.304 5-57 46.35 220 I330 A 30 255 122 133 0.219 7-65 54-o 326 1656 z 32 220 I30 90 0. 148 10.90 64.9 495 2151 J 34 185 139 46 0.072 18.20 83-i 880 303I Ji 33-3 198 135 63 0. 104 10.30 75-2 493 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. This amount is Wo° X 6.08 X 0.5, or 36 pounds. The length of the curve is — - — =754 feet; that is, the curve ends at a 1 2 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. 6 — > a ° Oh % Pi CO 0. co 6 > a) in >H O *a3 . & .5 a a 6 6 H .as co 3 § k 34 185 139 10 0.0165 11 .62 86.82 573 3217 I 34-2 181 145 24.22 1 1 1 . 04 1212 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 OABCDE in Fig. 33. By reference to this curve it is seen that the power is cut off 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 674 X i (32.1 + 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 17 Q traveled during this period is 8.95 X - L ^ 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 50-horsepower, direct-current motors whose characteristic curves are given in Fig. 23. The initial acceleration rate is to be 1.3 miles per hour per second and the schedule speed is specified at 15 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 f-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, 5 50- 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, 500- 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 acceleration of two miles per hour per second on a tangent level track. 18. If the schedule speed of the train in the foregoing problem is 25 miles per hour and the rate of braking is 2\ miles 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: 1, 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 1, 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. 1 2 3_ * -O O-i-O O-r-O O-i-O O-i ^n/v/vJ-a/wJ-aaaa-Laa/va-L -czf MVj-^JUUMiL- 1 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 PR 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 (1) 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 applied 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 5, 6, and 7. Switches 1 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 £ t8£ 2 3 4 )0-t-0 O-j-O O-i vna-'-aaaa-'-aaaa -o i_0 0-^0 0^0 oj 5 6 7 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, R m = resistance of motor, ?i, r 2 , r 3 , . . . , r n = the respective controller resistances in series with the motor when the controller arm is on contact studs 1, 2, 3, . . . , n, Fig. 36. E 2 , E 3 , . . . } E n = the respective counter electromotive forces generated at the instants when the arm makes contact with studs 2, 3, 4, . . . , n, E\, E \5J whence n = T--R m —&- (6) ■*- max J- max Since E 2 and E\ are generated at the same speed and with the respective field currents 7 max and 7 m i n , reference to the saturation curve shows that Ei E max -E/ E t = q Imin — . -r, ' (p) and therefore E 2 = gJEi', which, by substitution from (4) , becomes E 2 = Eq(i-K). (7) At the instant when the current has again decreased to 7 m i n the arm leaves stud 2 and E-E/ ri + R* Dividing (8) by (5), E — E 2 K -E^Ei' from which E 2 ' =E(i-K)+ KE 2 , whence by substitution from (7) EJ = E(i-K)+ EqK (1 - K). (9) Proceeding in a similar manner there results E t) Ez ( \ rz = y— - R m - — > (10) RAILWAY MOTOR CONTROL. 83 £ 3 = qE 2 ' = Eq (1 - K) + EfK (1 - K), (11) E 3 ' = E (1 - K) + KE 3 = E (1 - K) + £gX (1 - #) + Eq*K 2 (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 1 and 2 is Similarly, n-f.-^--^-«(i-JE). (13) -'max -'max r 2 -r3 = j — (£3 J- mflY J- E i ) = ^(i-K)=qK(r 1 -r i ), (14) -* max n-r 4 = -^ (£ 4 - £3) = ^(1 - X) =^('2 - r 3 ), (15) -* max -t 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 I max and R m . 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 1 the current flowing is /max = . * > (l6) Tl + Km where E\ is the counter electromotive force that is being generated at this instant. The other symbols retain their former significance. Herefrom r^-^-K-^-'- (17) ■*■ max 1 max At the instant when the arm leaves stud 1 the current flowing should be as before, /m in = ^^- (18) ri + Rm Dividing (18) by (16) and solving for E\ there results E/ = E(i -K)+KE 1 . (19) Again, at the instant when the arm touches stud 2 the current should again be E-E 2 consequently T2+ R m RAILWAY MOTOR CONTROL. 85 E u E 2 f N r 2 = Km - (21) ■*■ max ■* max As before, £ 2 = g£i', whence by substitution from (19) £2 =Eq(i -K) +qKEx. (22) The instant the arm leaves stud 2 the current diminishes to ?2 + R m Dividing (23) by (20) and solving for £ 2 ', E 2 ' =E(i-K)+ EqK (1 - K) + ?Z 2 £i. (24) Herefrom E r, Ez , x ^3 = 7 is the angle by which RAILWAY MOTOR CONTROL. 93 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 1, 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 1 and 4. When the controller handle is moved to the second running position switch 1 is opened, 94 TRACTION AND TRANSMISSION. 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 TO MOTORS 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 supplied 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 RAILWAY MOTOR CONTROL. 95 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. 35. 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 96 TRACTION AND TRANSMISSION. 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 Multi polarity 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 =^Z, 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 RAILWAY MOTOR CONTROL. 97 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 S N S N s N s [8 POLES] N S N S [4 poles] \ /Y 1 / r\ / \ o 2 Fig. 44. into the two parts 1-2 and 2-3 by a tap 2 at the middle point of the winding. Terminals 1 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 1 and 3 to the neutral point of the phase windings. The coils are so arranged that when thus connected they pro- 98 TRACTION AND TRANSMISSION. 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 1 and 3 to 8 16 POLES POLES L^L 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. RAILWAY MOTOR CONTROL. 99 (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., Vi = the synchronous speed of the first motor in rev. per min., V 2 = 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, p2 = number of pairs of poles of the second motor, Si = slip of the first motor, s 2 = slip of the second motor. Vi-*P (i) IOO TRACTION AND TRANSMISSION Then F > = ! * Pi and V _6os l f_6of/ V 1 -V\ _6of/ V\ Pi p»\ Vl } p2\ VJ which by substitution from equation (i) becomes F2 = 6°x^r. (2) Since V 2 - V 52= ~rr~' therefore V-V,.(i-sJ. (3) Substituting in equation (3) the value of V 2 given in equa- tion (2), there results v== 6of^p 1 V (i _ s2)j p2 which shows that as s 2 approaches zero V approaches the limiting speed, 60/ Pi + p2 Hence the synchronous speed of the two motors connected in direct concatenation is the same as that of a single motor having pi + p 2 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 . RAILWAY MOTOR CONTROL. IOI 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 auxiliary motor, the latter being employed during cascade ■=■ GROUND 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 102 TRACTION AND TRANSMISSION. 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 carrying out this method of control. 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. With a three-phase induction motor the same result is obtained by exchanging the connections 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- ling 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- RAILWAY MOTOR CONTROL. 103 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 either 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 104 TRACTION AND TRANSMISSION. 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. In operating an electric car equipped with hand control the power should never be turned off by a slow reverse movement of the controller handle, as destructive arcs are liable to occur upon a slow break. To lower the speed of a car, the power should be completely and suddenly shut off. Before the car has slackened its speed too much the controller handle can be brought up to the proper point. 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, RAILWAY MOTOR CONTROL. 105 resistance, or compensator circuits, and in general effect the changes in connection necessary in controlling the particular type 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- 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 io6 TRACTION AND TRANSMISSION. 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. Fig. 48. 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- RAILWAY MOTOR CONTROL. 107 tors a, b, and h, due to current received from train wires r, 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, 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 f 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 108 TRACTION AND TRANSMISSION. 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- 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 cylinder 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 RAILWAY MOTOR CONTROL. 109 motor car is provided with a current-limit relay that is designed and adjusted with reference to the requirements 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- 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 35-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, 500-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 2 20- 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 regulation 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 53 %. The motor current during the period of initial HO TRACTION AND TRANSMISSION. acceleration is approximately constant at ioo 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 2-IR 1 Vl E-IR h where E is the line voltage, I is the current traversing the motor and R is its resistance, and Vi 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 rinding 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 1 6- 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 (1) 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 H4 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 2 600 — 19.2 X 16.9 = 8.2 miles per hour. This speed is attained in 8,2 i.5 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 I 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 (miles per hour). Current per motor (amperes). Current per car (amperes). Time of speed acquire- ment (seconds). See table, page 64. 20 48.2 192.8 I3-84 22 42.I 168.4 16 26 24 37-4 149.6 19 45 26 33-9 135-6 23 65 28 31.0 124.O 29 22 3° 28.4 113. 6 36 88 32 26.3 105.2 47 78 ENERGY CONSUMPTION. 115 ; | 1 1 l 1 1 1 Z I LU 1 ° : 1 l <-> 1 1 LU 1 & < DC LU > < 2 en 1- _) / / J u. > LU Or ^^ m 1 1 1 \ 1 t 5 — 1 o LO S3U3dlAIV O O S±10A 00 ° bo O ■« CO Il6 TRACTION AND TRANSMISSION. After 50 seconds coasting begins and the current curve is completed by drawing the vertical line 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 ampere 2 -seconds. The mean square current over the given run which requires 144 seconds for its completion is 631 (amperes) 2 . Therefore the effective heating current of the motor is 25.1 amperes. 40. Effective 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 / (40 2 X 25) + (,S5 2 X 20) + ( 2 8 2 X 15) 25 + 20 + 15 v/ 40,000 + 24,500 + 11,760 _ 60 ~ 35 ' ENERGY CONSUMPTION. Iiy c c c 3 3 3 f c c c c 3 C 3 c 5 C 3 C (S3d3dWV) 3 C ) c > c 4 3 > 1 ~ |z |UJ 0: \o liii j> |H <-> LU 111. ILL. |LU C y Ol CD Q a: O 1- / )LTS ON MC /Or 1 Id > gf>^ j CD < c " CO Q O O Z 00 M UJ Uu CO CD O O O CO CD t= 52 •snoA aoiow ? A 3 2 a I cc \ O \ l- \ \ < \ Li. \ CC \ LU \ £ f-l \ O 21 a. UJI \ 0/ \ 7T V ^^^ CO Q . ^ 10 O . O be CO w o I< Id o •anoH a3d S3"im •S3a3dl^lV I c XN30 H3d 124 TRACTION AND TRANSMISSION. 45. Effect of Operating Conditions on Energy Consump- tion. — In order to determine the effect on the energy consumption of a railway equipment when the operating conditions are changed, such as altering the initial rate of acceleration, the length of run, the number and duration of stops, the gear ratio, the braking rate, and the line voltage, it is necessary to consider how the total energy taken from the trolley or third rail is expended. The energy supplied to a car or train during acceleration changes the momentum thereof, and the greater part of this energy ap- pears in the kinetic form, the remainder being expended in overcoming train resistance and in heating the starting rheostats and motor circuits. In bringing the car to rest subsequently the kinetic energy must be dissipated. Left to itself, the car would continue to move until all its energy of motion is lost in overcoming train resistance, and if, as is the usual case, the car is quickly brought to standstill after coasting for a time, the greater portion of the kinetic energy is consumed in heating the brake shoes and car wheels. Thus, the energy supplied to railway equipments is the sum of (a) the energy required to overcome the train resistance throughout the entire run, (b) the energy wasted in the starting rheostats, motors, and car wiring, and (c) the energy consumed in braking. A slight reduction in train resistance such as might be effected by the employment of ball or roller bearings in diminishing bearing friction, permits of a higher rate of acceleration with the same motor current. The greater the acceleration rate the more coasting is possible on a given run for the same schedule speed and the shorter is the time during which the motors receive power. A con- siderable saving of energy may result from the reduction ENERGY CONSUMPTION. 125 of train resistance to a minimum. With a given equipment the energy expended in overcoming train resistance is approximately constant for a given run. The energy lost in the starting resistances is proportional to the time that these devices carry current. The losses in the car wiring are usually small enough to be neglected in considerations of this kind. The motor iron losses and the loss in the gears are practically constant over the period during which the power is on. The copper loss in the motors 80 60 CO Q O40 o Ul CO 20 A p> ,* N CO UJ ^ Q. < ^\ fr ^S; ^£> xh> ^ ^0/ ^Sfs- ■-J ANCE 40 30 O I cc 20ui Q. 10 0.5 1.0 1.5 2.0 MILES PER HOUR PER SECOND Fig. 52- 2.5 3.0 is proportional to the square of the current, and therefore the higher rates of acceleration with the accompanying larger currents result in a greater loss and consequent increase of heating in the motors. On the other hand, increased acceleration implies a shorter time during which the motors receive energy, and therefore tends to reduce heating. These two opposing conditions suggest that there is a definite rate of acceleration which will yield a minimum heating in a given case. 126 TRACTION AND TRANSMISSION. The energy consumed in braking depends upon the brak- ing rate and upon the speed of the car when the brakes are applied. More coasting is permissible on a given run when high braking rates are employed, and the car speed at which braking begins is lower. Braking immediately after turning off the power and thus bringing the car to rest slowly results in inefficient operation. The curves of Fig. 52 show the motor current during the period of initial acceleration, the time of running on resist- ance, and the speed of the car at the instant of full- voltage application to the motors, in terms of the acceleration rates, for the 24.32-ton car already mentioned, which is equipped with four 50-horsepower, direct-current motors. These curves are plotted from the following data taken from the characteristic curves of the motors, Fig. 23. Acceleration rate. •25 •5 • 75 1 .0 1-25 1-5 i-75 2.0 2.25 Total tractive effort per motor. 222 374 526 678 830 982 1134 1286 1438 Accelerating current. 27.O 34-7 42. 2 49 56 64 70 77 85.0 Speed at full voltage with initial accel. current. 3i-8 25 5 22 19 7 18 1 16 9 16 15 2 14 5 Running time on resistance. 127.2 5IO 29.4 19.7 14-5 11. 3 9.1 7.6 6-5 (Train resistance taken as 70 pounds.) The curves verify the foregoing general statement that the greater the rate of acceleration the larger will be the current during uniform acceleration of the car but the shorter will be the time during which this current flows; and they show the dependence of these factors upon the rate of acceleration for this particular equipment. The ENERGY CONSUMPTION. 127 maximum schedule speed possible on any given run is a direct function of the rates of acceleration and braking. The maximum possible schedule speed increases with larger runs, provided all other conditions remain unaltered. Thus, in the case of the 24.32-ton car to which frequent reference is made, the relation between maximum schedule speed and the length of the run on level track, allowing for 40 .30 20 10 £ SPE LD $& £>S^ sc -\ED't)- D 0VV£ R CONS UMP" "ION / 0.5 1.0 1.5 MILES RUN Fig. 53- 2.0 2.5 3.0 20-second stops but no coasting, is shown in Fig. 53. This curve is based on data obtained from Fig. 31, on which a number of braking curves may be drawn corresponding to runs of various lengths. Proportionately less of the energy taken from the supply circuit is used to overcome the losses in other than train resistance for long runs than in short runs, and therefore the power consumption per mile is decreased by increasing the lengths of runs. This is also shown in Fig. 53 for the particular car under consideration; the curve of power con- sumption per car mile without coasting was computed in 128 50 40 1-30 z Ul o tr ui D.20 TRACTION AND TRANSMISSION. 10 6-CARTRAIN.-4 MOTOR CARS.-154 x <£f ^"^ TONS. AVG. BRAKING RATE1.75 \AS ^ffi-*' MILES PER HR. PER SEC. ST ATION^V •<* STOP-1 2 SECONDS. s$V <<<^ LvXr °//t '~// Q l !_. I. ' ' Uj// ■ off ul Q.I 1 l_ _1 1 0.5 1.0 1.5 2.0 RATE OF ACCELERATION IN MILES PER HOUR PER SECOND. Fig- 54- 1-30 ■z. LU o ^20 6 CAR TRAIN. 4 MOTOR CARS, 154 TONS. ACCELERATION 1.33, MILES PER HOUR PER SECOND, STATION STOP 10 SECONDS 0.5 I.O 1.5 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 recent 50 40 1-30 £20 10 6-CAR TRAIN.-4 MOTOR CARS.-154 TONS. which also must be a minimum. Therefore dz n Cn — n = 1 - — = o. :. y n = VCn, 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 [Cx y x = 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 = — = pl \ — Vx dx; y x v C therefore the total voltage drop is e = pI*\J-£ I ^dx= pl \j —- L* volts. (5) Since the total entering current, /, is equal to the product of I Q and the total length of the section, L, the value of */ C — from equation (5) becomes JC 2 P lVL . V7 = 3.^' consequently y x = Vx 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 ss: is SUBSTATION TRACK 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 )' 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 KirchhofT's laws, which result in the following equations, where the resistances THE DISTRIBUTING SYSTEM. 147 A = a + b +c| B = d +/ + g I ohms. C = b + d + /zj 4/i -bl s +IR = E BI 2 -dh -IR =-E -bh -dl 2 +CI Z = o /1 -/1 = / Solving for i? by means of determinants (7) (8) fl i4 o B -b -d 1 —1 -b -d C o A B (b -b (E-AI)/I -d -E/I d)C b A o B -b -d 1 —1 -b I -d -I c A - b 1 B -d — 1 (b+d) c o ohms. (9) RI = volts. (10) Whence the voltage impressed upon the load is E(b+d) 2 -E(A+B)C-{Ad 2 +Bb 2 -ABC)I , (b + d) 2 - (A +B)C The drop e between either substation and the load is e = xl = E — RI volts, (n) 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 148 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 either inclined or perpendicular to the axis of abscissae. The cotangent of the angle between a portion 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 ami 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 6oo-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 Ol I I I I III I I I I I I I I I I I ( 2 ) 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 R be the resistance in ohms per foot of combined conductor, the drop is e = Rlih = Rh(L - h) volts. (1) But I = Ii + h amperes; (2) hence e = Rl(i-fy h volts. (3) Therefore, for a given current /, the drop increases with increase of h from h = o to h = ~ • These equations also 2 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 Jx cost per kilowatt-hour delivered to the feeder be c 3 dollars, the annual expense for energy lost in the feeder is , = c^hPL do]lars> (i) 7 1000 A N At a cost of c 2 dollars per pound of feeder conductor and 152 TRACTION AND TRANSMISSION. at a rate for interest and depreciation of fa, the annual charge against capital outlay for feeder conductor is C/' = p2C 2 wLA 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 — I\ - — — — circular mils. (3) V 1000 ihom 1000P2C2W Hence the maximum economic drop is e = 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 (1) and (2) before differentiating in order to obtain a minimum. Boosters. — Jn 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, e f = maximum total drop in boosted feeder, I = maximum 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 = piif + g—^-j dollars, v 1000/ If h be the yearly effective hours of feeder operation and Cz be the cost in dollars of generating a K.W.-hour, the annual cost of energy lost in the feeder is C 2 = 7( * + g/) hc 3 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 mils, (6) x + e f W = —, — pounds. (7) x + e f and its weight is 154 TRACTION AND TRANSMISSION. At a cost of c 2 dollars per pound and a rate of interest, etc., of p2 per cent, the annual feeder expense is C, = C -*^ dollars. (8) x + e f The total annual feeder and booster expense therefore is C = C x + C 2 + ft, or C = Pl 0+ g JZ-)+ I ( x + *>* & + <^MR do n ars , ( Q ) \ iooo/ iooo x + ey In order that this expression may be a minimum its differ- ential coefficient with respect to x must equal zero, or dC u gl . I he 3 czpiivpIL 2 — = px H t — . — r^ = o; ax iooo iooo (x + e f y therefore ( r _L P \2 _ C2p2WpL 2 IOOO and V p!g + C 3 h f 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 e, multiplication of the term c 3 h in (io) 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. c 3 = [0.006]. w = 0.00000303. pi= [0.10]. c 2 = [0.17]. / = [300]. P2= [0.06]. g = [28]. x = 0.018 LV/ ; —e f . (11) V 2.8 + 0.006 h f For a total boosted-feeder drop of 50 volts and continuous operation of h = 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 c 3 . Assum- ing h = 1000 hours and c 3 = 0.01 the minimum length becomes L = 10,000 feet. 54. Track Rails. — The size of track rails is determined by consideration of the mechanical requirements of the rolling 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 o° 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 i56 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 traffic. 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 OF TRACK RAILS INCLUDING BONDS. Weight of rail, pounds per yard. Resistance per mile, ohms. 40 O.066 50 60 70 80 OO53 O.044 O.038 O.033 90 O.030 IOO O.027 no O.024 THE DISTRIBUTING SYSTEM. 1 57 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 auxiliary 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- i58 TRACTION AND TRANSMISSION. sent distances in feet from the power house, then the leakage current dl e , escaping at the point / to the soil from an elementary length, dl, of track, is represented by the proportionality di^ e A l , (l) and the total leakage current is proportional to the area 50 CO CO ai > h=2S < / r - * -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 a Jo edl. (2) 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, /, 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. 1 59 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 line. 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, A c = cross section of negative supplementary conduc- tor in circular mils. Then i = / (1 - -J amperes, (3) r = I^Z 0hms ' (4) The curve coordinating voltage to distance is therefore a parabola, and the area contained between it and the / axis, that is, the value of the integral in equation (2), is 1. L edl = -j-fif-j- - • (6) 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 zu 1 Ul Q a 16 Ll o z UJ < < ft _l U. o H z u 4 O DC Ul " 0. 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 main- 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. 161 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- GENERATOR BOOSTERS 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 studying 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 1 62 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. Inside 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. 1 2 I l| 2 3 4 6 8 10 12 16 18 20 24 30 36 48 II 18 31 42 55 70 109 130 151 205 294 408 604 .000131 . OOO080 . OOO0465 • OOOO343 .OOOO262 .0000206 .OOOOI32 .OOOOIII .00000955 .00000702 . 00000490 .00000353 .00000238 I 2 3 7 10 18 28 40 49 84 7 7 6 5 6 8 .000215 .OOOI06 .OOO067 .0000502 .OOOO241 .OOOO171 . OOOO0963 .OOOO0647 . OOOOO45 2 .OOOOO369 I 2 3 5 10 15 29 43 54 65 1 2 6 .OOO164 .OOO082 . OOOO502 .OOO0362 .OOOO181 .OOOOI2I .OOOO0623 .OOOO0421 .OOOOO335 .OOOOO278 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 0.01 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? S3- 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 pound 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 minimum feeder length for economic installation of a booster assuming an average booster efficiency of 85 per cent. 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 Mou tiers 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 requirements, a single movement of a controller handle on a simple switchboard serving to cut in SUBSTATIONS. 1 67 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 amplified 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 0.97 fO, £J£ ib^— 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 line of 25-cycle, n, 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 generators 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 170 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 Synchronous motor-generators . Induction motor-generators . . . .85% .84% Figs. 72 and 73 contain curves showing the operating characteristics of a shunt- wound, 25-cycle, 600-K.W. conver- 2500 25 50 75 100 125 150 175 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 172 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 1.0 o z 0.9 u o n: 0.8 go, 1- o DC 0.5 0.4 .-, Xw ^ ^0 "o^" / ^ & / / / V 100 200 300 LOAD IN KILOWATTS. Fig. 73. 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 kilo volt-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 1000-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 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. $80,000 67,500 27,000 $206,000 Motor generators. $55 000 118 000 18 000 $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 21.90 Motor-generator switch apparatus 3.33 The data concerning the converter equipment relate to an existing substation. 62. Location 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. 2 i± Jy 1 1 ~ _ COMPOSITE CONTACT CONDUCTOR 1_ 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, where the substations are represented by S. 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 77 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 K 2 /A, where K\ and K 2 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 T r K 2 and K X A = K 2 /A dollars. (1) 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 K 2 /A is, in this case, larger than K\A, and to maintain the equality of equation (1) the value of A must be increased. 17% 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 traffic. 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 w = nn'w' = [n'w'L] - • (2) X SUBSTATIONS. 179 With transformer substations there are no attendants and therefore C w 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 Iq mean effective amperes per foot, the watts lost in each half of the conductor, or A/2 feet, are, according to equation (5), § 48, pi o 2 \ 3 / 24 A. There being 8760 hours in a year, at a cost of Cz dollars per kilowatt- hour delivered from the substation, the annual charge for the energy lost in X feet of the conductor is = 8760 j^ Iflf dollars ( } 1000 12 A If the cost of conductor be c 2 dollars per pound and w be the weight of a mil-foot in pounds, at an interest rate of p 2 the annual capital charge against the contact conductor is C c " = piCiwAX dollars. (4) Since C c ' must equal C c " when the cross section A is most economical, equations (3) and (4) may be equated and solved for A as follows: A = 0.855 /(M/ P 3 circular mils. (5) V P2C2W 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 total annual charge against contact conductor is c e = £(c e ' + c c ") = 2 -~c:\ A A. or C c = [1.7 1 LIq Vpwp2C2C3\\ dollars. (6) Annual Charge against Substations. — If the total max- imum output of all substations be P kilowatts and if the 180 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/bn K.W. The over- load coefficient 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 for July 13, 1903. This substation was equipped with six 1500-K.W. converters each having efficiencies of 93.5, 95.75, 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. 181 2: 1- < cr l±J DL O z H z 3 CM CO CO < q lO r^ 6 q ID 1 — 1 l L 1 I - J 1 < DC 1= j 1 CO cr r> 1 <: CD CO 0) 10 H D. h- Z> O H Ul z CD < 1 n 1 n j < o > i 3 1 < Q ■Drr LO 6 1 ■y 1 — 1 O J H 1 <-r H 1 i/) 00 r ^l — > 1 rn 1 1 1 1 1 L V _J 10 CM 6 ID O L ■p L "1 UJ CMS O O O •SJJ.VM01LM 182 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 efficiency at any load be e, let the expression (1 — 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. 1 24 21.4 No. 2 15-5 I50 No. 3 8.8 7-5 No. 4 2.0 2.0 No. 5 O No. 6 O Total daily equivalent unit, hours, 45.9 The equivalent annual hours of operation of all units in this substation at full load are therefore Ji = 365 ^^ = 2792 hours. 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. I8 3 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 X, 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 .07 O.06 z Ld 5.05 U. U.04 .03 .02 , <4fcj L^c Mo I*f fee ?Ua px ' FUi 5t? L L ^~Md Si 04C ^0. -o.c >ooc •JTf > CONVERTER -TRANSFORMER UNITS. 500 CAPACITY, P n 1000 1500 IN KILOWATTS. 2000 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, 9, may be expressed analyti- cally as *=f3~gzPo, (7) where P is the rated capacity in kilowatts. 184 TRACTION AND TRANSMISSION. The following values are suggestive of the order of magni- tude of the constants / 3 and g 3 for conversion at 25 cycles from 1 1 ,000 volts to 600 volts : DEFICIENCY CONSTANTS Units. K.W. /.. &$• Transformer-reactance-converter Transformer-reactance-converter Transformers. . . 500 to 2000 200 to 500 100 to 750 0.072 0.087 0.024 O.OOOOI2 . 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 P 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 P = P/5nu, the annual loss of energy in all substations is PfJi P%h 8 b 2 nu P nmh kilowatt-hours. (8) Since n = L/\, if the cost per kilowatt-hour of energy delivered to the substation be c$ dollars, the annual charge against the substations for energy lost in them is c.'-m-FgfH'-'"- (9) The cost of one unit of capacity P kilowatts can be expressed analytically as / 3 ' + g/Po dollars, where / 3 ' and gz are constants determined by the manufacturer. The cost of all units to be installed in all substations is therefore nu(jz + Pgz/bnu), and, if p$ be the annual rate covering interest, depreciation, and obsolescence, the annual charge against cost of substation equipments is SUBSTATIONS. 185 C." = pznujj + Ppzgz'/b, or, since n = L/\, C," = \pf*] + [LPzfM i dollars. (10) The following values are suggestive of the order of magni- tude of the constants }z and gz . COST CONSTANTS Units. K.W. //.. g3- Transformer-reactance-converter. . . Transformer-reactance-converter. . . Transformers 500 to 2000 200 to 500 250 to 750 3200 2000 240 9-4 11 .0 2.66 The total annual charge against the substation equip- ments is equal to the sum of CJ and C 8 " as given in equa- tions (9) and (10), or is Ci ^M*i^] + [^] H[W i dona , (II) The Economic Spacing of Substations. — The economic value of X is such that the total annual charges or the sum of C w , C c , and C s , as given in equations (2), (6), and (11), shall be a minimum. To avoid needless repetition of the letters entering into the bracketed coemcients of these equations, these coemcients may be represented as follows: C c = A C X, c s =k s + k:/\ + k:\ and their sum as C = K a +(K w + K s f )/\ + (K c + K 8 ") X. To determine the minimum value of X, the differential 186 TRACTION AND TRANSMISSION. coefficient of C, with respect to X, must be placed equal to zero, or d£ == _ K w + K' s d\ X 2 Solving, + K c -\-K 8 = o. and substituting the values of the coefficients, x- / <"l + #•'<* feet . (13) y 1.71 Lh V P «^ 3 + f (^) The economic cross section, ^4, 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/S = 2500 K.W., 5 = 1.25, Iq = 0.00875 ampere per foot, p 2 = 0.06, h = 5000 hours, pz = 0.10, p = 10 ohms, c 2 =0.18 dollar, w = 0.00000303 pound, Cz = Cz = 0.0 1. SUBSTATIONS. I8 7 Then \ = [2 X 720 X 200,000 +0.10 X 2000 X 2 X 200,000] -7- 1. 71 X 0.00875 X 200,000 X Vio X 0.00000303 X 0.06 X 0.18 X 0.01 + z N9 w o.oi X 0.00006 X sooo~|\£ (2500) 2 X J 200,000 X 2 J/ = ([288,000,000 + 80,000,000] -T- [2990 Vo .000000003 2 7 +o.o469])2 / 368,000,000 £ o -1 = \/ ' ' — = 41,400 feet = 7.8s miles. V 0.169 +0.0469 Thus, the economic separation of converter substations on this 37.8-mile electric railway is 7.85 miles; consequently 30 40 50 SPACING IN THOUSANDS OF FEET. Fig. 79- 5 substations will be required, each equipped with two con- version apparatus units of 250 K.W. rated capacity. That 7.85 miles is the economic distance between substations is proved by computing the various cost items for the railway which depend upon this distance for different values of X, as in the following table, and as shown in Fig. 79. i88 TRACTION AND TRANSMISSION. Substation spacings in feet. Cost items. 20,000 30,000 41 ,400 50,000 60,000 Wages, C w Copper, C c Equipment, C s . . . . $14,400 3,385 18,558 $9,600 5,075 17,685 $6,960 7,000 17,440 $5,76o 8,460 i7,56o $4,800 10,130 17,765 Total $36,343 $32,350 $31,400 $3I,78o $32,695 64. Auxiliary Storage Batteries. — If a storage battery in series with a compound- wound booster 1 be connected between the positive outgoing and negative incoming feeders of a substation, the two may be so adjusted as to impress a constant voltage upon these feeders. As a result, a slight decrease of converter voltage under abnormal load allows the battery to discharge into the distributing system, and also a slight increase of converter voltage under subnormal load will cause the battery to receive a charging current from the converter. The use of a battery, therefore, re- lieves the substation units, the transmission line, and the power station apparatus of violent instantaneous fluctu- ations of load. If the battery be of sufficient capacity, it may also serve to carry the peak loads, of not too long duration, which are common on interurban systems. If, again, the battery be of very large capacity, it may serve to carry the characteristic peak loads of an urban system and may serve to supply power to the whole system in case of accident in the power station or on the transmission line. The use of a battery, therefore, may enable one to install smaller units in substations and in generating 1 For a discussion on the connections and operation of boosters and stor- age batteries see Chapter VIII, Dynamo Electric Machinery, Vol. I, by Sheldon and Hausmann. SUBSTATIONS. 1 89 stations and to operate them under better load factors and therefore at greater efficiencies. It also enables one to design the transmission line for average instead of maximum load conditions. The saving in investment for station equip- ments and line must however be balanced against the cost of batteries and boosters, and the decreased energy losses must be balanced against the energy losses attendant upon the use of the battery. Furthermore, the cost of extra attendance entailed by the use of batteries must be consid- ered. The proper capacity of such a battery is so closely dependent upon the characteristics of the substation load diagram that the advisability of its installation can be determined only from the study of the specific case. What is believed to be the largest storage battery installa- tion in the world is that which is used in connection with the electrical zone of the New York terminus of the N. Y. C. & H. R. R. R. The complete installation, divided into eight groups, is capable of delivering 22,000 amperes for one hour, which is sufficient to operate the whole system, under normal conditions, for one hour in case of failure of the generating apparatus. 65. Arrangement of Apparatus. — The arrangement of apparatus in a substation is governed to some extent by the character of the equipment and the size and shape of the available site. It is desirable to have all apparatus on one floor; but, if the equipment be large, the switch gear should be placed on a gallery so that the attendant may command a view of the whole station. In urban districts, where real estate is expensive, the transformers, high-tension switches, and lightning arresters are often placed on a second floor. Storage batteries when used in substations are usually located on another floor or 190 TRACTION AND TRANSMISSION. ^^^^^^^^^^ ^^^ gggT&> SUBSTATIONS. I 9 I in a separate building adjacent to the main substation. The path of energy from the transmission line to the dis- tributing feeders should be as short and direct as possible. This leads to the following arrangement across the station Fig. 81. from the transmission line: high-tension entrance devices, lightning arresters and switch gear, transformers, reactances, converters, low- tension switch gear, and outgoing feeders. Fig. 80 is a sectional view of a substation of the Milwaukee Electric Railway and Light Company. This substation has a rated capacity of 1200 K.W. for conversion from 66,000 volts alternating current to 1200 volts direct current. 192 TRACTION AND TRANSMISSION. Fig. Fig. 83. SUBSTATIONS. 193 Fig. 81 gives a view of the low-tension end of one of the substations of this road, the reactances surmounted by starting panels being shown as located in front of their respective converters. Fig. 82 shows the method of tapping Fig. 84. the transmission line on the substation roof, and shows the high-tension roof bushings for insulating the supply wires at their points of entrance to the substation. Figs. 83 and 84 respectively show the electrolytic lightning arresters and the high-tension oil switches and the methods em- ployed in their installation. 66. Portable Substations. — On most electric roads there are certain sections of the line on which abnormally 194 TRACTION AND TRANSMISSION. heavy traffic must be handled at infrequent intervals or only during a certain portion of the year, as for instance near fairgrounds, parks, or summer resorts. To meet such a condition and to guard against interruption of service due to accident to a unit in any substation, it is much cheaper to make use of portable substations than to in- stall permanent spare units. These substations consist of specially arranged cars containing complete substation equipments, of the converter or motor-generator type, with accessories. The standards as to track gauge, height of tunnels, and strengths of bridges limit their character- istics to 500 K.W., 60,000 volts, and 150,000 pounds weight. The external appearance of such a portable substation is shown in Fig. 85. The arrangement of apparatus is shown in the plan and elevation of Fig. 86, and Fig. 87 is a diagram of the circuit connections. The positive feeder cable is carried to a terminal block on the outside of the car near the roof, for convenient connection to the trolley wire or feeder. The incoming high-tension lines may be connected directly to the transmission line; but, if frequent or con- tinued use of the portable substation in one locality is necessary, disconnecting switches should be mounted on the nearest pole to facilitate disconnecting the oil switch without having to cut off power from the transmission line. The use of such portable stations insures continuity of supply with minimum investment in permanent substations, saves large investment in. copper and equipment on lines infrequently loaded, provides additional capacity at any point where there may be a temporary abnormally heavy traffic, and may furnish power for extensions during the period of construction. SUBSTATIONS. 195 1 TRACTION AND TRANSMISSION. SUBSTATIONS. PROBLEMS. 197 37. Derive an expression for the economic spacing of substations, the cross section of the composite contact conductor being prescribed by a mean effective drop of e volts at a point midway between substations. Suggestion. — Obtain an expression for A by using (3) of § 48, insert it in (3) and (4) of § 62, which then add, multiply by L/\ and use in place of (6) of § 62 for the economic determination. 6M)//?&/fr 0//$w'fofi U#/7l/7/fltf 7o7r<7/7sm/ss/0/7 //he 'ffes/sfance^. fuse* L/^t/'na dw/tcf) ' T olra ///?y \ : I,'/umlnating{ Qr/t/vw/fr" ■ XvrrMTravjfcr/ner 1 Vtf/t/netpr /fteceptjf/f i^wXUwwJ -r -5 farting $Mte/r -R^a/Vffi?// % Faded ~-B/Mw (jkiAi + \ 2 A 2 ) pounds. Substituting the values of A h A 2 , and X 2 = X — Xi, /X! 2 /! 2 , (X 2 -2XX 1 +X 1 2 )/ 2 2 \ , ,. W = 9 pw ( — — + — J pounds. (1) 200 TRACTION AND TRANSMISSION. For a minimum weight of conductor material, the differ- ential of W with respect to Xi must equal zero. Hence dW t r ,„M^ Wi^ „ — = i8p^— - — +— j-o, — = —■ (») -t 1 -t 2 If the drop to all substations be the same, Pi/A = P2/I2, and X1/1 = X2/2, (3) wherein Xi and X2 now represent the respective distances of the substations from the center of distribution. For any number of substations located at various points along a continuous roadway the distance of the center of distribu- tion from any point is X = 2X7/ 2/, each length being measured along the path taken by the transmission line. The location of the power station at the center of dis- tribution is subject to other considerations, such as the cost of real estate, future growth, facilities for the receipt of fuel and supplies and the removal of ashes, and the avail- ability of water for condensing purposes. In the case of hydraulic installations, the location of the power station is dependent on the hydraulic conditions ; and the transmission line extends from it to the nearest substation or to the one nearest the center of distribution, whichever may prove more economical. Private rights of way for the transmission line are to be preferred to public highways and generally result in final economy in operation. Rights of way along steam rail- roads are undesirable because of insulation troubles likely to result from coal smoke. It is not practical to make the right of way so wide as to prevent a pole or tower from TRANSMISSION LINES. 201 falling on the abutting property, but the right to trim trees on both sides should be secured. A width of from 50 feet to 100 feet is ample. The cost of right of way amounts to from 25 to 50 per cent of the total cost of the transmission line. All con- tracts for right of way should receive careful legal attention, 68. Number of Phases. — The proper basis for deter- mining the number of phases to be employed is the com- parison of the weights of conductor material necessary to transmit the same power, P kilowatts, over the same dis- tance, 5 feet, with the same loss, P' watts, and the same maximum voltage, E kilovolts, between any two conductors. In a system using n wires each of cross section A circular mils and carrying / amperes the loss is P'-2efe TOtt 8. (1) A npSP Therefore A = circular mils. (2) The total weight of the conductors is therefore W= nwA = —j- n 2 P pounds; (3) that is, the weight is proportional to the square of the product of the number of wires by the current flowing in each wire. The following table is based upon the current per wire in amperes for transmitting, at unit power factor, one kilowatt with a loss of one watt per foot of line at one effective kilovolt between wires of greatest potential differ- ence. With direct currents the equivalent voltage is V2 kilovolts. For the three-wire quarter-phase system, where the center conductor carries V2 times the current in the outer conductors, it is assumed that the cross sections of 202 TRACTION AND TRANSMISSION. the conductors will be so chosen that the loss per foot is the same, P'/3, in each conductor. The maximum voltage between any two conductors is assumed the same in all cases because its value determines the capacity and cost of each insulator. The center wire of the three-wire quarter- phase system, however, does not need to be so well insu- lated as the outside wires, and to this extent the above comparison is unfair to this system. Considering, however, that the conductor expense considerably exceeds the in- sulator expense in most cases, this system does not need to be considered in comparison with the three-phase system, which, as shown in the table, is superior to all systems using alternating currents. RELATIVE WEIGHTS OF CONDUCTORS. System. Two wires: Direct current Single-phase Three wires: Three-phase Quarter-phase: Right-hand wire Center wire Left-hand wire. . Four wires: Quarter-phase. . . . Amperes per Wire. V~ 2 E V: '"J" J = V 3 E V 3 p/2 v; E/V: e/v 2 P/2 V2 1 = E/V 2 P/2 I 72 rW. 1 2 2 I 4 1 3 3 1 1 2 I 6 1 2 J 1 4 4 Relative Total Weight. 50 75 150 TRANSMISSION LINES. 203 69. Frequency. — The Standardization Rules of the A. I. E. E. give 25 and 60 as standard frequencies. For transmission lines supplying converting substations one or the other should be used. The weights and costs of 60-cycle £ 50 * 40 \ Q. S30 z O 20 k t &>*. 0. %. 5 CYj JLES 10 •^ 1000 2000 CAPACITY IN KILOWATTS. Fig. 88. 3000 transformers are less than those for 25 cycles and the oper- ating efficiencies 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 1.00 .99 .98 .97 .96 .95 1 rvr 1 FS 25 CYC LES / s' 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 difficult 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 155 = 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 roads 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 line of equivalent length S feet supplying at a maximum P kilo- watts, divided equally among n substations, each of which contains two .converter units of rated capacity P/2 n kilo- watts. Assume further that the rated capacity of each of 206 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 4> and the voltage between wires be E kilovolts, the full load current per wire will be I = —p 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 3RPh phSP 2 ... = L —. — r- kilowatt hours. 1000 1000 Ah, 1 cos 2 If the mean annual cost of delivering a kilowatt hour to the middle of the line be c 3 dollars, the annual expense for energy lost in the line conductors will be C: = C ^ S J 2 a dollars. (1) 1000 AE 2 cos 2 v J If w be the weight of a mil-foot in pounds, c 2 be the cost per pound, and p 2 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 c " = 3 p 2 c<2wSA dollars. (2) Since equations (1) and (2) must be equal to each other for a minimum annual cost, they may be equated and solved for A, giving A = ■=— - 1/ — circular mils. (3) E cos 4> V 3000 P1C2W TRANSMISSION LINES. 207 Substituting this value of A in (2) and multiplying by 2 so as to include (1), the total annual charge against the conductors will be C c = C/+ C e " = r °- I096 f 5 Vc 3P hp 2 c 2 w] \ dollars, (4) L cos J E and representing the bracketed expression by K c , C c = KJE dollars. (5) Pole and Insulator Expense. — There is as yet no stand- ard form 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, X' feet, between poles. With poles of the flexible type the cost, c p , 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 kilo volt, c i} is practically constant. Since the number of poles to be used on a line of real length S f equals S'/X' and the number of insulators is three times this, if the annual interest and depreciation on these items be p p and p { respectively, the annual pole and insulator expense is C P = [p P c p S f /\ f ] + [3 p i c i S , /\ , \ E dollars, (6) and, representing the bracketed expressions by K p and K p ' respectively, C P = K P + K P '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. 208 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 t , can be expressed by the following formula, where E represents the high-tension kilovoltage, P\ the rated capacity in kilo- watts, and K and K' are constants : c t = (KE + K f ) 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 n in the n substations; each of capacity P/6n kilowatts. If p t be the rate of interest and depreciation on this apparatus, the annual expense for transformers in dollars is C t = 3 p t (KE + K') Vp/z + 6 p t n (KE + K*) Vp/6n, which by combining and transposing becomes (9) TRANSMISSION LINES. 209 and, if K t and K/ represent the bracketed expressions, the annual transformer expense may be represented as C t = K t + K/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 c a be the cost per unit per kilo volt and p a be the rate of interest and depreciation, the annual expense charge- able to these auxiliaries will be C a = [p a c a (n + i)]E, (n) and representing the bracketed expression by K a , C a = K a E 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 = c c + c p + c t + c a , C={K P + K t ) + K c /E + (K; + K/+ K a )E dollars, (13) g = -KJE* + {K v r + Ki + K a ) = o. 2IO TRACTION AND TRANSMISSION. Therefore the economic voltage between wires is W*tt1/+^ kilovolts/ (I4) Substituting the values of the constants from equations (4), (6), (9), and (11), E = (0.1096 PS /cos 4>) Vc3php 2 c 2 w 3 p&S'/W+s p t K Vp/ 3 (i + V 2 n) + p a c a (n + 1) 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 line, 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 I V3 E cos 4), and equating two expressions like equa- tion (4) , applied to lengths Sb and Se 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 + 2S E , (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 2 5 -cycle line having an equivalent length of S = 350,000 feet and a real length of 5 r = 450,000 feet, trans- mitting, at maximum rated load, P = 3000 kilowatts divided equally among n = 5 substations at the receiving end of the line. Let the annual effective power factor be cos 4> = 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. c p = [80]. w = 0.00000303. \' = [600]. p2 = [0.06]. Ci = [0.20]. c 2 = [0.18]. K = [0.50]. cs = [0.01]. E! = [65]. Pi= Pp= Pt= Pa = [O.I2]. C a = [50]. Substituting these values, K c = (0.1096 X 3000 X 350,000/0.9), V.oi X 10 X 3500 X .06 X .18 X 0.00000303 = 432,000, KJ = 3 X0.12 X0.2 X 450,000/600 = 54, K t f = 3 X 0.12 X0.5 Viooo (i + Vio) =23.75, K a = 0.12 X 50 X 6 = 36. Substituting these values in equation (14), the economic voltage is E = J 432 ' OOQ A = 61.7 kilovolts. v 54 + 23-75 +36 The American Institute of Electrical Engineers recom- mends as standard voltages for transmission circuits 6.6, 11, 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. Kilovolts between Wires. 44 55 61.7 66 Conductors: Kc/E... 9,810 7,200 2,378 4,050 1,044 1,582 7,860 7,200 2,970 4,050 1,314 1,980 7,OlO 7,200 3,330 4,050 1,467 2,220 6,550 7,200 3,56o 4,050 1,568 2,376 Poles and insulators: Kp'E Transformers: K t K t 'E Auxiliaries: K a E Total annual expense $25,094 $24,404 $24,307 $24,334 These results show that the additional annual expense would be but $97 at 55 kilovolts or $27 at 66 kilovolts, and therefore the latter voltage should be adopted. The use of the higher voltage also 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 cost. 72. Separation of Conductors. — The separation of con- ductors at the insulators must be sufficient so that, at the middle of the spans, the conductors may not swing so closely together as to occasion a discharge between them. A Umitation to the future further increase of voltage be- tween conductors is presented by the insulating properties of the atmosphere. If the voltage between two aerial conductors be gradually increased 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 conductors and the distance between them, and upon the temperature and pressure of the air. The 214 TRACTION AND TRANSMISSION. conductors when seen at night are surrounded by a lumi- nous envelope of red- violet color. The phenomenon is termed corona. At normal pressure and temperature, the air breaks down and becomes convectively conductive when subjected to a uniform electric field strength of 76 effective kilovolts per inch or 30 effective kilovolts per centimeter. The critical condition is determined by the maximum instan- taneous voltage gradient, and therefore the critical voltage for direct currents is V2 times the above value, or 107 kilo- volts per inch. These values do not apply when the dis- tances between the charged conductors, which occasion the electric field, are smaller than half an inch, as will be shown later. 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 divergence depends upon the sizes of the con- ductors and the distance between them. These factors and the value of the critical voltage between conductors are involved in the expression for the critical electric field in- tensity at the surface of the conductor, and therefore the electrical conditions for the starting of corona may be de- termined from the critical field intensity at the surface of the conductor. Curve I of Fig. 90, given by Ryan and based upon experiment, shows the relation which exists between critical surface intensity in effective kilovolts per inch and conductor diameters. Curve II of this figure gives the critical effective voltages between cylindrical con- ductors mounted coaxially within a hollow cylinder having an internal diameter of fifteen inches. It therefore follows that the corona envelope which surrounds the conductor is a region in which the air is made conducting because it is subjected to an electric field intensity of greater value TRANSMISSION LINES. 215 than 76 effective kilo volts per inch. The outside terminus of its radius is the equipotential surface having this critical value. The physical process underlying the initiation of corona is termed ionization by collision. Due primarily to the presence of radioactive substances on the earth, there are 250 £200 o z cc Ul Q. co 150 100 50 I \ \ \ TT V *&A tf Y *>)$& »>*■ Vn if* v <\ m "<* ^ . fe £A/ Sr, > / / .1 .2 .3 .4 .5 .6 DIAMETER IN INCHES Fig. 90. 70 II 60£ 50§ o Ul 30> < 20 ^ Z 10 co .8 always present in the atmosphere positive and negative ions, each carrying a charge of 4.9 X io~ 10 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 2l6 TRACTION AND TRANSMISSION. methods, is of the order 4 X io -11 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. One characteristic of corona, a perfectly satisfactory physical basis of which has not as yet been given, is that to start it around a conductor of given diameter a specific radial thickness of envelope is essential. The critical field intensity, if produced in- side the ultimate en- velope, will not initiate the phenomenon. Ryan has termed this thickness the striking distance and gives its value for con- ductors of various diam- diameter of conductor, inches, eters in the form of a Flg ' 91, curve as in Fig. 91. For conductors of "very great diameter" however he gives the " value of about 0.25 inch." To initiate corona be- tween conductors separated by a distance less than the sum of their respective striking distances requires a greater field intensity than if they were further separated. The critical voltage at which power loss begins through the atmosphere between two clean power- transmission con- ductors of D inches diameter and spaced d inches apart interaxially may be expressed by the following equation which embodies the researches of Ryan, Whitehead and Watson : x.07 o £.05 < K04 °.03 < DC .01 ! / CRITICAL CORONA STRIKING DISTANCES / / .4 E m = 47.8£>°- 8 log e -^ kilovolts (1) TRANSMISSION LINES. 217 at 20 degrees centigrade and 760 mm. pressure, for wire sizes between No. 16 and No. 0000; where E m is the maxi- mum value of the voltage on a representative single-wire 200 180 160 140 M20 it. u CO Uoo o > o _l *80 40 20 >^^ 4c /A/ 9^ ^< 1 ^ ^ \9- - %> ^ ^^ 4 ^ s^ 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 z dx a 2 = 2iii — — • r Integrating for values of x between o and r, there results <&2 = h *m- 224 TRACTION AND TRANSMISSION. Hence the total magnetic flux linked with each conductor of the two-wire line is $1 + $2 = i\ 2 l0g e + - : and therefore the inductance per centimeter length of the straight conductors, being the flux per unit current, in abso- lute units is d — y ix I = 2 log e h - centimeters. r 2 By reduction, the inductance per mile for a single wire becomes L = 741 logio + 80.5 fx io -6 henries. For copper and aluminum conductors n — 1. 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 6 by conventional definition. Similarly yn/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, 8, included between the axis of abscissae and the radius vector through any point, P c , of the circle, they might equally as well be specified by twice the area AOP c of the circular sector which corresponds with this angle, if the Fig. 96, radius were unity. This will become evident if it be con- n sidered that the circular sectorial area u c = — irr 2 , whence 2 7T 6 = i c \ that is, 6 varies directly with u c . The hyperbolic functions are not specified by the angle 6 but by twice the hyperbolic sectorial area AOP h = u h . Referring to a circle of unit radius, by definition xjOA = cos 6 = cos 2 u c and y c /x c = tan 2 u c ; similarly x h /OA = cosh 2 u h and y h /x h = tanh 2 u h , the final h signifying hyperbolic functions. The relations which exist between the coordinates of any 226 TRACTION AND TRANSMISSION. point, P h , on the hyperbola and the corresponding sectorial area u h may be derived from the equation of the equilateral hyperbola, x 2 — y 2 = r 2 . The area of the sector OAP h is Uh = area of triangle OQP h — area of segment AQP h or Mh = °^~ f X *ydx 2 J r -f^Vx 2 ^ 2 x h y h r 2 dx 2 2 r Therefore Xh + Jh = e' 2 . (i) r Since the equation of the hyperbola may be written as r 2 = (x + y) (x - y), x + y r wnence r x - 7 -y x h r 2u h r2 w By adding (i) and (2) Xn _ r 1/— * 2 V 2u h \ (3) In general, dropping the subscript of X, making the radius r = 1, and letting w = — A 3 = 1 ( € « + e -«) = coshw. (4) By subtracting (2) from (1) and expressing in general form y = iO w -*" M ) =sinhw, (5) and dividing (5) by (4), 2 = sin^« = tanhw _ (6) x cosh u TRANSMISSION LINES. 227 The ratio of the areas, u = 2 u h /r 2 , 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 u = 1 . Relations between the Functions. — The following useful formulae, 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 2 w — sinh 2 w = 1. (7) sinh (u =L v) = sinh u cosh v ± cosh u sinh v. (8) cosh (u ± v) = cosh u cosh v ± sinh u sinh v. (9) sinh 2U = 2 sinh u cosh u. (10) cosh 2 u = cosh 2 u + sinh 2 u. (1 1) cosh u =b sinh u = e ±u . (12) Differential Coefficients. — By successively differentiating equations (4) and (5) there results d sinh u e u + e~ u , d 2 sinh u . . , . : — - = = coshu: — — =smhu, (is) du 2 du 2 v ^ J COsh W e u — e~ u . , d 2 COsh « . , . ; = — = smnw; — — =coshw. (14) du 2 azr This repetition of the functions, after two successive differentiations, is the basis of their utility in problems of decay or attenuation. Tables. — An excellent set of tables and formulas relating to this subject is published by the Smithsonian Institution of Washington in Publication No. 187 1 bearing the title "Hyperbolic Functions." The numerical values of cosh and sinh for arguments from 0.00 to 8.45 are given in the following table. 228 TRACTION AND TRANSMISSION. HYPERBOLIC FUNCTIONS. u. sinh u. cosh u. u. sinh u. cosh u. u. sinh u. cosh u. o.oo O . OOOO I . OOOO O.50 O.5211 I. 1276 1 .00 I. 1752 1 -543i OI OIOO OOOI 51 5324 1329 o5 2539 6038 02 0200 0002 52 5438 1383 10 3356 6685 03 0300 0005 53 5552 1438 15 4208 7374 04 0400 0008 54 5666 1494 20 5095 8107 05 0500 0013 55 5782 1551 25 6019 8884 06 0600 0018 56 5897 1609 30 6984 1.9709 07 0701 0025 57 6014 .1669 35 7991 2-0583 08 0801 0032 58 6131 1730 40 I-9043 1509 09 0901 0041 59 6248 1792 45 2.0143 2488 10 I002 0050 60 6367 1855 5o 1293 3524 II II02 0061 61 6485 1919 55 2496 4619 12 1203 0072 62 6605 1984 60 3756 5775 13 I304 0085 63 6725 2051 65 5075 6 995 14 I405 0098 64 6846 2119 70 6456 8283 15 I506 0113 65 6967 2188 75 7904 2.9642 l6 1607 0128 66 7090 2258 80 2.9422 3-1075 17 I708 0145 67 7213 2330 85 3 -1013 2585 18 l8lO 0162 68 7336 2402 90 2682 4177 19 I9II 0181 69 7461 2476 95 4432 5855 20 20I3 0201 70 7586 2552 2.00 6269 7622 21 2115 0221 7i 7712 2628 05 3.8196 3-9483 22 22l8 0243 72 7838 2706 10 4.0219 4-1443 23 2320 0266 73 7966 2785 i5 2342 3507 24 2423 0289 74 8094 2865 20 4571 5679 25 2526 0314 75 8223 2947 25 6912 4.7966 26 2629 0340 76 8353 3030 30 4-937Q 5-0372 27 2733 0367 77 8484 3114 35 5-I95I 2905 28 2837 0395 78 8615 3199 40 4662 5569 29 294I 0423 79 8748 3286 45 5-75IO 5-8373 30 3045 0453 80 8881 3374 5o 6.0502 61323 31 3I50 0484 81 9 OI 5 3464 55 3645 4426 32 3255 0516 82 9150 3555 60 6.6947 6 . 7690 33 3360 0549 83 9286 3647 65 7.0417 7.1123 34 3466 0584 84 9423 374o 70 4063 4735 35 3572 0619 85 956i 3835 75 7 • 7894 7-8533 36 3678 0655 86 9700 3932 80 8. 1919 8.2527 37 3785 0692 87 9840 4029 85 8.6150 8.6728 38 3892 0731 88 0.9981 4128 90 9.0596 9. 1 146 39 4000 0770 89 1 .0122 4229 95 9.5268 9-5791 40 4I08 081 1 90 0265 433i 3.00 10.0179 10.0677 4i 42l6 0852 9i 0409 4434 05 10.5340 10.5814 42 4325 0895 92 0554 4539 10 11.0765 11.1215 43 4434 0939 93 0700 4645 15 11 .6466 11.6895 44 4543 0984 94 0847 4753 20 12.2459 12.2866 45 4653 1030 95 0995 4862 25 12.8758 12.9146 46 4764 1077 96 1 144 4973 30 13-5379 I3-5748 47 4875 1125 97 1294 5085 35 14-2338 14. 2689 48 4986 1174 98 1446 5199 40 14.9654 14.9987 49 5098 1-5 99 1598 53 Ul 45 15-7343 15.7661 TRANSMISSION LINES. 229 HYPERBOLIC FUNCTIONS. u. sinh u. cosh u. u. sinh u. cosh u. 3-50 16.5426 16.5728 6.00 201 . 7132 201 . 7156 55 I7-3923 17.4210 05 212.0553 212 •0577 60 18.2855 18.3128 10 222.9278 222 •9300 65 19.2243 19.2503 15 234-3576 234 3598 70 20. 2113 20. 2360 20 246.3735 246 3755 75 21.2488 21 .2723 25 259.0054 259 0074 80 22.3394 22.3618 30 272.2850 272 2869 85 23-4859 23.5072 35 286.2455 286 2472 90 24.6911 24.7II3 40 300.9217 300 9233 3-95 25-958I 25-9773 45 316.3504 3l6 3520 4.00 27. 2899 27.3082 50 332.5700 332 57i6 05 28.6900 28.7074 55 349.6213 349 6228 10 30. 1619 30.1784 60 367-5469 367 5483 15 31.7091 31.7249 65 386.3915 386 3928 20 33-3357 33-3507 7o 406.2023 406 2035 25 35-0456 35-0598 75 427.0287 427 0300 30 36.8431 36.8567 80 448.9231 448 9242 35 38.7328 38.7457 85 471-9399 47i 9410 40 40.7193 40.7316 90 496.1369 496 1379 45 42.8076 42.8193 6-95 521.5744 52i 5754 50 45.0030 45.0141 7.00 548.3161 548 3170 55 47.3109 47-32I5 05 576.4289 576 4298 60 49-7371 49.7472 10 605.9831 605 9839 65 52.2877 52.2973 15 637.0526 637 o534 70 54.9690 54-978i 20 669.7150 669 7157 75 57-7878 57-7965 25 704-0521 704 0528 80 60.7511 6o.7593 30 740.1497 74o 1504 85 63.8663 63.8741 35 778.0980 778 0986 90 67.1412 67.1486 40 817.9919 817 9925 4-95 70.5839 70.5910 45 859-93I3 859 93i8 5.00 74.2032 74.2099 5o 904.0210 904 0215 05 78 . 0080 78.0144 55 950.37H 95o 3716 10 82.0079 82.0140 60 999.0976 999 0981 15 86.2128 86.2186 65 1050 323 20 90.6334 90.6389 70 1 104 174 25 95.2805 95-2858 75 1160 780 30 100.1659 100. 1709 80 1220 301 35 105.3018 105.3065 85 1282 867 40 110.7009 110.7055 90 1348 641 45 116.3769 116. 3812 7-95 1417 787 50 122.3439 122.3480 8.00 1490 479 55 128.6168 128.6207 05 1566 698 60 I35-2H4 135-2150 10 1647 234 65 142.1440 142.1475 15 i73i 690 70 149.4320 149-4354 20 1820 475 75 157-0938 157.0969 25 1913 813 80 165.1482 165-1513 30 201 1 936 85 173.6158 173.6186 35 2115 090 90 182.5173 182 .5201 40 2223 533 95 191.8754 191 .8780 45 2337 •537 230 TRACTION AND TRANSMISSION. 76. Line Capacity. — To determine the capacity of a transmission line, consider two wires of indefinitely small diameters placed d! centimeters apart and having respec- P tively charges of + q and — q yS^>^ units per centimeter length of X ^\. conductor. The intensity of —+- h -^ the electric field at a point P, h ~ dl i Fig. 97, distant Y\ cm. from one Fi s- 97- w i r e and r 2 cm. from the other, that is, the electrostatic flux per unit area of equipo- tential surface or force exerted upon a unit positive charge at this point due to the charge on wire A alone, is 2 irn Yi and that due to the charge on wire B alone is p B = ZLAll = _ 2 l. 2 7rr 2 r 2 Representing the potential at the point P due to the charge on A by V A , and that due to the charge on B by V B , it follows from the definition of potential that dV A = 2_q dri kri , dV B 2 q and — = - -* dr 2 kr 2 where k is the permittivity or specific inductive capacity of the dielectric. If the potentials at the point O midway between the two very small wires due to their charges be respectively V A ' and V B f , then the potential difference between P and is the sum of '-fa *-¥><* . (3) Similarly, by differentiating (1) with respect to distance and (2) with respect to time, and combining the resulting expressions, there results the differential equation of volt- age propagation as d 2 F' dF f d 2 F f CL d_A +{RC+gL) ^ = ^_ RgEf (4) Equations (3) and (4) are identical as to V and E' ', and their solution indicates the current and voltage values at the point distant s from the generator at the time t in terms of the line constants. This general equation refers to any circuit with distributed capacity and inductance, 238 TRACTION AND TRANSMISSION. and its solution is of importance in telephonic and power transmission problems. 78. Attenuation and Wave-Length Coefficients. — The solution of the equation of wave propagation may readily be effected by not considering the short unsteady period immediately following the application of voltage to the line, for then the solution may be simplified by the introduction of the complex quantity which results in the elimination of the time variable. The resulting expressions are complex quantities and their interpretation must be made accord- ingly. Introducing the quadrantal operator, j =V— 1 , and counting the distance s positive from the receiving end of the line, equations (1) and (2) of § 76 for the steady state may be written* ^=(R+jcoL)I m (1) and ^=(g+ja>C)E m , (2) where E m and I m represent the maximum (or effective) values of electromotive force and current at any point on the circuit, (R + jwL) 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 d?E„ ds* = (R + ja>L) (g +icoC) E m = y*E m (3) rl 2 T and ^f = (R + jcoL) (g + j<*C) I m = y 2 I m , (4) * See p. 74, Alternating Current Machines (1908) by Sheldon, Mason, and Hausmann. TRANSMISSION LINES. 239 where y 2 = (R + jwL) (g + jcoC) for convenience. Equa- tions (3) and (4) are identical equations as to E m and I m and differ only in the terminal conditions, consequently the solution of one will suffice. Considering equation (4) and multiplying through by 2 — - 1 there results as dl m d 2 I m _ 2 j dl m } ds ds 2 m ds which when integrated becomes Replacing the constant of integration C\ by y 2 c 2 2 , where c 2 is also a constant, and separating the variables, there results dl m , = y ds. VlJ + c 2 2 Integration yields loge [c 3 (I. + V/ m 2 + ci)]= ys } where c 3 is another constant of integration. Writing in exponential form, this equation becomes or whence e 2ys e ys — - C 2 2 = 2l m —\ ci c 3 -*m ,7s - 2 r ..—ys = i _*«*- =Af ys_ Br ys 2C 3 2 where the two constants are A — and B — 2 3 • 2C 3 2 (s) 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 y = P+ja, (6) where (3 and a are its two rectangular components. Then /3 2 + 2 jap +JW = (R + j<*L) {g +ja:C), or (p 2 - a 2 ) + 2 ja0 = (Rg - a?CL) +j (guL + a>RC). This equation can be true only if a 2 - p 2 = to 2 CL - Rg, and if 2a(3 = o>(RC + gL). These are simultaneous equations which can be solved for a and p. Thus, substituting the value of a from the latter in the former gives the biquadratic /3 4 + (co 2 LC - Rg) P 2 -- (RC + gL) 2 = o; 4 whence p 2 = - "— C ~ Rg + - V(o?LC-Rg) 2 + co 2 (£C + gL) 2 2 2 and = v] [V(co 2 C 2 + g 2 ) (# 2 + o?L 2 ) - u 2 LC + i?g] ; (7) similarly a = V2 [V(co 2 C 2 + £ 2 ) (# 2 + co 2 Z 2 ) + co 2 LC - 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 I m = A (cosh ys + sinh ys) — B (cosh 7s — sinh ys) . = (A - B) cosh ys-\- (A + B) sinh ys. (1) TRANSMISSION LINES. 241 The voltage at the same point is found by differentiating (1) with respect to distance and substituting—^ 1 in equa- ls tion (2) of § 78. Since — cosh ys = 7 sinh ys as and — sinh ys = 7 cosh ys f as there results E m = P+? a n [(A - B) sinh ys + (A + B) cosh ys]. (2) The constants A and B of equations (1) and (2) may be determined from the conditions at the receiving end of the line. Let E r and I r be the maximum (or effective) values of the voltage and current at this terminal. Then for s = o, since cosh (o) = 1, and sinh (o) = o, I r = A - B and E r = ^P-{A+B). Substituting these values in (1) and (2) yields I m = I r cosh ys + E r i sinh ys (3) K -\-jcoL and E m = E r cosh ys + I r , . „ sinh ys. (4) g +J"C When s is reckoned from the generator toward the re- ceiving end of the line, these equations become I m = I g cosh 7s - E g Ja sinh 7s (5) K -\-jwL 242 TRACTION AND TRANSMISSION. and E m = E g cosh ys - I g * /~? a sinh ys. (6) The hyperbolic functions of the complex quantity y may be written cosh ys = cosh ((3s +jas) = cosh (3s • cos as+j sinh @s • sin as and sinh 75 = sinh (3s • cos as +7 cosh /5s • 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 i\ -\- ji% and a lagging current is represented by i\ — ji 2 . From equation (5) it is seen that for an infinitely long line, on which the current at the inaccessible end is zero, Ia - Eg R+j*L' 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 = I g (cosh ys — sinh 7s) = I g e~ ys . Similarly E m = E g e~ ys = E g e- ps e- jas , The exponential function with the imaginary exponent may be written in the trigonometric form by means of the expression e ±jas _ CO g aS _±_j g J n aS If a point r be chosen on this long line so that the distance between it and the point 5 will be an integral number of wave lengths, n, then cos as — j sin as = cos ar — j sin ar ; TRANSMISSION LINES. 243 consequently as + 2 wn = ar. Then the wave length herefrom is _ r ~ s _ 2ir A — — • n a As the frequency of the impressed electromotive force is cycles per second, the velocity of wave propagation CO 2 7T will be co x co v = — X = -• 2 7T a The expression for a in terms of the line constants is given in § 78. For a perfectly insulated resistanceless line a = co VLC, and the velocity of wave propagation is that of light, namely 3 X io 10 centimeters per second, or 186,000 miles per second. 80. 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, I go , entering it at the generator, called the charging current, is obtained from equation (5) of the preceding article for s = S = total length of the line, by placing I m = o. T l ot1 r 77 P+J* sinh yS -•■ nen *Oo = A? n , • r ' Z o" g R+jcoL cosIiyS Since — - — - = tanh yS, cosh 76 B -\- ja this becomes I g = E g — r— : tanh yS. (1) K -\-jloL 244 TRACTION AND TRANSMISSION. Substituting this value for I g in equation (6) of § 79, there results the voltage at any point distant s from the gen- erating end of the line as E = E g (cosh ys — sinh ys • tanh yS), (2) and the voltage at the receiving end for s = S as E ro = Eg (cosh 75 — sinh yS • tanh yS), or, since cosh^S — sinh 2 7S = 1, ^-cJtf-*"** (3) The regulation of the transmission line is then expressed as -, t ,. E rn - E r E g sech yS - E r , . Regulation = -^ = -« = - r - (4) 81. Numerical Illustration. — Let it be required to trans- mit 10,000 kilowatts at 60 cycles over a three-phase aerial transmission line 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~ 6 farad, g = practically zero. TRANSMISSION LINES. 245 The current per single circuit (or per wire) at the load end is T 10,000,000 I r = ■ ■ = 68.0 amperes, w 100,000 w 3 X 'j— X 0.85 V3 or I r = 68.0 [0.85 -7 sin (cos" 1 0.85)] = 57.8 - 35.87; 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 co = 377) are respectively |8 =V 2.88(^/0.090 + 0.5476 — 0.74) X io -3 =0.000412 and a = V2.88 (0.799 + 0.740) X io -3 = 0.00210. The hyperbolic and circular functions respectively of /fo 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 I a = (57-8 - 35.87X1.00765 X 0.8080 + 0.1239 X 0.5892.7) + 57-7| ' 4I2 | 2 ' 1J ) (0.1239X0.8080+1.00765X0.58927), Vo.30+0.747/ or J7°° (0.8142 + 0.06057) = (57-8 - 35-8/) (0.364 ~ 0.07157X0.1001 +0.59377) io 3 + (46.95 + 349 J) !o 3 = (12.04 + 9- 2 3i + 46.95 + 349i) iq3 = 58,990 + 12,7207, 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 60,400 volts. Fig. iox. The vector diagram, Fig. 101, 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 4'' — 12 25'), or 42 39'. The efficiency of transmission at full load is 57»7oo X 57-8 60,400 X 82.0 cos (42 39') = 0.915, or 91.5 per cent. TRANSMISSION LINES. 247 Since cosh yS = 0.8142 + 0.06057, the voltage at the receiving end on open circuit for the same impressed E.M.F. at the generator end is „ 58,000 + 12,720/ . ^r„= g V , '-7—T. = 74,IOO + 10,3007, 0.8l42 + O.OOO57 and the absolute value is 74,900 volts. Consequently the voltage regulation of the transmission line for 85 per cent power factor is 74,900 — 57,700 004- L=L2 ^ a±±L — = 0.208, or 20. 8 per cent. 57,7oo The charging current per single circuit or per wire is obtained from equation (1) of § 80 as t f o , -\ /0.412 + 2.1 A/0.1001 -f- o.c;9S7i\ '*' (58 -"° + I2 - 720 ^( o.30 + o. 7 4y )( o.8 I42 +o.o6o5y ) = (140.2 + 3°-3i) (1-678 + °-3 2 5i) (0.1174 + 0.477/) = -19.5 + n9-5i> and the absolute value is 121 amperes, and leads the voltage E r by 99 i6 7 . Therefore the charging current at the gen- erating end of the line leads the voltage at the same place by the angle 99 16' — 12 25', or by 86° 5i r . 82. Corona Loss. — It is found by experiment that the corona loss on a transmission line is proportional to the square of the excess voltage over the critical value at which corona is initiated and also to the frequency; thus the loss per mile in watts on a single-wire ground-return circuit is quite closely P = 0.024 j(E m -E cr )\ (1) where E m is the voltage (effective value in kilovolts) from conductor to neutral at any point on the line distant s miles from its generator end, and E cr is the effective value of the voltage at which corona appears. This equation is 248 TRACTION AND TRANSMISSION. similar to that formulated by Dr. Steinmetz. On a single- phase line and on a three-phase line (for corona loss per phase) the factor (E m — E cr ) 2 is respectively four and three times as large as for a single-wire circuit. Frequently portions of transmission lines are located in high altitudes, where the critical voltage is lower than normal, and corona loss ensues, which can be calcu- lated from the foregoing expression. The factor 0.024 is fairly constant; it does not depend on atmospheric pres- sure, size of wire, or conductor spacing, but it does seem to be influenced by the presence of smoke, dust, and snow in the air. Additional experimental verification of this nu- merical constant is very desirable. The method of measur- ing 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 transmission line is open-circuited, for then 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 E is just equal to the critical value E cr , 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 (2) of § 80. By substituting various values of 5 therein, and plotting the corresponding values of E in terms of distance, a voltage-distribution curve for the particular line will result. From this voltage-distance curve can be seen the distance, Sq, from the generator end of the transmission line at TRANSMISSION LINES. 249 which corona begins. Of course, this equation might be solved for s , but not knowing the phase of voltage E at the end of this part of the circuit, this plan leads to diffi- culty when applying the resulting expression to the solu- tion of actual problems. In order to determine the total corona loss on a repre- sentative single-wire open- circuited line, consider an element ds of the circuit, distant s miles from the point s where corona be- gins, for which the excess voltage is E m — E cr kilo- £f« volts; Fig. 102. The Fig. 102. power loss over this elementary line section in watts is dP = 0.024/ (E m -E cr ) 2 ds, and over the entire distance I = S — s the loss is P = 0.024/ f '' (E n - E er )* ds. d But from the equation referred to, E m = E cr (cosh ys — sinh ys tanh yl) ; therefore P = 0.024 fE cr 2 I (cosh ys — sinh 75 tanh yl — i) 2 ds, or P = o.024/£ cr 2 / cosh 2 75^ — 2 tanh 7/ / sinh ys cosh ys ds — 2 \ cosh ys ds + tanh 2 yl j sinh 2 ys ds I + 2 tanh yl \ sinh 75 ds-\- X'4 250 TRACTION AND TRANSMISSION. Upon integration this equation becomes P=o.oi2 - E cr 2 [sinh yl cosh yl + yl — tanh yl (cosh 2 yl — 1) T — 4 sinh 7/ + tanh 2 yl (sinh 7/ cosh yl — yl) + 4 tanh 7/ (cosh 7/ — 1) + 2 yl], and when simplified reduces to P = 0.0x2 JEJlU - ^^ - tanh' 7/] (2) as the expression for the total corona loss in watts on an open-circuited single-wire earth-return circuit. Thus for the 140,000-volt, 10,000-K.W., 500-mile, 60-cycle, three-phase transmission line of § 72, with No. 0000 stranded aluminum conductors placed 15 feet apart, the line con- stants 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. g is negligibly small = o. The attenuation and wave-lengths constants are respectively |3 = 0.000563 and a = 0.00214; whence 7 = 0.000563 + 0.002147. It will be observed that severe conditions are assumed in order to bring out the results more forcibly. When the line is open-circuited at the receiving end, the voltages in terms of the impressed voltage E g at several TRANSMISSION LINES. 251 points on the line, as determined from equation (2) of § 80, are given in the following table : Distance from gener- ator (miles). Eo Eg \Eg\ 40 IOO 200 300 400 500 I .O92—O. 112 j I . 2I2—0. 265 J I. 382 -O.487 J I. 503 -O.658 J I-575-0.764y 1.600—0. 799 J I . IO I.24 I .46 I.64 i-75 1.79 Thus, for a factor of safety of i.r, the length of line over which corona appears is 460 miles. The total power loss in watts per phase into the air is therefore, from equation (2), P = 0.012 X 60 X / ^oX i.i \ x 46q x k _ ^ 4>o5Q _ z i4 ^ - (-0.990 + 1.787)], or P= 0.72 X — — X 460 X 0.65 = 1700 k.w., 1000 which is equivalent to a current of per phase, current of 700 ^3 140 , or 2 1 amperes This current value almost equals the full-load 10,000 , or 23.8 amperes, which would enter 140 X 3 this unusually long transmission line. To this must be added at right angles the charging current due to the capacity of the line. Thus, an ammeter at the power house which supplies energy to this circuit would indicate approximately the same current when the far end of the transmission line is open-circuited as when connected to the full load, because of the breakdown of the air near the conductors. 252 TRACTION AND TRANSMISSION. 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 200 150 H _l O > 100 O _i / / / 50 / / / / 10 20 30 40 ELEVATION IN THOUSAND FEET Fig. 103. 50 60 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 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 TRANSMISSION LINES. 253 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 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 neutralization 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 254 TRACTION AND TRANSMISSION. between a wire and ground over an insulator or between two wires. The subsequent maintenance of the arc will be due to energy supplied 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 line, 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 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 TRANSMISSION LINES. 255 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 nor- mally 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 sup- press 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 solenoid; in another there is an electromagnetic blow-out ; and in another, for use on alternat- ing circuits, there is a series of gaps between electrodes made of metal which will not permit the maintenance of an arc at normal potentials. Another type, which has proved effective in the protection of station apparatus on alternating-current Fig. 105. 256 TRACTION AND TRANSMISSION. systems, consists of a series of aluminum electrodes upon whose surfaces are formed films of aluminum hydroxide, im- mersed at short distances from each other in a suitable elec- trolyte. The cross section of such an arrester is shown in Fig. 105, and is characterized by the conduction of very minute currents at normal voltage and of very large currents, without much elevation of temperature, at voltages slightly in excess of normal. 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 shattered 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 f SELECTIVE RELAY inn 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 TRANSMISSION LINES. 257 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. The arc ceases because the ground at the station robs it of its potential. Fig. 106 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. Efforts have been made to protect lines by ground wires erected above the line and connected with the ground at every fifth pole or so. The use of such wires has resulted in a reduction of 50 per cent in insulator failures. Ground wires but partially screen the line wires from electrostatic induction from cloud charges; and electromagnetic induc- tion, accompanying the currents which follow cloud dis- charges, may yield high voltages in the line wires. 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 0.85, the cost of line material as 0.24 dollars per pound, and all other factors as suggested in § 71. 44. What is the size and what must be the separation of the solid con- ductors of the transmission line of problem 43 for the avoidance of corona loss, with a factor of safety of 1.1 at an altitude for which the atmospheric pressure is 700 mm. Hg., and at a temperature of 30 C. 258 TRACTION AND TRANSMISSION. 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 efficiency 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. What will be the corona loss if the transmission line of problem 46 when located in a region for which the highest temperature is 30 C. and for which the minimum pressure is 600 mm., is open-circuited at the receiver? 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 t-u A f \ CO H H <30 O _j J \ / \ / \ \ 1 \ 5 u. 020 CO z / V J \ / < CO 10 I 1- 12 2 4 6 8 10 12 2 4 Q 3 10 12 LM. TIME IN HOURS 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 260 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 in 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. 26 1 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 efficiencies 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 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 n kilovolts. The size of a unit, 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 efficiency. Because the designed operating efficiency 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 frequent 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 20,000 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 fifth 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 cylinders 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 include 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 efficiencies. 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 steam. 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 10 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 efficiency 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 55 35 33 27 20 14 15 Compound noncondensing Simple condensing Compound condensing Turbines Superheated Steam: Compound condensing Turbines 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 lb. /in. 2 and the latter is 14.7 lb. /in. 2 , 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 (ttW) 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, T _ C temperature of the condensed steam (surface), f temperature of the discharge water (jet), T2 = temperature of the discharge water. Then the weight of cooling water, W, necessary to con- dense one pound of saturated steam, is W = 1 l_* pounds. ±2 — ± o 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 fore adapted for use where there is a limited 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 towers 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. 109, 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 in the cylindrical Fig. 109. 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 damper-controlled 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 nozzle 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. 27 1 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 J per cent. If the temperature, /, of the feed water be less than 212 , the steam be x part dry, or the steam be superheated / s ° 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 -^— (— — ) horsepower, 34.5 V 9704 / where r = latent heat of evaporation at the resultant pressure, a = heat in liquid at this pressure, and C = mean specific heat of the superheated sf earn. 272 TRACTION AND TRANSMISSION. The values of the various constants may be found in Engineering handbooks. The steam consumed in operating auxiliaries 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 n 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 employing different fuels, are given in the following table: STEAM STATIONS. HEIGHTS OF CHIMNEYS. 273 Fuel. Height in feet. Free-burning bituminous 80 IOO I20 I50 175 Anthracite, large sizes : Slow-burning bituminous 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 of 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 h feet, properly to carry off the gases from boilers of P horsepower, should have an equivalent cross section of A_O ll P i Vh square feet. 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 DC Ul a. u 2 DC < 01 T \, \ c ) •\ V < N • X • c I — ■ — X • PA O CU RSONS ' RTIS TL rURBlNE RBINES S. X RE :iproc; TING ENGINES 10 20 30 40 50 60 70 80 THOUSANDS OF KILOWATTS Fig. in. 90 100 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 lifting machinery and the replacing and repairing of boilers. The building should be well lighted, well ventilated, of fire-proof con- struction, and arranged with a view to extension in case of growth of demanded output. 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. 95. 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. 1 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 supplying 600- volt direct current to the distribution circuits in the immediate vicinity is housed under the same roof. 276 TRACTION AND TRANSMISSION. S-wsssssv 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 2 . 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 1 25 2.00 3.00 •5° •75 8.00 10.00 8.00 10.00 1 -5o 1 .40 2. $0 2.80 .70 i-5o 1 .20 2 .00 .40 .60 2 .00 2-75 15 ■30 .40 1 .00 ■50 1 .00 1-25 2 .00 9-5o 11.50 1-25 i-75 1.30 2.20 1.30 .60 1-25 2.25 .90 i-6 5 .40 •75 . 20 •35 3.00 .60 5.00 1 .00 .60 1 .00 22 .00 30.00 .40 .70 1 .00 2.50 6.00 7-5o 16.00 22 .00 .60 .80 22.00 32 .00 .60 1 .00 3.00 390 .20 ■30 •15 •35 .20 •30 1-25 i-75 2.00 2.00 4.00 6.00 280 TRACTION AND TRANSMISSION. 96. Cost of Steam Stations. — The table on the preced- ing page, due to H. G. Stott, includes the approximate cost per kilowatt of the various elements entering into the cost of a steam plant. A fair average cost per kilowatt is #100 for plants using reciprocating engines and #80 for those using steam-turbine units. 97. Operating Expenses. — Data concerning twenty- three stations of moderate capacity, using mostly bitu- minous coal ranging in price from #2.75 to #5 per gross ton, and all operated condensing, has been published re- cently by E. F. Tweedy. Fig. 115 shows the operating costs crO O u Xx O w _J> v£ IS) UJ r x O RECIPROCATING STEAM ENGINES. • STEAM TURBINES. X MIXED EQUIPMENT-ENGINES & TURBINES. EQUATION OF HYPERBOLIC CURVE y - 4 _j_ 900,000 \ \ \ n \ - \ O S c b>.^ ^„ x — s >-°-* "x ~ i e 3 ._!. I\f 1ILL ION 2 S OF 3 OW HO JRS* GEh i JER/ 3 \TEt 5 PE 7 R Y i EAR 3 9 Fig. 115. per kilowatt-hour in terms of total annual outputs. The highest load factor based upon rated capacity was 0.23, the lowest 0.11, and the average 0.17. The coal consumed per kilowatt- hour ranged from a little over 3 pounds for the larger plants to about 5 pounds for the smaller ones. The station rating in kilowatts per man employed in operating the station, ranged from about 100 K.W. for the HYDRAULIC STATIONS. 28l smallest stations to 250 K.W. for the largest. Fig. 116 shows the percentage distribution of operating costs among fuel, labor, and miscellaneous items. 100 MISCELLANEOUS COSTS AVERAGE 16.48$ q • \ (. /*— V * 1 .»'' 37 ^— 1— " ■**--. ~~^ -i if COST O : LABOR "*" AVERAGE 27.82$ r A 9 / 1 } \/ \ / COST OF FU AVERAGE 55. EL 70% 12 3 4 5 6 7 8 MILLIONS OF KILOWATT HOURS GENERATED PER YEAR. Fig. 116. HYDRAULIC STATIONS. 98. Turbines. — In procuring mechanical energy from water power two classes of turbines or water wheels may be utilized in conformity with American practice; namely, the reaction turbine and the impulse wheel. The reaction or pressure turbine of the mixed-flow type is applicable for low and moderate heads, say up to 150 feet, although this type has been used for heads up to 600 feet. It consists of a rotating wheel or runner carrying vanes or buckets to which water under pressure is delivered radially inward by means of stationary guide vanes surrounding the wheel, and from which the water is discharged partially in an axial and partially in a radial direction. Torque is developed by reaction, due to changing the direction of water flow. 282 TRACTION AND TRANSMISSION. As the buckets and wheel passages are always completely filled with water, it is not necessary to mount the turbine at the level of the discharged or tail water in order to realize the total head, if an air-tight draft tube leading from the wheel outlet down somewhat below the level of tail water be provided; for the falling water in the draft tube from the turbine creates a vacuum that is effective in sucking the water through the turbine, and which is equivalent to increasing the pressure of the inflowing water. Reaction turbines may be placed at any level up to about 20 feet above the tail race without loss of head. The power developed by a turbine under a given head is regulated by varying the amount of water admitted to the runner by means of gates. There are various types of gates, including the so-called cylinder, register, and wicket gates, the last being the most used. In this type the guide vanes are pivoted so that all may simultaneously approach or recede from their neighbors by the rotation of a single regulating shaft. In order to neutralize the end thrust due to the axial pressure of the water, as well as to secure higher speeds under a given head, it is common to place two turbine runners — of correspondingly reduced diameter for the same total power output — on a single shaft. Sometimes four and even six runners are coupled together to constitute a single unit. Fig. 117 shows a 9000 horsepower Allis- Chalmers horizontal twin turbine with the runners dis- mantled. The water enters through the wicket gates at the ends and within the bearings, passes through the wheels, and emerges at the bottom. Impulse wheels, suitable for heads above 150 feet, com- prise a number of buckets into which water is directed HYDRAULIC STATIONS. 283 284 TRACTION AND TRANSMISSION. through one or more nozzles at a velocity equal to V2 gH feet per second, where g is the acceleration due to gravity = 32 ft. per sec. per sec, and H is the head or height of water in feet. Each bucket forms two cups divided by a central ridge which separates the impinging water into two parts, each part being deflected backward to one side of the Fig. 118. wheel by the bucket. The effective head is that from the level of headwater to the nozzle, the head from the latter to the tailwater being lost; consequently the impulse wheel should be placed as low as possible. The flow of water is regulated by needle valves or by deflecting the nozzle. Fig. 118 shows a twin Pelton water wheel with its " hy- draulic relay " governor. Governors are used on both types of water turbines for automatically effecting the opening and closing of the regu- HYDRAULIC STATIONS. 285 lating gates or for deflecting the jet from the buckets of im- pulse wheels. As the force required for this purpose is very large, it is evident that the centrifugal ball governor cannot directly control the gate opening, but must do so through the intervention of a relay. Two general types of relay are used : mechanical relays, which derive power for their opera- tion from the water wheel by means of gears, pulleys, or other mechanical devices, and hydraulic relays, which are operated either by the pressure of water taken from the " penstock " or other source, or by oil supplied under high pressure from a reservoir. Turbines or water wheels are ordinarily direct-connected to the electric generators, but may be either geared or belted thereto, there being one prime mover for each gen- erator, and one or more additional turbines for the exciter units. Four generator units is considered the minimum number allowable for the attainment of a reasonable de- gree of insurance against shut-down. Having determined the number and size of the electric generating units from a study of the load curves on the power station, the size of the prime mover in horsepower is found by dividing the kilowatt rating of the generator by 0.746 times the efficiencies of the generator and mover. The efficiency of large generators at full load may be taken as between 93 and 97 per cent. The efficiency of turbines and water wheels is conventionally taken as 80 per cent, although efficiencies as high as 86 per cent have been attained. Some of the turbines of a hydroelectric power house should have a high efficiency at low-gate opening and others should have their greatest efficiency at full -gate, so as to realize a fairly high all-day plant efficiency under widely varying loads. Representative efficiency curves of 286 TRACTION AND TRANSMISSION, two modern reaction turbines at various gate openings are shown in Fig. 119. The power developed by a turbine or impulse wheel depends upon the quantity of water passing through it in 100 >80 o z 60 40 20 t •A V2 3 A GATE OPENING Fig. 119. FULL unit time, upon the available head of water, and upon the turbine efficiency, e, and is „ 62.4 OeH OeH , P = — — — = - — horsepow 550 8.81 er, where q is the discharge in cubic feet per second and which may be expressed empirically as q = KD 2 VH, 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 8.81 horsepower, HYDRAULIC STATIONS. 287 whence the proper wheel diameter for a given head is D = J*AlZ iee t. (1) v khK The values of K vary widely among the different designs of various manufacturers, but most values thereof lie between 2.3 and 3.5 for reaction turbines, and between 0.015 an d 0.024 f° r impulse wheels. For a given turbine the speed of the runner varies with the square root of the head. Let r be the r&iio of the peripheral velocity of the buckets to the theoretical velocity that water would acquire in falling freely a height equal to the head of water. Then the speed of the wheel in revolu- tions per minute is T7 60 r V2 gH tH* ( s F= w> = I53 ^T (2) The values of r range from 0.65 to 0.93 with different designs of reaction turbines and between 0.43 to 0.51 with impulse wheels. Having determined the turbine speed for a given head of water, the multipolarity of the alternators for the generation of electromotive forces of definite fre- quency becomes known. As an illustration of the foregoing, determine the proper number of poles for a 2000 K.W., 60-cycle, three-phase alternator which is to be driven by a Pelton water wheel on a head of 970 feet, the constants of the wheel being K = 0.019, r = 0.505, and e = 0.83. Taking the alternator efficiency as 92 per cent, the rating of the prime mover is 2000 0.746 X 0.83 X 0.92 = 3500 horsepower and the diameter of the water wheel is 1/ : ^ =8.0 feet. Therefore O.OI9 (970) 2 0,84 288 TRACTION AND TRANSMISSION. its speed is -%- 0.505 V970 = 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, (1) where the entire head is utilized at the dam, the power station being located at one end thereof; (2) where long pipe lines, canals, or flumes are required to transfer the water from the intake at the headworks 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. (1) 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 of flashboards, 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 GATES 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 efficiency 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 Fig. i2i. 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. 2Q2 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 penstock. It is usually cheaper, however, to use a pipe line which need not be level but can follow the contour of the land. Wood, cast-iron, or riveted wrought-iron pipe is used for such purposes. The transmission of water through pipes or canals is accompanied by a reduction in the avail- able head, the extent of which depends upon the size of the pipe or canal. This loss of head can be computed from expressions given in most books on Hydraulics. Provision must be made to prevent injury to penstocks or pipe lines which might occur when the turbine gates or water-wheel nozzles are regulated too quickly. Automatic relief valves of sufficient area may be employed at the lower end of the pipe, or either standpipes or surge tanks may be used to alter the velocity of the water in the pipes. Fig. 1 24 gives a sectional view of a typical power house in which impulse wheels are installed. Speed regulation of the prime movers is accomplished by deflecting the nozzles past the buckets and allowing part of the water to impinge upon heavy metal deflector plates. Frequently hydraulic developments have auxiliary steam or gas engine plants to supplement the water power during the dry seasons or during periods of peak loads. 100. Cost of Development. — The cost of a proposed hydraulic development depends largely upon the extent to which the stream flow is to be developed, upon the nature and remoteness of the power market, as well as upon various topographical, geological, and meteorological con- ditions of the locality. The decision as to the commercial feasibility of a proposed water-power development must embrace a careful study of all such factors which influence water supply, of the available head and its variations, of the power available with and without pondage, of the 2Q4 TRACTION AND TRANSMISSION. »ffi 3' HYDRAULIC STATIONS. 295 location and extent of the hydraulic construction and power house, of the probable market for the power gener- ated and its load factor, and the desirability of auxiliary power. Rough estimates in terms of generator capacity of the cost of turbine equipments may be derived from Figs. 125 and 126, which embody data from existing installations. 24 H -20 1- < o _l 5 16 DC U Q. CO ce < 12 \ V \ \ \ V \ ^2POj •VV. =3^0 S^^v. 20 40 60 80 HEAD IN FEET- Pig. 125. 100 120 The figures refer to reaction turbines and impulse wheels respectively, and include extra movers for exciter units, governors, and cost of erection. The following table, given by 0. S. Lyford, gives the item- ized cost (estimated or actual) per kilowatt of generator capacity of seven separate water-power developments in the same general district in our southeastern states, these powers being developed with heads varying from 30 to 120 feet, and with generator capacity varying from 10,000 to 296 TRACTION AND TRANSMISSION. £R8 <8 r^ m h 100 tj- "sj- co NNO0 00 CMVOMD^O t^ ro I>-00 ^vO *0 »■ h ntJ- o»o 1000 r-~ *o arOON^ -^-vo - ^ _ CO O00 On "<*■ IOVO ^O ro « \Q VO O ■ "*"-*— ^ w • a3 : c 3 . O g ■ B 4-> . . nS X5 • T3 3 • ^— ' W -^ : c +s a ■ _o 0) ™ : a 4J CD 3 C aj j_ w w-g ao) c^ CO 'J-' CO « 9i o o a3 cu ^•5 ,<£ 3-? £^ £ w O -m ^-> "£ aj rt-2 5fi 2-59 4-65 0.58 1 13 o-5i 4-33 o.54 1 -13 6i-70 55-53 .20 7 6-75 7.20 2.28 1.07 2-54 1.78 0.30 0.17 100.00 100.00 125.00 0.65 1.36 6.74 2.13 °-95 2-54 0-35 0.30 0.17 77-23 75.00 93-75 3 4 5 1 to £ * a oj am »i ■3 .a a 0) Mft to c 0) w O «i oj to O i-55 5-18 2.84 3-55 I. 16 I.Q7 0.44 O. 29 O. 29 1 -13 I 13 1 -i3 52.44 0.61 26.52 3.60 25-97 2. 16 4.06 6.76 4.06 5-5o I. 8l 3-05 i-75 I. 14 1. 14 0.81 0-54 o.54 2-54 1 .02 2-54 I.80 2-54 1 .07 0.30 O.3O 0.30 0.17 O.I7 0.17 75-87 80.00 52.94 IIO.OO 47-23 96.20 100.00 I37-50 12% 120.00 ii.S% 0.51 I 13 1.36 2.54 0.20 o. 20 5-94 100.00 125.00 n% 103. Costs per Kilo watt-hour. — The average annual cost per kilowatt-hour of output depends upon the annual 3°° TRACTION AND TRANSMISSION. load factor and upon the type of an installation. The an- nual load factor is the ratio of the annual output in kilo- watt-hours to 8760 times the rated capacity of the installed apparatus in kilowatts. Since the fixed charges are de- pendent upon the rated capacity but independent of the 60 50 40 30 -20 10 / S IS # i^ ^ &£ ^ •<0^ J ' -