TWELFTH LECTURE ELECTRIC RAILWAY TRAIN CHARACTERISTICS The performance of a railway consists of acceleration, motion and retardation, that is, starting, running and stopping. The characteristics of the railway motor are: 1. Reliability. 2. Limited available space, which permits less margin in the design, so that the railway motor runs at a higher temp- erature, and has a shorter life, than other electrical apparatus. The rating of a railway motor is therefore entirely determined by its heating. That is, the rating of a railway motor is that output which it can carry without its temperature exceeding the danger limit. The highest possible efficiency is therefore aimed at, not so much for the purpose of saving a few percent, of power, but because the power lost produces heat and so reduces the motor output. 3. Very variable demands in speed. That is, the motor must give a wide range of torque and speed at high efficiency. This excludes from ordinary railway work the shunt motor and the induction motor. The power consumed in acceleration usually is many times greater than when running at constant speed, and where acceleration is very frequent, as in rapid transit service, the efficiency of acceleration is therefore of foremost importance, while in cases of infrequent stops, as in long distance and inter- urban lines, the time of acceleration is so small a part of the total running time, that the power consumed during accelera- tion is a small part of the total power consumption, and high efficiency of acceleration is therefore of less importance. 150 GENERAL LECTURES Typical classes of railway service are : 1. Rapid transit, as elevated and subway roads in large cities. Characteristics are high speeds and frequent stops. 2. City surface lines, that is, the ordinary trolley car in the streets of a city or town. Moderate speeds, frequent stops, and running at vari- able speeds, and frequently even at very low speeds, are char- acteristic. 3. Suburban and interurban lines. That is, lines leading from cities into suburbs and to adjacent cities, through less densely populated districts. Characteristics are less frequent stops, varying speeds, and the ability to run at fairly high speeds as well as low speeds. 4. Long distance and trunk line railroading. Characteristics are: infrequent stops, high speeds, and a speed varying with the load, that is, with the profile of the road. 5. Special classes of service, as mountain roads and ele- vators. Characteristics are fairly constant and usually moderate speed; a constant heavy load, so that the power of accelera- tion is not so much in excess of that of free running; and usually frequent stops. This is the class of work which can well be accomplished by a constant speed motor, as the three- phase induction motor. The rate of acceleration and rate of retardation is limited only by the comfort of the passengers, which in this country permits as high values as 2 to 2 2 miles per hour per second, that is, during every second of acceleration, the speed increases at the rate of 2 to 2-2 miles per hour, so that one second after starting a speed of 2 to 2 2 miles per hour, 5 seconds ELECTRIC RAILWAY 151 after starting a speed of 5x2 to 25 — iotoi22 miles per hour, etc., is reached. Steam trains give accelerations of 5 mile per hour per second and less with heavy trains, due to the lesser maximum power of the steam locomotive. Speed Time Curves In rapid transit, and all service where stops are so fre- quent that the power consumed during acceleration is a large part of the total power, the speed time curves are of foremost importance, that is, curves of the car run, plotted with the time as abscissae, and the speed as ordinate. -2 ^ m ^H H Fi ^•' li - r ' 7 \. > rr v — \ L "''^^ \ 7 . \ t N. 7 I >\- "-• t^ t \ 1 7 V 1 t \ 1 7 Ur t j\ 7 1 \ _-6 -- F 1 1 N t I B t± _ 1^1^^ Fl^. 29. Choose for instance, a maximum acceleration and maxi- mum braking of two miles per hour per second, and assuming a retardation of one-quarter mile per hour per second by fric- tion (that is, assuming that the car slows down one-quarter mile per second, when running light on a level track) ; if then the time of one complete run between two stations is given equal to A B in Fig. 29, the simplest t)rpe of run consists of constant acceleration, from A to C, on the line A a, drawn 152 GENERAL LECTURES under a slope of two miles per hour per second ; at C the power is shut off and the car coasts on the slope C D, of one- quarter mile per hour per second, until at D, where the coast- ing line cuts the braking line bB, (which also is drawn at the slope of two miles per hour per second), the brakes are applied and the car comes to rest, at B. As the distance traveled is speed times time, the area A C D B so represents the distance traveled, that is, the distance between the two stations, and all speed time curves of the same type therefore must give the same area. During acceleration, energy is put into the car, and stored by its momentum, which is proportional to the weight of the car and the square of the speed. It is therefore at a maximum at C. A part of the energy represented by the car speed is con- sumed during coasting in overcoming the friction; the rest is destroyed by the brakes. Assuming, as approximation, con- stant friction, the energy consumed by the car friction on the track, for runs of the same distance, is constant, and the energy destroyed by the brakes is represented by the speed at the point B, where the brakes are applied. The lower therefore this point B is, the less power is destroyed by the brakes, and the more efficient is the run. More accurately, by pro- longing C D to E so that area D E G = B P G, the area A C E F also is the distance between the stations, and E F so would be the speed at which the car arrives at the next station, if no brakes were applied, and the energy correspond- ing thereto has to be destroyed by the brakes ; that is, represents the energy lost during the run, and should be made as small as possible, to secure efficiency. The ratio of the energy used for carrying the car across the distance between the stations — that is, energy consumed by track friction, (plus energy consumed in climbing grades, where such exist) to the total energy input, that is, track fric- ELECTRIC RAILWAY 153 tion plus energy consumed in the brakes, is the operation efficiency of the run. As an illustration, a number of such runs, for constant time of the run, of 130 seconds, and constant distance between the stations, that is, constant area of the speed time diagram, are plotted in Figs. 29 to 37. I. Constant acceleration of two miles per hour per second, coasting at one-quarter mile per hour per second, and braking at two miles per hour per second. Here the energy- consumed by the brakes is given by the speed E F = 34.5 miles per hour, while the maximum speed reached is 60 miles per hour. r r ^" F y. Si > > •- ■^, .^ k. __ '■ "•-« »:» J> L— J. * ") ST ■^- — V f '■ "■". A \ / V I f \ 1 ' j \ f \ V X, \ - /I F t MM _ _ ^ Fig. 30. 2. Acceleration and retardation at two miles per hour per second. Constant speed running between. Fig. 30. Compared with I, (which is shown in 30 in dotted lines), the maximum speed is slightly reduced, e. g., to 51 miles per hour, but the speed of application of the brakes, and therefore the energy lost in the brakes, is increased. That is, running at constant speed, between acceleration and braking, is less efficient than coasting 154 GENERAL LECTURES with decreasing speed. Besides this, at the low power required for constant speed running, the motor efficiency usually is aready lower. It therefore is uneconomical to keep the power on the motors after acceleration, and more economical to con- tinue to accelerate until a sufficient speed is reached to coast until the brakes have to be applied for the next station. Obviously, this is not possible where the distance between the stations is so great, that in coasting the speed would decrease too much to make the time, and so applies only to the case of runs with frequent stops, as rapid transit. 3. Constant acceleration of one mile per hour per second, braking at two miles, coasting one-quarter mile. Dia- •"" -1 ■"" —"' "~" '~" ""■ BOM ^^ MMM Fi i- 3/ / r ^ ^ / r*N "^" «<« *. ^ / 3 \ / i / •* . \ / / ** — 1^ *y I / — \)j i / s. f / \ / / / / / / \ / / \ y / V ^ \ A B _ Fig. 31. gram i is shown in the same figure 31, for comparison. As seen, with the lower rate of acceleration, the maximum speed is greater, and the lost speed, or speed E F, which is destroyed by the brakes, is greater, that is, the efficiency of the run is lower. 4. Constant acceleration and braking of one mile per hour per second, coasting at one-quarter mile. In this case. ELECTRIC RAILWAY 155 the run between the stations cannot be made in 130 seconds. For comparison, i is shown dotted in Fig. 32. Here the maxi- ^ X- El^ll''- />^ / \ 2 ^ ~1 "■ ---^^ 2 ^ L. Z!" ""::» ^ 1 2 ^"^"--i. Si i— ~7 "^~~5i- / ~7 C'» -.' 4^Z ' ^ 2 -Z %^ t^Z \\ -/—Z \S^ TJL \ S^ 2^-t S^ S^ t J S- ^ g. Fig. 32. mum speed and the lost speed are still greater, that is, the efficiency of the run still lower, and at least 145 seconds are required. That is, the higher the rate of acceleration and of braking, the less is the maximum speed required, and the higher the operation efficiency. With constant acceleration up to the maximum speed, the operation therefore is the more efficient the higher a rate of acceleration and of braking is used. While very rapid acceleration requires more power developed by the motor and put into the car, the time during which the power is developed is so much shorter, that the energy put into the car, or power times time of power applica- tion, is less than with the lower rate of acceleration. The highest operation efficiency, in the case of frequent stops, therefore is produced by constant acceleration at the highest permissible rate, coasting without power, and then braking at the highest permissible rate, as given by i. 156 GENERAL LECTURES During acceleration at constant rate, from A to C, the motor however runs on the rheostat. That is, at all speeds below the maximum, to produce the same pull as at the maxi- mum speed C, the motor consumes the same current and so the same power; while the power which it puts into the train is proportional ito the speed, and therefore is very low at low speeds. Or in other words, the motor during constant acceler- ation, consumes power corresponding to maximum speed, while the useful power corresponds to the average speed, which during A C is only half the maximum ; and so only half the available power is put into the car, the other half being wasted in the resistance, and the motor efficiency during constant acceleration therefore must be less than 50%. Constant acceleration up to maximum speed, while giving the best operation efficiency, so gives a very poor motor efficiency and thereby low total efficiency, (the total efficiency being the ratio of the useful energy to the total energy put into the motors, that is, is operation efficiency times motor efficiency). This is the arrangement necessary for a constant speed motor, as the induction motor; but it does not give the best total efficiency, but a better total efficiency is produced by accelerating partly on the motor curve, that is, at a decreasing rate. This sacrifices some operation efficiency, but increases the motor efficiency greatly, and so, if not carried too far, increases the total efficiency. The speed time curves of the motor are shown in Fig. 33, and the current consumption is also plotted in this figure. Acceleration is constant from A to M, on the rheostat, and at constant current consumption, from M, onwards, the accelera- tion decreases, first slightly, then faster, but the current also decreases, first rapidly, and then more slowly; and the ELECTRIC RAILWAY '57 efficiency, plotted in Fig. 33, rises from 0% at A, to 90% at M, and then remains approximately constant, while the speed still increases. — ■" f— -^ ~ ■ ■■ ~" ^ ■" " " " ■" ;»■ • -^ .» — '^ <^(i ,:*.' ^ *" [S ^(1 s !i ' *- «* -'' f J ^ /r e/i KU J toaa. y iM^y M \ / 1 (FC \ / 1 / \ / \, / ^( V / - .)( ,* i 1 /^ ~ ~ " - 1 / \ -> ^ ^ tS ( / s 1 / V / J s •«. / 1 ^ lie 1 J /" * _ /I y / / ' $„ )> ^> «:::: ■^ / ' y -^ >. --» \ / / -"t ;::: ^ -c j^ ^ "^^ ^ tv D ■ t \ ,^ \ / M N s.^ \ / "» l*- .^ \ "" \ \ \ '■ > \ — -S T ■~ ^ — >— L „^ J _^ . ^^ J _ _ 1 Fig. 34. with the speed time curves, is much less, and the power con- sumption therefore is less ; that is, the total efficiency is higher. 7. Fig. 35 gives another speed time curve in which, however, the motor is geared for too low a speed ; so the motor ■"■ "" ■" ■" ■" ~" ■■ "■ "" ""■ ^ "*" mm >— "■ ^" ■^ ~ /3 7w 5 c _ y -- ^ — ' — \ Jt / ^ > •c ^.. \ / x H --. ^. \ / ^ 0 k 1 1 / /' ^ \ A / \ & b i 1 ^ f^ \ J < y 1 1, P V V \ ^ /» r ■*' »^ N ) \ ■^ V 4 '> . \ / *'' " V J. \j t < 0 _ _ _ ^ __ ^ ^^ _, _ ^ _ „„ _ _ Fig. 36. be impaired again by carrying this too far. Usually the rheostat is all cut out and the acceleration continues on the motor curve, from about half speed onwards. 8. During the first half of the acceleration on the rheo- stat, when more than half the voltage is consumed ^n the rheostat, half the current can be saved by connecting two motors in series; that is, by series parallel control on the motors, as shown in Fig. 36. If, however, the series connec- tion of motors is maintained too long, as shown in Fig. 37, i6o GENERAL LECTURES so that the part of the curve S P gets too long, the average rate of acceleration, and so (the operation efficiency, is greatly reduced. That is, the lost area becomes so large, that the speed at application of the brakes, and so the power lost in brakes, is greatly increased. Series connection of motors, for efficient acceleration, therefore should not be maintained for any length of time after the rheostat has been cut out. ■" — ■" " ■■ n 6> 5/ r 5 ^^ , ...» c ,^ c^ ^ C -«., I *" -- '^ ^ / "~ ^ 1 / ^ "-■«. .^ i*»~. a / / ^■ --• ■-. ^^ \ ( / ■^ .*. .\ 2f / P n r y / y y \ \ f / \ ■X, "«-. .^ \ "~- -- ■— s. V^ "»» \, / "" "■" / /K s .- Fife. 37 In series parallel control, as shown in Figs. 36 and 37, some acceleration occurs on Lhe motor curve in series connec- tion. That is, A S is acceleration on the rheostat, in series connection, S P acceleration on the motor curve; P M on the rheostat in parallel connection, and M C on the motor curve in parallel connection. Compared with i, which is shown dotted in 9, the area A S P M H Ci is lost; and so the equal area H C D Di, has to be gained, giving a higher speed of application of the brakes D, but gaining power more than the ELECTRIC RAILWAY i6i increased power consumption in the brakes, by the higher motor efficiency. CONCLUSION In short distance runs the efficiency is highest in running on series parallel control as much as possible on the motor curve, with as high a rate of average acceleration and retarda- tion as possible, and coasting between acceleration and retarda- tion ; that is, not keeping the power on longer than necessary. The longer the distance, the less important is high rate of acceleration and retardation, and for long distance running the rate of acceleration and retardation is of little importance. Therefore speed time curves are specially important in rapid transit service, and in general, in running with frequent stops. The heating of the motor at high acceleration, that is, with large current, is less than with low acceleration, that is, smaller current, because the current is on a much shorter time. Feeding back in the line by using the motors as genera- tors is rarely used ; because with an efficient speed time curve, using coasting, the speed when putting on the brakes is already so low that usually not enough power can be saved to compen- sate for the complication and the increased heating of the motors, when carrying current also in stopping. The motors are occasionally used as brakes, operating as generators on the rheostat. This, however, puts an additional heating on the motors ; and is therefore not much used in this country, where the highest speed which the motor equipment can give is desired. ' With induction motors, feeding back in the line is simplest, because induction motors become generators above l62 GENERAL LECTURES synchronism, and so feed back when running down a long hill. Therefore on mountain railways, induction motors have the advantage. In an induction motor there is no running on the motor curve, and so the efficiency of acceleration is lower. Objection to the series motor is the unlimited speed ; that is, when running light, it runs away. In railroading this is no objection, because tlie motor is never running light and some- body is always in control. In elevator work the series motor is objectionable, due to the unlimited speed ; therefore a limited speed motor is neces- sary. In elevators frequent stops, and so efficient acceleration are necessary; therefore a compound motor is best, that is, a motor having a shunt field to limit the speed and a series field (which is ait out after starting) to give efficient acceleration.