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This document discusses traction and train movement. It covers: 1. Types of railway services including city/urban, suburban, and main line passenger services as well as freight services. 2. Speed-time curves which show the speed of a train over time and can be used to analyze train movement. Typical curves include periods of constant acceleration, acceleration on a speed curve, free running, coasting, and braking. 3. Simplified speed-time curves which use simpler geometric shapes like trapezoids or quadrilaterals to approximate actual speed-time curves for analysis purposes.

Engineering◦
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UNIT 4 TRACTION Speed-Time curve By: Ankit Aharwar Asst. Prof., EED, SGSITS Indore
Content  Traction systems  Methods of supplying power to electric trains  Technical aspects of railway electrification  Operating voltage  Mechanics of train movement  Speed time and distance time curves  Tractive effort  Train resistance and adhesion weight  Power and energy output from the driving axles specific energy consumption  Transmission of power from motor to wheel gearing overhead equipment  Negative booster.
Types of Railway services There are three types of passenger services offered by the railways : 1. City or Urban Service.: 2. Suburban Service: 3. Main Line Service: On goods traffic side also, there are three types of services (i) main-line freight service (ii) local or pick-up freight service and (iii) shunting service.
City or Urban Service  In this case, there are frequent stops, the distance between stops being nearly 1 km or less. Hence, high acceleration and retardation are essential to achieve moderately high schedule speed between the stations.
Suburban Service  In this case, the distance between stops averages from 3 to 5 km over a distance of 25 to 30 km from the city terminus. Here, also, high rates of acceleration and retardation are necessary.
Main Line Service  It involves operation over long routes where stops are infrequent. Here, operating speed is high and accelerating and braking periods are relatively unimportant.
Train Movement The movement of trains and their energy consumption can be conveniently studied by means of speed/time and speed/distance curves. As their names indicate, former gives speed of the train at various times after the start of the run and the later gives speed at various distances from the starting point. Out of the two, speed/time curve is more important because 1. its slope gives acceleration or retardation as the case may be. 2. area between it and the horizontal (i.e. time) axis represents the distance travelled. 3. energy required for propulsion can be calculated if resistance to the motion of train is known.
Speed-time curve  Typical speed/time curve for electric trains operating on passenger services is shown in Fig. It may be divided into the following five parts : 1. Constant Acceleration Period (0 to t1) 2. Acceleration on Speed Curve (t1 to t2) 3. Free-running Period (t2 to t3) 4. Coasting (t3 to t4) 5. Braking (t4 to t5)
Speed-time curve 1. Constant Acceleration Period (0 to t1) • It is also called notching-up or starting period because during this period. • The starting resistance of the motors is gradually cut out so that the motor current (and hence, tractive effort) is maintained nearly constant . • Which produces constant acceleration alternatively called ‘rheostatic acceleration’ or ‘acceleration while notching’.
Speed-time curve 2. Acceleration on Speed Curve (t1 to t2) • This acceleration commences after the starting resistance has been all cut-out at point t1 and full supply voltage has been applied to the motors. • During this period, the motor current and torque decrease as train speed increases. • Hence, acceleration gradually decreases till torque developed by motors exactly balances that due to resistance to the train motion. • The shape of the portion AB of the speed/time curve depends primarily on the torque/speed characteristics of the traction motors.
Speed-time curve 3. Free-running Period (t2 to t3) • The train continues to run at the speed reached at point t2. It is represented by portion BC in figure and is a constant-speed period which occurs on level tracks.
Speed-time curve 4. Coasting (t3 to t4) • Power to the motors is cut off at point t3 so that the train runs under its momentum, the speed gradually falling due to friction, windage etc. (portion CD). • During this period, retardation remains practically constant. • Coasting is desirable because it utilizes some of the kinetic energy of the train which would, otherwise, be wasted during braking. • Hence, it helps to reduce the energy consumption of the train.
Speed-time curve 5. Braking (t4 to t5) • At point t4, brakes are applied and the train is brought to rest at point t5. • It may be noted that coasting and braking are governed by train resistance and allowable retardation respectively.
Speed-time curves for different services
Speed-time curves for different services  Fig.(a) is representative of city service where relative values of acceleration and retardation are high in order to achieve moderately high average speed between stops. Due to short distances between stops, there is no possibility of free- running period though a short coasting period is included to save on energy consumption.  In suburban services [Fig.(b)], again there is no free-running period but there is comparatively longer coasting period because of longer distances between stops. In this case also, relatively high values of acceleration and retardation are required in order to make the service as attractive as possible.  For main-line service [Fig.(c)], there are long periods of free- running at high speeds. The accelerating and retardation periods are relatively unimportant.
Simplified Speed/Time Curve  For the purpose of comparative performance for a given service, the actual speed/time curve of previous figure is replaced by a simplified speed/time curve which does not involve the knowledge of motor characteristics.  Such a curve has simple geometric shape so that simple mathematics can be used to find the relation between acceleration, retradation, average speed and distance etc.  The simple curve would be fairly accurate provided it (i) retains the same acceleration and retardation and (ii) has the same area as the actual speed/time curve.
Simplified Speed/Time Curve The simplified speed/time curve can have either of the two shapes : (i) trapezoidal shape OA1B1C of figure where speed-curve running and coasting periods of the actual speed/time curve have been replaced by a constant speed period. (ii) quadrilateral shape OA2B2C where the same two periods are replaced by the extensions of initial constant acceleration and coasting periods.
Simplified Speed/Time Curve  It is found that trapezodial diagram OA1B1C gives simpler relationships between the principal quantities involved in train movement and also gives closer approximation of actual energy consumed during main-line service on level track.  On the other hand, quadrilateral diagram approximates more closely to the actual conditions in city and suburban services.
Average and schedule speed While considering train movement, the following three speeds are of importance : 1. Crest Speed. It is the maximum speed (Vm) attained by a train during the run. 2. Average Speed = In this case, only running time is considered but not the stop time. 3. Schedule Speed = Obviously, schedule speed can be obtained from average speed by including the duration of stops. For a given distance between stations, higher values of acceleration and retardation will mean lesser running time and, consequently, higher schedule speed. Similarly, for a given distance between stations and for fixed values of acceleration and retardation, higher crest speed will result in higher schedule speed. For the same value of average speed, increase in duration of stops decreases the schedule speed.
SI Units in Traction Mechanics 1. Force. It is measured in newton (N) 2. Mass. Its unit is kilogram (kg). Commonly used bigger units is tonne (t), 1 tonne = 1000 kg 3. Energy. Its basic unit is joule (J). Other units often employed are watt-hour (Wh) and kilowatt hour (kWh). 1 Wh = 1 J/s x 3600 s = 3600 J = 3.6 kJ 1kWh = 1000 x 1 J/s x 3600 s = 36 × 10^5 J = 3.6 MJ 4. Work. Its unit is the same as that of energy. 5. Power. Its unit is watt (W) which equals 1 J/s. Other units are kilowatt (kW) and megawatt (MW).
SI Units in Traction Mechanics 6. Distance. Its unit is metre. Other unit often used is kilometre (km). 7. Velocity. Its absolute unit is metre per second (m/s). If velocity is given in km/h (or km.ph), it can be easily converted into the SI unit of m/s by multiplying it with a factor of (1000/3600) = 5/18 = 0.2778. For example, 72 km.ph = 72 × 5/18 = 72 × 0.2778 = 20 m/s. 8. Acceleration. Its unit is metre/second^2 (m/s^2). If acceleration is given in km/h/s (or kmph.ps), then it can be converted into m/s2 by simply multiplying it by the factor (1000/3600) = 5/18 = 0.2778 i.e. the same factor as for velocity. For example, 1.8 km.ph.ps = 1.8 × 5/18 = 1.8 × 0.2778 = 0.5 m/s2
Quantities involved in traction mechanics