Explicit Train Performance Option (Input Form 8E)

The explicit train performance option allows the user to specify the travel profile which the train is to follow as it moves along its route. This travel profile is specified by means of a train speed versus time relationship. This speed versus time relationship, or table, is defined for each route, with all trains observing the speed-time profile for the route on which they are operating. There are two options

available when using explicit train performance: train heat rejection computed by the SES program (Train Performance Option 2), and train heat rejection profile input to the program by the user (Train

Performance Option 3).

Train Performance Option 2. When using explicit train performance with heat rejection computed by the program (Train Performance Option 2), the train follows the train speed versus time profile which is specified by the user. If the train is accelerating or running at constant speed, the tractive effort required to overcome the train resistance and produce the specified acceleration is computed and

“supplied” by the motors. From this tractive effort the motor current is computed by using the motor current versus tractive effort curve which is defined in the train data. This motor current is used with the appropriate value of the external (if any) and internal motor circuit resistance to compute the rate of power loss in the acceleration grids (if any). If no acceleration grids are present, the motor current is used with the internal motor resistance to compute the equivalent amount of heat generated and the heat is released instantaneously. During periods of braking, the rate of power dissipation in the deceleration grid is equal to the net change of kinetic and potential energy of the train. When using Train Performance Option 2, the user must complete all the train data forms up to, and including the motor characteristics data. However, the form describing the maximum acceleration rate and normal deceleration rate curve should be skipped, since this data is not used by the program (refer to Tables 6.1 and 6.2).

The speed-time profile consists of a table of times and corresponding train speeds. The time, which is entered in seconds, is the simulation time which has elapsed since the train was dispatched onto

Example 8.1 Figure 8.16 shows a typical train speed versus time profile for a station-to-station run. This figure shows a plot of train speed against the simulation time which has elapsed since the train was dispatched onto its route. Also shown is a tabular

representation of the same data, which is in the form the user would use to enter the speed-time profile into the program. The area under the speed-time plot is the distance traveled by the train, and the distance between stops should correspond to the station-to-station distance.

The program performs a linear interpolation between the points of the speed-time profile which are specified by the user. The user may specify gradual changes in

acceleration by specifying many points spaced close together. The user may also use fewer points to approximate the curve, but a curve with fewer points would have more abrupt changes in the train acceleration represented by the slope of the line of a speed versus time plot. The area under this curve, which is the distance traveled by the train, can be found using a trapezoidal integration method.

Trains are dispatched onto the route at the scheduling origin. The first point of the speed-time profile must be at time zero (0.0). The train is dispatched onto the route at the speed which corresponds to a time of zero on the speed-time profile. Trains are removed from operation when the front of the train goes beyond the forward end of the last track section. The location of the scheduling origin plus the distance traveled by the train during the length of the speed-time profile should be more than 50 feet, and preferably longer than the length of the track sections which have been defined for the route. To prevent a jam-up of trains at the end of the route, the speed-time profile is usually arranged so that the trains run out past the last track section at a reasonable operating speed.

Train Performance Option 3. Train performance Option 3 would be used when the speed-time profile and heat rejection-time profile are known to the user prior to the SES simulation. This information may be taken from either the manufacturer's estimates, a separate computer analysis of the train performance characteristics by using another computer program, or, if the system is operational, from measurements taken aboard operating trains.

The rates of power into the acceleration and deceleration resistor grids are specified by the user as time dependent functions. The units are kilowatts per train and this power is divided equally among the appropriate type of resistor grids which are located beneath each powered car. The rate of power

dissipation into the resistor grids is given as a time-dependent function which is combined with the speed-time profile. The combined speed and power dissipation profile has for each point in speed-time a value for train speed and rate of power into the deceleration grid. As in the speed-time table in Train Performance Option 2, the times are entered in seconds with each subsequent time equal to, or greater than the previous time. These times are the simulation time which has elapsed since an individual train has been

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dispatched onto its route. As with the train speed, the program performs a linear interpolation to find rates of power dissipation between the points which are specified by the user.

TIME SPEED

Figure 8.16 Sample Speed-Time Plot with Tabular Data

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A sample heat release profile for a cam-controlled train is shown graphically and in tabular form in Figure 8.17. This heat release profile, which provides representative values, corresponds to the speed-time profile which is shown in Figure 8.16. The characteristic peaks in the acceleration power dissipation, which occur between zero and 10 seconds, are caused by the insertion and removal of the acceleration resistor grids from the motor circuit to limit the current through the motors. The sharp peak in the deceleration power dissipation, which occurs from 44 to 57 seconds, is caused by the train braking to a stop from 35 mph.

The tabular data showing the train speed, acceleration power loss, and deceleration power loss versus time is listed in Figure 8.17. These data are in a form that would be used as input to the SES program for Train Performance Option 3. Since this data relates three dependent variables to one independent variable (time), one data point is required to show characteristic points in any of the three curves. However, for each point a correct value must be given for all three curves. The program performs a linear interpolation between the data points which are supplied by the user. A step function, which is a rapid change over a very short time interval, can be simulated by supplying two points at the same instant of time. The first point would be the value just prior to the step function and the second point would be the value just after the step. An example of this is shown in Figure 8.17 at 85 seconds. At this time the

traction power is shut off, and the train coasts for 10 seconds. The first point at 85 seconds, which defines the curve from 84 to 85 seconds, has an acceleration power loss of 2500 kilowatts. The second point at 85 seconds, which defines the curve from 85 to 95 seconds, has a value of 0 kilowatts. These two points act together to produce an abrupt change in the acceleration power loss at 85 seconds. Train speed is a smooth function, and its rate of change with respect to time is the acceleration. The user must be sure that the speed-time profile supplied to the program does not contain rapid changes in train speed that would exceed the acceleration capabilities of the train. The acceleration and deceleration power loss which is specified by the user when using Train Performance Option 3, can be released to the air directly or through the resistor grid time delay mechanism. The direct release of this heat into the air is known as instantaneous heat release. This mechanism is used if the user specifies a resistor mass of zero. Both the acceleration and deceleration resistor grid may be simulated or bypassed independently. Note: When using Train Performance Option 3 (Explicit, Train Heat Rejection Input), the user may not enter a value for both acceleration power loss and deceleration power loss for the same time entry. In other words, at any point in time, power can go into either the acceleration grid or the deceleration grid, but not both.

TIME TRAIN

Figure 8.17 Sample Heat Release Profile with Tabular Data

0 10 20 30 40 50 60 70 80 90 100 110 120

2. All train power is in KILOWATTS

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REFERENCES

1. “Aerodynamics of High-Speed Train,” T. Hara, M. Kawaguti, G. Fukuchi, A. Yamamoto. 1968. (“High Speeds Symposium,” Vienna 1968).

2. Hoerner, S.F., “Fluid Dynamic Drag,” published by author, Bricktown, N.J., 1965.

3. “Modell Untersuchungen Uber Das Widerstandsverhalten Von Zugen In Ein- und Zweigleisigen Tunnels Der Munchnew U-Bahn” (“Model Tests of Train Air Resistance in Single and Double Track Tunnels in the Munich Subways”), R. Frimberger, E. Lukas, October 1969.

4. Associated Engineers, A Joint Venture of Parsons, Brinckerhoff, Quade & Douglas, Inc., DeLeuw, Cather & Company and Kaiser Engineers, “Aerodynamic and Thermodynamic Validation Tests in Berkeley Hills Tunnel,” June 1973, Technical Report No. UMTA-DC-06-0010-73-1, Transit Development Corporation, Washington, DC.

5. Raskin, Donald and Ronald Yutko, “Energy Storage Propulsion Systems for Rapid Transit Cars,”

Report No. UMTA-NY-06-0006-75-1.

6. King, Charles and Alexander Kusko, “Flywheel Propulsion Simulation”, Report No.

UMTA-MA-06-0044-77-1.