Given a Traction-Effort vs Speed chart for a particular locomotive, in which the acceleration usually decreases with increasing speed, it is essential for the simulator to have a constant value of the acceleration such that the maximum speed is achieved in exactly the same distance as the variable acceleration curve: we call this the equivalent constant acceleration. More details about this can be found in the user-manual: this page focusses on a calculation procedure for the equivalent constant acceleration.
The xlsx-file provided takes discrete points from the "TE vs Speed" curve for a locomotive and charts out distance and time details assuming constant acceleration between each consecutive sample points. Since the discrete sample distance is very small, the approximation is close to the real value.
time-difference = velocity-difference/acceleration-value
Please note: acceleration between sample is computed using (TE x 9.8)/(Loco-Mass + Number-of-coaches x Mass-of-each-coach)), and loco mass is taken as 120 tons and each coach mass is taken as 50 tons.
In order to compute the equivalent acceleration by distance equalization, cumulative value of distance covered by the loco till it reaches the final velocity is taken and the following equation is applied.
a-eq=(vf-vi)/2*D
The above describes the theory that is implemented in the xlsx file. The xlsx file has two columns marked in light-green. These two columns are data pertaining to the specific locomotive. Other columns are to be put in based on the self-explanatory column headings (like number of coaches, weight of each coach, etc).
The maximum speed that the train is allowed to reach: this to be filled in column L (against what is written in light-green as "Final velocity"). After various intermediate calculations, the final equivalent constant acceleration is obtained in the unit m/s^2 and displayed in column N (against what is written in dark green).
For more information: please contact
Contact persons:
Prof. Narayan Rangaraj, Industrial Engineering and Operations Research (IEOR) IIT Bombay, Powai, Mumbai 400 076 Email: narayan.rangaraj@iitb.ac.in
and/or
Prof. Madhu N. Belur Department of Electrical Engineering, IIT Bombay, Powai, Mumbai 400 076 Email: belur@iitb.ac.in
Document last updated on 29th Sept 2020