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driving physics
Basic physical reasoning is quite simple: write a equation of motion a train. Applying Newton's second law (known as the law of force) and we get all the necessary information (time, distance, speed).
m a = F_e - F_b - F_a - F_v - F_r
where:
m ... weight of the train, a ... train acceleration, F_e ... traction engine force, F_b ... braking force, F_a ... inertial force during acceleration, F_v ... resistance force of vehicle, F_r ... resistance force of route
It occurs only when the vehicle acceleration. It depends on the size of acceleration (a [m/s^2]), accelerating the vehicle weight (m [kg]) and size of the coefficient of rotating masses (rho_d [-]).
F_a = a m (1 + rho_d)
Resistance force of vehicle is calculated by an empirical relationship. You need to know the tabulated values of dimensionless coefficients rho_a, rho_b, rho_c. This force is quadratically dependent on the speed of the train in km / h
F_v = m (rho_a v^2 + rho_b v + rho_c)
This force depends on the weight of train (m [kg]), gravitational acceleration (g [m / s ^ 2]) and gradient (slope [ppt]).
F_r = m g slope
To resolve the motion of the train we need to know its velocity dependence on time. Engine force and braking force will never work together, so consider a start, then F_b = 0
m a = F_e - F_a - F_v - F_r
Engine power F_e we can write as
F_e = (3600 P adhesion (v)) / v
where P [kW] is engine power, v [km/h] is the current speed, adhesion(v) [-] is the coefficient of adhesion of wheel depends on the speed and constant 3600 flows of dimension units.
Then we can write
m a = ( (3600 P adhesion(v)) / v ) - a m (1 + rho_d) - m (rho_a v^2 + rho_b v + rho_c) - m g slope
m a + a m (1 + rho_d) = ( (3600 P adhesion(v)) / v ) - m (rho_a v^2 + rho_b v + rho_c) - m g slope
a = [(3600 P adhesion(v)) / v ) - m (rho_a v^2 + rho_b v + rho_c + g slope) ] / [m (2 + rho_d)]
This equation we will solve by numerical method, see mathematical model
Adhesion by Curtius-Kniffler is in form
(adhesion [-]) = (7500.0 / (velocity [km/h]) + 44.0) + 161.0) * 0.001