TrafficControl: Improving Calculations for Acceleration

Until now. I've had a simplistic model for calculating train speeds. In this blog post, I'll refine it.

The train's desired speed is calculated as:

It is a calculation that does the job by taking the square root of the remaining distance minus the current speed. That function is mixing up the units and must be fixed.

Acceleration of trains are described by the speed-time curve:

1. Initially, the acceleration is constant
2. As the air resistance is increasing, the acceleration reduces and the train reaches its maximum speed.

After analysing some videos of accelerating trains, speed-time curves look as below:

I'll approximate the acceleration with a function:

• A is the rate of acceleration for speeds below C (0.7 m/s² in the example above)
• B is the rate of decline of acceleration (0.02 m/s³ in the example)
• C is the speed at which the decline starts (23 m/s in the example)

The function parameters will be different for different train types.

Retardation is harder to approximate, so I'll assume a constant retardation here.

With a constant rate of acceleration when braking, the braking distance is proportional to the speed squared:

D is a constant with a typical value of 2.