In my previous posts I lightly covered:

- the traction force (read the disclaimer, please)
- the resistance forces
- the brake force

The various combinations of these forces define the train driving regimes. These are the following (not sure if all the railway networks are defining theme in the same way):

**Maximum traction (starting)**. In this driving regime the traction force is the maximum and runs on the adhesion plateau of this force.

**Traction (cruising)**. Speed is above the adhesion limit and the train runs with active traction.

**No traction (coasting**– train runs down a long gradient with no need for traction). The train can run without traction force.

**Braking**. The trains need to slow down or stop.

A particular case of this regime is where the falling gradient is so steep that it requires the train to brake to maintain a safe riding. That falling gradient is considered detrimental for train riding (“damaging” is the direct translation but not sure it is right).

**Equilibrium speed**

For each regime we can define the combination of forces that are active.

For example, for Cruising we have traction and resistance forces. Their resultant force is (F-R).

In the graph above we notice that there is a speed at which the resultant force is null.

I promised I’ll mention Newton.

His first law of motion states that the train is at rest or in uniform motion until and unless a net force acts on it. Hence, when the resultant force is null then the train is having an uniform motion – speed is constant, acceleration is null.

This speed is called Equilibrium Speed (V_{E}). This is not the same as the equilibrium speed we find in the cant related equations.

If the train speed is below V_{E} then the train will naturally tend to accelerate to reach it. If the train speed is above V_{E} the train will tend to decelerate to V_{E}.

See?!

Equilibrium!

The next one will be tricky …