# Calculation of friction coefficient between wheel and road

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1. Nov 25, 2014

### Raj

Hi all,

I need to calculate the friction coefficient between road and the tyre of the car.
I came across few answers like which solves as from the following torque equation.

Engine torque = braking torque + acceleration troque + Inertial torque + drag torque + rolling resistance.

For braking, Engine torque = 0. and the braking torque is assumed to be Cp * (Braking pressure).Acceleration torque is taken as (F = (Mue)* (Normal force i.e., the weight on the wheel)).

The inertial component is taken as J*(omega_dot). where omega_dot is the derivative of angular velocity of the wheel.

is the inertial torque component significant? can it be neglected?

How can the Mue of the road at slip = 0 be calculated as the Mue varies with the slip?

2. Nov 25, 2014

### OldEngr63

You can neglect the inertial term provided you use massless wheels for which J = 0; otherwise, no, it must be included.

You are asking too much of a simple model here. The Coulomb friction model, Ffriction <= mu * Fnormal, does not depend on slip. When you use the equals sign, you are saying that slip is (1) impending or (2) slip is occurring.

3. Nov 25, 2014

### Raj

Thanks for the reply, I would like to know in the case where vehicle is already in slip. I read some where that the friction between the tire and road vary with the variation in slip. So, I am trying to calculate the variation of Mue(Braking force coefficient) with respect to slip. Please refer the following attachment to know about its variation.