# Calculating the Slip Ratio of a Vehicle Tire

I am trying to create a simulation to simulate a vehicle's tire using Pacejka's Magic Formula. From what I understand, the formula calculates the longitudinal force that the tire will experience using the slip ratio of the tire based on mimicking real data of tires.

Looking on Wikipedia about calculating the slip ratio, it just shows that the slip ratio is based on the linear velocity differences between the vehicle and the tire.

Is there a model out there that I could use to calculate the slip ratio of the tire based on the angular acceleration applied onto the tire by the engine, normal force, and other variables, so that I can use it in the Magic Formula to then calculate the acceleration of a vehicle?

• you can use your sleep definition for to calculate the tyre force or you can use this equation for the sleep $S=\dfrac {\omega R-V}{\left\| \omega R\right\| }$ , but you get problem when the vehicle velocity equal zero, to avoid this problem put small number in the denominator of the sleep equation. This sleep definition is not valid for reverse driving – Eli Mar 29 at 6:27
• I don't understand. Slip ratio is a velocity related quantity. Acceleration depends on slip, not the other way around. In simulation sense your ODE will be based on positions and velocities, and so for each time step those are known (and hence slip ratio is known). – ja72 Mar 29 at 13:53
• The acceleration I was talking about was the angular acceleration of the wheel being driven by the engine. Anyways, so I would first calculate the velocity of the wheel after the engine accelerated it in a time frame. Then I would plug that value into the slip ratio equation dividing it by the vehicle velocity. Then I plug the slip ratio into the magic formula then use the force value to accelerate the vehicle. Please correct me if I am wrong and thank you for the support! – angelo234 Mar 29 at 20:13