I think ‘slip ratio’ approach is flawed. Slip ratio is derived quantity and highly unrelated to problem of wheel dynamic.

There are two main regime of wheel rolling. First is static friction without slipping of tire over road. Nonzero ‘slip ratio’ in this regime is due to tire deformation rather than actually slipping. So you can safely assume slip = 0. In this regime friction force is arbitrary with maximal magnitude proportional to normal force (all applied to point of contact of tire with road).

Second regime is kinetic friction where tire actually slips. This regime is energy (and tire material) consuming as opposed to first. In this regime amount of slip determined by wheel dynamic and friction force proportional to normal force and directed opposite to surface slip velocity. Coefficient of kinetic friction is smaller than of static friction and depend on speed of surface slipping.

Wheel angular velocity in regime of real slipping determined mostly by engine. You have wheel rotating with angular velocity w under of load of kinetic friction angular momentum M and engine (with transmission) gives you angular acceleration.

First of all sorry for my bad english.

My problem is that im making car game where car moves only forward and backward and im trying to understand how to calculate traction force when tires are slipping. So cars tires are always slipping expect if there is no accelration, right? I am using slip ratio curve found here http://www.asawicki.info/Mirror/Car%20Physics%20for%20Games/Car%20Physics%20for%20Games.html and if i understood right it is always same amount of force delivered at same slip ratio assuming that load to tires is constant. If it is like this I need slip ratio to calculate traction force. From the same website I have used this formula to calculate slip ratio: slip ratio=(w*r-v)/abs(v), where w is tires angular velocity, r is tires radius and v is cars velocity. But the thing is how i calculate angular velocity if there is slip? I havent tried any solution yet cause im quite confused now. But I have thought simplifying this by assuming that cars slip ratio is 0 until traction force exceeds static friction and then calculating angular velocity using this equation a=M/J where a is angular accelration, M=moment on wheel and J=moment of inertia. From that I could calculate angular velocity like I can calculate velocity from accelration but I am not very familiar about moment of inertia so can I use it in situations like this? Im really confused about this now and I hope you understood my poor explanations so please help me and correct if i was wrong about something. I have tried to find solution to this from many websites but maybe im just dumb.. or lack skills of finding right things.