Tire force combining review

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Here is something interesting.

Pacejkas formula uses a linear approximation for the friction coefficient
mu = c1 * fz + c0

I've asked myself how mu(fz) would look like with the contact patch model (using the empiric equations for tire stiffness and conact length and assuming mu ~ pressure^(-1/3))


Blue curve 200mm wide tire
Red curve 275mm wide tire
Green linear approximation

Both curves have a steep increase at low loads < 1.5kN. This is mostly due to me using a constant contact width model I think. In reality contact width drops rapidly at low tire loads.

What you see is that the linear approximation is actually pretty good. Another observation is that the red curve segment (2-5kN) looks pretty much like the blue segment shifted vertically. The shift factor between them is 8%.

This means that the 275mm tire would have about 8% more grip than the 200mm tire. I'll try adding this tire geometry correction factor to vdrift to see how much effect it has. Might be a simple solution to the rwd sports cars rear grip problem.