Wheel rolling resistance

Before we dig into practical equations, I'll just say that tires are surprisingly complex in their behavior. There are a variety of equations that try to fit the experimental data reasonably well. Hard to say that any one is right or wrong.

That having been said, the first equation is pretty inconsistent with the everything that I've ever seen. Weight on the wheel should almost certainly be included and rolling resistance rarely approaches 0 at 0 velocity in the literature. Two forms cited by Gillespie [ 1] are:

$$ frac{F_{r}}{W} = f_r = 0.1(1+V/100) $$

for low speeds and

$$ frac{F_{r}}{W} = f_r = f_o + 3.24 f_s(V/100)^{2.5} $$

over a broader range of speeds. Were F_r, W, V and f_i are rolling resistance force, weight on the tire velocity and empirical constants. Units are lbf, lbf and mph (sorry!).

The second term looks like an expression for increased rolling resistance when steering/slipping. $alpha$ would be the slip angle of the tire. Something like that would be added to either of the above equation. To give you a sense of the what this looks like, check out this graph. Also for Gillespie: Lastly, with the above equations, you'll probably still have an issue with jittering around $V=0$ in a numerical simulation. Instead of using simply switching direction of force with the sign of velocity ($F_r*sign(V)$), try multiplying the force by $tahn(beta V)$ instead, to smooth out the transition ($beta$ is a parameter to control how sharp the transition is).

[ 1]Thomas, D. Gillespie. "Fundamentals of vehicle dynamics." Society of Automotive Engineering Inc (1992): 168-193.

to calculate fulcrum based rears wheels my formula : f²(w²divide by unit decimal digits) derive : V = mass gravitational force x psf vol : f²(w² x w¾) as value to minimal point to sling aerodinamic idea

time by ff (force G break) tq