I'm a games programmer, trying to write a simple car physics simulation. I'm aware that a car travelling in a straight line will exert a traction force that drives it forwards (by turning the wheels and pushing back against the ground), and that the main forces that act against this acceleration are aerodynamic drag and rolling resistance. But I can't seem to find a sensible way of calculating the rolling resistance for a given vehicle.
This page here claims that
$F_{rr} = C_{rr} * v$
That is, the force is proportional to a rolling resistance coefficient multiplied by the velocity. In my tests, this seems wrong, and the page itself (and the sources it cites) admit that they're on shaky ground in terms of explaining or proving that formula.
This page can't make up its mind. For most of the page it says that
$F_{rr} = C_{rr} * W$
That is, the force is equal to a coefficient multiplied by the weight ($mg$) of the vehicle - i.e. the force is the same regardless of velocity. It even provides a table of coefficients for different circumstances. But if the force is constant, won't a car in neutral with the engine off be accelerated backwards by this force? What is rolling resistance at velocity 0?
Then, for a bit of that page it claims that velocity is a factor in calculating the coefficient:
The rolling coefficients for pneumatic tyres on dry roads can be calculated as
$c = 0.005 + 1/p (0.01 + 0.0095(v/100)^2)$
where $c$ = rolling coefficient
$p$ = tyre pressure (bar)
$v$ = velocity (km/h)
This makes no attempt to explain what all those "magic numbers" mean, and still produces a coefficient of ~0.0088, which in a 1500 kg car would yield a force of 129 N whilst the car was standing still. That can't be right...
So, which is right? Given basic information about a vehicle (mass, velocity, information about the wheels and the surface they're rolling over), and ignoring aerodynamic drag, what's a sensible way to come up with a broadly plausible rolling resistance?
No comments:
Post a Comment