[ODE] RE: Calculating slip angle for a vehicle

[Ruud van Gaal]

>  I think I just had an epiphany. Most of the car physics I've 
> read up on talks about calculating the side slip angle first 
> then multiplying by the steerangle for the front wheels etc 
> etc.... However I was wondering what's wrong with this approach:
> 
> In car body space, the default heading of the wheel is 
> (1,0,0), pointing forward in the x direction ie not turned at 
> all. So if the wheel is turned with some heating H(x,y,z), 
> and you know that the velocity of the vehicle is V(Vx,Vy,Vz), 
> then won't the dot product of the two give you the cos of the 
> slip angle, and then you just plug that into acos(angle).

Not quite. The vehicle may be rotating itself, this makes for a different
wheel velocity for each wheel (if the car is changing heading, the left
wheel will move forward faster than the right, or vice versa).
Also, slip angle is based on the surface. So you have to project the wheel
vectors to the surface (using the surface normal and the wheel side vector
for example). Those are a bunch of dot products as well.
The steering angle can be ignored up to the end, where you just add it to
the slip angle. BTW in the end you don't end up calculating the slip angle
directly, since at low speed it will jitter due the floating point having
limited precision.

It's definitely not trivial in the end. :)

Cheers,
Ruud