Game Development Reference
In-Depth Information
When you turn the steering wheel in a car, the tires produce a centripetal force toward
the center of the curve via friction with the surface of the road. It follows that the max‐
imum static frictional force between the tires and the road must exceed the required
centripetal force. Mathematically, this takes on the following inequality:
µ s N > mv 2 /r
Centripetal acceleration is the square of the tangential velocity, v , divided by the radius
of the turn, r . This multiplied by mass of the vehicle, m , gives the force required to make
a turn. The available force is the static coefficient of friction times the normal force, N .
Rewriting this formula, we can develop a simplified maximum cornering speed as fol‐
lows:
v limit < μ N m
If this speed is exceeded, the cornering force will exceed the static coefficient of friction
and the tires will begin to slide. It may be tempting to replace the normal force, N , with
the weight of the vehicle (mass times gravity) and cancel out the mass of the car, but the
normal force may not always be simplified as such, as we'll discuss in a moment. Also,
in real life, the weight of a vehicle is rarely evenly distributed among all four tires and
is definitely not when the car is acceleration or decelerating. In general, acceleration
causes a weight shift to the aft tires, and deceleration causes weight to shift to the forward
tires. This is important because, depending on where the weight is, the front or back
tires will tend to have less available friction. If one or the other sets of tires begins to
slide, the car will either understeer or oversteer (see Figure 17-1 ).
Figure 17-1. Understeer on right, oversteer on left