Game Development Reference
Here d s is the skidding distance, g the acceleration due to gravity, µ the coefficient of
friction between the tires and road, V the initial speed of the car, and φ the inclination
of the roadway (where a positive angle means uphill and a negative angle means down‐
hill). Note that this equation does not take into account any aerodynamic drag that will
help slow the car down.
The coefficient of friction will vary depending on the condition of the tires and surface
of the road, but for rubber on pavement the dynamic friction coefficient is typically
around 0.4, while the static coefficient is around 0.55.
When calculating the actual frictional force between the tire and road, say in a real-time
simulation, you'll use the same formula that we showed you in Chapter 3 :
F f = µ W
Here F f is the friction force applied to each tire, assuming it's not rolling, and W is the
weight supported by each tire. If you assume that all tires are identical, then you can use
the total weight of the car in the preceding formula to determine the total friction force
applied to all tires.
When you turn the steering wheel of a car, the front wheels exert a side force such that
the car starts to turn. In terms of Euler angles, this would be yaw, although Euler angles
aren't usually used in discussions about turning cars. Even if the car's speed is constant,
it experiences acceleration due to the fact that its velocity vector has changed direction.
Remember, acceleration is the time rate of change in velocity, which has both magnitude
For a car to maintain its curved path, there must be a centripetal force (“center seeking”
in Greek) that acts on the car. When riding in a turning car, you feel an apparent
centrifugal acceleration, or force directed away from the center of the turn. This accel‐
eration is really a result of inertia , the tendency of your body and the car to continue on
their original path, and is not a real force acting on the car or your body. The real force
is the centripetal force, and without it your car would continue on its straight path and
not along the curve.
One of the most important aspects of racing is taking turns as fast as possible but without
losing control. The longer you can wait to decelerate for the turn, and the sooner you
can start accelerating again, the higher your average speed will be. It is interesting to
note that when people ride in racecars, what really surprises them isn't the acceleration
but the massive decelerations they can create through braking forces. A Formula One
car regularly experiences decelerations of 4g, with 5-6g being the extreme value for
certain race courses. Most road-legal sports cars can achieve about 1g of braking force.
This allows the racecars to maintain speed until just entering the corner.