Game Development Reference
In-Depth Information
Next we compute the maximum frictional force from Equation (8.32). If the engine torque
force is less than the maximum frictional force, the engine torque force is used in the equations
of motion. If the engine torque force is greater than the maximum frictional force, then the
wheels are sliding, and the maximum frictional force should be used in the equations of motion.
The value of the coefficient of friction in Equation (8.32) depends on the condition of the
tires and the surface on which the car is driving. A bald tire will have a lower coefficient of friction
than will a tire with a normal tread. A tire will have a lower coefficient of friction on ice than it
will on dry pavement.
One final note about maximum tire frictional force is that it applies to the total accelera-
tion of the car. A car going around a curve will experience a centripetal acceleration. The total
acceleration of the car is equal to the square root of the sum of the squares of the centripetal
and straight-line acceleration of the car.
2
⎛⎞
v
2
a
=
a
2
+
⎜
⎝⎠
(8.35)
total
straightline
One conclusion from Equation (8.35) is that a car that is accelerating into a curve is more
likely to skid than a car traveling at a constant velocity around the same curve.
Driving Around Curves
Up to this point the discussion on the physics of cars has focused on the straight-line motion
of a car. Of course, cars can't drive in a straight line forever. At some point they need to turn or
drive around a curve. Modeling a car driving around a curve can be separated into two areas
depending on whether the car is performing a high-speed or low-speed turn.
We'll start with the subject of a car driving around a curve at low speeds. As you would
expect, modeling low-speed curves is easier than modeling high-speed curves because some
factors, such as centripetal acceleration, can be ignored. The wheels can be assumed to be
rolling without slipping. Consider the car shown in Figure 8-10. The front wheels of the car are
turned at an angle,
d
, such that the car is making a right turn. If the car is traveling at a constant
speed, it will drive in a circle of radius,
r
c
.
d
r
c
l
d
+
Figure 8-10.
A car making a turn at low speeds
