Game Development Reference
In-Depth Information
The value of the coefficient of rolling friction tends to be significantly lower than the coef-
ficients of static or kinetic friction for the same object. For car tires, the coefficient of rolling
friction ranges from 0.01 to 0.02. 2
Computing Acceleration and Velocity
In order to create a car simulation, it is necessary to determine the acceleration and velocity of
the car at any point in time. The starting point for this analysis is Equation (8.11). In the preceding
sections, values were presented for the coefficient of rolling friction and drag coefficient of a car.
If the slope angle, frontal area, and air density are known, the only unknown quantity in
Equation (8.11) is the wheel torque, T w .
According to Equation (8.10), the wheel torque is the product of the engine torque, T e , the
current gear ratio, g k , and the final drive ratio, G . The engine torque, T e , can be obtained from
the torque curve of the engine. Torque curve data is usually presented either as a plot or as a
table of numbers. For game programming purposes, the torque curve needs to be expressed as
a mathematical expression. The easiest way to mathematically model a torque curve is with a
series of straight lines.
For example, the torque curve for the Boxster S as shown in Figure 8-2 can be approximated
by three straight lines. The first line extends from a torque value of 220 N-m at 1000 rpm up to
4600 rpm where the torque peaks at 309.2 N-m . A second line is drawn from 4600 rpm to the
redline value of 7200 rpm where the torque is approximately 227 N-m . Below 1000 rpm , the idle
speed of the engine, the torque will be assumed to be 220 N-m . The simplified torque curve is
shown in Figure 8-7.
Figure 8-7. Simplified torque curve for the Porsche Boxster S
 
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