Cars and Motorcycles - Physics for Game Programmers - page 215

Gears and Wheel Torque
The torque applied to the wheels of a car determines its acceleration. In general, the torque
applied to the wheels is not the same as the engine torque because before the engine torque is
applied to the wheels it passes through a transmission . A typical transmission cross-section is
shown in Figure 8-5. You can see that a modern transmission is quite complicated, with a lot of
gears, shafts, and other strange-looking things.

Figure 8-5. A cross-section of a transmission (Photo courtesy of Daimler-Chrysler)

You might ask yourself, “Why bother with a transmission? Why not connect the torque
from the engine directly to the wheels?” A big reason for the existence of transmissions is
performance. In looking at Figure 8-2, when the engine turnover rate is low, the torque and
therefore acceleration is relatively low as well. In fact, if the engine was connected directly to
the wheels, it would take the Boxster S over 16 seconds to accelerate to 100 km/hr . That would
be pretty boring performance for a sports car.
Fortunately, the acceleration of a car can be greatly increased by using a transmission.
What the gears inside the transmission do is to change the angular velocity and torque transferred
from the engine. To see how this is done, consider the two gears shown in Figure 8-6. The
second gear has twice the diameter of the first gear, so for every revolution the second gear
makes, the first gear will make two. The second gear has half the angular velocity of the first
gear. However, the torque that the second gear can exert is twice that of the first gear.

d 1 2 d 1

Figure 8-6. Gears are used to change angular velocity and torque.

The gear ratio between two gears is the ratio of the gear diameters. In Figure 8-6, the gear
ratio between the second and first gears would be 2:1. Car transmissions will typically have
between three and six forward gears and one reverse gear. There is also an additional set of
gears between the transmission and the wheels. In many cars, this gearset is known as the
differential . The gear ratio of this final gearset is known as the final drive ratio .