Game Development Reference
In-Depth Information
So what the transmission does is to (generally) increase the torque that comes out of the
engine at the cost of reducing the gear turnover rate. To determine the acceleration of the car,
we need the torque applied to the wheels. The wheel torque, T w , is equal to the engine torque,
T e , multiplied by the gear ratio, g k , of whatever gear the car is in and the final drive ratio, G , of
the car.
TTgG
=
(8.10)
we
k
Using Equation (8.10), the equation for the acceleration for the car shown in Figure 8-1 can
be modified in terms of the engine torque and gear ratios.
TgG
2
1
CvA
r
ek
a
=
m
g
cos
q
g
sin
q
D
(8.11)
r
rm
2
m
w
Another effect of the transmission gears is to change the angular velocity of the wheel rela-
tive to the turnover rate of the engine. The relationship between the engine turnover rate, Ω e ,
and wheel angular velocity, w w , becomes the following:
2
60
p
Ω
w
=
e
(8.12)
w
gG
The “60” term in Equation (8.12) is to convert the minutes in rpm to seconds. If the tires
roll on the ground without slipping, the translational velocity of the car, v , can be related to the
angular velocity of the wheel, and therefore to the engine turnover rate.
r
2
60
p
Ω
vr
=
w
=
w
e
(8.13)
ww
gG
k
In looking at Equations (8.11) and (8.13), we can make the following observations about
gear and final drive ratios:
The higher the gear ratio, the higher the acceleration and the lower the car velocity for a
given rpm .
Increasing the final drive ratio increases the acceleration for all gears but likewise
decreases the car velocity for a given rpm for all gears.
As an example of the gear ratios for a typical sports car, Table 8-1 shows the gear ratios for
the six forward gears of the 2004 Porsche Boxster S. The final drive ratio for the car is 3.44.
Table 8-1. Porsche Boxster S Gear Ratios
Gear
Gear Ratio
First
3.82
Second
2.20
Third
1.52
Fourth
1.22
Fifth
1.02
Sixth
0.84
 
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