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404 Multibody Systems Approach to Vehicle Dynamics
Steer angle (degrees)
50
40
30
20
10
0
10
20
30
40
50
RH wheel
LH wheel
Ackermann right
Ackermann left
50 40 30 20 10 0 10 20 30 40 50
Average steer angle ve right (degrees)
100
% Ackermann
80
RH wheel
60
40
20
0
20
50 40 30 20 10 0 10 20 30 40 50
Mean steer angle ve right (degrees)
Fig. 7.7
Steering geometry in comparison with Ackermann/Jeantaud geometry
the significance is sometimes overstated. Considering Figure 7.5, a turn at
50 mph (22 ms 1 ) road speed at 0.4g lateral acceleration may be calculated
as producing a yaw rate of 10.2 degrees/second. For a 2.7 m wheelbase
vehicle, this requires a mean steer angle of 1.26 degrees. The radius of turn is
123 m and so the Jeantaud modification gives 1.25018 degrees on the inner
wheel and 1.26552 degrees on the outer wheel – an included angle of 0.015
degrees. For a typical cornering stiffness of 1500 N/degree, this gives
a lateral force variation of 23 N between 0% Ackermann and 100%
Ackermann. The lateral forces to achieve 0.4g at 50 mph are over 5900 N
for a typical 1500 kg vehicle, so the Ackermann effect amounts for lateral
forces of some 0.4% of the total – a small modifier on the vehicle as a whole.
The level of Ackermann effect does come into play at parking speeds, however.
Typically, there is some inclination of the vehicle’s steering axis when
viewed from the front and side of the vehicle. These inclinations are known
as castor and steer axis inclination (SAI), or kingpin inclination (KPI)
respectively and are shown in Figure 7.8. Together with the offsets at
ground level between the geometric centre of the wheel, these inclinations
have the effect of moving the inboard wheel down and the outboard wheel
up. Figure 7.9 shows the inboard wheel being moved down as it goes onto
back lock. Given the constraint of the ground, this has the effect of imposing
a roll moment on the vehicle that is reacted by the front and rear suspensions
in series (Figure 7.10). The loading of the vehicle wheels becomes
asymmetric.
This asymmetry is of the order of 10 N in a typical family saloon and is of
little consequence. However, in a more stiffly sprung vehicle if the steering