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Simulation output and interpretation 409
of the wheels is possible. It is important for vehicle dynamicists to remember
that the overwhelming majority of the driving population genuinely believe
this is the way in which their vehicles function. For many typical drivers,
the belief exists that the tyres are little miniature ‘rails’ that the vehicle carries
around with itself to ‘lay tracks’ as it goes along.
In order to express something useful from the infinite number of combinations
of speed and steering angle that exist, the notion of a ‘gain’ becomes
helpful – an output divided by an input. Thus for a purely geometric vehicle,
the Yaw Rate Gain (YRG) could be expressed as
YRG
geom
mean
V
L
(7.13)
This may be recognized as describing the low speed region of Figure 7.6.
The higher speed region, even with a simplistic Newtonian friction model,
can be seen to have a non-linear YRG characteristic (Figure 7.14) since it is
possible to turn the front wheels to an angle that corresponds to a yaw rate
greater than that which the vehicle can achieve. The similarity between
Figures 7.6 and 7.14 should be apparent to the reader.
As previously noted, when a vehicle yaws less than expected, the term
‘understeer’ is used – the response of the vehicle is less than (‘under’) what
might have been expected. When a vehicle yaws more than expected, the
term ‘oversteer’ is used – the response of the vehicle exceeds (is ‘over’)
what might have been expected. So far only mechanisms for generating
understeer have been discussed. Remaining with the Newtonian friction to
describe the behaviour of the tyres, one further fundamental point is worth
establishing. For a vehicle travelling in a circular path, forward speed, V,
yaw rate, , and lateral (centripetal) acceleration, A y , are related with
Ay V
(7.14)
18
Yaw rate gain (deg/sec/deg axle steer)
16
30 degrees
14
20 degrees
10 degrees
12
5 degrees
2 degrees
10
1 degree
8
0.5 degree
6
4
2
0
0 20 40 60 80 100
Vehicle speed (mph)
Fig. 7.14
Yaw rate gains for an idealized vehicle with Newtonian friction