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408 Multibody Systems Approach to Vehicle Dynamics
where
road wheel angle (deg)
K understeer gradient (deg/g)
A y lateral acceleration (g)
L wheelbase (m)
R radius (m)
Note that the use of understeer gradient in degrees/g can be expressed at
either the axle or the handwheel if appropriate regard is taken of the steering
reduction ratio. For vehicle dynamicists it is easy to declare that the
only measure of consequence is the axle steer; however, this is to ignore the
subjective importance of handwheel angle to the operator of the vehicle.
Note also that this parameter K is not to be confused with the more common
‘stability factor’ K as developed by Milliken and Segel and used later
in this chapter.
Olley makes an important distinction between what he calls the primary
effects on the car affecting the tyre slip angles and secondary effects affecting
handwheel angles and body attitudes, which are acutely sensed by the
operator (Milliken and Milliken, 2001). Perhaps the biggest source of difficulty
between practical and theoretical vehicle dynamicists is that the
large modifiers of the primary vehicle dynamics are generally fixed by the
time the practical camp get their hands on a vehicle and so are not considered
by them; the secondary modifiers used to great effect to deliver the required
subjective behaviour of the vehicle for its marketplace are frequently overlooked
by the theoretical camp as being ‘small modifiers’ despite being
important to the emotional reaction of the driver to the vehicle. For this
entirely prosaic reason it is common that members of each fraternity understand
little of what goes on in the other.
7.3.3 Some further discussion of vehicles in curved path
Below the limiting yaw rate it is tempting to think that for a real vehicle the
behaviour is largely geometric in nature (Figure 7.13). This is essentially a
repeat of the Ackermann diagram in Figure 7.5 and equation (7.5).
The geometric yaw rate is achieved by some notional vehicle that may be
thought of as running on ‘blade’ wheels on indestructible ice – no sideslip
V
V mean
geom
L
180
L
Fig. 7.13
Geometric yaw rate expectations