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420 Multibody Systems Approach to Vehicle Dynamics
resulting from the averaging and the non-linearity of the tyre. Tyres with a
high load will not produce as much lateral force (in proportion to tyre
load) compared with other tyres on the vehicle.
More weight transfer at either end therefore reduces the total lateral
force produced by the tyres and causes that end to drift out of the turn.
It should be noted that this behaviour is true for all slip angles of interest;
at low slip angles, the cornering stiffness of the tyre is reduced non-linearly
with increasing load, promoting a larger slip angle at an axle with a
greater roll moment. At saturated slip angles, the peak lateral force is
reduced as a proportion of the vertical load, producing a lower coefficient
of friction for an axle with a greater roll moment. Thus mechanisms that
adjust sub-limit under- and oversteer also adjust departure plough and spin
behaviour.
Although substantially simplified, the preceding analysis helps with understanding
the essential mechanisms in play when a vehicle is cornering.
7.4 Transient effects
Vehicle dynamics would be a very simple field if the preceding text
described it entirely. However, the pneumatic tyres in use have some features
that add complication. The most significant of these is the need for
the tyres to have a slip angle in order to generate a lateral force. This can be
seen intuitively to lead to the need for a slip angle of the body as a whole
(Figure 7.26).
The need for a body slip angle gives rise to an additional yaw rate, rotating
the body to the correct slip angle, for a brief period near the start of
any manoeuvre. There is also a corresponding yaw rate reduction at the
end of a manoeuvre required to bring the vehicle back to its trimmed,
straight-ahead state. These variations in yaw rate are acutely remarked
by even the least skilled driver and greatly influence the emotional reaction
of the driver to the car – although the driver might not consciously
recognize it.
A vehicle that rotates slowly to give the required body slip angle feels sluggish
and unresponsive; a vehicle that overshoots and oscillates feels lively
and poorly controlled. Subjectively, these two states might be described as
Body slip
angle, β
Forward velocity, u
Yaw velocity,
Lateral velocity, v
Rear axle slip
angle, r
Front axle slip
angle, f
Fig. 7.26
Pneumatic tyres give rise to the need for a body slip angle