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410 Multibody Systems Approach to Vehicle Dynamics
Lateral acceleration gain
(m/s/s/deg axle steer)
14
12
10
8
6
4
2
30 degrees
20 degrees
10 degrees
5 degrees
2 degrees
1 degree
0.5 degree
Using the preceding relationship for geometric yaw rate gain, a geometric
lateral acceleration gain (AyG geom ) can be deduced for the geometric vehicle
in the region where
AyG
0
0 20 40 60 80 100
geom
A
y
mean
geom
mean
V
Vehicle speed (mph)
Fig. 7.15 Lateral acceleration gains for an idealized vehicle with
Newtonian friction
2
V L
(7.15)
At high speeds it can be seen that axle steer inputs of much in excess of half
a degree cause the available friction to saturate and that to retain proportional
control, the driver must keep inputs below this level. For this reason,
quite high reduction ratios are generally used in steering gears to give a reasonable
level of input sensitivity at the handwheel. For a European passenger
car, a reduction ratio of around 16–18:1 is typical (16 degrees of handwheel
giving 1 degree of axle steer), meaning that at the highest speeds shown in
Figures 7.14 and 7.15 handwheel inputs of 10–20 degrees are enough to
saturate the vehicle with respect to the available friction in a high grip environment.
For vehicles travelling faster – for example, on unrestricted autobahns
or competition vehicles – it can be seen that the overall steering ratio
is of importance in order not to have the vehicle overly sensitive to driver
inputs. There is, however, a trend among vehicle manufacturers to fit
numerically lower steering ratios over time – compare a 1966 Ford Cortina
at 23.5:1 with its current cousin the Focus at 17.5:1 – to promote a perception
of agility. This fashion will require the adoption of more adventurous
variable steering ratios (for example, as promoted by Bishop Technologies
or as implemented by BMW and ZF in the 2003 5 series ‘Active Front
Steer’ system) in order to retain sensitivity at high speeds. In low-grip environments,
the handwheel inputs needed to saturate the vehicle at speed are
tiny, scaling down with coefficient of friction, .
The range of lateral acceleration gains, from 0.6 ms 2 /degree at 20 mph to
12.9 ms 2 /degree at 100 mph, is quite a wide range to ask the driver to
accommodate. When high speed road systems lack curves of any kind there
is no feedback information to allow the driver to adapt and so extremely
straight designs of roads are unhelpful in this respect. Thus it is often true
that normal drivers get into difficulty when faced with an emergency evasive