4569846498

Simulation output and interpretation 403
So it can be seen that above a limiting speed, given by
V
lowlimit
gL
(( )/ 2)( / 180)
i
o
(7.7)
it is the surface grip that determines the limiting yaw rate and hence path
curvature. For typical passenger cars, the region in which geometry dominates
steering behaviour is small – up to about 15 mph. This is the speed
that may be counted as ‘low’ and in which Figure 7.5 is a reasonable
description of the behaviour of the vehicle. For vehicles such taxis and
heavy goods vehicles, the low speed region is of more importance simply
because these vehicles make more low speed, minimum radius manoeuvres.
However, they rarely perform these manoeuvres at speeds exceeding walking
pace and so the yaw rates remain low.
The steer angles required to avoid scrubbing at the inner and outer road
wheels, o and i are:
L
⎛180⎞
o
( R 0.5 t)
⎝ ⎠
(7.8)
L
⎛180⎞
i
( R 0.5 t)
⎝ ⎠
(7.9)
The angle of a notional ‘average’ wheel on the vehicle centre line, , is the
‘Ackermann’ angle – the approximate form is in common usage:
LR
⎛180⎞
L 180
( 0.25
2
R t ) ⎝ ⎠ ≈ ⎛ ⎞
R ⎝ ⎠
(7.10)
In 1817, Rudolph Ackermann patented geometry similar to this as an
improvement over a steered axle as was common on horse-drawn vehicles.
That the geometry we today call ‘Ackermann’ was in fact a modification
proposed by the Frenchman Charles Jeantaud in 1878 has been lost in the
mists of time. Some measure of how accurately the steering geometry corresponds
to the Ackermann/Jeantaud description is often quoted although
rarely defined. The authors use a description as given in Figure 7.7, which
in turn uses the simplified form of equation (7.10).
The Ackermann/Jeantaud angles are calculated as given in equations (7.8)
and (7.9). These are compared with the angles actually achieved by the
front wheels. A fraction of the compensation is expressed for the outer
wheel using mean for the mean of the actual angles:
Ackermann fraction
o
_ actual − mean
L/ ( 180/ )( L/ ) 0.5 t (180/ )
[ [ mean ]]
mean
(7.11)
This is the quantity graphed in Figure 7.7 as ‘% Ackermann’. The values
shown (around 40%) are typical for road cars. There exists some confusion
over the significance of Ackermann geometry. For ride and handling work,