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Tyre characteristics and modelling 307
Despite the advantage of a simple parameter set the main limitations of the
model include:
(i) The model cannot represent combined cornering and braking or cornering
and driving.
(ii) Lateral force and aligning moment resulting from camber angle are
not modelled.
(iii) The variation in cornering stiffness at zero slip angle with tyre load is
not considered.
(iv) The offsets in lateral force or aligning moment at zero slip angle due
to conicity and ply steer are not represented.
In order to calculate the longitudinal and lateral forces it is first necessary
to understand how the Fiala tyre model determines a resultant friction coefficient
as a function of the comprehensive slip ratio S L as shown in
Figure 5.61. The comprehensive slip ratio S L is taken to be the resultant of
the longitudinal slip coefficient S and the lateral slip coefficient S :
2 2
S L
S S
(5.55)
The instantaneous value of the tyre to road friction coefficient can then
be obtained by linear interpolation:
0 S L ( 0 1 ) (5.56)
The value of obtained can now be used to obtain a critical value of longitudinal
slip ratio S*, beyond which the tyre is sliding:
Fz
S* 2C
s
(5.57)
Friction coeff.
0
1
0.0 S L 1.0 Slip
Fig. 5.61 Linear tyre to road friction model. (This material has been reproduced
from the Proceedings of the Institution of Mechanical Engineers, K1 Vol. 214
‘The modelling and simulation of vehicle handling. Part 3: tyre modelling’,
M.V. Blundell, page 13, by permission of the Council of the Institution of
Mechanical Engineers)