Both MF variants are completed with a non-linear first order transient force lagging approach. With the kind of non-linearity used, it is taken into account that the decrease in contact forces might take place faster than a respective increase. This effect introduces a certain frequency-dependency of the mean tire force decrease, if wheel load variations apply.
Mathematically, the non-linear tire lag is described by the following non-linear first order differential equation, used for side force, longitudinal force, and aligning torque:
The following parameters and signals are used here:
| • |  is the constant relaxation length |
| • |  is the time dependent rolling speed |
| • |  is the constant upper bound for the resulting time constant |
| • |  is a reduction factor, describing the relation between time constant for force increase and time constant for force decrease |
| • |   is the stationary value of the respective force or torque (longitudinal force, side force, or aligning torque, respectively) |
| • |  is the resulting transient value of this force or torque |
See Also:
Modeling Approach
