I am using the brush model for one reason.

off all the model that I read in several books about vehicle dynamic, it is the only one that has a nice mathematical derivation that can model accurately a tire in the linear range and drift apart when the tire reach the non linear range (mean the point at which start losing grip.

I learn this model from the book Motor Vehicle Dynamics by Giancarlo Genta.

Chapter 2 is dedicated to tires and then go to derive the mathematics for a brush tire approximation.

The brush model is only accurate within the linear range in which the tire operates but in return we get a model that is well defined over the entire linear range for both lateral and longitudinal slip combined.

This is something the Magic can't do.

The magic formula is better because it model the non linear behavior when a tire loses grip, but this is a fitting curve with no real theoretical foundation and even when using it the model is one dimensional, you still have to use empirical circle of friction projections.

you can get an explanation in this video

https://www.youtube.com/watch?v=We5iNzg6AAAcheck out his previews videos as well, this professor explain the theoretical derivation of the brush model in detail.

at about 34:10 he explains that the model only generate decouple longitudinal and lateral forces. these are good for what is called steady state studies, but not for a simulation.

this is why I prefer the brush analytical tire model because provide a combined effect even if it loses accuracy in the non lineal range.

People may interpret that as bad or poor, but this are trades engineers has to do, take for example that modeling of beam and columns for buildings. The model of Young is only acurate in a very small linear range of compression of elongation for material like still and concrete. but again engineers do not make buildings that are suppose to operate in the nom linear range because at that point you have a much bigger problems to worry about.

Similarly vehicle are designed to drive on the

linear range of the tires, even professional race car drivers drive cars on the limit of the linear range, because one you pass that point the tire yield less performance.

It is only people who like to drift, do tire burn out and tail spins, that put the tire in the non linear rage so that the can get different behavior between front and rear tires.

odly enough for what I want to do, the brush model is incapable to producing an in place tire burn out.

this is because the tire model the force in the linear range dos not decay, so when the tire is at a maximum spins the force do not became lower than when the tire is a maximum stress but not sliding.

so maybe after all the tuning and calibration is done I add a Pajecka model as an option.

but in any case the tire model is well encapsulated in a function, it can be updated by anyone with interest, for now I am more concern with a completing the vehicle model and cover a wide range of drive modes from realistic to arcade.