Thermal Magic Formula Based Tire Model for Simulation use in Racing Applications

A new addition to the Magic Formula tire model is presented that will take thermal effects into account. A thermodynamic model is used to calculate the heat generation from the tire forces and hysteresis. An approximation of the tire surface temperature and force relationship is made with a non-linear function. Indoor tire testing data is used to fit the thermodynamic and grip modifying parameters. The proposed model has the advantage of using a temperature/grip coupling function that accounts for the initial rise and eventual fall off of grip with rising temperature that is typical for racing tires. This feature can make it especially useful for tuning a race car and training a driver for short, highly tire temperature dependent events like qualifying or autocross