Optimal tyre management of a formula one car

Optimal control calculations are used to study the effect of tyre wear on race car performance. This is achieved by solving a minimum lap time optimal control problem over multiple laps using a dynamical model of a Formula One car. A previously developed thermodynamic model is enhanced by adding an additional state for the carcass temperature of the tyres. The tyre grip is modelled as a function of the tyres' wear and temperature. Grip reduces when tyres get worn, or the tyres are not operated within their optimal temperature window. Overheating the tyres can accelerate wear, which in turn, degrades performance. The optimal control problem solver needs to 'manage' the state of tyres throughout a race (not just a single lap) to ensure that optimal race performance is achieved. At some point during a race a pit stop may be required to change worn tyres so that tyre grip can be restored. It is essential to understand the wear characteristics of various tyre compounds in order to determine the point when the time needed for a pit stop is justified in terms of subsequent racing performance.