Optimal Control of Overtaking Trajectories Under Aerodynamic Wake Effects in Motorsport

This paper presents a simulation framework for analysing race car overtaking manoeuvres under aerodynamic wake effects using optimal control theory. The proposed formulation integrates wake-dependent aerodynamic disturbances into a spatial-domain optimal control problem, enabling simultaneous optimisation of racing line and control inputs. A planar vehicle model representative of a modern FIA Formula 3 car is employed and calibrated using real telemetry data obtained from Campos Racing. Wake effects are modelled as distance- and offset-dependent aerodynamic loss factors that influence drag, downforce, and aerodynamic balance of the following vehicle. The framework is implemented using the Dymos optimal control library and applied to single-car and two-car overtaking scenarios on a closed circuit. Simulation results demonstrate that wake effects significantly modify optimal braking points, corner entry trajectories, and corner-exit strategies. Moreover, we show that optimal overtaking requires deliberate lateral deviations from the wake core to recover downforce and traction. The study highlights the importance of incorporating aerodynamic interaction effects into trajectory optimisation when analysing performance-critical motorsport manoeuvres.