A simple mono-dimensional approach for lap time optimisation

Lap time minimisation methods have great relevance in the analysis of race tracks, and in the design and optimisation of race vehicles. Several lap time minimisation approaches have been proposed in the literature, which are computationally demanding because they need to either solve differential equations or to implement a forward-backward integration based on an apex-finding method. This paper proposes an alternative method, based on a mono-dimensional quasi-steady-state numerical approach. The proposed approach uses a simplified vehicle model accounting for combined tyre-road interactions, aerodynamic effects, and power limitations. The method exploits the knowledge of the curvature of the trajectory, which is worked out through a rigorous approach that allows for the use trajectories defined with respect to ageneric curve parameter and not necessarily the arc length. An iterative routine is implemented that exploits the vehicle dynamics, without solving differential equations or performing forward-backward integrations from the trajectory apexes. Simulations are carried out on three different tracks and are shown to be computationally efficient. Despite being intentionally simple, the proposed method allows to grasp key aspects of the problem, such as the effect of the combined tyre-road interactions on the acceleration profiles, and the effect of aerodynamic drag and downforce on the position of the braking point on the track and on the speed profile.