A Simple Mono-Dimensional Approach for Lap Time Optimisation

Lenzo, Basilio; Rossi, Valerio · 2020 · Crossref

DOI: 10.3390/app10041498

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Summary

This paper addresses the computational inefficiency of existing lap time minimization methods in race vehicle dynamics. Traditional approaches, such as optimal control problems (OCP) and quasi-steady-state (QSS) methods, are computationally demanding because they require solving differential equations or performing forward–backward integrations from trajectory apexes. The authors propose a simplified, mono-dimensional QSS numerical approach that significantly reduces computational cost while capturing key physical constraints, including combined tyre–road interactions, aerodynamic effects, and engine power limitations. The method models the vehicle as a mass point moving along a predefined trajectory defined by a generic curve parameter, rather than strictly by arc length. A rigorous mathematical framework is developed to calculate trajectory curvature directly from this generic parameter, avoiding complex integrations. The optimization algorithm iteratively determines the optimal driver behavior (acceleration and braking) by checking if the vehicle speed satisfies the lateral acceleration limits imposed by the friction ellipse and aerodynamic downforce. The model accounts for speed-dependent grip limits and power constraints, identifying the "critical radius" of curvature where grip no longer limits speed. Simulations were conducted using MATLAB on three track configurations: circles (radii of 100 m and 200 m), an ellipse (semi-axes of 100 m and 150 m), and a straight-line hairpin bend. The study utilized a high-performance vehicle model with specific parameters for mass, drag, downforce, and power. Results demonstrated that the proposed method is computationally efficient, with calculation times of only a few seconds, significantly lower than the actual lap times and far faster than traditional OCP or QSS methods. The simulations successfully captured the interplay between longitudinal and lateral accelerations, showing how aerodynamic downforce increases maximum achievable speeds and how power limits restrict acceleration at higher velocities. The significance of this work lies in providing a fast, accurate tool for lap time optimization that is suitable for rapid design phase decisions and potential trackside usage, unlike slower existing methods. The approach allows engineers to analyze the effects of vehicle setup, such as aerodynamic balance and power delivery, on lap times without the heavy computational burden of solving differential equations. By simplifying the trajectory parameterization and avoiding apex-based integrations, the method offers a practical alternative for analyzing race track performance and optimizing vehicle dynamics.

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• braking response