Minimum Lap Time Simulation: F1 at Monaco

Engineering Question

How much of a Formula 1 lap can a deliberately compact model capture — and what does it reveal when cars from different eras are placed on the same track? Minimum lap time simulation answers both: it finds the fastest way around a circuit subject to the car's grip and power limits, and exposes the trade-offs a driver negotiates corner by corner.

Model and Assumptions

The vehicle is a 3-DOF formulation — a point mass with lateral and longitudinal tyre-force limits derived from a simplified Pacejka model. Finding the fastest lap is posed as a trajectory optimization problem: lap time is minimized as a nonlinear program, solved by direct collocation over a discretized representation of the track. Gear selection is omitted in this baseline version, keeping the focus on the trajectory and the tyre-limited acceleration envelope. The simulator was first built around the Circuit de Catalunya using Mercedes W12 data, for which accurate vehicle and track parameters were accessible. It was implemented in Python, with post-processing and animation in MATLAB.

Results

The GG-diagram — the envelope of simultaneously achievable longitudinal and lateral accelerations — provides a physically transparent link between the car's limits, the chosen driving line, and the resulting lap time. With Monaco data in hand, the model was used to resimulate Senna's 1988 qualifying lap in the McLaren MP4/4 and place it alongside Leclerc's 2024 Monaco qualifier on the same track model. Given the modest fidelity, the comparison is directional rather than quantitative, but the modern car's advantages in cornering and power delivery emerge clearly.

Significance

A 3-DOF model is intentionally minimal, yet it is enough to make the central mechanism of lap time — the interaction between tyre limits, driving line, and power delivery — physically legible. That transparency is what makes it a solid foundation: the same pipeline is the starting point for the higher-DOF vehicle models and detailed power-unit representations developed elsewhere in this portfolio.