F1 Suspension and Lap Time Simulation at Spa

Engineering Question

Suspension geometry does far more than absorb bumps: on a Formula 1 car it governs how load transfers between tyres, how camber evolves through a corner, and how the aerodynamic surfaces are held relative to the airflow. Capturing these effects in a lap time simulation requires a vehicle model that resolves full three-dimensional chassis motion together with the drivetrain — and still runs fast enough for trajectory optimization.

Model and Assumptions

The car is represented by a 17-degree-of-freedom spatial model. Six DOFs describe the chassis — longitudinal, lateral and vertical translation plus roll, pitch and yaw; two DOFs per wheel capture vertical suspension travel and wheel spin (eight in total); and three DOFs describe the rotational dynamics of the internal combustion engine, gearbox and final drive. The drivetrain DOFs couple back to the chassis through the rear-wheel spin dynamics and the reaction forces at the engine mounts and gearbox casing.

A full 3D kinematics model of a double-wishbone suspension with pushrod actuators — including heave springs, anti-roll bar, and anti-squat/anti-dive geometry — was constructed, then reduced algebraically to a 1D lumped-parameter approximation compatible with the 17-DOF model. Vertical wheel displacements map to camber angles, which feed the tyre forces through Pacejka's magic formula. This reduction sacrifices some fidelity for speed, which is essential inside the outer optimization loop. Aerodynamics is treated with fixed downforce and drag coefficients; aerodynamic roll and yaw sensitivity and tyre temperature dynamics are not modelled, so the results are best read as a vehicle-dynamics study rather than a full race-engineering tool.

Spa-Francorchamps

The circuit was discretized into 2000 segments. Each segment carries 17 state variables and 3 control variables — throttle/brake, steering angle, and gear selection — giving 40,000 variables to optimize over a single lap. The optimizer resolves gear selection and the coupled suspension–tyre–drivetrain dynamics simultaneously.

Drivetrain–Vehicle Coupling

The most revealing behaviour sits at the interface between gearshifts and vehicle dynamics. The torque interruption during upshifts, the engine-braking characteristic during downshifts, and the resulting load transfer through the drivetrain are all resolved by the model. It is precisely this coupling — the way a discrete gearshift perturbs tyre loads and chassis attitude mid-corner — that a 3-DOF point-mass model cannot represent, and that justifies carrying all seventeen degrees of freedom through the optimization.