Simulation
F1 Suspension and Lap Time Simulation at Spa
A 17-DOF F1 vehicle model with full 3D suspension kinematics and drivetrain coupling, used for minimum lap time simulation at Spa-Francorchamps with 40,000 optimization variables across 2000 track segments.
Links & Resources
Model Extension
The vehicle model used in previous lap time simulations had 3 degrees of freedom. This project extends it to 17. The new model includes 6 DOFs for spatial chassis motion — lateral, longitudinal, vertical, roll, pitch and yaw — plus 2 DOFs per wheel for vertical suspension travel and wheel spin (8 total), and 3 DOFs for the rotational dynamics of the ICE, gearbox and final drive. The drivetrain DOFs couple to the chassis through rear wheel spin dynamics and the reaction forces at the engine mounts and gearbox casing.
Suspension Kinematics
Following a published methodology for double wishbone suspension with pushrod actuators, a full 3D kinematics model was constructed including heave springs, anti-roll bar, and anti-squat/anti-dive geometry. From this model, a 1D lumped-parameter approximation compatible with the 17-DOF vehicle model is extracted algebraically. Vertical wheel displacements are linked to camber angles, which in turn affect tyre forces through Pacejka's magic formula. This simplification sacrifices some accuracy but keeps simulation times compatible with the outer optimization loop.
Track: Spa-Francorchamps
The circuit was discretized into 2000 segments. Each segment carries 17 state variables plus 3 control variables — throttle/brake, steering angle, and gear selection — yielding 40,000 optimization variables per lap. The optimizer resolves gear selection, active aerodynamic settings (treated as constant downforce and drag coefficients in this model), and the coupled suspension-tyre-drivetrain dynamics simultaneously.
One interaction that makes it into the animation only subtly: the coupling between gear shifts and vehicle dynamics. The torque interruption during upshifts, the engine braking characteristic during downshifts, and the load transfer through the drivetrain are all resolved by the model. Identifying this effect in the visualization is a reasonable test of whether the animation conveys the physics.
What Is Not Included
Aerodynamic roll and yaw sensitivity are not modelled — downforce and drag coefficients are fixed scalars. Tyre temperature dynamics are excluded. These are the natural extensions that would improve fidelity in a more comprehensive tool, and that motivate revisiting the aerodynamic side of the problem.