Tire dynamics. Grip & load transfer.
Fit a tire curve to synthetic measurements, then explore the load transfer that changes how much each axle can do.
Linear at first.
Then it saturates.
Fy = D sin(C atan(Bα − E(Bα − atan Bα)))D = μFz. The synthetic data uses B = 10, C = 1.4 and E = −0.5 with deterministic noise. These are invented demonstration parameters, not regression coefficients from team tire data.
The load moves forward.
For an illustrative 300 kg car with driver, a 2.06 m wheelbase and 48% static front weight, braking transfers ΔF = m a h / L from the rear axle to the front.
Requested deceleration is below the μg ceiling of this simple flat-road model.
One contact patch.
A shared force budget.
Braking and cornering compete for the same tire grip. This simplified circle shows the total-force limit Fx² + Fy² ≤ (μFz)². Real tires have load sensitivity and a more complicated combined-slip envelope.
Try reducing the controller’s grip ceiling ↗What you’re seeing.
My work: MATLAB multibody simulation with a tire model derived by regression from tire data. The original dataset and coefficients are not available in this portfolio. This experiment uses synthetic measurements to show the fitting process.
Limits: the displayed lateral curve assumes pure slip, constant load and no camber or temperature effects. The load-transfer calculation is quasi-static and ignores suspension pitch, aerodynamics and road inclination. A low residual on synthetic data validates the fit to this dataset, not a real tire.
Educational reconstructions of ideas from my work. Demo results are computed here; they are not team test results.