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Car, road and brake
A wheel brakes best near the slip where tyre grip peaks. With ABS the valves keep each wheel near that slip; without it a hard stop locks the wheels, which brakes with only about 68 percent of the peak grip and removes steering.
Model checks
The science
What is modelled
Four contact patches carry loads that shift forward under braking. Each wheel has a spin equation driven by brake torque and the tyre force; the tyre force follows a peaked slip curve scaled by the friction coefficient of the road and the wheel load, and the lateral force uses what is left of a friction circle. The ABS valve releases pressure when slip exceeds a target band and reapplies it below.
Equations
- Slip
s = (v - ω R)/v; tractionμ N f(s)with a peaked curvef. - Friction circle:
Fy,max = √((μ N)² - Fx²). - Load transfer:
Nfront = m g af + m a h / L. - Stop:
d ≈ v² / (2 a),a = μ g f(s) + crr g.
Checks run in the page
- ABS stopping distance against the closed form.
- Locked-wheel distance with the 68 percent sliding grip.
- Wheel-lock condition by brake torque on each surface.
- Load transfer and the sum of the wheel loads.
Honest simplifications
A reduced-order, planar vehicle with a made-up smooth tyre curve, fixed brake torques, no suspension, no brake fade (temperature is for display only), a simple on-off ABS valve and a locked-to-peak grip ratio that is an assumption. Not a tyre or homologation model, and not a guide to real-road braking.
What to try
- Press Wet road, ABS braking and then Wet road, wheels locked, and compare the stopping distances and the skid marks.
- Press Black ice: the distance becomes several times longer whatever the car does.
- Press Dry, braking in a turn to see how braking uses up grip that cornering needs.