Brake dynamometer + scale-model road, same simulated test
Each run is simulated once at 2000 steps per second, then played back on the brake tester (front) and the 1:5 model road (back) from the same data. The rider brakes at the painted line and at the same moment tries to swerve around a rock 9 m further on.
A tyre can push on the road with at most μ·N: the friction coefficient times the load pressing it down. On dry asphalt μ ≈ 0.85, so a tyre carrying 600 N can deliver about 510 N — in any direction, but only once.
Braking (along the wheel) and steering (sideways) share that one budget. Picture a circle of radius μ·N: the force arrow can point anywhere inside it. Spend most of it on braking and only a sliver is left for turning:
The console's round display shows this live for the front tyre.
Grip depends on how much the tyre slips: κ = (v − ω·r) / v. At κ ≈ 0.1 (the tyre turns 10 % slower than the road) friction peaks. Beyond that it falls, and at κ = 1 — a locked wheel — the tyre simply slides, with only 75–85 % of peak grip. A sliding tyre's force always points straight against its own sliding direction, so turning the bars changes nothing: there is no sideways grip left to steer with.
A bicycle stays up because the rider constantly steers the front wheel under the centre of mass. Lock the front and that tool is gone: the bike runs straight ahead and any small lean grows like an inverted pendulum (h·φ̈ = g·sinφ − ay·cosφ) until it falls. On dry asphalt something worse happens first: see point 6.
Braking shifts weight forward: Nf = m(g·lr + a·h)/L, Nr = m(g·lf − a·h)/L. The harder you stop, the lighter the rear gets — so the rear alone can only manage about 0.2–0.25 g on dry roads, a stopping distance two to three times longer. The front still rolls, so you can steer, but the sliding rear has no sideways grip: steer hard and it steps out.
With the centre of mass 1.0 m high and 0.55 m behind the front contact, the rear lifts once deceleration exceeds g·lf/h ≈ 0.55 g. Dry asphalt offers 0.85 g, so a hard-locked front pitches the bike over its front wheel. That's why the best dry stops on a bike are limited by tipping, not by grip.
The ABS watches wheel slip. When κ passes the peak (or the rear is about to lift) it dumps brake pressure, lets the wheel spin back up, then re-applies — about 10 times per second (watch the strip chart). The tyre hovers near peak grip instead of sliding, so the bike stops about as short as physics allows and the tyre keeps sideways grip for balance and steering. This lab's ABS is lean-aware (as modern IMU systems are): when the bike leans it leaves part of the friction circle for the turn. It can't create grip — on ice or with too little room you still hit the rock — but you hit it upright.
All the kinetic energy the front brake removes ends up as heat in a 120 g steel rotor: ΔT = W / (m·c) with c = 500 J/(kg·K). A 50 km/h stop is ~8.7 kJ in total — repeat a few and the rotor climbs past 300 °C. The glow colour ramp is exaggerated so you can see it from across the room: real steel only starts to glow visibly around 500 °C. It cools with a two-minute time constant.
| Rider + bike | m = 90 kg, wheelbase L = 1.00 m, CoM height h = 1.00 m, CoM→front contact lf = 0.55 m |
|---|---|
| Wheel | r = 0.34 m, I = 0.1 kg·m², peak slip ≈ 0.10–0.12 on asphalt, 0.3 on gravel |
| Surfaces (peak μ) | Dry 0.85 · Wet 0.55 · Gravel 0.45 · Ice 0.10 — each with its own Pacejka slip curve, sliding ≈ 0.75–0.86 × peak |
| Brakes | pressure rise 0.10 s; "lock" = 1.6× the torque the tyre could ever take; ABS ≈ 10 Hz |
| Rotor | 0.12 kg steel, c = 500 J/(kg·K) |
| Simulation | 2 kHz fixed step: wheel spin, combined-slip tyres with camber thrust, load transfer, pitch, lean (inverted pendulum), single-track yaw, a rider who balances by steering and plans a 1 m lane change |
| Test | rock (r = 0.3 m) 9 m past the brake line, rider aims 1 m to the left |
| 1 2 3 | Front lock · Rear lock · ABS | B / Space | Brake (run the test again) |
| G | Next grip | [ ] | Speed −/+ 5 km/h |
| V | Next view | X | Exploded view on/off |
| WASD | Fly (Shift = faster) | Q E | Turn left / right |
| C | Cinematic camera cuts | R | Reset view |
| N | Labels on/off | / | Hide / show UI |
| Ctrl/⌘+' | Render tuning | I / Esc | This panel |
Mouse: drag to orbit, right-drag to pan, scroll to zoom. Click the tyre to brake again, the drum to change the surface, the padlock or ABS ring to change the brake mode, and drag the console knobs to set speed and grip.