Bicycle Stability
Push a riderless bicycle to jogging speed and it balances itself: shove it sideways and it steers into the fall and recovers. This simulator integrates the linearized Whipple benchmark bicycle (Meijaard, Papadopoulos, Ruina & Schwab, 2007) — the standard model of bicycle dynamics, with lean and steer as the two degrees of freedom. Watch the rear view, the wandering path from above, and a strip chart of lean and steer angles. Sliders set the speed, the trail (how far the front contact patch sits behind the steering axis), the centre-of-mass height, and a toggle removes the wheels’ gyroscopic effect. A stability readout scans all speeds and reports the self-stable window — about 4.3 to 6.0 m/s for the benchmark — and a handlebar-nudge button demonstrates countersteering: the bike first leans opposite to the nudge, then carves that way.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Self-stability needs the front end to steer into the fall fast enough: gyroscopic torque from the front wheel and the caster action of trail both help, but the 2011 Science paper by Kooijman et al. showed neither is strictly necessary — mass distribution can do the job alone.
- Below the weave speed the bike oscillates itself over; above the capsize speed it leans over slowly. In between lies the self-stable window, and this simulator finds it by a Routh–Hurwitz scan of the benchmark equations.
- Countersteering is real and measurable: to turn left you first steer right, which drops the bike into a left lean — the nudge button shows the lean flipping sign against the steer input.
- Honest limits: the model is linear (valid for small lean and steer), has knife-edge wheels with no tyre slip, no rider control and no frame flex — the standard benchmark, not a full motorcycle simulator. Steer angles are drawn exaggerated for visibility.
- Runs 100% in your browser — simulations are computed locally on your device.
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