Bicycle Stability (2D)
This simulator integrates a small-angle roll equation for a side-view bicycle sketch: gravity applies an overturning torque about the rear contact, while a trail-like term (∝ v²) models how steering geometry couples lean to a restoring moment, and an optional gyroscopic term scales with wheel spin Iω² ∝ (v/R)². It is a teaching cartoon, not a full Whipple–Carvallo model.
Who it's for: Intro mechanics and conceptual vehicle dynamics; comparing when gyroscopic effects matter versus geometric trail.
Key terms
- caster / trail
- gyroscopic moment
- roll angle
- critical speed
- small-angle stability
How it works
Side-view caricature of bicycle roll: gravity tends to increase lean, while fork trail (caster) and spinning wheels add restoring torques that grow with speed. Real bicycles also weave and depend on rider input; this model isolates two textbook ingredients so you can see why a minimum speed helps and how trail and gyroscopic terms scale.
Key equations
Iφ̈ = mgh sin φ − β(v) v² φ − k_g I_w (v/R)² φ − cφ̇ (trail + gyro, small φ)
ω = v/R; larger trail and faster wheels raise the restoring stiffness at a given speed.
Frequently asked questions
- Is this enough to explain a real bicycle staying up?
- No. Real bicycles involve steer angle, frame compliance, tire slip, and rider control. Experiments show many bicycles can be self-stable in a speed window even with gyroscopic effects reduced, so trail and mass distribution matter a lot; this lab isolates two common textbook ingredients.
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