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.

Bicycle Stability (2D)

Side view: roll dynamics with fork trail and gyroscopic wheel torques — see speed, trail, and ω = v/R vs lean.

About this model

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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Bicycle Stability (2D)

About this model

How it works

Key equations

Frequently asked questions

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How it works

Key equations

Frequently asked questions