The self-stabilising dynamics of bicycles

TL;DR

This paper analyzes the self-stabilizing dynamics of bicycles, explaining how lean and steering interactions contribute to stability during fast, upright riding, with a focus on oscillation frequency and gyroscopic effects.

Contribution

It provides a detailed analysis of the physical mechanisms behind bicycle stability, emphasizing the role of lean-induced turning and self-steering without relying on gyroscopic effects.

Findings

Derived the frequency of lean oscillations during riding

Showed that gyroscopic effects are negligible in stability

Explained how lean and steering interactions stabilize the bicycle

Abstract

We analyse the classical problem of the stability of bicycles when moving quickly and upright. Developing a lean causes the front wheel to turn thereby setting the bicycle instantaneously into circular motion. The centripetal force associated with the lean-dependent turning circle gives a restoring torque which corrects the lean. The force also helps self-steer the front wheel, ensuring the bicycle continues in an essentially straight path. We give the frequency of lean oscillations about the vertical executed during riding. As in the literature, we discuss the neglect of gyroscopic effects, which experiment suggests are negligible.