  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.
