Why can you ride a bicycle?

Most of us have learned this skill in our childhood and use it quite often in our everyday live. Some even claim that it is impossible to forget once you have learned it. But scientists are still trying to understand how it works exactly. This mysterious skill is the ability to ride a bike. As we all know it takes some training and balance to keep a bike upright. Especially at low speeds the rider has to adjust the front wheel frequently to prevent herself from falling. At higher velocities considerably less effort has to be devoted to keeping the bike stable and even hands-off riding is possible. Indeed, above a certain speed even a riderless bike remains upright for a considerable amount of time.

The theoretical study of the bicycle mechanics is almost as old as the bicycle itself and and the model of Whipple [1], developed in 1899, is still in use today. Over the years the question has attracted some of the great physicists of their time and it was Sommerfeld who first gave an explanation for the stability of a bicycle [2]. According to this theory a bicycle is stabilized by the so called gyroscopic effect. This stabilizing effect is a result of precession: If the bike starts to fall to one side or another, while its front wheel is spinning, the wheel starts to precess, putting the bike on a curve that counteracts the initial imbalance.

Driven by the lack of experimental data on the subject D. Jones started a quest in the 1960s to construct an unrideable bike [3]. The obvious first step was to construct a bicycle with no gyroscopic effect. This bike was unable to remain stable without a rider, but was rather easy to ride. In his next step he described the caster effect, by which the bike can lower its center of mass when turning the front wheel if the steering geometry satisfies certain criteria [3]. This allowed Jones to build a nearly unridable bike and a bike with a much higher stability than usual bikes. Although disappointed that he could not construct a truly unridable bike Jones speculated that the main stabilizing forces for bicycles were identified.

This confidence was shaken only recently when a team from the University of Delft revised Sommerfelds original calculations and managed to build a bicycle without gyroscopic and caster forces, that is nonetheless stable [4]. They could also show that one can build bikes with caster and/or gyroscopic effect, that are not stable.

This leaves us without any clear physical picture of the effects that stabilize a bicycle in general. Other research also shows that the contribution of each effect to the overall stability depends on the rider [5], so that there might not be a universal answer. Or can one find the answer by treating Whipples model in its entirety as has not been done yet? Is it even necessary for the front wheel to steer, to achieve stability?

[1] F. J. W. Whipple, Quarterly Journal of Pure and Applied Mathematics 30: 312 (1899)

[2] F. Klein, A. Sommerfeld, ?ber die Theorie des Kreisels (Teubner, Leipzig),1910.

[3] D. E. H. Jones, Physics Today 23, 34 (1970)

[4] J. D. G. Kooijman et al. , Science 332, 339 (2011)

[5] P.A. Cleary, P. Mohazzabi, Eur. J. Phys. 32, 1293 (2011)

Stephan Koehler