Physics of skipping stones
What determines whether a flat stone thrown at a water surface will skip, and what throwing angle gives the most bounces?
History and references
Settled in 2004 by Christophe Clanet, Frederic Hersen, Lyderic Bocquet (CNRS / ENS Lyon).
Stone skipping is an ancient pastime, but the first rigorous physics treatment came from Lyderic Bocquet's 2003 American Journal of Physics analysis of the impact dynamics. The following year, Clanet, Hersen and Bocquet published controlled laboratory experiments in Nature using a stone-throwing machine, identifying a 'magic angle' of about 20 degrees between the stone and water at which the minimum impact speed for a successful bounce is lowest, and showing that spin stabilizes the stone's attack angle via gyroscopic precession, letting it skip repeatedly. Their result matched anecdotal folk wisdom about the best throwing technique and was later confirmed by 3D numerical simulations.
The playground game of stone skipping turns out to have a single optimal angle, discoverable with the same physics used for spacecraft reentry.
Explanations that circulated
- That any sufficiently flat, fast, spinning throw will skip regardless of angle; Clanet, Hersen & Bocquet showed there is a specific 'magic angle' (about 20 degrees between the stone and the water surface) below which a stone cannot rebound at all, no matter how fast or how much it spins.
References
- Secrets of successful stone-skipping, C. Clanet, F. Hersen, L. Bocquet, Nature, 2004
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