Question

How can you manage to skip a flat stone over water? How can you increase the number of skips? Explain how this works and how it was used in WW2 in a squadron called the Dam Busters?

Answer 1

A French physicist has revealed the science behind a popular pastime called stone skipping. Lydéric Bocquet from the University of Lyon-I derived mathematical expressions for what happens when a stone is made to skim across a river or lake. He also derived a formula for the maximum number of times a stone is able to “skip” before it finally sinks (L Bocquet 2003 Am. J. Phys. 71 150)

Intuition tells us that the best stones for skipping are flat and circular, and that they should be thrown quickly. A stone should also be “flicked” to give it a spin and should hit the water at a small glancing angle.

Bocquet considered the situation for a flat, thin stone thrown over a perfectly uniform water surface. He found that the main factors that determine whether the stone sinks or skims are the mass of the stone, its angle with respect to the horizon, its angle with respect to the surface of the water, its spin rate and its horizontal velocity. He calculated that small angles combined with high spin rates are best.

According to Bocquet, a stone will only bounce if its initial velocity exceeds a certain value. If the stone is also spinning, this introduces a stabilizing torque that can maintain the initial angle at which it hits the water - which helps the stone bounce again.

The maximum number of bounces depends on the rate at which the stone decelerates - which is in turn directly related to its initial velocity. In principle, a stone could be made to bounce many times by increasing its initial velocity. In practice, however, the number of bounces are limited by the angular destabilization factor - which is independent of the initial velocity. This means that the all-important initial “flick” is crucial. Bocquet believes that his results agree well with observations such as the increase in the number of bounces at the end of a throw - known as “pitty-pat”.

Ultimately he hopes that his calculations will allow someone to break the world record of 38 bounces which, if Bocquet is right, is achieved by throwing the stone at 12 metres per second with an initial spin of 14 revolutions per second.