

Stone skimming formula adds new spin19:00 16 October 02 The idle weekend pastime of skimming stones on a lake has been taken apart and reduced to a mathematical formula by a French physicist. Everyone knows a stone bounces best on water if it is round and flat, and spun towards the water as fast as possible. Some enthusiasts even travel to international stoneskimming competitions, like world champion Jerdone ColemanMcGhee, who made a stone bounce 38 times on Blanco River, Texas, in 1992. Intuitively, a flat stone works best because a relatively large part of its surface strikes the water, so there is more bounce. Inspired by his eightyearold son, physicist Lydéric Bocquet of Lyon University in France wanted to find out more. So he tinkered with some simple equations describing a stone bouncing on water in terms of its radius, speed and spin, and taking account of gravity and the water's drag. The equations showed that the faster a spinning stone is traveling, the more times it will bounce. So no surprise there. To bounce at least once without sinking, Bocquet found the stone needs to be traveling at a minimum speed of about 1 kilometer per hour. And the equations also backed his hunch that spin is important because it keeps the stone fairly flat from one bounce to the next. The spin has a gyroscopic effect, preventing the stone from tipping and falling sideways into the water. World record formTo match the world record of 38 bounces using a 10centimeterwide stone, Bocquet predicts it would have to be traveling at about 40 kilometers per hour and spinning at 14 revolutions a second.He adds that drilling lots of small pits in the stone would probably help, by reducing water drag in the same way that dimples on a golf ball reduce air drag. "Although I suppose that would be cheating," says Bocquet, whose report will appear in the American Journal of Physics. He and his team at Lyon hope to design a motorized "catapult" that can throw stones onto a lake with a precise speed and spin, to test if the predictions stand up. Bocquet adds that he is probably just rediscovering a piece of history. British engineer Barnes Wallis must have done the same sort of maths and experiments when he was designing his famous bouncing bombs for the Dambusters squadron during the Second World War.  Hazel Muir 
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Tim Stouse
