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February 02, 2006
Hopping stones
When I was a kid our family used to live only a few kilometers away from the River Rhine. At the weekends my father would often take me for a walk along the river. One of our favourite pastimes was to let pebbles hop over the water surface as often as possible. It is obviously something that has always fascinated people for this kind of game is already described by Homer. As far as I know, the world record is held by J. Coleman-McGhee who let his pebble hop 38 times.
Everyone who ever tried this out himself knows that the shape of the pebble and a few other things are important for success. Ideally, the pebble should be disc-like. It must be thrown in such a way that its flat side is parallel to the water surface and that it rotates around an axis perpendicular to its surface. Its hitting angle with the surface must be quite small. Therefore it's best to bend down close to the water when throwing the pebble. I think I finally got the hang of it after only a few hundreds of pebbles.
Trust a team of scientist to turn this into a scientific experiment. They created a 'model pebble', an aluminium disc (diameter: 2.5 cm, thickness: 2.75 mm), and a device that would throw the discs into the water. Two parameters could be varied: the velocity of the disc on leaving the throwing device (2.5 - 5 m/s) and the hitting angle between disc and water surface (15 - 45 degree). The spin of the disc was kept constant at 65 revolutions per second.
The scienstists found out that they achieved the best results, i. e. maximum number of jumps, if the times of contact between disc and water surface were very short, less than 0.1 sec in the experiments, because then only a small amount of energy would be lost by friction. Furthermore, the disc needed an initial velocity of at least 2.5 m/s. For the shortest contact times the disc had to hit the water at an angle of 20 degrees. At 45 degrees it wouldn't hop at all.
What is really fascinating about these experiments is what actually happens when the disc or pebble hits the water. Pictures taken with a high-speed camera revealed that the pebble will hit the water with its rear edge and glide through the water for a short way because it is stabilised by its rotation (around the axis perpendicular to its surface). Thereby a little wave is formed in front of the pebble. If the velocity of the pebble is still high enough it will eventually catch up with it and use it as a ramp for its next jump. The pebble will of course lose energy upon each new contact with the water surface, the jumps will become shorter and shorter and then its velocity will be too low to catch up with its 'bow wave' at all.
The physical principles in this harmless bit of fun were also used in warfare to destroy coastal fortifications. Bombs would be given a rotation around their longitudinal axis when dropping them into the coastal waters. On hitting the surface they would jump a few times just like a pebble. If timed correctly the last jump would bring them close to the dam where they would travel straight through the water being stabilised by their rotational movement and eventually hit and destroy the dam itself.
It is a bit of a comfort that nowadays these principles can be put to better use, though. A spaceship goes through a similar series of jumps on re-entering the atmosphere thereby losing a great deal of energy and heat. Studying pebbles might eventually lead to bit of optimisation in that area as well.
Posted by Mausi at February 2, 2006 09:37 PM
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