# The science of stone skipping

Which one of us, finding ourselves near a large body of calm water, has been able to resist the temptaion to indulge in the delightful activity of trying to skip stones across the surface? The number of skips that I am able to get before it sinks is three, maybe four. So it is a pleasure to see world champion Keisuke Hashimoto in acction. His wind up alone is thing of beauty. (Via Rusty Blazenhoff)

(To see the above, follow the link that the ‘video unavailable’ window provides.)

But he is still mortal and doesn’t always succeed.

[I]n February [2003], the American Journal of Physics published “a simplified description of the collisional process of the stone with water” by Lydéric Bocquet. Bocquet is a physicist at Claude Bernard Lyon University in Villeurbanne, France…. With each skip, gravity pulls the stone deeper under the surface, and the water exerts more drag on the stone. Eventually, the drag becomes so great that the stone can’t break free. A skipping stone spends 100 times longer in the air than it does on water, but air is 1,000 times less dense than water, so its effect on the flight is relatively minimal.

The key to a good skip, Bocquet says, lies in spinning the stone. On the water, a stone’s spin keeps it poised on its trailing edge, rather than somersaulting. In the air, spin provides stability, as with a Frisbee. If the thrower gets the stone off to a bad start, spin can bring it into better position before it hits the water.

Bocquet has developed a formula for estimating how many times a stone will skip based on spin and speed. He calculates, for instance, that for a stone to skip five times it has to spin five times per second; to skip 15 times (Bocquet’s personal record), it has to spin almost nine times per second. According to this formula, McGhee’s world record-setting throw was spinning nearly 14 times a second and moving at nearly 40 feet per second.

This article discusses the technique of the person who held the Guinness record as of 2003.

To achieve such results, McGhee starts by picking through piles of stones, turning each one over and feeling its weight. He sets the flattest-looking candidate in the crook of his pointer finger, curling his other fingers beneath it. Then he stands up straight, wrist cocked high above his head like a flamenco dancer with castanets. This stance used to be an oddity—most stone skippers crouched low to the water—but it’s now widely imitated. Although McGhee starts with the stone held high, he releases it at his side, as parallel to the water as possible. “The more parallel you throw it, the less energy it uses to try to fly right,” he says.

Stones that aren’t perfectly shaped, and ones that have a little heft, seem to work best. Waves and gusts of air can send a light, nicely rounded stone off course. “You’d have a hard time skipping a cracker,” McGhee says.

There is no question that the science is going to be extremely complicated because it involves non-linear hydrodynamics involving two different media (air and water) and impulsive collisions.

Since this article was written in 2003, there may well have been improvements in the records and the scientific understanding of the skipping process since then.

1. Jazzlet says

Hmmm, I may give that high start technique a try. It can’t be worse than my existing stooping technique, with which I *may* have been known to hit the beach …

2. Mano Singham says

antaresrichard,

Thanks for that link that took me down memory lane! I had seen that film when I was a boy but completely forgotten it because those films were utterly forgettable. But my friends and I were suckers for the cheesy Hercules, Jason, and other mythic hero films of that era and saw pretty much every one.

3. Rob Grigjanis says

antaresrichard @2: Ha, that dates me. I immediately guessed the film without looking. Nigel Green as Hercules, the year before he played the colour sergeant in Zulu.

4. pjabardo says

There is this old soviet book on dimensional analysis that deals with this phenomenon: Similarity and dimensional methods in mechanics by Sedov. Real nice read.

5. Rob Grigjanis says

pjabardo @6: It would be great to have a post on the power of dimensional analysis in general: from simple harmonic oscillators to setting bounds on proton decay (hint, hint, Mano?).

6. says

There was a stream not far from our house when I was a kid. It had cut through an area of slate and there was a reasonably sized pond area at one particular bend where the water slowed, spread out and calmed. It was the perfect location to skip stones as there were mounds of flat, smooth pieces of slate to skip. The trick was to find ones that were just the right size (small enough to grip between the fingers and thumb), very smooth and as flat and circular as can be. We would use a side throw with tons of spin. Very low to the ground for the launch, too. A good skip was at least 5 but we routinely got more, although I doubt we got into the double digits. The one thing I noticed back then was that the distances between skips always shortened (unless the stone just happened to hit a ripple on the water at just the right time). Consequently, after the first 2 or 3 skips you knew if it was going to be a good one.

I had no idea that one could be a “world champion” at such things. Perhaps my career would have diverged considerably had I known back then. Champion stone skipper. Ah, the money, the fame, the adoring fans, the groupies, the jet-setting lifestyle. Could I have handled it all? I guess we’ll never know.

7. John Morales says

[Last paragraph of first quotation in OP is duplicated]

8. Mano Singham says

John @#9,

I have corrected it. Thanks!