skipping stones

And when we came to that place where the little ships, drawn up on an oaken framework, were lying at rest supported above the (risk of) ground-rot, we saw some boys eagerly gesticulating as they played at throwing shells into the sea. This play is: To choose a shell from the shore, rubbed and made smooth by the tossing of the waves; to take hold of the shell in a horizontal position with the fingers; to whiff it along sloping and as low down as possible upon the waves, that when thrown it may either skim the back of the wave, or may swim as it glides along with a smooth impulse, or may spring up as it cleaves the top of the waves, and rise as if lifted up with repeated springs. That boy claimed to be conqueror whose shell both went out furthest, and leaped up most frequently.

Minucius Felix, an early Latin Christian apologist, observing Roman children play about 1700 years ago. (The Octavius 3.5-3.6, a.d.166?)

_~ ~ ^~ ~ _~ ~ ^~ ~Ducks and Drakes (England)~ _~ ~ ^~ ~ _~ ~ ^~

^~ ~ _~ ~ ^~ ~ _~ Stone skiffing (Ireland)~ ^~ ~ _~ ~ ^~ ~ _~ ~ ^~ ~ _~

~ ^~ ~ _~ ~ ^~ ~ _~ ~ ^~ ~Ricochet (France) _~ ~ ^~ ~ _~ ~ ^~ ~ _~ ~ ^~

^~ ~ _~ ~ ^~ ~ _~ ~Smutting (Denmark--go figure...)~ ^~ ~ _~ ~ ^~ ~ _~

"This is the one!"

The child scampers to the edge of the water, raises her arm up while bending her body, head close to the ground. Suddenly she flicks a rapidly spinning stone down towards the water, which then skips off the water, arcs upward then eases back down, again skipping...and again...and again....

"A sevener! I got a sevener--beat that!"

For the less competitive among us, however, skipping stones relaxes the soul--there is a humility to finding the perfect stone, only to cast it away and watch it playfully arc over waves, then sink...gone. Children pick it up easily. Drop a stone on the water, it sinks. Throw it hard at the water, and it bounces.

• Mostest

This is the one recognized by the Guinness Book of World Records. See below for the official rules--if you can break 38, you can be famous!

• Longest

This requires a slightly lowered trajectory angle--the idea is to get the stone to skip at an arc of about 45 degrees, allowing for great distance in a single skip. Alas, a great initial skip often results in a rough splash landing. The stones often curve as they arc, with a fine mist spinning off the rock--aesthetically pleasing, though the Guinness folks value quantity over quality.

• Heaviest

Big fun! Pick up the biggest flat rock you can possibly hope to get to spin, and launch. It is possible to get rocks of 5 to 10 pounds to skip. These rocks tend to plow through the waves like overweight labradors. They rarely truly skip--the rocks tend to sludge across the top of the water before sinking.*

1. The record is for the greatest number of skips made by a stone thrown by someone horizontally across water. One 'skip' is a forward movement of a stone over the water which sets off a visible series of concentric circles, MINUS either the first or the last of the circles.
2. The stone must be natural and not made specially for the attempt, and neither can it be smoothed down in any way.
3. No part of the person's body should touch the water during the throw and until the stone stops skipping.
4. Any attempts must be made in the presence of adjudicators approved by the International Stone Skipping Federation, the address of which is: PO Box 189, Driftwood, Texas, 78619, USA.
5. The attempt must be documented on film or videotape in such a manner that the entire skip may be viewed from start to finish in one continuous camera shot, and with a quality allowing for slow motion verification and count of each skip. The current (1995) record is: 38 skips

I grew up in the city, where there is no water.

In my apartment complex's courtyard, rainwater collected in the depressions in the concrete. After a large enough rain, there would be a pool of water some ten feet across to skip stones in.

I learned my physics from Andy Griffith. Stone-skipping in the country, under trees. Across lakes with tire swings, after trails where you could catch frogs. I did not see a frog until I moved to the desert. Paradoxically, the desert is full of amphibians. Drive at night around the otherwise arid dips in the valleys, full of brush, and you will hear frogs like the hum of a television. Animals here have a heightened talent for finding what they need. But — back to the slow philosophy of Andy Griffith — I wanted to live in the country, and do country things. So I made do by digging for bugs, and skipping stones.

All of the children in the apartment building congregated each day in the garden, picking leaves, rooting for insects. After the rain, we would gather around the puddles and skip stones. We all wanted to be country.

People have been skipping stones for thousands of years. I have said many times before that the basic principles of physics are enough to occupy and elighten any child. Of course, we had only ten feet of skipping space, so when we competed we competed for short, fast skips. Ever skipped a stone three times in an expanse of water the size of a small bedroom? It involves a lot of spin, and a thin, flat stone. Find something shaped like a penny, and you're ready for urban stoneskipping. To this day, my wrists are thin, and strong — ideal.

Skipping Stones is a multicultural children's magazine, printed on recycled paper with soy ink. It is published bimonthly during the school year. Those who were in elementary school at its inception are today finishing off credits for a Bachelor's — Skipping Stones has been around for fifteen years.

The magazine encourages learning new languages and embracing unknown cultures. As its website¹ says:

In Skipping Stones, you will find stories, articles and photos from all over the world: Native American folktales, photos by kids in India and the Ukraine, letters and drawings from South Africa ... and Lithuania, cartoons from China... Non-English writings are accompanied by English translations to encourage the learning of other languages.

Skipping Stones has been honored with the 1995 EdPress Golden Shoestring Award, the 1993 EdPress Distinguished Achievement Award and the 1989 Parent's Choice Award. More recently, it's earned the NAME Award from the National Association for Multicultural Education, the Positive Notes Award from the Earth Island Journal. In January, 2003, editor Arun Toké was honored by The Writer magazine with their 2002 Writer Award.

The physics of stoneskipping are simple, but complex. In common sense, it's simple — move something flat over water fast enough and straight enough, the water pushes back, and you have a skip. It's when you start playing with numbers that things get complex.

Today, the world record stands at 40 skips. Count to forty out loud. One too three four five and so on. Forty is a hell of a lot. Kurt Steiner tossed a rock across a Pennsylvania river in 2002 and made history.

If you're a physicist, the forces involved in stone skipping are child's play. The conversion of momentum. Common sense. It's the same reason we can water-ski: water pushes back. The force with which water pushes back is represented by pressure from the water itself multiplied by the surface area of the stone. Numerically, that's

ρU²S

Where ρ is the water's density, U is the stone's velocity, and S is the size of the area in contact with the water. Bigger surface area, higher velocity: more upward pressure. It's why you want flat, light stones.

Scientists skip stones in labs and measure every movement. They have found that this childhood game is a mind-bogglingly complex dance of hydrodynamics, elasticity and capillarity. Apply the equation above to some relaxed field-testing, assuming that the stone's movement is balanced — this is why you spin — and you'll find that there exists a minimum velocity at which any stone will, well, skip. Moving below that velocity, the stone will briefly skim across the surface of the water and sink. Skipping softball-sized rocks produces exactly that result: you'd need a strong arm to get up enough velocity to overcome the mass of the stone and get it bounding.

But wait! That equation doesn't explain everything!

You can't forget inertia. Simply, inertia is calculated thus:

mass × length × time^-2

Inertia is resistance to change in movement. You need spin, maintained by inertia, to keep the load balanced — otherwise, things get all out of harmony and you end up with your rock tumbling for a skip and sinking to oblivion.

Apply this principle to your average rock, and balance your equation against the upward lift principle outlined above, and you end up with

T = (MR/ρS)^-½/U. *

to define the interval between collisions between stone and water.

As stones skip across the water, they do not slow down. Successive photography in laboratory tests has confirmed this: the space interval between skips remains constant. What diminishes is the angle at which the stone deflects from the water. Each time the stone makes contact, it displaces more water on the way down than on the way up: trampolines are guilty of the same principle. You get less out of the bouncing surface than you put into it.

Eventually, the angle of deflection diminishes to nothing, and the stone surfs and sinks.

So, there's more to it than surface area, velocity, and water density. If you've skipped even a single stone, you know that more than half the sport of stoneskipping is in the angle of your throw.

The magic angle is 20 °. When you throw, you try to duplicate this angle. Stoneskipping is an act of patience and exactitude.

French scientists constructed a stone-skipping machine: a catapault that launched and spun stones. They did this because machines are more consistent than tiring arms.

The team, headed by University of Lyon physics professor Lydéric Bocquet, skipped stones at every imaginable angle. One imagines that, now and then, smooth rocks launched with a flick of wrists did not make their way into the recordings. But the result? Stones thrown at 20° had more chance of rebound.

rootbeer277 adds that the effect of spin in keeping the stone flat is due to the gyroscopic effect, and other tidbits.

¹ http://www.skippingstones.org/

* The Mystery of the Skipping Stone

Skipping Stones
http://www.skippingstones.org/

National Geographic
http://news.nationalgeographic.com/news/2004/01/0107_040108_stoneskipping.html

Physics Web
http://physicsweb.org/articles/world/19/2/6/1