How do pebbles skim on water? Neither medium seems especially elastic, so how do the stones bounce?
鈥� For the best results when skimming stones you need a flattish stone. The closer it is to circular, the better. It must be thrown so it is almost horizontal to the water鈥檚 surface, and also such that its trailing edge hits the water first. It is vital the action of throwing imparts spin to the stone.
Any solid body moving through a liquid experiences forces that oppose its motion. These forces are proportional to the cross-sectional area of the body and the square of its speed. Although only a part of a skipping stone is actually moving through water, with the rest travelling through air, these forces still have an effect on its forward motion.
Advertisement
There is a force exerted by the water at right angles to the spinning stone鈥檚 surface. It acts at the trailing edge of the spinning stone 鈥� because this is where the impact begins 鈥� and tends to turn the stone towards the horizontal. Because of its spin, though, the stone behaves like a gyroscope and refuses to change its orientation. Nevertheless, this force reduces the stone鈥檚 forward velocity somewhat.
There is also a force exerted by the water parallel to the stone鈥檚 surface, but this force is much smaller and so the stone鈥檚 velocity is barely changed by it on impact with the water. The net effect of these forces is that the stone flies from the water in a parabolic arc until it hits the water again and the whole process is repeated.
At each impact, the stone loses some of its kinetic energy, which is dissipated in the ripples that are created in the water. And as its velocity is gradually reduced, the impacts become closer together until the energy dissipated is greater than that lost in the impact and the stone sinks.
鈥淎t each impact the stone loses some of its kinetic energy, which is dissipated in the water鈥檚 ripples鈥�
Experiments show that skimming will not occur if the angle at which the flat surface of the stone hits the water is more than 45 degrees to the horizontal.
The minimum initial speed required by a stone varies with its inclination to the horizontal. The slowest speed for skimming being about 2.5 metres per second, when the inclination is about 20 degrees.
The fact that the water itself is not elastic is immaterial, but it is important that it gives way to the stone on impact.
Stones can also be skimmed on wet sand, and even on cloth-covered boards. In such cases, however, there is little or no give in the surface and the frictional grip at impact is sufficient to change the direction of the stone鈥檚 motion and also cause the stone to overcome the gyroscopic effect.
Skimming stones on water is an age-old pastime. The gunners of naval sailing ships worked out that it could be used to increase the range of cannonballs. These could be made to skip along the surface of the sea and hole enemy vessels near their waterline. However, to do this the cannon itself had to be near the sea surface, which meant the firing vessel needed perilously low ports. Indeed, some ships capsized after taking on water through those open ports. With cannonballs, the spin required by a skimming stone was unnecessary as their spherical symmetry precluded any gyroscopic effects.
鈥淪ome ships capsized after taking on water through open gun ports positioned too close to the waterline鈥�
famous bouncing bomb, created for the 1943 Dambusters raid on Germany in the second world war, worked on the same principal. He had to use cylindrical bombs, though, so he figured out he could ensure their stability by giving them spin about a horizontal axis at right angles to their direction of motion on the water.
Richard Holroyd, Cambridge, UK