QUESTIONS OF SCIENCE

Intro: Neither medium seems especially elastic in nature, so how do the stones bounce on water? There are practical implications of the science, as this article reveals.

ONE

FOR the best results, a circular, flattish stone is best. It must be thrown so it is almost horizontal to the water’s surface, and also such that its trailing edge hits the water first. It is vital the action of the 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 the water, with the rest travelling through air, these forces still have an effect on its forward motion.

There is a force exerted by the water at right angles to the spinning stone’s surface. It acts at the trailing edge of the spinning stone – because this is where the impact begins – 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’s forward velocity somewhat.

There is also a force exerted by the water parallel to the stone’s surface, but this force is much smaller and so the stone’s 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.

The minimum initial speed required by a stone varies with its inclination to the horizontal. 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 slowest speed for skimming is 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’s 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.

Barnes Wallis’s famous bouncing bomb, created for the 1943 Dambusters raid on Germany in the Second World War, worked on the same principle. 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.

TWO

IN a paper published in the journal Nature, in 2004, the French physicist Lydéric Bocquet and his team of researchers revealed some of the secrets of successful stone skimming. They found that the optimum angle of attack is 20 degrees. So, even when the stone is thrown horizontally, the leading edge should be 20 degrees higher than the trailing edge. This maximises the number of jumps by limiting the contact time between the stone and the water, which is proportional to the energy dissipated.

The thrower also imparts spin to the pebble, providing a gyroscopic effect that stabilises its flight and preserves the original angle of attack when it bounces. In the absence of spin, the water would impart a torque (or turning force) on the stone and, because the trailing edge is the first to make contact with the water, this would tend to make it tumble.

The actual physics of stone skimming is not perfectly understood. However, the bounce could be understood as a result of the conservation of momentum and Newton’s third law: when the stone exerts a force on the water, the water exerts an equal and opposite force on the stone. This lifting force is proportional to the density of the water, the surface area that is wetted and the square of the forward speed of the stone. Also, the bow wave created ahead of the stone when it strikes the water might act like a water-ski jump – helping to launch the next hop. This minimises the contact time between the stone and the water, which in turn maximises the number of jumps.

Although ensuring the optimal angle of attack as the stone strikes the water, and imparting just enough spin to maintain stable flight are important, there are other factors. Selecting the correct size and shape of stone and having a fast throwing arm are examples.

Given that the urge to skim stones has been with us for thousands of years and the rules – getting the greatest distance or number of bounces – have remained unchanged since the ancient Greeks, perhaps this should become an Olympic sport. In the meantime, the current world record stands at 51 skips, set by Russell Byars in Pennsylvania on 19 July 2007.

. Science Book