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THE LAST WORD

Water stonesHow do pebbles skim on water? Neither medium seems especially elastic, so how do the stones bounce?

n 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’s 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.

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.

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’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 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 HolroydCambridge, UK

This week’s questionsTalk The TalkAt what age do regional accents stick with the speaker? My cousin

moved from Newcastle, in north-east England, to London, in the south, when he was 5. He spoke with a north-eastern accent before he moved, but now there is no trace of it. He speaks like a Londoner. Yet my sister moved to London to go to university aged 19, and she has lived there for 12 years now, but still has her original north-eastern accent. So at what age does this process of accent-change stop happening? And why?David HughesSouth Shields, Tyne and Wear, UK

P(ale) imiTaTionWhy does alcohol-free beer taste so different, and generally nowhere near as pleasant, as ordinary beer? Is it purely the presence or lack of alcohol? I’m not convinced that it is, because I added some neutral alcohol spirit to an alcohol-free lager we have here in the Netherlands to make it up to the strength of ordinary beer. My friends and I can report that it tasted absolutely foul.

So what else is missing from alcohol-free beer that makes it taste so different?Anton ShawDelft, The Netherlands

cheesed offWhy are soft cheeses, like Brie and Camembert, runny? How does their manufacture differ from hard cheeses such as cheddar and comté?Dorothy HarkerMelton Mowbray, Leicestershire, UK

“at each impact the stone loses some of its kinetic energy, which is dissipated in the water’s ripples”

“some ships capsized after taking on water through open gun ports positioned too close to the waterline”

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