Stone-skimming science
Skimming stones almost horizontally across water so that they skip as far as possible without sinking is a favourite pursuit of youngsters, though it appears to be a trivial way of passing the time. However, if the mechanics of the process are analysed, as they are by a group of three French scientists in a paper published in Nature for 1 January, there is more to the pursuit than meets the eye.
The writers point out that skimming stones across water has been popular
for thousands of years, the rules remaining unchanged since ancient Greek
times. The world record, set in 1992, is claimed to be 38 rebounds. By
studying the collision of a spinning disc with water the investigators
have discovered that for satisfactory results an angle of about 20 degrees
between the stone and the water surface yields the greatest number of
bounces.
Four parameters are involved in the skimming process. They are the translational
and spin velocities, the attack angle of the stone at the surface, and
the collision time. Rotation stabilises a thrown stone by a gyroscopic
effect. The lowest translational velocity for a rebound is delivered
at 20 degrees, and impacts at more than 40 degrees do not provoke rebound.
With a 20 degree impact angle the number of bounces that follow reaches
a maximum, since the amount of energy dissipated at the point of collision
is directly proportional to the collision time.
The experiments that resulted in these conclusions were performed using
an aluminium disc of radius 2.5cm and thickness 2.75mm. Of course, in
real life the stones picked for skimming vary greatly in size and shape.
Sometimes they are flat, sometimes triangular in section. Moreover, if
you try skimming them in the sea there are the wavelets to take into
account.
There is far more, indeed, in stone skimming than a mathematical model.
If you are at the side of the pond, or on the margin of the beach, first
select your stone. Its dimensions and shape will make all the difference
in the world to how many bounces you can achieve, whatever science you
bring to back up your effort. And sometimes nature offers little choice
in this respect.
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