Football and mathematics: the amazing Magnus effect

Inflating the soccer ball makes it look like a sphere. To be a good approximation of the sphere, a priori the ideal would have been to use a regular polyhedron with as many faces as possible, that is to say the icosahedron which has twenty faces.

The closest to a sphere is the icosahedron. Unfortunately, even inflated, its spikes would make its rebounds random. The idea is to cut off the annoying ends. We get the truncated icosahedron. It is made up of 12 pentagons and 20 hexagons.

We thus obtain the soccer ball. It is this angular profile that allows it to catch the air, whatever its degree of wear and whatever the climatic conditions.

A soccer ball is not a perfect sphere, which accentuates the effects. © Herve LehningDR

The Magnus effect in football

An effect is obtained by rotating the ball on itself. This effect was scientifically studied by Heinrich Magnus (1802-1870), which is why it is called the Magnus effect. Here is its mechanism.

As the balloon spins, it carries the air with it, all the better for being irregular. This movement of rotation causes a difference in pressure between the two sides of the ball which, as a result, is offset to the side with the lowest pressure. Depending on the kick of the ball, several different effects can be produced.

To cut a ball, just brush it up and down, causing it to rotate. The range of its trajectory is reduced and it bounces less high. The reverse movement has the opposite effect, although it is more difficult to achieve. Finally, you can brush the ball on the side which gives it amazing effects.

As the air is thinner at altitude, the effects are reduced there. This can cause surprises to players. Thus, during the 1986 World Cup in Mexico, at 2,600 meters above sea level, Michel Platini missed a decisive free kick, probably because he had not taken this difference into account.