MATHEMATICS AND FOOTBALL

Fotball spectators often clap players who score form the corner or from another position a goal which the opponent’s placement can’t stop.

In this cases the ball moves on a trajectory which differs from the usual one by surprinsingly twisting.

How is this phenomenon explained? To be able to answer this question, we start from the proven by experience truth that a body which falls or it’s freely thrown, if during its moving it’s also spinning, then it won’t move on an ordinary trajectory but on a “false” one.

So, if the player wants to score on the “false” trajectory, he has to hit the ball in order that it would execute a rotating movement.

For the ball to rotate it mustn’t be hit centrally, but to the left or the right of its center, depending on the direction we want it to spin.

The odd trajectory of the spinning body was firstly explained in 1852,by the German physician Heinrich Gustav Magnus(1802-1870) and that’s why this phenomena was called “The Magnus Effect”

This way, the ball that spins is in contact with a certain quantity of air, which spinning produces a circulated current of air.

In the same time, the rotating ball executes a rectilinear motion and this way the air will move on the contrary.

The simple arrows represent the way of the movement of the air spinned by the ball and the double arrows represent the air movement in relative rest.

In the part noted with A(the right part of the ball),the ways of the movements of the two layers of air are opposite, so they get thinner and the resultant speed of the air will get smaller.

In the part noted with B(the left part of the ball),the ways of the movements of the two layers of air are the same, so they meet and the resultant speed of the air will get bigger.

Where the speed of the air is faster there appears a decrease of static pressure which results an absorption effect(according to a law introduced by the Swiss physician Daniel Bernaulli-1700-1782).As a result to the difference of pressure which forms between the right and the left side(between A and B),the ball moves sideways from the higher pressure to the lower one.

A similar phenomenon appears at the tennis game or table tennis game, when the partners play a game with “cut” or “twisted” balls. It is specified that bowling players know the phenomenon. Coming back to the football game, we must notice that scoring a goal form the corner involves knowing a few laws of physics too.