IOP Institute of Physics

# Topic of the Moment – Football

As the World Cup gets underway in Brazil, we look at some of the physics of the beautiful game.

Although footballers play using highly trained intuition rather than precise calculation, you can see physics in almost every aspect of the game.

An education resource produced by IOP even uses football themes to provide insight into physics topics – passing the ball forms the basis of discussions of trajectories and friction, while how to stay on your feet is used to explain the idea of centre of gravity.

And the goal-line technology introduced to minimise refereeing errors in the most important circumstances is clearly dependent on physics to function.

But one footballing situation particularly stands out as relevant to physicists: the free kick.

Since the goal is typically defended with a wall of players, scoring a goal means that the attacking player must bend the ball around that wall. Doing so takes advantage of a phenomenon known as the Magnus Effect, after Gustav Magnus who investigated it in 1852.

Striking the ball off-centre gives it a spin, which changes the airflow around the ball and creates a turbulent wake. The airflow is deflected in the direction of spin, giving the ball a horizontal force and resultant motion.

The amount of curvature in the ball’s path can also increase mid-flight. This happens when the ball slows enough that the airflow around it instantaneously changes from chaotic flow  to laminar flow. The air pressure on the ball, and therefore the drag it experiences, increases, slowing it down further and heightening the influence of the Magnus Effect. (In the absence of gravity, the ball would eventually produce a spiral flightpath.)

It’s a tough skill to get right – only about a tenth of direct free kicks in the English top flight find the back of the net. The structure of the ball and atmospheric disturbances within the stadium can have an effect.

But ultimately the amount of curvature produced mainly depends on the coefficient of friction between ball and boot, how far off-centre it’s struck, and its speed. So to bend it like Beckham, kick a dry ball at an angle – and belt it hard.

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