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Free Kick and Physics

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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