# Football Boomeranging? Is It Possible?

Michael Stevens from the great YouTube channel Vsauce investigates the question whether it’s possible to curve a ball so much that, instead of following the banana-like path of a curling cross, it travels along a circular trajectory before coming back to the player again. In other words, is it possible to “boomerang” a football?

But first, watch Michael’s video – after that, I’ll tell you what I don’t overly agree with.

(Cool video, right? 😉 )

But there’s one thing I don’t like about the video: It’s the explanation of the Magnus effect, which is the name for the physical effect that forces a ball on a curved trajectory.

In the video (at 1:10 mins), it seems that the air, which normally flows around an non-spinning ball, disappears on one side of the ball if it’s spinning and causes a higher air pressure on the other side. “More air = more pressure”, if you like.
But that’s not quite true, as the rest of this article should show! (Don’t be afraid – it might look more complicated than it really is.)

The football’s rotation results in different airflow speeds at the opposing sides of the ball. The air is slowed down at the side which moves in the “direction of travel” (= against the direction of the past-moving air), whereas the opposite happens on the other side of the ball: There, the air is dragged along the ball’s surface since the direction of motion of the air (relative to the ball) has the same direction as the velocity of the ball surface.

Well…I wouldn’t be talking physics here, if there weren’t some equation appropriate for our situation: Bernoulli’s equation in fluid dynamics will do. (This principle assumes various kinds of approximations like , for example, the incompressibility of air. This assumption isn’t quite correct, but we will ignore this, because the resulting error is neglegibly small.)
Here’s Bernoulli’s equation (in a simple version):

$\frac{v^2}{2}+\frac{p}{\rho}=\text{const.}$

The variables which are interesting for our purposes are the speed $v$ and the pressure $p$ of a fluid. To put it simply, we just can say “the sum of speed and pressure is constant”. (By this, we just overlook all the other things in the equation while simultaneously knowing that this doesn’t affect our train of thought.) This means: If the speed of a fluid increases, the pressure has to decrease.

Thus, due to the fast moving air on one side of the ball, the pressure decreases on this very side. At the same time, the pressure at the opposite side is comparatively high because the speed of the airflow is slower there. This is exactly what we call the Magnus effect! The ball is deflected towards the side of the ball which rotates against the ball’s direction of motion, because there’s a corresponding pressure gradient.

(This effect becomes also visible in a “Venturi meter” and you can also understand the principle of a perfume bottle by looking at this special kind of tube.)

However, Michael Stevens does fantastic videos – you should check out his channel! 🙂