The physics of bending it like Beckham

What are the physics behind the beautiful game?
05 June 2018

Interview with 

Hugh Hunt, Cambridge University, Ruth Fox, Cambridge United


What physics underlie the game of football? Georgia Mills teamed up with footballer, Ruth Fox and engineer, Hugh Hunt, to break down how to “bend it like Beckham”, and to investigate some unusual marble statues...

Ruth - It’s a statue to commemorate where the football rules were first written down I believe.

Georgia - I like this first rule: it’s 1848, the laws of the university football club. This club shall be called the University Football Club. It’s kind of like fight club, the first rule of football club is call it Football Club.

Cambridge has a lot of love for football then so we’re joined by engineer extraordinaire, Hugh Hunt, who’s going to tell us a bit about how physics comes into it.

Hugh - Well, football’s a great game, as we know, but a ball just doesn’t move in a straight line. I suppose if you’re out on the International Space Station it does. There’s aerodynamics, there’s spin, there’s bouncing, there’s all sorts of things and so balls in the air is really interesting.

Georgia - Now I’m thinking about a football game in space. But you’re going to tell me a little bit about how some of the physics works and Ruth is very kindly going to help us out with some demos, show us the skills because you and I, Hugh, are not so good at the actual football part.

Ruth has immediately began putting us all to shame.

Hugh - I’m lucky if I can kick a ball once.

Georgia - Hugh, you mentioned physics and football are related, so how do the two go hand in hand?

Hugh - The first thing I think is spin. And the very first thing we kind of know is if you’ve got a ball and you bounce it, if there’s some spin on the ball it’s going to move off in a different direction, so if you’re playing the game you’ve got to read the spin. If you see that the ball is spinning, you’ve got to know that it’s not just going to come straight to you, it’s going to do some different things.

Then if you’re playing the game you can put spin on to make it bounce into different directions but it moves through the air just like in tennis or cricket, you’ve got a spinning ball moving through the air that curves - bend it like Beckham we’ve all heard. You can curve the ball left and right, you can curve the ball up and down.

Georgia - Ruth, this is something you would do in a game?

Ruth - Yeah, absolutely. There’s a variety of different passes you can use: spinning is one of the ones I particularly do use. Sort of switching, playing and pinging it on the opposite wing is definitely something that I do, and free kicks as well. I always enjoy taking free kicks. You can completely make the goalkeeper go absolutely the wrong way, so yeah.

Georgia - Can you give me a little demo then? Can you bend it like Beckham for us now? Alright we’re backing up… here we go.

Beautiful spin and Hugh’s kicked it back. That was a beautiful demo. The ball definitely curved through the air. Hugh, how is that working?

Hugh - Well it’s interesting. I noticed as we were playing with that that there’s dew on the grass and as the ball gets wetter and heavier it behaves more differently. It’s harder when the ball is wet, is that right?

Ruth - Yeah. I think when it’s not pumped up great.

Georgia - That’s my fault. Sorry about that. I brought a half deflated ball.

Hugh - That’s interesting too because we think that a softer ball is easier because we don’t like to get hurt. But the professionals like to play with a really hard ball because when you’re kicking the ball, the ball squashes up, deforms a lot, and it’s really quite hard to control a ball that’s not round.

Georgia - When it’s spinning, to my mind something that’s round when it moves through the air, no matter what it does, it should go in a straight line because there’s no sort of corners. You know like a bird would use wings to direct itself, it’s just a ball. So how does the physics works that makes it turn around in the air?

Hugh - If you imagine, for the moment, that the ball is stationary and that the air is moving, so it’s like a wind tunnel experiment. So you put the ball in a certain place and spin it, what the air is going to do it’s going to be dragged over the top of the ball. Moving air around the ball, well you need forces to do that. And Newton’s third law of  motion that every action has an equal and opposite reaction, if there’s a forced required to move around the ball then there’s an equal and opposite force on the ball. So spinning the ball give you a sideways force. And you can spin it one way and you get a force to the left. The other way you get a force to the right, and then up and then down. I can demo that with this lightweight ball.

Georgia - You wouldn’t see this on a proper football pitch. This is a nice, very light, bouncy red ball.

Hugh - I can put some backspin on this ball and…

Georgia - So a slap to the ball out of the air.

Hugh - And it goes right over Ruth’s head.

Georgia - Yeah. It sort of went forward and then kind of stopped in mid air.

Hugh - If you try to do a pass from one side of the ground to the other, you want it to get there as quickly as possible, but you don’t want it to go out of play, so you want to dip it down so you put topspin on.

Georgia - So it’s the air around the ball being dragged by the movement of the ball spinning, which then exerts a force on the ball and changes its direction?

Hugh - That’s right. And it’s called the Magnus effect.

Georgia - Does the Magnus effect come into things off the football pitch?

Hugh - Oh well, absolutely. There’s a famous example of this back in 1943 when the Dambusters did their dambusters raid in Germany with the bouncing bombs. And Barnes Wallis put backspin onto the bouncing bombs to enable them to bounce on water, and it was all to do with Magnus effect.

Georgia - We mentioned this, I brought an woefully under inflated ball. So why does having more air in a ball mean it’s better on a football pitch?

Hugh - You want to have a ball that doesn’t lose much energy when you kick it. And a soft ball, when you kick it hard, it’s going to squash up, it’s going to change, it’s going to become a bit like a doughnut. The amount of energy that’s lost in all that  motion of the ball, the ball just doesn’t go very fast and it’s hard to control it, hard to get spin on it; you don’t know how it’s going to behave.

If the ball’s nice and tight and hard, then it’s much easier to control. That’s right isn’t it Ruth?

Ruth - Yeah, I absolutely agree. Although, when it’s too hard it’s very painful to head.

Georgia - Right. So when you have that much air sort of all squashed up, it just doesn't allow you to compress it which (a) might mean that when it hits your head your head gets compressed instead, but it it’s too squishy then that energy gets lost from the kick?

Hugh - Yeah. It’s all about energy. The design of the ball is quite interesting. The more pressure you put into it the stronger the ball has to be, which means that the materials you use you have to make a ball thicker and heavier. And just generally it’s more difficult to make a ball that contains high pressure so there’s, if you like, engineering limitations.


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