Science Questions

Could playing football at high altitude affect how you kick the ball?

Sun, 27th Jun 2010

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Rick Britton asked:

In case you didnít know, itís the soccer World Cup in South Africa at the moment. The tournamentís being held in high altitude in some cases, so a couple of workmates told me that thin air could be affecting the movement of the ball through the air, but I'm sceptical. So whatís the science?


Chris -   Well actually, there is quite a bit of science behind this and in fact, your mates, Rick, are probably right it turns out. If you look at how footballs behave when they spin through the air as they fly, when they fly at slow speeds, what they are doing is parting the air stream and the air forms a nice even layer on either side of the football.  It forms whatís called laminar flow around the football and because the air is sticking to the surface of the ball, itís applying a drag to it.  But if you speed the ball up even more, so you go past a threshold point at which the air flowing past the ball is no longer in this lamina configuration.  It becomes so called turbulent.  Suddenly, people have found, the drag on the football plummets and becomes much, much lower, even though you've increased the speed and the increase would be only at small amount, you suddenly got a very, very low level of drag, and it then begins to increase again gently.  

So when footballers are doing these incredible, sort of Ďbananaí shots, what they're doing is cannoning the ball away at about 30 metres a second, 70 miles an hour, and at that speed, the air is travelling in a turbulent way past the ball.  So the amount of drag is actually quite low, but as the ball slows down, it then goes into the Ďhigh drag regimeí as itís known.  In other words, the speed becomes such that instead of the air being turbulent around the ball, it begins to stick to the surface of the ball again and that increases the drag very markedly, and this abruptly decelerates the ball, and it can also make a changed direction which is why the ball can slew into the goal in this bizarre way that we sometimes see.  So, speed is of the essence and therefore, the amount of thatís sticking to the ball is important.  So if you look at whatís going on in Jo-burg, that stadium is at about 4,000 feet.  Thereís an index that people use on aeroplanes which is called the indicated air speed.  This is a record of how fast the air is apparently going past the aeroplane, and we know by rule of thumb that itís about 2% wrong for every thousand feet in height you go up.  So in other words, at 4,000 feet, it would be 4 times 2% which is an 8% error.  In other words, the ball will be feeling drag as though it were going about 8% more slowly than it really is.  So when your footy player is booting the ball, having trained at sea level, knowing how the ball performs in air of the density you're going to get at sea level, actually the speeds they're booting it at to make these effects happen are going to be all wrong because the ball is actually travelling and experiencing drag about 8% lower than it ought to at sea level. Therefore, this will if you're a highly seasoned, highly practiced footballer, unless you have an opportunity to realise this is whatís happening, there could be an error in the way that you're going to boot the ball.  Itís amazing to think how much there is going on in physics in football, isnít it?

Andrew -   Yeah, well that Wayne Rooney is well-known for his love of physics.

Chris -   But not for his knowledge of it nor his ability to score goals this year unfortunately.


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