Sunday, 29 April 2012

The Physics of Soccer: How does 'Curl' work?

Welcome to the second post in our series on the physics of sport. How can soccer players cause a ball's trajectory to change in the air? And what are the different ways they can do this?

Last week we posted on how 'swing bowling' worked in cricket. Ian Lynch (@Ingotian on twitter) pointed out that the physics would surely be very similar in each of the subjects, indeed the end results are practically identical. However, when we investigate further, we realise that there are some distinct differences between the two. Before we get to those, lets watch a video of Roberto Carlos putting this skill in action:
This is one of the most extreme exhibitions of curl ever shown, and shows the effect easily. You can see, especially from the angle at 52 seconds, that ball originally does not go towards the goal. However, after a very short time, it seems to turn strongly and goes in. So what is it that leads to this strange phenomenon?

If you watch closely, you will notice that Carlos hit the ball slightly off centre. This gives the ball spin, and it is this spin that leads to the curl. The reason for this is due to something called the Magnus effect. This principle says that when an object spins in a fluid, whether a gas or a liquid, it creates a sort of whirlpool around itself, which leads to the object being pulled to one side. When a ball moves without spin, the air around it looks like this:

As air passes over the curved surfaces, it is forced to speed up. When a fast-moving fluid passes over an object, it puts less pressure on it than if the fluid was moving slowly. However, because all of the ball's surface is curved, the effects cancel out and the ball travels straight. However, the effect is different when the ball is spinning:

The side on the top is spinning with the airflow. This creates less drag on the air on that side and therefore it moves faster. Because the air is moving faster, it has lower pressure. The ball feels a force towards the patch of low pressure, causing it to curve towards that way.

The force can be put in any direction. A ball that has top spin, which is more applicable to a sport like tennis, will dip very quickly, making it very easy to hit hard and still get in the court, whereas a ball with backspin will instead glide as the Magnus effect will help to give it lift.

The Magnus effect is a more specific part of Bernoulli's principle, which says that if a fluid's speed increases, its pressure decreases. This is used extensively in engineering. For example, this is a diagram of an airplane wing:

The air on the top curved side has to move faster, lowering its pressure, and causing the plane to move up. We can also see this in other sports, like golf.

There is another force that increases this effect, called the 'Wake deflection force'. Last week, we talked about the boundary layer of a travelling ball:

This is where we start to see the similarities between cricket ball swing, and soccer curl. Just as the smooth and rough sides of the cricket ball would cause the air going past it to go in a specific direction, so does the spin of the soccer ball:

The famous quotation from Newton, says that 'Every action has an equal and opposite reaction'. Therefore, the action of the Wake being pushed downwards has the reaction of pushing the ball upwards, creating a force which pushes in the same direction as the force from the Magnus effect, increasing the overall movement. However, this Wake deflection force does not apply at very fast speeds, when the air cannot be deflected. This means that on very powerful strikes, the ball travels without curving for a short amount of time before it slows down enough that the air can catch it and it can start to curve. This amount of time is usually very short, but this is what leads to the unpredictability of well hit curling shots.

And my last point on the subject of curl, as an Englishman, I am obliged to show what is perhaps one of the greatest curling free kicks of all time:

Ok, so we have finished talking about curl, haven't we? We learnt about spin, but have a look at this video:

From the angle at 5 seconds, we can easily see the ball curve in the air. However if we watch the ball from the angle at 10 seconds, it spins, but not enough to create the large curve in its trajectory that we see. This type of free kick is known as Cristiano Ronaldo's 'Knuckleball', and there is a very specific technique to it. Ronaldo hits the ball very differently to when he wants to do a normal curling shot. Instead of hitting with the inside of his foot, he hits right in the centre of the ball with the laces of his boot. This means he can put a huge amount of power into the ball without making it spin.

In the last part of the post, we considered the ball as being perfectly smooth. However, in practice, it is not. The ball has prominent seams. When the ball is spinning fast, the change from these seams is unnoticeable. But when the ball is barely spinning, like in the Knuckleball, they can catch the air. The ball floats, and then dips quickly. What makes this even more devastating, is that the air can catch on one side but not the other very easily. This means that the ball acts almost like a beach ball. It glides through the air, and can move in any direction with incredible ease. The changes can come very late in the ball's flight and all of these effects add up to create an almost impossible to predict trajectory. This sort of thing, though not seen often in soccer, can be very common in other sports. For example, the name 'Knuckleball' came from a pitch in baseball which employed the same properties to get the same results. These pitches/shots are very effective, but the skill to hit or throw a ball and put no spin on it is one that requires huge amounts of practice and a large amount of skill. Cristiano Ronaldo, one of the best soccer players in the world, is one of few who have perfected it.

To conclude, Spin causes a ball to curl. The faster the spin, the more extremely the ball curls. However, due to minor imperfections in the ball, if a player can hit it without spin, it will still curl in a chaotic manner that can create big problems for goalkeepers.

We hope you enjoyed this post. If you you want to get in touch you can follow and mention us on twitter, @theaftermatter, email us at or search "The Aftermatter"on Facebook.

Ned Summers

Check out our last two posts:
The Physics of Cricket: What is 'Swing Bowling'? - The first instalment of our "The physics of sport" series. How does a bowler make a cricket ball swing? We assure you, it is very different to how soccer balls curl!
Untitled - [yes, that's the title] (Guest post from TheCompBlog) - A guest post not about physics, but just as interesting!

What are we posting about next:
The Physics of Rugby: Forward Passes and Relativity - How can a backwards pass look like they are going forward, and why is it so difficult for referees to judge?

If you have ideas for posts we would love to heard them. Contact details are above.


  1. This comment has been removed by a blog administrator.

  2. As a 2d drawing If a ball rotates cw moving upwards then surely the air across the left surface travels faster in relation to the ball surface? Or if the spin speed matched the movement (like a wheel) the air speed across the right side is zero? I must really be missing something.