Bend It Like Magnus

It’s World Cup time, and around the world football and soccer fans are lining up to complain about how stupid the word “soccer” is. 31 of the world’s best footballing nations (and England) came to Brazil for a chance at glory and honor in the world’s favorite pastime. While many of the people in the U.S.A. may have only watched by accident, chances are good that you saw something remarkable this year. No, it’s not the US watching soccer once the cup’s over – that has no chance of happening. Take a look at this free kick (I humbly suggest muting the video and watching the first 45 seconds):

What did we just witness? The ball curves wildly before going in the net, completely ruining the keeper’s day. How does a soccer ball curve like that? Is this player so much better than the rest of us that physics decided to give him a pass on this one? Granted, Roberto Carlos played for Brazil, so he actually is better than the rest of us, but in fact the reason why this works is something called the Magnus Effect.

The shot started with Carlos making strong contact with the ball, sending it flying through the air. But on a curving shot there’s literally a twist: Carlos struck the ball off-center, with the outside of his left foot, causing the ball to rotate rapidly. In more sciencey terms, when Carlos made contact, he imparted both a force to make the ball move towards the goal, and a force to make the ball spin. It’s the spin that is important for curve.

This spin causes the ball to take a curved path due to the Magnus effect. How the Magnus effect produces a curve is a bit complicated, so let’s break this down like a scientist would. To start, as the ball moves through the air, the air parts around the ball. Behind the ball, the airstreams that separated come back together again. However, because the ball is moving significantly faster than the air, there’s a gap between the back side of the ball and where the air streams reunite. The ball is like a rock in a fast flowing river – the water splits around the rock, then swirls to fill in behind the rock, causing turbulence. This backfilled area is called the “wake” of the ball, and it points away from the direction the ball will fly.

The black lines are the air. The ball is a ball.

The black lines are the air. The ball is a ball. The “space” labeled WAKE is an area of turbulent airflow, which is really hard to draw on a computer.


Now that we know how a ball moves through the air, let’s add in some spin. If we look at the back side of a rotating ball, we can see a direction of rotation, which we can use to figure out how the ball will curve. In the video above, the ball is rotating like this:

There. Nice and simple.

There. Nice and simple.


Air will stick to the surface of the spinning ball like it’s made out of syrup. This means that the air will flow around the ball in the same direction that it’s spinning. So the air along the left side of this ball gets dragged to the right, along with the spin of the ball.

The air follows the spin of the ball.

The air follows the spin of the ball.


So far, so good. We still have to add in the fact that the ball is moving forward, so let’s look at a top view of what’s happening now:

We're switching back to a top view of the ball now. From here on, it's only top views.

We’re switching back to a top view of the ball now. From here on, it’s only top views.


Because the ball is moving forward, the air can be thought of as moving “backward”, along the surface of the ball. As it does so, the air streams still separate around the ball, like in the first image, then come back together again. But, because of the way the air is flowing around the ball (because of the spin), the air stream splits in a really odd way, like so:

Well, that doesn't look like Figure 1. I wonder why?

Well, that doesn’t look like Figure 1. I wonder why?


The air is flowing in such a way that the streams meet again off-center! This may not seem worthy of an exclamation point, but this is extremely important for how the Magnus effect works. Because the streams meet back up to the right of center, the wake that should be directly behind the ball is now pushed over to the right side of the ball. In other words, there is effectively more space for the air to fill on the left side of the wake.

The blue area is larger than the red area, but they have the same amount of air in them.

The fact that the blue and red shaded areas aren’t the same size gets pretty important in about a sentence.


The blue shaded area is much larger than the red shaded area. However, the amount of air on either side of the ball remains the same. This means that the air on the left (blue area) has to spread out more to fill the space. Since the same amount of air needs to fill more space, this creates a lower air pressure pocket on the left side of the ball – sort of a “gap” in the air. And because the air around the ball is flowing preferentially to the right, the ball itself is being forced to “roll” back to the left, to fill in the gap in the air caused by its own rotation.

Interesting side note - this can't happen in space, because there's no air to differentially displace.

Interesting side note – this can’t happen in space, because there’s no air to differentially displace.


Still with me? Because it’s about to get even crazier.

Now that we have some idea about how a shot can curve, let’s look at another video and think about it like a scientist again – does what we know now explain the way the ball moves in this video? Let’s go to the slow-motion replay (I suggest skipping ahead to about 45 seconds, but the video is announced by a Brit so you may want to watch the whole thing):

Well, if you look from behind the player, it looks like we may not have the whole picture. For one thing, the ball is barely spinning, and for another, it looks like it swerves right before cutting back to the left! What explanation do we have for this?

As it turns out, there’s something seemingly innocuous that we overlooked: the ball has seams. That means that the surface of the ball isn’t smooth. It may seem small and obvious, but this irregularity causes strange effects to happen if the ball ISN’T spinning. When the ball is rotating very slowly, air doesn’t stick as well to the ball’s surface. This allows the ball’s seams to disrupt the airflow. When this happens, the disrupted air becomes turbulent. This turbulent air can swirl back towards the ball, giving it a little push. But, because there’s no way to predict which seam will produce a turbulent patch at any given time, the ball’s direction cannot be predicted. Especially by our poor keeper in the video above. Anybody who has watched a baseball pitcher throw a knuckleball has seen the same effect; it just tends to be more noticeable on a soccer ball because it moves slower than a baseball, allowing the air more time to nudge the ball in a random direction.
What makes these shots remarkable is that the ball itself is responsible for the forces that change its motion. With the Magnus effect, the fact that the ball is spinning puts a force on the air, causing the ball to bend and dip in amazing ways. And even with no spin, just the simple fact that the ball has seams causes it to move back and forth. This is why a simple ball can get the world so incredibly excited – any shot can go in at any time, as long as Magnus is on your side!

Further reading:


6 thoughts on “Bend It Like Magnus

  1. Pingback: Qual é o efeito Magnus? | Dicas e Curiosidades™


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