From Serena Williams’s floating backhand slice to Tiger Woods’s surgically accurate fade drive, sportspeople are masters of the magically bending ball. King of the castle was David Beckham, a magician when it came to swinging around a defensive wall. His free kick would lazily curve away, and… wait, what’s happening? It’s going completely the wrong way!
Gotcha. Sometimes—just sometimes—physics has a little fun with you. Meet the inverse Magnus effect.
Normally, backspin holds a ball aloft, topspin keeps it low and deadly, and left or right sidespin will curve it left or right to infuriate your opponent or dodge an obstacle. This is down to the ordinary Magnus effect.
The Magnus effect is all about sticky air. Suppose I’m David Beckham, squaring up a shot at goal from outside the box. I strike the football off-centre, sending it flying through the air, spinning as it goes.
As the air rushes past, it tries to hug the ball. The side turning towards me, the retreating side, is turning the same way as the oncoming air. This makes it stickier than the side turning against the air, the advancing side. By pulling more air around on one side, the wake behind the ball gets pushed to the other side, like this:
But why does the ball’s path bend? It’s Newton’s Third Law: every action has an equal and opposite reaction. Forcing the wake one way—the action—causes an opposite reaction force on the ball, curving its path towards the retreating side. It flies around the wall, beats the keeper, and hits the back of the net. Goal!
The sticking air forms a thin layer on either side. These layers, called boundary layers, come in two distinct flavours. If the air in a layer is steady and even, it’s called laminar. Otherwise, it’s unsteady and tumultuous, called turbulent. These photographs show them in action:
Rough balls, like tennis or golf balls, always have turbulent boundary layers. But if the ball is smooth enough, the layers can be either laminar or turbulent. This depends on the speed of the air relative to the spinning surface of the ball. If the relative speed is below a certain threshold, the layer will be laminar; beyond that threshold, the layer is turbulent. There’s no in-between—it’s either one or the other.
Here’s where physics starts playing pranks. If the ball is flying through the air at just the right speed, then one side will be turbulent while the other stays laminar. How can that be?
The advancing side is turning against the air. This means its relative speed is greater than that of the retreating side, which is turning with the air. So, if the ball is moving just fast enough, these relative speeds can straddle the turbulence threshold—in other words, we can make the advancing side turbulent and the retreating side laminar.
In the ordinary Magnus effect, it’s the retreating side that’s stickier. But turbulent boundary layers stick much better than laminar ones. That’s why golf balls are dimpled and tennis balls are furry: the deliberate roughness makes the layers turbulent, reducing drag and strengthening the Magnus effect.
But when there’s one of each flavour of boundary layer, the turbulent advancing side sticks better than the laminar retreating side, making the ball bend the other way:
This is the inverse Magnus effect, and it’ll send poor David Beckham’s free kick straight into the stands. Whoops.
It isn’t a mathematical flight of fancy, either. A regulation football spinning at 5–10 revolutions per second will bend the wrong way when travelling around 20 kph(1). Although that’s rather slower than the 70–100 kph free kick a professional will hoof, it’s certainly possible. Especially if I’m the one doing the kicking.
The critical speed is a little low because of the ball’s stitching, which favours turbulent boundary layers. If it didn’t have any seams, like one of those plastic ones you might have played with as a kid, you could kick it at least twice as fast with the same rotation rate and still get it to bend the wrong way(1,2).
So when you’re playing against a bunch of kids in a primary school playground, watch out for the inverse Magnus effect. They could be channeling the anti-Beckham.
(1) Understanding the effect of seams on the aerodynamics of an association football, Carrè, Goodwill & Haake, 2005.
(2) Inverse Magnus effect on a rotating sphere: when and why, Kim, Choi, Park & Yoo, 2014.
(Cover photo: Flickr/glennharper)