Bend it like McCabe: How World Cup players curve the ball

In last night’s 2023 FIFA Women’s World Cup game against Canada, Republic of Ireland captain Katie McCabe scored directly from a corner.

The only way to perform such a feat is to get the ball’s flight to bend through the air. Whether intentionally or not (McCabe herself is the only person who can answer that!), that’s exactly what the Irishwoman did on Wednesday night, getting the ball to swing out several metres before nestling in the back of the Canadian net.

Despite McCabe’s heroics, the Irish team lost 2-1 and were eliminated from the knockout stages of the World Cup finals before their final group stage match against Nigeria next week.

But McCabe’s goal is a terrific example of a skill vital in modern football and many other ball sports: how to get the ball to curve. It was mastered and became famous through footballers like Roberto Carlos and David Beckham. Now you can add Katie McCabe’s name to that list.

How do they do it? As a football-playing physicist (and “football”- not “soccer”-saying), this topic is close to my heart.

The Magnus effect

“You have to put spin on the ball,” University of Adelaide professor Derek Leinweber tells Cosmos. Leinweber is a world renowned nuclear and particle physicist who is also an expert on aerodynamics in ball sports.

Leinweber explains that curveballs are due to the “Magnus effect” governed by the Magnus force which moves a spinning ball up, down, left or right depending on its rotation. This is named after 19th century German physicist Heinrich Gustav Magnus.

Because of the ball’s spin, a difference in the air pressure on either side of the ball is created. On one side of the ball there is a region of higher pressure and on the other side air pressure is lower. The Magnus force travels from the high-pressure region to the low.

Hence, a ball kicked with backspin will lift. Topspin makes the ball “dip” in its flight, dropping more than it would under the effect of gravity alone. Clockwise or anti-clockwise spin, when viewed from above, will make the ball arc through the air (towards the right or left respectively) like in Katie McCabe’s corner against Canada.

“All these aerodynamics are governed by the boundary layer right next to the ball,” Leinweber says. “The air molecules are stationary against the skin of the ball. Away from the ball, the air is passing as if the ball wasn’t even there. In between those two extremes is the boundary layer. And the boundary layer is about a millimetre in thickness.”

All about that flow

The bend on the ball depends on the spin that players can put on their shots and passes. The aerodynamics in play are well understood.

“There are two ways the air moves around the ball,” Leinweber says. “At low speeds, you’ll have a laminar flow. That’s a nice, uniform, layered type of distribution in the in the air density. Or you can have turbulent flow.”

Laminar flow, he explains, produces a very large “wake” behind the ball as it moves through the air, generating a high level of drag.

These aerodynamics can have a major impact in other sports involving balls as well. Leinweber notes the somewhat surprising fact that golf balls travel further in air than in a vacuum. That is because golfers add backspin to their strikes which causes the ball to lift and travel further.

How well a ball can bend in the air also depends on its manufacture. Modern footballs, like the 2023 FIFA Women’s World Cup official match ball, are extremely smooth and encourage laminar flow.

“If you think about ball roughness, anything that’s going to disturb that boundary layer is going to spoil the Magnus effect,” Leinweber says. “If your ball is rough, you’re going to spoil the boundary layer – it’s not going to stay next to the ball. The pressure differentials that get set up in the Magnus force then aren’t next to the ball and the ball doesn’t bend as much.”

Turbulence and “knuckle balls”

But sometimes turbulence is what football players are after to score goals.

Turbulent flows are created when the ball is kicked hard and is moving very fast, Leinweber explains. This “hugs” the ball and creates a much smaller wake, allowing the ball to move at higher speeds for longer.

“This shows up when players kick a knuckleball, where there is no spin on the ball, just coming forward and maybe slowly turning,” Leinweber says. “As it slowly turns, you might have a rough panel with a seam, and it would trip turbulence.

“When you trip turbulence, the air hugs the ball, and it pulls away. Then as it turns another panel may trip turbulence and pull the ball the other way. So micro textures on the ball come into play where the ball is kicked in a knuckleball-type fashion.”

This is why knuckleballs become quite unpredictable and dip and swerve in the air.

Leinweber also explains how football players can time their shots to transition from turbulent to laminar flow to become harder to stop.

“You can kick the ball hard to get into that turbulent flow, then it slows down as it comes up to the goal. Then it may actually trip into that laminar flow, in which case the drag coefficient becomes much larger. When the drag increases all of a sudden, then the ball will dip.”

Simple really. Who’d want to be a goalkeeper?