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Aerodynamics in the beautiful game

21 November 2022

The ball for the 2022 World Cup has the right aerodynamic properties to perform as expected.

The 2022 FIFA World Cup will be held in Qatar from 20 November to 18 December. Each new World Cup provides the opportunity for new technologies to shine, particularly for the most important piece of equipment in the most important event in the world’s most popular sport: the ball. For discussions of the aerodynamics of balls with spin, the piece I wrote for Physics Today prior to the 2010 World Cup, including the references in it, is a good place to start learning about the Magnus force and other fun soccer physics.

Adidas has provided balls for the World Cup since 1970. The balls many of us played with in our youth were not so different from early World Cup balls. The traditional design with 20 white hexagons and 12 black pentagons, a color scheme that helped viewers a half century ago follow the ball on black-and-white televisions, used to have its panels stitched together by hand. The last 32-panel ball used in the World Cup was the Fevernova, which was used in 2002 in Japan and Korea, albeit with a new color scheme.

For the 2006 World Cup, Adidas reduced the number of panels to 14. And with the 2010 World Cup, Adidas further reduced the number of panels and began texturing the ball to reduce the air drag. In the years since, the number and texture of the panels have varied for each World Cup. As have the panel shapes: Making spherical soccer balls with fewer panels isn’t easy; the designers seem as though they may have had lessons in topology!

Figure 1. Close-up of Al Rihla’s surface features. Credit: John Eric Goff

For the upcoming World Cup, Adidas created the Al Rihla (“the journey” in Arabic). The new ball has been fitted with 20 panels, 8 of them triangular and 12 that resemble the outline of a Drumstick ice cream cone. Surface texturing includes debossing, as shown in figure 1. What is required of Al Rihla is what was required of its predecessors: It must behave in ways familiar to elite soccer players, and one of those ways is aerodynamic performance.

I investigated the aerodynamics of World Cup soccer balls with my colleagues Sungchan Hong of the Tokyo Institute of Technology and Takeshi Asai of the University of Tsukuba. Figure 2 shows the Al Rihla ball on a sting, ready for testing in a wind tunnel. Force sensors on the sting are capable of reading aerodynamic forces on the nonspinning ball along three orthogonal directions. Side and lift forces are perpendicular to the direction of air flow. Those forces are important when investigating knuckling effects seen on balls kicked with little to no spin.

Here I’ll focus on the drag force, which is the force the ball experiences in the direction of air flow. It is a major player, along with the ball’s weight, in determining the ball’s trajectory. The magnitude of the drag force may be written as FD = ½CDAρv2, where A is the cross-sectional area of the ball (a diameter of approximately 0.22 m means A ≈ 0.038 m2), ρ ≈ 1.2 kg/m3 is the density of air, v is the speed of oncoming air, and CD is the dimensionless drag coefficient. Students often learn about the dynamic pressure when presented with Bernoulli’s equation in introductory physics. Multiplying that pressure by the ball’s cross-sectional area gives a force. The drag coefficient is the factor that accounts for all of the interesting fluid dynamics.

Figure 2. Al Rihla mounted on a sting in front of a wind tunnel at the University of Tsukuba. Credit: John Eric Goff

Figure 3 shows the speed-dependent drag coefficient for Al Rihla and its three predecessors. The Jabulani, a ball with eight panels, was created for the 2010 World Cup in South Africa. The Brazuca ball used in Brazil for the 2014 World Cup and the Telstar 18 ball used in Russia for the 2018 World Cup both had just six panels, although their panel shapes and surface texturing were quite different. The four balls were tested in two of an infinite number of possible orientations; figure 3 shows results representative of other orientations. Although Al Rihla’s drag coefficient is smaller than those of the other balls at low speeds, it is in line with the high-speed drag coefficients for Telstar 18 and Brazuca. That suggests that at ball speeds typical of long kicks, corner kicks, free kicks, and penalty kicks, Al Rihla should fly through the air in ways that will not surprise players.

The precipitous rise in the drag coefficient as ball speed drops is called the “drag crisis.” At high speeds, the boundary layer of air separates from the ball near the back, away from the oncoming air. That turbulent flow of air leads to a chaotic wake behind the ball. When ball speed drops below the threshold for the drag crisis, turbulent boundary-layer separation turns to laminar boundary-layer separation. The boundary layer separates closer to halfway between front and back of the ball, in the path of oncoming air. The drag coefficient thus increases, and the wake of air behind the ball is more regular. Increasing surface roughness helps reduce the speed where the drag crisis occurs, which may seem counterintuitive. Added surface roughness helps delay separation of the boundary layer, pushing the separation farther back on the ball.

Figure 3. Drag coefficient versus air speed for soccer balls used in recent World Cups. Credit: John Eric Goff

The outlier in figure 3 is Jabulani. The big flaw of that ball is that its drag crisis occurs at too high a speed. There are too many corner kicks and free kicks that have the ball moving at around 20 m/s (≈ 45 miles per hour) at some point in the trajectory. During some long kicks, the Jabulani ball would appear to slow too quickly while in flight. That was because the air flow around the ball passed the drag crisis turning point, which meant the drag coefficient rose drastically. One can see such an effect if one hits a beach ball hard. The beach ball slows rapidly, and the reason is not just because it has a large cross-sectional area. A typical beach ball does not have much surface roughness.

Surface roughness plays a crucial role in determining the speed that triggers the drag crisis. Consider the surface properties listed in the table below. Lengthening, widening, and deepening seams all contribute to increased surface roughness. Despite its surface texturing, Jabulani was simply not rough enough to keep its drag crisis onset at a relatively low speed.

Surface properties of recent World Cup soccer balls

When Brazuca came along four years later, it had not only two fewer panels but also a longer total seam length and wider and deeper seams than those on Jabulani. Telstar 18’s panel count matched Brazuca’s, but Telstar 18’s vastly different panel shapes led to a significantly longer total seam length. To make up for that potentially rougher surface, Telstar 18 had narrower and shallower seams than those on Brazuca. Telstar 18 also had surface texturing that was not as raised as on Brazuca. Just by rubbing the panels, one can easily tell that the Brazuca is rougher than the Telstar 18.

For the upcoming World Cup, panel number on the Al Rihla ball jumped to 20, but its total seam length is comparable to that of Brazuca. Al Rihla’s wider and deeper seams compared with those on Brazuca are accompanied by smoother panel texturing. Instead of the raised texturing on Brazuca’s panels, Al Rihla’s surface uses debossing, which makes the panel surfaces feel much smoother than those on Brazuca.

The desire for a new ball with each new World Cup means creating a ball with unique panels and new surface features. But each time the panel number and panel shape change, corresponding changes need to be made to the width and depth of seams and to the surface texturing. Those counterbalancing changes should then produce a ball with drag coefficients like those seen in figure 3. Al Rihla looks like it will perform in ways players are used to.

John Eric Goff is a physics professor at the University of Lynchburg.

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