Designers Fine-tune the Aerodynamics of World Cup Soccer Balls

By James Case

The FIFA World Cup of football (soccer in the U.S.) has been contested quadrennially since 1930, with a gap between 1938 and 1950 because of World War II. In the early years, the host country furnished the official match balls, which were sometimes of disputed quality. Adidas, which began making soccer balls in 1963, won the contract to furnish the official World Cup ball in 1970, and has yet to relinquish it. That year’s ball, dubbed the “Telstar” (see Figure 1), was the first to consist of 12 black pentagonal leather panels and 20 hexagonal white ones, stitched together to resemble a truncated icosahedron, or “buckyball.” The blend of black and white panels made the redesigned balls especially visible on the black and white TV screens of the day. 

Until 1954, soccer balls consisted of a dozen roughly rectangular panels. The balls for that year’s World Cup in Switzerland were the first to be made of 18 such panels, in an effort to produce a more nearly spherical ball better able to hold its shape under game conditions. Because leather balls absorb water when used in the rain, and because the added weight causes head and neck injuries, repeated efforts were made to develop satisfactory rubber balls, as well as water-resistant coatings for leather ones. For the 1982 World Cup, played in Spain, Adidas supplied the Tango ball, which had rubber inlays over the seams to make the surface smoother and to keep water from seeping in. But the rubber wore unevenly during play, and the balls had to be replaced as the games went on. That was the last genuine leather ball used in World Cup play; subsequent models were made of polyurethane. The Fevernova, used in the World Cup sponsored by Korea and Japan in 2002, was the last to use the 32-panel buckyball configuration.

For the 2006 World Cup, held in Germany, Adidas introduced the radical Teamgeist design, whose 14 “thermally bonded” panels were intended to create a smooth, consistent kicking surface, making the trajectory more nearly independent of the part of the ball that was kicked. The Teamgeist was followed four years later by the even more radical Jabulani (see Figure 2), whose eight “spherically molded” and thermally bonded panels were intended to provide the smoothest and least deformable ball yet.

But the Jabulani was wildly unpopular with goalkeepers, who complained that balls kicked hard and without spin followed erratic paths, similar to those of a knuckleball in baseball, making them hard to catch. This is clearly unfair – some of the paths followed by such a ball will be far more erratic than others, increasing the role of chance relative to skill in the outcome of games. The ball selected for the 2014 World Cup in Brazil—the Brazuca (see Figure 3)—has been subjected to extensive wind tunnel testing, in an effort to confirm that its design reduces, without completely eliminating, this “knuckling effect,” a purely aerodynamic phenomenon. (The name Brazuca was chosen by public vote in Brazil, with more than a million citizens participating.)

When launched on a given trajectory, spinning balls are subject to the aerodynamic forces lift and drag. Drag acts in the direction opposite to that of the velocity vector, lift in a direction orthogonal to both the velocity vector and the ball’s axis of rotation. Despite the lack of any axis of rotation, spinless balls remain subject to normal forces acting in directions orthogonal to the velocity vector. And these forces, having no obvious preference among the available directions, tend to change abruptly and unpredictably in both direction and magnitude, thereby producing the erratic trajectories so vexing to catchers and goalkeepers.

Stanley Corsin, a professor of mechanics at Johns Hopkins University, studied such trajectories during the 1950s, in part by dropping spinless ping pong balls down the three-story stairwells outside his office in Maryland Hall. He also persuaded Hoyt Wilhelm, then of the Baltimore Orioles and one of the most accomplished knuckleball pitchers in baseball history, to participate in a series of tests conducted at the Army’s Aberdeen Proving Ground.

The recent comparative wind tunnel tests on the Jabulani and Brazuca balls measured both drag and normal forces. It has long been known that almost any smooth convex projectile will experience a relatively sudden and rather dramatic increase in drag as its speed is reduced by atmospheric friction. This “drag crisis” kicks in at higher speeds for perfectly smooth balls than for those with appreciably rougher surfaces. Indeed, Adidas was obliged to roughen the surface of the Jabulani ball prior to the 2010 World Cup in an effort to make it follow trajectories similar to those of its predecessors. Significantly, the six-panel Brazuca has 68% more total seam length (and therefore roughness) than the eight-panel Jabulani.

With regard to drag, the results of the recent wind tunnel experiments shown in Figure 4 are typical of various orientations. The drag coefficients for all three balls tested increased from less than 0.2 to more than 0.4 in relatively short order, assuming an intermediate value of 0.3 at airspeeds of about 12 meters per second for the Brazuca, about 17.5 m/s for the Jabulani, and about 22 m/s for a perfectly smooth ball of the same size. Such experiments had to be performed several times over, as non-uniform balls perform differently in different orientations. However, the companion results tend to confirm the expectation that the Brazuca ball is subject to significantly weaker drag forces at intermediate speeds—say 10 to 20 m/s—than the Jabulani, while the drag on both is roughly equal at speeds above 25 m/s.

Obtaining measurements of the normal forces, which are far smaller than the drag force, is more delicate. The wind tunnel experiments were conducted by Takeshi Asai and Sungchan Hong of the University of Tsukuba, in Japan, who recorded the results on a personal computer using an analog-to-digital converter with a sampling rate of 1000 Hz in test runs slightly more than eight seconds in duration. The normal forces on the two balls were measured in two different orientations (A and B) at airspeeds of 20 and 30 m/s. The results of the lower-speed tests are shown in Figure 5. Clearly, the normal forces, together with the range over which they varied, were far smaller on the Brazuca than on the Jabulani ball, in both orientations. Thus, goalkeepers in Brazil can anticipate weaker “knuckleball” effects on intermediate-speed kicks.

The results for the higher speed were less definitive, with the forces buffeting the Jabulani somewhat weaker and less variable in orientation A, but significantly stronger and more variable in orientation B. Yet because the strongest and most variable normal forces observed in any of the tests were those affecting the Jabulani in orientation B, it is at least possible that the Brazuca will outperform its predecessor on high-speed kicks as well. Results of the wind tunnel tests were forwarded for analysis to John Eric Goff, a professor of physics at Lynchburg College in Virginia and the author of a well-known book¹ on the physics of sports. He fit the variable drag coefficient data from Figure 4 to curves of the form \[C_D(s) = a + \frac{b}{[1+e^{(s-\mu)/\sigma}]}~,\] where the constants \(a\), \(b\), \(\mu\), and \(\sigma\) are parameters to be chosen, and constructed sample trajectories for both balls by integrating numerically the equations of motion \[\ddot{x}=-\beta{f(s)}{\dot{x}}~and~\ddot{y}=-\beta f(s){\dot{y}}-g,\] in which \(\beta = \rho{A}/2m\), \(s=\sqrt{\dot{x}^2+\dot{y}^2}\), and \(f(s)=s{C_{D}}(s)\). From this he concluded that the two balls would follow quite similar paths when launched at speeds approximating 30 m/s, but significantly different ones when launched at lower speeds.

Impressive as all this is, more could be done, for both soccer balls and baseballs. The availability of high-resolution time series data of the sort depicted in Figure 5 suggests that the addition of stochastic terms \(u(t)\) and \(v(t)\) to the right-hand sides of the foregoing equations of motion would permit the simulation of quite realistic knuckleball trajectories. In this way, it might be possible to test the long-standing hypothesis that knuckling effects are greatest on balls launched at or just slightly above the speeds at which the slope of the graph of \(C_{D}(s)\)is greatest.

 

¹ Gold Medal Physics, Johns Hopkins University Press, Baltimore, 2009. 

References

[1] J.E. Goff, T. Asai, and S. Hong, “A Comparison of Jabulani and Brazuca Non-spin Aerodynamics,” Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, March 2014; doi: 10.1177/1754337114526173; http://pip.sagepub.com/content/early/ 2014/03/17/175433114526173.

James Case writes from Baltimore, Maryland.