1 A Comparison of Jabulani and Brazuca Non-Spin Aerodynamics Proc JMechE Part P: J Sports Engineering and Technology ():1 13 The Author(s) 2 Reprints and permission: sagepub.co.uk/journalspermissions.nav DOI:doi number John Eric Goff Department of Physics, Lynchburg College, Lynchburg, Virginia 241, USA Takeshi Asai and Sungchan Hong Institute of Health and Sports Science, University of Tsukuba, Tsukuba-city, 3-874, Japan Abstract Wind-tunnel experimental measurements of drag coefficients for non-spinning Jabulani and Brazuca balls are presented. The Brazuca ball s critical drag speed is lower than that of the Jabulani ball, and the Brazuca ball s super-critical drag coefficient is larger than that of the Jabulani ball. Compared to the Jabulani ball, the Brazuca ball suffers less instability due to knuckle-ball effects. Using drag data, numerically-determined ball trajectories are created and it is postulated that though power shots are too similar to notice flight differences, goal keepers are likely to notice differences between Jabulani and Brazuca ball trajectories for intermediate-speed ranges. This latter result may appear in the 214 World Cup for goal keepers used to the flight of the ball used in the 2 World Cup. Keywords Jabulani, Brazuca, football, soccer, aerodynamics, drag coefficient, wind tunnel, computational modeling, knuckle-ball 1. Introduction Much of the world is riveted by FIFA World Cup action, which takes place every four years. Since 197, Adidas has provided the ball used at the World Cup. The 22 World Cup in Japan and South Korean used the Fevernova ball, the last World Cup ball with the more traditional 32-panel design consisting of 2 hexagonal panels and 12 pentagonal panels (similar to a truncated icosahedron). The 26 World Cup in Germany used a thermally-bonded 14-panel ball called the Teamgeist. Adidas created the Jabulani ball for the 2 World Cup in South Africa, a ball that experienced some controversy. 1 Having just eight thermally-bonded panels, Adidas had to texture the surface to make up for a reduced number of seams. As balls get smoother, the speed at which the drag coefficient experiences a precipitous drop, called the critical drag speed, increases. 2 By continually reducing panel number, Adidas had to add panel roughness if balls were to follow similar trajectories that previous balls followed. For the 214 World Cup in Brazil, Adidas created the Brazuca ball, which has Corresponding author;
2 just six thermally-bonded panels. Because there were so few panels, the ball, like the Jabulani ball, has been textured to increase surface roughness. Despite fewer panels, the Brazuca ball has nearly 68% longer total seam length (3.32 m vs 1.98 m) than the Jabulani ball. This paper reports results of wind-tunnel experiments on balls used at the two most recent World Cup events. Wind-tunnel results are used to create model trajectories that will show how differences in aerodynamic properties lead to differences in flight trajectories. Soccer, perhaps more than any other sport due to its global popularity, has been studied extensively by scientists and engineers for a few decades now. Some of that soccer work, 3,4,,6,7 like the work discussed in this paper, seeks to understand how the technical evolution of the soccer ball affects play at the highest level. For a more extensive coverage of contemporary soccer research, readers are referred to a recent review article 8 on sport aerodynamics. That article contains a section on soccer with copious references to aerodynamics research performed mostly in the current century. Since that review article was accepted, more research has been published 9,,11,12 that has furthered our understanding of soccer aerodynamics. 2. Wind-Tunnel Experiment Aerodynamic forces acting on different types of balls were measured in a low-speed wind tunnel at the University of Tsukuba that has a 1. m 1. m rectangular cross section with a turbulence level less than.1%. Two full-sized official FIFA soccer balls were tested: the Adidas Jabulani (.22-m diameter and.438-kg mass), used in South Africa for the 2 FIFA World Cup, and the Adidas Brazuca (.22-m diameter and.433-kg mass), used in Brazil for the 214 FIFA World Cup. Based on ball diameter and wind-tunnel size, the blockage was about 1.7%. Each soccer ball was attached to a stainless steel rod; such a sting setup ensures that the ball remains in equilibrium during testing. Figure 1 shows the Brazuca ball on the rod just before testing began. The position of the support rod relative to the bluff body is important in a wind-tunnel experiment, which means selecting an appropriate support orientation. For the experiments the ball was supported from the rear, 13 a location considered to have a comparatively smaller effect on the separation of the boundary layer from the ball s surface. Data were acquired over a period of s using a six-component sting-type balance (LMC-622; Nissho Electric Works Co., Ltd.), and they were recorded on a personal computer using an A/D converter board with a sampling rate of Hz. Each ball was set to be geometrically symmetrical; the ball panels were therefore asymmetrical in the vertical direction. The aerodynamic forces were measured at wind speeds in the range 7 m/s v 3 m/s (1.7 mph v 78.3 mph). That speed range corresponds to a range in Reynolds number of roughly, < Re <,, where Re = v D/ν, 14 with D =.22 m, the ball s diameter, and ν = 1.4 m 2 /s, the kinematic viscosity. The force from the rod on the ball acts in the direction opposite to that of the wind and equals the drag force, F D. The drag coefficient, C D, is then extracted from 14 F D = 1 2 ρac D v 2, (1) where A =.38 m 2 is the cross-sectional area of the ball and ρ = 1.2 kg/m 3 is the air s mass density. Also studied were effects that lead to the knuckle-ball 1 phenomenon whereby a ball with little to no spin experiences forces perpendicular to its velocity that are due to an asymmetric boundary layer separation. Asymmetries arise because flow on one side of the ball may move over geometric asymmetries not encountered on the side directly opposite. The knuckle-ball effect is named after the baseball pitch with little to no spin. Here the air moving over the ball stitches separates farther aft than the flow over a smoother portion of the ball. 16 Figure 2 shows the two orientations, labeled A and B, that were studied for the knuckle-ball effect. For each orientation, the force on the ball was measured at two speeds, 2 m/s (44.7 mph) and 3 m/s (67.1 mph). The force was decomposed into two orthogonal components: the side force and the lift force, oriented horizontally and vertically, respectively, in Figure 2.
3 3. Wind-Tunnel Results and Discussion Figure 3 shows wind-tunnel experimental drag coefficient results for the Jabulani and Brazuca balls in orientation A. Also shown are the experimental error bars as well as comparison data 13 for a smooth ball the size of a soccer ball. As expected, the smooth ball data shows a critical-drag speed larger than that of the rougher soccer balls. Figure 4 shows experimental C D data for both balls in orientations A and B. To keep that plot less cluttered, error bars are not shown, though error bars for orientation B are similar to what is seen in Figure 3 for orientation A. The most striking feature of the wind-tunnel results is that the Brazuca ball s critical speed, i.e. the speed where there is a precipitous drop in C D, is lower than that of the Jabulani ball. This result may seem counterintuitive given that the Brazuca ball has two fewer panels compared to the Jabulani ball, but recall that the overall seam length on the Brazuca ball is nearly 68% longer than on the Jabulani ball. The Brazuca ball s drag coefficient curve is more similar to that of the 32-panel Adidas Tango 12 ball 6 used in the 212 UEFA European Championship, than it is to the Jabulani ball s C D curve. Also seen in Figure 4 is that the Brazuca ball s drag coefficient for high speeds, i.e. in the super-critical region, is larger than the Jabulani ball s drag coefficient. At the highest speed tested, i.e. v = 3 m/s, C D =.17 for the Brazuca ball and C D =.2 for the Jabulani ball. The drag coefficient data suggest that there will possibly be noticeable differences between ball aerodynamics in the 2 World Cup than the 214 World Cup. Compared to the Jabulani ball, the Brazuca ball has less drag on it for intermediate speeds, i.e. m/s v 2 m/s (22.4 mph v 44.7 mph). The intermediate-speed-range shots in the 214 World Cup will be faster because of less drag than in the 2 World Cup. For balls at speeds in excess of approximately 2 m/s (.9 mph), the Brazuca ball s larger drag coefficient means that goal keepers in Brazil will encounter more rapid deceleration compared to the 2 World Cup. Brazuca ball s smaller critical speed has implications for knuckle-ball effects. Figure shows lift and side forces at speed 2 m/s on the two balls of interest oriented in the two ways shown in Figure 2. Figure 6 is identical to Figure, except the speed is 3 m/s. Each of the two aforementioned figures was created by recording the force for 9 s. Oscillation periods are in the.1 s.2 s range, meaning the forces are not oscillating too rapidly to average out during a typical ball flight. At an intermediate-kick speed of 2 m/s, compared to the Brazuca ball, the Jabulani ball shows significantly greater forces transverse to air velocity. That result suggests that a non-spinning Jabulani ball will be more erratic in its flight compared to a non-spinning Brazuca ball. The aforementioned result is explained by the fact that the Jabulani ball s critical speed is greater than the Brazuca ball s critical speed. For intermediate-speed kicks, the air s boundary layer experiences both laminar and turbulent separation from the Jabulani ball. A Brazuca ball at 2 m/s experiences only turbulent separation of the boundary layer because the speed is super-critical. The fact seen in Figure 4 that C D data for the A and B orientations are more similar for the Brazuca ball than for the Jabulani ball means that a Jabulani ball with little-to-no spin will be more erratic compared to the Brazuca ball. Moving to a power-shot speed like 3 m/s, Figure 6 shows an expected increase in the resulting forces. Although position A for the Jabulani ball is more stable than position A for the Brazuca ball, the Jabulani ball in position B is clearly the most unstable of all combinations of ball type and orientation evaluated. This result is attributed to the more asymmetric distribution of panel boundaries on the Jabulani ball compared to the Brazuca ball. The nearly 68% greater total seam length on the Brazuca ball means surface roughness is more evenly distributed over the ball s surface than it is on the Jabulani ball. 4. No-Spin Model Trajectories Possible no-spin soccer trajectories are now considered. Though the model ball will not be spinning, knuckle effects are ignored. Drag coefficient data acquired from the wind-tunnel experiments is used to make comparisons between Brazuca ball and Jabulani ball trajectories.
4 There are two forces on a soccer ball moving through the air. The first acts down on the ball, the ball s weight, mg, where m is the ball s mass and g = 9.8 m/s 2 is the constant magnitude of gravitational acceleration near Earth s surface. The second force is the drag force, which points opposite the ball s velocity and has a magnitude given by equation (1). The buoyant force on the ball from the air is ignored because that force is small ( 1.% of the ball s weight), and it is essentially accounted for when the weight of a ball is measured on a scale. Taking the x axis to point along the horizontal and the y axis to point vertically upward, Newton s second law reduces to ẍ = β v C D ẋ (2) and ÿ = β v C D ẏ g, (3) where β = ρa/2m, v = ẋ 2 + ẏ 2, and a dot signifies one total time derivative. For the Brazuca ball, β =.27 m 1 ; for the Jabulani ball, β =.21 m 1. The difference in β values is due to the Jabulani ball s mass being 1.1% larger than the Brazuca ball s mass. Equations (2) and (3) can be solved numerically with appropriate initial conditions using a fourth-order Runge-Kutta algorithm. 17 For the speed-dependent C D in equations (2) and (3), linear interpolation between experimental wind-tunnel data points is used. To account for drag differences in the A and B configurations, C D data from the two orientations are averaged. See Figure 7 for average C D data. For those readers who wish to create their own trajectories, but desire an analytic equation for C D, the following is offered: 18,19 b C D = a +, (4) 1 + e [(v vc)/vs] where a, b, v c, and v s are fitting parameters. For the Brazuca ball: a =.18899, b =.27177, v c = m/s, and v s =.6823 m/s. For the Jabulani ball: a =.18433, b = , v c = m/s, and v s = m/s. Data-fitting curves using equation (4) are shown in Figure 7. Differences between trajectories using a linear interpolation scheme and equation (4) are small enough to have no influence on the conclusions reached in this paper. Analyzed first is a power shot taken 2 m from the goal, perhaps from a free kick. The ball is kicked with an initial speed of 3 m/s (67.1 mph) at an angle of above the horizontal. Figure 8 shows model trajectories for the power-shot case. Because ball speeds throughout the trajectories are all super-critical in this power-shot case, the Brazuca ball s C D is about 1% larger than the Jabulani ball s C D. Compared to the Brazuca ball, the Jabulani ball arrives at the goal in about 1 ms less time (.737 s vs.72 s), and passes through the goal plane about 6.8 cm higher (1.6 m vs.938 m) and 4.2% faster (2.23 m/s vs m/s). With a final height difference less than one-third the ball s diameter, there are not enough differences between the two trajectories in Figure 8 to postulate that goal keepers will notice much difference between power shots taken in 214 and those taken in 2. Goal keepers may, however, notice differences in the next shot considered. Suppose the ball is kicked 2 m from the goal at an intermediate speed of 2 m/s (44.7 mph). To pass through the goal plane at a reasonable height, the launch angle needs to increase from the power-shot case to 22. Figure 9 shows model trajectories for the intermediate-speed case. Considering all speeds throughout the trajectories, the Brazuca ball never quite reaches the critical region shown in Figure 7, meaning its C D is relatively constant. The Jabulani ball, however, spends its entire flight in the critical region, meaning its C D increases as its speed decreases. Consequently, compared to the Jabulani ball, the Brazuca ball arrives at the goal plane in. s less time (1.189 s vs s), and passes through the goal plane about 1.3 m higher (1.64 m vs.31 m) and 22.6% faster (16.3 m/s vs 13.7 m/s). Given more than a meter height difference and nearly 23% speed difference, differences between intermediate-speed shots in 214 and 2 will be significant.
5 Including knuckle-ball effects serves only to exacerbate the differences observed in the prior analysis. At 2 m/s, the Brazuca ball has a drag force of about 1.64 N, whereas the Jabulani balls has a 2.19-N drag force. Figure shows that the lift and drag forces on the Jabulani ball are comparable or larger than the drag force it experiences. At 3 m/s, the Brazuca ball has a 4.1-N drag force on it; the Jabulani balls has 3.41 N of drag force. Although Figure 6 shows that those drag forces are comparable to the lift and side forces each ball experiences, the Jabulani ball has the greater possibility for more erratic flight.. Conclusions Wind-tunnel experiments show that the Brazuca ball has a lower critical speed than that of the Jabulani ball. The difference in the drag and critical speeds are large enough that intermediate-speed kicks should exhibit noticeable changes in flight patterns for players who participated in the World Cup in both 2 and 214. Computer trajectories for launch speeds at 2 m/s at a distance of 2 m from the goal suggest that goal keepers will see the ball crossing the goal plane more than a meter higher in 214 than in 2. Power shots at high speeds, however, should not result in noticeable differences. There is not enough difference in the super-critical drag coefficients between Brazuca and Jabulani balls to lead to significantly different power-shot trajectories. Because of the ball s reduced critical speed, goal keepers are likely to notice a significant reduction in erratic ball trajectories in the 214 World Cup compared to the 2 World Cup. The Brazuca ball s lower critical speed results in more stable behavior compared to the Jabulani ball. This effort tested and modeled only balls without spin. The next set of wind-tunnel experiments will determine lift coefficients for spinning balls. Adding lift, also known as the Magnus force, 2 to the trajectory model is trivial. 21 A future publication will report lift coefficients and compare three-dimensional trajectories between balls used in the World Cup in 2 and 214. References 1. Lewis M. Official World Cup ball, Jabulani, getting the blame for soft goals - Robert Green - and missed ones. New York Daily News; 14 June Achenbach E. The effects of surface roughness and tunnel blockage on the flow past spheres. J Fluid Mech. 1974;6: Asai T, et al. Fundamental aerodynamics of the soccer ball. Sports Eng. 27;:1. 4. Alam F, et al. A comparative study of football aerodynamics. Proc Eng. 2;2: Alam F, et al. Aerodynamics of contemporary FIFA soccer balls. Proc Eng. 211;13: Asai T, et al. Characteristics of modern soccer balls. Proc Eng. 212;34: Alam F, et al. Effects of surface structure on soccer ball aerodynamics. Proc Eng. 212;34: Goff JE. A review of recent research into aerodynamics of sport projectiles. Sports Eng. 213;16: Myers T, Mitchell S. A mathematical analysis of the motion of an in-flight soccer ball. Sports Eng. 213;16: Choppin S. Calculating football drag profiles from simulated trajectories. Sports Eng. 213;16: Kray T, et al. Magnus effect on a rotating soccer ball at high Reynolds numbers. J of Wind Eng & Ind Aero. 214;124: Lluna E, et al. Measurement of Aerodynamic Coefficients of Spherical Objects Using an Electro-optic Device. IEEE Trans on Instr & Meas. 213;62: Achenbach E. Experiments on the flow past spheres at very high Reynolds numbers. J Fluid Mech. 1972;4: White FM. Fluid Mechanics. 7th ed. New York (NY): McGraw Hill; Ito S, et al. Factors of unpredictable shots concerning new soccer balls. Proc Eng. 212;34: Adair RK. The Physics of Baseball. 3rd ed. New York (NY): Harper Perennial; Press WH, et al. Numerical Recipes: The Art of Scientific Computing. New York (NY): Cambridge University Press; 1986.
6 18. Giordano NJ, Nakanishi H. Computational Physics. 2nd ed. Upper Saddle River (NJ): Pearson/Prentice Hall; Goff JE, Carré MJ. Soccer lift coefficients via trajectory analysis. Eur J Phys. 2;31(4): Daish CB. The Physics of Ball Games. London (UK): The English Universities Press Ltd; Goff JE, Carré MJ. Trajectory analysis of a soccer ball. Am J Phys. 29;77(11):2 7.
7 Fig. 1. Adidas Brazuca soccer ball mounted on stainless steel rod in preparation for wind-tunnel experiment. Also shown are axes associated with the various force directions.
8 Fig. 2. The two orientations used to study knuckle-ball effects. Also shown are axes associated with the various force directions. The drag force would be measured perpendicular to the axes shown.
9 .6..4 Brazuca (A) Jabulani (A) Smooth C D v (m/s) Fig. 3. Wind-tunnel experimental drag coefficient results for the Brazuca and Jabulani balls in orientation A. Error bars show experimental uncertainty. Drag data 13 for a smooth sphere the size of a soccer ball is shown for comparison.
10 .6. C D.4.3 Brazuca (A) Brazuca (B) Jabulani (A) Jabulani (B) v (m/s) Fig. 4. Wind-tunnel experimental drag coefficient results for the Brazuca and Jabulani balls in orientations A and B.
11 1 1 Jabulani (A) Jabulani (B) Brazuca (A) Brazuca (B) Fig.. Lift and side forces at an air speed of 2 m/s (44.7 mph) for the orientations shown in Figure 2.
12 1 1 Jabulani (A) Jabulani (B) Brazuca (A) Brazuca (B) Fig. 6. Lift and side forces at an air speed of 3 m/s (67.1 mph) for the orientations shown in Figure 2.
13 .6..4 Brazuca (AB average) Jabulani (AB average) Fit C D v (m/s) Fig. 7. Wind-tunnel experimental drag coefficient results for the Brazuca and Jabulani balls for orientations A and B averaged together. The fitted curves come from equation (4).
14 y (m) Brazuca Jabulani 3 2 Goal Plane x (m) Fig. 8. Computational trajectories for Brazuca and Jabulani balls kicked 3 m/s (67.1 mph) at an angle of above the horizontal. The goal plane is 2.44 m (8 ft) high.
15 y (m) Brazuca Jabulani 3 Goal Plane x (m) Fig. 9. Computational trajectories for Brazuca and Jabulani balls kicked 2 m/s (44.7 mph) at an angle of 22 above the horizontal. The goal plane is 2.44 m (8 ft) high.
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