Original Article
Aerodynamic and surface comparisons between Telstar 18 and Brazuca
Proc IMechE Part P: J Sports Engineering and Technology 1–7 Ó IMechE 2018 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1754337118773214 journals.sagepub.com/home/pip
John Eric Goff1, Sungchan Hong2 and Takeshi Asai2
Abstract Aerodynamic coefficients were determined for Telstar 18 and Brazuca, match balls for the 2018 and 2014 World Cups, respectively. Experimental determination of aerodynamic coefficients prompted the development of computationally determined soccer ball trajectories for most launch speeds experienced in actual play. Although Telstar 18’s horizontal range will be nearly 10% shorter than Brazuca’s horizontal range for high-speed kicks, both Telstar 18 and Brazuca have similar knuckling effects due to nearly equal critical speeds and high-speed drag coefficients that differ by less than 10%. Surface comparisons suggest why aerodynamic properties for the two World Cup balls are so similar.
Keywords Brazuca, Telstar 18, football, soccer, aerodynamics, drag coefficient, side coefficient, lift coefficient, wind tunnel, computational modeling, knuckle-ball
Date received: 18 February 2018; accepted: 3 April 2018
Introduction Adidas has provided the match ball for the World Cup since 1970. Up to and including the 2002 World Cup hosted by Japan and South Korea, which used the Fevernova ball, the balls’ designs consisted of the traditional 20 hexagons and 12 pentagons. That 32-panel design was changed to the 14-panel Teamgeist ball used in Germany for the 2006 World Cup. When the Jabulani ball was introduced for the 2010 World Cup in South Africa, the panel number had been reduced to eight, which required panel texturing so that the ball’s aerodynamics would not be similar to that of a smooth ball. Smooth balls have larger critical speeds (i.e. the speed at which the drag coefficient precipitously increases as ball speed decreases) than rough balls.1 The design of the Brazuca ball was such that, despite having just six panels, two fewer than Jabulani, the total seam length of Brazuca was 68% longer than Jabulani’s total seam length.2 As the authors of this article demonstrated,2 the drag crisis, which is the transition from turbulent to laminar boundary-layer separation as ball speed decreases past the critical speed, occurred for Jabulani in a range of speeds where the majority of corner and free kicks take place. Brazuca’s greater seam length helped increase its surface roughness, which pushed its drag crisis to a lower speed than Jabulani and kept the drag coefficient fairly constant in the range of speeds common for corner and free kicks.
Russia will host the 2018 World Cup, and Adidas has unveiled the Telstar 18 to be used as the official match ball. Like Brazuca, Telstar 18 has six thermally bonded textured panels, but the panel shapes are quite different. This article reports results of wind-tunnel experiments on Brazuca and Telstar 18, verifying previously published work2 for Brazuca and introducing new data for Telstar 18. Wind-tunnel results were used to create model trajectories that illustrate how the balls’ aerodynamic properties lead to various flight trajectories. Much work has been performed on the aerodynamics of soccer balls, and readers are referred to some recently published research.3–7 A relatively recent review article8 on sport aerodynamics provides readers with additional references to work on soccer ball aerodynamics. Understanding of soccer ball aerodynamics has been further enhanced by more research that has been published9–14 since the aforementioned review article appeared. The work presented here not only 1
Department of Physics, Lynchburg College, Lynchburg, VA, USA Faculty of Health and Sports Sciences, University of Tsukuba, Tsukuba, Japan
2
Corresponding author: John Eric Goff, Department of Physics, Lynchburg College, Lynchburg, VA 24501, USA. Email:
[email protected]
2
Figure 1. Telstar 18 soccer ball mounted on stainless steel rod in preparation for wind-tunnel experiment.
contributes to an understanding of World Cup soccer ball aerodynamics, but it also makes connections between ball surface and aerodynamics.
Experimental methods The following two sections describe experiments performed with wind tunnels and measurement techniques to determine surface properties.
Wind-tunnel experiments All wind-tunnel experiments were carried out at the University of Tsukuba in Japan. The low-speed wind tunnel contains a rectangular cross-sectional area of 1:5 m 31:5 m . The turbulence level is less than 0.1%. Telstar 18 and Brazuca balls were placed in the wind tunnel by attaching them to a stainless steel rod. Balls were supported from the rear (i.e. the opposite side from which the air came). Supporting from the rear minimizes the support’s influence on boundary-layer separation.15 Figure 1 shows the Telstar 18 attached to the rod. All balls tested had a diameter of 0.22 m, which means wind-tunnel blockage was approximately 1.7%. Data were obtained during a period of 9 s while air moved over the soccer balls. A six-component stingtype balance (LMC-6522, Nissho Electric Works Co., Ltd., Japan) determined forces with a sampling rate of 1000 Hz. Experiments were performed in the temperature range 8 8 C 16 8 C. Balls were not spinning in the wind tunnel, which means there were an infinite number of choices for ball orientations. Two orientations were chosen, one called the ‘‘0° Orientation’’ and one called the ‘‘45° Orientation.’’Figure 2 shows the two balls tested in the two orientations chosen. Aerodynamic forces were measured at wind speeds in the range of 7 m=s4v435 m=s (16 mph4v 478 mph) with speed increments of approximately 1 m/s. The selected speed range corresponds to a range in Reynolds number of approximately 105 \ Re \ 53105 , where Re = v D=n,16 D = 0:22 m is the ball’s
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Figure 2. The two orientations chosen for the two balls tested in the wind tunnel. Note that the ‘‘45° Orientation’’ is obtained by rotating the ‘‘0° Orientation’’ 45° clockwise about an axis perpendicular to the photos.
diameter, and n = 1:543105 m2 =s is the kinematic viscosity at 24 8 C. That temperature was chosen because the 2018 World Cup will be played in the summer at similar temperatures. The force from the rod on the ball acting in the direction opposite to that of the wind equals the drag force, FD . The drag coefficient, CD , is then extracted from White16 FD =
1 r A C D v2 2
ð1Þ
where A = 0:038 m2 is the cross-sectional area of the ball and r = 1:2 kg=m3 is the air mass density. The force in the horizontal direction is the side force, FS , with corresponding side coefficient, CS , extracted from White16 FS =
1 r A CS v2 2
ð2Þ
The force in the vertical direction is the lift force, FL , with corresponding lift coefficient, CL , extracted from White16 FL =
1 r A C L v2 2
ð3Þ
For balls without spin and perfectly symmetric shedding of their boundary layers, the side and lift coefficients should be zero. World Cup soccer balls, specifically the two tested for this work, are neither perfectly symmetric nor could they be placed perfectly on the support rod. Asymmetric shedding of boundary layers is thus expected, as are nonzero side and lift coefficients. Such asymmetric forces lead to knuckle-ball effects that have been studied for soccer balls17,18 and baseballs.19
Surface measurement techniques Surface properties were extracted from the balls. Total seam lengths, height and width of the seams, were
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Results Results from wind-tunnel experiments, surface measurements, and trajectory analyses are summarized in the following three sections.
Wind-tunnel results and discussion
Figure 3. Schematic representation of the measuring procedure for determining a World Cup soccer ball’s seam height and width.
determined. The height and width were measured using a high-speed, two-dimensional laser scanner (LJV7000, Keyence Corp., Japan). The length of the panel joints was measured using a curvimeter (Concurve 10, Koizumi Sokki Mfg Co., Ltd., Japan). To measure these parameters, all seams of the soccer balls were covered using clay with the height of the imprint representing the panel joint depth and the width representing the panel joint width. Figure 3 shows the schematic representation of the surface measurement procedure. Validity of the aforementioned surface measurements was checked using up-close photography and the software Tracker.20 The software is free, extremely easy to use, and provided visual and quantitative confirmation of the more accurate laser-scanning technique as previously described. The width of a US nickel served as the reference length as shown in Figure 4.
It is emphasized at the outset of this section that the two orientations chosen for this study represent each ball’s no-spin aerodynamics. Significant changes in the aerodynamic coefficients are not expected to occur with other ball orientations. Although no real-world soccer kick will have exactly the ‘‘0° Orientation’’ or ‘‘45° Orientation’’ for its entire flight, results here provide reasonable aerodynamic comparisons between the two balls tested. Figure 5 shows wind-tunnel results for the balls’ drag coefficients while in the ‘‘0° Orientation.’’Figure 6 shows experimental CD data for balls in the ‘‘45° Orientation.’’ Brazuca and Telstar 18 have approximately the same critical speed for both orientations, but Telstar 18 has slightly larger drag coefficients for turbulent boundary-layer separation. A slight reduction in range for high-speed kicks is thus expected during the 2018 World Cup compared to similar kicks in the 2014 World Cup. Telstar 18 has a smaller drag coefficient than Brazuca in the narrow speed range between 12 m=s (27 mph) and 15 m=s (34 mph), suggesting that Telstar 18 might appear slightly faster for some shortrange passes through the air. Figures 7 and 8 show wind-tunnel results for CS for the balls in the ‘‘0° Orientation’’ and the ‘‘45° Orientation,’’ respectively. Telstar 18 and Brazuca have erratic side coefficients for speeds below the critical speed. Telstar 18’s side coefficients for speeds above the
Figure 4. Telstar 18 images in the left column and Brazuca images in the right column. The width of a US nickel provided the standard of length (see middle row). All numbers are in millimeters.
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Figure 5. Wind-tunnel experimental drag coefficient results for the balls in the ‘‘0° Orientation.’’ Straight lines are drawn between data points to aid the eye.
Figure 8. Wind-tunnel experimental side coefficient results for the balls in the ‘‘45° Orientation.’’ Straight lines are drawn between data points to aid the eye.
Figure 6. Wind-tunnel experimental drag coefficient results for the balls in the ‘‘45° Orientation.’’ Straight lines are drawn between data points to aid the eye.
Figure 7. Wind-tunnel experimental side coefficient results for the balls in the ‘‘0° Orientation.’’ Straight lines are drawn between data points to aid the eye.
critical speed are a little closer to zero compared to those of Brazuca, which suggests more symmetric
Figure 9. Wind-tunnel experimental lift coefficient results for the balls in the ‘‘0° Orientation.’’ Straight lines are drawn between data points to aid the eye.
shedding of the boundary layer off Telstar 18 than Brazuca, at least in the horizontal direction for the ‘‘0° Orientation.’’ Figures 9 and 10 show wind-tunnel results for CL for the balls in the ‘‘0° Orientation’’ and the ‘‘45° Orientation,’’ respectively. This time, however, Brazuca shows lift coefficients closer to zero than Telstar 18 for speeds greater than the critical speed. The suggestion now is a more symmetric shedding of the boundary layer off Brazuca than Telstar 18, which is the opposite conclusion reached when examining the side coefficients. Note that rotating a ball 90° means the magnitudes of the side and lift coefficients are exchanged because both coefficients arise from the same aerodynamic phenomenon, namely, an asymmetric separation of the boundary layer. Thus, Telstar 18 and Brazuca should have similar knuckle-ball effects for ball speeds greater than the critical speed.
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Table 1. Seam properties of World Cup soccer balls. Ball
Number of panels
Total seam length (m)
Seam height (mm)
Seam width (mm)
Telstar 18 Brazuca
6 6
4.32 3.32
1.1 1.4
3.3 4.0
Figure 10. Wind-tunnel experimental lift coefficient results for the balls in the ‘‘45° Orientation.’’ Straight lines are drawn between data points to aid the eye.
Surface measurement results For two significant figures, results found using the laser-scanning method matched with Tracker results. Measurement of the heights of the square-shaped textures on the two balls were \ 0:15 mm for Telstar 18 and \ 0:20 mm for Brazuca. Based on physical touch, the textures on Brazuca are higher than Telstar 18. The results of the surface measurements, and verified by photography for Telstar 18 and Brazuca, are displayed in Table 1. Telstar 18 and Brazuca have similar aerodynamic properties, despite Telstar 18’s 30% longer total seam length. To compensate for Telstar 18’s increased surface roughness created by a longer seam length, Telstar 18 has shallower and narrower seams. Brazuca’s square-shaped textures are taller. The seam and panel surface differences offset each other; thus, the two balls have similar critical speeds and similar aerodynamic properties.
No-spin model trajectories Although most balls kicked in the air have at least a little spin, only no-spin soccer trajectories were considered in this study. Aside from not yet having aerodynamic data for spinning Telstar 18 balls, the trajectory analysis presented in this section provides a reasonable comparison of the balls’ trajectories. Because side and lift coefficients were measured, ‘‘knuckle’’ effects were able to be modeled. The balls in the computational model were assumed to be kicked in one of the two orientations shown in Figure 2. An additional assumption was made that ball orientations do not change while in flight.
Figure 11. Trajectory prediction for horizontal range as a function of launch speed for the ‘‘0° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
The model soccer ball was kicked with an initial speed, v0 , at an angle, u0 , with the horizontal. The mass of the model soccer ball, m, is altered for each World Cup ball simulated: Telstar 18 (0.429 kg) and Brazuca (0.426 kg). During its flight, a soccer ball encounters a force from the air and a force from Earth. The buoyant force on the ball is a negligible 1.5% of its weight, so the buoyant force may be ignored. The force from the air has the three components given by equations (1)–(3). Newton’s second law gives m
d2~ rðt Þ ~D + F ~S + F ~L + m~ =F g dt2
ð4Þ
~D , points anti-parallel to the where the drag force, F ~S , is perpendicular to the ball’s velocity; the side force, F ball’s velocity and parallel to the ground; the lift force, ~L , is perpendicular to both F ~D and F ~S and sits in the F plane made by the ball’s weight and the ball’s velocity; and ~ g is the acceleration due to gravity, points down, and has a magnitude of g = 9:8 m=s2 . The procedure followed here is laid out elsewhere21 to solve equation (4). The computational solution was determined using a fourth-order Runge–Kutta algorithm.22 For the aerodynamic coefficients, CD , CS , and CL , linear interpolation between the data found in the wind-tunnel experiments was used. With lines connecting data points, the speed-dependent aerodynamic functions are as shown in Figures 5–10. The launch angle was assumed to be u0 = 258 for all trajectories. The qualitative conclusions do not change
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Figure 12. Trajectory prediction for horizontal range as a function of launch speed for the ‘‘45° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
Figure 14. Trajectory prediction for lateral deflection as a percentage of horizontal range for the ‘‘45° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
Figure 13. Trajectory prediction for lateral deflection as a percentage of horizontal range for the ‘‘0° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
Figure 15. Trajectory prediction for the percent change in horizontal range when the lift coefficient is set to zero for the ‘‘0° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
with other launch angles. Figures 11 and 12 show horizontal range as a function of launch speed for the ‘‘0° Orientation’’ and the ‘‘45° Orientation,’’ respectively. As previously noted, Brazuca’s slightly smaller drag coefficient for speeds greater than the critical speed means its horizontal range is slightly larger than that for Telstar 18. For hard kicks launched faster than 30 m/s (67 mph), Brazuca’s range is 9%–10% longer than that for Telstar 18. Figures 13 and 14 show the amount of launch-speeddependent lateral deflection as a percentage of the horizontal range for the ‘‘0° Orientation’’ and the ‘‘45° Orientation,’’ respectively. Telstar 18 is closer to 0% than Brazuca for speeds greater than 25 m/s (56 mph), which suggests that players will notice less knuckling effects with Telstar 18 compared to Brazuca when they kick for long distance. Lateral deflections for both balls do not exceed more than 4% of their horizontal ranges.
Figures 15 and 16 show the percent change in the horizontal range when the lift coefficient is set to zero for the ‘‘0° Orientation’’ and the ‘‘45° Orientation,’’ respectively. As noted earlier, the knuckling effects for Telstar 18 and Brazuca switch in size when changing from the ‘‘0° Orientation’’ to the ‘‘45° Orientation.’’ For high-speed kicks, Telstar 18’s vertical knuckling effects lead to an approximate 5% change in its horizontal range, compared to approximately 2% for Brazuca. Rotating orientations 90° essentially switches the conclusions made for Figures 13 and 14 with the conclusions made for Figures 15 and 16.
Conclusion This work compares Telstar 18 and Brazuca in anticipation of the 2018 World Cup in Russia. Due to
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7 References
Figure 16. Trajectory prediction for the percent change in horizontal range when the lift coefficient is set to zero for the ‘‘45° Orientation.’’ The launch angle was u0 = 258 . Symbols are not data; they help distinguish the curves.
Brazuca’s slightly smaller drag coefficient for speeds larger than the critical speed, Telstar 18’s horizontal ranges for high-speed kicks will be 9%–10% shorter than the corresponding horizontal ranges seen for Brazuca during the 2014 World Cup in Brazil. Knuckling effects, however, are similar between Telstar 18 and Brazuca. Those effects alter horizontal ranges and add lateral deflections roughly 2%–5% of the horizontal ranges. Telstar 18 and Brazuca have similar aerodynamic properties, which is due to the fact that although Telstar 18’s seams are shallower and narrower than Brazuca’s, Telstar 18 has 30% longer seam length. Telstar 18’s square-shaped surface textures are also shorter than those on Brazuca. The authors of this article are anxious to watch the 2018 World Cup to see whether modeling predictions presented here are realized during play. The work presented here tested and modeled only World Cup balls without spin. The next set of windtunnel experiments will determine aerodynamic coefficients for spinning balls. Modifying the trajectory analysis is straightforward and will follow previously published work.23 Acknowledgements Thanks goes to this article’s two referees, whose suggestions greatly improved the quality of this work. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.
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