Drag force in the wind tunnel

The wind tunnel tests were conducted using different new soccer balls, namely, Brazuca (Adidas, six-panel), Cafusa (Adidas, 32-panel), Jabulani (Adidas, eight-panel), Teamgeist 2 (Adidas, 14-panel) and conventional (Vantaggio, Molten, 32-panel). The balls were mounted as shown in Figure 1. Two panel orientations of the soccer balls identified as orientations A and B (see Figure 2) were used for the study and the corresponding aerodynamic properties were measured.

Figure 1 Photograph of the wind tunnel test setup. Full size image

Figure 2 Soccer balls used for the test and their panel orientations. (a, b) Adidas Brazuca: small dimple and six panels, (c, d) Adidas Cafusa: small grip texture and 32 modified panels, (e, f) Adidas Jabulani: small ridges or protrusions and eight panels, (g, h) Adidas Teamgeist 2: small protuberances and 14 panels; (i, j) Molten Vantaggio (conventional soccer ball): smooth surface and 32 pentagonal and hexagonal panels. (Photo by S.H.). Full size image

It was observed that the drag varied substantially with the ball type (Figure 3). The variation of the drag coefficient with the panel orientation was also significant for Cafusa and Jabulani, whereas it was relatively small for Brazuca, Teamgeist 2 and the conventional ball. The drag crisis regime, which indicates a sudden change in the drag coefficient C d , was lowest for Brazuca, followed by the conventional ball, Cafusa, Teamgeist 2 and Jabulani, in increasing order. In the case of Cafusa, C d decreased from ~0.5 to ~0.2 or less at a Reynolds number Re of 1.7 × 105 for panel orientation A and at Re of 1.5 × 105 for panel orientation B (Figure 3b). The critical Reynolds numbers for Cafusa were ~2.9 × 105 (C d ≈ 0.14) and ~2.4 × 105 (C d ≈ 0.16) for panel orientations A and B, respectively. The critical Reynolds number for Jabulani for panel orientation B was ~3.6 × 105 (C d ≈ 0.12), which was less than the value of ~3.3 × 105 (C d ≈ 0.16) for panel orientation A. These values were less than those for the other balls (Figure 3c). The variation of the drag coefficient with the panel orientation was observed to be small for Brazuca, Teamgeist 2 and the conventional ball (Figures 3a, 3d and 3e). The critical Reynolds numbers for Brazuca were determined to be ~2.5 × 105 (C d ≈ 0.15) and ~2.2 × 105 (C d ≈ 0.16) for panel orientations A and B, respectively. The corresponding values for Teamgeist 2 were ~3.0 × 105 (C d ≈ 0.17) and ~2.8 × 105 (C d ≈ 0.15) and those for the conventional ball were ~2.5 × 105 (C d ≈ 0.16) and ~2.8 × 105 (C d ≈ 0.17), respectively. It was further observed that the variation of the drag on Jabulani with the panel orientation was relatively substantial for Reynolds numbers in the range of 3.0 × 105–5.0 × 105.

Figure 3 Variation of the drag coefficient with the type of ball and panel orientation: (a) Brazuca, (b) Cafusa, (c) Jabulani, (d) Teamgeist 2, (e) conventional ball. Full size image

Side and lift forces in the wind tunnel

Figure 4 shows the scatter diagrams of the lift and side forces that acted on the soccer balls. The diagrams indicate that the irregular fluctuations increased as the flow velocity was increased from 20 to 30 m·s−1. The same trend was observed when the panel orientations were changed. The change in the irregular fluctuation with increasing speed was least for Teamgeist 2 (Figures 4g-1 and 4h-1) and greatest for panel orientation A of Jabulani (Figure 4f-1). The irregular fluctuation was more prominent for the conventional ball when the flow velocity increased. The SD of the side and lift forces also increased with increasing flow velocity (Figures 4k and 4l). This trend was also observed when the panel orientation was changed. The SD of the forces was highest for Jabulani for a flow velocity of 20 m·s−1 and the irregular fluctuations were observed at the intermediate velocity. The SD of the side forces for panel orientation A of Jabulani did not increase with increasing flow velocity. Furthermore, the SD of the side and lift forces for panel orientation B of Jabulani decreased with increasing flow velocity, which was different from the cases of the other balls.

Figure 4 Scatter plots of the side and lift forces of the balls and SDs of the respective forces for each flow velocity (after 9 s). As the flow velocity increased from 20 m·s−1 (a–j) to 30 m·s−1 (a-1– j-1), the irregular fluctuations of the side and lift forces increased. The SD of the side (k) and lift (l) forces increased with increasing flow velocity. Full size image

The correlation between the growth rates of the SD of the side and lift forces when the flow velocity was increased from 20 to 30 m·s−1 and the extended total distances of the panel bonds are shown in Figure 5. Here, the growth rate is defined as the average of the SD of the side and lift forces. The extended total distance of the panel bonds and the number of panels were as follows: 3.32 m and six panels for Brazuca, 4.47 m and 32 panels for Cafusa, 1.98 m and eight panels for Jabulani, 3.47 m and 14 panels for Teamgeist 2 and 3.84 m and 32 panels for the conventional ball. A strong correlation was observed between these parameters and the flow velocity increment (r = 0.64).

Figure 5 Correlation between the growth rate of the SD of the side and lift forces with increasing flow velocity and the extended total distance of the panel bond. Full size image

Figure 6 shows the unsteady aerodynamic forces (side force and lift force) of each soccer ball as amplitudes in the low-frequency range (10 Hz and lower) as per Fast Fourier Transform (FFT). This tended to increase the amplitudes by approximately 2.5 Hz in most cases. In particular, panel orientation B of the Jabulani ball (Figures 6f and 6f-1) and panel orientation B of the conventional ball (Figures 6j and 6j-1) indicated greater amplitudes compared to the other soccer balls in this lower frequency region (2.5 Hz).

Figure 6 Amplitude with respect to unsteady aerodynamic forces (blue line: side force, red line: lift force) of soccer balls derived using FFT at flow speed of 30 m·s−1. (a, b) Brazuca, (c, d) Cafusa, (e, f) Jabulani, (g, h) Teamgeist 2 and (i, j) conventional ball. Full size image

Deviations of the coordinates of the impact points

The balls were actually launched by an impact-type kick robot toward a goal net 25 m away and the points at which they hit the goal net were plotted as shown in Figure 7. The initial velocity of the launch was 30 m·s−1 and the number of ball rotations was less than 1 (no rotation). The launch was repeated 20 times for each panel orientation of each type of ball. The points of impact of Brazuca and the conventional ball were observed to be relatively stable, whereas those of the other three balls (Cafusa, Jabulani and Teamgeist 2) varied substantially with the panel orientation. The impact of Jabulani was unstable and its trajectory varied considerably with the panel orientation (Figure 7c). The trajectories of Cafusa and Teamgeist 2 also varied significantly with the panel orientation (Figures 7b and 7d). The changes in the flight characteristics (points of impact) of Cafusa and Teamgeist 2 with the panel orientation were particularly drastic, which indicated that their panel orientation significantly affected their flight characteristics. Brazuca and the conventional ball exhibited relatively stable and regular flight trajectories compared to Cafusa, Teamgeist 2 and Jabulani, whose panel shapes varied significantly with the orientation and were characterized by relatively irregular flight trajectories. Despite Cafusa having the same number of panels (32) as the conventional ball, it exhibited a large variation in its flight trajectory with the panel orientation.

Figure 7 Comparison of the flight characteristics (points of impact) of the different balls for different panel orientations (initial launch velocity of 30 m·s−1 and angle of 15°). (a) Brazuca, (b) Cafusa, (c) Jabulani, (d) Teamgeist 2, (e) conventional ball. Full size image

Furthermore, the standard deviations (SDs) of the impact point of Cafusa for orientations A and B were respectively 0.17 and 0.16 m in the vertical direction and 0.36 and 0.68 m in the horizontal direction. The corresponding values for Jabulani were 0.14 and 0.51 m and 0.49 and 0.43 m, those for Teamgeist 2 were 0.13 and 0.16 m and 0.22 and 0.32 m, those for the conventional ball were 0.36 and 0.19 m and 0.51 and 0.48 m and those for Brazuca were 0.45 and 0.22 m and 0.22 and 0.20 m. Thus, the SDs of the impact point of Cafusa for panel orientation B was the highest in the horizontal direction, whereas that of Jabulani for panel orientation B was the highest in the vertical direction.

In the scatter plots of the SDs in Figure 8, the horizontal axis represents the SDs of the side and lift forces, respectively and the vertical axis represents the horizontal and vertical SDs of the impact point of the ball on the goal, respectively. A strong correlation was observed between the SDs of the horizontal impact point and the side force (r = 0.62) (Figure 8a) and between the SDs of the vertical impact point and the lift force (r = 0.53) (Figure b).