## 2 Methods  
### Wind-Tunnel Experiment  
For this study, we used a re-circulating wind tunnel (San Technologies Co., Ltd., Tochigi, Japan) located at the University of Tsukuba (Figure 1). The maximum wind velocity of the tunnel was 55 m/s, the outlet dimensions were 1.5 m \(\times\) 1.5 m, the wind velocity distribution was within \(\pm\)0.5%, and the turbulence was less than or equal to 0.1%. The wind tunnel system was able to automatically measure the wind velocity at 0.1 m/s intervals from the Pitot-static tube located above the measurement position of the soccer ball. To ensure that the flow generated from the Pitot-static tube would have no direct effect on the flow around the ball, the ball was positioned at the exact center of the nozzle cross section and the distance between the nozzle and the ball was adjusted to zero for the measurements. For example, when the wind speed was set to 25 m/s, the measured mean wind speed was 25.28 m/s, with a deviation from the measurement position in the range \(-\)0.46% to 0.45% and a wind speed distribution within \(\pm\)0.5%. Similarly, the degree of turbulence downstream of the nozzle when the wind speed was 25 m/s was 0.05 to 0.06, which was within approximately \(\pm\)0.1%, so the error from the ball position had little effect on the wind speed. Furthermore, the measuring system can automatically measure the dynamic pressure at 0.1 Pa intervals by means of the Pitot-static tube placed above the measuring portion of the soccer ball. The length of the sting used in this study was 0.6 m, and its width was 0.02 m. All the soccer balls used in this study had the same diameter of 0.22 m, weight of 0.429 \(\pm\) 0.001 kg, and internal pressure of 0.9 kgf/cm\({}^{2}\). To measure the force of the soccer balls, we attached a round-shaped plate to the rear of the soccer ball to fix it and connected it to the sting. In this arrangement, there was no imbalance caused by changes such as distortions from a round sphere. Figure 1: Wind-tunnel setup. An old-type soccer ball (TUJI-FA, Nassau, Figure 2a) and a new-type soccer ball (Nassau, Figure 2c) were mounted on the wind tunnel for the experiments. The new soccer ball has the same four-panel structure as the old ball. However, a groove in the pattern was introduced into the new-type soccer ball (Figure 2b). The seams on the surface of the two soccer balls used in this experiment were 10 mm wide and 3.8 mm deep. The groove introduced into the new soccer ball (T2) was 450 mm long (450 \(\times\) 4 = 1800 mm total length at all four locations), 5 mm wide, and 2 mm deep (Figure 3). The grooves were carved on the ball surface using a press machine. The difference between a seam and a groove is that a seam is generated between two panels that are tied together, and, depending on the soccer ball type, they are sewn with thread or bond. A groove is a pattern introduced directly to the surface of a panel; it has a unique shape with a slightly different depth and width from that of a seam. The aerodynamic forces on the ball were measured at two different panel orientations, i.e., A and B (Figure 4). Panel orientation (A) positions the air valve front and center, while panel orientation (B) (which is the opposite of orientation (A)) positions the point where the seams meet directly opposite the air valve at the front and center. T1_A indicates the old Type 1 soccer ball positioned at orientation A, and T1_B indicates the same ball positioned at orientation B. Similarly, T2_A indicates the new Type 2 soccer ball positioned at orientation A, and T2_B indicates the same ball positioned at orientation B (Figure 4). We measured the aerodynamic forces applied to each ball at 1 m/s intervals at a wind velocity (\(U\)) ranging from 7 m/s (\(Re\approx 1.0\times 10^{5}\)) to 30 m/s (\(Re\approx 4.7\times 10^{5}\)), the speed interval most commonly used by actual soccer players.