## 1 Introduction  
In the last few years, the design of the official soccer balls has changed in each FIFA World Cup. In particular, between the 2006 World Cup in Germany (Teamgeist, 14-panels, Adidas) and the 2018 World Cup in Russia (Telstar 18, 6-panels, Adidas), the shape of the official soccer balls changed significantly. The number of ball panels was considerably reduced from 32 (used from the 1970 World Cup in Mexico until the 2002 World Cup in South Korea and Japan), to 14 (2006 World Cup), 8 (2010 World Cup), and 6 (2014 and 2018 World Cup). Furthermore, from the 2008 EURO Cup event, the surface roughness of the soccer balls changed from being very smooth to having small protrusion patterns with different shapes, such as square, triangular, and hexagonal [1]. The players, the coaches, and the spectators are very interested in the aerodynamics and flight trajectories of the new type of soccer balls. Many studies on the effects of the soccer balls' shapes on aerodynamics and flight trajectories have been conducted [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. Studies on the effects of the panel orientation variations, owing to the number of panels reduction, on the aerodynamics and flight trajectories of the soccer balls have also been published [14, 15, 16, 17, 18]. In modern soccer balls, not only the number of panels but also the surface roughness (bumps and dimples) significantly change, substantially affecting the ball aerodynamics [1, 19, 20, 21, 22]. Additionally, depending on the type of soccer ball and its producer, the material used for the ball surface varies considerably. Specifically, the aerodynamic properties change significantly depending on whether the seam structure between the soccer ball panels is made using stitching threads or adhesive bonds. This increases or decreases the distance of the soccer ball, and also affects the stability of the ball during flight [8, 19]. It is considered extremely difficult to directly compare such soccer balls as is. A review on these soccer balls was also published [23].  
However, in all previous studies, only new soccer balls were tested to study their aerodynamics. While in international events such as the FIFA World Cup, it is possible to use a new ball for each game, in games not involving the professional teams, such as amateurs, schools, and club teams, used balls are utilized. However, no fluid dynamics studies were ever conducted on used soccer balls. For this reason, in this study, we analyzed the flight trajectories and aerodynamics of soccer balls kicked 1000 times (used balls) by a robot for a certain period. In this study, we used three new and three used soccer balls (1 Telstar 18 (Adidas), 2 Merlin (Nike), 3 Derbystar (Select Sports)) designed by three different manufacturers. We compared the aerodynamics of these soccer balls through wind tunnel tests. Additionally, we studied the effects of the soccer ball conditions (used vs. new) on the aerodynamic forces acting on the ball by analyzing the flight trajectories of each ball. Based on the results obtained from these experiments, we aim to elucidate the aerodynamic characteristics and flight trajectory characteristics of the used soccer balls.