## 1 Introduction  
Due to scientific research in the 1960s, footwear started to be designed to improve athletic performance, prevent injuries, provide comfort in sports situations, and protect the foot [1]. These modifications can improve functional factors by changing frictional force, stability, flexibility, and weight, which are footwear's characteristics [2]. The characteristics of footwear can be changed through a combination of materials and designs used for the upper, midsole, and outside--the structure of footwear [3]. The outside is the lowest part of footwear and is the part making contact with the ground [4,5]. Although the outside affects various footwear characteristics, its most crucial role is to provide frictional force between the surface and the footwear [6,7]. Frictional force is the resistance between two objects coming into contact [8]. In sports, frictional force aids in movements such as running, stopping, acceleration, and sudden directional change [8, 9, 10]. At this time, there is a required frictional force for these movements, and it has been reported to be 0.15-0.3 for walking [11], 0.6-0.7 for running [6], and around 1.0 for sports situations [8]. If the frictional force is too low, slipperiness occurs upon movement, so athletic performance declines and injuries are caused [7]. On the other hand, increasing the frictional force can improve performance, but it does not have an effect after certain levels [9,12]. Furthermore, excessive frictional force can cause non-contactinjuries by causing foot fixation to occur during movement [2; 12; 13; 14; 15]. Therefore, setting the proper range of the frictional force to maximize athletic performance while minimizing injury occurrence would be a significant factor in sports situations. The frictional force of footwear can be changed by modifying the contacting surface material, outside material, and outside pattern [6; 16]. Previous footwear research has been carried out investigating the frictional force depending on the outside materials [7; 17] and patterns [18; 19] in soccer [20; 21], American football [8; 22], basketball [4; 17], and tennis [14; 23; 24; 25] to find out the effects of frictional force on movement. The rationale for why studies on the frictional force of footwear are continuously conducted in various sports is that the required level of frictional force depends on the surface characteristics [16] and the movement required for each sport [1]. Hence, accurately understanding body movement and surface characteristics in sports games is essential to finding the proper scope of frictional force. Tennis is played on various surfaces, including grass, clay, and hard court [26]. It is a sport where the front, back, left, and right directional changes are significant [23]. In tennis, directional change movements cause a sliding phenomenon, in which intentional sliding occurs between foot and surface, unlike in other sports games. This sliding phenomenon may occur during dynamic and powerful tennis movements when the horizontal force exceeds the maximum static frictional force [27]. Proper sliding may enhance athletic performance through a quick change of direction with improved stability [24] and reduce injuries by decreasing joint loading [26]. The sliding motion improving athletic performance and reducing injuries is reportedly decided by the size of the frictional force between the surface and footwear [28]. The sliding motion was frequently seen on the clay court in the past [29], but the motion has often been seen on the hard court recently [30]; therefore, tennis shoes' frictional force on the hard court has become more critical. For this reason, several biomechanical studies on tennis shoe frictional force have been conducted [14; 24; 30; 31; 32]. Biomechanical studies have reported frictional coefficients between 0.3 and 0.68 on a hard court [14; 32], while frictional coefficients between 0.72 and 1.8 depending on normal forces during mechanical testing were observed [28; 31].