# Surface Patterns for Drag Modification in Volleyballs
## 1 Introduction  
When a spherical ball moves through the air, a long tangle of swirling air trails behind it [1; 2; 3; 4; 5; 6]. A turbulent flow causes to slow the ball down. This phenomenon emerges due to drag [4]. At low speeds, the wake is large and the drag is high, while for a ball moving faster than a certain speed, the wake suddenly shrinks and the drag coefficient plummets. The rapid decrease in the drag force is known as drag crisis [4]. The drag crisis occurs when the laminar flow of air in a boundary layer near the ball begins to separate and becomes turbulent [1; 3]. Competitive players can take advantage of the strange aerodynamic effects in volleyball games [4]. The aerodynamic lift and drag forces can make a volleyball swerve up or down and/or side to side: lift acts in a direction perpendicular to motion and drag acts to directly oppose motion [5]. Drag crisis is still a puzzling phenomenon in fluid mechanics [6].  
Ball trajectories are influenced entirely by gravity and aerodynamics [5; 7]. The aerodynamic forces are sensitive to the surface properties of balls. Surface modification in balls is therefore an important task: for instance, dimples on golf balls [5]. A moving ball has a high-pressure area on its front side and leaves behind a turbulent wake region, resulting in lower pressure and higher drag. The drag force can be reduced by dimples on a ball when they induce a thin turbulent boundary layer of air on its surface and lower drag because turbulent boundary layer flow has a larger momentum than laminar boundary layer flow and thus delays separation [8]. Dimples allow the smoothly flowing air to follow the ball surface a little farther around the back side and consequently reduce the drag force as the size of the wake decreases. The spinning action of a golf ball makes the air pressure on the bottom of the ball higher than on the top, generating pressure imbalance and an upward lift force on the ball [5]. Since surface roughness plays a significant role in the turbulence dynamics near the surface, there are recent fruitful efforts for flow control through engineering surfaces [9; 10; 11; 12; 13]. The aerodynamic drag force on a ball depends on its diameter, speed and surface roughness [14]. The drag force can be smaller on a rough ball than a smooth ball, especially at speeds in ball sports [14]. Zigzag paths (knuckleballs) have been reported for volleyballs with the typical ball velocity and the correspondingReynolds number \(\sim\)4 \(\times 10^{5}\)[15]. Practically, aerodynamic modification through pattering surfaces is a plausible task to scientists and engineers [5; 16; 17; 18; 19; 20; 21; 22; 23; 24]..  
In this paper, we demonstrate how surface patterning modifies aerodynamic performance of volleyballs. Particularly we explain why aerodynamic characteristics along transverse and diagonal directions are different in conventional volleyballs with six panels and how isotropic aerodynamics is achieved through isotropic surface patterning with hexagons or dimples. This result gives insight into surface-mediated flight controls of projectiles through resisting fluid media.