# Investigation of Reverse Swing and Magnus Effect on a Cricket Ball Using Particle Image Velocimetry
## 1 Introduction  
The unique design of a cricket ball allows a bowler to influence both its lateral and vertical movement through the air. Cricket balls are constructed from a cork center and four quadrants of leather tightly stitched around it, forming a primary seam--which sits proud of the surface by 0.5 to 0.8 mm--and two internally stitched quarter seams, resulting in a surface that is almost flush [1]. Figure 1 illustrates the bowler's grip on a cricket ball, which is comprised of six rows of stitching about 20 mm wide in total. To extract lateral movement--known as swing--the bowler may angle the primary seam to the direction of its initial trajectory. This angle is typically around \(\beta=15^{\circ}\). This creates asymmetry in the separation points of the viscous boundary layers on each hemisphere either side of the seam, resulting in a lateral aerodynamic force. This explanation for swing was first theorized by [PERSON] [2]. Although swing can be exploited by a skillful bowler, it is not guaranteed during a match and its presence is controlled by several external factors. Cricket is unique in that the same ball is used over a significant period of time (80+ overs), and the wear and deterioration of the surface will influence the fluid dynamics governing swing. There are several manufacturers of top-quality cricket balls (Dukes, Kookaburra, and Sanspareils Greenlands), each of which produce a ball with a different design of primary seam, resulting in unique swing characteristics. It is of no coincidence that Dukes balls are renowned for swing, as it is their design which has the proudest seam. There are different surfacetextures and rates of surface deterioration for balls produced in different colors: red, white and pink. There are also environmental factors: drier outfields create more abrasive surfaces and variable weather conditions can create microturbulence in the air, which can disrupt the boundary layer on the surface of the ball and influence swing. Of the conditions which are under the control of the bowler and fielding side, swing is principally governed by the Reynolds number (Re--see nomenclature) and the non-dimensional surface roughness (_k/d_) of the ball. The former is limited by the maximum delivery speed of the bowler and aerodynamic drag over the trajectory; the latter is influenced by wear and deterioration as the match progresses, in addition to careful polishing and maintenance within the laws of the game. The most successful exponents of swing typically bowl at speeds in excess of 80 mph (>36 m/s). They also impart a small backspin, which creates enough gyroscopic inertia to stabilize the seam in the  
Figure 1: (**a**) Illustration of a right-handed bowler’s grip on a cricket ball for swing; (**b**) conventional swing, i.e., away-swing to right-handed batsman (RHB) and (**c**) reverse swing, i.e., in-swing to RHB. The laminar separation bubble is highlighted by the grey in-fill. moving frame of reference; there will be little or no swing if the seam wobbles in flight--a consistent pressure asymmetry will not be maintained. In the early overs at the start of a match, while the ball is new and has a smooth lacquered surface, the bowler will typically seek to extract conventional swing (CS) from the ball. To prolong CS, the bowler and fielding side will seek to keep one side as smooth as possible by polishing the ball over the course of the innings. As the ball ages further and the surface deteriorates, reverse swing (RS) can occur. Here, the ball will swing in the opposite direction to CS. CS is well understood, and several articles provide a detailed explanation [3; 4]. An illustration of the boundary layer profiles for this case are shown in Figure 1b. Note that the boundary layer thickness (\(<\)1 mm under match conditions) is greatly exaggerated for illustration. The bowler angles the seam to its principal trajectory by approximately \(\beta\) = 15\({}^{\circ}\), providing the asymmetric conditions necessary for swing.