# Investigation of Reverse Swing and Magnus Effect on a Cricket Ball Using Particle Image Velocimetry
## 2 Literature Review
### Flow Separation on Spheres and Cricket Balls
In practice, cricket balls are imperfect spheres with manufacturing irregularities and an inherent surface roughness, which are exacerbated as the ball ages and wears. Direct side force measurements on new and aged stationary Dukes cricket  
Figure 2: Variation of separation angles (with respect to the stagnation point) for smoothed and roughened spheres. Red represents the difference in separation angle either side of the ball during conventional swing (CS); solid blue shows reverse swing (RS) on an old ball and hatched blue denotes RS on a new ball. Triangles represent roughened non-seam side (NSS) and squares represent seam roughness. balls in a wind tunnel by [PERSON] et al. [4] are presented in Figure 3 as a function of Re. Note that [PERSON] et al. [4; 5] investigated an extensive series of balls aged under first-class match conditions and provided by professional cricketers. For the results presented in Figure 3, the seam angle was set at \(\beta=15^{\circ}\). The critical Re reduces as the ball ages, due to the increasing surface roughness. Interestingly, it shows that RS on a new Dukes ball can be achieved if bowled at 100 mph (Re-\(2.2\times 10^{5}\)), suggesting that the surface roughness of a new ball is in the range \(0<k/d<250\times 10^{-5}\). [PERSON] et al. [5] collected side force measurements on a double-sized scaled model (of the same dimensions and surface roughness as that used in this study) and showed that this 3D printed double-sized model had a similar aerodynamic behavior to a real Dukes ball that is approximately 25 overs old. The critical region (\(1.65\times 10^{5}<\) Re \(<1.75\times 10^{5}\)) is marked in Figure 3. The non-dimensional side force coefficients for CS (C\({}_{Z}\)-0.3) are comparable with the results of other studies on stationary balls [9; 10]. Note that the magnitude of C\({}_{Z}\) for RS is less than that for CS either side of the critical Re (Re\({}_{\rm crit}\)). Sustained swing over the full trajectory of flight is further complicated by aerodynamic drag, which will continually decrease Re; the net lateral movement will be reduced if the ball experiences a combination of both CS and RS. Swing can be elusive and the appropriate conditions for its manifestation, even with experience, may be elusive. In practice, the bowler will impart a small backspin on the ball. [PERSON] et al. [11] found that the optimum spin rate to achieve maximum swing is around 10 rev/s. However, it has been shown that a high backspin can reduce the lateral force [12]. It is argued that the rotation exaggerates the surface roughness and any other protrusions or irregularities, including the quarter seams and logo embossments, disrupting the boundary layer. This rotation effect has been put forth as a skeptical argument against the existence of an LSB on the NSS of a rotating cricket ball in the context of a match [13]. The presence of the LSB on a non-rotating cricket ball was first demonstrated by [PERSON] et al. [5] and later validated by [PERSON] et al. [14]. [PERSON] et al. demonstrated this phenomenon using heated flow visualization and pressure measurements on both a double-scaled ball and on actual cricket balls aged under first-class match conditions. [PERSON] et al. modelled a cricket ball as a sphere with a trip to act as the seam, showing the formation of the LSB using oil flow visualization experiments in a  
Figure 3: Variation of non-dimensional side force (C\({}_{y}\)) with Reynolds number (Re) for Dukes balls at different stages of wear, showing the transition from CS to RS. The double-sized ball used in this paper is comparable in surface roughness to the 25-over-old ball. The critical region for the 25-over-ball is highlighted (\(1.65\times 10^{5}<\) Re\({}_{\rm crit}<1.75\times 10^{5}\)). Adapted from [4]. wind tunnel. Images from the above papers are shown in Figure 4. [PERSON] et al. also showed that an LSB forms over the SS at low Re during the CS regime. Earlier experiments by [PERSON] et al.