# Investigation of Reverse Swing and Magnus Effect on a Cricket Ball Using Particle Image Velocimetry
## 2 Literature Review
### Magnus Effect  
Video analysis reveals that swing bowlers apply a typical backspin of around 10 rev/s when they release the ball. In addition to stabilizing the seam, the rotation of the ball induces a Magnus force in the vertical axis (orthogonal to the direction of any swing). This deviation from the main trajectory influences the location of where the ball pitches and is also important to spin bowling. The bowler's hand position to apply backspin is illustrated in Figure 5a. The Magnus force is governed by Re and the spin ratio, \(\alpha\) (see nomenclature), which describes the ratio of the tangential velocity on the surface of a rotating body to the velocity of the freestream. A typical swing bowler, operating at 40 m/s (\(\sim\)90 mph) with a backspin of 10 rev/s, will therefore create a spin ratio of \(\alpha\)-0.06.  
[PERSON] [13] has demonstrated the Magnus effect on a cricket ball in a water channel using dye flow visualization. [PERSON] and [PERSON] [9] collected lift force measurements on a cricket ball rotating about its axis (i.e., \(\beta=0^{\circ}\)) up to spin ratios of \(\alpha=0.3\), showing that the lift coefficient can reach \(C_{L}=0.3\).  
For a rotating sphere in the conventional Magnus regime (Figure 5b), the upper (retreating) side of the ball provides extra momentum to the boundary layer, and so separation is delayed. In addition, if Re is in the super-critical or trans-critical flow regime, the increased relative speed between the surface and the freestream will cause earlier boundary layer separation on the lower (advancing) side. For \(\theta_{\text{ret}}>\theta_{\text{adv}}\), the Magnus force provides lift, and this is classified as conventional Magnus. The boundary layers can be laminar or turbulent, as long as they are operating in the same flow regime.  
It has been theorized that if bowlers impart a large enough backspin on the ball, then the Magnus effect is inversed and the pressure asymmetry and wake switch direction, as illustrated in Figure 5c. ([PERSON] has speculated in sports journalist articles that this is exploited in a singular fashion, such that the ball pitches further from the batsman than expected.) This inversion effect has been demonstrated computationally and experimentally on smooth rotating spheres [16; 17; 18] and dimpled golf balls [19]. It is often explained by an effective Re on the advancing and retreating sides based on the velocity difference, which is the combination of Re and \(\alpha\). [PERSON] and [PERSON] [19] identified that the inverse  
Figure 4: Evidence of a laminar separation bubble on the NSS using two different methods: (**a**) heat flow method on a double-sized cricket ball model [5] and (**b**) oil flow visualization on a sphere with a trip [14].  
Magnus effect on a golf ball only occurs when Re is close to the critical regime. For a dimpled golf ball, which has a roughness that is comparable to the seam of a cricket ball, they found that a sufficient backspin causes the effective Re on the retreating side to reduce to the sub-critical regime, where laminar separation occurs. At this point \(\theta_{\text{ret}}<\theta_{\text{adv}}\) and an inverse Magnus force is generated. It is expected that a similar behavior would occur for a cricket ball, under appropriate conditions.