# Investigation of Reverse Swing and Magnus Effect on a Cricket Ball Using Particle Image Velocimetry
## 3 Experimental Methods  
The experiments were conducted in the open-jet wind tunnel in the Department of Mechanical Engineering at the University of Bath. The working section of the tunnel had a circular nozzle of diameter 0.76 m, a collector with a diameter of 1.1 m, and a working length of 1.5 m. The free-stream turbulence intensity of the tunnel was less than 1%. To assess the boundary layer in a greater level of detail, a hollow, scaled model with twice the diameter (\(d=142\) mm) of a standard cricket ball was manufactured from rapid prototype nylon in two hemispheres that were bonded together. This model featured an accurate, scaled representation of the seam and was a replica of that used by [PERSON] et al. (2015), who assessed the surface roughness equivalent to a ball aged 25 overs--see data in Figure 3. The scaled model did not have a logo embossment, or a secondary seam, features which may affect boundary layer separation. A real cricket ball is worn under match conditions (consequently increasing the surface roughness during the course of a match), whereas the surface roughness of the model was an artefact of the rapid prototyping method. However, the scaled model was appropriate for the experiments, due to the required resolution of the PIV measurements, and the maximum free stream velocity that the wind tunnel could achieve. The surface of the scaled cricket ball had a black, matt finish to minimize any reflections from the PIV laser light. (Minimizing the laser reflections would be very difficult to achieve with a real cricket ball, without compromising the surface features.) The arrangement for the ball in the wind tunnel is shown in Figure 6. The ball was mounted to a rotating shaft, which was spun by a direct current motor up to speeds of 300 rpm to simulate the backspin imparted on the ball by the bowler. The tunnel blockage was approximately 5%. For all measurements which investigated swing, the angle between the seam and the freestream was fixed at \(\beta=15^{\circ}\). Figure 5: (**a**) Side-on illustration of a bowler’s grip on a cricket ball showing direction of spin; (**b**) conventional Magnus force; and (**c**) inverse Magnus force. PIV images were captured by an 8 MP digital CCD (Charged Coupled Device) camera. The free-stream was seeded with oil particles by a TSI Incorporated six-jet droplet generator, which produced a typical droplet diameter of 1 \(\upmu\)m. The droplets were illuminated using a 120 mJ dual-head Nd:YAG laser that generated a sheet of light approximately 1 mm thick. The time between consecutive laser pulses was set to \(\Delta\)t = 4 \(\upmu\)s. The operation of the laser and camera was controlled using a TSI Model 610034 synchronizer. PIV measurements for the reverse swing experiments were taken in the lateral \(x\)-\(y\) plane passing through the centroid of the ball (\(z\) = 0) with the camera mounted above the working section, directed downwards--see Figure 6a. For experiments in which the ball was not rotating, 500 image pairs were collected at a capture rate of 7.5 Hz, from which a time-average was taken. When backspin was applied, images were phase-locked with the rotational frequency of the ball to ensure that any eccentricity did not affect the time-averaged results. To capture the flow field around both the SS and NSS, the ball could be rotated in both directions about the \(z\)-axis (as demonstrated in Figure 7a for the NSS and Figure 7b for the SS). Thus, the camera and laser set-up remained in situ. A wide-angled lens with a 50 mm focal length was used to capture the entire NSS or SS, and a lens with a 100 mm focal length was used to interrogate the area around the point of boundary layer separation on the NSS. The pixel size was approximately 0.06 mm with the 50 mm lens and 0.03 mm with the 100 mm lens. The 50 mm lens was also used for the experiments investigating the Magnus effect, resulting in a pixel size of 0.09 mm. The f-number was set to between \(f\)/5.6 and \(f\)/8.