Fluid Mechanics of Cricket Ball Swing
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19th Australasian Fluid Mechanics Conference Melbourne, Australia 8-11 December 2014 Fluid Mechanics of Cricket Ball Swing R. D. Mehta Sports Aerodynamics Consultant Mountain View, CA 94043, USA Abstract visualization using thermal imaging, they proposed that reverse swing occurs due to the presence of a laminar separation bubble. The ability to make a cricket ball deviate laterally in flight It is discussed below why this mechanism is not likely to occur in (“swing”) has intrigued cricket players and spectators for years, practice. All the measurements shown in this article are taken arguably since the advent of the game itself. The basic from the author’s own research described by Bentley et al . [2]. aerodynamic principles responsible for the swing of a cricket ball were identified decades ago and many papers have been Aficionados know cricket as a game of infinite subtlety, not only published on the subject. Over the last 35 years or so, several in strategy and tactics, but also in its most basic mechanics. On experimental investigations have also been conducted on cricket each delivery, the ball can have a different trajectory, varied by ball swing, which revealed the amount of attainable swing and changing the pace (speed), length, line or, most subtly of all, by identified the parameters that affect it. Those findings are swinging the ball through the air so that it drifts sideways. The summarized here with updates on phenomena such as late swing actual construction of a cricket ball and the principle by which and the effects of weather conditions on swing. The concept of the faster bowlers swing the ball is unique to cricket. The outer “reverse swing” that became popular in the late 1980s and how it cover of a cricket ball consists of four or two pieces of leather, can be achieved in practice is also discussed, together with the which are stitched together. Six rows of prominent stitching role of “ball tampering.” In particular, the ability of some along its equator make up the “primary” seam, with typically 60 bowlers to effectively swing an old ball in the conventional, to 80 stitches in each row. On the four-piece balls, used in all first reverse and the relatively newly termed “contrast swing” mode is class and international matches, each hemisphere also has a line addressed. The well understood “Magnus” effect on a spinning of internal stitching forming the “quarter” or “secondary” seam. ball is often used by the slower spin bowlers to make the ball drift through the air. It is discussed here how some fast bowlers Fluid Mechanics of Conventional Swing can also generate the same effect. Very recently, it has become apparent that bowlers are able to release a cricket ball without Fast bowlers in cricket make the ball swing by a judicious use of any spin imparted to it. This can lead to a very interesting the primary seam. The ball is released with the seam at an angle “knuckling” effect, similar to that often seen in baseball. to the initial line of flight. Over a certain Reynolds number (Re) range, the seam trips the laminar boundary layer into turbulence Introduction on one side of the ball whereas that on the other (nonseam) side remains laminar (figure. 1). By virtue of its increased energy, the The first published scientific account of cricket ball swing was by turbulent boundary layer separates later than the laminar layer Cooke [5], who gave an explanation of why it was possible for and so a pressure differential, which results in a side force, is fast bowlers to make a new cricket ball “swerve” and why it generated on the ball as shown in figure 1. became more difficult to do this when the shine had worn off the ball. Since then, several articles have been published on the theories of cricket ball swing [7,11,12]. Later on, Barton [1], Bentley et al . [2] and Mehta et al . [13] described detailed experimental investigations where the magnitude of the side force that produces swing and the factors that affect it were determined; see Mehta [14] for a detailed review of the earlier work. The relatively new concept of “reverse swing,” which first became popular in the late 1980s and 1990s, was first explained and discussed by Bown & Mehta [4]. A preliminary analysis of cricket ball swing using computational fluid dynamics was described by Penrose et al . [21]. The flow field around a cricket ball was measured and described by Grant et al . [6] and Sayers & Figure 1. Schematic of flow over a cricket ball for conventional swing. Hill [22] published some measurements of the aerodynamic forces on a spinning cricket ball. Some of the myths and In order to show that such an asymmetric boundary layer misconceptions surrounding cricket ball aerodynamics were separation can indeed occur on a cricket ball, a ball was mounted presented by Mehta [15] and an overview of cricket ball in a wind tunnel and smoke was injected into the separated region aerodynamics was given in Mehta [16]. A relatively new concept (wake) behind the ball where it was entrained right up to the of contrast swing was introduced by Mehta [17] in 2006 and that separation points (figure 2). The seam has tripped the boundary of “Malinga” swing in 2007 [18]. A detailed and more recent layer on the lower surface into turbulence, evidenced by the review of sports ball aerodynamics, which includes cricket balls, chaotic nature of the smoke edge just downstream of the was given in Mehta [19]. Lock et al . [10] presented some surface separation point. On the upper surface, a smooth, clean edge flow visualization and pressure measurements demonstrating confirms that the separating boundary layer was in a laminar conventional and reverse swing. Recently, Scobie et al . [24] state. Note how the laminar boundary layer on the upper surface proposed an alternative fluid mechanic mechanism for reverse has separated relatively early compared to the turbulent layer on swing. Based on their pressure measurements and surface flow the lower surface. The asymmetric separation of the boundary layers is further confirmed by the upwardly deflected wake, which implies that a downward force is acting on the ball. Figure 3. Pressure distributions on a cricket ball held at a seam angle of Figure 2. Smoke flow visualization of flow over a cricket ball. Flow is 20°. from right to left. Seam angle = 40°, flow speed = 17 m/s, Re = 850,000. are known, the aerodynamic forces due to the airflow can be In order to confirm that an asymmetric boundary layer separation easily evaluated. The spin rate and velocity of the ball at the end on a cricket ball leads to a pressure differential across it, 24 of the ramp were measured using strobe photography. Figure 4 pressure taps were installed on a ball along its equator, in a plane shows the measured side force (F), normalised by the weight of perpendicular to that of the seam (figure 3). the ball (mg), and plotted against the ball’s velocity; the side force is averaged over five cricket balls that were tested extensively. At nominally zero seam angle (seam straight up, facing the batsman) there is no significant side force, except at high velocities when local roughness, such as an embossment mark, starts to have an effect by inducing transition on one side of the ball. However, when the seam is set at an incidence to the oncoming flow, the side force starts to increase at about U = 15 m/s (34 mph). The normalised side force increases with ball velocity, reaching a maximum of about 0.3 to 0.4 before declining rapidly. The critical velocity at which the side force starts to decrease is about 30 m/s (67 mph). This is the velocity at which the laminar boundary layer on the nonseam side also undergoes transition and becomes turbulent. As a result, the asymmetry between the two sides (difference in the locations of the boundary layer separation points) is reduced and the side force starts to decrease. Figure 3. Cricket ball with the core removed and 24 pressure taps (1 mm diameter) installed along the equator. Figure 4 shows the measured surface pressures on this ball mounted in a wind tunnel with the seam angled at 20° to the oncoming flow. At low values of Re or velocity (U), the pressure distributions on the two hemispheres are equal and symmetric, so there would be no side force. At U = 25 m/s, the pressure dip on the right-hand (seam-side) face of the ball is clearly lower than that on the left-hand (nonseam-side) face, which would result in the ball swinging towards the seam side. The maximum pressure difference between the two sides occurs at U = 29 m/s (65 mph), when the boundary layer on the seam side is fully turbulent while that on the nonseam side is still laminar. Even at the highest velocity achieved in this test (U = 37 m/s, 83 mph), the asymmetry in pressure distributions is still clearly exhibited, although the pressure difference is reduced. The actual (critical) velocities or Re at which the asymmetry appears or disappears were found to be a function of the seam angle, surface roughness, and free-stream turbulence; in practice it also depends on the spin rate of the ball, as shown and discussed below. In order to measure the forces on spinning cricket balls, balls Figure 4. Variation of normalized side force with flow speed; averaged were rolled along their primary seams down a ramp and projected over five balls.