Aero@tnamic Cofficients qJf Stationary and Spinning Cricket Balls A.T. Sayerso and N.l. Lelimob Received 6 February 2OO7 and accepted 8 June 2OO7 The flight of a cricket ball after leaving the hand of 1. lntroduction a bowler is, for given atmospheric conditions, prin- The game of cricket is a multi-million dollar sport attracting cipally governed by the speed of the ball, the angle thousands of live spectators in stadiums, while millions watch on television throughout the world. The fascination of the game of the seam to the direction of any rotational flight, is of course the duel between the batsman and the bowler. And spin applied to the and the state its outer ball, of while bowlers are often elevated by their supporters to a god-like surface with regard to the degree of wear and status due to their exploits in controlling the flight or movement roughness. This paper desuibes the design of a of the ball after bouncing on the pitch, it is doubtful that either wind tunnel test rig to accurately measure the net they or the bowlers themselves understand the physical prin- ciples behind such feats. Two important phases exist in the drag and side (swing) on stationary and W, forces delivery of a cricket ball. The first is a free flight phase lasting spinning cricket balls. The measurements were per- from the time the ball ^eaves the bowler's hand to when it formed on new unused balls and arfficially rough- bounces on the pitch. During this time, the movement of the ball ened balls at wind tunnel air velocities between it totally under the control of aerodynamic forces. The second phase is the flight of the ball after bouncing off the pitch, and 6 and 40 mls (2.7 x 104< Re < 7.8 x 10s), and seam moving on towards the batsman. This second phase is in the angles between 0 and 90o. The spin speed range was main governed by the orientation of the ball when it hits the pitch, between 2 and 8 revolutions per second (rps). From and is outside the control of the bowler. This paper is concerned the basic data, aerodynamic W, drag and side force with the aerodynamics of the first free flight phase. cofficients are presented and display anomalies to The data of Achenbachl'2 for flow past smooth spheres account for the behaviour of the ball during play. hardly assists in explaining the reasons for the flight trajectories of a cricket ball. This is because the outer leather covering of the It/umerous critical Reynolds numbers are shown to ball is to some extent rough, even when new, while during the side exist where discontinuities in W and force oc- course of a game, it becomes pitted and roughened from contact cur, with the pitch. There is also a primary 'seam', which is raised about 2 mm Additional Keywords: Seam, lift, drag, side forces above the spherical surface of the ball. On either side of this primary seam and parallel to it around the surface are two rows Nomenclature of 80 to 90 stitches that stand about 1 mm above the spherical Roman surface. Some designs of ball, known as four-piece balls, may t C d drag coefficient {= Dl (0.5 pnU d' l+17 also have a secondary seam with internal stitching atright angles C t lift coefficient { = Ll(0.5 ptc(J2 d2 l4)} to the primary seam. Finally, the bowler can impart spin up to C, side force coefficient {= S/(0.5pnUtd'147y about 15 revolutions per second (rps) about an axis through the D drag force (x direction) N centre of the ball, giving rise to a Magnus effect force. Hence the d diameter of ball m orientation of the seam to the direction of flight, the speed of the L lift force (y direction) N ball (i.e. the Reynolds number), and whether the ball is spinning N spin speed of ball rev/s about some axis will all to some extent influence the motion of the Re Reynolds number (pUd/p) ball through the air. The speed at which the bowler delivers the S side force (z direction) N ball can be categorized as fast bowling, where the speed is in the U free stream velocity m/s range 36 < U < 4I+ m/s (130 to150+ km/h); medium pace x longitudinal co-ordinate axis m bowling,intherange26 < U < 36mls (95 to 130km/h);and slow y vertical co-ordinate axis m bowling, in the speed range2} < U < 26 m/s (70 to 95 kmft). In z transverse co-ordinate axis m fast bowling the batsman is deceived into playing a poor shot by the sheer speed of the ball. The ball is generally held with the Greek seam plane vertical, aligned down the pitch and delivered so that T, seam angle about y-ans degrees the seam plane remains upright as it travels through the air with T, seam angle about e-axis degrees very little lateral swing. In mediumpace seambowling, the seam It absolute viscosity of free stream Pas plane is angled to the flight direction to give the ball 'swing' in p density of free stream kdm' the air, while in slowbowling, thebowlerimparts significant spin to the ball, which influences its flight path through the air and the direction of movement of the ball, off the pitch, after it " MSA|MechE Professor, Department of Mechanical Engineering, University of Cape Town, Rondebosch, 77OO, South Africa. E-mail: bounces. However, all types of bowlers are able to spin the ball Anthony.Sayers @ uct. ac.za to give added 'movement' to it as it flies through the air. Shining b Post-graduate Student, Department of Mechanical Engineering, of the ball surface to keep it smooth on one side of the seam whilst University of Cape Town allowing the other side to become rough and worn through play R & D Journal, 2007, 23 (2) of the South African Institution of Mechanical Engineering 25 Aerodynamic coefficients of stationary and spinning cricket Batts can affect the boundary layer flow, and therefore the pressure mine, by direct measurement, a comprehensive set of data of the distribution around the surface of the ball, thus further influenc- aerodynamic forces of both stationary and spinnin_e cricket ing the net force on the ball. balls. This was done for different orientations of the seam ro rhe Lighthill3, in a discussion of the pressure distribution around free stream, for a wide range of seam angles at bowlin_s speeds a sphere, mentions in passing the swing of a cricket ball. Mehta up to 40 m/s, and for spin speeds up to 15 rps. Experimenrs \\ ere and Wooda and Metha5 quantified important parameters in the also performed on an artificially roughened ball. bowling of a cricket ball stating that the critical Reynolds number for transition from a laminar to a turbulent boundary layer was 1.1 Orientation of the ball approximately 1.5 x 105, which is slightly lowerthan fora smooth The important physical parameters, which affect the fli_eht of rhe sphere, and which coffesponds to a speed of about 32 m/s ball, are shown in figures I and 2.The ball has three mutuallr (115 km/h). perpendicular axes x,!, zinthe hori zontal,vertical and sideu'ar s Although there is much experimental data describing the directions respectively. It is assumed to move throu_eh still air. aerodynamic characteristics of smooth and rough spheres and and this is reproduced in a wind tunnel by holdin_e the ball stationary in an air stream p baseballs,r'2'6-to the special surface characteristics of a cricket of density and dynamic r-iscositr ,u. ball renders the use of that data unsuitable for the prediction of flowing in thex-direction and perpendicular to the l'-: plane u ith the aerodynamic forces on a cricket ball. Of cricket ball data, velocity U.In general the resultant force acting on the ball can Bartontt suspended a cricket ball, pendulum like, in an air stream be resolved into three mutually perpendicular componenrs. and measured the transverse angular deflection, from which he namely the drag force D,thelift forc e Landthe side force 5 actinq calculated the side force on the ball. This was done for seam in the x-, y-, and z-directions respectively. Whether or not all o angles of I 5 and 30' to the air stream. When used ( 10 over) balls three component forces are present will depend upon the seam were similarly tested, he found that at 0o seam angle, a relatively angle of the ball and any spin that may be applied to it. The t-ir e large side force also unexpectedly developed. He regretted that parallel lines angled across the surface depict the priman seam tests were not carried out at 0o on a new ball. Bartonrralso and its associated lines of stitching. experimented with spinning balls, the spin being imparted by rolling the balls down a ramp and projecting them into the air v, stream. The side forces were calculated from measured deflec- U, tions upon landing, and known datum conditions. Barton also p stated that his experiments contained weaknesses pertaining to u the means of suspension of the ball and the simplified math- tx Tt= 0o T, 7=90' ematical analysis used, indicating that further detailed experi- Figure 2: Plan view of ball with the seam plane turned about the ments in the same vein should be conducted. Sherwin and y-axts Sprostonr2 placed a trip wire around a smooth sphere to simulate the seam on a cricket ball and compared the sideways force and Figure 2 shows a plan view of the ball with the seam turned drag force with that on a cricket ball at seam and corresponding through angle 7n about the vertical y-axis.