Spinning Cricket Balls

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. In this contl-euration. trip wire angles of 30' and 45". The force measurements were a drag force D and side force S will exist in the x- and :-directions made using a strain gauge attached to the cricket ball support respectively, but there should in theory be no lift force in the sting. In a review of the aerodynamics of sports balls, Mehta5 y-direction since the flow field and therefore the pressure distn- presented further unpublished data for stationary and spinning bution on either side of the horizontal x-zplane is symmetncal. cricket balls and Sayers and Hillt3 presented stationary and The above considerations are for a new stationary ball, and an)' spinning ball data for slow and medium pace bowling speeds up spin imposed on the ball about any axis through its centre, or an\ to 30 m/s. The phenomenon of reverse swing was investigated asymmetrical wear on the surface of the ball will change those by Sayersto using an enlarged model cricket ball and reducing the considerations. Forexample, spin about the z-axis in figure 2 w ith results to forces on an actual ball using similarity considerations. T, - 0" will make the ball rise or dip due to a Magnus effect force The current paper describes experiments carried out to deter- being set up in the vertical *-y plane, while spin applied about the vertical y-axis will generate a Magnus effect side force in the z-direction parallel to the horizontal x-zplane. 2. Experimental Apparatus 2.1 Wind tunnel The experiments were carried out in an U open-jet return circuit wind tunnel, which was driven by a l2-bladed variable-pitch axial flow fan. The open jet test section was 610 mm wide x 430 mm high, with corner fillets at the throat exit, and a working test p section length of 1 m, the areareduction ratio from the settling chamber to the throat being 19:I. The velocity variation across the test section jet was better than I per cent while the turbulence intensity was better than 0.4 %o. Reliable wind tunnel testing p requires the turbulence intensity to be better than 0.6 %ots. In this wind tunnel, low turbulence intensity is achieved by the provi- sion of a long flow path between the fan and the settling chamber, Figure 1: The mutually perpendicular axes of the ball

26 R & D Journal, 2007, 23 (2) of the South African Institution of Mechanical Engineering Aerodynamic Coefficients of Stationary and Spinning Cricket Balls the location of damping screens between the last set of corner had a hole drilled through its centre and perpendicular to the turning vanes and the settling chamber, and a large contraction plane of the seam, and also one drilled through the centre in the ratio between the settling chamber and the test section. plane of the seam, such that the ball was a tight push fit on the The maximum velocity attainable in the test section was support shaft. 4I mls. With the cricket ball in the test section, its area projected upstream in y-zplane resulted in a solid blockage ratio of 1.5 per 3. Experimental Method cent, which is considered negligible for this open-jet wind The experiments are divided into those for stationary and tunnelr6. A three-component (lift , drag,pitch) proprietary aero- rotating balls. The total measured drag is made up from the drag dynamic wind tunnel balance which was located below the test of the ball itself plus the tare drag of the supporting steel shaft. section permitted the cricket ball to be located in the air streaffi, For both the vertically and horizontally mounted balls the tare and the ensuing lift and drag forces were digitally measured with drag was determined by spanning the shaft across the wind an uncertainty that depended on the flow Reynolds number. tunnel air stream with the ball held in front of, butjust separated from it so that it did not touch the shaft. The drag and lift force 2.2 Lift drag and side force measurement on the shaft alone were then recorded over the wind speed range The aerodynamic forces on the ball were required to be measured 0 to 40 m/s. with the minimum interference from any supporting sting or drive mechanism required to spin the ball. Figure 3 shows the square 3.1 Stationary ball experiments frame that was constructed to support both the stationary and The new stationary ball was mounted on the vertical support spinning ball. It is formed from four aluminium bars 700 mm long shaft as in figure 3a with the seam plane lying in the vertical by 30 mm wide by 15 mm deep. The bars are screwed together at r-y plane with /" = 0'. The lift and drag forces were then recorded their corners with corner blocks to provide added rigidity. The for a wind speed range of 6 3 U 3 40 ml s in 2 m/s increments. This two vertical bars have roller bearings housed in them and these was repeated for selected seam plane angles in the range provide support for a 6 mm diameterT}0 mm long rotating steel 5' 3 y, S 90'. For the measurement of the corresponding side shaft on which the cricket ball is mounted. A 40 W variable speed force, the frame was turned so that the support shaft lay drive motor is supported on a bracket attached to one of the horizontally across the air stream as in figure 3b. Commencing vertical legs of the frame and a flexible coupling between the with the seam plane lying in the horizontal x-z plane, it was motor shaft and the ball shaft allows the ball to be rotated at any incremented clockwise in the range 5o( 7. < 90" until it lay in the desired spin speed. A short stub sting could be screwed onto vertical y-zplane, the lift and drag forces being measured over a vertical or horizontal bar of the frame, which permitted the the 6 to 40 m/s wind speed range for each angular increment as whole assembly to be mounted on the aerodynamic balance with before. the ball shaft either vertical or horizontal. This construction For the roughened ball, the above procedure was repeated, ensured that only the ball and short lengths of the ball support with the upstream projected areas of both the smooth and shaft were exposed to the wind tunnel air stream, the remainder roughened surfaces facing upstreambeing initiallythe same, but of the support frame being outside of the air stream. When the projected area of the rough surface decreasing as yn mounted on the balance, the lift and drag forces were measured increased from zero until only the smooth surface faced up- to an uncertainty of 0.05 N and 0.02 N respectively. stream when 7" = 90o. When measuring the corresponding side forces for the rough ball, the rough surface faced in the positive y-direction with the plane of the seam initially lying in the x-z plane with y,= 0o. The seam plane was then incremented clockwise in th erange 5' < y, < 90o and also anti-clockwise in the range -5o( T< -90, the smooth and rough surfaces facing upstream, when 7. = 90" and 7. = -90orespectively. 3.2 Spinning ball experiments The all-smooth and roughened ball were first spun about the z-axis (figure 3b) with the seamplane lyingin the verticalx-yplane with y" = 0'. Each ball was spun in both the clockwise (backspin) and anti-clockwise (topspin) directions at selected spin rates up to 14.5 rps and the lift and drag again measured over the speed Figure 3: (a) Vertical seam plane lift and drag experiments range6S U <40 m/sin2 m/sincrements. (b) Effective vertical seam plane, side force experiments The effective side force was measured by spinning the ball about the vertical y axis (figure 3a) with the seam plane lying in 2.3 Cricket balls the x-z plane with the roughened surface facing the positive The four cricket balls used were standard two-piece, 156 gram, y-direction. For the same increments in wind speed, similar 7 | mm diameter, solid hide red balls manufactured by increments in spin speed, and for clockwise and anti-clockwise A.G. Thomson. There were six rows of stitches that protruded rotation, lift and drag forces were again measured. approximately 2 to 3 mm above the smooth surface, while the actual seam where the two halves of the cover joined, was 4. Results and Discussion approximately 2mmabove the smooth surface. Two of the balls The data is presented as lift, drag and side force coefficients had one half surface artificially roughened with emery cloth to (C,, C * C") for the ball over the Reynolds number range 50000 to simulate a used ball. Each all-smooth (new) and roughened ball 200000 conesponding to the velocity range of l2 to 40 m/s. This

R & D Journal, 2007, 23 (2) of the South African Institution of Mechanical Engineering 27 Aerodynamic Coefficients of Stationary and Spinning Cricket Bails

will allow the data to be applied to the ball flight at any altitude. 0.4 Some discreet lift, drag and side force data is included where appropriate. It is noted that a force coefficient remaining con- E 0.2 stant with increasing Reynolds number implies that the force on O E o.o the ball is increasing as the square of the wind velocity, so care oC) must be taken not to interpret an increasing or decreasing force 3 -o.z O t-r coefficient as an increase or decrease in the absolute force, other .o -+ 15 deg -+ 20 deg -0.4 than at a fixed Reynolds number. The force coefficient could ; x- 30 deg + 45 deg P decrease between wind speeds even though the force itself -+ 60 deg -+- 65 deg -0.6 -+ 70 deg -+ 75 deg lncreases. ^ -+- 80 dee -*- 90 de The drag forces on the horizontal and vertical shafts with the -0.8

ball detached from it are shown in figure 4. A power s0000 l 00000 1 s0000 200000 curve fit shows that each is approximately parabolic with highly Reynolds number acceptable R2 values. The shaft drag at any particular velocity Figure 6: Variation of side (swing) force coefficient at various seam calculated from the curve fit equations was subtracted from the plane angles 7, for the new non-spinning ball combined ball and shaft drag measurements to give the actual drag on the ball. There was no measurable difference in the shaft side force coefficient along the z-axis is shown in figure 6 tor drags when they were spinning, and no measurable lift on either different vertical seam plane angles. the static or spinning shafts. Atzero seam angle there was no side force for all u'ind speeds. This is because of symmetry of the flow and hence the pressure 3.5 distribution on either side of the x-y plane. For other seam an_eles the 3 flow is asymmetrical and a side force in the :-direction o D:0.001U 216s4 Vertical ensues. Between 15" and 60", C, remains sensibly constant. but 2.5 r Horizontal R2 : 0.9998 z^. at65o,70o and 75" it suddenly reduces to a ne-gative value of bo2 GI -0.2 at velocities of 36, 22 and 12 mls respectively. i.e. the ball 'o undergoes reverse swing. This is surprising fi 1.5 as it is _generallr cB ar accepted by players and commentators that reverse su'in_s 22te4 D :0.0005U usually occurs only after about thirty to forty 'overs' u'hen the - 0.5 R2: 0.9996 new ball has become roughened on one side of the seam. At 80 the side force is negative at all wind speeds but lou'er in 0 magnitude than for the 70 and 75" seams with a tendencv ro r0 20 30 40 s0 Wind speed (n/s) approach zero as the velocity is further increased, until at 90' the Figure 4: Support shaft drag variation with wind speed seam plane is lying in the y-z plane with the flow a,_eain bein_s symmetrical about the vertical x-y plane. The positive side force at all velocities up to 60" seam angle is due to boundary laver flou' 4.1 Stationary new ball variations. The boundary layer remains laminar on the +: surface The net Co of the ball along the x-axis is shown in figure 5. up to the seam until it reaches the seam when it is then tripped At wind velocities below about 22mls (Re 100000) the seam = by the seam into a turbulent boundary layer. The consequence angle has little effect on the drag, but at higher velocities, of this is a reduction of pressure on the +e surface caused by' the increasing the seam angle systematically reduces the drag. For boundary layer remaining attached as a turbulent one for a a 90" seam angle at36 m/s (Re 163000), the decrease in drag = greater distance around the remainder of the +z surface. On the coefficient from that at 0o is approximately 20 Vo.With the seam smooth -e side of the ball the laminar boundary layer is not plane vertical, the pressure distribution on either side of the affected by the seam and separates relatively early around that horizontalx-zplane is a mirror image which resulted in no net lift surface, to give a higher relative pressure on that surface. The force either positive or negative in the vertical y-direction. The net result is a positive e-direction side force. The reverse swing that occurs between seam angles 65 0.70 of " o 0deg n 15deg a20deg x 30deg x45deg o 60deg 0.65 + 65 deg r 70 deg o 75 deg o 80 deg r deg 90 0.7 0.60 tr rrla C) 0.6 .C) 0.55 !ts( C) rrr:l Eot oaHuf,gnnugu o 0.50 C) O o 2.0 rps bo al E o.+ 63 0.4s (.) o 5.2 rps o zi;;i;n!!!il 8 o.: o 7.0 rps 0.40 aa aaaa bo ryK-\, a 9.6 rps 0.3 5 Ao, -t\ x 12.0 rps 0.1 x 0.30 14.4 rps 0.0 50000 I 00000 1 50000 200000 Reynolds number 50000 100000 I 50000 200000 Figure 5: Variation of net drag coefficient at varying seam plane Reynolds number angles T, for the new non-spinning ball Figure 7: Effect of ball spin rate on the new ball drag coefficlent

28 R & D Journal, 2007, 23 (2) of the South African Institution of Mechanical Engineering Aerodynamic Coefticients of Stationary and Spinning Cricket Balls and 90' is also due to laminar boundary layer separation now has almost no effect on the drag until only the smooth surface occurring on the smooth +z side of the ball before the seam is up to the seam line faces upstream, the seam then lying in the reached. Since the seam is angled and recedes from the flow y-z plane with T" - 90". Althou Eh Co for the smooth and rough- around the surface, the final pressure distribution is due to a ened ball were expected to be the same at 40 m/s when complex interaction between the separation point and the local T" - 90o, there is a 6 Vo difference which is within acceptable seam location. experimental error. Although the pressure distributions on the surfaces on either side of the vertical seam are different due to 4.2 Spinning new ball the different surface roughnesses, when resolved perpendicular The drag coefficient for the new topspin ball with the seam lying to the horizontal x-z plane, they are mirror images above and in the vertical plane, x-y is shown in figure 7 for topspin where below that plane and should therefore in theory cancel each it is seen to be weakly dependent on high spin speeds. Further, other to give zero net lift. In practice it was found that a weak and similar drag values were obtained for backspin. In figure 8, with variable lift occurred, which are attributable to non-uniform topspin applied, the lift coefficient curves show two distinct surface roughness elements and manufacturing imperfections. regions. For all spin speeds, as the ball velocity increases, the In comparing figures 10 and 6, the effect of surface roughness lift is negative until at a velocity of approximately Il m/s on the side force for positive %, is immediately evident. (Re = 80000) it undergoes a step change to a positive lift of approximately the same magnitude. The almost constant value of C,at higher velocities is indicative of the lift increasing with *, 0.60 the square of the velocity. The lift force is the same for spin 3 o.4o speeds up to 9.6 rps, and only above this value does the spin !E o.2o speed have any effect on C,. Because of flow symmetry on either E() side of the vertical x-y plane, there was no net side force on the E 0.00 ball. € -o.zo (.)

0.4 E-o+o 0.3 -0.60 0'2 s0000 100000 1s0000 200000 E Reynolds number .e 0.1 C) E 0.0 Figure 10: Side force coefficient for the stationary roughened ball at c.) positive seam plane angles 7, g -0. I E -o.z In figure 6, for small seam angles and notably even at zero '-0.3 seam angle, a substantial side force exists until a particular -0.4 Reynolds number is attained, when it becomes negative, i.e. -0.5 reverse swing occurs. For the 0o seam angle at all Reynolds 50000 100000 150000 numbers, the boundary layer over the smooth side is laminar and Reynolds number therefore separates early around that surface. Reverse swing Figure 8: Lift coefficient variation at fixed spin speeds for the new ball occulred at different critical Reynolds numbers as the seam angle changed and can be explained by the angle of the seam and the size of the surface roughness elements together playing an 0.9 o0deg o15deg a20deg x30deg x45deg important part in the boundary layer flow regime. Reverse swing 0.8 o60deg r70deg o80deg r90d occurred at seam angles of 0o, 15' and 20 , although high wind 0.7 tr stream velocities were required to achieve this. This is often c) 0.6 O found in practise when fast bowlers achieve reverse swing after !E 0.5 i::lntntrrrrrrr c) about 30 to 40 'overs' of ball use, when a surface on one side of o AA AAAAAAAAAA o 0.4 oo 6S ot< 0.3 0.2 0.6

0.1 .e 0.4 0.0 !tC) s0000 100000 l 50000 200000 g 0.2 Reynolds number C) (.) Figure 9: Drag coefficient for the stationary roughened ball at positive g 0.0 seam plane angles 7, € f; -o.z 4.3 Stationary roughened ball o The drag coefficients for positive values of seam plane angle y, are shown in figure 9 and are seen to be slightly lower than for s0000 100000 1s0000 200000 the new ball of figure 5. Reynolds number The most notable difference is that although the area of rough- Figure 1 1: Side force coefficient for the stationary roughened ball at ness exposed to the free stream is decreasing as increases, it X, negative seam plane angles 7,

R & D Jountal, 2007, 23 (2) of the South African Institution of Mechanical Engineering 29 Aerodynamic Coefficients of Stationary and Spinning Cricket Balls

the seamplane is highly roughened while the other is maintained 'float' the ball. For wind speeds greater than 22m/s (Re = 100000 I as smooth as possible. A further increase in seam angle caused the lift force became unstable at some Reynolds numbers but the reverse swing to disappear, the swing becoming positive, until general tendency is for the lift to increase negatively u'ith the once again manifesting itself at the 60o seam angle and occurring square of the wind speed as indicated by the almost constant at progressively lower wind velocities as the seam angle in- value of C,between 1 1 800 < Re < 1 82000. It is interestin_e to note creased further. The implication of this is that provided the seam that the variation of C,with Re follows similar trends for all spin angle is large enough, even the slow bowler can achieve reverse speeds. At any given wind speed the spin speed has a si-snificant

swing of the ball. When 1, increases negatively with more of the effect on the side force both in magnitude and direction. In fi,eure roughened surface being exposed to the wind stream (figure 1 1), l4,,theeffect of spin at low wind speeds is to induce ne-eatir.e side the side force is predominantly negative other than at 0o and 90". force. This gradually changes to a positive side force through Between 65o and 80" the forces were extremely unstable after a combination of extremely complicated boundary laver t-lou about 32 mls(Re =14500). interactions involving the Magnus effect and the movement of the critical boundary layer separation point as the Revnolds number changes. It should be remembered that the spin speed 0.7 o 4.8 rps o 7.8 rps " 10.5 rps of the ball surface, which induces circulation and the resultant 0.6 nll.8r?s xl3.2rPs xl3.8rPs E : o Magnus effect, varies between the full peripheral speed at the c.) 0.5 xa?Hfi O lsEnxEUUunE seam, to zero at the axis of spin. E 0.4 C) o 0.25 O 0.3 bo cd o.2o a 0.2 E c :g o 15 0.1 5o o.ro 0.0 3 o.o5 50000 100000 l 50000 200000 ooo Reynolds number B -o.os ; 5.1 .ps -t- 7 4.ps Figure 12: Drag coefficient for a top-spinning roughened ball at -x- 8 -o.ro a- I1.4 rps -x l3.lrps TY= Oo -G 14.l rps = I -l.5rps -0. 15 4.4 Spinning roughened ball 25000 75000 125000 I 75000 As expected, the drag for the spinning ball was the same for Reynolds number topspin and backspin, as well as being independent of the spin Figure 14'. Side force coefficient for the roughened ball with topspin speed, and the topspin Co is shown in figure 12. Tv= 0o Although it is in general only 5 7o lower than for the spinning ^1 new ball of figure 7, the close grouping of the curves for each 5. Error Analysis regime suggests that the spinning rough surface contributes An error analysis was performed on the data by the method of significantly to the drag reduction. Kline and McClintockrT for single sample experiments. Of the independent variables required for the calculation of C,,. C. and 0.4 C,, the density and area were determined through the measure- ment of pressure, temperature and diameter using standard high 0.2 sensitivity instruments. The lift, drag and velocity contributed |.'l G) varying uncertainties depending on the wind tunnel velocin'. O 0.0 E As the velocity decreases towards zero, then since the uncer- c.) -0.2 o tainty in its measurement remains constant, the uncertainties in O ,E -0.4 C,, Co and C, tend towards infinity. The magnitudes of the J uncertainties of pressure, temperature and diameter were of the -0.6 order l0-s, while those for lift, drag and velocity were of the order -0.8 l0 3. Since the total uncertainty is given by the square root of the 2s000 75000 l 25000 17 5000 sum of the squares of the individual variable uncertainties, onlv Reynolds number the uncertainties in lift, drag and velocity measurements were of significance. In figure 5, as the wind speed increased, the Figure 13: Lift coefficient for the roughened ball with topspin at uncertainty in the drag progressively decreased until at the TY= 0o maximum wind speed of 40 m/s the measured drag was 1.88 N The lift coefficient curves in figure 13 show C,to be strongly with an uncertainty of approximately I Vo.The maximum mea- negative at low wind speeds and all spin speeds. At a wind speed sured side force of 1.15 N in figure6 has an uncertainty of 4Vc of 1 2mls (Re = 54000) the lift becomes positive for the spin speed but smooth trends in all the side force curves of this figure, other range 4.2to 10.9 rps and remains at a constant elevated value than where recognised discontinuities due to boundary layer until Re = 83000 when it again becomes negative. At spin speeds flow changes occur, support the validity of the measurements. of 1 2.4, 14.3 and 1 5 .8 rps the negative lift coefficient decreases steadily towards zero. A critical range of spin speeds therefore 6. Conclusions exists over which unexpected dipping or rising of the bowled ball The data curves presented in this paper illustrate the wide can occur and this is the range utilised by slow spin bowlers to

30 R & D Journal, 2007, 23 (2) of the South African Institution of Mechanical Engineering Aerodynamic Coeflicients of Stationary and Spinning Cricket Balls variety offorces that can occur on a cricket ball during use. The the Institution of Mechanical Engineers Part C, 1982,197 ,259- orientation of the seam, the surface roughness through wear and 263. the degree of spin applied to the ball, all affect the flight of the 17. Kline SJ and McClintock FA, Describing uncertainties in ball to some degree, and although the absolute values of the single sample experiments, Mechanical Engineering, 1 953, 7 5, forces acting on the ball may at times be small, they can never- 3-8. the-less lead to significant deviations in its flight trajectory over the length of the playing pitch. These data sets will be used for correlating the results of numerical computational fluid dynam- ics (CFD) simulations of a cricket ball in free flight and will also be useful to those researchers engaged in flight trajectory prediction and analysis. Cricket balls are manufactured by numerous commercial companies. Within the prescribed design parameters of size and weight, the height of the primary seam, the number and height of the stitches and the surface characteristics of the outer cover material can vary. Therefore even for from one ball to another, variations in aerodynamic forces may occur and thus the data presented here is only broadly indicative of the aerodynamic coefficients to be expected.

References I. Achenbach E, Experiments on the flow past spheres at very high Reynolds numbers, Journal of Fluid Mechanics 1972,54, 565 -575. 2. Achenbach E,T\e effects of surface and tunnel blockage on the flow past spheres, Journal of Fluid Mechanics 1974,65, tt3 - 125. 3. LighthiU MJ, Laminar Boundary Layers (edited by L Rosenhead.), Clarendon Press, Oxford,1963. 4. Mehta RandWoodD, Aerodynamics of the cricketball,New Scientist, 1980, 87 (1219), 442 - 447 . 5. Mehta & Aerodynamics of sports balls, Annual Review of Fluid Mechanics, 1985, 17, 151 - 189. 6. Briggs lJ,Effect of spin and speed on the lateral deflection (curve) of a baseball; and the Magnus effect for smooth spheres, Ame ric an J oumal of P hy s ic s, 19 59, 27 (8), 5 89 - 5 96. 7. Watts RG and Sawyer 4 Aerodynamics of a knuckleball, Ame ric an J ournal of P hy s ic s, I97 5, 43 ( I I ), 960 - 963. 8. Frohlich C, Aerodynamic drag crisis and its possible effect on the flight of baseballs, A me rican J ourttal of Phy sic s, 1984, 52 (4),325 -334. 9.Watts RG and Ferrer R, The lateral force on a spinning sphere: Aerodynamics of a curveball, American Journal of Physics, 1987,55 (1),40 - 4. I0. Adair RK, The physics of baseball, Physics Today,1995, 5, 26-3r. ll. Barton, NG, On the swing of a cricket ballinflight, Proceed- ings of the Royal Society of LondonA,1982,379,109 - 131. 12. Sherwin K and Sproston I Aerodynamics of a cricket ball, Inte rnational J ournal of M e chanic al Engineering Education, t982,7t -79. 13. Sayers AT. and Hill A, Aerodynamics of a cricketb all, Journal of Wind Engineering and Industrial Aerodynamics, L999,79, t69 - 182. 14. Sayers, AT,On the reverse swing of acricketball-modelling and measuremenrs, Proceedings of the Institution of Mechani- cal Engineers Part C,2001,215,45 - 55. 15. Pope A and Harper JJ, Low Speed Wind Tunnel Testing. JohnWiley, New York, 1966.

16. S ay e r s AT and B a I I D R, B lockage corrections for rectangular flat plates mounted in an open jet wind tunnel, Proceedings of

R & D Jountal, 2007, 23 (2) of the South African Institution of Mechanical Engineering 31