STEVE HAAKE TECHNOLOGY UNIVERSITY OF SHEFFIELD ts por S engin eering

Sports engineering has emerged in Introduction The economics of sport the last two decades as a legitimate ou may have only just heard of I am often told that sport is big business area of research. However, some are sports engineering but it is not a and a few years ago, when grants were still not sure what sports engineering Ynew topic by any means. Over scarce, I wondered where the money is all about and, if it does work, isn’t three hundred years ago, a mechanical was spent. The pie chart in Figure 1a it just cheating? Steve Haake, of the line call device was introduced to Real shows that consumer expenditure in University of Sheffield, has looked at , whilst in 1672 Newton sport in the UK exceeded £15 billion in the economics of sport to see why discussed the way spinning tennis balls 2001. Going clockwise from the top, the it’s so popular and discusses its deviated in flight. More recently, in 1910, first three portions of the chart show attraction to students. Some Sir J.J Thompson gave an explanation that £5.5 billion was spent on products, examples from tennis, and of the dynamics of flight in i.e. clothes and , equipment, wheelchair racing are described to Nature, using the analogy of electron boats and publications. Equipment and show how mainstream engineering beam trajectories. In the last decade or apparel – usually associated with sports principles can be used to analyse so, sports engineering has become very engineering – make up about £4.5 and redesign . popular across the world, particularly in billion per annum of consumer the UK. So what is fuelling this interest expenditure. These sectors saw and is sport ‘big business’ as many significant growth in the 1970s and people say? There is a lot of hype 1980s due to public sector sports surrounding sport, often in the claims of provision and local government equipment manufacturers. So does investment in sports centres. Since the sports engineering work and, if it does, 1990s, however, public investment has isn’t the application of engineering to stopped and participation has remained static. Luckily for sports equipment

sport simply cheating? ingenia manufacturers, sports participants now 23 TECHNOLOGY

Other Expenditure engineering. Loughborough and Birmingham have well established Sport Related Travel courses on sports technology and Sport Clothing and sports and materials science, Footwear respectively. These three institutions alone currently represent yearly intakes Sports TV and video of around 100 students and teach courses such as sports equipment design, ergonomics, vibration and dynamics, aerodynamics and sports materials. At the University of Sheffield, Sport Equipment the elective on Sports Engineering on Health and Fitness the MEng programme in Mechanical Engineering is the most popular final Sport Related year option, with over 80% of the class Publications choosing to take the subject. Combining Spectators sport with engineering is, therefore, an Boats extremely attractive option for students. Participation

Figure 1a Breakdown of UK consumer spending on sport Research in sports (Source: Sport market forecasts, Sports Industries Research Centre, engineering 2001) So what kind of research is there in sports engineering that makes it so interesting? Nearly every university spend more than they did 10 to 15 are currently around 20 undergraduate engineering faculty will have produced years ago, possibly because equipment courses involving the technology or work relating to sport. At Sheffield, the costs almost 30% less in real terms engineering of sport. The University of Department of Mechanical Engineering than it used to. Bath has recently set up BEng and has carried out research into the In the UK, interest in sport has been MEng programmes in sports dynamics of tennis, the aerodynamics fuelled in the last decade by football and by its television coverage (worth around £1.6 billion over three years). With government spending on sport for this decade approaching £750 Sport related publications (b) million, participation is set to rise, Boating

which will in turn boost expenditure on Participation equipment and apparel. This is seen in Sports gambling the chart in Figure 1b, which shows that the sale of sports equipment Sport clothing and footwear should grow by more than 30% Sport related travel between 2000 and 2005. This is over Sports TV and video twice that predicted for the economy Health and fitness

as a whole. Sport is, indeed, very Spectator spending healthy and research in sports Sports equipment engineering should benefit through the General consumer spending growth in sports equipment sales. Sport total

Undergraduates and sports 051015 20 25 30 35 engineering

ingenia Percentage growth in sport spending 2000 to 2005 Over the last decade, academia has woken to the realisation that sport can Figure 1b Predicted growth in sport compared to the growth in general consumer be used to enhance students’ interest in spending. mainstream engineering. In the UK there (Source: Sport market forecasts, Sports Industries Research Centre, 2001) 24 advantage ofa flexiblebeammodel of theballafterimpact.Themain a shot,andthevelocity, angleandspin predict themotion oftheracketduring experimental results andisableto verified towithinafewpercent of vibration. Themathematicalmodelwas and thepositionsofnodes measurements todetermineitsstiffness dimension andthrough vibration direct measurement ofmassand model theracketare foundthrough impact. Theparametersrequired to dominated bythevelocityof increase withdeformation,whichis stiffness anddampingoftheball velocities incontrolled tests.The measuring contacttimesandrebound damping fortheballare foundby model oftheracket.Thestiffness and model oftheballandaflexiblebeam impact baseduponaviscoelastic has resulted inamathematicalmodel of mass andmomentofinertia.Thework spin, stringtype,configuration, Other experimentshaveincludedangle, type, impactpositionandvelocity). had five(balltype,stringtension,racket variables toaminimum;thisexperiment area involveskeepingthenumberof 2(a)).Oneoftheproblems inthis Figure variety ofstringtensions(see positions ondifferent racketswitha tennis balldesignsinavarietyofimpact Impacts were carriedoutusingdifferent Rackets andballs performance. equipment inrelation toits important designparametersfor project’s remit wastodeterminethe TennisInternational Federation.The of Sheffield onbehalfofthe has beencarriedoutattheUniversity Figure 2showssomeoftheworkthat TennisInternational Federation T UK. sort ofworkthatisbeingdoneinthe outlined belowtogiveaflavourofthe wheelchair athletics.Someoftheseare mountaineering iceaxedesignand of football,thedesigniceskates, ennis research withthe peso 5 mph. speeds of150 trajectory model,validupto serve has allowedthedevelopment ofa large rangeofspinsandvelocities and coefficients havebeendeterminedfora cause themtoflyfaster. Dragandlift have dragcoefficients reduced, which which are usedforalongperiodcan down,however,soon worn andballs coefficient byupto10%.Thefeltis few shotswhichcanincreases thedrag out ofthecantendtofluff upaftera influence theirflight.Tennis ballsfresh that thefeltismainparameterto than thenewersmoothones. and cut-upgolfballsflewalotfurther golf ballswhenplayersfoundthatworn accident earlyoninthedevelopmentof smooth. Thiswasactuallyfoundoutby makes itflyalotfurtherthanifwere majority ofagolfball’s trajectorywhich coefficient istherefore lowforthe Reynold’s numbers.Thedrag dimples causetransitionatquitelow contrasted withgolfballswhere the constant forallspeeds.Thisis drag coefficient remains roughly balls shownosuchtransitionandthe Reynold’s numbers.Interestingly, tennis low speed)toturbulentflowathigh at lowReynold’s numbers(equivalentto caused byachangefrom laminar flow from hightolowdragcoefficient is r speeds, dependinguponthesurface values candrop toaround 0.1athigh generally around 0.5atlowspeedsand coefficients ofsmoothspheres are upon theamountofspin.Drag lift coefficients ofupto0.2,depending tennis ballsisapproximately 0.6,with shown thatthedragcoefficient of Sheffield, CambridgeandNASA)has .Research inwindtunnels(at streamlines passingoverarotating Figure 2(b)showsanimageof T the player. energy lossintheballandpoorfeelby tennis racketwhichcontributetoboth it canmimicthereal-life vibrationsofa over asimplerrigidbodymodel,isthat oughness ofthesphere. Thetransition ennis ballaerodynamics TECHNOLOGY Returning totennisballs,itisclear Returning to hard courtsurfaces. lower andfaster, nearer inperformance impact andcausetheballtorebound try toreduce energylossesduring balls havebeenusedonclaycourtsto surfaces. Forinstance,dynamicallystiff construction ofballsfordifferent Manufacturers trytooptimisethe causes theballtorebound steeply. less than65%ofitsimpactspeedand which reduces theball’s rebound to hand, hasahighcoefficient offriction speed atlowangles.Clay, ontheother to rebound withabout70%ofitsinitial coefficient offriction,whichallows aball Figure 2(c). dimple intheballduringimpactseen the ballandcausingcharacteristic appears asawavetravellingaround localised massoftheball,which shell duringimpact.Thisfluxisthe ball, andbythemomentumfluxof dynamic stiffness anddampingofthe is dominated,therefore, bythe friction measure. Theball’s interaction characterised purely byacoefficient of impact, whichallowsthesurfacetobe clay. Thissimplifiesthemodellingof even ‘soft’surfacessuchasgrassand rigid incomparisontotennisballs, all courtsurfacescanbeconsidered (see Figure 2(c)).Theworkshowedthat effect ofthesurfaceonballrebound Another setofexperimentsstudiedthe T string tensionandcourtconstruction. as ballconstruction,racketdesign, effects ofequipmentparameters,such which canbeusedtolookatthe Basic, tennis dynamics,writteninVisual combined tocreate aunifiedmodelof ball/surface impact.Thesewere one foraerodynamics andoneforthe created, onefortheball/racketimpact, Three analyticalmodelswere therefore A completemodeloftennis models. Oneeffect oftheusenew lighter polymerandcarbonfibre phased outinfavourofthenewer, as theoldwoodenracketshave been drastically overthelastthree decades ennis courts Grass surfacesgenerallyhavealow T ennis racketshavechanged 25 ingenia ebound speed of the ball and ebound to within 1%. the recoil of the racket to within the recoil is due to 5%. The discrepancy vibrations in the racket. A flexible ball beam model predicts r freely suspended tennis racket at suspended tennis freely 45 m/s at 6000 frames per second. The ball and the deform about 30 body mm. Rigid the dynamics is able to predict r ennis Federation has looked at all has looked ennis Federation T tennis. the dynamics of aspects of has been An analytical model the motion of to predict produced with the its impact the ball from the air and racket, flight through court to impact with the tennis It has been arrival at the receiver. of racket affects used to assess the the game. and ball design on (a) a tennis ball hitting a Image of Figure 2Figure for the International Recent work TECHNOLOGY on a rigid surface at 35 m/s. The internal accounts for nearly half of the ball’s pressure ball. to an unpressurised compared stiffness ball. The boundary layer separates late on the ball. The boundary layer separates late The top surface and early on the bottom one. of the airflow subsequent deflection downwards deflection due to the spin. indicates an upwards

(c) tennis ball The vertical impact of a pressurised (b) tennis a clockwise rotating across Streamlines

ingenia 26 TECHNOLOGY

30

25 velocity 20 15

10 spin 5

0 -0.16 -0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16 -5

-10

Imparted spin (rev/s) and velocity (m/s) -15 Impact point of centre of foot from centre of ball (m)

Figure 3a A finite element of the lower leg impacting with the ball used to study (b) the effect of kicking position and friction on the ball launch characteristics materials in rackets has been the the ITF to introduce a larger ball into the to a maximum of about 15 revolutions increase in the polar moment of inertia rules of tennis precisely to do the per second (94 rad/s, 900 rev/min) of the racket, reducing the likelihood opposite – to slow the game down. before decreasing to zero as the foot that the racket will twist in the player’s hits the edge of the ball. What is hand, which in turn reduces mishits. Football research interesting is that reducing the The sweet spot of modern tennis Modelling football kicks coefficient of friction to zero does not rackets is also larger – this is the area During every FIFA World Cup, talk reduce the spin to zero for off centre on the strings of the racket that gives inevitably touches on the fabulous free hits, as the ball deforms around the foot the best feel to the player. The sweet kicks that fool defenders and allowing torque to be applied to it. In spot is, in fact, three spots. The first is goalkeepers alike by the amount that practice, this allows the player to impart the point at which the coefficient of they deviate during flight. There is still spin even in extremely wet conditions. restitution of the racket is greatest and no published work detailing lift and drag is quite close to the throat of the racket, characteristics on a spinning football, Aerodynamics of footballs which is where the centre of mass is but Yamagata University, the University Wind tunnel tests were carried out at located. The second is the centre of of Sheffield and Fluent Europe have the University of Sheffield on a quarter percussion or the region on the racket combined their results to go part way scale model of a football to determine where the translation and rotation to explaining the physics behind the its drag coefficient. Figure 4(a) shows during impact with the ball combine to kicks. Yamagata University created an that the drag coefficient for a football give no reaction at the hand. This tends experimentally verified finite element goes through transition from laminar to to be near the centre of the racket. The model of a lower leg impacting with a turbulent flow at a much lower last ‘sweet spot’ is the first node of football. Figures 3(a) and (b) show the Reynold’s number than a smooth vibration which again is near the centre model 4 ms after impact, and the sphere, which is due to the seams on of the racket. Hitting this point doesn’t velocity and spin of the launched ball the football tripping the boundary layer. excite the fundamental vibrations of the for different offsets of the impact For a football, the drag coefficient drops racket, which, in turn, feels good to the location from the centre of the ball. from about 0.5 at low velocities and player. Clearly, near the centre of the ball, no Reynold’s numbers to about 0.2 at The mathematical model developed spin is imparted to the ball and it has a higher velocities. Figure 4(b) shows the by the University of Sheffield and the maximum velocity of about 25 m/s equivalent drag forces on a standard International Tennis Federation can be (90 km/h, 56 mph). As the player kicks sized football. The drag force is given by used either to limit the development of more off centre, the velocity decreases F = 1 ρAC ν2 tennis equipment or encourage it. until it approaches zero, when the D 2 D Manufacturers can use it to look at the centre of mass of the foot and leg where ρ is the density of air, A is the effects of new racket, ball or surface moves outside the ball (i.e. the foot just cross sectional area of the ball, CD is the designs on the improvement of skims the outside of the ball). The spin drag coefficient and v the velocity. The performance. Indeed, the research increases as the player hits more to the drag force is dominated by the square ingenia described here, was used directly by side of the centre of mass, increasing of the velocity and this can clearly be 27 TECHNOLOGY

seen in Figure 4(b). However, what can and using a computational fluid this kick, the ball travels relatively also be seen is that there is a minimum dynamics model of a football created straight into the top corner of the net in in the drag force at around 8.4 m/s by Fluent Europe. It was found that the about 0.9 s. The non-spinning shot is (19 mph, 30 km/h) and a maximum at lift coefficient rises from zero for a non- affected significantly by the seams, about 7.5 m/s (17 mph, 27 km/h). Thus, spinning ball to about 0.2 for a ball with since any slight movement makes the as a football slows down in its flight, it 100 rad/s of spin (950 rad/s). A separation points alter position, giving experiences a sudden jump in drag trajectory model was used to combine an apparently random sideways force force of about 25% (0.5 N compared to all the information gleaned so far to and deviation. This is known as the 0.4 N). These higher drag forces occur study the effects of free kick strategy ‘knuckle ball’ effect in and is

at the end of the trajectory where the using fixed CD and CL values. difficult for keepers to guard ball is travelling slowest and so act to against because of the difficulty in emphasise any lateral deviations that Simulating free kicks predicting where the ball will deviate to. occur due to spin. Two kicks were studied using Typical reaction times of athletes are Lift and drag coefficients on spinning information from the model of the around a quarter of a second so this footballs are difficult to gain and leg/ball impact. The first was a fast free type of shot only leaves around 0.65 s estimates have been found by looking kick at 27 m/s with no spin (60 mph, for the goalkeeper to get to the right at controlled trajectories in sports halls 96 km/h). Figure 4(c) shows that, with place to make a save.

0.6 2.5 (a) 17 mph 19 mph 45 mph 0.5 2.0 27 km/h 30 km/h 72 km/h 0.4 1.5 0.3 Smooth sphere 1.0 0.2 Force, N Quarter scale football 0.1 0.5 Drag Coefficient, Cd (b) 0.0 0.0 50,000 150,000 250,000 350,000 450,000 024681012141618202224 Reynolds Number Velocity (m/s) Figure 4a Drag coefficient vs Reynold’s number b) measured drag forces on a quarter scale football vs Reynold’s number c) trajectories for the flight of two free kicks based upon varying foot impact location to View from half way line give a fast non-spinning shot and a slower spinning 6 shot. (c) Kick 2 4

20 18 2 Height (m) 16 Kick 1 14 12 0 10 Kick 1 -6 -4 -2 0 2 4 6 8 27 m/s Kick 2 Distance from centre of goal (m) 6 no spin 18.5 m/s 4 64 rad/s sidespin 2 0 Side line view 6 -2 -4 (c) Kick 2 Distance from freekick (m) -6 4 -8 Plan view -10 2 ingenia -12 Height (m) (c) -14 Kick 1 -16 0 -12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 02468101214 16 18 20 Distance from centre of goal (m) Distance from free kick (m) 28 TECHNOLOGY

The second simulated free kick had a lower velocity of 18.5 m/s (42 mph, 67 km/h) but with 64 rad/s sidespin (10 rev/s). This shot curves significantly in the air and takes approximately 1.6 s to reach the top corner of the net. So, although the goal keeper has more time to make a save, the deviation is used to disguise the direction of the ball. The shot shown here is likely to bend significantly more than shown due to the higher drag force experienced at the end of the trajectories as the ball goes through transition from turbulent back to laminar flow as shown in Figure 4(a), which has not yet been incorporated into the model. Football manufacturers have understood the significance of the boot/ball interaction on spin for a number of years and have tried to increase the coefficient of friction using geometrical features and new materials on the leather uppers of the to increase spin. For football manufacturers, one of the main innovations in recent years has been the use of polymer coatings on the outside of the ball to inhibit water absorption which could increase the mass of the ball significantly during a game.

Improving elite performance in wheelchair racing The UK government invests heavily in the UK’s elite sportsmen and -women through the various ruling bodies and some of the money is now being Figure 5 Aerodynamic analysis of wheelchair racing required modelling of both earmarked for technological the chair and the athlete development. One such project looked a Model of a wheelchair drawn using Pro-Engineer at the design of racing wheelchairs for b An athlete modelled using actual dimensions and Poser human modelling software the UK wheelchair racing squad via c Fluid flow lines at 7 m/s around the combined model the support of UK Athletics. The optimisation problem was that of improving performance by maximising modelling software. The wheelchair and caused by separation over the the athlete’s power input while athlete were combined and converted shoulders of the athlete. Modifications reducing energy losses from to a mesh suitable for CFD analysis were made to the model of the athlete aerodynamic drag and from wheel (see Figures 5(a) and (b)). CFD analysis and wheelchair to improve interactions with the surface. of the model was carried out by moving performance. Clearly, the results cannot Pro-Engineer CAD software was the surface and the fluid over the model be shown here due to the confidentiality used to assemble a 3D model of a at 7 m/s to simulate a moving required prior to the Athens Olympics in racing wheelchair, whilst a wheelchair. The flow pattern shown in 2004. However, the work has shown representative athlete was created by Figure 5(c) shows recirculation behind how to reduce the drag coefficient of ingenia Sammie CAD Ltd with Poser human the wheelchair and a large wake the athlete and wheelchair which, when 29 TECHNOLOGY

In , for example, from an engineering Conclusions Sports engineering in the UK has a bright point of view, novel materials … and future. The sports industry is forecast to grow faster than the economy, with innovative features could be used … sports equipment growing more than twice as fast. Research in sports However, this would change the game to the engineering is both exciting and challenging and in the future it could help extent that it simply wouldn’t be cricket. the UK to be more successful in major international competitions. Sports engineering is attracting implemented, should benefit the UK’s What is clear, is that the rules of sport many students to courses around the wheelchair athletes, particularly at the are not based around technology, country and the fact that sport can be next Olympic Games in Athens in 2004. science or engineering, but upon used as a mechanism to teach tradition and the need to preserve the mainstream engineering principles and sport’s identity. In cricket, for example, the excitement of engineering should from an engineering point of view, novel not be underestimated. ■ Is sports engineering materials could be used in the bat and another way of cheating? innovative features could be used on the Many sports engineers work for ‘both ball to make it swing more. However, Acknowledgements sides’, these being the equipment this would change the game to the Many thanks to the International manufacturers and athletes on the one extent that it simply wouldn’t be cricket. Tennis Federation for their financial hand and the sports governing bodies The ruling bodies of sport need to support and use of their wind tunnel; on the other. Some sports have be aware of the technological Dr Takeshi Asai at Yamagata University embraced technology and have allowed developments to ensure that nothing for collaboration on football impacts; changes to be made. For instance, too innovative appears. Sports Fluent Europe for their help in the there are no restrictions on the materials engineers, on the other hand, try to aerodynamic analysis of footballs; and that can be used in the polevault and push the envelope of innovations within UK Athletics for their financial support spectacular gains were made in the these rules. As long as all innovations and permission to discuss results 1960s and 1970s when glass fibre adhere to the rules there is simply no relating to wheelchair racing. poles replaced the old wooden poles. In question of ‘cheating’. This creates a the 1980s, in the javelin, a new rule was balance between technology and introduced which moved its centre of tradition with the rules as the boundary Further information mass forward to stop it flying so far and between them. Both sides need to www.sports-engineering.org.uk endangering athletes. Golf, on the other work together to satisfy the demand for Sports Engineering, published quarterly hand, has a number of rules limiting the ever improving performance by athletes by Blackwell Science. specifications of equipment that can be and the public without compromising Sports market forecasts 2001–2005, used in tournament play, as does tennis. the integrity of the sport. Sports Industry Research Centre, Sheffield, email: [email protected]

Dr Steve Haake is Senior Lecturer in Mechanical Engineering at the University of Sheffield and runs the Sports Engineering Research Group. He is Editor of Sports Engineering and Chairman of the International Sports Engineering Association. One day soon, ingenia he will play more sport rather than just write about it! 30