Shuttlecock aerodynamics - World Badminton€¦ · Shuttlecock aerodynamics Alison J. Cooke EDC, Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2

Shuttlecock aerodynamics

Alison J. Cooke

EDC, Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK

AbstractBadminton is as popular as lawn tennis (when `popular' is de®ned by the number ofadults who play the game). Indeed, the origin of the game, played with a feathershuttlecock, in the mid-19th century is said to predate lawn tennis. The invention of thecheaper, more durable synthetic shuttlecock in the 1950s gave the game a wider appeal.Yet, manufacturers have still to produce a synthetic shuttlecock that exactly mirrors the¯ight of the feather shuttlecock during the game of badminton, a goal they have strivingto reach for over 40 years.

This paper describes experiments which were devised to understand the ¯ow regimearound a shuttlecock and to accurately determine a data set of aerodynamic coef®cientsfor selected feather and synthetic shuttlecocks. The drag, lift and pitching momentcoef®cients were measured for a range of Reynolds Numbers (based on maximum skirtdiameter) selected to cover most velocities reached in a badminton game;13 000 < Re < 190 000 (3 to 44 m s±1). The results form part of a wider programmeof research which examined the differences between feather and synthetic shuttlecocksand ultimately led to a new product.

Keywords: aerodynamic, badminton, drag, lift, pitching moment, shuttlecock

Nomenclature

Cd Aerodynamic drag coef®cientCl Aerodynamic lift coef®cientCm Aerodynamic pitching momentD Drag forced Maximum diameter of shuttlecock skirtF Force applied across strain gauge load cellg Gravitational accelerationH Length of shuttlecockL Lift forceM Aerodynamic pitching momentm Shuttlecock massmbuoyancy Mass equivalent to buoyancy force on shuttlecock immersed in water

Ó 1999 Blackwell Science Ltd · Sports Engineering (1999) 2, 85±96 85

Correspondence address:Dr A.J. Cooke, Engineering Design Centre, Department ofEngineering, Cambridge University, Trumpington Street,Cambridge CB2 1PZ.Tel.: +44 1223 332742, Fax: +44 1223 332662.E-mail: [email protected]

Introduction

Badminton as it is known today seems to haveoriginated from `shuttlecock and battledore' in the1860s, probably at Badminton House in Avon. Thepresent formal rules for the game were laid down in1893 (when the Badminton Association of Englandwas formed), and they evolved around the charac-teristics of the feather shuttlecock. Some rules havechanged since then.

Although the original feather shuttlecock designused for badminton can be traced to the mid-19thcentury, the modern day shuttlecock form wasestablished around 1910; before then it was morebarrel shaped. The hand-manufactured feather shut-tlecock was the only available badminton projectileuntil the 1950s, when the development of injectionmoulding as a manufacturing process had advancedenough to facilitate the production of syntheticshuttlecocks. Synthetic shuttlecocks are more dura-ble and hence cheaper to use. This developmentincreased the popularity of the game as more peoplecould afford to play it. Indeed, in the decade from1983 to 1993, badminton was the most popularracket sport, despite newly arrived squash and well-established lawn tennis (Taylor & Haake 19981 ). Themost recent results from the same survey estimatedthat 2% of the adult population (16-years-old andover) regularly play badminton, compared to 2% fortennis and 1% for squash.

So what will players be using for shuttlecocks inthe future? In March 1994 The New Scientist(Cooke et al. 19942 ), reported that ``within

18 months a new generation of shuttlecocks withcarbon feathers could transform players' atti-tudes.'' Whilst the timescale for such radical newproduct development was ambitious, it is not outof the question that shuttlecocks may indeed bemanufactured in the future with the use of carbon®bre technology. However, top class players stillprefer the feather shuttlecock and consequentlythese are used in all major badminton competi-tions. These players believe that the syntheticshuttlecock still does not behave like a feathershuttlecock.

This paper examines the ¯ow regime around theshuttlecock and, by measurement and comparisonof the aerodynamic design data sets for feather andsynthetic shuttlecocks, discusses some of the majordesign features which probably explain this per-ceived difference in ¯ight behaviour.

Shuttlecock selection for research

There is a large variety of shuttlecocks available inshops today, each of which is marketed as havingadvantages over the others. The shuttlecocksselected for this research were all manufacturedby Carlton (Saffron Walden, UK),3 who providedaccess to details of manufacturing constraints,player opinion and previous shuttlecock designand development. Two shuttlecocks were analysed:a feather shuttlecock and a synthetic shuttlecock.

The feather shuttlecock was chosen as a controlin order to establish the aerodynamic characteris-tics of a recognized high performance product

meff Effective mass of shuttlecock immersed in waterP Force applied axially on strain gauge load cellS Square of maximum skirt diameterT0 Moment applied to strain gauge load cell at position X0

V Shuttlecock velocityVterm Shuttlecock terminal velocity relative to waterx0 Distance measured along strain gauge load cell from bearing tipX0 Position of application of force F, x0 � 15 mma (Angle of) incidence of shuttlecockq Air densityql Density of liquid

Shuttlecock aerodynamics · A. J. Cooke

86 Sports Engineering (1999) 2, 85±96 · Ó 1999 Blackwell Science Ltd

de®ning the badminton game. A Carlton Champi-onship was selected as a popular synthetic shuttle-cock for comparison with the feather product. TheChampionship was designed to simulate a feathershuttlecock, both aesthetically and in ¯ight behav-iour. (It was also designed to have a high spin/rotation rate about its major axis, similar to thefeather shuttlecock.) These shuttlecocks are shownin Fig. 1, with representative dimensions given inTable 1. Both shuttlecocks rotate about the majoraxis in ¯ight. In this research, all measurementswere taken when the shuttlecocks had reachedsteady state rotation, i.e. the maximum rotationachieved. Further work on the spin dynamics canbe found in Hubbard & Cooke (19974 ).

Flow regimes

The shuttlecock is a bluff body and, as such, thepredominant drag regime is base drag. Base drag

strongly depends on the base pressure which, inturn, depends on the form of the wake behind thebody. A full literature review and discussion on¯ow over 2D and 3D bluff bodies relating to theshuttlecock is given in Cooke (1992).

Three techniques were adopted to examine thegeneral ¯ow regime around the shuttlecock: smoke¯ow visualization; pitot-static pressure measure-ments in wake traverses giving radial velocitypro®les and surface static pressure measurementsin solid models.

Two features of the shuttlecock of particularnote and how these affect the ¯ow regime and dragare discussed here; namely, the skirt porosity andthe air jet emerging along the major axis of theshuttlecock (Fig. 1).

Air jet

Static pressure measurements for a full scale solidwooden shuttlecock model suggested that the ¯owover a shuttlecock separates over the nose andre-attaches on the skirt. This is fully described inCooke (1992). However, Figs 2 and 3 from thesmoke ¯ow visualization experiment for thesynthetic (Championship) and feather productionshuttlecocks at Re � 4400 (v � 1 m s±1), showsthat air ¯ows through the gap in the shuttlecock skirt.

Figure 1 Shuttlecock selection.

Table 1 Shuttlecock dimensions

Shuttlecock Model

Feather Championship

Skirt diameter, d (mm) 66.0 65.5

Shuttlecock length, H (mm) 86.0 81.5

A. J. Cooke · Shuttlecock aerodynamics


This ¯ow leads to a jet of air along the axis of theshuttlecock.

The radial pro®les of axial wake velocity con-®rmed that there is a strong jet passing through thecentre of the wake of both shuttlecocks and that,behind the more solid part of the skirts, there is astagnation area. As was seen by observing theaccumulation of smoke behind the feathers, thisstagnation area seems to be more severe in the caseof the Feather shuttlecock where the featherspresent a more complete blockage.

The jet of air through the Feather shuttlecockinteracts with the outer ¯ow to produce an unsteadyand irregular wake pattern. The outer ¯ow tends tocurl inwards towards the shuttlecock axis, whereup-on it meets the fast-moving jet of air which tends tocurl outwards into the stagnation area behind thefeathers. Where the two ¯ows meet, an unsteady¯ow is produced which is then dissipated down-stream. Unlike in the ¯ow over a 2D bluff body(Maull 1978), no strong, regular vortex pattern

emerges. Therefore, it is unlikely that the air jet (orbase bleed) emerging along the centre line of theshuttlecock reduces the drag in the same way that itwould in the case of a 2D bluff body. Indeed, the airjet was found to increase the drag on the shuttlecock,similar to the effect described by Calvert in his studyof ¯ow regimes of solid and porous cones (Calvert1967). In short, the air jet emerging along the axis ofthe shuttlecock entrains the wake air, reducing thewake pressure and hence increasing the drag.

Skirt porosity

In addition to the jet of air passing through the gapin the shuttlecock skirt, the synthetic shuttlecocksalso exhibit a certain amount of skirt porosity.Figure 3 shows the high level of skirt porosity forthe synthetic shuttlecock. The air can be seenbleeding through the skirt (the upper half of theshuttlecock wake in the ®gure). Unlike the syn-thetic shuttlecock, the Feather shuttlecock has little

Figure 3 Smoke ¯ow over championship shuttlecock atRe � 4400 (v � 1 m s±1).

Figure 2 Smoke ¯ow over feather shuttlecock at Re � 4400(v � 1 m s±1).



or no skirt porosity other than the gap. Conse-quently, the air strikes the feathers and is de¯ectedover them. Even though the synthetic shuttlecockmay appear to have more base bleed than thefeather shuttlecock, because of its skirt porosity,there will be no drag reduction because there is nostrong vortex structure.

Drag coef®cient measurement

This section describes the experimental determi-nation of the aerodynamic drag coef®cient using amechanical drag balance and a terminal velocitytechnique.

Wind tunnel experiment with mechanical drag balance

The drag measurements for the shuttlecocks werecarried out in a low speed wind tunnel (Fig. 4),capable of a maximum airspeed of 45 m s±1.

The wind tunnel balance was originally built tomeasure the drag, lift and pitching moment ofaerofoils; measuring drag forces in the range 0±7 N. The maximum system error was 0.02 Nwhich gave a high percentage error in the drag

results at low velocities (Re < 40 000). The termi-nal velocity technique was developed as an alter-native experiment for this low velocity region andwill be described in the following section.

A sting was designed to hold the shuttlecockparallel to the airstream. It contained a low frictionbearing at its tip to allow free rotation of theshuttlecock.

To eliminate the necessity of measuring a stakedrag tare, a shroud was inserted over the stake. Theshuttlecock drag was then measured directly fromthe drag balance.

Each shuttlecock model was mounted on thesting and the drag was recorded for the shuttlecockonce it had reached a steady rotation. The dragcoef®cients were calculated using Equation 1.

Cd � D= 12 qV 2S �1�

where S is based on maximum skirt diameter.The results are presented in Fig. 5 for the feather

and synthetic shuttlecocks. A full discussion on theblockage effect and system errors, and how thesewere measured, is given in Cooke (1992).

Figure 4 Drag balance experiment.



Terminal velocity experiment for drag measurement

A terminal velocity experiment was devised to givealternative results to the wind tunnel experiment atlow Reynolds Numbers (13 000 < Re < 30 000). Inthis range large errors existed in the wind tunnelexperiment.

In this experiment shuttlecocks were droppedthrough a liquid medium and the terminal velocitywas measured by using a laser beam system (Fig. 6).

The equation of motion for a fully submergedshuttlecock falling vertically in a liquid is:

mvdv

dy� meffg ÿ 1

2 CdSqlv2 �2�

where meff is effective mass, de®ned as meff �m ± mbuoyancy.

At terminal velocity, dv/dy � 0, giving thefollowing expression for terminal velocity:

vterm ��2meffg

qlCdS

s�3�

The kinematic viscosities of several liquids wereconsidered in order to achieve the desired range ofReynolds Number, but water proved to be the mostconvenient medium. The Reynolds Number wascontrolled by varying the shuttlecock terminalvelocity. This was achieved by varying the watertemperature to adjust its kinematic viscosity and byadjusting the mass of the shuttlecock.

Equations 2 and 3 were used to calculate thedepth at which the shuttlecock would reach termi-nal velocity. If m � 0.04 kg, ql � 991 kg m±3,CdS � 0.002, v � 0.99 vterm, then y � 0.08 m.The height of the water above the laser beamswas greater than this value to ensure that theterminal velocity was attained before the shuttle-cock passed through the ®rst laser beam.

The drag on the shuttlecock at terminal velocitywas equal to its effective weight (allowing for thebuoyancy effect). The effective mass was measuredby weighing the submerged shuttlecock on a springbalance.

Variation of the shuttlecock mass enabled vari-ation of the terminal velocity and, therefore,Reynolds Number. To achieve this, the centre ofthe shuttlecock noses were drilled out and leadweights inserted.

Equation 3 was used to calculate the value of Cd

at each Reynolds Number. A set of readings for thefeather and synthetic shuttlecocks was taken atambient temperature (approx. 17°C).

The Reynolds Number was varied by changingthe water viscosity. The viscosity was increased bydecreasing the water temperature using ice. The icewas left in the column overnight in order toestablish a homogeneous temperature of approxi-mately 4°C. The results are shown in Fig. 5. Allerrors are fully discussed in Cooke (1992).

Figure 5 Drag coef®cients vs. Reynolds Number.



In principle, Cd for Re > 30 000 could be mea-sured by increasing the temperature of the waterand hence decreasing the viscosity. However, thiswas not necessary as the wind tunnel experimentwas accurate for most of this range.

Analysis of skirt deformation

The skirts of the synthetic shuttlecocks weresuspected of deforming at high speeds. The feathershuttlecock is inherently more stiff as the spines ofthe feathers are tubular, which implies smallerdeformations for the feather shuttlecocks at highspeeds. It was necessary to verify whether there wasskirt deformation in the synthetic shuttlecocks athigh speeds and, if so, what effect this was havingon the drag coef®cients. The veri®cation wascarried out using a video camera and an imageprocessing system as described below.

A Panasonic F10 CCD camera and system kitwere erected alongside the working section to ®lmthe shuttlecock during the drag measurements. Astrobe effect shutter of 1/1000 s was used tominimize blurring. A PC-based image processingsystem was used to determine skirt diameterdeformation at high Reynolds Number (Re �165 000, v � 38 m s±1 approx.).

Measurement of lift and pitching moment coef®cients

To enable a computer prediction of the angularresponse of the shuttlecock, particularly at the apexof its trajectory, data sets of the lift and pitchingmoment coef®cients were required in addition tothe drag coef®cient. A multicomponent straingauge load cell was designed for these measure-ments over a range of incidences (0±30°). Itincorporated 8 strain gauges and was suitable forwind tunnel use. The design calculations werebased on strain gauge theory described by Potma(1967). The load cell is shown in Fig. 7.

The load cell incorporated three Wheatstonebridge circuits: two full bridges, measuring forces Pand F, and one half bridge circuit, measuring thebending moment, T0.

Wind tunnel experiments

The experimental set up was similar to previousexperiments (Fig. 4), but the sting was replaced bythe load cell. The bearing of the load cell waspushed into the nose of the shuttlecock to a depthof 5 mm. The load cell was then connected to thedata processing equipment via cables through thetunnel ¯oor downstream of the shuttlecock.

Figure 6 Water column experiment.



The loads on feather and synthetic shuttlecockswere measured at incidences of 0, 10, 15, 20, 25 and30° over a range of Reynolds Number50 000 < Re < 160 000 (11 m s±1 < v < 37 m s±1).In all cases, the shuttlecock was allowed to rotateon the sting but it was found that at higherincidences (> 30°) the shuttlecock did not freelyrotate (due to restriction by the sting). In the caseof the synthetic shuttlecock, this caused skirtdeformation.

Results

A computer program used the strain gauge mea-surements from The load cell to calculate P, F andT0 for the shuttlecock. These were then used tocompute the lift, drag and pitching momentcoef®cients using the equations below. The frameof reference was transferred to the centre of gravity.This later facilitated the analysis of the equations ofmotion when the shuttlecock was treated as a bodywhich rotated about its centre of gravity. Thecoef®cients are used to predict the shuttlecock motion.

Lift;L � F cos aÿ P sin a �4�

Drag;D � F sin a� P cos a �5�

Pitching Moment;M � T0 � Fx00 �6�

where x0¢ is the distance from position O on theload cell to the centre of gravity. The lift andpitching moment coef®cients were then calculatedfrom:

Cl � L= 12 qV 2S and Cm �M= 1

2 qV 2SH: �7�

The drag coef®cient results in Fig. 5 suggest thatthe errors in the calculated forces due to theequipment are not substantial. In the ®gure it canbe seen that the Cd values agree closely with theresults from both the wind tunnel and terminalvelocity.

The drag, lift and pitching moment coef®cientsare shown in Figs 8, 9 and 10 for a range ofReynolds Number and at various constant inci-dences. In these ®gures, the lift, drag and pitchingmoment coef®cients are plotted vs. incidence atRe � 53 000 and Re � 145 000 (equivalent toapproximately 11 and 32 m s±1). These aerody-namic coef®cients were used in the computerprogram to predict the angular response of theshuttlecock.

Figure 7 Strain gauge load cell.



Discussion

In the following, the values of the aerodynamiccoef®cients for the production shuttlecock modelsare compared. The majority of the results arepresented in terms of Reynolds Number based onthe maximum skirt diameter (0 < Re < 200 000corresponds to 0 < v < 45 m s±1), covering therange of velocities found in a typical badmintongame.

The drag coef®cients

Figure 5 shows the drag coef®cients for eachshuttlecock from the three experiments. The feath-

er shuttlecock has a constant drag coef®cient (atapprox. 0.48) over the whole range of ReynoldsNumber (13 000 < Re < 190 000). The drag coef-®cients for the synthetic shuttlecock decrease withincreasing Reynolds Number. The lower values ofCd from the water column experiment are explainedby the variation in skirt diameter between differentshuttlecocks of the same model. (A 2-mm differ-ence in diameter can effect the drag coef®cient by0.03.) The drag coef®cients for both shuttlecockmodels in Fig. 5 show that the coef®cients areapproximately equivalent and constant (at approx.0.48) up to a Reynolds Number of about 70 000 (or16 m s±1). This result is both encouraging andsurprising.

It is encouraging because the development ofthe synthetic shuttlecock has aimed to reproducethe ¯ight characteristics of a feather shuttlecock.This result proves that, up to a ReynoldsNumber of 70 000, the drag characteristics forthe synthetic shuttlecock match those of thefeather shuttlecock.

The similarity between the drag characteristicsof the synthetic and feather shuttlecocks is surpris-ing because it is generally found that the dragcoef®cient of an object decreases with increasingporosity, as described in Hoerner (1965). Syntheticshuttlecocks are more porous than the feathershuttlecocks and therefore it might be expectedthat its drag coef®cient were smaller. If thesynthetic (the most porous shuttlecock) and thefeather shuttlecock are compared in Fig. 5 it can beseen that the drag coef®cients are equivalent up to aReynolds Number of approximately 70 000.Therefore, the shuttlecock porosity does not seemto be affecting the drag characteristics in the usualmanner. As mentioned earlier, the predominantfeature of the ¯ow over and through the shuttle-cock is the air jet and this dominates any skirtporosity effects.

The jet of air would have a `jet-pump' actionsimilar to the air ¯owing over the shuttlecock, asreported by Hoerner (1950). The jet of air entrainsthe dead air in the wake, causing a furtherreduction in the static pressure in the shuttlecockstagnation area.

Figure 10 Pitching moment coef®cients (load cell).

Figure 8 Drag coef®cients vs. incidence (load cell).

Figure 9 Lift coef®cients vs. incidence (load cell).



Skirt deformation

Above a Reynolds Number of 70 000 the dragco-ef®cient decreases for the synthetic shuttlecockand remains constant for the feather shuttlecock. Ithas long been suspected that one of the disadvan-tages of the synthetic shuttlecock is that the skirtmaterial ¯exibility causes the skirt to deform during¯ight.

The images processed for analysis of skirtdeformation at high Reynolds Numbers showedthat the synthetic shuttlecock (considered to bethe most ¯exible of the synthetic models) didexperience skirt deformation at high ReynoldsNumbers ± in this case a diameter reduction ofabout 1 mm at app-roximately 165 000 (velocityabout 38 m s±1). Conversely, the feather shuttle-cock has no measurable skirt deformation at thesame Reynolds Number.

It is interesting to note that, of all the shuttle-cocks examined, those which demonstrated thegreatest reduction in drag coef®cient were thosewhich had the deepest pressing during the manu-facturing process (i.e. the deviations from a circlearound the skirt base were largest). It is highlyprobable that the deep pressing is the cause of a`concertina' effect which facilitates the closing upof the skirt at high Reynolds Numbers.

Drag at incidence

Figure 8 indicates that the drag coef®cients arefairly constant over the range of incidence coveredby the experiment.

Comparison with previous work

The drag coef®cient data from three other sources,Wichers Schreur (unpublished data), Ward-Smith& Gibson (Unpublished data)5 and Peastrel et al.(1980), generally agree with this work even thoughthey all consider shuttlecocks of different makes (allmeasurements were normalized to account for areadifferences, i.e. diameter variations).

Wichers Schreur measured the drag on severalshuttlecock models. A drag coef®cient of 0.5 was

found for an RSL feather shuttlecock as opposedto a Carlton feather shuttlecock which was usedin this work. Even so, both sets of data are inagreement within experimental error. WichersSchreur used a technique for measuring the stakedrag tare and this is more susceptible to errorsthan the shrouded experimental technique. Thisprobably helps to explain the scatter of his datapoints.

Ward-Smith & Gibson reported a constant dragcoef®cient of 0.51 (based on the frontal area) for aMoroe Seisakusho Company Ltd. feather shuttle-cock. This result has been converted to a dragcoef®cient based on skirt area. Again, this favour-ably agrees with the data from this work on theCarlton Feather shuttlecock.

Lift and pitching moment coef®cients

The load cell experiment measured the drag, liftand pitching moment coef®cients for theshuttlecocks at various incidences over the rangeof Reynolds Number, 50 000 < Re < 160 000(12 m s±1 < v < 35 m s±1).

Lift

Figure 9 shows the lift coef®cients plotted vs.incidence for both shuttlecocks at Re � 53 000and Re � 145 000 (the minimum and maximumReynolds Numbers tested). At 0° incidence, it isreasonable to apply a no-lift condition for anaxi-symmetric bluff body (e.g. ®g. 33 in Hoerner1965 and ®g. 9 in Bostock 1974).

As expected, Fig. 9 shows an approximatelylinear increase in lift coef®cient with incidence.The data for the feather shuttlecock shows veryclose agreement between the low and high Rey-nolds Numbers. There is a smaller increase in liftcoef®cient with incidence for the synthetic shuttle-cock at the higher Reynolds Number, most prob-ably explained by decreased frontal area. Variationsin this effect between the shuttlecocks may bepartly due to differences in skirt porosity whichchange the effective frontal area. The lift coef®-cients for the respective shuttlecocks are similar.



The feather shuttlecock reaches a Cl of 0.38 at anincidence of 30° and the synthetic shuttlecock hassimilar characteristics, reaching a Cl of approxi-mately 0.3 at an incidence of 30°.

Pitching moment

As can be seen in Fig. 10, the pitching moment isalways negative and is thus a restoring moment.Hence, the shuttlecock is always stable. Thepitching moment coef®cients (based on the lengthof the shuttlecock) approximately follow the sametrends as the lift coef®cients in both ®gures.

Conclusions

Little technical information is available on thesubject of shuttlecocks. However, in this research,shuttlecock aerodynamics was investigated by:

· considering relevant literature on 2D and 3Dbluff bodies;

· performing ¯ow visualization experiments todetermine ¯ow regimes;

· comparisons of aerodynamic coef®cient measure-ments for synthetic and feather shuttlecocks;

· discussing particular design features affectingshuttlecock aerodynamic coef®cients.

It was found that:

· the shuttlecock is a bluff body and the predom-inant drag mechanism is base drag.

· Increased porosity does not necessarily reducethe drag coef®cient. The introduction of the gapin the shuttlecock skirt was found to increasedrag coef®cient because of the strong axial air jet,producing a jet-pump effect.

· The drag coef®cients of the feather and syntheticshuttlecock were approximately constant (at 0.48)and equivalent up to Reynolds Numbers of70 000 (16 m s±1). Above Re � 70 000, the dragcoef®cient decreased for the synthetic shuttle-cock and stayed constant for the feather.

· It was shown that this decrease in drag coef®cientwas due to a reduction in frontal area caused byskirt deformation.

· The lift coef®cients for both shuttlecocksincrease with increasing incidence, reachingvalues over 0.3 at 30° incidence.

· The pitching moment coef®cient measurementsfor both shuttlecocks suggested that the aerody-namic centre is always behind the centre ofgravity, i.e. the shuttlecocks are stable at alltimes.

These conclusions were used in the development ofa new synthetic shuttlecock product, as discussed inDixon & Cooke (1995) and Cooke (1996).

Acknowledgements

The author is grateful for the ®nancial support ofthe EPSRC and Dunlop Slazenger throughout theresearch. She would also like to thank DunlopSlazenger for free access to information about theproducts and Dr L. C. Squire for his technicalsupport.

References

Bostock, B.R. (1974) Slender Bodies of Revolution at Incidence,PhD Thesis, Cambridge University, Cambridge, UK.

Calvert, J.R. (1967) The Separated Flow behind AxiallySymmetric Bodies, PhD Thesis, Cambridge University,Cambridge, UK.

Cooke, A.J. (1992) The Aerodynamics and Mechanics ofShuttlecocks, PhD Thesis, Cambridge University,Cambridge, UK.

Cooke, A.J. (1996) Shuttlecock design and development.Sports engineering ± design and development (ed. S. J.Haake). Proceedings of the 1st International Conferenceon the Engineering of Sport. Blackwell Science, Oxford,UK.

Cooke, A.J. & Mullins, J. (1994) The ¯ight of theshuttlecock, New Scientist, 1916, March6 .

Dixon, J. & Cooke, A.J. (1995) Managing product design: acase study from the consumer sports industry. ProductDesign Seminar 1995, Teaching Company Directorate.7,87,8

Hoerner, S.F. (1950) Base drag and thick trailing edges.Journal of the Aeronautical Sciences, 17, 622±628.

Hoerner, S.F. (1965) Fluid Dynamic Drag. Hoerner FluidDynamics10 , Midland Park, NJ, USA.

Hubbard, M. & Cooke, A.J. (1997) Spin dynamics of thebadminton shuttlecock. Biomechanics Conference,Tokyo University.11



Maull, D.J. (1978) Mechanisms of two and three-dimensionalbase drag. Symposium on Aerodynamic Drag Mechanisms ofBluff Bodies and Road Vehicles. Plenum Press12 , New York,NY, USA.

Peastrel, M., Lynch, R. & Armenti, A. Jr (1980) Terminalvelocity of a shuttlecock in vertical fall. American Journalof Physics, 48, 511.

Potma, T. (1967) Strain Gauges: Theory and Application.Philips Paperbacks14 , Eindhoven, The Netherlands.

Taylor, P. (1998) The economics of the sports productsindustry. Sports Engineering ± Design and Development (ed.S.J. Haake). Proceedings of the 2nd International Con-ference on the Engineering of Sport. Blackwell Science,Oxford, UK.



Shuttlecock aerodynamics - World Badminton€¦ · Shuttlecock aerodynamics Alison J. Cooke EDC, Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2

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