Mechanics, Virginia Tech, Hall,Blacksburg, VA 332Norris 24061,USA. *Author ([email protected]) for correspondence IN 47907,USA. Mechanical Engineering, PurdueUniversity, 585PurdueMall,West Lafayette, Blacksburg, VA 24061,USA. 382 Received 10May2013; Accepted30September2013 1 flying snakeundulatesfromsidetoside,sendinglarge-amplitude Southeast Asiaknownfortheirabilitytoglide.Whengliding, a ‘Flying’ snakesareagroupoffivespeciesarborealin Wake dynamics,Particleimage velocimetry KEY WORDS:Flyingsnake,Gliding,Bluffbodyaerodynamics, gliding performanceofflyingsnakes. movements ofaerialundulationarerequiredtofullyunderstand the more complexmodelsthataccountfor3Deffects andthedynamic glide atsteepanglesandoverawiderangeofattack,but These aerodynamiccharacteristicshelptoexplainhowthesnakecan near-maximum lift-to-dragratiosoverawiderangeofparameters. aerodynamic behaviorbymaintainingsignificantliftproductionand sectional geometryoftheflyingsnakedemonstratedrobust up tothehighestangleofattacktested(60 a gentlestallregionthatmaintainedrelativelyhighliftproductioneven airfoils andcirculararcairfoils.Inaddition,thesnake’s shapeexhibited many othershapesincludingbluff bodies,thickairfoils,symmetric geometry generatedsignificantlylargermaximumliftcoefficients than Within themeasuredReynoldsnumberregime( 35 maximum lift-to-dragratioof2.7,maintainedincreasesinliftupto sectional shapeproducedamaximumliftcoefficient of1.9and range ofReynoldsnumbersandanglesattack.Thesnake’s cross- shedding characteristicsoftheshapeacrossabehaviorallyrelevant to determineliftanddragcoefficients, wakedynamicsandvortex- time-resolved (TR)digitalparticleimagevelocimetry(DPIV)wereused profile ofanairfoilamoretypicalflyer. Forcemeasurementsand tunnel toisolatetheeffects of2Dshape,analogouslytostudyingthe low Reynoldsnumbers.We usedastraightphysicalmodelinwater snake’s cross-sectionalshapetodetermineitscontributionglidingat Here, weaimedtounderstandtheaerodynamicpropertiesof axis, formingageometrywithfore–aftsymmetryandthickprofile. shape bysplayingitsribsandflatteningbodyinthedorsoventral Chrysopelea paradisi surface intheabsenceofwings.Whengliding,flyingsnake is theuniquecross-sectionalshapeofbody, whichactsasthelifting A prominentfeatureofglidingflightinsnakesthegenus Daniel Holden gliding performance how abluff bodycross-sectional shapecontributesto Aerodynamics oftheflyingsnake RESEARCH ARTICLE © 2014.PublishedbyTheCompanyofBiologistsLtd|JournalExperimentalBiology(2014)217,382-394doi:10.1242/jeb.090902 INTRODUCTION ABSTRACT Department of Mechanical Engineering, Virginia Tech, of 100SRandolphHall, Department deg, andexhibitedtwodistinctlydifferent vortex-sheddingmodes. 1 , JohnJ.Socha morphs itscircularcross-sectionintoatriangular 2 Department of EngineeringScienceand of Department 2, *, NicholasD.Cardwell

deg). Overall,thecross- Re=3000–15,000), this Chrysopelea 3 School of 1 and PavlosP. Vlachos considerably different aerodynamicperformance, characterizedby aerodynamic implicationsofthis shapeareunknown. closely resemblesabluff bodythanastreamlinedairfoil, and the Socha, 2011). maneuverability byactiveturning(Socha,2002;Sochaetal., 2005; the flyingsnakes,capableofglideratiosashigh4.5 and Chrysopelea paradisi aerodynamics ofcross-sectionalshapetheparadisetreesnake, aerodynamics (Miklaszetal.,2010).Here,wefocuson the Miklasz etal.,2010)andonlyonestudytodatethatconsidered 2002; SochaandLaBarbera,2005;etal.,Socha,2006; in snakes,withpreviousstudiesfocusingonkinematics(Socha, particular, littleisknownaboutthephysicalmechanismsofgliding gliding flight(Dudleyetal.,2007;DudleyandYanoviak, 2011). In and thefargreaternumberofindependentevolutionaryorigins al., 2013),despitetheirlarge morphologicalandtaxonomicdiversity et al.,2010;MiklaszParkandChoi,Bahlman (Emerson andKoehl,1990;McCay, 2001;Bishop,2007;Alexander fewer studiesontheaerodynamicsofanimalsthatcanonlyglide 2009; Johanssonetal.,2010).Incomparison,therehavebeenfar 2008; UsherwoodandLehmann,2009;Spedding, 2005; Tobalske, 2007;HedenströmandSpedding,2008;Songetal., patterns andfluid–structureinteractions(Lehmann,2004;Wang, kinematics, steadyandunsteadyeffects, 2Dand3Ddynamics,wake received focusedattention,leadingtoextensiveunderstandingof flight, theaerodynamicbasisofflightinbirds,batsandinsectshas Hedenström etal.,2007;Riskin2008;Hubel2010). Yanoviak etal.,2011) toflappingbats(Tian etal.,2006; aerially locomotes,fromglidingants(Yanoviak etal.,2005; flying snakesstrikinglyuniquecomparedwithanyotheranimalthat with fore–aftsymmetry. Thesefeaturesmaketheglidingsystemof exhibit bilateralsymmetry, andyetitsribsplayingcreatesanairfoil engineered flyers:theundulationresultsinabodythatdoesnot with symmetriesdrasticallydifferent fromallotherbiologicalor combination ofundulationandbodymorphingproducesaglider 1).This unconventional cross-sectionalshape(Socha,2011) (Fig. the side,flatteningoutindorsoventralaxisandcreatingan al., 2005).Uponbecomingairborne,thesnakefirstsplaysitsribsto traveling wavesposteriorlydownthebody(Socha,2002;Sochaet downward-projecting ‘lips’ ateachedge(Fig. surface) andaconcavebottom (theventralsurface),withtwo the cross-sectionalshapeconsists ofasemi-triangulartop(thedorsal width intheairincreasesmostrelativetoitsnormalcondition, similar toaroundedtriangle(Socha,2011). Atmid-body, wherethe much ofthebodybetweenheadandtailshapeisroughly its length.Althoughthetotal3Dshapeisnotpreciselyknown, for Chrysopelea paradisi Compared withconventional airfoils,bluff bodiesexhibit The cross-sectionalshapeofanairborne Although manyopenquestionsremaininthestudyofanimal . Thisspeciesisthemostproficientgliderof 3 C. paradisi :

1). Thisprofilemore varies along

The Journal of Experimental Biology snake-like geometriessustainedincreasesinliftuptoanangleof possesses certainfavorableaerodynamiccharacteristics.Themost cross-sectional shape,buttheresultssuggestedthatsnake models werecoarseandonlyroughlyapproximatedthesnake’s true absence ofabackboneprotrusion(Miklaszetal.,2010).These to addresstheeffects ofdegreebodyconcavityandpresenceor semi-circular tubingtomodelthesnake’s cross-section,andaimed forces andvortex-sheddingcharacteristics. asymmetry, thicknessandangleofattackaffect theflowstructure, 2009) andthickairfoils(Sarraf,2010)haveshownthatshape section (Yoon etal.,2010),asymmetricbluff bodies(HuandZhou, (Williamson, 1996).Studiesoncylinderswithrectangularcross- the vortexshedsdownstreamandastreakensues interrupted, and,throughinteractionwiththeoppositesidevortex, reaches apointwhenthesupplyofvorticityfromshearlayeris rolls intoavortex.Thevortexgrowsinstrengthandsizeuntilit boundary layersuppliesvorticitytotheshearlayer, whichinturn 1996). Thevortex-sheddingprocessbeginsastheseparated boundary layerwiththefreeshearandwake(Williamson, Generally, bluff bodyflowsexhibitinteractionoftheseparating vortex sheddingandsignificantprofiledragduetoseparation. RESEARCH ARTICLE B A The previousstudyofflyingsnakeaerodynamicsusedsimple S fluctuatingstructuresenergy L′ energy fraction L J digitalparticleimagevelocimetry FSE EF DPIV D C Raspectratio C AR ω timeresolved λ α robustphasecorrelation U TR powerspectraldensity St properorthogonaldecomposition RPC Re PSD POD List of symbolsand abbreviations List of L D coefficient oflift coefficient ofdrag characteristic lengthusedtocalculate lift force advance ratio drag force modulation frequency modulation amplitude angle ofattack freestream veolcity Strouhal number Reynolds number St number C c lift anddragcoefficients ( velocimetry (DPIV),referredtohereafterasTRDPIV, todetermine cell measurementsandtime-resolved(TR)digitalparticleimage stereo imagingofthesnakesinflight(Socha,2011). We usedload 1827. We usedahigh-fidelitymodelofthesnake’s shape,basedon Reynolds regimes. understanding ofbiologicalliftingsurfacesandflightinlow unsteady effects. Morebroadly, thisstudycontributestoourgrowing foundation forfutureworkthatwillincorporatebodymovementand aerodynamic characteristicsoftheflyingsnakesandwillserveasa enable gliding.Thisisthefirststudyfocusedonsteady-state aerodynamic performanceofthebluff bodyaloneissufficient to shape ofaflyingsnake,andspecificallyevaluateswhetherthe quantify theaerodynamicperformanceofanatomicallysimilar Reynolds numberdynamicsimilarity. Ourstudyisthefirstto speed, low-turbulencewatertunnel(flume)atvelocitiesthatsatisfy and Reynoldsnumbers.Theexperimentswereperformedinalow- geometry acrossabehaviorallyrelevantrangeofanglesattack and vortex-sheddingcharacteristicsofthesnake’s cross-sectional performance ofthe2Dcross-sectionalshape known. physics thatunderliethesnake’s aerodynamicbehaviorarenot glide. (3)Thefluiddynamicswerenotstudied,andthereforethe experience increasingReynoldsnumberwithinthecourseofasingle to theinitialtake-off velocity, meaningthatthesnakemust trajectory theforwardspeedcanincreasebyafactorofsixrelative ( in arangeofReynoldsnumbersthatcharacterizeitsglidingflight exhibits significantvariationinbodysizeandglidespeed,resulting Only oneReynoldsnumberwasexamined. differences inshapemayincurlarge differences inflowpatterns.(2) not reflectthesnake’s truecross-sectionalshape,andsmall represents onlyapreliminaryanalysis.(1)Thesimplegeometrydid 2010) providedsomeinsightintoflyingsnakeaerodynamics,it snake’s forceproduction. that theventrallyprojectinglipsareimportantfeaturesfor filled, themodeldisplayedsmallestliftcoefficients, suggesting angles ofattack60 of attack.Stallwasgentle,withliftproductionoccurringevenat maximum lift-to-dragratiosof2.4–2.8acrossawiderangeangles attack of30 Re Here, wecomprehensivelycharacterizedtheaerodynamic Although thestudybyMiklaszandcolleagues(Miklaszetal., ~5000–15,000) (Sochaetal.,2005).Furthermore,inaglide The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902

deg, withamaximumliftcoefficient of1.5and

deg. Whentheventralconcavitywasfully with achord, The modelwasrapidprototypedfromABSplastic geometry usedinthisstudy(fromSocha,2011). Miklasz etal.,2010).(C)Cross-sectional the twoventrallyprojectinglateraledges(from view showingthetriangulardorsalsurfaceand ventral view(photo:J.J.S.).(B)Lateral/ventral Chrysopelea paradisi. Fig. C

L 1. Bodyshapeoftheflyingsnake and C D c , respectively),wakedynamics , of25.4 mm. (A) Airbornesnakein Chrysopelea paradisi C. paradisi Boie 383

The Journal of Experimental Biology producing amaximumlift/dragratio( of 3000–7000.Thelift-to-dragratioexhibitedsimilarbehavior, at higherReynoldsnumbers,butdidnotoccurnumbers observed at rapidly increased.A strongReynolds numberdependencewas higher anglesofattack,theliftgraduallydecreasedwhiledrag rapidly increased,producingamaximumliftcoefficient of1.9.For 384 RESEARCH ARTICLE pressure predominantly governsbothlift anddrag,with signifying theonsetofstall. These plotsclearlyshowthatthe components representingthemomentum deficitofthewakeand drastic changesinboththe parallelandnormalmomentum corresponded toalarge riseinthepressurecoefficient aswell For anglesofattackgreaterthan 35 normal momentumupto45 increase intheparallelmomentum,whichwasoffset bypreserved reduction inthepressurecomponentaccompaniedbyanegative of attackbetween20and60 model producedalarge pressure forceassociatedwithliftforangles perpendicular momentumfluxcoefficients. Fig. components: thepressurecoefficients andtheparallel TRDPIV liftanddragcoefficients weredecomposedintothethree show goodagreementandarewithintheuncertaintyranges. The These twodifferent methods ofdeterminingtheaerodynamicforces and arecomparedwiththeforcemeasurementsfor to thepeakinliftforhigherReynoldsnumbers. which thedragcoefficient graduallyincreased.At occurred betweenangleofattack 2).Thelargest increaseinliftcoefficient coefficients thereafter(Fig. coefficients foranglesofattack The snake’s cross-sectionalgeometry producednegativelift Force measurements: lift and drag coefficients Force liftanddrag measurements: RESULTS L/D C h eut rmteTDI oc siae r hw nFg 3 The resultsfromtheTRDPIV forceestimatesareshowninFig. L –2.5 –2.0 –1.5 –1.0 –0.5 –1.0 –0.5 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 1 0 102030405060 0 –10 0 0 1 102030405060 –10 0 CD AB α 3 deg.Atthisangleofattack,apeakinliftoccurred =35 α (deg) α (deg)

deg followedbyasubsequentreduction.

deg. Atα α

deg, thelarge increaseindrag 5degandα =5 L − / 10 to5 D 3 deg,weobserveda =35 ) of2.7atα deg, andpositive

3 showsthatthe α 3 deg,during =35 3 deg,thelift =35 C –1.0 –0.5 CL D 3 degdue =35 0.4 0.8 1.2 1.6 2.0 0.5 1.0 1.5 2.0 Re=13,000. –10 0 10 20 50 40 30 10 60 –10 0 0 0 0 0.5 1.0 1.5 2.0 35 deg Re 15,000 13,000 11,000 9000 7000 5000 3000 –10 deg then increasedagain at α observed inFigs observation providesinsightthat helpstoexplaintheliftenhancement of thesevorticesissignificantly increasedfor energy forallanglesofattack,Fig. small numberofmodesissufficient tocapturethemajority ofthe reconstructed withfewermodesthanintheothercases.Although a in spaceandtime,thatthedynamicsofflowfieldcan be produced thelowestentropy, meaningthatthiscaseismoreordered entropy plotsinFig. accurately reconstructedusingthetwomostenergetic modes.The also shownthatthedynamicsofKármánvortexstreetscan be cylinders (Cruz,2005)andaliveswimmingfish(Epps,2010) have studies onthewakeproducedbycircularcylinders(Ma,2000), half- contain nearly70%ofthefluctuatingstructuresenergy (FSE).POD streets producedbythemodel,aremostenergetic modesand that thefirsttwomodes,whichcorrespondtoKármánvortex Re=13,000. Theenergy fractions showninFig. 5 orthogonal decomposition(POD)analysisare shown inFig. The energy fractionsandentropycalculationsfromtheproper 7000 and9000. pressure forceassociatedwithliftbetweenReynoldsnumbersof function ofReynoldsnumber. There wasasteepincreaseinthe techniques describedaboveforanangleofattack35 drag andreducedlift. acceleration lossesinthestreamwisedirectionresultincreased normal momentumcomponents,andalsothatincreasedconvective counteracting effects betweenthecontributionsofparalleland measurements decompositionmodesandflow field orthogonal Proper =0 and20 i.4comparestheforcecoefficients computedfromthedifferent Fig. α (deg) C D The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 deg andsignificantlydecreased at35 2 and3.Theentropygradually increasedbetween

5B showthatanangleofattack35 α 60 deg 4 deganddecreased at =45

5A,B revealsthattheorganization Re, Reynoldsnumber. coefficient versusdragcoefficient. ( ratio (L Plots ofliftcoefficient ( characteristics of Fig. coefficient ( α ). (D)Polarplotshowinglift

.Liftanddrag 2. / D , C)versusangleofattack C D

, B),andlifttodrag 5A clearlyindicate

α deg. Theentropy 6 deg. =60 α C. paradisi. 3 deg.This =35 C L , A),drag

deg asa

deg for

The Journal of Experimental Biology in theflowwithinwhichmeanlocalstreamwisevelocityis further downstreamshowsimilarstructureswithdecreasedstrength. beginning oftheseparatedboundarylayer. Thevorticeslocated vorticity thatextendfromtheperimeterofvortextowards vortical structurewithaconcentratedcoreandlongbranchesof located directlybehindthemodel,whichisthenfollowedbyalarge attack. Eigenmode2containsapairofsmallervorticalstructures attack aresignificantlylarger thanthosefortheloweranglesof deflected downwards.Thevortexpatternsofthehighestangle α from thecameraandwasnotresolved.Theeigenmodesfor this angleofattack,butregionintheflowfieldwasblocked structure thatformedintheconcaveventralsurfaceofmodelat The velocityfieldshapesalsosuggestthattheremaybeavortex rotating vorticesthatdecreaseinstrengthwithdownstreamposition. mode shapes.Eigenmodes1and2for dimensionless vorticityoverlaidwiththevelocityvectorsof attack of0,35and60 force with95%confidenceinterval; an angleofattack of35 Fig. components yieldsthetotalforcecoefficient fields.U computedfromthetimer-resolveddigitalparticleimagevelocimetry(TRDPIV)flow ofthese TRDPIV measurements,whichweredecomposedintothepressure,parallelmomentumandperpendicularcomponents.Thesummation Fig. RESEARCH ARTICLE 3 degshowsimilarbehavior, butwithstrongervorticesthatwere =35 The meanrecirculationregionofawakeisdefinedasthe Spatial eigenmodes1and2areplottedinFig.

.Liftanddragacross Re 4. Liftanddragcalculationsusingtwodifferentmethods. 3.

C CL –0.5 L –1.0 –0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 –10 0 0

5000 0

deg. SeeFig. 7000 10

deg andRe=13,000.Theseplotsshow for oneangleofattack. U 20 TRDPIV

3 fordetails. 9000 Re , TRDPIV-estimated forcewith95%confidenceinterval. 30 α 11,000 0degexhibitcounter- =0 40 50

5C foranglesof Comparison ofthe different techniquesand componentsusedtocalculatethe force coefficients for 13,000 60

α (deg) Comparison ofliftanddragforcesfor C C –1.5 –0.5 D –1.0 D –0.6 –0.4 –0.2 0.5 1.0 1.5 2.0 1 02 04 060 50 40 30 20 10 0 –10 0.2 0.4 0.6 0.8 0 0

5000 h eiclto ein hw nFg 6for the recirculationregionsshowninFig. between thesetwopointstofindtheexactlocation.Thisresultsin changes signandthenperformingaweightedlinearinterpolation calculated acrossthewakebyfirstfindingpointswhere the wakealongstreamwisedirectionwhere region producedbythesnakemodelisdefinedlocationsin namely, wake vorticesareformingclosertothedorsalsurface,augmenting decrease ofthemeanrecirculationfor0to35 of therecirculationregionincreasedbetween45and60 enveloped alarger regiononthedorsalsurface.Thelengthandsize downwards. Atthehighestanglesofattack,recirculationregion 35 gradually increased.Astheangleofattackincreasedfrom0to region decreasedwithReynoldsnumberandthedragcoefficient showed similarbehavior(Fig. larger dragcoefficients (Williamson, 1996).Thesnakemodel decrease withincreasing opposite indirectionwithrespecttothefreestreamvelocity, For acylinder, thelengthofmeanrecirculationisknownto deg, therecirculationregionlengthdecreasedandwasdeflected 7000 u × U The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 <0. Hence,theboundaryenclosingrecirculation 9000 Re Re=13,000 computedfromforcemeasurementsand 11,000 Re, producingalarger basesuctionand

6B), asthelengthofrecirculation 13,000

Re=13,000. F deg impliesthatthe Normal momentum Parallel momentum Pressure U TRDPIV U Measured force U Normal momentum Parallel momentum Pressure U TRDPIV Measured force , loadcell-measured TRDPIV F F TRDPIV u × U=0. Theseare

deg. The u 385 × U U ;

The Journal of Experimental Biology 386 RESEARCH ARTICLE frequency (St construct contoursofspectralenergy asafunctionofdimensionless spectral energy asafunctionoffrequencyiscalculated and we X calculated alongalltheTRDPIV velocitymeasurementpointsatthe velocity fieldsareshowninFig. showed Strouhalnumberslarger than0.24. number slightlylessthan0.24,andathigherReynoldsnumbers it densities. AtlowReynoldsnumbers, Strouhal numberpeakof0.16,whichalsohadlarger power higher anglesofattack( produced thehigherStrouhalnumberpeakof0.24,whereas the shedding behaviors.Loweranglesofattack(upto 7),whichindicatesthepresenceoftwodifferent vortex- (Fig. The spectraoftheforcemeasurementscollapsedintotwopeaks lost, reducingliftandincreasingdrag. wake elongatesforthehigheranglesofattack,addedsuctionis the vortex-inducedsuctionandtherebyincreasinglift.Once Spectral analysis Spectral location onthe maps (Fig. wake.

/ c c c –0.5 Y/ Y/ Y/ C Plots ofthespatiallyresolvedpowerspectra The dominantspectralcomponents observedinthesespectral –0.6 –0.4 –0.2 –0.8 –0.6 –0.4 –0.2 0.5

–1 λ 0.2 0.4 0.2 0.4 n/FSE =2 location,asshowninFig. 0 1 0 0 10 10 10 10 01230 123 C 60 deg 35 deg –3 –2 –1 0 0 deg 10 A 0 9) showgood agreement withthepower spectral 0 number) plottedalongthe y -axis. 1 Y / α C Mode 1 X/c X/cX Mode, n 3 degandabove)producedthelower =35 =0 correspondstothecenterline ofthe 10 1 2 9 forRe=13,000.Thespectraare

ω* 8B. Foreverypoint,thesignal –5 α =35 –4 x 3 –3 -axis andspanwise(Y α (deg) deg exhibitedaStrouhal –2 20 0 60 45 35 –1 10 8 6 4 2 0 2 4 6 4 2 0 2 4 1 5 0 5 1 0 2 Entropy 1 0.385 0.390 0.395 0.400 0.405 0.410 0.415 0.420 0.425 v-component 2 α 3 0 3 deg) =30 0 4 B 5 / 10 C ) 1 20 Mode 2 trajectories provides insightintothevortex-formation and-shedding shedding frequencyof position, withmostofthepowerconcentratedatvortex- attack of0 Re=13,000 areplottedinFig. The meanvortextrajectoriesfor theupperandlowervorticesfor suggests amorecomplexand turbulent wake. peaks athigherfrequencies. This yieldsabroadspectrumand additional dominantfrequenciesemerge, shownashighpower spectra furtherrevealthatforthehigheranglesofattack, estimated fromtheforcespectra(Fig. These observationsareconsistentwiththesheddingfrequencies dominant sheddingfrequencyisreducedtoapproximately 45 and60 as thewakewasdeflectedfurtherdownward.Anglesofattack of of 35 around thecenterlineandexpandinginwidth.Theangleofattack spreads, andthewakeshiftsdownwards,becomingasymmetric angle ofattackincreasesto20and35 can bedirectlyestimatedtobetween observing thehigh-intensityspectralband,widthofwake greatest symmetryinthewakeabout densities (PSDs)oftheforcemeasurements(Fig. Trajectories and strength of coherent structures coherent Trajectories of andstrength X/c α (deg) /c 30 2 deg showedthegreatestdegreeofasymmetryabout 40 deg exhibitedthehighestpowermagnitudesbuthere

The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 deg showedanarrowbandinfrequencyandvertical 50 3 60 St≈ Fig. decomposed velocityfield; in theseplots. velocity modeshapes,whicharealsoshown contours werecomputedfromthePOD angles ofattack.Dimensionlessvorticity (C) PODeigenmodes1and2forseveral the leveloforganizationvelocityfields. energy. (B)Plotofentropy, whichrepresents eigenvalue; FSE,fluctuatingstructures for severalanglesofattackat energy distributionofindividualeigenmodes Proper orthogonaldecomposition(POD) 0.24. Thisanglealsoshowedthe

5. Orderandvorticityinthewake.

10A. Theanalysisofthevortex

7). However, theTRDPIV ω

deg, theenergy spectrum Y *, vorticityofthe / C Y =–0.6 and0.6.Asthe / C =0. Moreover, by

7). Theangleof c , chord. Re=13,000. St≈ Y / 0.16. C (A) λ =0 n ,

The Journal of Experimental Biology performance, maintaininghighliftcoefficients between while gliding.Overall,thisshapeexhibitedarobustaerodynamic the body, itmustcontributegreatlytothesnake’s forceproduction Because thisshapeoccursalongalarge percentageofthelength behaviorally relevantrangeofReynoldsnumberandangleattack. sectional shapeofonespeciesflyingsnake( This studyinvestigatedtheaerodynamiccharacteristicsofcross- model. Themaximumcirculationoftheuppervortexfor for anglesof0to35 angles ofattackdidnotconverge. Thepointofmaximumcirculation downstream ofthemodel’s centroid. Thetrajectoriesathigher converged onnearlythesametrajectoryat~1.5chordlengths of over1chord.ThetrajectoriesforthevortexpairsstateI trajectories coveredamuchwiderrangewithverticaldifference vertical positionof~0.6chords.TheinitialpointsthestateII formation process,ismuchmorecompactwithadifference ininitial stage ofthetrajectoriesforstateI,whichcorrespondstovortex- processes andthedownstreamevolutionofwake.Theinitial RESEARCH ARTICLE DISCUSSION 60 at occurred closertothemodelthanforotheranglesofattack,and Y LЈ Y LЈ

dB/Hz α / / –0.8 –0.6 –0.4 –0.2 –0.8 –0.6 –0.4 –0.2 deg andnear-maximum −70 −60 −50 −40 −30 −20 −10 6 degitwaslocatedthefarthestdownstream. =60 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0 0 0 –0.5 –0.5 AB A B 0.1 0 0 deg occurredat~1chorddownstreamofthe 0.2 St 0.5 0.5 L 0.3 / D values overarangeofangles 1.0 1.0 α=35 deg 0.4 X/LЈ −70 −60 −50 −40 −30 −20 −10 1.5 1.5 0

C. paradisi)acrossa 0.1 2.0 2.0 α α 0.2 =20 and 4 deg =45 St Re=13,000 Re=9000 Re=7000 Re=5000 2.5 2.5 α (deg) 0.3 20 35 0 45 60 α (deg) 3.0 3.0 combination ofmorecoherentvorticeswiththeclosure wake in turnisrelatedtothebasepressureandformdragofbody. The trajectories merge revealthe approximatewakeclosurepoint,which the vorticesaremoreorganized. Thelocationsatwhichthevortex 6, 10).ThePODentropyshowninFig. help toexplainthemechanismresponsibleforthisbehavior(Figs the peakisreal.Thevortexdynamicsandtrajectoryanalysis coarse semi-circularmodel)(Miklaszetal.,2010)allconfirmedthat measurements andinthepreviousstudyofflyingsnakeshape(i.e. different loadcellsetups,intheindependentlyderivedTRDPIV force that thispeakwasanexperimentalartifact,butitsoccurrenceintwo Reynolds numbers(greaterthan7000).Initially, wewereconcerned 1.9, whichoccurredduetoaspikeinthepressuretermforhigher perpendicular projection. the rangewherecross-sectionalshapepresentsminimum also exhibitedthesmallestdragcoefficients, likelybecausethisis formation ofavortex‘trapped’ inthecavity. Theseanglesofattack ventral surfaceproducedalow-pressurezone,perhapsduetothe 5 on thetotalaerodynamicforces.Lowanglesofattack( from theTRDPIV forcedecompositionhadthegreatestinfluence attack between15and40 60 55 50 45 40 35 30 25 20 15

deg) producednegativeliftcoefficients becausetheconcave The angleofattack35 0.4

For anangleofattack35 versus (A)angleofattackat Fig. interpolating themean the Strouhalnumber. snake model, zero. Theaxeswerescaledusingtheperpendicularprojectionof

.Recirculationregionsinthewake. 6. (B) 13,000. ( measurements showingpowerasafunctionofStrouhalnumber number. Fig. St) andangleofattackforReynoldsnumbers(A)7000 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902

.Two vortex-sheddingbehaviorsrevealedbyStrouhal 7. L Power spectraldensities(PSDs)oftheforce ′ , whichisthecharacteristiclengthusedtocalculate

deg. AsshowninFig. u

deg producedthelargest liftcoefficient of -velocity fieldtodeterminewhereitequals

deg, therecirculationregionwasfoundby Re=13,000 and(B)Reynoldsnumber. 5B revealsthatfor Recirculation region

3, thepressureterm α α =–10 to 3 deg =35 387

5,

The Journal of Experimental Biology across whichspectralanalysiswasperformed. 388 RESEARCH ARTICLE attack, corresponding toaStrouhalnumber of0.24,produced shifted fromtheroundedapexto theleadingedge.Loweranglesof shedding characteristicsastheseparation pointonthedorsalsurface higher anglesofattack( analysis, indicatingthatthelower anglesofattack( Two different Strouhal numbers wereobservedinthespectral vortex-shedding behaviors,which dependontheangleofattack. indicates thatthesnake’s cross-sectionalshapedisplayeddifferent The congruenceofresultsfromdifferent methodsofanalysisclearly induced liftprocesses. the spikeinliftand negative pressurepeakatthedorsalsurface.Thisalsosuggests that larger high-pressurezonein theventralregionandamoresignificant downwards). Asaresult,thehigherReynoldsnumbersproduced a wake exhibitsstrongdownwash(higherdeflectionofthetrajectories convergence pointsarecloser tothebodysuctionsideandthat case ofα suggest thatavortex-inducedlift-generationprocessisatplay. Forthe vortices intheproximityofsuctionsidebody(thetopsurface) the degreeofasymmetrywakeandstrengthformed vortex-induced liftaugmentationobservedfor in closerproximitytothesuctionsideofairfoilhelpsexplain The controlvolumeusedfortheTRDPIVforceestimatesisboundedby velocity spectrawerecalculatedandthecontrolvolumeforforceestimates. (B) Diagramshowinghorizontalstationsatwhichthespatiallyresolved the maximumandminimum angles ofattacktested,and Strouhal number. Fig. X Vortex-shedding behavior 2 , Y B A LЈ −1

Y c

.Plotsshowingthecharacteristiclength, L 8. / 0 1 and Y X −10 1 Y −5

(mm) 10 3 deg,wenoticethatpeakcirculationandtrajectory =35 −15 0 5 2 . Also,thereddottedlinedenotesstreamwiselocation 10123 2 1 0 −1

(A) Thesnake’s profilewasrotatedthroughtherangeof −10 L / D observed atα L y ′ -coordinates foreachangleofattack. wasfoundbytakingthedifference between −5 α =40–60 X (mm) X/c Y Y 0 1 2 3 degistheresultofvortex- =35 deg) demonstrateddifferent 5 ′ , usedtocalculatethe α calculations spectra power Location of 3 deg.Moreover, =35 α 10 =0–30 α (deg) 15 deg) and 60 55 50 45 40 35 30 25 20 15 10 5 0 X X 2 1 , maximum producing amaximum angle from21to 40 the liftcurveatlowanglesof attack,butalsoincreasedthestall increasing airfoilthicknessfrom 15to35%decreasedtheslopeof Studies onthick,symmetric airfoils (Sarraf,2010)foundthat as thethickerairfoilsandbluff bodiesproducedhigherstall angles. than 20%.Thicknessalsoappears tobeanimportantcharacteristic, semi-circular modeldecreasedthe maximumliftcoefficient by more et al.,2010)foundthatfillingintheconcaveventralsurfaceof the 0.8 to1.0(MurphyandHu,2009).Miklaszcolleagues(Miklasz Strouhal numbers. of curvatureattheleadingedgeandproducedcorrespondinglylower number. Athighanglesofattack,the shapepresentsasharpradius oriented atloweranglesofattackandproducedahigherStrouhal sectional shapehasalarge radiusofcurvatureneartheapexwhen rounding radius(HuandZhou,2009).Similarly, thesnake’s cross- cylinders showedthattheStrouhalnumberincreasedwithincreasing leading edge.Previousstudiesonroundingcornersofsquare whereby theseparationpointshiftedonsuctionsidetowards observed whentheseairfoilsreachedacriticalangleofattack, sharp decreaseinStrouhalnumber(from0.3to0.2)wassimilarly that dependontheangleofattackandthickness(Sarraf,2010).A thickness alsoproducedtwodifferent vortex-sheddingmechanisms airfoils.Inparticular, thick,symmetricairfoilsof15–35% (NACA) previously studiedNationalAdvisoryCommitteeforAeronautics 3). fluid dynamicforces(supplementarymaterialMovie magnitudes, correspondingtoincreaseddragandfluctuationsinthe ( 1,2).Higheranglesofattack (supplementary materialMovies power concentratedatthedominantStrouhalnumber attack showedgreaterspectralorganization, withthemajorityof smaller vortices(asshownbythePODanalysis).Loweranglesof 2010), whichproducedmaximumC NACA 0012(Alametal.,2010)andNACA 0015-0035(Sarraf, maximum liftcoefficients than symmetricairfoils,suchasthe the S1223airfoil(Selig,2005)generatedsignificantlylarger empty semi-circularflyingsnakemodels(Miklaszetal.,2010), and with camber, suchasthecirculararc(Sunada, 1997),half-fulland high pressurezonewithinthecavity. Otherairfoilsandbluff bodies coefficients overawiderange ofanglesattackbymaintaininga may allowthesnake’s cross-sectionalshapetogeneratelarge lift ventrally protrudinglipsisanimportantlift-producingfeaturethat force production.Specifically, theconcaveventralsurfacewith sectional shapeappearstoplayanimportantroleinaerodynamic higher stallangleandlarger liftcoefficients afterstall. α semi-circular modelproducedamorerapidincreasein circular modelsshowedasharpincreasein maximum liftcoefficient andhigherdragcoefficients. The semi- 2010), theanatomicallysimilarsnakeshapeexhibitedalarger circular modelstestedasafirst-orderapproximation(Miklaszetal., low Reynoldsnumberrange.Comparedwiththeprevioussemi- out-performed theotherairfoilsandbluff bodieswithinthesnake’s airfoils (Figs sectional shapewiththatofsomewell-knownbluff bodiesand We comparedtheaerodynamicperformanceofsnake’s cross- inspired corrugatedairfoil,whichproducedmaximum Comparison with bluff bodiesandlow-speed airfoils Comparison withbluff St=0.16) producedmuchlarger vorticalstructuresandcirculation =0 and10 The vortex-sheddingbehaviorofthesnakemodelissimilarto The dorsoventral(top–bottom)asymmetryofthesnake’s cross- L The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 / deg, butouranatomicallysimilarmodelexhibiteda D 11, 12).Surprisingly, thesnake’s geometrygenerally values overawiderangeofanglesattack.The deg. Ourmodel ofthesnake’s cross-sectional L / D of 2.8,andalsomaintainednear- L values of1to1.2,oraninsect- L / D at L C / L D α values of 3 deg, =30 between

The Journal of Experimental Biology with asingle,dominantsheddingfrequencyatStrouhalnumberof~0.24. turbulent, containingabroaderspectrumofflowstructures.Bycontrast,below Re=13,000, twochordsdownstreamofthecentroidexperimentalmodel.Theseplotsdemonstratethatbeyond Fig. produce positiveliftcoefficients at camber, whicharetypicallyoperatedathigherReynoldsnumbers, 1997; Selig,2005)(Fig. streamlined airfoils(e.g.theS1223airfoil)(SeligandGuglielmo, significantly different behaviorcomparedwithmoreconventional model, whichhadathicknessof29%(Miklaszetal.,2010). model producedlarger dragcoefficients thanthesemi-circular is larger. Iftrue,thismayalsoexplainwhytheanatomicalsnake drag coefficient becausetheperpendicularprojectionofairfoil angle of35 shape possessedathicknessof39%(relativetothechord)andstall RESEARCH ARTICLE Y c Y c / / The liftcurveofthesnake’s cross-sectional geometrydisplays −0.8 –0.6 −0.4 −0.2 −0.8 −0.6 −0.4 −0.2

.Characterizationofthewakebypowerspectra. 9. 0.2 0.4 0.6 0.2 0.4 0.6 0 0 0 0

B A

deg. Thisgreaterthicknessmayhaveledtoanincreased 0.5 0.5 Y/c –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.2 0.6 0.8 0.4 0 0 12). Streamlinedairfoilswithpositive 1.0 1.0 0 deg 0.25 St α 0.5 0degandrapidincreasesin =0 1.5 1.5 X/c X/c –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.2 0.6 0.8 0.4 0 .50.5 0.25 0 20 deg St 2.0 2.0 Spatially resolvedpowerspectraofthe –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.2 0.6 0.8 0.4 2.5 2.5 0 .50.5 0.25 0 35 deg St α =35 α (deg) α (deg) 3.0 3.0 maintained increasesinliftupto model didnotproducepositiveliftcoefficients until resulting inacatastrophicstallforanaerialvehicle.Thesnake After thisstallangle,theliftcoefficient decreasesrapidly, possibly lift uptothestallangle,whichoftenoccursat trajectory, duringwhichthebodylikelyencountersveryhighangles allow thesnaketodevelopliftduringballisticdivephaseofits particular, thegradualstallbehaviorathighanglesofattackmay pitch axismayvarybyover60 posture duringatrajectory, inwhichthebody’s orientationinthe force-producing mechanismsdespiteitscontinuouslychanging stall region.Thesecharacteristicsmayexplainthesnake’s favorable 60 45 35 15 0 60 35 0 deg, theflowexhibitsamoreconventionalstructureofbluff bodywake –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.2 0.6 0.8 0.4 0 95% confidenceintervalsofthemeantrajectoriesareshown. respectively. (B)Ten vortextrajectorieswereaveraged,andthe by diamondandsquarepoints,fortheupperlowervortices, respectively. Thelocationofmaximumcirculationisrepresented upper andlowervorticesrepresentedbysoliddottedlines, results at Fig. .50.5 0.25 0 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902

0 Plotsshowingthevortexidentification andtracking 10. v 45 deg -velocity componentforseveralanglesofattackat St Re=13,000. –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.4 0.2 0.6 0.8 0 .50.5 0.25 0 (A) Themeanvortextrajectories,withthe α =35 α 60 deg St 3 degandexhibitedagradual =35 deg, thewakebecomesmore

deg (Sochaetal.,2005).In (dB Hz) –70 –60 –50 –40 –30 –20 –10 α 2 degorless. =20 α 1 deg,but =10 389

The Journal of Experimental Biology transition betweenfallingandglidinginanyglideevent. 390 RESEARCH ARTICLE attack alongthebody, thesnakemaybeoperatinginanear-maximum (Socha etal.,2010).Ifthisangleisreflectiveoftheactual angle of25 snake hasbeenshowntoorientitswholebodyroughlyatanaverage variation inangleofattackalongthesnake’s bodyisunknown,the 35 snake shouldoptimizeitsglideangleandbodyposturetoproducea 35 the snake’s cross-sectionalshapeoccurred atanangleofattack 2005; Miklaszetal.,2010).Themaximumliftcoefficient and significantly giventhesnake’s complex kinematics(Sochaetal., attack alongthesnake’s bodyare unknown,andthesemayvary Socha etal.,2010),theactuallocalReynoldsnumberandangleof has beenidentifiedinpreviouskinematicstudies(Sochaetal.,2005; Although theglideangleandrelativebodyorientationof of attack(i.e.>45 C Implications snakes for inflying gliding C −0.5 –1.0 L L,max deg angleofattackoverthemajorityitsbody. Whiletheactual deg. Ourresultssuggestthat,formaximumhorizontalgliding,the 1.0 2.0 0.5 1.5 2.5 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 2.4 1.0 2.0 −10 0 10

3 (Sunada, 1997) deg (inaflow-relevantreferenceframe)whilegliding (Sunada, 1997) Circular arc Flat plate 0

deg). Thismaybecriticalfortheprocessof 12 27 10 ° °

40 ° 20 10 10 (Murphy andHu,2009) α (deg) ° 4 30 30 Asymmetric cylinder ° ° (Miklasz etal.,2010) (Alam, 2010) 35 NACA 0012 (Miklasz etal.,2010) ° Half-full model Full model Snake model current study 30 S1223 airfoil, Corrugated airfoil, Circular arc,Re=4000 NACA 0035,Re=5ϫ10 NACA 0012,Re=10,500 NACA 0012,Re=5300 Half-full model, Current study, Re =15,000 Current study, Re =5000 Re 40 (Murphy andHu,2009) 11 12 ° Corrugated airfoil Re=140,000 C. paradisi ° Re=15,000 6 ° Re=58,000 7 L ° 10 50 8 / 5 D ° 18 5 ° of 18 ° 33 21 40 ° ° ° UIUC Applied Aero Group UIUC AppliedAero 60 acceleration (Sochaetal.,2010).Ourresultssuggestthatsnakesusing as little13 snake accelerates,itproducesmoreliftanditsglideangleshallowsto angle (asgreatas62 snake jumpsintotheairandbeginsballisticdive,itfallsatasteep angle changeswithinaglidetrajectory(Sochaetal.,2005).Afterthe attack, whichmayhelpexplainthesnake’s performanceastheglide near-maximum lift-to-dragratiosoverawiderangeofangles radically different orientations. motion, similaraerodynamicperformanceismaintaineddespitethe and trailingedgesreversepositionsduringthesnake’s undulatory an importantcharacteristic,becauseitmeansthatwhentheleading fore–aft symmetryofthesnake’s cross-sectional shapeappearstobe control, suchastochangeitspitchangleorinduceaturn.The However, itcouldpossiblyusethisnegativeliftrangeforpurposesof unlikely thesnakeuseslowanglesofattack(<10 of thesnake’s cross-sectionalshape inthenegativeliftrange,itseems lift productionrange.Consideringthepooraerodynamicperformance

University ofIllinois The snake’s cross-sectionalshapemaintained highliftvaluesand S1223 airfoil 12 Fig. several bluffbodiesandairfoils. Fig. ° NACA 0025 NACA 0035 NACA 0015

11. 2 Comparisonofliftcoefficientversus angleofattackfor 12. The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902

deg, anditcanevenproduceanetpositiveupwards 13 ° 10 6

deg) asaresultoflowliftproduction.Asthe Comparison ofmaximumliftcoefficient ( to otherairfoilsatintermediate Fig. various bluff bodiesandairfoils. and stallangleversusReynoldsnumberfor

1 Performance ofsnakeshaperelative 11. These studiesarereferencedin

deg) duringgliding. Re. C L,max )

The Journal of Experimental Biology thus experienceenhancedliftwhenatanglesofattack35 intermediate-sized snakescrosstheReynoldsnumberthreshold,and snakes alsoexhibitlowerperformance.Itispossiblethatthe snakes glidemoreeffectively thanthelargest snakes,the smallest of bodysizeonglideperformance.Althoughintermediate-sized Lastly, the exhibit subtledifferences inshapethathavenotyetbeenrecorded. augmentation anddragreduction.Alternatively, smallersnakesmay Reynolds numberbyexploitingothermechanismsforlift snakes maycompensatefortheaerodynamicdeficitsoflower 2005; Socha,2011), thiscontrastingevidencesuggeststhatsmaller physiologically similartothelarger ones(SochaandLaBarbera, that smallersnakesappeartobemorphologicallyand performance shouldoccurathigherReynoldsnumbers.Considering of 2Dsnakegeometry, whichindicatesthatthebestaerodynamic performance relativetolarger snakesstandsincontrasttoourstudy smaller bodywidthandlowerglidespeeds).Theirsuperior snakes operateatlowerReynoldsnumbers(resultingfromtheir minimum glideangles(SochaandLaBarbera,2005).Thesesmaller snakes, capableofcoveringgreaterhorizontaldistancesatlower intermediate-sized using equilibriumgliding.Additionally, ithasbeenobservedthat capture theperformanceofrealsnakes,orthatsnakesarenot 2005). Thisdemonstratesthatour2Dmodelsareinsufficient tofully glide anglesasshallow13 not beabletoproduceglideanglesoflessthan20 examine theaerodynamic performanceof these measurements, severaldifferent typesofanalyseswere employed to forces, andTRDPIV wasusedtoobtainflowfieldmeasurements. From Load cellmeasurementswereperformed todeterminethefluiddynamic Two typesofexperimentalmeasurement techniqueswereusedforthisstudy. ( Socha etal.,2010).Basedontheresultsfromthisstudy than thosereportedhere(3.08–4.33versus2.7)(Sochaetal.,2005; shallowing phaseofthetrajectory;thesevaluesare14–60%larger equilibrium glidingtoestimatethemaximum produce moreshallowglidesandcovergreaterhorizontaldistances. increased acrossthethresholdof α RESEARCH ARTICLE performance offlyingsnakes. movements, arerequiredtofullyunderstandtheaerodynamic more complexmodels,includingthosethatincorporatedynamic behavior, utilizingmultiplephysicalmechanisms. Futurestudieson between itsmorphologicalcharacteristicsanddynamicgliding mode ofaeriallocomotionlikelyresultfromacomplexinteraction Overall, theaerodynamicforcesproducedbysnake’s unique structures thatcouldalsochangetheaerodynamicperformance. also neglectedinthisstudy, mayproducecomplex3Dflow body aerodynamicperformance.Sweepangleeffects, whichwere segments, whichmayhaveasignificanteffect onthesnake’s whole- Thus, thewakefromupstreammayinteractwithdownstream body upstream anddownstreambodysegmentsiscontinuouslychanging. posture isconstantlyreconfiguredsuchthatthespacingbetween its cross-sectionalshape.Inaddition,asthesnakeundulates,body snake’s aerodynamicforceproduction beyondwhatisdeliveredby including three-dimensionalandunsteadyeffects, mayaugmentthe explains thesnake’s glidingperformance. Othermechanisms, MATERIALS ANDMETHODS L 3 degwouldexperienceaboostinliftastheReynoldsnumber =35 / Previous studiesonflyingsnakekinematicsusedassumptionsof In conclusion,ouranalysisofa2Dgeometryonlypartially D max =2.7) andassumingequilibriumgliding, Re=7000 transitionmayhelptoexplainafurtherfeature C. paradisi

deg havebeenobserved(Sochaetal., are betterglidersthanthelargest Re=7000, enablingthesnaketo C. paradisi’s cross-sectional L / D C. paradisi values duringthe

deg, butinfact

should deg. where directed travelingwavethatmovesdownthebody: approach istocomparetheglidespeedwithofposteriorly undulation islessimportantforforcegenerationthanflapping.A second magnitude greaterthanthatofflappingflyers,suggestingthesnake’s motion. Thehighvalueof movement ofthebodyinvolvedinaerialundulationisreciprocating amplitude. Here,weassumethatthecyclicside-to-sideandvertical where snakes as: stiffness. The experimentswereconductedin aclosed-loopwatertunnelat Aluminium rods were embeddedinthemodeltoincrease itsstrengthand 2D segmentofthesnake’s bodywhen gliding andtoreduceendeffects. prototyped fromABSplasticwith an aspectratioof20tosimulateasingle et al.,2005;Miklasz2010;Socha etal.,2010).Themodelwasrapid used asthecharacteristiclengthto determinetheReynoldsnumber(Socha body widthofthesnakewhilegliding. Asinotherstudies,thechordwas typical valuesofgliding(Sochaetal.,2005), reaching ashigh of theorder1,withvaluesforinsectsextendinglowerandlarge birds motion withthereciprocatingofitswings.Forflappingflyers, animal flightistheadvanceratio, determining whetheraquasi-steadyapproachcanbeusedforstudying fully explaininghowinsects,birdsandbatsfly. A usefulindexfor al., 2010),andconventional,steady-stateaerodynamicsareinsufficient for flyers (Wang etal.,2004;Wang, 2005;Warrick etal.,2005;Johansson Unsteady 3Deffects arewellknowntoaffect theaerodynamicsofflapping aerodynamic forces,PODandcoherentstructureidentificationtracking. shape, includingaspectralanalysis,PIV-based estimationofthe experimental modelachord( snake’s flattenedbody(Socha,2011). Thegeometrywasscaledtogivethe cross-sectional geometry, designedfromananalysisofaerialimagesthe The experimentalmodelisananatomicallysimilarreplicaofthesnake’s attack ( model inordertoisolatetheeffects ofcross-sectionalshapeandangle for afirst-orderstudyofthesnake’s aerodynamics. This dimensionalanalysissuggeststhataquasi-staticapproachisreasonable approximated bythesteady-stateconditionsofanyparticularbodyposture. undulation. Therefore,theforcesonsnakecanbereasonably dominated bytheoverallforwardmotionofsnakeandnotitsaerial Together, theseindicesstronglysuggestthatthesnake’s aerodynamicsare Justification for 2Dandquasi-steadymodeling Experimental modelandtestfacility During itsglide,thesnakeassumesan coefficients areaffected lessbyARandinsteaddepend more directlyon Doenhoff, 1959).However, forhigherARwings,theliftanddrag end-effects, three-dimensionalityandlift-induceddrag(AbbottVon the liftanddragcoefficients canbestronglyinfluencedbytheARdueto apparatus. in thisstudymayyieldinsightintoonecomponentofthesnake’s gliding that 3Deffects arenotimportant, butsimplythatthegeneralapproachused that areorthogonaltothefreestreamflow. Furthermore,thisdoesnotsuggest angle ofattack.Thisargument onlyappliesforportionsofthesnake’s body investigation oftheeffects of theaerialsnake’s cross-sectionalshapeand steady approachisareasonablefirstapproximationforan initial in combinationwiththehighadvanceratio,suggeststhata2Dand quasi- 2011), whichcanbeconsideredinthemediumtohighARrange.ThisAR, can haveanARoftheorder8–10(SochaandLaBarbera,2005;Socha, three straightsectionsconnectedwithcurvedsegments.Eachsection In thisstudy, wemodeledthesnake’s bodyusing a large aspectratio(AR) U U α ) onaerodynamicperformance.GenerallyforwingswithlowAR, w is glidespeed, is thetravelingwavespeed.Thisvalueof The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 J =4 (Vogel, 2003;DicksonandDickinson,2004).Using J J ′ ω = = isundulationfrequencyand c U ωλ U U J ) of25.4 w for thesnakeismorethananorderof ≈≈ ≈≈ J .4ms 0.24 m .4ms 0.24 m . s 8.9 m , whichcomparestheanimal’s forward . s 8.9 m mm, whichrepresentsthemaximum S -like shapecomposedoftwoto − − − 1 − 1 1 1 J 0,(1) , 30 7,(2) , 37 can beestimatedinflying J λ is evenhigher. isundulation 391 J α is .

The Journal of Experimental Biology 392 RESEARCH ARTICLE measurements. For allanglesofattackexcept 35 TRDPIV test conditionswasbasedonobservations fromtheloadcell numbers weretestedforanangleof attackof35 attack weretestedataReynolds numberof13,000andfourReynolds case selectioninformedbytheforce measurementresults.Fiveanglesof was conductedonasubsetofthetotal experimentalparameterspace,with characteristics includingvorticity, strainrateandfieldpressure.Thisanalysis instantaneous, spatiallyresolved velocity vectorstoquantifyflowfield We usedTRDPIV (Willert andGharib,1991;Adrian,2005)tomeasure where calculating thecorrespondingStrouhalnumber: The frequenciesfromthespectralanalysiswerenon-dimensionalizedby determine thedominantspectralcomponentsofforcemeasurements. angle ofattack,weperformedspectralanalysisontheforcetimeseriesto chord lengthofthemodel. water, attack ( different Reynoldsnumbersrangingfrom3000to15,000,and15anglesof of possiblesnakeflightkinematics,weexploredaparameterspaceseven the snake’s overallaerodynamicperformance.To encompassalarge range measured asafunctionofReynoldsnumberandangleattacktodetermine The liftanddragproducedbythesnake’s cross-sectionalgeometrywere Vlachos, 2009). and flowuniformityatthetestlocationbetterthan99%(Weiland and produce alow-turbulencefreestreamoflessthan3%atspeedsupto1 Virginia Tech. Thetunnelhasatestsectionof0.6×0.6×1.5 where measurement beforeeachtrial.Theforcecoefficients weredefinedas: experimental setupandmodelwasaccountedforbyzeroingtheforce of 1000 Redmond, WA, USA)andaDAQboard(NIPCI-6251)atsamplingrate and dragforcesweremeasuredsimultaneouslyusingfour5 contained inarigidtrusssystemmountedwatertunnel(Fig. spanned theentirewidthbetweensidewallswithaclearanceof~1 boundary layerandpreventedseparation.To eliminate3Deffects, themodel geometry (Narasimha,1994),whichpromotedtheformationofastable leading edgeoftheacrylicsidewallswasdesignedwithsuper-elliptical sidewalls topreventinteractionwiththeflowinwatertunnel.The support arms.Thesearmswerecompletelyencasedbyacrylic amplifiers; OmegaEngineering,Stamford,CT, USA)mountedtothemodel cells (LCFD-5,accuracy:±0.15%FSO,DMD-465WB,strain-gage Aerodynamic forcemeasurements Aerodynamic Flow fieldmeasurements be atapproximately should benotedthatthemeanclosurepointofwakeisalsoexpected to the highestenergy andsignificant variationbetweenanglesofattack.It chords downstreamofthemodel’s centroidwasselectedbecauseitshowed Several different streamwise locationswereanalyzed,andapositionof2 field spectrawerecalculatedalongthereddashedlineshowninFig. way andwerecomparedagainsttheforcespectralanalysis.Thevelocity measurements’, below)andtheresultswerenon-dimensionalized same on thetime-resolvedvelocityfieldmeasurements(describedin‘Flow field characteristic lengthscaleofthewake.Spectralanalysiswasalsopreformed 8A).Thisdimension( (Miranda, 2005)(Fig. defined astheprojectionofmodelperpendiculartofreestream To investigatehowvortexsheddingvariedwithReynoldsnumberand The datawererecordedusingLabVIEW software(NationalInstruments, U f L α is thevortex-sheddingfrequencyandL Hz. Eachtrialconsistedof30 ) rangingfrom− and is thefreestreamvelocity, D are themeasuredliftanddragforces, X / C =2. 10 to60 C C D L St e Fg 13).Theexperimentalsetupwas deg (Fig. = = = l ρ ρ is thespanofmodeland Ulc Ulc U 2 fL 2

s ofrecording.Theweightthe D L 2 2 ′ ,(5) ,(3) ,(4) ′ L isacharacteristiclength,

deg. Thisselectionofthe ′ ) essentiallyscalesthe

deg, weobserved ρ isthedensityof

lb (22N)load

m andcan 13). Lift c

is the m

mm.

8B.

s − 1 was 109.34 μm which wasrequired tocapturethefullwidthofwake. Themagnification interrogation regionofthehigher angles ofattackwas1280×1024 region foranglesofattackupto 35 maximum expectedvortex-shedding frequencyof15 was sufficient toresolveawiderangeoffrequenciesinthewake, witha pulsed imagesofparticlemotionat apair-sampling rateof500 Integrated DesignTools, Tallahassee, FL,USA)wasusedtorecorddouble- Research, Portland,OR,USA).A high-speedvideocamera(XS-3, wavelength, 10 illuminated byaplanarlasersheet(~1 spheres (meandiameter, 126.4 surface andacrylicforthelaserplanetopass. surface atthetopofwatertunneltocreateastableinterfacebetween the mirror wasmountedonanacrylic‘boat’,whichslightlydepressedthe free back throughthetestsection,eliminatingshadowcastbymodel. The snake modelatthetopofexperimentalsetuptoreflectlaser plane sidewalls, asshowninFig. was selectedbecauseitmorerepresentativeofglidingbyanadult snake. negligible Reynoldsdependence.Theangleofattackvariationat dorsal) oftheairfoil. upside downtoallowforbetterilluminationofthesuctionside(anatomically setup usedfortheTRDPIVexperiments.Theexperimentalmodelismounted flow fieldmeasurements.Thissideviewshowstheimportantfeaturesof the experimentalmodel.(B)CADmodelofsetupusedfor gauge amplifierswereusedtomeasuretheaerodynamicloadsproducedby measurements. Fourhigh-accuracyloadcellsandhigh-frequencystrain aided design(CAD)modeloftheexperimentalsetupusedforforce Fig. B model Experimental A The watertunnelwasseededwithsmall,neutrallybuoyant,hollowglass In thesetests,theexperimentalmodelwasrigidlymountedtoacrylic sidewalls Acrylic sidewalls Acrylic

13. Forcemeasurementsetupinthewatertunnel. mounts Water tunnel The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902

pixel

mJ dualheadlasersystem(PegasusPIV, NewWave − 1 , producingaparticle imagesizeof2–4 4.2 chords 13B. A concavemirrorwasmountedabovethe 1.25 chords 2.1 chords Water tunnel μm) thatactedasflowtracersandwere mounts

deg was1280×512 3.75 chords

mm thickness)usinga527

Hz. Theinterrogation Interrogation regions Concave mirror model Experimental Acrylic boat (A) Computer- 1280 1280 pixels andthe arms Support cells Load

pixels. ϫ1024 pixels ϫ512 pixels

Re=13,000 Hz, which

pixels,

nm

The Journal of Experimental Biology p water, type ofanalysiswould notsuffice. temporal dynamics oftheflow, andthereforeaspatial-ortemporal-only purposes ofthiswork,itisimportant toanalyzethecombinedspatio- such asspectralanalysisarelimited tothetemporaldomainonly. Forthe flow fieldcanprovideonlyqualitative comparisons,andotherapproaches angle ofattackandReynoldsnumber. In contrast,directobservationofthe quantitatively comparethespatio-temporal characteristicsoftheflowacross vortex-shedding behaviors.We chosePODbecauseitprovidestheability to used PODtocomparethedominant,orthogonalmodesofdifferent (Berkooz, 1993;Ma,2000;Cruz,2005;Smith,Epps,2010).Here, we complicated flowfieldsintotheirenergetically dominanteigenmodes been usedinawidevarietyofproblemsfluidmechanicstodecompose that optimallycapturetheaverageenergy content(Smith,2005).PODhas technique usedtodecomposeanensembleofsignalsintoorthogonalmodes POD (alsoknownasKarhunen–Loévedecomposition)isamathematical where integral: equation toacontrolvolumethatisstatisticallysteadyyieldsthefollowing measurements. Theapplicationoftheintegralformmomentum TRDPIV measurementsforcomparisonwiththedirectloadcellforce 2006; Ragni,2009)wasusedtoestimatetheliftanddragcoefficients from A velocityfieldmomentum-basedapproach(e.g.Unal,1997;Oudheusden, RESEARCH ARTICLE grid spacingof8 detection (Westerweel, 2005).The finalvelocityfieldshadauniformvector vectors werevalidatedusingvelocitythresholdinganduniversaloutlier three passeswith32×32 processed usingtwopasseswith64×64 iterative process(Schrijer, 2008).AllTRDPIV measurementswere of thevelocityfieldsbetweeniterationswereemployedtostabilize instantaneous velocityfields.Gaussianimagemaskingandspatialfiltering (Scarano, 2002)tocorrelatetheimagepairsandmeasure Eckstein, 2009b)wasusedwithmultigriditerativedeformablewindows negligible. Eqn experimental modelsothatviscousstressesandturbulentare of thecontrolvolume,showninFig. POD Force calculations TRDPIVmeasurements from where the controlvolumetoyieldaerodynamicforces(perunitlength): measurements alone. components. Suchphysicalinsightcouldnotbeattainedbyforceload cell around thebodywithrespecttoeachotherandpressure significance ofchangesintheparallelandnormalconvectiveacceleration forces exertedonthebody. Inparticular, wecandetermine therelative calculation oftheflowcomponentsthatcontributetogeneration (Liu, 2006;Charonkoetal.,2010).Theuseofthisapproachenablesadirect computed usingtheomni-directionalvirtualboundaryintegrationtechnique is thepressureforceactingoncontrolsurfaceboundaries,whichwas can becalculateddirectlyfromtheflowfieldmeasurements.Thelastterm and thesecondterms,referredtoasperpendicularmomentumfluxes, and werethereforeneglectedinEqn.6. surfaces ofthecontrolvolumewerecomputedandfoundtobenegligible, forces resultingfromtheshearstressesalongverticalandhorizontal is thepressureandτ Robust phasecorrelation(RPC)(Eckstein,2008;Eckstein,2009a; The firstterms,whichwillbereferredtoastheparallelmomentumfluxes, U F u → → and is thevelocityvector, is theaerodynamicforceactingonmodel, v

are the 6 canbesimplifiedandre-writteninCartesiancoordinatesfor Duunyuvnxpny Lvvnxvunypnx pixels. FUnUspnns  = = – – = ρ⋅ ρ⋅ is theviscousstresstensor(Ragni,2009).Theboundary ∫∫ ∫∫ ρ⋅ −ρ x  ∫∫ ss and )() () pixel interrogationwindows.Aftereachpass,the )() () ()   y ddd,(8) n components ofvelocity(Ragni,2009).The → ddd,(7)  is theoutwardpointingunitnormalvector, + +  ⋅− ρ⋅ dd,(6) ⋅− ρ⋅ 8B, wastakensufficiently farfromthe ∫ ∫ +

pixel interrogationwindowsand () −  + τ⋅ ρ isthedensityof modes whosestrengthsvaryasafunctionoftime. structure, becauseavortexcanbecomposedofthesuperpositionmultiple all modes,indicatingamoreturbulentflow. would implythattheenergy intheflowismoreuniformlydistributedacross would indicateaveryorganized flow, whereasanentropyvaluenearone condition. SimilartotheinterpretationofEF, anentropyvalueofnearzero information containedacrossthemodestoonesinglenumberforeachtested respectively (Cruz,2005).Theuseofentropyallowsustoconsolidatethe in thefirstmodeorenergy isevenlydistributedbetweenallmodes, The entropycanrangefrom0to1,indicatingthattheenergy iscontained structure, andwascomputedasfollows: uniform modeenergy distribution. low energy content.Incontrast,averyturbulentflowwillhavemore very dominantmodeswhilethevastmajorityofwillhave approaching zero.A veryorganized wakewouldhaveasmallnumberof dominant modeshavinghighfractionsandthelowestonesasymptotically total. Hence,EFwilltakevaluesbetween0and100%,withthemost provides theratioofenergy ofanindividualmodewithrespecttothis FSE correspondstothecumulativeenergy contentof these possiblevortexcorelocations,computedusingthe therefore atthecenterofswirlingmotion.Next,strength of neighbors containedeachofthefourpossibledirectionlabelsand was neighbors forthedirection-spanningpropertytoseewhetherthese vector pointedto.Thesecondpasscheckedeachpoint’s surrounding each gridpointintheflowfielddependingonwhichquadrantvelocity the velocityfieldstoidentifypossiblevortexcores.Thefirstpasslabeled criterion (Zhou,1999;Jiangetal.,2002).Two passeswereperformedon compile thetrajectoryofeachvortex. tracking algorithmdescribedpreviously(Gifford, 2011) wasusedto calculated aroundiso-contoursoftheswirlingstrength.Thevortex- complex eigenvalueofthevelocitygradienttensor. Thecirculation( of eachgridpointwascalculatedbycomputingtheimaginarypart of the et al.,2005)]toeliminateincorrectidentifications.Theswirlingstrength compared againstathresholdvalue[2.6%ofthemaximum(Chakraborty Agency (DARPA) grant W911NF1010040 toJ.J.S.andP.P.V. This researchwas partially supportedbyDefenseAdvanced ResearchProjects D.H., J.J.S.,N.D.C.andP.P.V. analysedthedataand wrotethemanuscript. D.H., J.J.S.andP.P.V. designedtheexperiments; D.H. conductedtheexperiments; The authorsdeclarenocompetingfinancialinterests. point-based velocity‘labeling’ algorithmandtheswirlingstrength( dynamics. Two different methodswereusedtoidentifyvortexcores:a Analysis ofthesecoherentstructurescangiveinsightintocomplexwake Bluff bodyflowsaredominatedbytheformationandsheddingofvortices. where eigenmode The fluctuatingstructuresenergy (FSE)andenergy fraction(EF)of using themethodofsnapshots(seeSirovichandKirby, 1987;Smith,2005). Funding Author contributions Competing interests structures coherent Identification andtrackingof However, itshould benotedthatamodeisnotnecessarilyvortical Entropy isameasureofthecomplexityandorderspatio-temporal The PODmethodwasimplementedforthemeansubtractedflowfields λ i is theeigenvalueofmode i The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 are definedas: Entropy = − S , FSE EF log i 1 i = = , andN N ∑ FSE i N = ∑ i λ N = 1 i 1 λ FlgE (11) . EF log EF i (10) , is thetotalnumberofmodes. ii () N λ ci modes andEF criterion, was Γ ) was 393 λ (9) ci )

The Journal of Experimental Biology i,X. Liu, a X. Ma, oaso,L . of .adHdntö,A. Hedenström, and M. Wolf, L.C., Johansson, emn,F. Lehmann, D. Thompson, and R. Machiraju, M., Jiang, and Y. Winter, R., vonBusse, M., Wolf, L.C., Johansson, A., Hedenström, G. Spedding, and A. Hedenström, A.R. Gifford, ils,K,LBrea . hn .adSca J. Socha, and X. Chen, M., LaBarbera, K., Miklasz, M.G. McCay, mro,S .adKel M.A.R. Koehl, and S.B. Emerson, emn,F. O. Lehmann, ue,T . ikn .K,Sat,S .adBee,K.S. Breuer, and S.M. Swartz, D.K., Riskin, T. Y., Hubel, Y. Zhou, and J.C. Hu, iad,S. Miranda, B.P. Epps, 394 RESEARCH ARTICLE http://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.090902/-/DC1 Supplementary materialavailableonlineat csen A. Eckstein, bot .H n o onof A.E. Von Doenhoff, and I.H. Abbott, upy .adH,H. Hu, and J. Murphy, References Supplementary material csen A. Eckstein, uly . yns . aoik .P,Brel . rw,R .adMGie J. A.C. McGuire, Eckstein, and R.M. Brown, B., Borrell, S.P., Yanoviak, G., Byrnes, R., Dudley, S.P. Yanoviak, and R. Dudley, din R.J. Adrian, lxne,D . og . atn .D,Brhm .A n ak A.R. Falk, and D.A. Burnham, L.D., Martin, E., Gong, D.E., J. Mi, Alexander, and H. Guo, H.X., Yang, Y., Zhou, M.M., Alam, iko,W .adDcisn M.H. Dickinson, and W. B. Dickson, R. Adrian, and S. Balachandar, P., Chakraborty, hrno .J,Kn,C . mt,B .adVahs P. P. Vlachos, and B.L. Smith, C.V., King, J.J., Charonko, rz A.S. Cruz, G. Berkooz, ala,J . wrz .M,Rsi,D .adBee,K.S. Breuer, and D.K. Riskin, S.M., Swartz, J.W., Bahlman, ihp K.L. Bishop, bird andbatwakes. a four-exposurePIVsystem. tandem wings. animal flight. Mech. Polypedates dennysi. morphological changeintheevolutionofanovellocomotortype:‘flying’ 217-ff. Barcelona,Spain:EurographicsAssociation. Naturwissenschaften region detection.In brachyotis and wingkinematics:theflightoflesserdog-facedfruitbat, 316 G.R. Spedding, J. FluidsEng. stagnating flowssubjecttofreestreamturbulence. extracted fromPIVdata.Exp.Fluids sectional shapeonflyingsnakeaerodynamics. correlation. Evolution particle imagevelocimetry(DPIV). Summary ofAirfoilData corrugated airfoil.In Fluids necessity? A. flight. Integr. Comp.Biol. aerodynamics ofrevolvingwings. dromaeosaurid Microraptorgui. Model testsofglidingwithdifferent hindwingconfigurationsinthefour-winged number airfoilwake. 169. between localvortexidentificationschemes. 2593-2606. passive controlledwakeflowdownstreamofahalfcylinder. Sci. Technol. pressure fieldcalculationsfromparticleimagevelocimetrymeasurements. orientation duringglidinginsugargliders(Petaurusbreviceps). flows. Annu.Rev. FluidMech. ( performance andaerodynamicsofnon-equilibriumglidesinnorthernflyingsquirrels luoy sabrinus Glaucomys (2007). Glidingandthefunctionaloriginsofflight:biomechanicalnoveltyor , 894-897. (2006). Instantaneouspressureandmaterialaccelerationmeasurementsusing (2000). Dynamicsandlow-dimensionalityofaturbulentnearwake. 45, 485-500. 410 (2010). Anerrorthresholdcriterionforsingularvaluedecompositionmodes 44, 1931-1946. (2005). Flowcontrolofasharp-edgedairfoil. . J.Exp.Biol. , 29-65. (1993). Theproperorthogonaldecompositionintheanalysisofturbulent Annu. Rev. Ecol.Evol.Syst. Meas. Sci.Technol. (2005). Twenty yearsofparticleimagevelocimetry. (2007). Aerodynamicforcegeneration,performanceandcontrolofbody (2009). Wing–wakeinteractionreducespowerconsumptionininsect (2005). Characterizationbyproper-orthogonal-decompositionofthe (2009a). Assessmentofadvancedwindowingtechniquesfordigital J. R.Soc.Interface (2009b). Digitalparticleimagevelocimetry(DPIV)robustphase (2001). Aerodynamicstabilityandmaneuverabilityoftheglidingfrog 21, 105401. (2011). Thephysicalmechanismofheattransferaugmentationin 131 (2008). PhasecorrelationprocessingforDPIVmeasurements. Exp. Fluids (2004). Themechanismsofliftenhancementininsectflight. (2007). Batflightgeneratescomplexaerodynamictracks. , 011206. J. R.Soc.Interface Proceedings oftheSymposiumonDataVisualisation 2002 rceig fte47thAIAA AerospaceSciencesMeetingand Proceedings ofthe Exp. Fluids ). J.R.Soc.Interface (2009). Aerodynamiccharacteristicsofasymmetricbluff bodies. 91, 101-122. J. Exp.Biol. . NewYork, NY: DoverPublications. 213 51, 926-936. (2009). Anexperimentalinvestigation on abio-inspired 46, 765-775. , 3427-3440. Exp. Fluids 25, 539-575. (2011). Animalaloft:theoriginsofaerialbehaviorand Proc. Natl.Acad.Sci.USA 20, 055401. 48, 81-103. 5 J. Exp.Biol. , 595-601. 204 Meas. Sci.Technol. (2008). Beyondrobins:aerodynamicanalysesof 48, 355-367. , 2817-2826. (1959). 38, 179-201. (2004). Theeffect ofadvance ratioonthe 7 (1990). Theinteractionofbehavioraland 41, 227-240. , 61-66. 10, 20120794. (2002). A novelapproachto vortex core J. FluidMech. 207 Theory ofWing Sections:Includinga Exp. Mech. (2010). A quantitativecomparison of , 4269-4281. J. HeatTransfer (2010). Theultra-lowReynolds (2010). Effects ofbodycross- (2005). Ontherelationships 20, 075402. AIAA J. 107 50, 1335-1348. 535 Exp. Fluids (2010). Wake structure (2010). Assessmentof , 2972-2976. , 189-214. 43, 716. Exp. Fluids J. Exp.Biol. 133 , 021901. (2013). Glide 39, 730-742. Cynopterus 39, 159- Science J. Fluid (2010). frogs. Meas. , pp. Exp. 210 , ei,M .adGgilo J. Guglielmo, and M.S. Selig, ioih .adKry M. Kirby, and L. Sirovich, M.S. Selig, F. F. J. Schrijer, mt,T. R. Smith, F. Scarano, J., Chen, M., Kostandov, T. L., Hedrick, J., Iriarte-Díaz, D.J., Willis, D.K., Riskin, oh,J. Socha, oh,J. Socha, Y C.H.K. Williamson, ak .adCo,H. Choi, and H. Park, B.W. Oudheusden, arf C. Sarraf, oh,J. Socha, oh,J . ils,K,Jfr,F n lco,P. P. Vlachos, and F. Jafari, K., Miklasz, J.J., Socha, ilr,C .adGai,M. Gharib, and C.E. Willert, hu J. Zhou, D. Ragni, R. Narasimha, in . rat-iz . ideo,K,Gla,R,Irei . omr . Sullivan, A., Roemer, E., Israeli, R., Galvao, K., Middleton, J., Iriarte-Diaz, X., Tian, S. K. Sunada, Breuer, and S. Swartz, G. K., Spedding, Bishop, R., Galvao, E., Israeli, X., Tian, A., Song, etrel J. Westerweel, on .H,Yn,K-.adCo,C.-B. Choi, and K.-S. Yang, D.-H., Yoon, M. LaBarbera, and T. O’Dempsey, J.J., Socha, M. LaBarbera, and J. Socha, aoik .P,Mn,Y n uly R. Dudley, and Y. Munk, S.P., Yanoviak, sewo,J .adLhan F. O. Lehmann, and J.R. Usherwood, B.W. Tobalske, ag .J,Brh .M n ikno,M.H. Dickinson, and J.M. Birch, Z.J., Wang, Z.J. Wang, eln,C n lco,P. P. Vlachos, and C. Weiland, oe,S. Vogel, M.F. Unal, arc,D . oase .W n oes D.R. Powers, and B.W. Tobalske, D.R., Warrick, nva,S . uly .adKsai M. Kaspari, and R. Dudley, S.P., anoviak, J. Aircr. m-selig/uiuc_lsat/s1223/s1223_liftcm.html of humanfaces. resolution ofiterativePIVinterrogation. 13, R1-R19. orthogonal decomposition:atutorial. Mech. boundary layerstatesandstallestablishment. S.M. Swartz, and of batwingkinematics. K.S. Breuer, D.H., Laidlaw, 074005. flying snake, 181-193. J. Exp.Biol. Exp. Fluids Fluids transonic airfoilbasedonparticleimagevelocimetry. 5 trajectory dynamicsandthekinematicsofglidinginaflyingsnake. Eng. 1100. channel flow. angle ofincidence. performance oftwospeciesflyingsnakes( Aeronautics andAstronautics. the NewHorizonsForumandAerospaceExhibit. gliding inaflyingsnake, Comp. Biol. ants. Nature . og . wrz .adBee,K. Breuer, and S. Swartz, kinematics anddynamicsofbatflight. A., Song, A., 763. J. (2008). Aeromechanicsofmembranewingswithimplicationsforanimalflight. interaction usingleadingedgeblowingflowcontrol. aerial descentinarborealants. 1847. improve aerodynamicefficiency byremovingswirl. Fluids Struct. hovering hummingbird. experiments. low Reynoldsnumberhoveringflight:two-dimensionalcomputations Press. , 045002. 46, 2096-2106. 119 17, 358-360. 28, 477-539. (1999). Mechanismsforgeneratingcoherent packetsofhairpinvorticesin 34, 72-79. (2010). Thicknesseffect ofNACA foilsonhydrodynamicglobalparameters, , 129. (2003). (1997). ForcepredictionbyPIVimaging:amomentum-basedapproach. (2009). Surfacepressureandaerodynamicloadsdeterminationofa (2005). Dissectinginsectflight. (1997). AirfoilsectioncharacteristicsatalowReynoldsnumber. (2005). S1223liftandpitchingmomentplots.http://aerospace.illinois.edu/ (2002). Glidingflightintheparadisetreesnake. (2002). IterativeimagedeformationmethodsinPIV. (2011). Glidingflightin (2006). Becomingairbornewithoutlegs:thekinematicsoftake-off ina 40, 988-992. 51, 969-982. 213 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.090902 (2009). PIV-based investigationsofanimalflight. 433 (2005). Low-dimensionalmodellingofturbulenceusingtheproper hyoee paradisi Chrysopelea J. Exp.Biol. (1994). Leadingedgeshapeforflatplateboundarylayerstudies. J. FluidMech. 11 (2005). UniversaloutlierdetectionforPIVdata. (2008). Effect ofpredictor–correctorfilteringonthestabilityandspatial (2007). Biomechanicsofbirdflight. , 965. , 3269-3279. J. Opt.Soc.Am.A , 624-626. Comparative Biomechanics (2006). Non-intrusiveloadcharacterizationofanairfoilusingPIV. Phys. Fluids (1996). Vortex dynamicsinthe cylinderwake. (2010). Aerodynamiccharacteristicsofflyingfishinglidingflight. J. Theor. Biol. Nature Chrysopelea (1987). Low-dimensionalprocedureforthecharacterization 207 (1991). Digitalparticleimagevelocimetry. 387 , 449-460. 435 Integr. Comp.Biol. (2009). A mechanismformitigation ofblade-vortex , 353-396. 22, 043603. (1997). High-liftlowReynoldsnumberairfoildesign. . J.Exp.Biol. , 1094-1097. Chrysopelea (2005). Effects ofsizeand behavioronaerial 4 Nonlinear Dyn. , 519-524. paradisi 254 Bioinspir. Biomim. Exp. Fluids (2010). Flowpastasquarecylinderwith an Annu. Rev. FluidMech. , 604-615. (2008). Phasingofdragonflywingscan (2011). Evolutionandecologyofdirected (2005). Directedaerialdescentincanopy . Princeton,NJ:PrincetonUniversity . J.Exp.Biol. Chrysopelea J. FluidsStruct. (2006). Directmeasurementsofthe (2004). Unsteadyforcesandflowsin : turningasnakeintowing. 209 (2005). A 3-Dkinematicanalysisof J. Exp.Biol. (2008). Quantifyingthecomplexity 51, 944-956. Reston, VA: AmericanInstituteof J. R.Soc.Interface 45, 927-941. Exp. Fluids , 3358-3369. 41, 275-307. (2005). Aerodynamicsofthe 1 , S10-S18. Nature ). Meas. Sci.Technol. 208 (2010). Non-equilibrium J. Exp.Biol. 210 26, 559. Exp. Fluids , 1817-1833. 47, 411-426. Exp. Fluids Meas. Sci.Technol. 37, 183-210. 418 , 3135-3146. Bioinspir. Biomim. Annu. Rev. Fluid vs Exp. Fluids , 603-604. 5 , 1303-1307. robotic wing 208 39, 1096- 46, 749- J. Fluids , 1835- Integr. AIAA Exp. 20, 10, J.

The Journal of Experimental Biology