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Unsteady Lift Generation on Sliding and Rotating Flat PlateWings

H. Babinsky1 and A. R. Jones2

University of Cambridge, Cambridge, CB2 1PZ, UK

The unsteady lift generation on impulsively started wings in linear and rotating motion has beenobserved experimentally at Re=60,000. Sliding wings replicate a simple unsteady motion where the only three-dimensional effects are introduced by the finite span of the wing. The waving wing experiment is a fully three-dimensional simplification of the flapping wing motion observed in nature. It replicates the spanwise velocitygradient and the wing starting and stopping acceleration. This setup preserves key features of the wing strokewhich are neglected in other approaches while the simple geometry allows identification of fundamentaleffects. The flow development has been studied using high speed PIV to capture the unsteady velocity field.Unsteady lift and drag forces have been recorded for several different sets of wing kinematics. A transienthigh lift peak due to the presence of a strong leading edge vortex has been observed during the first chord-length of travel. After the separation of this initial leading edge vortex, weaker leading edge vorticies formand lift values level off. Qualitatively the flow patterns observed on the sliding wing are similar to those on thewaving wing. Spanwise examination of the flow suggests that three-dimensional effects are small.

Nomenclature

α – Angle of incidenceΓ – Circulationλ – Magnitudeof vortex detection criterion (seeref. xiii )ω – Rotational velocity

AR – Wing aspect ratio (L/c)c – Wing chordlengthCL – Lift coefficiente – PercentageerrorL – Wing spanmeasured from watersurfaceto tipt – TimeU – Steady-state free-streamvelocity (at ¾ wing span)x – Travelleddistance(at ¾ wing span)

I. Introduction

Current micro air vehicle (MAV) designs are inspiredby natural fliers, but none approachthe efficiency orfunctionality demonstratedby birdsand insects. Bird and insectflight is dividedby a steepdeclinein gliding airfoilperformancebetween Reynoldsnumbersof 104 and 105, marking the boundary between steady and unsteadylif tgenerating mechanismsobserved in naturei. It is in this regime that MAVs must both generatesuffi cient lift andperform manoeuvresin both calm andgusty conditions.In nature,flight in this Reynoldsnumberregime is primarilyflapping wing fli ght, andit is generally thought that someform of unsteadyaerodynamic phenomena are necessaryto achievethe necessary lift coefficients. While many unsteady flow effectshavebeenidentified so far, the relativeimportanceof these phenomenaand thesignif icanceof 3-dimensionality arenot well understood.

1 Readerin Aerodynamics,AIAA AssociateFellow2 ResearchStudent, AIAA Member.

39th AIAA Fluid Dynamics Conference22 - 25 June 2009, San Antonio, Texas

AIAA 2009-3689

Copyright © 2009 by H. Babinsky and A.R. Jones. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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Force measurements and flow visualizations have been performedusingmechanical wing flappersdesignedtomimic insect wing kinematics, but it canbe diff icult to draw fi rm conclusions from the resulting flowii , iii , iv. Muchsimpler flows canbeobtainedfrom animpulsively startedwing as occursin thebeginning of the translational phaseof an insect wing stroke. While useful for fundamental studies, this model oversimplifies the wing kinematics.Anotherapproachis to investigateairfoi ls undergoinga pitch andplungemotionv, vi, vii. While usefulfor fundamentalstudiesof flapping lift andthrust,this approach neglects the three-dimensionalityof the flow. A quasi-steady setupwasdeveloped by Usherwood andEllingtonviii in which the wing rotates like a propeller. This quasi-steadymodelpreservesthe three-dimensional flow asa velocity gradientin the spanwise direction,but neglects the starting andstoppingthat occurs at thebeginning and end of the translationalphaseof the insect wing stroke.As thestroke of arealistic flapping wing is only a few chord lengths long, theseaccelerationsareexpectedto havea significant effecton the flow field. Nevertheless,propellerexperiments have greatly helped to understand the attached leading edgevortex, first observedon mechanical wing flappers, and demonstrated that this vortex can generate suff icient lif t.However,it remains unclear how quickly the flow developsand to what extent lessonslearnedfrom quasi-steadypropellerexperiments canbeapplied to truly unsteadyflapping. Othersiii haveshownthathighly unsteadyeffects atthe beginning andendof the flappingcycle canproduce significant additional lift but it is unclear what the relativeimportanceof these effects is. As far as MAV’s are concerned a further uncertainty arisesfrom the fact that all theabove experimentsare concentrated at very low Reynoldsnumbersandtheexistenceof a stableleading edgevortexat higherReynoldsnumbers is still uncertain.

Not all unsteady effects increaselift. In the 30s, Wagnerdescribed the delay in circulationgrowth for a wing acceleratingto Re = 105 at anglesbelow steady statestall ix. While thereareanumberof phenomenainvolved, thesimplestinterpretation of thiseffect is that the starting vortex inducesa downwash on the mainwing which reduces the local angle of attack. This effectdiminishesasthe starting vortex movesaway from the wing andthis leadsto an asymptotic rise in wing lift with time, asseeninFigure 1. Wagnermodeled this theoretically assuming a line ofdiscontinuity shed from the trailing edge which convectsdownstreamat the freestream velocity. This canbe thought of asa continuous distribution of vortex centers shed from the trailingedge, endingwith thestarting vortex. Theresultis a gradual buildin circulation which asymptotically approaches a steady statevalue, reaching approximately 90% after 6c of travel. Since thetranslational phase of an insect’s wingbeat will last only a fewchordlengths, thisdelay in lif t generationcould besignificant.

The aimsof the researchreportedhere are to understand unsteady lif tgeneration at Reynolds numberstypical for micro-air vehicles (10,000– 60,000). In particular thesignificance of three-dimensionaleffectsis to be determined.Since thepresence of a stable leading edgevortex (LEV) is thought to be crucialfor the production of high lif tcoefficients at low Reynoldsnumbers,the question addressed hereis whethersuchan LEV developsatReynolds numbersabove 10,000 andto what extent three-dimensionalityisnecessaryto sustain it. There are twoaspects to three-dimensionali ty, firstin termsof the wing planform (finitespan) and second in the motion

Figure 1. Lift variation on an impulsively startedwing according to Wagnerix

Figure 2. The CUED tow tank

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(rotatingvs sliding) andboth are thought to affectthe flow development. Finally, thetimescaleof unsteady effectsisaddressed.For example,if a stable LEV develops,how quickly doesthelift build up relativeto a wing stroke (whichis only a few chordlengths)or is thelift limited by the Wagnereffect.

The sliding and waving wing experimentsare designed to produce a simple, yet fully three-dimensional andunsteady flow field. Thesliding wing preservesthegeometric effects of 3-dimensionality but at uniform flow acrossthewing. In contrast,thewaving wing experiencesa spanwisevelocity gradient in thesamemanner asthepropellerexperiments, but in this setup theacceleration at thebeginning and end of thewing stroke is preservedaswell. Thismodel of the translational phaseof an insect wing stroke allows for the identification of lift -generating flowstructures,quantification of the relative importance of steadyand unsteadyeffects,andprovidesdata which canbeusedto validate unsteady three-dimensional CFD results.

II. Experimental Method

All experiments have beenconductedby towing or rotating awing model through a tank fi lled with (still) water. By usingwateras the working medium it is possible to achieve the requiredReynolds numberswith relatively slow motions,giving very hightemporal resolution while at the sametime providing an optimalenvironment for force measurements and optical flow diagnostics.Allowing sufficient settling time between experiments (10-15minutes) the residual free-stream turbulence in the tank is belowmeasurement uncertainty.The tow tank, as seenin Figure 2, hasa1m squarecross section. The central section (2m in length) isconstructedof Perspex, with an additional glass end window toenablePIV imaging.

Two types of experimentshave performed, both using similarwing geometrybut different kinematics.The first is an impulsivelystartedflat-plate wing (2.5% thickness with roundedleadingandtrailing edges)moving in a ‘sliding’ motion (similar to a fixedwing). Details of theseexperiments and a full discussionof theresultscanbefoundin Beckwithx. Thesecondset ofexperimentsinvestigatedan impulsivelystartedrotating wing as reportedby Jonesxi. Here we review both setsofexperimentsandincludenew results.In both casesthe wing had a chordlength of 0.12m and a thickness of 2.5%.Two wing spanswereinvestigated to give aspectratios of 2 and 4. Note that, if the water surface is consideredasareflection plane,the aspect ratio refers to the semi-spanof anequivalentwing. For bothtypes of experiments a splitter platewas fitted just under the watersurface to eliminateany free-surfacewave effects.

For the sliding wing experiments (see Figure 3) thedesired Reynolds number of 60,000 was achieved with atowing speed of 0.48 m/s.The plate wasaccelerated (linearlyin time) from restto full speed over a streamwise distance of0.072m, which is equivalent to 0.6c. More details can befound in ref. x.

The waving wing motion was programmed using threedifferent velocity profiles: li near, sinusoidal, andexponentialin time as shown in Figures4 and 5. The wing wasacceleratedsuch that it reached its maximum velocity aftertravelling a distance of 0.10, 0.25, or 0.60 chord lengths (atthe¾ span)for eachprofile. Velocity profiles weresymmetricsuch that the wing decelerated in the same way beforereaching a maximum wave of 90 degrees.The maximumvelocity was chosen as that which gives a local wingReynoldsnumber of 60,000 at 3/4 span.

Figure 3. Tow carriage with waving arm

Figure 4. Waving wing rotational velocity vs time

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Force Measurements

Two-component force balance measurements weretaken in bothwaterandair. Datawassampledat 7 kHz withand without a 30 Hz low pass filter. Lift and dragcoefficientswereobtained by subtracting the inertial forcesmeasured in air from the forces measuredin water andnormalizing by the local wing velocity to calculate theeffective wing lift coefficient. Force data wasaveraged over10 runs.

Figure6 shows the lift coefficient valuesobtained usingthe unfiltered data, data acquired using a hardware30 Hzlow-passfilter, and the samedata with a moving-averagesmoothingapplied.The unfiltered lift signalcontainshigh-frequencyelectrical noise near 100Hz and a mechanicalvibration near 15-20 Hz. The force data shown in thefollowing plots was acquired with the low-pass fi lter inplace to remove the electrical noise, andfurthersmoothingwasappliedto eliminate thesignalfromthevibrations.

Particle Image Velocimetry

To obtain PIV data for chordwiseslices, the horizontallaser sheet entered the tank throughthe side wall and thecamera wasplacedbelow the tank. Spanwisevelocity datawas obtainedwith a vertical light sheetentering from thesideanda camerapositionedat thefar endof the tank.Eachexperiment wasrepeated between5 and 20 times,analysisof early data demonstrated that a smaller number ofaverageswassufficient in all cases.Vestosint 7182particleswith a nominal diameterof 30µmandspecific gravityof 1.02 were used to seed the flow. Images were taken at frame rates between 50 and 750Hz at a resolution of1024×1024pixelswith a 20×20cm field of view. The width of the image is 1.6chordlengthsor about28degof travelfor thewavingwing. Theseframeratesresultin a 5 pixel particle displacementwithin imagepairs.PIV images wereprocessedin two passes with interrogation windows decreasing from 32×32 to 16×16 pixels with Gaussianweighting and 50% overlap. The resulting vector fields were averaged acrossthe runs, producing a set ofinstantaneousaveragevelocity fieldsas thewing wavesthroughthe field of view.

Experimental Uncertainty

The total error for the PIV measurements, etot = ebias+ erms, was first estimated using the trends and valuesreportedin the li teraturexii. For thecurrent PIV setup,ebias≈ -0.01dueto the lossof pixels. Therandomerror canbeexpressedas the sumof the uncertainty due to particle image diameter of 3 pixels, displacement between1 and 3pixels, anddensityaveraging 8 particles per window: erms = 0.009+ 0.01 + 0.025= ±0.04. The total error becomesetot = +0.03/-0.05 pixels. Error was also estimated by evaluating PIV imageswith a known displacement. Anartific ial image wasgeneratedwith an averageof 15 3-pixel particlesper 16×16interrogation widow. This imagewasdisplacedby 1, 2, 3, or 4 pixels and evaluated with the LaVision DaVis 7.2 software. (Cross-correlation modewith standardcorrelation function and 3 passeswith Gaussianweighted interrogationwindows decreasing from64×64 to 16×16 pixels.) The RMS error for theseimageswith constantdisplacement was ±0.01 of a pixel. Toaccountfor theerrordueto imperfect particle imageshapes, intensities,and imagenoise, real imagesof the wavingwing wereartifici ally displaced and evaluated.The RMS error for theseimageswas0.03of a pixel, or 1.7%of thedisplacement. Thisvalueagreesvery well with thevalueestimatedfromtheliterature.

Figure 5. Waving wing rotational velocity vs distancetravelled (at ¾ wing span)

Figure 6. Raw, filtered and smoothed force data

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Figure 7. Unsteady lift coefficients on the waving wing for three levels of acceleration (solid line: 0.25 c, dashed line: 0.6 c,dotted line: 0.1 c)

III. Results

Figure7 shows the averagedand smoothed lift coefficients determined on the waving arm for all accelerationpatternsunder study. Two angles of attackhavebeen selected,5° which is nominally in theattachedflow regime fora flat platein steadyflowx, and 15° which is abovethestall angle. It canbeseen that theeffect of angle of attackisprimarily confinedto changingthe magnitudeof the measured force,while thereis little changeof the actualforcebehaviour. Al l curves follow a characteristic pattern, where there is an intial steep increasein li ft coefficient,followed by a sharpdrop anda subsequent recoveryto anintermediatelevel thatis thenmaintained for therestof theconstantvelocityportion of thestroke.

It appearsthat after a motion of about 2-3 chordlength (at ¾ span,equivalent to rotation between35 and 50degrees)the lift reachessomething closeto a steady-state value. The main differences dueto different accelerationpatternsare observed in theearly stagesof a wing stroke. Theslowest acceleration(wheremaximumwing rotational

speed is reachedafter 0.6 chordlengthsat ¾ span) exhibitsa significantly reducedlif t peak. Apart from thesinusoidalacceleration, the initial peak in lift coeffi cient is alsoobservedto occur laterduring thestroke,centredat around1 chordlength of travel, which is well after the maximumspeed hasbeenreached. For the two faster accelerationsthere is lit tle difference in the observed force peaks. Al lcurvesshowa very pronounced maximum approximately50% above the steady-state value at around 0.6chordlengths travelled (in all cases this is after themaximum velocity hasbeenreached). It appearsthat oncethe wing accelerates to top speed faster than a giventhreshold, the magnitudeof acceleration is no longer afactor. Likewise, in thesecases, the exact pattern of theacceleration is also no longer significant, most of thecurves seenin Figure 7 lie more or less on top of eachother. The fact that the details of the acceleration patternare significant for the slowest motion studied, suggeststhatthis is nearthethreshold.

Figure 8. Comparison of unsteady lift coefficientsobserved for rotating and sliding wing (max. speed

reached after 0.6 chords of travel)

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Figure8 comparestheunsteady lift coefficients observedon the rotating andsliding wing. Here,only theslowestacceleration pattern is compared (faster accelerations were not available for the sliding wing). It is striking howsimilar the forcehistoryfor thetwo different casesis. Both exhibit an initial forcepeakfollowedby a minimumanda subsequent‘flattening out’ of the lift value. However, in the caseof the sliding wing it was also possible todeterminethe long-term averageforce coeff icient (indicatedby thedashedline) andthis suggestthat, in the case ofthegreaterangle of attack, quasi-steady behaviour may not have beenreachedevenafteralmost5 chordsof travel.

Also shownin Figure 8 is the expected li ft distribution following Wagner’s theory(using the long-term steadystatevalue asthe asymptotic lift coefficient).For the lower angle of attack (which is nominally in attachedflow) itappearsthat some of the unsteady lift behaviourcan be attributedto this effect,however,at largeranglesof attackand during the initial phase of the motion other unsteady aerodynamic factorsare clearly dominating the forcehistory.

In order to aid the identification of the causesof the initial lift peak, Figure9 comparesthe velocity fieldmeasuredon the rotating wing (linear acceleration, 0.25chordsto top speed)at threetimesin the early part of themotion: close to the maximum lift, in the minimum and oncethe almost quasi-steady state hasbeenreached.Toclearly identify vortices in the flow the λ-criterion proposed by Graftieaux et alxiii has been implemented.Asdescribed by Morganet alxiv this greatlyhelps to identify vorticesembedded in complexflows. It canbe seen fromFigure 9 that thereare noticeabledifferences in the flow patterns observed at these threedifferent times.At first (A),a distinct leading edgevortex is formed on the suction side of the plate, while the starting vortex is seen justdownstreamof the trailing edge.When the minimum of the lift is reached (B), this vortex hasshedand movesdownstream, while a new LE vortex is forming. In the final images(C), severalvortices can be seento co-existabove the wing and after this time there is a continuous pattern of shedding vortices in a quasi-periodic fashion.From theseimagesone might concludethat the cause for the rapid build up of lift during the initial stagesof thewing motion is dueto thedevelopmentof theattachedleadingedge vortex (and themovementof thestarting vortexawayfrom thewing).

Figure 9. Flowfield observed at three times during the unsteady motion. A: near the initial lift peak, B: at the minimum,C: at the onset of the quasi-steady period. The images in the centre show the velocity vectors while the pictures on the

right have contours of the λ-criterion superimposed.

In order to determine whether the leading edgevortex is responsible for the lift generatedin theearlypartof themotion, its circulation hasbeenestimated by integrating the tangential velocity along the contour of λ=0.7 for allframes recordedduring the initial acceleration. This hasbeenshown to give good estimatesfor the actualvortexstrengthxiv. The resulting non-dimensionalcirculation is shown in Figure10, together with two samplesof theintegrationpath.

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Figure 10. Calculation of LE vortex strength

It can beseenthat theLE vortex circulation increases rapidly duringtheearly part of themotion andthat theLEvortex breaksoff from the leading edgeat about thesametime aswhenthepeakin lift is observed.After the vortexhas separatedfrom theleading edge, theautomatic routine produces moreerraticattemptsto follow thevortexthat isnow moving downstream.Nevertheless,it appearsas if the detachedvortex now remainsmoreor lessat the samestrength.

Based on theseobservations Figure 11 now proposesthat the flow on the impulsively startedrotating wingdevelops in threestages.First, during the ‘t ransient’ stage,the leading edgevortexgrowsrapidly and stays attachedto the plate.Most of the li ft is concentrated hereand it increasesbecauseof the combinedeffect of the LE vortexgrowing and thestarting vortex moving away fromthe wing. This phaseends when the vortex shedsfrom the leading edge. Theultimatestrength of theLE vortexandits developmentis influencedby theaccelerationpattern;slower accelerationsproduceaslower vortex growth and reduce the strength atseparation. However above a certain level ofacceleration the vortex development becomesindependent from the kinematics. During thesecond, ‘development’ phase the leading edgevortex sheds from the plate and a new vortexforms.Because the first vortex is no longer closetothe platesurfaceits effect on lift is diminishedandthe new LE vortex does not achieve the sameultimate strength before it sheds.In this phasethetotal lift is relatively low. Finally in the‘established flow’ phase a periodic pattern ofvortex shedding from the leadingedge is observed.

Figure 11. The three stages of flow development on animpulsively started waving wing: Transient, Development and

Established flow

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During this phase there are typically 3-4 vortices presentabovethe plate at all times giving a relatively high liftcoefficient.

Three-dimensional effects

Figure12 shows three cross-sections of the λ-distribution (for absolutevaluesabove 0.6) measured at threespanwiselocations on the wing. Note that the accompanyingvelocity vectorshave beenscaled with the local free-streamvelocity which is variable acrossthe span. It can be seenthat the flow is similar in all locations suggestingthattherearefew three-dimensional effectson thewing. All vorticesappear to beof similar sizeandat a comparablestage of their development.There is, however,some indication that the vortex on the outer sections detachessomewhatearlier from the surface, and this could be the result of the outer wing having travelled further in non-dimensionalterms(i.e. chord lengths) or an effectof theinteraction with thetip flow.

Figure13 showssimilar data obtained at thelif t peakon the reducedaspect ratio wing (AR=2). It can be seen thateven at this low aspect ratio, there are no obviousthree-dimensional effects.All vorticeslook similar to eachotherbut thereis a slight indication that the vortex coresareslightly further away from the surfacein the moreoutboardlocations.

Figure 12. λ-distribution measured at three spanwise cross-sections. Aspect ratio 4.

Figure 13. λ-distribution measured at three spanwise cross-sections during the initial lift peak (0.5 chordstravelled at ¾ span). Aspect ratio 2.

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Figure 14 comparesthe spanwise velocity distribution measured just downstream of the wing during the earlypart of the motion. The first imageshows a well-definedtip vortex and evidenceof spanwise flow alongthe wing.However,as the flow developsa second vortex, oriented in the samedirection as the tip vortex, appearsfurtherinboard.

Figure 14. Spanwise cross-section of flow behind the wing.

To investigate the causes of this second vortex, some flowvisualisationwith hydrogen bubbles was performed. An example isseen in Figure 15. Here a series of detachedleadingedgevorticescanbe seenclearly, running almost parallel to the leadingedge. The tipvortex is also seenrelatively clearly. Although this imageis not verywell definedthere is some indication that the secondvortex seen inthepreviousfigureis formed from thedetachedLE vorticesrolling upindependently from the tip vortex slightly inboardfrom the tip. Thissuggestionsis confirmed by the observation that the secondvortexseen in Figure 14 only appears well after the lif t peak, that is after thefirst LE vortex hasdetachedfrom thesurface.However,this aspectofthewing flow remainssubject for furtherstudy.

IV. Conclusions

Experiments have been performed on simple flat plate wings inunsteadysliding and rotating motionat Re= 60,000.In particular, thedevelopment of lift during the early part of a suddenly acceleratingmotion was studied. It was found that all of the flows investigatedshowedremarkably similar behaviour. Very early during the motion(near theendof the acceleration) a pronounced peakin lift coefficientwasobserved, followed by a drop in lift and an eventual recoveryto

quasi-steadylevels. Up to a (yet to bedetermined) thresholdvalue a greaterinitial accelerationcausesanearlierandmorepronouncedinitial lift peak. Oncea certain level of acceleration hasbeenexceededthelif t peak is independentof wing kinematicsappearing approximately after 60%of chordlengthstravelled(at ¾ wing span) and giving a peakmagnitudeof about 1.5 times thequasi-steadyvalue. The initial peakin lif t is attributedto the growthof anattachedleading edgevortex and the sudden drop in lif t is causedby the detachmentof this from the surface.Three-dimensional effects, whether aspect ratio or motion kinematics,werefound to besmall. However,nearthe wing tipthereis someindicationthattheleadingedgevorticesdo not immediately mergewith thetip vortexbut ratherform asecondstreamwise vortexof the samesense.

Figure 15. Flow visualisation, AR4 wing

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AcknowledgmentsTheauthorswould like to acknowledgethesupportof AFOSRand EAORD, who supportedthis researchunder grantFA 8655-07-1-3082.

References

i Ellington,C. P., “I nsectsversusbirds: thegreatdivide,” 44th AIAA AerospaceSciencesMeetingandExhibit , AIAA 2006-35,2006Elli ngton,C. P.,“I nsectsversusbirds:thegreat divide,” 44thAIAA AerospaceSciences MeetingandExhibit , Vol. AIAA2006-35,Reno,Nevada,9-12 January2006. 2006-35, Reno, Nevada,9-12 January 2006.ii Dudley,R., “The Biomechanics of InsectFlight”, PrincetonUniversity Press, 2000iii Birch, J.M., Dickson,M.H., Dickinson, M.H., “Forceproduction andflow structureof theleadingedgevortexon flappingwingsat high andlow Reynoldsnumbers”,J Exp.Biology,207,pp.1063-1072,2004iv Ellington,C.P.,vandenBerg,A.P.,Will mot, A.P.,Thomas,A.K.R., “L eading-edgevorticesin insectflight”, Nature,384,pp. 626-630,1996v Okamoto,M. and Azuma,A., “Experimental Study on AerodynamicCharacteristicsof Unsteady Wings at Low ReynoldsNumbers,” AIAA Journal , Vol. 42, No. 12,December 2005, pp. 2526–2536vi Ol, M., “Vort ical Structuresin High FrequencyPitch and Plungeat Low ReynoldsNumber,” 37thAIAA Fluid DynamicsConferenceandExhibit , Vol. AIA A 2007-4233, Miami, FL, 25 - 28 June2007vii Radespiel,R.,Windte,J.,and Scholz, U., “Numerical and ExperimentalFlow Analysisof Moving Airfoils with LaminarSeparationBubbles,”44thAIAA AerospaceSciencesMeetingandExhibit , Vol. AIA A 2006-501, Reno,Nevada,9-12 January2006viii Usherwood,J.R.,Ellington, C.P., “Theaerodynamics of revolving wings:I. model hawkmothwings”, J.Exp.Biology, 205,pp. 1547-1564,2002Usherwood,J.R.,Ellington, C.P.,“The aerodynamicsof revolving wings:II . Propeller forcecoefficientsfrom mayfl y to quail”, J.Exp. Biology, 205,pp.1565-1576, 2002ix Wagner,H. UberdieEnstehung desdynamischenAuftriebesvon Tragflugeln.Aangew.Math.Mech.5, 17-35, 1925x Beckwith,R.M.H., Babinsky, H., “Impulsively StartedFlat Plate“, AIAA -2009-78947th AIAA AerospaceSciencesMeeting includingTheNewHorizonsForumand AerospaceExposition, Orlando, Florida,Jan. 5-8, 2009xi Jones,A.R., Babinsky, H. “Three-Dimensional Waving Wingsat Low ReynoldsNumbers”,AIAA -2009-790, 47th AIAAAerospaceSciencesMeeting includingTheNewHorizonsForumandAerospaceExposition, Orlando,Florida,Jan. 5-8, 2009xii Raffel, M., Wil lert, C.E. andKompenhans,J., Particle ImageVelocimetry: A PracticalGuide, Springer,1998xiii Graftieaux,L., Michard,M., andGrosjean,N., “Combiningpiv, podandvortex identification algorithmsfor thestudyof unsteady turbulent swirlingflows”, MeasurementScienceandTechnology, 12 (2001), pp.1422–1429xiv Morgan,C.E.M., Babinsky, H., Harvey, J.K., “V ortexDetection Methodsfor Usewith PIV and CFD Data”,AIAA-2009-74,47th AIAA AerospaceSciencesMeeting includingTheNewHorizonsForumand AerospaceExposition, Orlando, Florida,Jan. 5-8, 2009