THESIS K A K I T A H f l A M

THE "CLAP AND FLING" LIFT MECHANISM

by

Maheran Nuruddin

Dissertation submitted for the Degree of

Master of Science

of the

University of Newcastle Upon Tyne

September 1993

CONTENTS

PageACKNOWLEDGEMENTS

ABSTRACT

INTRODUCTION............................................... 1

CHAPTER 1: GENERAL INTRODUCTION TO FLYING.................. 31.1: Development of aerodynamic 1ift.................5

1.1.1: To prove that the stagnation pointsmove downwards........................... 7

1.1.2: The establishment of circulationround the aerofoi1.......................8

1.2: Sustained forward f1ight....................... 101.3: Hovering flight................................ 12

1.3.1: Normal hovering......................... 131.3.2: "Exceptional" hovering.................. 16

CHAPTER 2: "CLAP AND FLING" LIFT MECHANISM................ 172.1: Hovering flight of Encarsia formosa and the

"f1i ng" mechani sm.............................. 172.1.1: The "f1i ng"............................. 20

2.2: Two-dimensional analysis of the "fling"process........................................ 222.2.1 : Lighthi11!s ana lys is . . . . . . . . . . . . . . . . . . . .242.2.2: To calculate circulation as a

i ncreases............................... 252.2.3: To analyse the aerodynamics of the

"clap and fling" mechanism using aconformal mappi ng technique............. 26

2.2.4: The complex potential and circulationfor the "fling" process.................31

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CHAPTER 3: VISCOUS EFFECTS................................423.1: Vorticity in viscous flow region............... 423.2: Effects of the acceleration and deceleration

of the external stream on the surfaces of awing...........................................45

CHAPTER 4: THREE-DIMENSIONAL EFFECTS......................594.1: Three-dimensional model of flow around the

wings..........................................594.2: Three-dimensional motion of Encarsia formosa...66

CONCLUSION................................................68

REFERENCES 69

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ACKNOWLEDGEMENTS

I am very grateful to my supervisor, Dr. R.R.Kerswell forhis guidance, helpful suggestion, useful comments andconstant encouragement during the course of my study.

I would like to express my thanks to Dr. R.S.Johnson for hisguidance and to all staff in the Department of AppliedMathematics who have contributed to this work in one way oranother.

I take this opportunity to express my appreciation to MARAInstitute of Technology for offering me the opportunity andproviding me the financial support throughout my studies atthe University of Newcastle Upon Tyne.

Finally, I wish to express my gratitude to my husband,Jaaffar Hassan, my daughter, Amalina Jaaffar, my parents andfriends for their support and encouragement.

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THE "CLAP AND FLING" LIFT MECHANISM

by

Maheran Nuruddin

ABSTRACT

In 1973, Wei s-Fogh demonstrated that the high 1i ftcoefficient necessary for hovering flight in certain insectsis incompatible with classical aerodynamics principles andproposed a new mechanism of lift generation, the "clap andfling" mechanism, whereby the wing movements generatecirculation around the wings. A two-dimensional, inviscidanalysis by Lighthi11 (1973) showed that the ci rculationgenerated by the "fling" is sufficient to permit sustainedflight. Viscous effects act to enhance this circulation bythe production of a patch of vorticity at the wing's leadingedge. A discussion is also offered of the three-dimensionalaspects of the "clap and fling" mechanism. An associateddownflow due to tip vortices tends to reduce the liftexperienced by the wings slightly.

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INTRODUCTION

A flying animal has a beauty of its own!

One of the important practical aims of research into fluiddynamics is to improve locomotion through fluid media. Overmany years, this has led to the design of efficient vehiclesfor locomotion through air or water. A modern aeroplane i sone of the remarkable products of such research. It wouldnot have been invented if Nature had not provided theobvious prototype in flying animals. The aerodynamic flightperformance of flying animals has led to remarkable resultsthat suggest new engineering possibilities. Therefore it isof interest to pursue research both into aerodynamics andbiofluiddynamics.

Flight has many different functions: food-seeking, food-taking, migration, and reproduction purposes. Evolutionarydevelopment of flying in different insect groups must haveresulted from advantages in food-seeking, dispersal and alsofrom the pressures brought about by predators. Smart andHughes (1972) relate the phenomenon of development of insectflight to the appearance of tall terrestrial plants, whichare food sources suitable for crawling insects. This couldhave favoured the evolution of aerodynamic surfaces orwi ngs.

Many different capabilities are needed by flying animals.Sustained forward flight needs wing motion to yield lift andthrust. In order for a flying animal to propel itself alonga horizontal course, its body must be subjected to lift, anupward force equal in magnitude but opposite in direction toits own weight, and to thrust, a propulsive force sufficientto overcome the backward drag of the air moving past itsbody. In f lyi ng animal s, 1 i ft and thrust are both providedby the same aerodynamic surfaces.

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Most flying animals are also capable of hovering flighteither for prolonged periods or for short intervals intaking-off and landing. The problem of weight support isdifferent for hovering flight. The majority of hoveringanimals support their weight by motions which can beunderstood in terms of classical aerodynamic principles.However smaller flying animals adopt a different mode ofhovering. Weis-Fogh (1972,1973) was the first to investigatehow animals hover in still air. He made a study of modes ofhovering flight in insects, birds and bats. He demonstratedthe use of a mode of motion which he cal led "normalhovering" and also discovered various exceptional modes ofhovering. He showed that insects of sizes below about 2mmare prevented by the viscosity of the air from using normalhovering. He proposed that they use a mechanism of liftgeneration previously unknown to aerodynamists: the "clapand fling" mechanism.

The main purpose in this dissertation is to study this "clapand fling" mechanism of lift generation as practised by thechalcid wasp, Encarsi a formosa. an economically importantparasite used in the biological control of greenhouseamphids. Motivated by the observations of Weis-Fogh,Lighthill analysed the "clap and fling" mechanism through apurely inviscid, two-dimensional flow. This is di scussed i ndetai 1 in Chapter 2. The flow pattern wi 11 be modified dueto the presence of vi scous effects and this is dealt wi th inChapter 3. Finally, in Chapter 4, some consideration is madein fitting the two-dimensional motion ideas into a three-dimensional model of the flow around the real wings ofEncarsia formosa.

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CHAPTER 1

GENERAL INTRODUCTION TO FLYING

The main purpose of thi s chapter i s to di scuss some generalaspects of flying. To understand animal flight, anunderstanding of the basic science of aerodynamics isnecessary, that is, the motion of bodies through air. Astudy into the aerodynamic aspects of animal flight isprimarily concerned with the forces which result from thei nteraction of the flying animal with the air.

The motion of a flying animal in air corresponds to themotion of a body immersed in a fluid. The motion of the bodyis related to the lift and drag components of the resultantdynamic force R (in this case aerodynamic force) exerted onthe body by the fluid. Drag £?, the resistance to motion, isthe component of the resultant force opposite to thedirection of motion U and lift L is the component normal toits direction (Figure 1.1).

L

Figure 1. 1

Only certain shapes will produce a high lift-drag ratio andhence be effici ent enough to be practical. Such bodi es areusually termed aerofoils and for flying animals, the wings

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act as aerofoils. In this chapter we are concerned with thelift experienced by an aerofoil. We calculate the lift usingthe theory of classical aerodynamics in which we model theflow as being a two-dimensional, irrotational motion of aninviscid, incompressible fluid. Such approximations areknown to give good results.

theAn

Inviscid flow means that the viscosity of the fluid isassumed to be zero and as a result no viscous drag isproduced. Incompressibi1ity of the fluid means that thedensity of the fluid is constant. Motion in whichvorticity is zero is said to be irrotational.i rrotational flow (wi th veloci ty potenti al 0) of anincompressible fluid (with streamfunction ¥), can bedescribed by the complex potential w = 0 + f¥ where thecomplex plane is defined by z - x + iy. The complexpotential property of the flow makes it possible for us toassociate the flow around a two-dimensional aerofoil withthat around a circular cylinder by means of a mathematicaltechnique known as conforms! transformation. Atransformation by means of an analytic relation between twocomplex variables is said to be a con formal transformationas in Fi gure 1.2.

z - planef-.z =

- plane

Joukowski transformation

Figure 1.2

Suppose that it is possible to establish a conformal mappingbetween the complex variable £ and z, given by f such that£=f(z). Then, by means of the transformation equation above,we can deduce the flow past the aerofoi1 by solving for thecorresponding flow past the circular cylinder.

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In Section 1, we discuss the mechani sm by which 1 i f t isproduced on a circular cylinder placed in an inviscid,i ncompressi ble, i rrotational flow. This will lead us tofinding the lift exerted on a two-dimensional aerofoil sincethe lift is the same as that produced on a circularcylinder. This is then followed by a discussion on the twoextremes in flying: sustained forward flight is discussed inSection 2 and the other extreme of flying, hovering, wherethe animal remai ns motionless in still air, is brieflydescribed in Section 3.

1.1: Development of aerodynamic lift

A side force or "lift" on a body arises from the combinedeffect of the forward motion of the body due totransl ational wind velocity and the circulation round it andis independent of the size, shape and orientation of thebody - in the confines of inviscid theory.

Figure 1.3

We consider the flow due to a circular cylinder placedhori zontally in a uniform stream of inviscid, i ncompressi blefluid. The streamline pattern is illustrated in Figure 1.3.The 1 ine PQRS is a streaml i ne cal led the dividingstreamli ne, si nee it separates the fluid which passes overthe top and below the cylinder. The points Q and R arestagnati on poi nts at the foremost and rearmost of the

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cyli nder. The veloci ty di stribution is symmetric about QR.By Bernoulli's theorem, the pressure distribution over thecylinder on the top side is the same as that on the bottomside, therefore there is no lift. Symmetry about TU showsthat there is also no drag.

Figure 1.4

Next we consider a circular cyli nder in a uni form streamwith circulation K in a clockwise sense. The circulation maybe produced in practice by rotating the cylinder about itsaxis. The viscosity of the real fluid would then producesuch circulation. The streamlines are then as illustrated inFigure 1.4. The circulation causes the stagnation points tomove downwards (this is proved in Section 1.1.1). The speedis increased on the upper surface (indicated by crowdedstreamlines in Figure 1.4) and decreases over the lowersurface (the streamlines are spread apart in the diagram) ofthe cylinder. From Bernoulli's theorem, pressure on thelower surface is greater than that on the upper surface.Thus the cylinder will experience a force in a directionperpendi cular to the uni form stream and upwards (1i ftforce). This lifting effect produced by the circulation iscalled the Magnus effect. Symmetry about TU is stillmai ntai ned. Hence there wi 11 be no force in the horizontaldirection i.e. no drag.

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The result that for any two-dimensional body, when it isplaced in a flow of inviscid fluid with or withoutcirculation, the drag is zero, is sometimes referred to asd'Alembert's paradox. Rigid bodies do of course experience aresistance to their motion through a real fluid.

1.1.1: To prove that the stagnation points move downwards

Consider the flow with no circulation about the circle |£|=ain a uniform stream (i/,0). The complex potential is givenby:

2

w(U = u f C + ~ 1 .....................(1.1)

using Milne-Thompson's Circle Theorem, and the complexvelocity is:

dw = u - iv = U f 1 - £ 1. .............(1.2)

dwThe stagnation points are found from _ = 0 that is:

U2a

which implies that C - ±a. Therefore stagnation points Q andR in Figure 1.3 are -a and a respectively.

Now, in adding a circulation K round the cylinder, we add auniform line vortex at the origin which corresponds to a

7 Kcomplex potential of -*- In C- Hence the total complex

potential at £ is2

w(C) = U f C + I 1 + 4£ ln C ...........(1.3)

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The complex velocity is2.. f , a 1

= " I 1 " ?2 J7/f

But C = ae , therefore

dw -2ie 7/fe2na

-ye

,- , ,(1.4)

= i<*T7'e f 2sine K

The stagnation points occur where

= 0,

and hence they are given by the points:

9 = siin"1 f - 7S^^ 4na

Since sin 0 is negative, the values of 9 are in the thirdand fourth quadrant which correspond to the stagnationpoi nts bei ng shi fted downwards.

1.1.2: The establishment of circulation round the aerofoil.

Figure 1.5

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The initial flow when a two-dimensional aerofoil movesthrough an inviscid, incompressible fluid at rest is asshown in Figure 1.5. The rear stagnation point lies on theupper surface of the aerofoil, and fluid is forced to flowround the sharp trailing edge, where the speed is very high.This is associated with low pressure at the trailing edge Aand a higher pressure at the stagnation point B. There is avery high speed at A and zero speed at B, therefore fluidrapidly decelerates from A to B, as shown in Figure 1.6(a).This causes the boundary layer to separate from the aerofoilsurface (Figure 1.6(b)).

Figure 1. 6(a)

Figure 1.6(b)

A localised patch of vorticity is generatedischarged downstream or "shedded" (the WagnerKelvin's Circulation Theorem this leaves anopposite circulation in place about the aerofoiillustrated in Figure 1.7 .

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K

Figure 1.7

1.2: Sustained forward flight

In order for a flying animal to have sustained forwardflight, it must be able to generate enough lift to balancebody weight and enough thrust to balance body drag. Theseare the basic aerodynamic requirements.

Path of motion of plate

Figure 1.8

To understand this, we consider a flat plate held with itssurface inclined by a smal1 angle (a) to a current of ai r,as shown in Figure 1.8. It is exposed to two forces: abackward drag (D) tending to displace the plate downstream;and an upward 1 i ft (Z.) tendi ng to rai se the plate in adirection normal to the air stream. The resultant force (/?)acting on the plate is inclined backwards to the vertical byan angle (|5) which depends on the 1 i ft/drag ratio of theplate.

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Path of motion

Figure 1.9

Each narrow longitudinal section of the wing can be regardedas an aerofoil moving in the air whose reaction depends onits shape, speed and direction of motion relative to theair. If the wing is moving horizontally relative to the air,it will generate lift, provided its 'chord1 is inclined at apositive angle to its direction of motion. It will generatea forward propulsive force ( P ) if the path of motion isdirected downwards at an appropriate angle to thehorizontal. As illustrated in Figure 1.9, the resultantforce R has a vertical upward component ( V} and a forwardpropul si on component ( P) .

During hori zontal f 1 ight at constant speed, the 1 i f t of thewings must be exactly equal to the weight of the flyinganimal, and the external propulsive force applied to thebody must be equal but opposite to the drag. The distinctivefeature of an actively flying animal is that the wingsthemselves provide the propulsive thrust as well asgenerating the lift.

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Fcrkhidmatan: :-n Abdui Razafc

Instiu:' > 'AKA-10450 Shah

wlan;(or Darul

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The amount of lift and drag generated by the air against awing can be calculated by:

Lift - ̂ CLSptf ......................... (1 .5)

Drag = ̂ CDSplf ......................... (1 .6)

where Q is the lift coefficient, CD is the dragcoefficient, S the area of the wing, p the density of theair and U the velocity of the air stream relative to thesurface of the wing.

It may be worthwhile to note that, observations stronglyshows that the maximum animal mass for a mode of 1i fe thatincludes a requirement for weight support by sustainedforward flight is around 12kg.

1.3: Hovering flight

Hovering flight, as defined by Sir James Lighthill [2], isthe movement of wings through which the body of an animalremains effectively motionless in still air. It is acharacteri stic of flying insects, and is used in many modesof their life especially their symbiosis with the floweringpi ants.

The animal's weight must be supported without the help ofhorizontal relative wind. Due to this reason, the size ofhoveri ng animals must be smal1. The upper limit size forhovering animal is a mass of around 20g.

Hovering is also possible in flying animals other thaninsect such as the Hummingbirds with mass at most 20g andsmall bats with masses around 10g. The same hovering motionsare used by larger animals (weighing more than 20g) to

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support their weight during taking off and landing but forvery short intervals, such as in aquatic birds.

1.3.1: Normal hovering

Normal hovering motions are an adaptation of the motionsused for forward flight. Weis-Fogh [3] defined it as (a)active flight on the spot in still air by means of wingswhich are moved (b) through a large stroke angle and (c)approximately in a horizontal plane, while (d) the long axisof the body is strongly inclined relative to the horizontal,sometimes almost to a vertical position.

Figure 1.10

Horizontal movement of wings relative to the air is neededto generate lift for weight support. But since hoveringanimals as a whole remain motionless during hovering, theanimals have to tilt the long axis of the body towards thevertical (Figure 1.10), so that the wings beat back andforth in an almost horizontal plane.

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In his broad study on animals capable of sustained hoveringflight, Weis-Fogh (1972, 1973) has identified that theHummingbirds and insects of eleven different orders adoptthe common pattern of motion of which he named "normal"hovering, with the following principle exceptions: certainvery smal1 insects such as the chalcid wasp Encarsiaformosa. Lepidoptera such as butterflies, Odonata (dragonflies) and Diptera (hoverf1ies); which have a modified formof "normal" hovering. To arrive at the above conclusion,Weis-Fogh [3] did direct cinematography observation onhovering motions and calculated the mean lift coefficient C^required by various species for weight support in "normal"hovering flight. Table 1 on the next page shows some of theresults of these calculations with asterisks attached toinsects under the exceptional groups. Excluding thoseexceptional groups, Table 1 shows that the CL are small,seldom exceeding 1.0. In other words, the motions of"normal" hovering can support the weight of each of theanimals concerned without requiring the production of highmean lift coefficient.

Weis-Fogh estimated the CL by using the equation below. Fora given angular velocity 0 of wing beat:

Lift/unit area of wing =

where U, the horizontal velocity of a small area (S) of wingthrough the air, is Q times its distance from the hingeaxis. Hence the total lift can be written as

L = p̂02SCL ............................ .(1 .7)

where CL is a weighted mean of the sectional liftcoefficient CL. Since the lift must balance the weight, itfollows that

= mg ............................(1.8)

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TABLE 1

Bats:Plecotus auritus

Bi rds: Hummi ngbi rdsAmazi1ia fimbriata

Coleoptera: beetlesMeJolontha vulgar isAmphitna 1 Ton solstitial isHeliocopris sp.

Lepidoptera: butterf1ies,moths* Pier is napiSphinx 1 igustriManduca sextaMacroglossum stellatarum

Hymenoptera: wasps, beesVespa crabroBombus terrestrisApis mellifica*Encarsia formosa (C

Diptera: crane flies, moTipula sp.Aedes aegyptiEristalis tenax

*Drosophila viri1 is*Syrphus spp.

Odonata: dragon flies*Aeshna grandis

Averagecoeff ici entof lift,CL

(1.3)

2.0

0.6Us 0.7

0.5Dths

(2.2)1 .21 .2

rum 1 . 1

0.81 .20.8

Icid wasp) (5.0)"uitoes & flies

0.80.60.91 .0

(2 to 3)

Reynoldsnumber,(Re)

14000

7500

4700300023000

1400630067002800

420045001900

15

7701702000210500

(2 to 3) 1750

Revised estimates (Ellington (1974))

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For a given aerofoil the coefficients of lift and dragdepend not only on the angle of attack but also on Reynoldsnumber (Re). This is particularly so in tiny insects, wherethe Reynolds number is small and viscous effects areimportant. The general expression in calculating Reynoldsnumber used by Weis-Fogh is

(Re) = = .........................(1.9)

where c is the wing chord, ̂ is the viscosity of the air and

the ratio H is called kinematic viscosity v. The Reynolds

number for various hoveri ng animal s is al so gi ven i n Table1. In the range of Re between 10 and 100 where the dragtends to be larger than the liftj normal flight would bedifficult. Above 100-200 the lift/drag ratio has improvedsufficiently for normal flight to be operative.

1.3.2: "Exceptional" hovering

In tiny insects, where Re may be as low as 10 or evensmaller, there are major problems in achi evi ng 1i ft. Butevolutionary opportunities for insects have given rise tomuscular development, which allows the wings to beat at veryhigh frequency, and also to aerodynamically novel modes offlight which permit weight support at low Re. In Encarsi aformosa. a special movement of the wing known as "clap andfling" mechanism is used. This mechanism is studied indetail in the following chapters.

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CHAPTER 2

"CLAP AND FLING" LIFT MECHANISM

According to classical aerofoil theory, the lift forceacting on an aerofoil is proportional to the circulationaround the aerofoil. This circulation is produced by therelease of a "starting vortex" soon after the aerofoil isset into motion from rest (this is the Wagner effect,discussed in chapter 1).

Weis-Fogh observed that the wings of the Encarsia formosa donot follow the normal motions associated with hovering.Instead the wasp adopt a special wing movement where thewings come together at the top of the stroke. Seeing this,he proposed that this novel movement, the "clap and fling",produced the necessary circulation to be generated aroundthe wings rather than waiting for the Wagner effect to takeeffect.

In this chapter, we shall describe the "clap and fling"mechanism of circulation generation for the tiny wasp,Encarsi a formosa. A summary of Lighthill's two-dimensi onalinviscid flow analysis of the mechanism is presented inSection 2.

2.1: Hovering flight of Encarsia formosa and the "fling"mechanism

Figure 2.1 shows the morphology of Encarsi a formosa. aninsect of size around 1mm, which Weis-Fogh used for hisstudy of hovering flight in very small insects.

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IHcSlO KA.U.ttiSAM

Figure 2.1

The pictures of free flying Encarsia as illustrated inFigure 2.2 on the next page was obtained by Weis-Fogh bymeans of high speed cinematography. In the diagram, theanimal is seen at a somewhat slanting angle with its longaxis slightly tilted towards the reader. The sequence ofmovements contains three phases: (i) the "clap", whichinitiates the process, where the 2 pairs of wings arebrought together as a single vertical plate behind its backwith leading edge vertically above trailing edge (no. 0),( i i ) the "f 1 i ng" , can be i deal i zed as an openi ng up of thetwo wings as if hinged along the lower edge (nos. 1 and 2),and (iii) the flip whereby after the two wings break apart(nos, 3-5) the two wings rotate as a whole so that theundersides become their topsides and vice-versa (nos. 7-9).The motion (nos. 3-13) is the "normal" hoveri ng unti1 thenext clap occurs (nos.14-16).

'8«ah»gian Rui-akan & Perkhidmttan Pemfcwni

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Stroke 2 ends Stroke 3 starts

15 16

HorizontalJ2mm

Figure 2.2

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