Support and deformability in insect wings

Transcription

1 J. Zool., Lond. (1981) 193, Support and deformability in insect wings ROBIN J. WOOTTON Department of Biological Sciences, University of Ex (Accepted 13 May 1980) (With 1 plate and 12 figures in the text) r Coupled investigations of insect wing movements and detailed wing morphology are in progress, and some functional principles underlying wing design are emerging. High speed cine and still photography and stroboscopy indicate that most wings undergo orderly deformation in flight. Common patterns are described and their significance discussed in the light of recent aerodynamic studies. Many aspects of wing morphology-venational features, relief, thickened areas, flexionlines and vein fractures-may be related to the control of three-dimensional shape while beating. It is usually possible to distinguish areas specialized for deformability, and for support and the limiting of deformation. Some structural adaptations for these roles are described and illustrated. Contents Introduction Approach and methods The deformable wing: principles..,. Observed patterns of deformation Torsion Camber change Transverse bending Structural adaptations for support and deformability Adaptations to a supporting role.... Adaptations within the deformable areas.. Camber change Section control Torsion control Adaptations for transverse flexion Conclusion References Page Introduction The primary function of wings is flight; yet flight studies and insect wing morphology have remained for the most part separate disciplines. The extensive literature on the wings of insects, essentially descriptive, comparative and systematic, seldom refers to the modes of flight of their owners. Before the last decade, Rohdendorf (1949, ) and Edmunds & Traver (1954) were almost alone in attempting to interpret wing form with reference to flight, and their papers contained no detailed flight observations. Students of insect flight have contributed to functional wing morphology, but in limited areas. Jensen (1956), Weis-Fogh (1956), and Pfau (1977, 1978) have studied the morphological basis, control and aerodynamic significance of the profile changes in locust fore wings during the flapping cycle. Nachtigall (1967) and Martin & Carpenter (1977) have /81/ $02.00/ The Zoological Society of London

2 448 R. J. WOOTTON considered aerodynamic implications of surface scales and wing plan in glid.ing butterflies. Weis-Fogh (1973) took account of wing shape in deriving expressions for calculating flight performance in hovering insects. The recent concern with non-steady-state aerodynamic effects in flapping flight has drawn attention to some dynamic aspects of wing design. Weis-Fogh (1973) suggested that wings, like those of syrphine Diptera, with a relatively stiff anterior area and a soft, flexible trailing edge separated by a longitudinal flexion line, may be adapted for the creation of non-steady lift by the flip effect. An important contribution is due to Norberg (1972), who has shown that the pterostigma of Odonata, and by implication of other insects which possess one, may act passively as an inertial regulator of wing pitch, thereby helping to maintain an aerodynamically useful profile and angle of attack during the flapping cycle. Nonetheless wings remain the most neglected component of the insect flight system. In particular, very little attention has been given to the functions of those characters which most concern the systematic entomologist : the arrangement of veins, thickened areas, fractures and lines of flexion; all of which have been used extensively for classification and phylogenetic reasoning in almost complete ignorance of their adaptive significance. The purpose of this paper is to begin to rectify this situation, by outlining some fundamental principles underlying the design of insect wings and suggesting practicable approaches to their functional morphology. Approach and methods A comprehensive analysis of the structural engineering of an insect wing would be prohibitively difficult, as its loading forces in nature are complex, constantly changing, and effectively impossible to measure. Moreover many such analyses would be required before one could beginto generalize. As so often with biological problems, useful and valid simplifications are needed which enable one relatively quickly to reach general principles, which can then be examined in their wider biological context. An integrated approach to functional wing morphology requires information in four interrelated areas. First, it is important to know precisely what happens to wings in normal flight, with regard not only to the kinematic parameters normally studied, but also to the changes in shape of the wings during the beat cycle. Limited, non-quantitative, but often useful information of this kind may be gained from high quality still photographs, such as those of Dalton (1975, 1977), and from stroboscopic and cinematographic study of tethered insects; but a full quantitative picture can only be achieved by analysis of high speed cine film of insects in free flight. This is in progress, using a Hycam high speed cine camera, manufactured by John Hadland (Photographic Instruments) Ltd., and capable of operating at up to 11,000 frames per second. Some observations and illustrations from the work are included in this paper, Second, detailed morphological study of the wings is required, with particular reference to those aspects of structure which facilitate and control the changes of shape visible in flight, and may hence be interpreted in the light of the kinematic studies. Nomarski differential interference contrast microscopy (Nomarski, 1959, and scanning electron microscopy are proving particularly useful in this area. Third, the observed kinematics need to be interpreted in aerodynamic terms. Free flight cine films demonstrate, and enable one to measure the immediate effects of particular kinematic patterns; but their aerodynamic interpretation is often far from straightforward. This precise area is being studied by Ellington (1977, 1980), and aspects of insect aerodynamics are under investigation by several other workers. Ellington (1980) is a convenient source of references to recent work.

3 INSECT WINGS 449 Finally, much detailed information is needed on flight behaviour : the range and significance of flight patterns shown by a diversity of insects in the field. Only with this information can the particular aerodynamic resources of an insect be fully understood in the context of its overall biology. The present paper emphasizes the first two areas-kinematics and structure-and presents some general principles of functional wing morphology based on qualitative observations, in advance of more precise quantitative information on selected groups. The principles highlight some aspects which appear to be particularly worth investigating, and provide a partly hypothetical basis for future work. The deformable wing : principles In considering insect wings, whether for comparative illustration or aerodynamic analysis, some simplifications are inevitable. Two in particular are common: to regard the wing as essentially flat, and as effectively rigid. Neither is true, and the latter can be seriously misleading. Classical aerodynamic theory developed from studies on fixed rigid wings, and it is natural and apparently logical to compare the flapping wings of animals with rigid manmade aerofoils. An important property of flapping animal aerofoils, however, is deformability. Some controlled change of wing shape during the beat cycle may prove to be essential for the development of adequate net lift and thrust. It is shown by all actively flying animals so far studied., and is in general most pronounced in hovering, manoeuvring and slow flight, and least so in fast forward flight. In flying vertebrates, the fine control of the three-dimensional shape of the wing is effected by the complex wing musculature, acting with precision on the bones of the arm and hand, on flight feathers, and within the bat patagium. However, insects, uniquely among flying animals, have no intrinsic wing muscles. All active control of wing shape during the flapping cycle must therefore be remote, the necessary forces being transmitted outward from the base of the wing by its skeletal components. At any moment in the cycle, the shape of the wing may be considered as resulting from at least four factors: the aerodynamic forces due to the relative airflow; the inertial bending moments, particularly as the wing changes in angular velocity around the point of stroke reversal; the forces exerted on the wing base by muscles and neighbouring skeletal elements; and the architecture of the wing itself. The importance of a possible fifth component-hydraulic pressure within the vein lacunae-has not yet been confirmed. The venation pattern is hence significant not only through its passive supporting role, but also in the dynamic control, both active and passive, of the three-dimensional form of the wing. Figures 3, 4(b), 6 and 8 are taken variously from still photographs and high speed cine film. The principal patterns of deformation which they show will be discussed further; but it is clear at this stage that the validity of comparing insect wings with rigid aerofoils is limited. While some parts of the wings are relatively stiff, others are clearly highly deformable, and are altering in shape and sometimes even in area from instant to instant during the flapping cycle. A more useful analogy is a sail. Here too the propulsive forces are exerted by the airflow on a flexible membrane, which without adequate support and control would flutter uselessly like a flag, but which is caused to assume an aerodynamically effective profile both by

4 450 R. J. WOOTTON the spars and by the crew. The sail section may be improved by rigid battens which are inserted into the membrane and further limit and direct its deformation. The weave of the sail-whether for example it is cut squarely or on the bias-may further affect the section, and can be chosen for optimal performance. Clearly the analogy should not be taken too far. Sailing boats are gliders; they are not propelled through still air by actively flapping sails. Nonetheless the comparison is useful in making functional sense of observed structural differentiation within the insect wing. It is possible to distinguish two kinds of component within the wing: passively deforrnable areas, which undergo appreciable passive change in shape when subjected to aerodynamic loading ; and supporting and deformation-limiting areas, whose comparative stiffness both supports the wing and restricts the movement and distortion of the deformable areas, preventing them from fluttering, and optimizing their aerodynamic contribution. If we pursue the sail analogy, the deformable areas correspond to the cloth, the supporting and deformation-limiting areas to the spars: mast, boom and gaff. Within the deformable areas one would examine both venation and cuticle ultrastructure for profile controlling analogues to battens and weave. The functional division is not absolute, as deformability varies in degree. Supporting areas inevitably deform to some extent when loaded ; primarily deformable areas commonly have their own internal supports, rendering them stiffer along some axes than others; and gradients of stiffness may exist. Nonetheless the division is valid as a first approximation and is useful in providing a direction from which the complex problems of wing engineering may be approached. Figure 1 shows the distribution of deformable and supporting zones in a selection of wings, as judged both from flight observations using stroboscopy and photography, and from examination and manipulation of freshly killed insects. Wings whose functional subdivisions are distinguished in this way are easily compared visually, and some generalizations can be drawn. The three veins C, Sc and R,* separate or to some extent fused, almost always together perform a supporting role, at least in the proximal part of the wing. The bases of CuA and CUP usually form another supporting area. The area between the bases of R and CuA is sometimes supporting, sometimes deformable. The clavus may also be either. The area containing the distal branches of R, Rs, M, and sometimes of CuA is normally deformable in orthodox membranous wings. An expanded vannus is always deformable. Hind wings which are firmly coupled to the fore wings sometimes derive their principal support from the latter, and may themselves be almost wholly deformable (e.g. Fig. I(f)). The deformable and supporting zones are clearly related functionally to lines of weakness and flexion in the wing. These may be boundaries between the zones, like the nodal line of cicadas: or they may subdivide them, allowing relative movement of the subdivisions. Attention has been drawn elsewhere (Pfau, 1977, 1978; Wootton, 1979) to the roles of the claval furrow and median flexion line in permitting relative movement of the preradial and postradial areas and claws of the fore wing base of locusts-all supporting zones-alternately creating and eliminating the Z-shaped profile described by Jensen (1956), and thereby altering and controlling the angle of attack of the distal, deformable part of the wing. Jensen also showed how flexion along the claval furrow in the latter part of the downstroke leads to an increase in the camber of the fore wing, and in the lift * The nomenclature adopted follows Wootton (1979)

5 INSECT WINGS 45 1 FIG. I. Distribution of supporting areas (stippled), deformable areas (unstippled) and flexion lines (dashed) in some wings. (a) Schisfocercu greguriu (Orthoptera); (b) Muniolu tithonus (Lepidoptera); (c) Siulis lururiu (Neuroptera); (d) Culocoris sp. (Heteroptera); (e) Syrphus ribesii (Diptera); (f) Vespulu germunicu (Hymenoptera). m.f.l., median flexion line; cl.f., claval furrow; tr.f.l., transverse flexion line. Scale lines = 5 mm.

6 452 R. J. WOOTTON coefficient. The further possible significance of longitudinal and transverse flexion lines and vein fractures will be discussed later. Observed patterns of deformation No account of the kinematics of fast free flight in an insect has yet been published. However, the classic studies of tethered flight by Jensen (1956) on Schistocerca gregariu, Zarnack (1972) on Locusta migratoria, and Nachtigall(l966) on the calliphorid fly Phormia regina, closely simulate fast forward flight and remain the most detailed kinematic analyses of any insect flight to date. In each case, a representative cross-section of the fore wing was found to maintain a positive, though variable, angle of attack for the greater part of each d.ownstroke. The same sections of the Schistocercu fore wing and the wing of Phormiu showed a positive angle of attack during the early part of the upstroke, but not the later part. The leading edge of the mid section of the hind wing of Schistocerca maintained a negative angle of attack throughout the upstroke; but as the lift at no time fell to zero, this probably gives a misleading impression of the wing as a whole. It is reasonable to suppose, with the authors, that during these peri0d.s of strong translational movement with a positive angle of attack, quasi-steady-state aerodynamic conditions are operating: that is to say that the forces on the wing inmotion at any instant are the same as those which the wing would experience if it were in steady flow at the same velocity and angle of attack. This is probably also true of the greater part of both the morphological upstroke and the downstroke of insects performing normal hovering. and slow flight in the normal hovering position with an almost horizontal stroke-plane (Weis-Fogh. 1973) although non-steady effects may also be important (Ellington, 1980). It is less safe to explain other forms of hovering exclusively in terms of quasi-steady-state aerodynamics (Ellington, 1980), and similar caution is needed where the angle of attack changes appreciably during the half-stroke, as in the latter part of the upstroke of Plzorntia. Around the points of stroke reversal, where the wings are decelerating and then accelerating into the new half-stroke, while undergoing rapid torsion and in many cases the sequence of movements of the clap and fling (Weis-Fogh, 1973) or the near clap and fling (Ellington, 1980), non-steady effects are clearly predominant or exclusive. Ellington (1980) conveniently summarizes the present state of knowledge of these mechanisms, many of which are still poorly understood. The variation in relative importance of steady and non-steady effects during the flapping cycle appears to be reflected by the observed patterns of change in the three-d.imensiona1 form of the wings. This usually remains more or less constant during the supposedly steady phase of the stroke, and may be expected to be interpretable primarily in terms of steady-state aerodynamics. Around the stroke reversal points, however, the changes in shape may be complex, and are correspondingly difficult to interpret. Their immediate aerodynamic effects are clearly non-steady, but it is often quite obscure whether particular observed phenomena are beneficial, adverse or unimportant. The principal kinds of deformation are as follows. Torsion With the possible exception of some elytra, all wings may be assumed to undergo some

7 INSECT WINGS 453 torsion in flight. Two kinds may be distinguished, which interact, but differ in their relative contributions during the flapping cycle: active torsion, applied at the base by the muscles of thorax and axilla; and passive torsion, imposed upon the whole wing by the aerodynamic and inertial loads. Actively imposed torsion is particularly marked at stroke reversal, although it may well occur at other parts of the cycle. Aerodynamic torsional forces are probably operating almost throughout the cycle, during most of which they are being opposed by elastic restoring forces in the supporting members of the wing. A wing undergoing lift in an airflow tends to be twisted by the aerodynamic force unless the centre of pressure, through which the force may be considered to act, lies on the axis of torsion of the wing. In a fixed wing such twisting 1ead.s to a spanwise gradient in angle of attack (Fig, 2). In many insect wings, the main supporting area is close to the leading edge, and the wing base is anterior to the geometrical mid line (Fig. 1). The torsional axis is thus well forward, and may be in front of the centre of pressure, so that the angle of attack tends to diminish from base to tip. In a fixed wing this would. result in a base-to-tip decrease in net aerodynamic force, but this would be counteracted in a flapping wing by the effect of the spanwise velocity gradient, so that the resultant forces would be more evenly distributed along the wing. FIG. 2. How the relative positions of the centre of pressure (CP) and the axis of torsion (AT) affect aerodynamic torsion of fixed wings. Dark arrows indicate direction of relative wind; light arrows the lift, shown at the centre of pressure. A base-to-tip diminution of angle of attack is visible in the deformable areas of many insect wings; particularly those, like most Diptera and agrionid and anisopterous Odonata, where the trailing edge is flexible and relatively unsupported (Fig. 3). The extent and form of the torsion would depend not only on the stiffness of the wing, but also on the extent to which the membrane is supported within the deformable area, and by the nature of the support. There is clearly scope for investigating these effects by flow-tunnel testing of variously supported real and model wings. As the wing decelerates, is actively twisted, and accelerates around the point of stroke reversal inertial forces may become overwhelmingly important ; and they must profoundly influence the pattern of torsion at this stage, particularly in asymmetrically supported wings. In changing from the pronated to the supinated position and vice versa the broad wing membrane of Agrion (Odonata) can clearly be seen to pass the leading edge spar mainly under its own momentum (D. J. S. Newman, pers. comm.); and it is probable that the same is true in many insects whose wings are similarly supported.

8 454 R. J. WOOTTON Active torque is applied to the wing at its base and transmitted distally by the longitudinal veins and hard cuticle of the supporting areas. Orthodox membranous fore wings and uncoupled hind wings normally undergo pronation at the beginning of the morphological downstroke and supination at its end. Where the wing is stiff, or short, or where its anterior and posterior supporting areas are long, torsion may appear simultaneous throughout the span, but it must in fact always pass along the wing as a wave, which may itself have aerodynamic consequences (Weis-Fogh, 1973). In the absence of external forces the velocity of propagation u of a torsion wave along a beam is given by U = G/p where G is the shear modulus and p the density of the material. The precise mode of propagation of torsion along an insect wing will hence be markedly influenced by the wing FIG. 3. Aerodynamic torsion in the downstroke of free-flying Synzpetrum striolntitm (Odonata). Original, from a high-speed cine film. Fic. 4. Propagation of a tip-to-base torsion wave following supination of the leading edge and ambient vein. (a) diagrammatic. (b) Cnlliphora er~throrephnla (Diptera) hovering freely; original, from a high-speed cine film.

9 INSECT WINGS 455 morphology, travelling more rapidly along the stiff supporting members than the softer deformable areas. Although the initial twist will pass rapidly outwards along the main wing supports, its passage through the wing as a whole may be modified and locally damped or eliminated by flexion lines and patches of soft cuticle in the veins. Moreover, not all torsion waves move outwards. In the Diptera which I have examined-tipula, Syrphus, Dasyphora, Calliphora-torsion in the stiff leading edge causes a sharp angular movement of the ambient vein which creates a relatively slow reverse wave passing from tip to base through the soft deformable area (Fig. 4(a), (b)), and D. J. S. Newman (pers. comm.) has found a similar effect in agrionid and anisopterous Odonata. Active torsion is a necessary component of the flapping cycle, as it helps to create an appropriate angle of attack for each part of the stroke. The pattern of twist-propagation within the wing at stroke-reversal will influence both the terminal form, and the speed and timing of its assumption. In addition the torsion process is itself believed to have useful non-steady-state aerodynamic effects (Bennett, 1970). In the fling mechanism it is assumed to increase lift, both by establishing circulation without translational movement of the wing (Weis-Fogh, 1973), and by enhancing this circulation by the creation of a flow separation bubble (Lighthill, 1973). It may operate elsewhere in the absence of fling by creating such bubbles, which for a few chord-lengths permit a large angle of attack and hence unusually high lift coefficients (Newman, Savage & Schouella, 1977; Ellington, 1980). Weis-Fogh (1973) further suggested that rapid torsion of the stiff anterior area of the wing of syrphine Diptera, while the soft posterior area remains stationary, could create an early bound vortex and so enhance lift: the so-called flip mechanism. It has not been confirmed. Camber change Both the supporting areas-by relative movement along flexion-lines-and the passively deformable areas of many insect wings develop camber during the downstroke. This is predictably most obvious in broad wings, but probably occurs generally. At stroke reversal the camber usually changes, and may indeed be reversed for the upstroke, so that the morphologically dorsal surface is concave (Fig. 5). Camber reversal is particularly associated with extreme torsion, such as occurs in most Diptera and Odonata, and in some other groups in normal hovering and slow flight (Fig. 6(a); Dalton, 1975 pls 8, 17, 18, 20, 52, 62, 68, 74; 1977 pls 11, 15, 27, 29). As with torsion, both active and passive components of camber may be recognized. Actively imposed changes in the profile of the supporting areas, like those described in the fore wing of Schistocerca by Jensen (1956) and Pfau (1977, 1978), will inevitably impose forces on the deformable areas. The general occurrence of the median flexion-line and the claval furrow-the latter is almost ubiquitous-suggest that profile-altering mechanisms similar to those of Schistocerca may be equally widespread (Wootton, 1979), and this is borne out by examination and manipulation of the wings of a wide range of freshly killed insects. Further, passive, curvature of the deformable areas, analogous to the bellying of a sail, is likely to be imposed wherever lift is generated. The active development of camber is closely related to torsion, as it seems usually to be initiated by pronation or supination of the leading edge. In forms with coupled wings, fore wing torsion may result in the development of a marked angle between fore and hind wings

10 456 R. J. WOOTTON at the beginning of the upstroke, creating in effect a single strongly cambered aerofoil (Fig. 6(b)). The vaiue of wing camber under steady-state conditions is clear. In the range of Reynolds number within which insects operate (Re < 4 x lo4) an arched plate gives higher lift coefficient values than a flat plate (Hertel, 1966). Any non-steady benefits are less apparent. It is interesting to note that the fling process in Pieris brassicae and the lacewing Clrrysopa carnea involves considerable longitudinal flexion of the paired wings as they peel apart progressiveiy from the leading to the trailing edge (Ellington, 1980). FIG. 5. Reversal of camber, with extreme torsion. Diagrammatic. Arrows indicare the direction of motion of the wing. (a) FIG. 6. Camber reversal. (a) Chrysopa sp. (Neuroptera) flying upside down, immediately following take-off. (b) Gruphocephalu coccbiea (Hornoptera), showing reversed camber of the composite aerofoil at the beginning of the upstroke. Traced from Dalton 1975, pls 17, 13. (b)

11 INSECT WINGS 457 Active alteration of camber by the raising and lowering of flaps may be important in manoeuvring and in the maintenance of stability. D. J. S. Newman (personal communication) has shown that Agrion (Odonata) asymmetrically lowers the cubitoanal region of fore and hind wings during the downstroke when turning; and Pringle (1961) described how the hind wing of bees-linked with the fore wing in a single aerofoil-may similarly be depressed in the control of rolling movements. Transverse bending Many wings, particularly fore wings and uncoupled hind wings, show some degree of transverse ventral flexion; occurring at the bottom of the downstroke or during the upstroke, either in every beat or during particular manoeuvres. I have observed this in the forc wings of Siulis (Neuroptera), Mystacites (Trichoptera), Dusyphoru and Culliphoru (Dip t era), Triu Ieurodes (Homop t era), Culocor is (He ter op t era) and Sirex ( H ymenop t era). It has also been described in Phormia (Nachtigall, 1966) and Encursiu (Weis-Fogh, 1973), and is visible in published photographs of Lithosiu and Phlogophoru (Lepidoptera), and Vespulu (Hymenoptera) (Dalton, 1975); and Muscu (Diptera) and Pyrochrou (Coleoptera) (Dalton, 1977). On morphological evidence it occurs widely in each of these groups, and in others : most Plecoptera; cicadoid and some cicadelloid, fulgoroid and psyllid Homoptera; and most Ephemeroptera (Edmunds & Traver, 1954). Dorsal flexion is usually slight or negligible. Ventral bending may take place over the entire distal part of the span by simple elastic deflection (Figs 7(a), 8(a)), but is frequently localized at a particular transverse line. This is not particularly characteristic of the deformable areas. In some cases, e.g. mirid Heteroptera, many Diptera, Encursia, the flexion line may cross, and hence interrupt, a supporting and deformation-limiting area, so that the entire tip, or indeed a major part of the wing may be deflected ventrally (Figs 7(c), 8(b); Nachtigall, 1974 pl. 31). Frequently, though, as appears to be the case in cicadas (Nachtigall, 1974 pl. 4), Sirex and Vespufu (Fig. 8(c)) the supporting leading edge of the wing remains straight, or nearly so, only the area behind this being deflected (Fig. 7(b)). The transverse flexion line is often then in FIG. 7. Three kinds of transverse ventral flexion. Diagrammatic; explanation in the text. tr.f.l., transverse flexion line.

12 458 R. J. WOOTTON effect a boundary between a basal supporting area, which continues along the leading edge, and a distal deformable area. It is suggested that ventral bending may serve several functions, which may be distinct or operate in combination. All require further investigation. (a) Aerofoil attitude control. Where the leading edge bends only slightly or not at all, flexion may serve to permit controlled relative movement between the distal deformable area and the rest of the wing, allowing the former to assume the optimal camber and a more favourable angle of attack than the broadly attached base would otherwise permit. This may be particularly useful in normal hovering and slow flight with the b0d.y nearly FIG. 8. Transverse flexion. (a) Lifhosiu Iurideoiu (Lepidoptera); (b) Culliphoru eryrhvocephulu (Diptera) hovering freely; (c) Vespulu vulgaris (Hymenoptera) ; (d) Sialis luiaria (Neuroptera) tethered ; (e) Phlogophora meficulosa (Lepidoptera). (a), (c), (e) adapted from Dalton 1975, pis 40, 62, 44; (b), (d) original, from high speed cine film.

13 INSECT WINGS 459 vertical and an almost horizontal stroke plane; particularly in insects with coupled wings and a consequent restriction on wing-twisting. Dalton s photograph of Vespula (Dalton, 1975 PI. 62) (Fig. 8(c)), and Weis-Fogh s illustrations of hovering Manduca sexta (Lepidoptera, Sphingidae) (Weis-Fogh, 1973) show the necessary combination of torsion and ventral flexion ; Vespula having and Manduca apparently lacking a specific transverse flexion line. (b) Enhancement of wing drag. Weis-Fogh (1976) has concluded that tiny insects which have low operative Reynolds numbers do not use the drag of the wings to row themselves through the air. Evidence is now appearing, however, that some larger, broad-winged insects, e.g. butterflies, make significant use of wing drag for propulsion (Ellington, 1980). Preliminary observations on tethered Sialis give the impression that flexion of the wing tip, combined with camber reversal in the deformable area, may lead to the development of considerable wing drag on the upstroke-which has a strong backward componentand that the insect may be generating thrust by this means. Confirmation must await a quantitative free flight investigation. (c) Feathering. In insects where wing-twisting is relatively slight, ventral bending may perhaps reduce the drag and negative lift forces in the upstroke. This may operate for example in some Lepidoptera (Fig. 8(e)), and in Trichoptera. (d) Shock absorption, reducing stresses on the wing at the point of stroke reversal. This may apply widely in combination with other functions, especially in wings which are relatively large, with high inertia. (e) Increasing the amplitude of the wing-stroke. Those Diptera and Hymenoptera which show ventral flexion near the base are capable of considerable wing twisting, and make extensive use of slow and near-hovering flight which requires high lift. Ventral flexion increases the amplitude of the wing sweep. Combined with sharp supination at the end of the morphological downstroke, it appears to cause the main part of the wing, distal to the flexion line, to assume a positive angle of attack almost at the beginning of the upstroke. This part is then sharply accelerated as the wing simultaneously straightens and swings dorsally (Weis-Fogh, 1973 fig. 14; Nachtigall, 1966 figs 21,43). It is reasonable to suppose that this may increase the lift from each stroke without greatly altering its duration. (f) Unknown beneficial non-steady effects Weis-Fogh (1973) briefly compared the wing action, combining bending and rapid supination, at the start of the upstroke of Encarsia with the rapid torsion movement in syrphine hoverflies ; using the term flip for both. The similarity with Syrphinae lies in the rapid torsion of the anterior part of the aerofoil -in Encarsia the whole fore wing-in comparison with the more flexible part-the hind wing in Encarsia. Weis-Fogh s aerodynamic explanation of the flip has not been confirmed, but it is not impossible that ventral flexion combined with rapid torsion may enhance lift by non-steady methods. Structural adaptations for support and deformability The observed patterns of change in wing form during flight which have been described tend to support the validity of distinguishing between primarily supporting and primarily deformable areas. This is amply confirmed by examination of wing structure, which reveals striking adaptations for stiffness and deformability clearly zoned within the wing.

14 460 R. J. WOOTTON Adaptations to a supporting role Insect veins are typically sclerotized tubes, and hence adapted as supporting members, being for their weight stiff and strong both in bending and torsion. The strength and stiffness of an area of wing can be increased in three ways. (a) Vein enlargement, thickening and fusion. The diameter, and therefore the second moment of area of the veins may be increased. This will increase the probability of failure by elastic buckling unless the thickness of the wall is maintained, with a corresponding and undesirable increase in mass per unit length. Fusion of neighbouring veins into a single strong tube would give a stronger, stiffer member, weight for weight, than the equivalent individual veins lying side by side. Basal fusion of veins is of course common in many insect groups. Cicadomorph Homoptera and aculeate Hymenoptera provide good examples of the fusion of Sc, R and Rs into a single strong, thick vein in the anterior supporting zone of the fore wing (Figs l(f), 11). (b) Increased relie( The relief of the wing may be heightened, so that the supporting area becomes a three-dimensional structure which acts as a beam. The most obvious example is corrugation or fluting, where veins are alternately concave and convex in position; but other patterns occur. Rees (19751) has sectioned some corrugated wings, and has analysed theoretically how the properties of corrugated beams strengthened by tubes vary with the dimensions of their components. The wings of palaeopterous insects, both fossil and extant, are extensively fluted, with the main longitudinal veins alternately convex and concave throughout. This is usually assumed to be a primitive condition. Wing fluting is seldom complete in neopterous orders, but persists most frequently in the supporting areas. In particular, C, Sc and R, when present as separate veins, almost invariably form a beam of triangular section, as frequently do CuA, CUP and 1A. It is however incorrect to assume that corrugation is necessarily an adaptation for rigidity: as we shall see, it is a common feature of the deformable zones of wings. Corrugated areas are stiff enough to perform a supporting role only if the longitudinal veins are (C).. k-1- \-/ FIG. 9. Leading edge supporting devices in fore wings. (a) primary antenodal cross-veins in Aeshira (Odonata); (b) costal brace in Ephemera (Ephemeroptera); (c) terminal cross-ties in Eristalis (Diptera).

15 INSECT WINGS linked strongly enough to resist both flattening and bending along axes parallel to the veins. This is usually achieved by strong cross-veins in the plane of the membrane but may also involve 3-dimensional structures, such as the primary antenodal crossveins of many Odonata (Fig. 9(a)) and the costal brace of Ephemeroptera (Fig. 9(b)). In relatively small wings proximal and distal bracing may be adequate to maintain the triangular crosssection (Fig. 9(c)). Rees (1975b), using model wing sections in a water tunnel, has confirmed that corrugation has negligible adverse aerodynamic effect in the range of Reynolds number where insects operate, and Newman, Savage & Schouella (1977) have shown that high relief at the leading edge of model wings with a dragonfly-like section may enhance lift by helping the creation of a flow-separation bubble. (c) Membrane thickening. The wing membrane itself may be thickened and heavily sclerotized. Besides being characteristic of protective elytra, which contribute little to flight, thickening is found in the fore wings of many Orthoptera and Dictyoptera, and occurs most spectacularly in the hemielytra of Heteroptera, where the deformable area is membranous and the supporting and deformation-limiting area thickened (Fig. l(d)). No clearer demonstration of functional differentiation could be desired. Adaptations within the deformable areas It is reasonable to expect that the structure of the deformable areas might show adaptations to (i) facilitate camber change; (ii) optimize the section throughout the area; and (iii) optimize the pattern of torsion at stroke reversal. (i) Camber change Alteration in camber requires flexion along longitudinal or radial axes of the wing. The main veins usually-though not invariably-run more or less radially, and in the absence of cross veins (Fig. lo(a)) the membranous spaces between them would give ample flexibility. The deformable areas of several groups of rather small insects entirely lack cross veins : for example Aphidoidea and Psyllidae (Hemiptera), and Psychodidae, Simuliidae and Cecidomyiidae (Diptera); and the same is true of most Lepidoptera, including some of the largest forms (Fig. l(b); Dalton, 1975 pl. 39). Some other insects, mostly small but also including some surprisingly large species, lack veins of any kind in their deformable areas, or in a large part of them. Examples include many parasitoid families and some Sphecidae, Apidae and Formicidae (Hymenoptera) ; Hippoboscidae and some Cecidomyiidae (Diptera) ; Aleyrodidae, Miridae and Reduviidae (Hemiptera). The majority of insects have cross-veins. Where these are relatively weak they permit considerable alteration in camber. Nonetheless special adaptations are usual, The following can be recognized : (a) Fluting (Fig. lo(b)). As we have seen, a fluted (=corrugated) wing area in which the longitudinal veins are strongly cross-linked is particularly resistant to bending in any plane, and also stiff in torsion. Where the cross-veins are absent, weak or interrupted, however, a fluted membrane is stiff to transverse flexion, but particularly mobile dong axes parallel to the veins. Such a membrane may moreover be liable to flattening under pressure, which could lead to an increase in effective wing area; but it is not clear how 46 I

16 462 R. J. WOOTTON frequent or important this may be. Adaptations to prevent flattening, like the unfluted margin of the vannus of acridiid Orthoptera, are probably common. Fluted deformable membranes are familiar in the remigium of Ephemeroptera and Odonata and in the vannus of Orthoptera, Phasmida and Dictyoptera, and they also occur in the remigium of some Orthoptera (e.g. Acridiidae), Dictyoptera and Neuroptera. In many of these, intercalary veins are developed, of opposite aspect to the longitudinal vein branches between which they lie. Others, e.g. Corydulis (Neuroptera), show corrugation without intercalary veins ; in this particular case apparently maintained by V-shaped cross-veins. FIG. 10. Adaptations to flexibility-diagrammatic. (a) no cross-veins; (b) fluting, with weak or interrupted crossveins: (c) flattened, flexible cross-veins; (d) flexion lines. Several adaptations to flexibility may be identified in the cross-veins which connect the vein branches in mobile fluted membranes. In Agrion (Odonata) they are interrupted at their point of contact with some longitudinal veins. In the vannus of Acheta domestica (Orthoptera) all the cross-veins are of a highly flexible type in which the wall is made up of alternating narrow bands of normal and thin cuticle (Plate I(a)). Similar veins are found in many insect groups, and will be referred to as annulate. (b) Flut membranes with weakened cross-veins (Fig. lo(c)). The wings of Panorpa (Mecoptera) have dichotomously branching longitudinal veins linked by numerous short cross-veins. In the supporting zone in the basal part of the wing these cross-veins are

17 PLATE I. Flexible veins. (a) Acheta domesticn (Orthoptera): annular cross-vein in the hind wing vannus. (b) Panorpa sp. (Mecoptera): soft, flattened cross-vein in the deformable area of the fore wing. (c) Chrysopa sp. (Neuroptera) fore wing. Rs interrupted by soft cuticle where crossed by median flexion line. (d) Ammophila sabulosu (Hymenoptera) fore wing. Rs narrowed where crossed by median flexion line. (e) Sialis lutaria (Neuroptera) fore wing. Thyridial area of soft cuticle where median flexion line lies along MP. (f) Calliphora vomitoria (Diptera). Annulate cross-vein rs-m where crossed by median flexion line. (a), (b), (c) scanning electron micrographs. (d), (e), (f) Nomarski.

18 464 R. J. WOOTTON normal and strong. In the deformable distal part of the remigium, however, nearly all the cross-veins are weakened and flattened for part of their length (Plate I(b)). (c) FZat nienihranes with one or two longitudinal or radial Jexion lines (Fig. 10(d)). The remigium of many insects is divided for all or part of its length by a longitudinal line of weakness which I have called the medianflexion line (Wootton, 1979). Its position relative to the longitudinal veins is variable, but it usually originates close to the media. Near the wing base it may form a longitudinal hinge-line between adjacent supporting zones (see p. 4501, and there and in the deformable area it may assist in camber change (Dalton, 1975 pls 17, 18, 66; 1977 pl. 22). In Hymenoptera it is usually branched. Vein branches are not always longitudinally direct: in many insects they run obliquely to the hind margin. Oblique veins would tend to oppose longitudinal flexion of the kind required for camber change, and in such insects the median flexion line may remain more or less longitudinal, and so cross the vein branches. In Chrysopa (Neuroptera), for example, it crosses branches of MA and Rs, and the paths of these veins are briefly altered and aligned immediately behind the flexion line to form a composite vein, the false media, along which it lies. Where the median flexion line crosses longitudinal veins or cross-veins these are sometimes abruptly interrupted by soft cuticle (Plate I(c)) ; sometimes narrowed (Plate (I(d)) ; sometimes locally desclerotized over a considerable area, giving rise to fenestrae or thyridia (Plate J(e)); and sometimes partly or wholly of the annulate type described above (Plate I(f)). Similar structures are found in association with the claval furrow. Other examples where a few lines of weakness aid the flexibility of flat deformable areas are the vanni of Plecoptera, Dermaptera, corydalid Neuroptera and Trichoptera; in all of which the radiating fold lines incidentally have this effect. (i i) Secfion control Little is known about the control of wing section, but it may be a major factor in understanding venation, particularly vein alignment. This is an area where experiment on models could give fascinating results. At this stage two points are worth making. First, in wings whose leading edge is supported, but whose posterior supporting zone is short so that the deformable zone occupies most of the trailing edge, the branches of the longitudinal veins may curve and generally run obliquely to the hind margin. Were the veins truly longitudinal, fluttering would be unavoidable in wings of this kind; and oblique support is essential for the maintenance of an effective section. Secondly in the wings of many Diptera a transverse gradient of deformability seems to exist, as judged by manipulation and from the relative thickness of the veins. This may well be important in profile control. (iii) Torsion control The control of the mode of propagation of active torsion through the wing is complex, and involves adaptations, some already discussed, in the supporting as well as the deformable areas. The comparatively low shear moduli of the latter would tend to slow the passage of the torsion wave unless the area were partly or wholly enclosed by stiff elements. Within the deformable area such waves would tend to be damped by veins aligned parallel to their direction of passage, and facilitated by those lying obliquely or perpendicular. As

19 INSECT WINGS 465 we have seen oblique veins are in any case typical of the flexible posterior areas where slow torsion waves occur. Adaptations for transverse flexion Since transverse bending is mainly ventral, a transverse flexion-line usually functions as a one-way hinge. Localization of bending may sometimes be brought about by alignment of cross-veins, but fractures are also common. Edmunds & Traver (1954) drew attention to the line of fractures across the fore wings of most Ephemeroptera, and showed how their being confined to the concave veins would allow the wing to bend ventrally but not dorsally. Another familiar alignment of fractures is the nodal line of the fore wing of Cicadoidea. Similar flexion lines, with or without clear vein fractures, occur in Hylicidae and certain Fulgoroidea and PsylIidae among Hemiptera; in most Plecoptera and Trichoptera; in Sialis (Neuroptera) ; in many Hymenoptera; and in the Carboniferous Protorthoptera, Family Blattinopsidae. In all these examples the flexion line seems to represent the boundary between the basal supporting areas and the distal deformable area of the remigium. c+sc R c+sc R Rs Rs Mt2 Mlt2 CUA Dorsal view Ventral view FIG. 11. The nodal line of Fidicina viridis (Homoptera: Cicadidae). (a), (b), (c) dorsal and ventral views of details; not to same scale; (d) diagram of ventral flexion in a vein with a ventral band of soft cuticle. Explanation in the text. *

20 466 R. J. WOOTTON Elsewhere, transverse bending may occur across a supporting zone. Weis-Fogh (1973) drew attention to the line of bending across the fore wing of Encarsia. Other well-known examples are the flexion lines, often with one or more costal breaks, across the wing bases of many Diptera (Nachtigall, 1974 pl. 31) and the cuneal fracture in the hemielytra of several families of Heteroptera (Fig. I(d)). One-way transverse bending is sometimes ensured by the asymmetric structure of the vein fractures. Figure 11 shows those along the nodal line of a cicada fore wing. C + Sc has a band of soft cuticle across the ventral side only (Fig. 1 l(a)). M is interrupted by soft cuticle both above and below-but the ventral band is clearly broader (Fig. 1 I(c)). A band of soft cuticle runs along CuA, and is truncated dorsally, but broad, complete, and reaching the claval furrow on the ventral side (Fig. 1 l(b)). The mechanism allows ventral bending because the soft cuticle is stiff in tension, but unstable and liable to buckle in compression (Fig. I I(d)). FIG. 12. Transverse flexion of a cambered membrane attached to a stiff cambered base. (a) ventral, with marginal buckling; (b) ventral with camber reversal; (c) resistance to dorsal flexion. Often, however, one-way bending is a simple consequence of the relief of the wing. The basal supporting area of wings with a nodal line is usually cambered., with the dorsal side convex, even though the camber may alter by hingewise bending along the median flexion line. It is easy to show that a deformable membrane attached. to a stiffer cambered base may flex only ventrally (Fig. 12). Manipulation of a simple model demonstrates that a flexible but inelastic convexly cambered membrane easily bends ventrally relative to a similarly cambered stiff base, but that this necessitates either local buckling at the membrane edges (Fig. 12(a)) or the development of concave camber in the membrane (Fig. 12(b)). The latter is clearly visible in Sialis and Phlogophora (Fig. 8(d, e)) where it is achieved by concave bending along the median flexion line. An attempt to bend the membrane dorsally results in lateral forces which tend to increase the camber, and hence the stiffness of the entire structure: a self-reinforcing situation (Fig. 12(c)). Dorsal flexion is therefore only possible if failure occurs, by buckling or tearing. Strongly maintained camber is therefore enough in itself to ensure that flexion is unidirectional. Conclusion Although our knowledge is very far from complete, it is now possible to draw a tentative picture of the mode of operation of a typical, fairly generalized uncoupled wing.

21 INSECT WINGS 461 The forces leading to pronation and supination, acting anteriorly and posteriorly to the pleural wing process, which serves as a fulcrum, cyclically alter the section of the wing base, usually by effecting hingewise longitudinal bending along the median flexion line and the claval furrow. This process is well-known only in locusts (Pfau, 1977, 1978); but probably occurs widely, with some variation in detail. The forces involved in changes in section at the base are in turn transmitted via the stiff supporting and deformation-limiting areas to the deformable distal and aerodynamically most effective part of the wing, determining or strongly influencing its angle of attack, and limiting the moulding effect of the relative airflow. The precise form of the deformable area at any instant during the cycle is the result of the interaction of the airflow, the forces exerted by the adjacent supporting areas, and the structure of the deformable area itself. The latter will in most cases show adaptations to facilitate camber change, which may include the distal part of the median flexion line, or other mechanisms already described; and adaptations, including the arrangement and structure of the veins and the structure of the membrane, to control the form of the section. The pattern of change in wing-shape around the points of stroke-reversal again results from the aerodynamic and basally applied forces and the architecture of the wing; together now with the kinetic energy gained. during the previous half-stroke and the energy elastically stored in deforming the wings. A torsion wave passes along the wing; the relative positions of the supporting zones change, and the sections of the deformable areas are altered; and transverse flexion may occur, particularly at the end of the downstroke, frequently along lines predetermined by vein alignments or by fractures or weaknesses in the veins, and perhaps to some extent under active control. This account is incomplete even for a generalized single wing, and would certainly be inadequate for many specialized wings, and for the composite aerofoils formed by coupled wings. Many of the same principles and mechanisms must nonetheless apply to these; and further investigation will show how far. In an individual insect the variations in wing kinematics which bring about its available range of flight manoeuvres will come principally from changes in the strength, pattern and timing of the forces applied at the wing base, through their effects on the path, amplitude, frequency and symmetry of the beat, and also on the patterns of change in wing shape which they control. Between species, however, variation will result not only from such neuromuscular differences, but also from the architecture and engineering of the skeletal components of the pterothorax, and in particular of the axillae and the wings themselves. It is these last which are the principle concern of comparative functional wing morphology. Now required are comparative, and where appropriate quantitative investigations within particular groups, relating the detailed kinematics of the wings both to their structure and to the behaviour and overall biology of the insects. In this way a general understanding of the principles underlying wing design should progressively emerge, to complement the present active research in aerodynamics, energetics, and neuromuscular and sensory physiology in the development of an holistic picture of the processes of insect flight. I am indebted to Chatto and Windus Ltd., and to Mr Stephen Dalton for permission to trace five of his published photographs for Fig. 6 and 8. Our research would be impossible without the frequent generous loan of a high speed cine

22 468 R. J. WOOTTON camera belonging to Exeter University s Faculty of Engineering. Miss Christine Fowler, Mr Frank Knowles, Mr John Siewruk and especially Mr D. J. S. Newman have all taken films which have contributed to the conclusions and illustrations in this paper; and I am particularly grateful to David Newman for many hours of fruitful discussion, and for allowing me to quote some unpublished observations on dragonflies. Mr C. P. Ellington and Dr P. W. Carpenter have assisted me greatly with aerodynamic problems; and Charles Ellington, David Newmaii and Pamela Wootton have kindly read and commented on the manuscript. REFERENCES Bennett, L. (1970). Insect flight: lift and rate of change of incidence. Science, N. Y. 167: Dalton, S. (1975). Borne on the wind. London: Chatto and Windus. Dalton, S. (1977). The nziracle offlight. London: Sampson Low. Edmunds, G. F. Jr., & Traver, J. R. (1954). The flight mechanics and evolution of the wings of Ephemeroptera, with notes on the archtype insect wing. J. Wash. Acad. Sci. 44: Ellington, C. P. (1977). The aerodynamics of normal hovering flight : three approaches. In Cornparativep/i~siologywater, ions and fluid nzechanics: Schmidt-Nielson, K., Bolis, L. & Maddrell, S. H. P. (Eds). Cambridge: University Press. Ellington, C. P. (1980). Vortices and hovering flight. In Instationore E ekte an schwingenden Tierflugehr: Nachtigall, W. (Ed.). Wiesbaden. Hertel, H. (1966). Sfructure,forni and niovement. New York: Reinhold. Jensen, M. (1956). Biology and physics of locust flight The aerodynamics of locust flight. Phil. Trans. R. SOC. (B.) 239: Lighthill, M. J. (1973). On the Weis-Fogh mechanism of lift generation. J. fluid Mech. 60: 1-7. Martin, L. J. & Carpenter, P. W. (1977). Flow-visualisation experiments on butterflies in simulated gliding flight. Fortschr. Zool. 24: Nachtigall, W. (1966). Die Kinematik der Schlagfliigelbewegungen von Dipteren. Methodische und analytische Grundlagen zur Biophysik des Insektenflugs. 2. vergl. Phj,siol. 52: Nachtigall, W. (1967). Aerodynamische Messungen am Tragfliigel-System segelnder Schmetterlinge. Z. vergl. Physiol. 54: Nachtigall, W. (1974). Insects in flight. London: George Allen and Unwin. Newman. B. G., Savage, S. B. & Schouella, D. (1977). Model tests on a wing section of an Aeshna dragonfly. In Scale effpcfs in animal locon~oriori: Pedley, T. J. (Ed.). London : Academic Press. Nomarski, G. (1955). Microinterferometre differential P ondes polarisees. J. Phys. Radium, Paris 16: Norberg, R. A. (1972). The pterostigma of insect wings, an inertial regulator of wing pitch. J. romp. Physiol. 81: Pfau, H. K. (1977). Zur Morphologie und Funktion des Vorderflugels und Vorderflugelgelenks von Locusm nzigratoria L. Fortschr. Zool. 24: Pfau, H. K. (1978). Funktionsanatomische Aspekte des Insektenflugs. Zool. Jb. (Anat.) 99: Pringle. J. W. S. (1961). The flight of the bumble bee. Not. Hisr. Mag. August-September 1961: Rees, C. J. C. (19750). Form and function in corrugated insect wings. Nature, Lond. 256: Rees, C. J. C. (19756). Aerodynamic properties of an insect wing section and a smooth aerofoil compared. Nature, Lo/td. 258: Rohdendorf, B. B. (1949). [Evolution and classification of the flight apparatuses of insects] Trudypaleont. Insr. 16: [In Russian]. Rohdendorf, B. B. (1958-9). Die Bewegungsorgane der Zweiflugler-Insekten und ihre Entwicklung. Wiss. Z. Humbolr-Univ. Bed. (Math.-nat.) 8: ; ; Weis-Fogh, T. (1956). Biology and physics of locust flight IV. Notes on sensory mechanisms in locust flight. Phil. Trans. R. Soc. (B.) 239: Weis-Fogh, T. (1973). Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. esp. Biol. 59: Weis-Fogh, T. (1976). Energetics and aerodynamics of flapping flight: a synthesis. In Imect flight: Rainey, R. C. (Ed.). Oxford: Blackwells. Wootton. R. J. (1979). Function, homology and terminology in insect wings. Syst. Entorn. 4: Zarnack, W. (1972). Flugbiophysik der Wanderheuschrecke (Locrista rnigratoria L.) 1. Die Bewegungen der Vorderfliigel. J. conip. Physiol. 78: