Flexural stiffness in insect wings

Flexural stiffness in insect wings

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The forces generated during flapping flight depend on both the motion of a wing and its three-dimensional shape. Flying vertebrates, such as birds and bats, can control many aspects of wing shape by muscular contractions that alter the alignment of wing bones, the position of feathers or the tautness of wing membranes (Kent, 1992). Flying insects have far less active control over the three-dimensional shape of their wings, as insect flight muscles are restricted to the wing base. Insect wings are largely passive structures, in which muscular forces transmitted by the wing base interact with aerodynamic andinertial forces generated by the wing’s motions. The architecture of the wing (vein arrangement, three-dimensional relief, flexion lines, etc.) and the material properties of its elements determine how the wing will change shape in response to these forces (Wootton, 1992).

Many insect wings undergo significant bending and twisting during flight (Dalton, 1975; Wootton, 1990a), which may alter the direction and magnitude of aerodynamic force production. Wing deformations enhance thrust production in some species by creating a force asymmetry between half-strokes, and can increase lift production by allowing wings to twist and generate upward force throughout the stroke cycle (Wootton, 1990a). The structure of insect wings thus appears to permit certain beneficial passive deformations while minimizing detrimental bending that would compromise force production. Yet our understanding of how insect wing design affects flexibility and passive wing deformation is limited.

Insect wing veins are the primary supporting structures in wings. The arrangement of veins and complexity of vein branching varies widely among insects, and venation pattern is often used to characterize orders and families. Basal groups of insects (such as odonates) generally possess wings with a large number of cross-veins (also present in early fossil wings), whereas more derived groups have wings in which the number of cross-veins is reduced and the main wing support is shifted anteriorly (Wootton, 1990a).

Several studies have demonstrated the functional significance of specific vein arrangements in insect wings. For example, the pleated, grid-like arrangement of leading edge veins in dragonfly wings helps strengthen the wing to spanwise bending (Newman and Wootton, 1986; Wootton, 1991), posteriorly curved veins in flies generate chordwise camber when a force is applied to the wing (Ennos, 1988), and the fanlike distribution of veins in the locust hindwing causes the wing margin to bend downward when the wing is extended (Herbert et al., 2000; Wootton, 1995; Wootton et al., 2000). Beyond these specialized mechanisms, however, the functional significance of the enormous differences in overall venation pattern in insect wings remains unclear. Given the large phylogenetic changes in cross-venation, vein

2979The Journal of Experimental Biology 206, 2979-2987 ©2003 The Company of Biologists Ltd doi:10.1242/jeb.00523

During flight, many insect wings undergo dramatic deformations that are controlled largely by the architecture of the wing. The pattern of supporting veins in wings varies widely among insect orders and families, but the functional significance of phylogenetic trends in wing venation remains unknown, and measurements of the mechanical properties of wings are rare. In this study, we address the relationship between venation pattern and wing flexibility by measuring the flexural stiffness of wings (in both the spanwise and chordwise directions) and quantifying wing venation in 16 insect species from six orders. These measurements show that spanwise flexural stiffness scales strongly with the cube of wing span, whereas chordwise flexural stiffness scales with the square of chord length. Wing size accounts for over 95% of the variability in measured flexural stiffness; the residuals ofthis relationship are small and uncorrelated with standardized independent contrasts of wing venation characters. In all species tested, spanwise flexural stiffness is 1–2 orders of magnitude larger than chordwise flexural stiffness. A finite element model of an insect wing demonstrates that leading edge veins are crucial in generating this spanwise–chordwise anisotropy.

Key words: insect flight, flexural stiffness, wing, wing flexibility, wing vein, independent contrast, finite element model.

Summary

Introduction

Flexural stiffness in insect wings I. Scaling and the influence of wing venation

S. A. Combes* and T. L. Daniel

Department of Biology, University of Washington, Seattle, WA 98195, USA *Author for correspondence (e-mail: scombes@u.washington.edu)

Accepted 3 June 2003 diameter and spatial distribution of veins (Fig.·1), one might expect insect wings to display large mechanical differences that would affect their deformability during flight. On the other hand, differences in venation pattern may reflect alternative designs that provide insect wings with similar overall mechanical and bending properties while allowing veins to be rearranged for other reasons. Quantitative measurements of wing stiffness that would allow one to distinguish between these hypotheses remain limited to a small number of studies. Wing stiffness has been assessed by applying point forces to isolated wing sections, indragonflies (Newman and Wootton, 1986) and locusts (Wootton et al., 2000), or at the center of pressure to produce torsion, in flies (Ennos, 1988) and butterflies (Wootton, 1993). Steppan (2000) measured bending stiffness in dried butterfly wings, and Smith et al. (2000) measured material stiffness

(Young’s modulus, E) of insect wing membrane from locust hindwings. Although each of these studies provides insight into the functional wing morphology of the species examined, the measurements are difficult to compare in a broader phylogenetic context because of variations in technique.

In this study, we examined the relationship between insect wing flexibility and venation by measuring flexural stiffness (EI) and quantifying venation pattern in 16 insect species fromsix orders. Flexural stiffness is a composite measure of the overall bending stiffness of a wing; it is the product of the material stiffness (E, which describes the stiffness of the wing material itself) and the second moment of area (I, which describes the stiffness generated by the cross-sectional geometry of the wing). Because insect wings bend spanwise (from wing base to wing tip) and chordwise (from leading to trailing edge) during flight, we measured flexural stiffness in both of these directions.

Correlations between venation pattern and wing flexural stiffness may arise either from a functional relationship between these traits or simply as a result of the shared phylogenetic history of the species examined. To remove the effects of phylogeny from this study, we calculated standardized independent contrasts (Felsenstein, 1985; Garland et al., 1999) of venation and stiffness measurements, and examined the correlations between these contrasts to assess the relationship between wing venation pattern and flexural stiffness.

Finally, we created a simplified finite element model of an insect wing, in which we can alter the stiffness of specific wing veins (or remove veins entirely) and perform numerical experiments to assess the resulting flexural stiffness of the whole wing. This

S. A. Combes and T. L. Daniel

Odonata

Isoptera Neuroptera

Hymenoptera

Diptera

Lepidoptera

Pachydiplax longipennis Lestes sp.Ischnura sp.

Hemerobius sp. Pepsis sp.

Sceliphron sp. Bombus sp.

Tipula sp. Villa sp.

Eristalis sp. Calliphora sp.

Manduca sexta

Ochlodes sylvanoidesPieris rapae

Zootermopsis angusticollis Aeshna multicolor

Fig.·1. Drawings of forewings from insects used in this study, arranged on the phylogenetic tree used to calculate independent contrasts. Veins are drawn at actual thickness; wings are not shown to scale. Genus and species names (when known) are shown under each wing, and orders are listed at their branching points. Branching and divergence dates of orders were derived from Kristensen (1991), Kukalova-Peck (1991), Whiting et al. (1997) and Wootton (1990b). Branching patterns and divergence dates within orders were derived from Benton (1993), Maddison (1995a,b), Trueman and Rowe (2001) and Wiegmann and Yeates (1996).

2981Wing venation and scaling of flexural stiffness modeling approach allows us to examine the functional significance of various wing veins in generating the overall patterns of flexural stiffness measured in real wings.

Materials and methods

Insect collection and handling

We measured flexural stiffness and wing venation pattern in the forewings of 16 insect species from six orders: Odonata (two dragonfly and two damselfly), Isoptera (termite), Neuroptera (lacewing), Hymenoptera (two wasp and one bee), Diptera (four flies from different families) and Lepidoptera (two butterfly and one hawkmoth); see Fig.·1 for species names. We measured spanwise and chordwise flexural stiffness in 2–10 individuals of each species, depending on availability.

Insects were collected locally or obtained from laboratory colonies and placed in a humidified container at 4°C until experiments were performed. Within 1 week of capture, we cold-anaesthetized an insect, recorded its mass, removed one forewing, and placed the insect back in the humidified container. We photographed the wing and measured its flexural stiffness in the spanwise direction within 1·h of removing the wing from the insect (during which time the stiffness of the wing does not change appreciably, according to trials). We then repeated this process for the other forewing, measuring flexural stiffness in the chordwise direction.

Flexural stiffness measurements

We measured flexural stiffness of wings by applying a point force to bend the wing in either the spanwise or chordwise direction, and using the measured force and wing displacement to calculate overall flexural stiffness EIwith a beam equation (see below). We glued wings to glass slides using cyanoacrylate glue cured with baking soda, at either the wing base (for spanwise measurements) or the leading edge (for chordwise measurements; Fig.·2A). We then fixed the slide to the left side of the apparatus shown in Fig.·2B and adjusted the right arm so that the pin contacted the wing on its dorsal surface. We applied the point force at 70% of wing span or chord length because the pin slipped from the wing if it was placed too close to the edge. We performed four measurements with point loads of varying magnitude, lowering the right side of the apparatus with a micrometer, measuring force and displacement and returning to the zero (unloaded) position between each measurement. We then flipped the slide over and repeated the measurements, loading the wing from the ventral side.

We removed the slide and measured the distance from the point of wing attachment to the point of force application to determine the effective beam length (L). We calculated EIover this distance as in Gordon (1978):

EI = FL3/ 3d·, (1) where Fis applied force and dis wing displacement at the point of force application (70% span or chord). This equation provides a measure of the flexural stiffness over the entire beam length, and assumes that the beam is homogeneous (see Discussion for an analysis of the beam equation assumptions). Because the equation applies only to small displacements, we removed any measurements where wing displacement was more than 5% of the effective beam length (where d>0.05L). We averaged the repeated measurements on each side into a single dorsal and a single ventral value and tested for a significant difference (P<0.05) between dorsal and ventral values with a Wilcoxon signed rank test.

We plotted spanwise and chordwise flexural stiffness against several measures of wing and body size: wing span and maximum chord length (measured in NIH Image), wing area (measured in Matlab; see below) and body mass. We also combined these size measurements using principal components analysis into a measure of overall size (including all four variables) and a measure of wing size (including wing span, chord and area). To verify our technique for measuring EI, we measured

70% span 70% chord

Flexible beam Wing

Sensor

Micrometer Pin

Fig.·2. Method used to measure insect wing displacement in response to an applied force. (A) For spanwise measurements, point forces were applied at approximately 70% of wing span, near the leading edge (top). For chordwise measurements, point forces were applied at 70% of chord length, midway between the wing base and tip (bottom). (B) Wings were fixed to the left side of the apparatus, and the right side was lowered until a pin attached to a flexible beam contacted the wing. A micrometer was then used to lower the right arm by a known distance, applying a point force that moved the wing down and the flexible beam up. The motion of the beam was recorded viaan optical sensor, and used to calculate the applied force and displacement of the wing.

force and displacement of a thin, rectangular glass coverslip (a homogeneous beam of linearly elastic material) at three different lengths (with 3, 4 and 4.85·cm of the coverslip extending past the point of attachment). We then calculated EI for each beam length, measured the thickness and width of the coverslip, and calculated I, the second moment of area as in Gordon (1978): I = wt3 / 12·, (2)

Wing shape and venation measurements

From photographs of each wing, we created a black silhouette in Photoshop and used NIH Image to measure wing span and chord. For one wing of each species, we handdigitized the wing veins in Photoshop so that both the position and precise diameter of the veins were represented (Fig.·1).

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