Stacey A. Combes

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

SUMMARY 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 of this 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.

Flexural stiffness in insect wings II. Spatial distribution and dynamic wing bending

SUMMARY The dynamic, three-dimensional shape of flapping insect wings may influence many aspects of flight performance. Insect wing deformations during flight are largely passive, and are controlled primarily by the architecture and material properties of the wing. Although many details of wing structure are well understood, the distribution of flexural stiffness in insect wings and its effects on wing bending are unknown. In this study, we developed a method of estimating spatial variation in flexural stiffness in both the spanwise and chordwise direction of insect wings. We measured displacement along the wing in response to a point force, and modeled flexural stiffness variation as a simple mathematical function capable of approximating this measured displacement. We used this method to estimate flexural stiffness variation in the hawkmoth Manduca sexta, and the dragonfly Aeshna multicolor. In both species, flexural stiffness declines sharply from the wing base to the tip, and from the leading edge to the trailing edge; this variation can be approximated by an exponential decline. The wings of M. sexta also display dorsal/ventral asymmetry in flexural stiffness and significant differences between males and females. Finite element models based on M. sexta forewings demonstrate that the measured spatial variation in flexural stiffness preserves rigidity in proximal regions of the wing, while transferring bending to the edges, where aerodynamic force production is most sensitive to subtle changes in shape.

Into thin air: Contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta.

SUMMARY During flapping flight, insect wings must withstand not only fluid-dynamic forces, but also inertial-elastic forces generated by the rapid acceleration and deceleration of their own mass. Estimates of overall aerodynamic and inertial forces vary widely, and the relative importance of these forces in determining passive wing deformations remains unknown. If aeroelastic interactions between a wing and the fluid-dynamic forces it generates are minor compared to the effects of wing inertia, models of insect flight that account for passive wing flexibility would be far simpler to develop. We used an experimental approach to examine the contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta. We attached fresh Manduca wings to a motor and flapped them at a realistic wing-beat frequency and stroke amplitude. We compared wing bending in normal air versus helium (approx. 15% air density), in which the contribution of fluid-dynamic forces to wing deformations is significantly reduced. This 85% reduction in air density produced only slight changes in the pattern of Manduca wing deformations, suggesting that fluid-dynamic forces have a minimal effect on wing bending. We used a simplified finite element model of a wing to show that the differences observed between wings flapped in air versus helium are most likely due to fluid damping, rather than to aerodynamic forces. This suggests that damped finite element models of insect wings (with no fluid-dynamic forces included) may be able to predict overall patterns of wing deformation prior to calculations of aerodynamic force production, facilitating integrative models of insect flight.

Flexible Wings and Fins: Bending by Inertial or Fluid-Dynamic Forces?

Abstract Flapping flight and swimming in many organisms is accompanied by significant bending of flexible wings and fins. The instantaneous shape of wings and fins has, in turn, a profound effect on the fluid dynamic forces they can generate, with non-monotonic relationships between the pattern of deformation waves passing along the wing and the thrust developed. Many of these deformations arise, in part, from the passive mechanics of oscillating a flexible air- or hydrofoil. At the same time, however, their instantaneous shape may well emerge from details of the fluid loading. This issue—the extent to which there is feedback between the instantaneous wing shape and the fluid dynamic loading—is core to understanding flight control. We ask to what extent surface shape of wings and fins is controlled by structural mechanics versus fluid dynamic loading. To address this issue, we use a combination of computational and analytic methods to explore how bending stresses arising from inertial-elastic mechanisms compare to those stresses that arise from fluid pressure forces. Our analyses suggest that for certain combinations of wing stiffness, wing motions, and fluid density, fluid pressure stresses play a relatively minor role in determining wing shape. Nearly all of these combinations correspond to wings moving in air. The exciting feature provided by this analysis is that, for high Reynolds number motions where linear potential flow equations provide reasonable estimates of lift and thrust, we can finally examine how wing structure affects flight performance. Armed with this approach, we then show how modest levels of passive elasticity can affect thrust for a given level of energy input in the form of an inertial oscillation of a compliant foil.

Linking biomechanics and ecology through predator–prey interactions: flight performance of dragonflies and their prey

SUMMARY Aerial predation is a highly complex, three-dimensional flight behavior that affects the individual fitness and population dynamics of both predator and prey. Most studies of predation adopt either an ecological approach in which capture or survival rates are quantified, or a biomechanical approach in which the physical interaction is studied in detail. In the present study, we show that combining these two approaches provides insight into the interaction between hunting dragonflies (Libellula cyanea) and their prey (Drosophila melanogaster) that neither type of study can provide on its own. We performed >2500 predation trials on nine dragonflies housed in an outdoor artificial habitat to identify sources of variability in capture success, and analyzed simultaneous predator–prey flight kinematics from 50 high-speed videos. The ecological approach revealed that capture success is affected by light intensity in some individuals but that prey density explains most of the variability in success rate. The biomechanical approach revealed that fruit flies rarely respond to approaching dragonflies with evasive maneuvers, and are rarely successful when they do. However, flies perform random turns during flight, whose characteristics differ between individuals, and these routine, erratic turns are responsible for more failed predation attempts than evasive maneuvers. By combining the two approaches, we were able to determine that the flies pursued by dragonflies when prey density is low fly more erratically, and that dragonflies are less successful at capturing them. This highlights the importance of considering the behavior of both participants, as well as their biomechanics and ecology, in developing a more integrative understanding of organismal interactions.

Wing flexibility enhances load-lifting capacity in bumblebees

The effect of wing flexibility on aerodynamic force production has emerged as a central question in insect flight research. However, physical and computational models have yielded conflicting results regarding whether wing deformations enhance or diminish flight forces. By experimentally stiffening the wings of live bumblebees, we demonstrate that wing flexibility affects aerodynamic force production in a natural behavioural context. Bumblebee wings were artificially stiffened in vivo by applying a micro-splint to a single flexible vein joint, and the bees were subjected to load-lifting tests. Bees with stiffened wings showed an 8.6 per cent reduction in maximum vertical aerodynamic force production, which cannot be accounted for by changes in gross wing kinematics, as stroke amplitude and flapping frequency were unchanged. Our results reveal that flexible wing design and the resulting passive deformations enhance vertical force production and load-lifting capacity in bumblebees, locomotory traits with important ecological implications.

Artificial insect wings of diverse morphology for flapping-wing micro air vehicles.

The development of flapping-wing micro air vehicles (MAVs) demands a systematic exploration of the available design space to identify ways in which the unsteady mechanisms governing flapping-wing flight can best be utilized for producing optimal thrust or maneuverability. Mimicking the wing kinematics of biological flight requires examining the potential effects of wing morphology on flight performance, as wings may be specially adapted for flapping flight. For example, insect wings passively deform during flight, leading to instantaneous and potentially unpredictable changes in aerodynamic behavior. Previous studies have postulated various explanations for insect wing complexity, but there lacks a systematic approach for experimentally examining the functional significance of components of wing morphology, and for determining whether or not natural design principles can or should be used for MAVs. In this work, a novel fabrication process to create centimeter-scale wings of great complexity is introduced; via this process, a wing can be fabricated with a large range of desired mechanical and geometric characteristics. We demonstrate the versatility of the process through the creation of planar, insect-like wings with biomimetic venation patterns that approximate the mechanical properties of their natural counterparts under static loads. This process will provide a platform for studies investigating the effects of wing morphology on flight dynamics, which may lead to the design of highly maneuverable and efficient MAVs and insight into the functional morphology of natural wings.

Turbulence-driven instabilities limit insect flight performance

Environmental turbulence is ubiquitous in natural habitats, but its effect on flying animals remains unknown because most flight studies are performed in still air or artificially smooth flow. Here we show that variability in external airflow limits maximum flight speed in wild orchid bees by causing severe instabilities. Bees flying in front of an outdoor, turbulent air jet become increasingly unstable about their roll axis as airspeed and flow variability increase. Bees extend their hindlegs ventrally at higher speeds, improving roll stability but also increasing body drag and associated power requirements by 30%. Despite the energetic cost, we observed this stability-enhancing behavior in 10 euglossine species from 3 different genera, spanning an order of magnitude in body size. A field experiment in which we altered the level of turbulence demonstrates that flight instability and maximum flight speed are directly related to flow variability. The effect of environmental turbulence on flight stability is thus an important and previously unrecognized determinant of flight performance.

Resilin in dragonfly and damselfly wings and its implications for wing flexibility

Although there is mounting evidence that passive mechanical dynamics of insect wings play an integral role in insect flight, our understanding of the structural details underlying insect wing flexibility remains incomplete. Here, we use comparative morphological and mechanical techniques to illuminate the function and diversity of two mechanisms within Odonata wings presumed to affect dynamic wing deformations: flexible resilin vein‐joints and cuticular spikes. Mechanical tests show that joints with more resilin have lower rotational stiffness and deform more in response to a load applied to an intact wing. Morphological studies of 12 species of Odonata reveal that resilin joints and cuticular spikes are widespread taxonomically, yet both traits display a striking degree of morphological and functional diversity that follows taxonomically distinct patterns. Interestingly, damselfly wings (suborder Zygoptera) are mainly characterized by vein‐joints that are double‐sided (containing resilin both dorsally and ventrally), whereas dragonfly wings (suborder Epiprocta) are largely characterized by single‐sided vein‐joints (containing resilin either ventrally or dorsally, but not both). The functional significance and diversity of resilin joints and cuticular spikes could yield insight into the evolutionary relationship between form and function of wings, as well as revealing basic principles of insect wing mechanical design. J. Morphol., 2011.

Rolling with the flow: Bumblebees flying in unsteady wakes

SUMMARY Our understanding of how variable wind in natural environments affects flying insects is limited because most studies of insect flight are conducted in either smooth flow or still air conditions. Here, we investigate the effects of structured, unsteady flow (the von Karman vortex street behind a cylinder) on the flight performance of bumblebees (Bombus impatiens). Bumblebees are ‘all-weather’ foragers and thus frequently experience variable aerial conditions, ranging from fully mixed, turbulent flow to unsteady, structured vortices near objects such as branches and stems. We examined how bumblebee flight performance differs in unsteady versus smooth flow, as well as how the orientation of unsteady flow structures affects their flight performance, by filming bumblebees flying in a wind tunnel under various flow conditions. The three-dimensional flight trajectories and orientations of bumblebees were quantified in each of three flow conditions: (1) smooth flow, (2) the unsteady wake of a vertical cylinder (inducing strong lateral disturbances) and (3) the unsteady wake of a horizontal cylinder (inducing strong vertical disturbances). In both unsteady conditions, bumblebees attenuated the disturbances induced by the wind quite effectively, but still experienced significant translational and rotational fluctuations as compared with flight in smooth flow. Bees appeared to be most sensitive to disturbance along the lateral axis, displaying large lateral accelerations, translations and rolling motions in response to both unsteady flow conditions, regardless of orientation. Bees also displayed the greatest agility around the roll axis, initiating voluntary casting maneuvers and correcting for lateral disturbances mainly through roll in all flow conditions. Both unsteady flow conditions reduced the upstream flight speed of bees, suggesting an increased cost of flight in unsteady flow, with potential implications for foraging patterns and colony energetics in natural, variable wind environments.