Graham K. Taylor

Flying and swimming animals cruise at a Strouhal number tuned for high-power efficiency

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U). St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2 < St < 0.4 (refs 3–8). Because natural selection is likely to tune animals for high propulsive efficiency, we expect it to constrain the range of St that animals use. This seems to be true for dolphins, sharks and bony fish, which swim at 0.2 < St < 0.4. Here we show that birds, bats and insects also converge on the same narrow range of St, but only when cruising. Tuning cruise kinematics to optimize St therefore seems to be a general principle of oscillatory lift-based propulsion.

Details of Insect Wing Design and Deformation Enhance Aerodynamic Function and Flight Efficiency

Locust Wing Aerodynamics Insect wings function as deformable aerofoils, but the precise aerodynamic benefits of the observed deformations have remained obscure. Previous models have treated the wing as a flat plate, lacking any deformation, even though it is clear that the locust wing can twist and rotate along its length. Young et al. (p. 1549) validate a computational fluid dynamic model, using particle imaging velocimetry and smoke visualization of the flow around actual locusts, and use the model to investigate the effect of measured changes in wing shape during a stroke cycle. The complexity of insect wing venation directly affects the aerodynamics of flight via the intermediary of wing deformation. Measurements of locust wing kinematics validate a fluid dynamics model of the aerodynamic effects of wing deformation. Insect wings are complex structures that deform dramatically in flight. We analyzed the aerodynamic consequences of wing deformation in locusts using a three-dimensional computational fluid dynamics simulation based on detailed wing kinematics. We validated the simulation against smoke visualizations and digital particle image velocimetry on real locusts. We then used the validated model to explore the effects of wing topography and deformation, first by removing camber while keeping the same time-varying twist distribution, and second by removing camber and spanwise twist. The full-fidelity model achieved greater power economy than the uncambered model, which performed better than the untwisted model, showing that the details of insect wing topography and deformation are important aerodynamically. Such details are likely to be important in engineering applications of flapping flight.

Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanisms, controlled primarily via angle of attack.

SUMMARY Here we show, by qualitative free- and tethered-flight flow visualization, that dragonflies fly by using unsteady aerodynamic mechanisms to generate high-lift, leading-edge vortices. In normal free flight, dragonflies use counterstroking kinematics, with a leading-edge vortex (LEV) on the forewing downstroke, attached flow on the forewing upstroke, and attached flow on the hindwing throughout. Accelerating dragonflies switch to in-phase wing-beats with highly separated downstroke flows, with a single LEV attached across both the fore- and hindwings. We use smoke visualizations to distinguish between the three simplest local analytical solutions of the Navier–Stokes equations yielding flow separation resulting in a LEV. The LEV is an open U-shaped separation, continuous across the thorax, running parallel to the wing leading edge and inflecting at the tips to form wingtip vortices. Air spirals in to a free-slip critical point over the centreline as the LEV grows. Spanwise flow is not a dominant feature of the flow field – spanwise flows sometimes run from wingtip to centreline, or vice versa – depending on the degree of sideslip. LEV formation always coincides with rapid increases in angle of attack, and the smoke visualizations clearly show the formation of LEVs whenever a rapid increase in angle of attack occurs. There is no discrete starting vortex. Instead, a shear layer forms behind the trailing edge whenever the wing is at a non-zero angle of attack, and rolls up, under Kelvin–Helmholtz instability, into a series of transverse vortices with circulation of opposite sign to the circulation around the wing and LEV. The flow fields produced by dragonflies differ qualitatively from those published for mechanical models of dragonflies, fruitflies and hawkmoths, which preclude natural wing interactions. However, controlled parametric experiments show that, provided the Strouhal number is appropriate and the natural interaction between left and right wings can occur, even a simple plunging plate can reproduce the detailed features of the flow seen in dragonflies. In our models, and in dragonflies, it appears that stability of the LEV is achieved by a general mechanism whereby flapping kinematics are configured so that a LEV would be expected to form naturally over the wing and remain attached for the duration of the stroke. However, the actual formation and shedding of the LEV is controlled by wing angle of attack, which dragonflies can vary through both extremes, from zero up to a range that leads to immediate flow separation at any time during a wing stroke.

Sensory Systems and Flight Stability: What do Insects Measure and Why?

Abstract In the absence of much passive stability, flying insects rely upon active stabilisation, necessitating the provision of rich sensory feedback across a range of modalities. Here we consider from a sensory perspective what quantities flying insects measure, in order to ask from a mechanical perspective why they should want to do so. We consider each of the sensory modalities separately and uncover three general principles. Firstly, we find that insects have evolved to measure changes in kinematic state, rather than absolute state. For example, although the antennae may be loosely thought of as airspeed sensors, we show that they are configured as a sophisticated adaptive sensing system which is much more appropriate for measuring changes in airspeed than absolute airspeed. Secondly, we find that insect sensory systems are tuned to sense self-motion components in specific directions. For example, certain visual interneurons of flies operate as matched filters that are tuned to detect the optic flow fields induced specifically by rotation about one particular axis. Thirdly, we find that insects commonly combine sensory input from across modalities to form composite, multi-modal quantities which they use as feedback to the control system. For example, certain individually identified descending interneurons combine input from the compound eyes, ocelli, antennae, and cephalic wind-sensitive hairs into one composite signal which is then used in flight control. We infer from these three general organisational principles that insects are configured to sense excitation of their natural modes of motion. This natural-mode sensing hypothesis: (1) explains why insects should want to sense changes in state rather than absolute state; (2) predicts what specific directions of motion they should sense, and (3) specifies how sensory input from different modalities should be combined.

The aerodynamics of Manduca sexta: digital particle image velocimetry analysis of the leading-edge vortex.

SUMMARY Here we present the first digital particle image velocimetry (DPIV) analysis of the flow field around the wings of an insect (the tobacco hawkmoth Manduca sexta, tethered to a 6-component force-moment balance in a wind tunnel). A leading-edge vortex (LEV) is present above the wings towards the end of the downstroke, as the net upward force peaks. Our DPIV analyses and smoke visualisations match the results of previous flow visualisation experiments at midwing, and we extend the experiments to provide the first analysis of the flow field above the thorax. Detailed DPIV measurements show that towards the end of the downstroke, the LEV structure is consistent with that recently reported in free-flying butterflies and dragonflies: the LEV is continuous across the thorax and runs along each wing to the wingtip, where it inflects to form the wingtip trailing vortices. The LEV core is 2-3 mm in diameter (approximately 10% of local wing chord) both at the midwing position and over the centreline at 1.2 m s-1 and at 3.5 m s-1 flight speeds. At 1.2 m s-1 the measured LEV circulation is 0.012±0.001 m2 s-1 (mean ± s.d.) at the centreline and 0.011±0.001 m2 s-1 halfway along the wing. At 3.5 m s-1 LEV circulation is 0.011±0.001 m2 s-1 at the centreline and 0.020±0.004 m2 s-1 at midwing. The DPIV measurements suggest that if there is any spanwise flow in the LEV towards the end of the downstroke its velocity is less than 1 m s-1. Estimates of force production show that the LEV contributes significantly to supporting body weight during bouts of flight at both speeds (more than 10% of body weight at 1.2 m s-1 and 35-65% of body weight at 3.5 m s-1).

Mechanics and aerodynamics of insect flight control

Insects have evolved sophisticated flight control mechanisms permitting a remarkable range of manoeuvres. Here, I present a qualitative analysis of insect flight control from the perspective of flight mechanics, drawing upon both the neurophysiology and biomechanics literatures. The current literature does not permit a formal, quantitative analysis of flight control, because the aerodynamic force systems that biologists have measured have rarely been complete and the position of the centre of gravity has only been recorded in a few studies. Treating the two best‐known insect orders (Diptera and Orthoptera) separately from other insects, I discuss the control mechanisms of different insects in detail. Recent experimental studies suggest that the helicopter model of flight control proposed for Drosophila spp. may be better thought of as a facultative strategy for flight control, rather than the fixed (albeit selected) constraint that it is usually interpreted to be. On the other hand, the so‐called ‘constant‐lift reaction’ of locusts appears not to be a reflex for maintaining constant lift at varying angles of attack, as is usually assumed, but rather a mechanism to restore the insect to pitch equilibrium following a disturbance. Differences in the kinematic control mechanisms used by the various insect orders are related to differences in the arrangement of the wings, the construction of the flight motor and the unsteady mechanisms of lift production that are used. Since the evolution of insect flight control is likely to have paralleled the evolutionary refinement of these unsteady aerodynamic mechanisms, taxonomic differences in the kinematics of control could provide an assay of the relative importance of different unsteady mechanisms. Although the control kinematics vary widely between orders, the number of degrees of freedom that different insects can control will always be limited by the number of independent control inputs that they use. Control of the moments about all three axes (as used by most conventional aircraft) has only been proven for larger flies and dragonflies, but is likely to be widespread in insects given the number of independent control inputs available to them. Unlike in conventional aircraft, however, insects’ control inputs are likely to be highly non‐orthogonal, and this will tend to complicate the neural processing required to separate the various motions.

Deformable wing kinematics in free-flying hoverflies

Here, we present a detailed analysis of the deforming wing kinematics of free-flying hoverflies (Eristalis tenax, Linnaeus) during hovering flight. We used four high-speed digital video cameras to reconstruct the motion of approximately 22 points on each wing using photogrammetric techniques. While the root-flapping motion of the wing is similar in both the downstroke and upstroke, and is well modelled as a simple harmonic motion, other wing kinematic parameters show substantial variation between the downstroke and upstroke. Whereas the magnitude of the angle of incidence varies considerably within and between different hoverflies, the twist distribution along the wing is highly stereotyped. The angle of incidence and camber both show a recoil effect as they change abruptly at stroke reversal. Pronation occurs consistently after stroke reversal, which is perhaps surprising, because this has been found to reduce lift production in modelling studies. We find that the alula, a hinged flap near the base of the wing, operates in two discrete states: either in plane with the wing, or flipped approximately normal to it. We hypothesize that the alula may be acting as a flow-control device.

Photogrammetric reconstruction of high-resolution surface topographies and deformable wing kinematics of tethered locusts and free-flying hoverflies

Here, we present a suite of photogrammetric methods for reconstructing insect wing kinematics, to provide instantaneous topographic maps of the wing surface. We filmed tethered locusts (Schistocerca gregaria) and free-flying hoverflies (Eristalis tenax) using four high-speed digital video cameras. We digitized multiple natural features and marked points on the wings using manual and automated tracking. Epipolar geometry was used to identify additional points on the hoverfly wing outline which were anatomically indistinguishable. The cameras were calibrated using a bundle adjustment technique that provides an estimate of the error associated with each individual data point. The mean absolute three-dimensional measurement error was 0.11 mm for the locust and 0.03 mm for the hoverfly. The error in the angle of incidence was at worst 0.51° (s.d.) for the locust and 0.88° (s.d.) for the hoverfly. The results we present are of unprecedented spatio-temporal resolution, and represent the most detailed measurements of insect wing kinematics to date. Variable spanwise twist and camber are prominent in the wingbeats of both the species, and are of such complexity that they would not be adequately captured by lower resolution techniques. The role of spanwise twist and camber in insect flight has yet to be fully understood, and accurate insect wing kinematics such as we present here are required to be sure of making valid predictions about their aerodynamic effects.

Deformable wing kinematics in the desert locust: how and why do camber, twist and topography vary through the stroke?

Here, we present a detailed analysis of the wing kinematics and wing deformations of desert locusts (Schistocerca gregaria, Forskål) flying tethered in a wind tunnel. We filmed them using four high-speed digital video cameras, and used photogrammetry to reconstruct the motion of more than 100 identified points. Whereas the hindwing motions were highly stereotyped, the forewing motions showed considerable variation, consistent with a role in flight control. Both wings were positively cambered on the downstroke. The hindwing was cambered through an ‘umbrella effect’ whereby the trailing edge tension compressed the radial veins during the downstroke. Hindwing camber was reversed on the upstroke as the wing fan corrugated, reducing the projected area by 30 per cent, and releasing the tension in the trailing edge. Both the wings were strongly twisted from the root to the tip. The linear decrease in incidence along the hindwing on the downstroke precisely counteracts the linear increase in the angle of attack that would otherwise occur in root flapping for an untwisted wing. The consequent near-constant angle of attack is reminiscent of the optimum for a propeller of constant aerofoil section, wherein a linear twist distribution allows each section to operate at the unique angle of attack maximizing the lift to drag ratio. This implies tuning of the structural, morphological and kinematic parameters of the hindwing for efficient aerodynamic force production.

Smoke visualization of free-flying bumblebees indicates independent leading-edge vortices on each wing pair

It has been known for a century that quasi-steady attached flows are insufficient to explain aerodynamic force production in bumblebees and many other insects. Most recent studies of the unsteady, separated-flow aerodynamics of insect flight have used physical, analytical or numerical modeling based upon simplified kinematic data treating the wing as a flat plate. However, despite the importance of validating such models against living subjects, few good data are available on what real insects actually do aerodynamically in free flight. Here we apply classical smoke line visualization techniques to analyze the aerodynamic mechanisms of free-flying bumblebees hovering, maneuvering and flying slowly along a windtunnel (advance ratio: −0.2 to 0.2). We find that bumblebees, in common with most other insects, exploit a leading-edge vortex. However, in contrast to most other insects studied to date, bumblebees shed both tip and root vortices, with no evidence for any flow structures linking left and right wings or their near-wakes. These flow topologies will be less efficient than those in which left and right wings are aerodynamically linked and shed only tip vortices. While these topologies might simply result from biological constraint, it is also possible that they might have been specifically evolved to enhance control by allowing left and right wings to operate substantially independently.