A computational fluid dynamic (CFD) modelling approach is used to study the unsteady aerodynamics of the flapping wing of a hovering hawkmoth. We use the geometry of a Manduca sexta-based robotic wing to define the shape of a three-dimensional 'virtual' wing model and 'hover' this wing, mimicking accurately the three-dimensional movements of the wing of a hovering hawkmoth. Our CFD analysis has established an overall understanding of the viscous and unsteady flow around the flapping wing and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. <P> A coherent leading-edge vortex with axial flow was detected during translational motions of both the up- and downstrokes. The attached leading-edge vortex causes a negative pressure region and, hence, is responsible for enhancing lift production. The axial flow, which is derived from the spanwise pressure gradient, stabilises the vortex and gives it a characteristic spiral conical shape. <P> The leading-edge vortex created during previous translational motion remains attached during the rotational motions of pronation and supination. This vortex, however, is substantially deformed due to coupling between the translational and rotational motions, develops into a complex structure, and is eventually shed before the subsequent translational motion. <P> Estimation of the forces during one complete flapping cycle shows that lift is produced mainly during the downstroke and the latter half of the upstroke, with little force generated during pronation and supination. The stroke plane angle that satisfies the horizontal force balance of hovering is 23.6 degrees , which shows excellent agreement with observed angles of approximately 20-25 degrees . The time-averaged vertical force is 40 % greater than that needed to support the weight of the hawkmoth.

Mean lift coefficients have been calculated for hawkmoth flight at a range of speeds in order to investigate the aerodynamic significance of the kinematic variation which accompanies changes in forward velocity. The coefficients exceed the maximum steady-state value of 0.71 at all except the very fastest speeds, peaking at 2.0 or greater between 1 and 2 ms-1. Unsteady high-lift mechanisms are therefore most important during hovering and slow forward flight. In combination with the wingtip paths relative to the surrounding air, the calculated mean lift coefficients illustrate how the relative contributions of the two halfstrokes to the force balance change with increasing forward speed. Angle of incidence data for fast forward flight suggest that the sense of the circulation is not reversed between the down- and upstrokes, indicating a flight mode qualitatively different from that proposed for lower-speed flight in the hawkmoth and other insects. The mid-downstroke angle of incidence is constant at 30-40 degrees across the speed range. The relationship between power requirements and flight speed is explored; above 5 ms-1, further increases in forward velocity are likely to be constrained by available mechanical power, although problems with thrust generation and flight stability may also be involved. Hawkmoth wing and body morphology, and the differences between males and females, are evaluated in aerodynamic terms. Steady-state force measurements show that the hawkmoth body is amongst the most streamlined for any insect.

High-speed videography was used to record sequences of individual hawkmoths in free flight over a range of speeds from hovering to 5 ms-1. At each speed, three successive wingbeats were subjected to a detailed analysis of the body and wingtip kinematics and of the associated time course of wing rotation. Results are presented for one male and two female moths. The clearest kinematic trends accompanying increases in forward speed were an increase in stroke plane angle and a decrease in body angle. The latter may have resulted from a slight dorsal shift in the area swept by the wings as the supination position became less ventral with increasing speed. These trends were most pronounced between hovering and 3 ms-1, and the changes were gradual; there was no distinct gait change of the kind observed in some vertebrate fliers. The wing rotated as two functional sections: the hindwing and the portion of the forewing with which it is in contact, and the distal half of the forewing. The latter displayed greater fluctuation in the angle of rotation, especially at the lower speeds. As forward speed increased, the discrepancy between the rotation angles of the two halfstrokes, and of the two wing sections, became smaller. The downstroke wing torsion was set early in the halfstroke and then held constant during the translational phase.

The amplitude and time course of muscle length changes were examined in vivo in tethered, flying bumblebees Bombus lucorum. A ‘window’ was cut in the dorsal cuticle and aluminium particles were placed on the exposed dorsal longitudinal muscle fibres. Muscle oscillations were recorded using high-speed video and a high-magnification lens. The amplitude of muscle length changes was 1.9 % (s.d.=0.5 %, N=7), corresponding to the commonly quoted strain of 1–3 % for asynchronous muscle. Higher harmonics, particularly the second, were found in the muscle oscillations and in the wing movements. The second harmonic for wing movements was damped in comparison to that for muscle length changes, probably as a result of compliance in the thoracic linkage. Inclusion of the second harmonic in the driving signal for in vitro experiments on glycerinated fibres generally resulted in a decrease in the work and power, but a substantial increase was found for some fibres.

The properties of asynchronous insect flight muscle have been examined using a glycerol- extracted single-fibre preparation of dorsal longitudinal muscle from the bumblebees Bombus lucorum and B. terrestris. Chemical, mechanical and thermal conditions were controlled with the objective of maximizing power output. The problems arising from diffusion limitation were avoided through a combination of fibre paring and the use of an ATP backup system. Work and power output tended to increase with increasing oscillatory strain in the range 1–5 %. Workloop shape, and hence work and power, varied with fibre extension; optimum extensions ranged from 4 to 12 %. The mechanical performance of glycerinated bumblebee muscle fibres was strongly temperature-dependent, and rate processes (frequency, power) displayed higher thermal sensitivities than processes associated with tension development (work). The experimental conditions that maximized the power output were identified as: oscillatory strain epsilon=4-5 %, extension epsilono=8-10 %, oscillation frequency f=50 Hz and temperature T=40°C. The maximum power output observed under these ‘optimal’ conditions was about 110 W kg-1 (muscle), demonstrating for the first time that glycerinated fibres are capable of producing the power predicted from free-flight studies to be required for flight: 100 W kg-1.

Flight performance seems to change systematically with body size: small animals can hover and fly over a wide range of speeds, but large birds taxi for takeoff and then fly over a narrow speed range. The traditional explanation for this is that the mass-specific power required for flight varies with speed according to a U-shaped curve, and it also scales between m 0 and m 1/6 , where m is body mass. The mass-specific power available from the flight muscles is assumed to scale as m −1/3 . As available power decreases with increasing body size, the range of attainable flight speeds becomes progressively reduced until the largest animals can only fly in the trough of the U-shaped curve. Above a particular size, the available power is insufficient and flapping flight is not possible. The underlying assumptions of this argument are examined in this review. Metabolic measurements are more consistent with a J-shaped curve, with little change in power from hovering to intermediate flight speeds, than with a U-shaped curve. Scaling of the mass-specific power required to fly agrees with predictions. The mass-specific power available from, the muscles, estimated from maximal loading studies, varies as m 0.13 . This scaling cannot be distinguished from that of the power required to fly, refuting the argument that power imposes an intrinsic scaling on flight performance. It is suggested instead that limitations on low-speed performance result from an adverse scaling of lift production with increasing body size.

Using high-speed cinematography, bumblebees in free flight were filmed over a range of forward airspeeds. A detailed description of the wing tip and body kinematics was obtained from a three-dimensional reconstruction of the twodimensional film image. A technique for determining quantitatively the angle of attack of the wing was developed. Kinematic parameters found to vary consistently with airspeed were body angle, stroke plane angle, geometrical angle of attack, and rotational angles of the wings at the ends of half-strokes. Results of a morphological analysis of the wings and bodies of thoseinsects filmed in free flight are presented for use in later calculations of the lift and power requirements of forward flight.

This paper examines the aerodynamics and power requirements of forward flight in bumblebees. Measurements weremade of the steady-state lift and drag forces acting on bumblebee wings and bodies. The aerodynamic force and pitching moment balances for bumblebees previously filmed in free flight were calculated. A detailed aerodynamic analysis was used to show that quasi-steady aerodynamic mechanisms are inadequate to explain even fast forward flight. Calculations of the mechanical power requirements of forward flight show that the power required to fly is independent of airspeed over a range from hovering flight to an airspeed of 4.5 ms −1

The efficiency and mechanical power output of insect flight muscle have been estimated from a study of hovering flight. The maximum power output, calculated from the muscle properties, is adequate for the aerodynamic power requirements. However, the power output is insufficient to oscillate the wing mass as well unless there is good elastic storage of the inertial energy, and this is consistent with reports of elastic components in the flight system. A comparison of the mechanical power output with the metabolic power input to the flight muscles suggests that the muscle efficiency is quite low: less than 10%.

1. All of the wing fringe cilia of Thrips physapus , except those along the hindwing leading edge, pivot in elongated sockets which lock them into two positions. 2. The wings lie parallel over the abdomen when not in use, with the cilia locked in the closed position at an angle of 15-20° to the wing axis. The closing of the fringes prevents entanglement of the trailing edge cilia and lateral projection of the forewing leading edge cilia. 3. During flight the cilia are locked in the open position, doubling the wing area. The locking force is stronger than the combined aerodynamic and inertial forces on the cilia. 4. The fringes are opened by abdominal combing and closed by tibial combing. 5. The same morphological features are found in other members of the sub-order Terebrantia. Parallel wings at rest are characteristic of this suborder, and the collapsible fringe system is viewed as an effective method for parking the wings. 6. The fringes of the sub-order Tubulifera are not collapsible. The wings overlap on the abdomen at rest and a similar parking problem does not arise.