It has been shown that conventional aerodynamic theory, which was based on steady flow conditions, cannot explain the generation of large lift by the wings of small insects (for reviews, see Ellington, 1984a;Spedding, 1992). In the past few years, much progress has been made in revealing the unsteady high-lift mechanisms of flapping insect wings. Dickinson and Götz (1993) measured the aerodynamic forces of an airfoil started rapidly at high angles of attack in the Reynolds number (Re) range of the fruit fly wing (Re=75-225; for a flapping wing, Re is based on the mean chord length and the mean translation velocity at radius of the second moment of wing area). They showed that lift was enhanced by the presence of a dynamic stall vortex, or leading edge vortex (LEV). After the initial start, lift coefficient (CL) of approximately 2 was maintained within 2-3 chord lengths of travel. Afterwards, CL started to decrease due to the shedding of the LEV. But the decrease was not rapid, possibly because the shedding of the LEV was slow at such low Re; and The unsteady aerodynamic forces of a model fruit fly wing in flapping motion were investigated by numerically solving the Navier-Stokes equations. The flapping motion consisted of translation and rotation [the translation velocity (ut) varied according to the simple harmonic function (SHF), and the rotation was confined to a short period around stroke reversal]. First, it was shown that for a wing of given geometry with ut varying as the SHF, the aerodynamic force coefficients depended only on five non-dimensional parameters, i.e. Reynolds number (Re), stroke amplitude (Φ), mid-stroke angle of attack (αm), non-dimensional duration of wing rotation (∆τr) and rotation timing [the mean translation velocity at radius of the second moment of wing area (U), the mean chord length (c) and c/U were used as reference velocity, length and time, respectively]. Next, the force coefficients were investigated for a case in which typical values of these parameters were used (Re=200; Φ=150°; αm=40°; ∆τr was 20% of wingbeat period; rotation was symmetrical). Finally, the effects of varying these parameters on the force coefficients were investigated.In the Re range considered (20-1800), when Re was above ~100, the lift (CL) and drag (CD) coefficients were large and varied only slightly with Re (in agreement with results previously published for revolving wings); the large force coefficients were mainly due to the delayed stall mechanism. However, when Re was below ~100, CL decreased and CD increased greatly. At such low Re, similar to the case of higher Re, the leading edge vortex existed and attached to the wing in the translatory phase of a half-stroke; but it was very weak and its vorticity rather diffused, resulting in the small CL and large CD. Comparison of the calculated results with available hovering flight data in eight species (Re ranging from 13 to 1500) showed that when Re was above ~100, lift equal to insect weight could be produced but when Re was lower than ~100, additiona...

It has been shown that quasi-steady analysis cannot predict the aerodynamic forces and power requirements of insects in hovering (Ellington, 1984b,c) or forward flight (Dudley and Ellington, 1990b;Willmott and Ellington, 1997b). Researchers have been working to shed light on the unsteady mechanisms of aerodynamic force generation and predict satisfactorily the power requirements in such cases.Dickinson and Götz (1993) measured the aerodynamic forces on an aerofoil started impulsively at a high angle of attack in the Reynolds number (Re) range of a fruit fly wing and showed that lift was enhanced by the presence of a dynamic stall vortex, or leading-edge vortex (LEV). But lift enhancement was limited to only 2-3 chord lengths of travel because of the shedding of the LEV. For most insects, a wing section at a distance of 0.75R (where R is wing length) from the wing base travels approximately 5.3 chord lengths during an up-or downstroke in hovering flight (Ellington, 1984b); in forward flight, the section would travel an even larger distance during a downstroke. Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion were studied using the method of computational fluid dynamics. The Navier-Stokes equations were solved numerically. The solution provided the flow velocity and pressure fields, from which the vorticity wake structure and the unsteady aerodynamic forces and torques were obtained (the inertial torques due to the acceleration of the wing-mass were computed analytically). From the flowstructure and force information, insights were gained into the unsteady aerodynamic force generation. On the basis of the aerodynamic and inertial torques, the mechanical power was obtained, and its properties were investigated.The unsteady force mechanisms revealed previously for hovering (i.e. delayed stall, rapid acceleration at the beginning of the strokes and fast pitching-up rotation at the end of the strokes) apply to forward flight. Even at high advance ratios, e.g. J=0.53-0.66 (J is the advance ratio), the leading edge vortex does not shed (at such advance ratios, the wing travels approximately 6.5 chord lengths during the downstroke).At low speeds (J≈0.13), the lift (vertical force) for weight support is produced during both the down-and upstrokes (the downstroke producing approximately 80% and the upstroke producing approximately 20% of the mean lift), and the lift is contributed mainly by the wing lift; the thrust that overcomes the body drag is produced during the upstroke, and it is contributed mainly by the wing drag. At medium speeds (J≈0.27), the lift is mainly produced during the downstroke and the thrust mainly during the upstroke; both of them are contributed almost equally by the wing lift and wing drag. At high speeds (J≈0.53), the lift is mainly produced during the downstroke and is mainly contributed by the wing drag; the thrust is produced during both the down-and upstrokes, and in the downstroke, is contributed by the wing lift and in the upstrok...

SUMMARYWhen an insect hovers, the centre of mass of its body oscillates around a point in the air and its body angle oscillates around a mean value, because of the periodically varying aerodynamic and inertial forces of the flapping wings. In the present paper, hover flight including body oscillations is simulated by coupling the equations of motion with the Navier-Stokes equations. The equations are solved numerically; periodical solutions representing the hover flight are obtained by the shooting method. Two model insects are considered, a dronefly and a hawkmoth; the former has relatively high wingbeat frequency (n) and small wing mass to body mass ratio, whilst the latter has relatively low wingbeat frequency and large wing mass to body mass ratio. 2 and the other (due to wing inertial force) is proportional to wing mass to body mass ratio. For many insects, the values of 1/cn 2 and wing mass to body mass ratio are much smaller than those of the hawkmoth, and the effects of body oscillation would be rather small; thus it is reasonable to neglect the body oscillations in studying their aerodynamics.

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered-a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier -Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed.

Inspired by the high performance of rotary and insect flapping wings capable of vertical takeoff and landing and hovering (VTOLH), a novel flapping wing rotor (FWR) has been developed by combining the above two types of wing motions. The FWR offers an alternative configuration for micro air vehicles (MAV) of such high flight performance. Unlike the well-studied aerodynamics of rotary and insect-like flapping wing with prescribed wing motion, the aerodynamic lift and efficiency of the FWR associated with optimal kinematics of motion has not been studied in a systematic manner before. This investigation is therefore focused on the FWR optimal kinematic motion in terms of aerodynamic lift and efficiency. Aerodynamic analysis is conducted for a FWR model of aspect ratio 3.6 and wing span 200mm in a range of kinematic parameters. The analysis is based on a quasi-steady aerodynamic model with empirical coefficients and validated by CFD results at Re~3500. For comparison purpose, the analysis includes rotary and insect-like flapping wings in hovering status with the FWR at an equilibrium rotation speed when the thrust equals to drag. The results show that the rotary wing has the greatest power efficiency but the smallest lift coefficient. Whereas the FWR can produce the greatest aerodynamic lift with power efficiency between rotary and insect-like flapping wings. The results provide a quantified guidance for design option of the three types of high performance MAVs together with the optimal kinematics of motion according to flight performance requirement.