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We studied the effects of wing deformation on the aerodynamic forces of wings of hovering hoverflies by solving the Navier-Stokes equations on a dynamically deforming grid, employing the recently measured wing deformation data of hoverflies in free-flight. Three hoverf lies were considered. By taking out the camber deformation and the spanwise twist deformation one by one and by comparing the results of the deformable wing with those of the rigid flat-plate wing (the angle of attack of the rigid flatplate wing was equal to the local angle of attack at the radius of the second moment of wing area of the deformable wing), effects of camber deformation and spanwise twist were identified. The main results are as follows. For the hovering hoverf lies considered, the time courses of the lift, drag and aerodynamic power coefficients of the deformable wing are very similar to their counterparts of the rigid flat-plate wing, although lift of the deformable wing is about 10% larger, and its aerodynamic power required about 5% less than that of the rigid flat-plate wing. The difference in lift is mainly caused by the camber deformation, and the difference in power is mainly caused by the spanwise twist. The main reason that the deformation does not have a very large effect on the aerodynamic force is that, during hovering, the wing operates at a very high angle of attack (about 5odeg) and the flow is separated, and separated flow is not very sensitive to wing deformation. Thus, as a first approximation, the deformable wing in hover flight could be modeled by a rigid flat-plate wing with its angle of attack being equal to the local angle of attack at the radius of second moment of wing area of the deformable wing. [ABSTRACT FROM AUTHOR]

When 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. The main results are as follows. (i) The body mainly has a horizontal oscillation; oscillation in the vertical direction is about 1/6 of that in the horizontal direction and oscillation in pitch angle is relatively small. (ii) For the hawkmoth, the peak-to-peak values of the horizontal velocity, displacement and pitch angle are 0.11 U (U is the mean velocity at the radius of gyration of the wing), 0.22=4mm (c is the mean chord length) and 4 deg., respectively. For the dronefly, the corresponding values are 0.02U, 0.05c=0.15mm and 0.3 deg., much smaller than those of the hawkmoth. (iii) The horizontal motion of the body decreases the relative velocity of the wings by a small amount. As a result, a larger angle of attack of the wing, and hence a larger drag to lift ratio or larger aerodynamic power, is required for hovering, compared with the case of neglecting body oscillations. For the hawkmoth, the angle of attack is about 3.5 deg. larger and the specific power about 9% larger than that in the case of neglecting the body oscillations; for the dronefly, the corresponding values are 0.7 deg. and 2%. (iv) The horizontal oscillation of the body consists of two parts; one (due to wing aerodynamic force) is proportional to 1/cn2 and the other (due to wing inertial force) is proportional to wing mass to body mass ratio. For many insects, the values of 1/cn2 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. [ABSTRACT FROM AUTHOR]

Aerodynamic force generation in hovering flight in a tiny insect, Encarsia formosa, has been studied. The Reynolds number of the flapping wings (based on the mean chord length and the mean flapping velocity) is around 15. The flapping motion of the insect is unique in that the wing pair "claps" together near the end of an upstroke and "flings" open at the beginning of the subsequent downstroke. The method of solving the Navier-Stokes equations over moving overset grids is used. The fling produces a large lift peak at the beginning of the downstroke, the mechanism of which is the generation of a vortex ring containing a downward jet in a short period; the clap produces a large lift peak near the end of the subsequent upstroke by a similar mechanism. Because the vorticity generated during the clap and fling diffuses rapidly, the clap and fling has little influence on the flows in the rest part of the stroke cycle. The mean lift is enough to support the weight of the insect. The lift peaks due to the clap and fling result in more than 30% increase in mean lift coefficient compared to the case of flapping without clap and fling. [ABSTRACT FROM AUTHOR]

Miniature insects fly at very low Reynolds number (Re); low Re means large viscous effect. If flapping as larger insects, sufficient vertical force cannot be produced. We measure the wing kinematics for miniature-insect species of different sizes and compute the aerodynamic forces. The planar upstroke commonly used by larger insects changes to a U-shaped upstroke, which becomes deeper as size or Re decreases. For relatively large miniature insects, the U-shaped upstroke produces a larger vertical force than a planar upstroke by having a larger wing velocity and, for very small ones, the deep U-shaped upstroke produces a large transient drag directed upwards, providing the required vertical force. [ABSTRACT FROM AUTHOR]