SUMMARY The aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. Available morphological and stroke-kinematic parameters of dragonfly (Aeshna juncea) are used for the model dragonfly. Six advance ratios (J; ranging from 0 to 0.75) and, at each J, four forewing-hindwing phase angle differences(γd; 180°, 90°, 60° and 0°) are considered. The mean vertical force and thrust are made to balance the weight and body-drag, respectively, by adjusting the angles of attack of the wings, so that the flight could better approximate the real flight. At hovering and low J (J=0, 0.15), the model dragonfly uses separated flows or leading-edge vortices (LEV) on both the fore- and hindwing downstrokes; at medium J (J=0.30, 0.45), it uses the LEV on the forewing downstroke and attached flow on the hindwing downstroke; at high J (J=0.6, 0.75), it uses attached flows on both fore- and hindwing downstrokes. (The upstrokes are very lightly loaded and, in general, the flows are attached.) At a given J, at γd=180°, there are two vertical force peaks in a cycle, one in the first half of the cycle, produced mainly by the hindwing downstroke, and the other in the second half of the cycle, produced mainly by the forewing downstroke; atγ d=90°, 60° and 0°, the two force peaks merge into one peak. The vertical force is close to the resultant aerodynamic force[because the thrust (or body-drag) is much smaller than vertical force (or the weight)]. 55-65% of the vertical force is contributed by the drag of the wings. The forewing-hindwing interaction is detrimental to the vertical force (and resultant force) generation. At hovering, the interaction reduces the mean vertical force (and resultant force) by 8-15%, compared with that without interaction; as J increases, the reduction generally decreases (e.g. at J=0.6 and γd=90°, it becomes 1.6%). A possible reason for the detrimental interaction is as follows: each of the wings produces a mean vertical force coefficient close to half that needed for weight support, and a downward flow is generated in producing the vertical force; thus, in general, a wing moves in the downwash-velocity field induced by the other wing, reducing its aerodynamic forces.

SUMMARY The longitudinal stabilization control of a hovering model insect was studied using the method of computational fluid dynamics to compute the stability and control derivatives, and the techniques of eigenvalue and eigenvector analysis and modal decomposition, for solving the equations of motion (morphological and certain kinematical data of hoverflies were used for the model insect). The model insect has the same three natural modes of motion as those reported recently for a hovering bumblebee: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. Controllability analysis shows that although unstable, the flight is controllable. For stable hovering, the unstable oscillatory mode needs to be stabilized and the slow subsidence mode needs stability augmentation. The former can be accomplished by feeding back pitch attitude, pitch rate and horizontal velocity to produce \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\delta}{\bar{{\phi}}}\) \end{document} orδα 2; the latter by feeding back vertical velocity to produce δΦ or δα1 (δΦ, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\delta}{\bar{{\phi}}}\) \end{document}, δα1and δα2 denote control inputs: δΦ and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\delta}{\bar{{\phi}}}\) \end{document} represent changes in stroke amplitude and mean stroke angle, respectively; δα1represents an equal change whilst δα2 a differential change in the geometrical angles of attack of the downstroke and upstroke).

The lift and power requirements of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. The graph of power against flight speed is U-shaped, suggesting that a dragonfly might have a preferred cruising speed. Considerable variation in the relative phase between fore- and hindwings results in only very small change in power requirement. This suggests theat the forewing-hingwing interaction is weak and furthermore, might explain why phase angles ranging from to are employed by dragonflies in hovering and forward flight.