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Flight maneuver of a damselfly with phase modulation of the wings.

We developed a numerical model for four-wing self-propulsion to calculate effectively the flight velocity generated with varied wing motions, which satisfactorily verified biological experiments. Through this self-propulsion model, we analyzed the flight velocity of a damselfly (Matrona cyanoptera) at varied phases. The results show that after phase modulation of the wings, the aerodynamic performance of the forewing is affected by the incoming flow and an effective angle of attack, whereas that of the hindwing is dominated by the vortex interaction and induced flow generated by the shed vortex of the forewing. Cooperating with the flow interaction, in stable flight, the hindwing in the lead phase has a larger vertical velocity, whereas the forewing in the lead phase has a larger horizontal velocity. Regarding the aerodynamic efficiency, the forewing in the lead phase has greater horizontal efficiency, whereas the hindwing in the lead phase has greater vertical efficiency; the overall efficiency does not vary with the phase. This work interprets that a dragonfly adopts the hindwing in the lead phase to generate a larger lift, thus supporting the larger body weight, whereas a damselfly adopts the forewing in the lead phase to have a greater forward velocity, which can supplement the lack of flapping frequency.