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We investigated the effect of the wing–wing interaction, which is one key aspect of flight control, of damselflies (Matrona cyanoptera and Euphaea formosa) in forward flight that relates closely to their body morphologies and wing kinematics. We used two high-speed cameras aligned orthogonally to measure the flight motions and adopted 3D numerical simulation to analyze the flow structures and aerodynamic efficiencies. The results clarify the effects of wing–wing interactions, which are complicated combinations of biological morphology, wing kinematics and fluid dynamics. As the amplitude of the hindwing of M. cyanoptera is larger than that of E. formosa, the effect of the wing–wing interaction is more constructive. Restricted by the body morphology of E. formosa, the flapping range of the hindwing is below the body. With the forewing in the lead, the hindwing is farther from the forewing, which is not susceptible to the wake of the forewing, and enables superior lift and thrust. Because of the varied rotational motions, the different shed direction of the wakes of the forewings causes the optimal thrust to occur in different wing phases. Because of its biological limitations, a damselfly can use an appropriate phase to fulfill the desired flight mode. The wing–wing interaction is a compromise between lift efficiency and thrust efficiency. The results reveal that a damselfly with the forewing in the lead can have an effective aerodynamic performance in flight. As an application, in the design concept of a micro-aircraft, increasing the amplitude of the hindwing might enhance the wing–wing interaction, thus controlling the flight modes.

We reveal the hindwing kinematics of a damselfly that are optimal for the thrust efficiency, which is a major concern of a bio-inspired micro-aerial vehicle. The parameters of the hindwing kinematics include stroke-plane angle, rotational duration, and wing phase. We developed a numerical self-propulsion model to investigate the thrust efficiency. The correlation analysis and optimal analysis were used to investigate the relation between varied hindwing kinematics and thrust efficiency. The results show that the optimal wing kinematics of the hindwing occur at a large stroke-plane angle and a small rotational duration, in which the thrust efficiency might increase up to 22 % compared with the original motion of the hindwing. The stroke-plane angle is highly positively correlated with thrust efficiency, whereas the rotational duration is moderately negatively correlated; the wing phase has the least correlation. The flow-field analysis indicates that a large stroke-plane angle combined with a small rotational duration has a weak forewing-hindwing interaction, generating a small resulting force on the hindwing, but the force comprises a small negative horizontal force, which hence increases the thrust efficiency. In a flight strategy for a micro-aerial vehicle, a large stroke-plane angle combined with a small rotational duration yields an optimal thrust efficiency, which is suitable for a flight of long duration. A small stroke-plane angle combined with a large rotation is suitable for hovering flight because it leads to a large negative horizontal force and a small vertical force. This work provides insight into the design of a tandem-wing micro-aerial vehicle.