In this work we studied the differences in flight kinematics and aerodynamics that could relate to differences in wing morphologies of a dragonfly and a damselfly. The damselflies and dragonflies normally fly with the fore wing or hind wing in the lead, respectively. The wing of the damselfly is petiolate, which means that the wing root is narrower than that of the dragonfly. The influence of the biological morphology between the damselfly and the dragonfly on their hovering strategies is worthy of clarification. The flight motions of damselflies and dragonflies in hovering were recorded with two high-speed cameras; we analyzed the differences between their hovering motions using computational fluid dynamics. The distinct mechanisms of the hovering flight of damselflies (Matrona cyanoptera) and dragonflies (Neurothemis ramburii) with different phase lags between fore and hind wings were deduced. The results of a comparison of the differences of wing phases in hovering showed that the rotational effect has an important role in the aerodynamics; the interactions between fore and hind wings greatly affect their vortex structure and flight performance. The wake of a damselfly sheds smoothly because of slender petiolation; a vertical force is generated steadily during the stage of wing translation. Damselflies hover with a longer translational phase and a larger flapping amplitude. In contrast, the root vortex of a dragonfly impedes the shedding of wake vortices in the upstroke, which results in the loss of a vertical force; the dragonfly hence hovers with a large amplitude of wing rotation. These species of Odonata insects developed varied hovering strategies to fit their distinct biological morphologies.

Unlike other insects, a butterfly uses a small amplitude of the wing-pitch motion for flight. From an analysis of the dynamics of real flying butterflies, we show that the restrained amplitude of the wing-pitch motion enhances the wake-capture effect so as to enhance forward propulsion. A numerical simulation refined with experimental data shows that, for a small amplitude of the wing-pitch motion, the shed vortex generated in the downstroke induces air in the wake region to flow towards the wings. This condition enables a butterfly to capture an induced flow and to acquire an additional forward propulsion, which accounts for more than 47% of the thrust generation. When the amplitude of the wing-pitch motion exceeds 45°, the flow induced by the shed vortex drifts away from the wings; it attenuates the wake-capture effect and causes the butterfly to lose a part of its forward propulsion. Our results provide one essential aerodynamic feature for a butterfly to adopt a small amplitude of the wing-pitch motion to enhance the wake-capture effect and forward propulsion. This work clarifies the variation of the flow field correlated with the wing-pitch motion, which is useful in the design of wing kinematics of a micro-aerial vehicle.

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.

Butterflies fly with an abdomen oscillating relative to the thorax; the abdominal oscillation causes body parts to undulate translationally relative to the center of mass of a butterfly, which could generate a significant effect on flight. Based on experimental measurements, we created a numerical model to investigate this effect in a free-flying butterfly (Idea leuconoe). We fixed the motions of wing-flapping and thorax-pitching, and parametrized the abdominal oscillation by varied oscillating phase. To concentrate the analysis on translational dynamics, we used a motion of a thorax-abdomen node, a joint that the thorax and the abdomen rotate about, to express the translational motion of body parts relative to the center of mass. The results show that the abdominal oscillation enhances lift and thrust via the translational motion of the thorax-abdomen node relative to the center of mass. With the abdominal oscillating phase recorded from real butterflies, the abdominal oscillation causes the thorax-abdomen node to move downward relative to the center of mass in downstroke and move upward relative to the center of mass in upstroke. This constructive movement amplifies the wing-flapping speed relative to the center of mass, which enhances the angle of attack and the strength of leading- and trailing-edge vortices on the wings. The wings thereby generate increased values of instantaneous lift and thrust by 50.32% and 32.57% compared to the case of no abdominal oscillation. Natural butterflies are stated to utilize a particular phase offset of abdominal oscillation to fly. With comparing varied oscillating phases, only the abdominal oscillating phase recorded from natural butterflies produces the best constructive effect on the translational motion of thorax-abdomen node, which maximizes the lift and thrust generated on the wings. It clarifies that butterflies use this specific range of abdominal oscillating phase to regulate the translational motion between the thorax-abdomen node and the center of mass to enhance flight. Our work reveals the translational mechanism of the abdominal oscillation, which is as important as the thorax-pitching effect. The findings in this work provide insight into the flight of butterflies and the design of micro aerial vehicles.

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 hence provides insight into the design of a tandem-wing micro-aerial vehicle.