Effects of phase lag on the hovering flight of damselfly and dragonfly

Subtle frequency matching reveals resonant phenomenon in the flight of Odonata

In this work, we investigate the connection between the flight flapping frequency and the intrinsic wing properties in Odonata (dragonflies and damselflies). For such large flying insect species, it has been noted that the wingbeat frequency is significantly lower than the structural resonance of the wing itself. However, the structural resonance mechanism is often evoked in the literature for flying and swimming animals as a means to increase locomotion performance. Here, we show that the flight of Odonata is based on a nonlinear mechanism that strongly depends on the wingbeat amplitude. For large flapping amplitudes (as observed in natural flight), the resonant frequency of the wings decreases with respect to its value at low amplitudes to eventually match the wingbeat frequency used in flight. By means of this nonlinear resonance, Odonata keep a strong wing stiffness while benefiting from a passive energy-saving mechanism based on the dynamic softening of the wing.

Unsteady Aerodynamic Forces of Tandem Flapping Wings with Different Forewing Kinematics

Dragonflies can independently control the movement of their forewing and hindwing to achieve the desired flight. In comparison with previous studies that mostly considered the same kinematics of the fore- and hindwings, this paper focuses on the aerodynamic interference of three-dimensional tandem flapping wings when the forewing kinematics is different from that of the hindwing. The effects of flapping amplitude (Φ1), flapping mean angle (ϕ1¯), and pitch rotation duration (Δtr1) of the forewing, together with wing spacing (L) are examined numerically. The results show that Φ1 and ϕ1¯ have a significant effect on the aerodynamic forces of the individual and tandem systems, but Δtr1 has little effect. At a small L, a smaller Φ1, or larger ϕ1¯ of the forewing can increase the overall aerodynamic force, but at a large L, smaller Φ1 or larger ϕ1¯ can actually decrease the force. The flow field analysis shows that Φ1 and ϕ1¯ primarily alter the extent of the impact of the previously revealed narrow channel effect, downwash effect, and wake capture effect, thereby affecting force generation. These findings may provide a direction for designing the performance of tandem flapping wing micro-air vehicles by controlling forewing kinematics.

Investigating the Mechanical Performance of Bionic Wings Based on the Flapping Kinematics of Beetle Hindwings

The beetle, of the order Coleoptera, possesses outstanding flight capabilities. After completing flight, they can fold their hindwings under the elytra and swiftly unfold them again when they take off. This sophisticated hindwing structure is a result of biological evolution, showcasing the strong environmental adaptability of this species. The beetle's hindwings can provide biomimetic inspiration for the design of flapping-wing micro air vehicles (FWMAVs). In this study, the Asian ladybird (Harmonia axyridis Pallas) was chosen as the bionic research object. Various kinematic parameters of its flapping flight were analyzed, including the flight characteristics of the hindwings, wing tip motion trajectories, and aerodynamic characteristics. Based on these results, a flapping kinematic model of the Asian ladybird was established. Then, three bionic deployable wing models were designed and their structural mechanical properties were analyzed. The results show that the structure of wing vein bars determined the mechanical properties of the bionic wing. This study can provide a theoretical basis and technical reference for further bionic wing design.

The Lift Effects of Chordwise Wing Deformation and Body Angle on Low-Speed Flying Butterflies

This work investigates the effects of body angle and wing deformation on the lift of free-flying butterflies. The flight kinematics were recorded using three high-speed cameras, and particle-image velocimetry (PIV) was used to analyze the transient flow field around the butterfly. Parametric studies via numerical simulations were also conducted to examine the force generation of the wing by fixing different body angles and amplifying the chordwise deformation. The results show that appropriately amplifying chordwise deformation enhances wing performance due to an increase in the strength of the vortex and a more stabilized attached vortex. The wing undergoes a significant chordwise deformation, which can generate a larger lift coefficient than that with a higher body angle, resulting in a 14% increase compared to a lower chordwise deformation and body angle. This effect is due to the leading-edge vortex attached to the curved wing, which alters the force from horizontal to vertical. It, therefore, produces more efficient lift during flight. These findings reveal that the chordwise deformation of the wing and the body angle could increase the lift of the butterfly. This work was inspired by real butterfly flight, and the results could provide valuable knowledge about lift generation for designing microaerial vehicles.

Decoupling wing-shape effects of wing-swept angle and aspect ratio on a forward-flying butterfly

The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.

Design optimization and wind tunnel investigation of a flapping system based on the flapping wing trajectories of a beetle's hindwings

To design a flapping-wing micro air vehicle (FWMAV), the hovering flight action of a beetle species (Protaetia brevitarsis) was captured, and various parameters, such as the hindwing flapping frequency, flapping amplitude, angle of attack, rotation angle, and stroke plane angle, were obtained. The wing tip trajectories of the hindwings were recorded and analyzed, and the flapping kinematics were assessed. Based on the wing tip trajectory functions, bioinspired wings and a linkage mechanism flapping system were designed. The critical parameters for the aerodynamic characteristics were investigated and optimized by means of wind tunnel tests, and the artificial flapping system with the best wing parameters was compared with the natural beetle. This work provides insight into how natural flyers execute flight by experimentally duplicating beetle hindwing kinematics and paves the way for the future development of beetle-mimicking FWMAVs.

Tandem-wing interactions on aerodynamic performance inspired by dragonfly hovering

Dragonflies possess two pairs of wings and the interactions between forewing (FW) and hindwing (HW) play an important role in dragonfly flight. The effects of tandem-wing (TW) interactions on the aerodynamic performance of dragonfly hovering have been investigated. Numerical simulations of single-wing hovering without interactions and TW hovering with interactions are conducted and compared. It is found that the TW interactions reduce the lift coefficient of FW and HW by 7.36% and 20.25% and also decrease the aerodynamic power and efficiency. The above effects are mainly caused by the interaction between the vortex structures of the FW and the HW, which makes the pressure of the wing surface and the flow field near the wings change. During the observations of dragonfly flight, it is found that the phase difference (γ) is not fixed. To explore the influence of phase difference on aerodynamic performance, TW hovering with different phase differences is studied. The results show that at γ = 22.5°, dragonflies produce the maximum lift which is more than 20% of the body weight with high efficiency; at γ = 180°, dragonflies generate the same lift as the body weight.

Beneficial wake-capture effect for forward propulsion with a restrained wing-pitch motion of a butterfly

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.

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 (FW) is affected by the incoming flow and an effective angle of attack, whereas that of the hindwing (HW) is dominated by the vortex interaction and induced flow generated by the shed vortex of the FW. Cooperating with the flow interaction, in stable flight, the HW in the lead phase has a larger vertical velocity, whereas the FW in the lead phase has a larger horizontal velocity. Regarding the aerodynamic efficiency, the FW in the lead phase has greater horizontal efficiency, whereas the HW 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 HW in the lead phase to generate a larger lift, thus supporting the larger body weight, whereas a damselfly adopts the FW in the lead phase to have a greater forward velocity, which can supplement the lack of flapping frequency.

Effect of wing-wing interaction coupled with morphology and kinematic features of damselflies

We investigated the effect of the wing-wing interaction, which is one key aspect of flight control, of damselflies (Matrona cyanopteraandEuphaea 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 ofM. cyanopterais larger than that ofE. formosa, the effect of the wing-wing interaction is more constructive. Restricted by the body morphology ofE. 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.

Enhanced lift and thrust via the translational motion between the thorax-abdomen node and the center of mass of a butterfly with a constructive abdominal oscillation

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.

Kinematics Measurement and Power Requirements of Fruitflies at Various Flight Speeds

Energy expenditure is a critical characteristic in evaluating the flight performance of flying insects. To investigate how the energy cost of small-sized insects varies with flight speed, we measured the detailed wing and body kinematics in the full speed range of fruitflies and computed the aerodynamic forces and power requirements of the flies. As flight speed increases, the body angle decreases and the stroke plane angle increases; the wingbeat frequency only changes slightly; the geometrical angle of attack in the middle upstroke increases; the stroke amplitude first decreases and then increases. The mechanical power of the fruitflies at all flight speeds is dominated by aerodynamic power (inertial power is very small), and the magnitude of aerodynamic power in upstroke increases significantly at high flight speeds due to the increase of the drag and the flapping velocity of the wing. The specific power (power required for flight divided by insect weigh) changes little when the advance ratio is below about 0.45 and afterwards increases sharply. That is, the specific power varies with flight speed according to a J-shaped curve, unlike those of aircrafts, birds and large-sized insects which vary with flight speed according to a U-shaped curve.