Flying in reverse: kinematics and aerodynamics of a dragonfly in backward free flight

Induced Power Scaling Alone Cannot Explain Griffenfly Gigantism

Paleozoic skies were ruled by extinct odonatopteran insects called "griffenflies," some with wingspans 3 times that of the largest extant dragonflies and 10 times that of common extant dragonflies. Previous studies suggested that flight was possible for larger fliers because of higher atmospheric oxygen levels, which would have increased air density. We use actuator disk theory to evaluate this hypothesis. Actuator disk theory gives similar estimates of induced power as have been estimated for micro-air vehicles based on insect flight. We calculate that for a given mass of griffenfly, and assuming isometry, a higher density atmosphere would only have reduced the induced power required to hover by 11%, which would have supported a flyer 3% larger in linear dimensions. Steady-level forward flight would have further reduced induced power but could only account for a flier 5% larger in linear dimensions. Further accounting for the higher power available due to high-oxygen air and assuming isometry, we calculate that the largest flyer hovering would have been only 1.19 times longer than extant dragonflies. We also consider known allometry in dragonflies and estimated allometry in extinct griffenflies. But such allometry only increases flyer size to 1.22 times longer while hovering. We also consider profile and parasite power, but both would have been higher in denser air and thus would not have enhanced the flyability of larger griffenflies. The largest meganeurid griffenflies might have adjusted flight behaviors to reduce power required. Alternatively, the scaling of flight muscle power may have been sufficient to support the power demands of large griffenflies. In literature estimates, mass-specific power output scales as mass0.24 in extant dragonflies. We need only more conservatively assume that mass-specific muscle power scales with mass0, when combined with higher oxygen concentrations and induced power reductions in higher-density air to explain griffenflies 3.4 times larger than extant odonates. Experimental measurement of flight muscle power scaling in odonates is necessary to test this hypothesis.

Olfactory sampling volume for pheromone capture by wing fanning of silkworm moth: a simulation-based study

Odours used by insects for foraging and mating are carried by the air. Insects induce airflows around them by flapping their wings, and the distribution of these airflows may strongly influence odour source localisation. The flightless silkworm moth, Bombyx mori, has been a prominent insect model for olfactory research. However, although there have been numerous studies on antenna morphology and its fluid dynamics, neurophysiology, and localisation algorithms, the airflow manipulation of the B. mori by fanning has not been thoroughly investigated. In this study, we performed computational fluid dynamics (CFD) analyses of flapping B. mori to analyse this mechanism in depth. A three-dimensional simulation using reconstructed wing kinematics was used to investigate the effects of B. mori fanning on locomotion and pheromone capture. The fanning of the B. mori was found to generate an aerodynamic force on the scale of its weight through an aerodynamic mechanism similar to that of flying insects. Our simulations further indicate that the B. mori guides particles from its anterior direction within the ~ 60° horizontally by wing fanning. Hence, if it detects pheromones during fanning, the pheromone can be concluded to originate from the direction the head is pointing. The anisotropy in the sampling volume enables the B. mori to orient to the pheromone plume direction. These results provide new insights into insect behaviour and offer design guidelines for robots for odour source localisation.

Postural Change of the Annual Cicada (Tibicen linnei) Helps Facilitate Backward Flight

Cicadas are heavy fliers well known for their life cycles and sound production; however, their flight capabilities have not been extensively investigated. Here, we show for the first time that cicadas appropriate backward flight for additional maneuverability. We studied this flight mode using computational fluid dynamics (CFD) simulations based on three-dimensional reconstructions of high-speed videos captured in a laboratory. Backward flight was characterized by steep body angles, high angles of attack, and high wing upstroke velocities. Wing motion occurred in an inclined stroke plane that was fixed relative to the body. Likewise, the directions of the half-stroke-averaged aerodynamic forces relative to the body (local frame) were constrained in a narrow range (<20°). Despite the drastic difference of approximately 90° in body posture between backward and forward flight in the global frame, the aerodynamic forces in both flight scenarios were maintained in a similar direction relative to the body. The forces relative to the body were also oriented in a similar direction when observed during climbs and turns, although the body orientation and motions were different. Hence, the steep posture appropriated during backward flight was primarily utilized for reorienting both the stroke plane and aerodynamic force in the global frame. A consequence of this reorientation was the reversal of aerodynamic functions of the half strokes in backward flight when compared to forward flight. The downstroke generated propulsive forces, while the upstroke generated vertical forces. For weight support, the upstroke, which typically generates lesser forces in forward flight, is aerodynamically active in backward flight. A leading-edge vortex (LEV) was observed on the forewings during both half strokes. The LEV's effect, together with the high upstroke velocity, increased the upstroke's force contribution from 10% of the net forces in forward flight to 50% in backward flight. The findings presented in this study have relevance to the design of micro-aerial vehicles (MAVs), as backward flight is an important characteristic for MAV maneuverability or for taking off from vertical surfaces.

Maneuvering Characteristics of Bilateral Amplitude-Asymmetric Flapping Motion Based on a Bat-Inspired Flexible Wing

Flapping-wing micro air vehicles (FWMAVs) have gained much attention from researchers due to their exceptional performance at low Reynolds numbers. However, the limited understanding of active aerodynamic modulation in flying creatures has hindered their maneuverability from reaching that of their biological counterparts. In this article, experimental investigations were conducted to examine the effect of the bilateral amplitude asymmetry of flexible flapping wings. A reduced bionic model featuring bat-like wings is built, and a dimensionless number ΔΦ* is introduced to scale the degree of bilateral amplitude asymmetry in flapping motion. The experimental results suggest that the bilateral amplitude-asymmetric flapping motion primarily induces maneuvering control forces of coupling roll moment and yaw moment. Also, roll moment and yaw moment have a good linear relationship. To achieve more efficient maneuvers based on this asymmetric motion, it is advisable to maintain ΔΦ* within the range of 0 to 0.4. The magnitude of passive pitching deformation during the downstroke is significantly greater than that during the upstroke. The phase of the peak of the passive pitching angle advances with the increase in flapping amplitude, while the valleys lag. And the proportion of pronation and supination in passive pitching motion cannot be adjusted by changing the flapping amplitude. These findings have important practical relevance for regulating turning maneuvers based on amplitude asymmetry and help to understand the active aerodynamic modulation mechanism through asymmetric wing kinematics.

Effect of stroke plane inclination on the hovering aerodynamic performance of tandem flapping foils

The four-winged form of dragonfly and damselfly allows them to fly with great agility and endurance, which are accomplished by independently controlling the kinematics of each wing. In this study, we performed numerical simulations of two tandem airfoils oscillating along an inclined stroke plane atRe=157. We investigated the effects of the stroke plane angle (β)of forefoil and hindfoil on the aerodynamic performance of dragonflies (or damselflies) hovering flight. Simulations were conducted for parallel and non-parallel stroke planes of forefoil and hindfoil oscillating with three phase differences:ϕ=0o,90oand180o. For parallel stroke planes, the results show that the total lift increases withβ, whereas the total thrust decreases in same condition. In addition, the total lift and thrust decrease with an increase inϕ. The forefoil performance is affected by the flow induced by hindfoil's leading-edge vortices, and the hindfoil interactions with forefoil's wake vortices significantly affect the hindfoil's performance. The findings demonstrate that non-parallel stroke planes exert detrimental effects on the total lift forϕ=0oand90o. However, forϕ=180o, the lift augmentation of 46% is obtained in the case where the forefoil stroke plane angle is smaller than the hindfoil. The results obtained during this investigation can help in optimizing the wing kinematics during the micro air vehicles development.

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.

Role of the caudal peduncle in a fish-inspired robotic model: how changing stiffness and angle of attack affects swimming performance

In fish, the tail is a key element of propulsive anatomy that contributes to thrust during swimming. Fish possess the ability to alter tail stiffness, surface area and conformation. Specifically, the region at the base of the tail, the caudal peduncle, is proposed to be a key location of fish stiffness modulation during locomotion. Most previous analyses have focused on the overall body or tail stiffness, and not on the effects of changing stiffness specifically at the base of the tail in fish and robotic models. We used both computational fluid dynamics analysis and experimental measurements of propulsive forces in physical models with different peduncle stiffnesses to analyze the effect of altering stiffness on the tail angle of attack and propulsive force and efficiency. By changing the motion program input to the tail, we were able to alter the phase relationship between the front and back tail sections between 0° and 330°. Computational simulations showed that power consumption was nearly minimized and thrust production was nearly maximized at the kinematic pattern whereφ= 270°, the approximate phase lag observed in the experimental foils and in free swimming tuna. We observed reduced thrust and efficiency at high angles of attack, suggesting that the tail driven during these motion programs experiences stalling and loss of lift. However, there is no single peduncle stiffness that consistently maximizes performance, particularly in physical models. This result highlights the fact that the optimal caudal peduncle stiffness is highly context dependent. Therefore, incorporating the ability to control peduncle stiffness in future robotic models of fish propulsion promises to increase the ability of robots to approach the performance of fish.

Wing Kinematics and Unsteady Aerodynamics of a Hummingbird Pure Yawing Maneuver

As one of few animals with the capability to execute agile yawing maneuvers, it is quite desirable to take inspiration from hummingbird flight aerodynamics. To understand the wing and body kinematics and associated aerodynamics of a hummingbird performing a free yawing maneuver, a crucial step in mimicking the biological motion in robotic systems, we paired accurate digital reconstruction techniques with high-fidelity computational fluid dynamics (CFD) simulations. Results of the body and wing kinematics reveal that to achieve the pure yaw maneuver, the hummingbird utilizes very little body pitching, rolling, vertical, or horizontal motion. Wing angle of incidence, stroke, and twist angles are found to be higher for the inner wing (IW) than the outer wing (OW). Unsteady aerodynamic calculations reveal that drag-based asymmetric force generation during the downstroke (DS) and upstroke (US) serves to control the speed of the turn, a characteristic that allows for great maneuvering precision. A dual-loop vortex formation during each half-stroke is found to contribute to asymmetric drag production. Wake analysis revealed that asymmetric wing kinematics led to leading-edge vortex strength differences of around 59% between the IW and OW. Finally, analysis of the role of wing flexibility revealed that flexibility is essential for generating the large torque necessary for completing the turn as well as producing sufficient lift for weight support.

Modeling and Control of an Articulated Multibody Aircraft

Insects use dynamic articulation and actuation of their abdomen and other appendages to augment aerodynamic flight control. These dynamic phenomena in flight serve many purposes, including maintaining balance, enhancing stability, and extending maneuverability. The behaviors have been observed and measured by biologists but have not been well modeled in a flight dynamics framework. Biological appendages are generally comparatively large, actuated in rotation, and serve multiple biological functions. Technological moving masses for flight control have tended to be compact, translational, internally mounted and dedicated to the task. Many flight characteristics of biological flyers far exceed any technological flyers on the same scale. Mathematical tools that support modern control techniques to explore and manage these actuator functions may unlock new opportunities to achieve agility. The compact tensor model of multibody aircraft flight dynamics developed here allows unified dynamic and aerodynamic simulation and control of bioinspired aircraft with wings and any number of idealized appendage masses. The demonstrated aircraft model was a dragonfly-like fixed-wing aircraft. The control effect of the moving abdomen was comparable to the control surfaces, with lateral abdominal motion substituting for an aerodynamic rudder to achieve coordinated turns. Vertical fuselage motion achieved the same effect as an elevator, and included potentially useful transient torque reactions both up and down. The best performance was achieved when both moving masses and control surfaces were employed in the control solution. An aircraft with fuselage actuation combined with conventional control surfaces could be managed with a modern optimal controller designed using the multibody flight dynamics model presented here.

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.

Towards locust-inspired gliding wing prototypes for micro aerial vehicle applications

In aviation, gliding is the most economical mode of flight explicitly appreciated by natural fliers. They achieve it by high-performance wing structures evolved over millions of years in nature. Among other prehistoric beings, locust is a perfect example of such natural glider capable of endured transatlantic flights that could inspire a practical solution to achieve similar capabilities on micro aerial vehicles. An investigation in this study demonstrates the effects of haemolymph on the flexibility of several flying insect wings proving that many species exist with further simplistic yet well-designed wing structures. However, biomimicry of such aerodynamic and structural properties is hindered by the limitations of modern as well as conventional fabrication technologies in terms of availability and precision, respectively. Therefore, here we adopt finite-element analysis to investigate the manufacturing-worthiness of a three-dimensional digitally reconstructed locust wing, and propose novel combinations of economical and readily available manufacturing methods to develop the model into prototypes that are structurally similar to their counterparts in nature while maintaining the optimum gliding ratio previously obtained in the aerodynamic simulations. The former is assessed here via an experimental analysis of the flexural stiffness and maximum deformation rate as EI s = 1.34 × 10-4 Nm2, EI c = 5.67 × 10-6 Nm2 and greater than 148.2%, respectively. Ultimately, a comparative study of the mechanical properties reveals the feasibility of each prototype for gliding micro aerial vehicle applications.

Remote radio control of insect flight reveals why beetles lift their legs in flight while other insects tightly fold

In the research and development of micro air vehicles, understanding and imitating the flight mechanism of insects presents a viable way of progressing forward. While research is being conducted on the flight mechanism of insects such as flies and dragonflies, research on beetles that can carry larger loads is limited. Here, we clarified the beetle midlegs' role in the attenuation and cessation of the wingbeat. We anatomically confirmed the connection between the midlegs and the elytra. We also further clarified which pair of legs are involved in the wingbeat attenuation mechanism, and lastly demonstrated free-flight control via remote leg muscle stimulation. Observation of multiple landings using a high-speed camera revealed that the wingbeat stopped immediately after their midlegs were lowered. Moreover, the action of lowering the midleg attenuated and often stopped the wingbeat. A miniature remote stimulation device (backpack) mountable on beetles was designed and utilized for the free-flight demonstration. Beetles in free flight were remotely induced into lowering (swing down) each leg pair via electrical stimulation, and they were found to lose significant altitude only when the midlegs were stimulated. Thus, the results of this study revealed that swinging down of the midlegs played a significant role in beetle wingbeat cessation. In the future, our findings on the wingbeat attenuation and cessation mechanism are expected to be helpful in designing bioinspired micro air vehicles.

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.

The reverse flight of a monarch butterfly (Danaus plexippus) is characterized by a weight-supporting upstroke and postural changes

Butterflies are agile fliers which use inactive and active upstrokes (US). The active US plays a secondary role to the downstroke (DS), generating both thrust and negative vertical force. However, whether their active halfstroke function is fixed or facultative has not been clarified. We showed that during multiple backward flights of an individual, postural adjustments via body angles greater than 90°, with pitch-down and pitch-up motions in the DS and US, respectively, reoriented the stroke plane and caused the reversal of the aerodynamic functions of the halfstrokes compared with forward flight. The US and DS primarily provided weight support and horizontal force, respectively, and a leading edge vortex (LEV) was formed in both halfstrokes. The US's LEV was a Class II LEV extending from wingtip to wingtip, previously reported albeit during the DS in forward flight. The US's net force contribution increased from 32% in forward to 60% in backward flight. Likewise, US weight support increased from 8 to 85%. Despite different trajectories, body postures and force orientations among flight sequences in the global frame, the halfstroke-average forces pointed in a uniform direction relative to the body in both forward and backward flight.

The impact of dragonfly wing deformations on aerodynamic performance during forward flight

Bulk wing kinematics and wing deformations of free-flying dragonflies of the species Pachydiplax longipennis were measured in a controlled environment. Both upright and inverted straight flights were recorded and analyzed. The inverted dragonflies exhibited similar bulk kinematics to the upright specimens in the global frame, but wing deformations were generally consistent in the body-relative frame. The deformations primarily comprised camber during the body-relative downstroke and twist during the body-relative upstroke. Based on these data, models were developed to incorporate the measured kinematics and deformations into computational fluid dynamics simulations. Both isolated and tandem wings were simulated (rigid and deforming in each case), allowing the effects of deformations and wing-wing interactions to be examined independently. During the upstroke the addition of deformation reduced flow separation on the outboard sections of the wing, whereas the impact of the deformation during the downstroke was found to be dependent on the wing kinematics. The simulations of tandem wings indicated that they produce more force than isolated wings, but the wing deformations reduced the impact of this wing-wing interaction. The changes in average lift and thrust induced by the wing deformations were relatively minor and dependent on the flight orientation, but the aerodynamic efficiency of the deforming wings was significantly higher than that of the rigid wings for all examined cases, including the inverted flights for which the deformations were in the opposite (global) sense to the upright flights.

Computational investigation of wing-body interaction and its lift enhancement effect in hummingbird forward flight

A lift enhancement mechanism due to wing-body interaction (WBI) was previously proved to be significant in the forward flight of insect flyers with wide-shape bodies, such as cicada. In order to further explore WBI and its lift enhancement effect in a flapping flight platform with different wing and body shapes, numerical investigations of WBI were performed on the forward flight of a hummingbird in this paper. A high-fidelity computational model of a hummingbird in forward flight was modeled with its geometric complexity. The wing kinematics of flapping flight were prescribed using experimental data from previous literature. An immersed-boundary-method-based incompressible Navier‒Stokes solver was used for the 3D flow simulations of the wing-body system. Analyses on aerodynamic performances and vortex dynamics of three models, including the wing-body (WB), wing-only (WO), and body-only (BO) models, were made to examine the effect of WBI. Results have shown significant overall lift enhancement (OLE) due to WBI. The total lift force of the WB model increased by 29% compared with its WO/BO counterparts. Vortex dynamics results showed formations of unique body vortex pairs on the dorsal thorax of hummingbird where low-pressure zones were created to generate more body lift. Significant interactions between body vortex and leading-edge vortex (LEV) were observed, resulting in strengthened LEVs near the wing root and enhanced wing lift generation during downstroke. Parametric studies showed strong OLEs over wide ranges of body angle and advance ratio, respectively. The contribution of OLE from the hummingbird body increased with increasing body angle, and the wing pair's contribution increased as advance ratio increased. Results from this paper supported that lift enhancement due to WBI is potentially a general mechanism adopted by different kinds of flapping-wing flyers, and demonstrated the potential of WBI in the design of flapping-wing micro aerial vehicle (MAV) that pursue higher performance.