Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach

Insect wings are deformable structures that change shape passively and dynamically owing to inertial and aerodynamic forces during flight. It is still unclear how the three-dimensional and passive change of wing kinematics owing to inherent wing flexibility contributes to unsteady aerodynamics and energetics in insect flapping flight. Here, we perform a systematic fluid-structure interaction based analysis on the aerodynamic performance of a hovering hawkmoth, Manduca, with an integrated computational model of a hovering insect with rigid and flexible wings. Aerodynamic performance of flapping wings with passive deformation or prescribed deformation is evaluated in terms of aerodynamic force, power and efficiency. Our results reveal that wing flexibility can increase downwash in wake and hence aerodynamic force: first, a dynamic wing bending is observed, which delays the breakdown of leading edge vortex near the wing tip, responsible for augmenting the aerodynamic force-production; second, a combination of the dynamic change of wing bending and twist favourably modifies the wing kinematics in the distal area, which leads to the aerodynamic force enhancement immediately before stroke reversal. Moreover, an increase in hovering efficiency of the flexible wing is achieved as a result of the wing twist. An extensive study of wing stiffness effect on aerodynamic performance is further conducted through a tuning of Young's modulus and thickness, indicating that insect wing structures may be optimized not only in terms of aerodynamic performance but also dependent on many factors, such as the wing strength, the circulation capability of wing veins and the control of wing movements.     

Numerical investigation of the aerodynamic characteristics of a hovering Coleopteran insect

The aerodynamic characteristics of the Coleopteran beetle species Epilachna quadricollis, a species with flexible hind wings and stiff elytra (fore wings), are investigated in terms of hovering flight. The flapping wing kinematics of the Coleopteran insect are modeled through experimental observations with a digital high-speed camera and curve fitting from an ideal harmonic kinematics model. This model numerically simulates flight by estimating a cross section of the wing as a two-dimensional elliptical plane. There is currently no detailed study on the role of the elytron or how the elytron-hind wing interaction affects aerodynamic performance. In the case of hovering flight, the relatively small vertical or horizontal forces generated by the elytron suggest that the elytron makes no significant contribution to aerodynamic force.     

How Could Beetle＇s Elytra Support Their Own Weight during Forward Flight？

The aerodynamic role of the elytra during a beetle＇s flapping motion is not well-elucidated, although it is well-recognized that the evolution of elytra has been a key in the success of coleopteran insects due to their protective function. An experimental study on wing kinematics reveals that for almost concurrent flapping with the hind wings, the flapping angle of the elytra is 5 times smaller than that of the hind wings. Then, we explore the aerodynamic forces on elytra in free forward flight with and without an effect of elytron-hind wing interaction by three-dimensional numerical simulation. The numerical results show that vertical force generated by the elytra without interaction is not sufficient to support even its own weight. However, the elytron-hind wing interaction improves the vertical force on the elytra up to 80%; thus, the total vertical force could fully support its own weight. The interaction slightly increases the vertical force on the hind wind by 6% as well.     

Structural dynamics and aerodynamics measurements of biologically inspired flexible flapping wings

Flapping wing flight as seen in hummingbirds and insects poses an interesting unsteady aerodynamic problem: coupling of wing kinematics, structural dynamics and aerodynamics. There have been numerous studies on the kinematics and aerodynamics in both experimental and computational cases with both natural and artificial wings. These studies tend to ignore wing flexibility; however, observation in nature affirms that passive wing deformation is predominant and may be crucial to the aerodynamic performance. This paper presents a multidisciplinary experimental endeavor in correlating a flapping micro air vehicle wing's aeroelasticity and thrust production, by quantifying and comparing overall thrust, structural deformation and airflow of six pairs of hummingbird-shaped membrane wings of different properties. The results show that for a specific spatial distribution of flexibility, there is an effective frequency range in thrust production. The wing deformation at the thrust-productive frequencies indicates the importance of flexibility: both bending and twisting motion can interact with aerodynamic loads to enhance wing performance under certain conditions, such as the deformation phase and amplitude. By measuring structural deformations under the same aerodynamic conditions, beneficial effects of passive wing deformation can be observed from the visualized airflow and averaged thrust. The measurements and their presentation enable observation and understanding of the required structural properties for a thrust effective flapping wing. The intended passive responses of the different wings follow a particular pattern in correlation to their aerodynamic performance. Consequently, both the experimental technique and data analysis method can lead to further studies to determine the design principles for micro air vehicle flapping wings.     

Vortexlet models of flapping flexible wings show tuning for force production and control

Insect wings are compliant structures that experience deformations during flight. Such deformations have recently been shown to substantially affect induced flows, with appreciable consequences to flight forces. However, there are open questions related to the aerodynamic mechanisms underlying the performance benefits of wing deformation, as well as the extent to which such deformations are determined by the boundary conditions governing wing actuation together with mechanical properties of the wing itself. Here we explore aerodynamic performance parameters of compliant wings under periodic oscillations, subject to changes in phase between wing elevation and pitch, and magnitude and spatial pattern of wing flexural stiffness. We use a combination of computational structural mechanics models and a 2D computational fluid dynamics approach to ask how aerodynamic force production and control potential are affected by pitch/elevation phase and variations in wing flexural stiffness. Our results show that lift and thrust forces are highly sensitive to flexural stiffness distributions, with performance optima that lie in different phase regions. These results suggest a control strategy for both flying animals and engineering applications of micro-air vehicles.     

Time-Varying Wing-Twist Improves Aerodynamic Efficiency of Forward Flight in Butterflies

Insect wings can undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. Here we use computational models derived from experiments on free-flying butterflies to understand the effect of time-varying twist and camber on the aerodynamic performance of these insects. High-speed videogrammetry is used to capture the wing kinematics, including deformation, of a Painted Lady butterfly (Vanessa cardui) in untethered, forward flight. These experimental results are then analyzed computationally using a high-fidelity, three-dimensional, unsteady Navier-Stokes flow solver. For comparison to this case, a set of non-deforming, flat-plate wing (FPW) models of wing motion are synthesized and subjected to the same analysis along with a wing model that matches the time-varying wing-twist observed for the butterfly, but has no deformation in camber. The simulations show that the observed butterfly wing (OBW) outperforms all the flat-plate wings in terms of usable force production as well as the ratio of lift to power by at least 29% and 46%, respectively. This increase in efficiency of lift production is at least three-fold greater than reported for other insects. Interestingly, we also find that the twist-only-wing (TOW) model recovers much of the performance of the OBW, demonstrating that wing-twist, and not camber is key to forward flight in these insects. The implications of this on the design of flapping wing micro-aerial vehicles are discussed.     

Aerodynamic Interactions Between Wing and Body of a Model Insect in Forward Flight and Maneuvers

The aerodynamic interactions between the body and the wings of a model insect in forward flight and maneuvers are studied using the method of numerically solving the Navier-Stokes equations over moving overset grids. Three cases are considered, including a complete insect, wing pair only and body only. By comparing the results of these cases, the interaction effect between the body and the wing pair can be identified. The changes in the force and moment coefficients of the wing pair due to the presence of the body are less than 4.5% of the mean vertical force coefficient of the model insect; the changes in the aerodynamic force coefficients of the body due to the presence of the wings are less than 5.0% of the mean vertical force coefficient of the model insect. The results of this paper indicate that in studying the aerodynamics and flight dynamics of a flapping insect in forward flight or maneuver, separately computing (or measuring) the aerodynamic forces and moments on the wing pair and on the body could be a good approximation.     

Automated Kinematics Measurement and Aerodynamics of a Bioinspired Flapping Rotary Wing

A physical model for a micro air vehicle with Flapping Rotary Wings (FRW) is investigated by measuring the wing kinematics in trim conditions and computing the corresponding aerodynamic force using computational fluid dynamics.In order to capture the motion image and reconstruct the positions and orientations of the wing,the photogrammetric method is adopted and a method for automated recognition of the marked points is developed.The characteristics of the realistic wing kinematics are presented.The results show that the non-dimensional rotating speed is a linear function of non-dimensional flapping frequency regardless of the initial angles of attack.Moreover,the effects of wing kinematics on aerodynamic force production and the underlying mechanism are analyzed.The results show that the wing passive pitching caused by elastic deformation can significantly enhance lift production.The Strouhal number of the FRW is much higher than that of general flapping wings,indicating the stronger unsteadiness of flows in FRW.     

Resilin in dragonfly and damselfly wings and its implications for wing flexibility

Although there is mounting evidence that passive mechanical dynamics of insect wings play an integral role in insect flight, our understanding of the structural details underlying insect wing flexibility remains incomplete. Here, we use comparative morphological and mechanical techniques to illuminate the function and diversity of two mechanisms within Odonata wings presumed to affect dynamic wing deformations: flexible resilin vein‐joints and cuticular spikes. Mechanical tests show that joints with more resilin have lower rotational stiffness and deform more in response to a load applied to an intact wing. Morphological studies of 12 species of Odonata reveal that resilin joints and cuticular spikes are widespread taxonomically, yet both traits display a striking degree of morphological and functional diversity that follows taxonomically distinct patterns. Interestingly, damselfly wings (suborder Zygoptera) are mainly characterized by vein‐joints that are double‐sided (containing resilin both dorsally and ventrally), whereas dragonfly wings (suborder Epiprocta) are largely characterized by single‐sided vein‐joints (containing resilin either ventrally or dorsally, but not both). The functional significance and diversity of resilin joints and cuticular spikes could yield insight into the evolutionary relationship between form and function of wings, as well as revealing basic principles of insect wing mechanical design. J. Morphol., 2011. © 2011 Wiley‐Liss, Inc.     

Particle-Image Velocimetry and Force Measurements of Leading-Edge Serrations on Owl-Based Wing Models

High-resolution Particle-Image Velocimetry （PIV） and time-resolved force measurements were performed to analyze the impact of the comb-like structure on the leading edge of barn owl wings on the flow field and overall aerodynamic performance. The Reynolds number was varied in the range of 40,000 to 120,000 and the range of angle of attack was 0° to 6° for the PIV and -15° to ＋20° for the force measurements to cover the full flight envelope of the owl. As a reference, a wind-tunnel model which possessed a geometry based on the shape of a typical barn owl wing without any owl-specific adaptations was built, and measurements were performed in the aforementioned Reynolds number and angle of attack： range. This clean wing model shows a separation bubble in the distal part of the wing at higher angles of attack. Two types of comb-like structures, i.e., artificial serrations, were manufactured to model the owl＇s leading edge with respect to its length, thickness, and material properties. The artificial structures were able to reduce the size of the separation region and additionally cause a more uniform size of the vortical structures shed by the separation bubble within the Reynolds number range investigated, resulting in stable gliding flight independent of the flight velocity. However, due to increased drag coefficients in conjunction with similar lift coefficients, the overall aerodynamic performance, i.e., lift-to-drag ratio is reduced for the serrated models. Nevertheless, especially at lower Reynolds numbers the stabilizing effect of the uniform vortex size outperforms the lower aerodynamic performance.     

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones—micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 10⁴–10⁵ or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems.This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.     

Kinematic compensation for wing loss in flying damselflies

Flying insects can tolerate substantial wing wear before their ability to fly is entirely compromised. In order to keep flying with damaged wings, the entire flight apparatus needs to adjust its action to compensate for the reduced aerodynamic force and to balance the asymmetries in area and shape of the damaged wings. While several studies have shown that damaged wings change their flapping kinematics in response to partial loss of wing area, it is unclear how, in insects with four separate wings, the remaining three wings compensate for the loss of a fourth wing. We used high-speed video of flying blue-tailed damselflies (Ischnura elegans) to identify the wingbeat kinematics of the two wing pairs and compared it to the flapping kinematics after one of the hindwings was artificially removed. The insects remained capable of flying and precise maneuvering using only three wings. To compensate for the reduction in lift, they increased flapping frequency by 18 ± 15.4% on average. To achieve steady straight flight, the remaining intact hindwing reduced its flapping amplitude while the forewings changed their stroke plane angle so that the forewing of the manipulated side flapped at a shallower stroke plane angle. In addition, the angular position of the stroke reversal points became asymmetrical. When the wingbeat amplitude and frequency of the three wings were used as input in a simple aerodynamic model, the estimation of total aerodynamic force was not significantly different (paired t-test, p = 0.73) from the force produced by the four wings during normal flight. Thus, the removal of one wing resulted in adjustments of the motions of the remaining three wings, exemplifying the precision and plasticity of coordination between the operational wings. Such coordination is vital for precise maneuvering during normal flight but it also provides the means to maintain flight when some of the wings are severely damaged.     

Modulation of leading edge vorticity and aerodynamic forces in flexible flapping wings

In diverse biological flight systems, the leading edge vortex has been implicated as a flow feature of key importance in the generation of flight forces. Unlike fixed wings, flapping wings can translate at higher angles of attack without stalling because their leading edge vorticity is more stable than the corresponding fixed wing case. Hence, the leading edge vorticity has often been suggested as the primary determinant of the high forces generated by flapping wings. To test this hypothesis, it is necessary to modulate the size and strength of the leading edge vorticity independently of the gross kinematics while simultaneously monitoring the forces generated by the wing. In a recent study, we observed that forces generated by wings with flexible trailing margins showed a direct dependence on the flexural stiffness of the wing. Based on that study, we hypothesized that trailing edge flexion directly influences leading edge vorticity, and thereby the magnitude of aerodynamic forces on the flexible flapping wings. To test this hypothesis, we visualized the flows on wings of varying flexural stiffness using a custom 2D digital particle image velocimetry system, while simultaneously monitoring the magnitude of the aerodynamic forces. Our data show that as flexion decreases, the magnitude of the leading edge vorticity increases and enhances aerodynamic forces, thus confirming that the leading edge vortex is indeed a key feature for aerodynamic force generation in flapping flight. The data shown here thus support the hypothesis that camber influences instantaneous aerodynamic forces through modulation of the leading edge vorticity.     

Design and Demonstration of Insect Mimicking Foldable Artificial Wing Using Four-Bar Linkage Systems

In this work, we develop an artificial foldable wing that mimics the hind wing of a beetle （Allomyrina dichotoma）. In real flight, the beetle unfolds forewings and hind wings, and maintains the unfolded configuration unless it is exhausted. The artificial wing has to be able to maintain a fully unfolded configuration while flapping at a desirable flapping frequency. The artificial foldable hind wing developed in this work is based on two four-bar linkages which adapt the behaviors of the beetle＇s hind wing. The four-bar-linkages are designed to mimic rotational motion of the wing base and the vein folding/unfolding motion of the beetle＇s hind wing. The behavior of the artificial wings, which are installed in a flapping-wing system, is observed using a high-speed camera. The observation shows that the wing could maintain a fully unfolded configuration during flapping motion. A series of thrust measurements are also conducted to estimate the force generated by the flapping-wing system with foldable artificial wings. Although the artificial foldable wings give added burden to the flapping-wing system because of its weight, the thrust measurement results show that the flapping-wing system could still generate reasonable thrust.     

Constraints on the wing morphology of pterosaurs

Animals that fly must be able to do so over a huge range of aerodynamic conditions, determined by weather, wind speed and the nature of their environment. No single parameter can be used to determine-let alone measure-optimum flight performance as it relates to wing shape. Reconstructing the wings of the extinct pterosaurs has therefore proved especially problematic: these Mesozoic flying reptiles had a soft-tissue membranous flight surface that is rarely preserved in the fossil record. Here, we review basic mechanical and aerodynamic constraints that influenced the wing shape of pterosaurs, and, building on this, present a series of theoretical modelling results. These results allow us to predict the most likely wing shapes that could have been employed by these ancient reptiles, and further show that a combination of anterior sweep and a reflexed proximal wing section provides an aerodynamically balanced and efficient theoretical pterosaur wing shape, with clear benefits for their flight stability.     

Nanomechanical properties of wing membrane layers in the house cricket (Acheta domesticus Linnaeus)

Many insect wings change shape dynamically during the wingbeat cycle, and these deformations have the potential to confer energetic and aerodynamic benefits during flight. Due to the lack of musculature within the wing itself, the changing form of the wing is determined primarily by its passive response to inertial and aerodynamic forces. This response is in part controlled by the wing’s mechanical properties, which vary across the membrane to produce regions of differing stiffness. Previous studies of wing mechanical properties have largely focused on surface or bulk measurements, but this ignores the layered nature of the wing. In our work, we investigated the mechanical properties of the wings of the house cricket (Acheta domesticus) with the aim of determining differences between layers within the wing. Nanoindentation was performed on both the surface and the interior layers of cross-sectioned samples of the wing to measure the Young’s modulus and hardness of the outer- and innermost layers. The results demonstrate that the interior of the wing is stiffer than the surface, and both properties vary across the wing.     

Skipping flights in Ypthima butterflies (Lepidoptera: Nymphalidae)

The skipping flight patterns of three species of Ypthima (Lepidoptera: Nymphalidae) were analyzed using high‐speed video recordings to clarify how wings move and how driving forces are produced. All three species showed a flight pattern that includes a pause that accounts for about 50% of a flap cycle when their wings completely close after each upstroke. The observed pause causes the “skipping” flight trajectory based on the clap–fling mechanism. Pause duration was correlated with upstroke wing motion, suggesting the contribution of the latter to a long pause duration. This is also supported by the temporal relationship between the wing and body motions. The aerodynamic power necessary for the pause flight was calculated for the three species.     

Flow Visualization of Rhinoceros Beetle (Trypoxylus dichotomus) in Free Flight

Aerodynamic characteristics of the beetle,Trypoxylus dichotomus,which has a pair of elytra (forewings) and flexible hind wings,are investigated.Visualization experiments were conducted for various flight conditions of a beetle,Trypoxylus dichotomus:free,tethered,hovering,forward and climbing flights.Leading edge,trailing edge and tip vortices on both wings were observed clearly.The leading edge vortex was stable and remained on the top surface of the elytron for a wide interval during the downstroke of free forward flight.Hence,the elytron may have a considerable role in lift force generation of the beetle.In addition,we reveal a suction phenomenon between the gaps of the hind wing and the elytron in upstroke that may improve the positive lift force on the hind wing.We also found the reverse clap-fling mechanism of the T.dichotomus beetle in hovering flight.The hind wings touch together at the beginning of the upstroke.The vortex generation,shedding and interaction give a better understanding of the detailed aerodynamic mechanism of beetle flight.     

Upstroke wing flexion and the inertial cost of bat flight

Flying vertebrates change the shapes of their wings during the upstroke, thereby decreasing wing surface area and bringing the wings closer to the body than during downstroke. These, and other wing deformations, might reduce the inertial cost of the upstroke compared with what it would be if the wings remained fully extended. However, wing deformations themselves entail energetic costs that could exceed any inertial energy savings. Using a model that incorporates detailed three-dimensional wing kinematics, we estimated the inertial cost of flapping flight for six bat species spanning a 40-fold range of body masses. We estimate that folding and unfolding comprises roughly 44 per cent of the inertial cost, but that the total inertial cost is only approximately 65 per cent of what it would be if the wing remained extended and rigid throughout the wingbeat cycle. Folding and unfolding occurred mostly during the upstroke; hence, our model suggests inertial cost of the upstroke is not less than that of downstroke. The cost of accelerating the metacarpals and phalanges accounted for around 44 per cent of inertial costs, although those elements constitute only 12 per cent of wing weight. This highlights the energetic benefit afforded to bats by the decreased mineralization of the distal wing bones.     

The Role of Soft Vein Joints in Dragonfly Flight

Dragonflies are excellent flyers among insects and their flight ability is closely related to the architecture and material properties of their wings.The veins are main structure components of a dragonfly wing,which are found to be connected by resilin with high elasticity at some joints.A three-dimensional (3D) finite element model of dragonfly wing considering the soft vein joints is developed,with some simplifications.Passive deformation under aerodynamic loads and active flapping motion of the wing are both studied.The functions of soft vein joints in dragonfly flight are concluded.In passive deformation,the chordwise flexibility is improved by soft vein joints and the wing is cambered under loads,increasing the action area with air.In active flapping,the wing rigidity in spanwise direction is maintained to achieve the required amplitude.As a result,both the passive deformation and the active control of flapping work well in dragonfly flight.The present study may also inspire the design of biomimetic Flapping Micro Air Vehicles (FMAVs).