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.     

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.     

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’.     

Aerodynamics of a bio-inspired flexible flapping-wing micro air vehicle

MAVs (micro air vehicles) with a maximal dimension of 15 cm and nominal flight speeds of around 10 m s?1, operate in a Reynolds number regime of 10? or lower, in which most natural flyers including insects, bats and birds fly. Furthermore, due to their light weight and low flight speed, the MAVs' flight characteristics are substantially affected by environmental factors such as wind gust. Like natural flyers, the wing structures of MAVs are often flexible and tend to deform during flight. Consequently, the aero/fluid and structural dynamics of these flyers are closely linked to each other, making the entire flight vehicle difficult to analyze. We have recently developed a hummingbird-inspired, flapping flexible wing MAV with a weight of 2.4-3.0 g and a wingspan of 10-12 cm. In this study, we carry out an integrated study of the flexible wing aerodynamics of this flapping MAV by combining an in-house computational fluid dynamic (CFD) method and wind tunnel experiments. A CFD model that has a realistic wing planform and can mimic realistic flexible wing kinematics is established, which provides a quantitative prediction of unsteady aerodynamics of the four-winged MAV in terms of vortex and wake structures and their relationship with aerodynamic force generation. Wind tunnel experiments further confirm the effectiveness of the clap and fling mechanism employed in this bio-inspired MAV as well as the importance of the wing flexibility in designing small flapping-wing MAVs.     

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.     

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).     

A Quasi-Steady Lifting Line Theory for Insect-Like Hovering Flight

A novel lifting line formulation is presented for the quasi-steady aerodynamic evaluation of insect-like wings in hovering flight. The approach allows accurate estimation of aerodynamic forces from geometry and kinematic information alone and provides for the first time quantitative information on the relative contribution of induced and profile drag associated with lift production for insect-like wings in hover. The main adaptation to the existing lifting line theory is the use of an equivalent angle of attack, which enables capture of the steady non-linear aerodynamics at high angles of attack. A simple methodology to include non-ideal induced effects due to wake periodicity and effective actuator disc area within the lifting line theory is included in the model. Low Reynolds number effects as well as the edge velocity correction required to account for different wing planform shapes are incorporated through appropriate modification of the wing section lift curve slope. The model has been successfully validated against measurements from revolving wing experiments and high order computational fluid dynamics simulations. Model predicted mean lift to weight ratio results have an average error of 4% compared to values from computational fluid dynamics for eight different insect cases. Application of an unmodified linear lifting line approach leads on average to a 60% overestimation in the mean lift force required for weight support, with most of the discrepancy due to use of linear aerodynamics. It is shown that on average for the eight insects considered, the induced drag contributes 22% of the total drag based on the mean cycle values and 29% of the total drag based on the mid half-stroke values.     

Centripetal Acceleration Reaction: An Effective and Robust Mechanism for Flapping Flight in Insects

Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation. Here, we formulate a force partitioning method (FPM) and implement it within a computational fluid dynamic model to provide an unambiguous and physically insightful division of aerodynamic force into components associated with wing kinematics, vorticity, and viscosity. Application of the FPM to hawkmoth and fruit fly flight shows that the leading-edge vortex is the dominant mechanism for lift generation for both these insects and contributes between 72–85% of the net lift. However, there is another, previously unidentified mechanism, the centripetal acceleration reaction, which generates up to 17% of the net lift. The centripetal acceleration reaction is similar to the classical inviscid added-mass in that it depends only on the kinematics (i.e. accelerations) of the body, but is different in that it requires the satisfaction of the no-slip condition, and a combination of tangential motion and rotation of the wing surface. Furthermore, the classical added-mass force is identically zero for cyclic motion but this is not true of the centripetal acceleration reaction. Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization. This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.     

Flight of Sharovipteryx mirabilis: the world's first delta-winged glider

The 225 million-year-old reptile Sharovipteryx mirabilis was the world's first delta-winged glider; this remarkable animal had a flight surface composed entirely of a hind-limb membrane. We use standard delta-wing aerodynamics to reconstruct the flight of S. mirabilis demonstrating that wing shape could have been controlled simply by protraction of the femora at the knees, and by variation in incidence of a small forelimb canard. Our method has allowed us to address the question of how identifying realistic glide performance can be used to set limits on aerodynamic design in this small animal. Our novel interpretation of the bizarre flight mode of S. mirabilis is the first based directly on interpretation of the fossil itself and the first grounded in aerodynamics.     

How do birds' tails work? Delta-wing theory fails to predict tail shape during flight.

Birds appear to use their tails during flight, but until recently the aerodynamic role that tails fulfil was largely unknown. In recent years delta-wing theory, devised to predict the aerodynamics of high-performance aircraft, has been applied to the tails of birds and has been successful in providing a model for the aerodynamics of a bird's tail. This theory now provides the conventional explanation for how birds' tails work. A delta-wing theory (slender-wing theory) has been used, as part of a variable-geometry model to predict how tail and wing shape should vary during flight at different airspeeds. We tested these predictions using barn swallows flying in a wind tunnel. We show that the predictions are not quantitatively well supported. This suggests that a new theory or a modified version of delta-wing theory is needed to adequately explain the way in which morphology varies during flight.     

Wing design and scaling of flying fish with regard to flight performance

Fin and body dimensions of six genera of flying fish (Exocoetidae) were examined to study variation in morphological parameters in relation to aerodynamics performance. The fins are modified as wings for gliding flight. Fin area and fin span increase with increasing body mass, whereas the percentage of wing area contributed by the pectoral fins and the percentage of the caudal fin area contributed by the hypocaudal lobe remain constant. The aerodynamic design of flying fish approximates the monoplane-biplane classification proposed by Breder (1930). Scaling relationships for wing loading and aspect ratio indicate that wing morphology in the Exocoetidae is more similar to birds and bats than to other gliders. The flight performance of flying fish is a high-speed glide with a relatively flat trajectory. The wing, as indicated by the aspect ratio, is designed for high lift with low drag characteristics.     

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.     

Effects of corrugation of the dragonfly wing on gliding performance

We investigate the aerodynamic performance of the dragonfly wing, which has cross-sectional corrugation, via a static 2-dimensional unsteady simulation. Computational conditions are Re=150, 1400, and 10,000 with angles of attack ranging from 0° to 40°. From the computational results, lift coefficients are increased by the wing corrugation at all Reynolds number. However, the corrugation has little influence on the drag coefficients. The flows such as vortex in the valley of corrugation and near the edge of the corrugation are locally different from those of an elliptic wing. However, such local flows have little influence on the time averaged wing performance. From the numerical experiment presented in this study, it is determined that suction side corrugations of the wing have very little influence on increase of the lift coefficient at a positive angle of attack.     

Aerial locomotion in flies and robots: kinematic control and aerodynamics of oscillating wings

Flight in flies results from a feedback cascade in which the animal converts mechanical power produced by the flight musculature into aerodynamic forces. A major goal of flight research is to understand the functional significance of the various components in this cascade ranging from the generation of the neural code, the control of muscle mechanical power output, wing kinematics and unsteady aerodynamic mechanisms. Here, I attempted to draw a broad outline on fluid dynamic mechanisms found in flapping insect wings such as leading edge vorticity, rotational circulation and wake capture momentum transfer, as well as on the constraints of flight force control by the neuromuscular system of the fruit fly Drosophila. This system-level perspective on muscle control and aerodynamic mechanisms is thought to be a fundamental bridge in any attempt to link the function and performance of the various flight components with their particular role for wing motion and aerodynamic control in the behaving animal. Eventually, this research might facilitate the development of man-made biomimetic autonomous micro air vehicles using flapping wing motion for propulsion that are currently under construction by engineers.     

Computational Aerodynamic Analysis of a Micro-CT Based Bio-Realistic Fruit Fly Wing

The aerodynamic features of a bio-realistic 3D fruit fly wing in steady state (snapshot) flight conditions were analyzed numerically. The wing geometry was created from high resolution micro-computed tomography (micro-CT) of the fruit fly Drosophila virilis. Computational fluid dynamics (CFD) analyses of the wing were conducted at ultra-low Reynolds numbers ranging from 71 to 200, and at angles of attack ranging from -10° to +30°. It was found that in the 3D bio-realistc model, the corrugations of the wing created localized circulation regions in the flow field, most notably at higher angles of attack near the wing tip. Analyses of a simplified flat wing geometry showed higher lift to drag performance values for any given angle of attack at these Reynolds numbers, though very similar performance is noted at -10°. Results have indicated that the simplified flat wing can successfully be used to approximate high-level properties such as aerodynamic coefficients and overall performance trends as well as large flow-field structures. However, local pressure peaks and near-wing flow features induced by the corrugations are unable to be replicated by the simple wing. We therefore recommend that accurate 3D bio-realistic geometries be used when modelling insect wings where such information is useful.     

Investigation of Unsteady Aerodynamic Characteristics of a Seagull Wing in Level Flight

Unsteady aerodynamic characteristics of a seagull wing in level flight are investigated using a boundary element method.Anew no-penetration boundary condition is imposed on the surface of the wing by considering its deformation.The geometry andkinematics of the seagull wing are reproduced using the functions and data in the previously published literature.The proposedmethod is validated by comparing the computed results with the published data in the literature.The unsteady aerodynamicscharacteristics of the seagull wing are investigated by changing flapping frequency and advance ratio.It is found that the peakvalues of aerodynamic coefficients increase with the flapping frequency.The thrust and drag generations are complicatedfunctions of frequency and wing stroke motions.The lift is inversely proportional to the advance ratio.The effects of severalflapping modes on the lift and induced drag(or thrust)generation are also investigated.Among three single modes(flapping,folding and lead & lag),flapping generates the largest lift and can produce thrust alone.For three combined modes,both flapping/foldingand flapping/lead & lag can produce lift and thrust larger than the flapping-alone mode can.Folding is shown toincrease thrust when combined with flapping,whereas lead & lag has an effect of increasing the lift when also combined withflapping.When three modes are combined together,the bird can obtain the largest lift among the investigated modes.Eventhough the proposed method is limited to the inviscid flow assumption,it is believed that this method can be used to the designof flapping micro aerial vehicle.     

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.     

The Aerodynamics of Flapping Animal Flight

Our understanding of the aerodynamics of flapping animal flightis largely based on the quasi-steady assumption: the instantaneousaerodynamic forces on a flapping wing are assumed to be identicalwith those which the wing would experience in steady motionat the same instantaneous speed and angle of attack. Researchup to a decade ago showed that the assumption was sufficientto explain the flight of the vast majority of animals, but didnot rule out the possibility that alternative aerodynamic mechanismswere employed instead. Results are presented here for four hoveringanimals for which the quasi-steady explanation fails. Theseanimals apparently use lift mechanisms that rely on vorticesshed during the rotational motion of the wing at either endof the wingbeat. The postulated rotational lift mechanisms shouldalso apply to other hovering animals, even though the quasi-steadyassumption could explain their flight. Measurements of the wingforces produced by locusts cast doubt on the validity of thequasi-steady assumption for fast forward flight as well.     

Artificial evolution of the morphology and kinematics in a flapping-wing mini-UAV

Birds demonstrate that flapping-wing flight (FWF) is a versatile flight mode, compatible with hovering, forward flight and gliding to save energy. This extended flight domain would be especially useful on mini-UAVs. However, design is challenging because aerodynamic efficiency is conditioned by complex movements of the wings, and because many interactions exist between morphological (wing area, aspect ratio) and kinematic parameters (flapping frequency, stroke amplitude, wing unfolding). Here we used artificial evolution to optimize these morpho-kinematic features on a simulated 1 kg UAV, equipped with wings articulated at the shoulder and wrist. Flight tests were conducted in a dedicated steady aerodynamics simulator. Parameters generating horizontal flight for minimal mechanical power were retained. Results showed that flight at medium speed (10-12 m s(-1)) can be obtained for reasonable mechanical power (20 W kg(-1)), while flight at higher speed (16-20 m s(-1)) implied increased power (30-50 W kg(-1)). Flight at low speed (6-8 m s(-1)) necessitated unrealistic power levels (70-500 W kg(-1)), probably because our simulator neglected unsteady aerodynamics. The underlying adaptation of morphology and kinematics to varying flight speed were compared to available biological data on the flight of birds.     

Wind,Waves, and Wing Loading: Morphological Specialization May Limit Range Expansion of Endangered Albatrosses

Among the varied adaptations for avian flight, the morphological traits allowing large-bodied albatrosses to capitalize on wind and wave energy for efficient long-distance flight are unparalleled. Consequently, the biogeographic distribution of most albatrosses is limited to the windiest oceanic regions on earth; however, exceptions exist. Species breeding in the North and Central Pacific Ocean (Phoebastria spp.) inhabit regions of lower wind speed and wave height than southern hemisphere genera, and have large intrageneric variation in body size and aerodynamic performance. Here, we test the hypothesis that regional wind and wave regimes explain observed differences in Phoebastria albatross morphology and we compare their aerodynamic performance to representatives from the other three genera of this globally distributed avian family. In the North and Central Pacific, two species (short-tailed P. albatrus and waved P. irrorata) are markedly larger, yet have the smallest breeding ranges near highly productive coastal upwelling systems. Short-tailed albatrosses, however, have 60% higher wing loading (weight per area of lift) compared to waved albatrosses. Indeed, calculated aerodynamic performance of waved albatrosses, the only tropical albatross species, is more similar to those of their smaller congeners (black-footed P. nigripes and Laysan P. immutabilis), which have relatively low wing loading and much larger foraging ranges that include central oceanic gyres of relatively low productivity. Globally, the aerodynamic performance of short-tailed and waved albatrosses are most anomalous for their body sizes, yet consistent with wind regimes within their breeding season foraging ranges. Our results are the first to integrate global wind and wave patterns with albatross aerodynamics, thereby identifying morphological specialization that may explain limited breeding ranges of two endangered albatross species. These results are further relevant to understanding past and potentially predicting future distributional limits of albatrosses globally, particularly with respect to climate change effects on basin-scale and regional wind fields.