Details of insect wing design and deformation enhance aerodynamic function and flight efficiency

Effects of structural flexibility of wings in flapping flight of butterfly

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

Aerodynamic effects of corrugation and deformation in flapping wings of hovering hoverflies

We investigated the aerodynamic effects of wing deformation and corrugation of a three-dimensional model hoverfly wing at a hovering condition by solving the Navier-Stokes equations on a dynamically deforming grid. Various corrugated wing models were tested. Insight into whether or not there existed significant aerodynamic coupling between wing deformation (camber and twist) and wing corrugation was obtained by comparing aerodynamic forces of four cases: a smooth-plate wing in flapping motion without deformation (i.e. a rigid flat-plate wing in flapping motion); a smooth-plate wing in flapping motion with deformation; a corrugated wing in flapping motion without deformation (i.e. a rigid corrugated wing in flapping motion); a corrugated wing in flapping motion with deformation. There was little aerodynamic coupling between wing deformation and corrugation: the aerodynamic effect of wing deformation and corrugation acting together was approximately a superposition of those of deformation and corrugation acting separately. When acting alone, the effect of wing deformation was to increase the lift by 9.7% and decrease the torque (or aerodynamic power) by 5.2%, and that of wing corrugation was to decrease the lift by 6.5% and increase the torque by 2.2%. But when acting together, the wing deformation and corrugation only increased the lift by ~3% and decreased the torque by ~3%. That is, the combined aerodynamic effect of deformation and corrugation is rather small. Thus, wing corrugation is mainly for structural, not aerodynamic, purpose, and in computing or measuring the aerodynamic forces, using a rigid flat-plate wing to model the corrugated deforming wing at hovering condition can be a good approximation.

Elastic deformation and energy loss of flapping fly wings

During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m(2) near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m(2)). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.

Anisotropy and non-homogeneity of an Allomyrina Dichotoma beetle hind wing membrane

Biomimetics is one of the most important paradigms as researchers seek to invent better engineering designs over human history. However, the observation of insect flight is a relatively recent work. Several researchers have tried to address the aerodynamic performance of flapping creatures and other natural properties of insects, although there are still many unsolved questions. In this study, we try to answer the questions related to the mechanical properties of a beetle's hind wing, which consists of a stiff vein structure and a flexible membrane. The membrane of a beetle's hind wing is small and flexible to the point that conventional methods cannot adequately quantify the material properties. The digital image correlation method, a non-contact displacement measurement method, is used along with a specially designed mini-tensile testing system. To reduce the end effects, we developed an experimental method that can deal with specimens with as high an aspect ratio as possible. Young's modulus varies over the area in the wing and ranges from 2.97 to 4.5 GPa in the chordwise direction and from 1.63 to 2.24 GPa in the spanwise direction. Furthermore, Poisson's ratio in the chordwise direction is 0.63-0.73 and approximately twice as large as that in the spanwise direction (0.33-0.39). From these results, we can conclude that the membrane of a beetle's hind wing is an anisotropic and non-homogeneous material. Our results will provide a better understanding of the flapping mechanism through the formulation of a fluid-structure interaction analysis or aero-elasticity analysis and meritorious data for biomaterial properties database as well as a creative design concept for a micro aerial flapper that mimics an insect.

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 10⁵ 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.

Time-varying span efficiency through the wingbeat of desert locusts

The flight performance of animals depends greatly on the efficacy with which they generate aerodynamic forces. Accordingly, maximum range, load-lifting capacity and peak accelerations during manoeuvres are all constrained by the efficiency of momentum transfer to the wake. Here, we use high-speed particle image velocimetry (1 kHz) to record flow velocities in the near wake of desert locusts (Schistocerca gregaria, Forskål). We use the measured flow fields to calculate time-varying span efficiency throughout the wing stroke cycle. The locusts are found to operate at a maximum span efficiency of 79 per cent, typically at a plateau of about 60 per cent for the majority of the downstroke, but at lower values during the upstroke. Moreover, the calculated span efficiencies are highest when the largest lift forces are being generated (90% of the total lift is generated during the plateau of span efficiency) suggesting that the combination of wing kinematics and morphology in locust flight perform most efficiently when doing the most work.

Characteristics of vortex formation and thrust performance in drag-based paddling propulsion

Several characteristics of drag-based paddling propulsion are studied with a simple mechanical model and a measurement technique for mapping three-dimensional flow fields. In drag-based propulsion, the temporal change of the vortex strength is an important parameter in the relationship between vortex formation and thrust generation. Our results indicate that spanwise flow behind the paddling propulsor significantly affects tip vortex development and thrust generation. The distribution of spanwise flow is dependent on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared with a rectangular propulsor. For the low Reynolds number case, spanwise flow is not as strong as that for the high Reynolds number case. Without sacrificing total impulse, the flexible propulsor can smooth out thrust peaks during sudden stroke motions, which is favorable for avoiding structural failures and stabilizing body motion. We also explored the role of stopping vortex shedding in efficient thrust generation by determining the relationship between stroke angles and total impulses generated by paddling propulsors.

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.

First controlled vertical flight of a biologically inspired microrobot

In this paper, we present experimental results on altitude control of a flying microrobot. The problem is approached in two stages. In the first stage, system identification of two relevant subsystems composing the microrobot is performed, using a static flapping experimental setup. In the second stage, the information gathered through the static flapping experiments is employed to design the controller used in vertical flight. The design of the proposed controller relies on the idea of treating an exciting signal as a subsystem of the microrobot. The methods and results presented here are a key step toward achieving total autonomy of bio-inspired flying microrobots.

A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.

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.

Aerodynamics of tip-reversal upstroke in a revolving pigeon wing

During slow flight, bird species vary in their upstroke kinematics using either a ‘flexed wing’ or a distally supinated ‘tip-reversal’ upstroke. Two hypotheses have been presented concerning the function of the tip-reversal upstroke. The first is that this behavior is aerodynamically inactive and serves to minimize drag. The second is that the tip-reversal upstroke is capable of producing significant aerodynamic forces. Here, we explored the aerodynamic capabilities of the tip-reversal upstroke using a well-established propeller method. Rock dove (Columba livia, N=3) wings were spread and dried in postures characteristic of either mid-upstroke or mid-downstroke and spun at in vivo Reynolds numbers to simulate forces experienced during slow flight. We compared 3D wing shape for the propeller and in vivo kinematics, and found reasonable kinematic agreement between methods (mean differences 6.4% of wing length). We found that the wing in the upstroke posture is capable of producing substantial aerodynamic forces. At in vivo angles of attack (66 deg at mid-upstroke, 46 deg at mid-downstroke), the upstroke wings averaged for three birds produced a lift-to-drag ratio of 0.91, and the downstroke wings produced a lift-to-drag ratio of 3.33. Peak lift-to-drag ratio was 2.5 for upstroke and 6.3 for downstroke. Our estimates of total force production during each half-stroke suggest that downstroke produces a force that supports 115% of bodyweight, and during upstroke a forward-directed force (thrust) is produced at 36% of body weight.

Ontogeny of lift and drag production in ground birds

The juvenile period is often a crucial interval for selective pressure on locomotor ability. Although flight is central to avian biology, little is known about factors that limit flight performance during development. To improve understanding of flight ontogeny, we used a propeller (revolving wing) model to test how wing shape and feather structure influence aerodynamic performance during development in the precocial chukar partridge (Alectoris chukar, 4 to >100 days post hatching). We spun wings in mid-downstroke posture and measured lift (L) and drag (D) using a force plate upon which the propeller assembly was mounted. Our findings demonstrate a clear relationship between feather morphology and aerodynamic performance. Independent of size and velocity, older wings with stiffer and more asymmetrical feathers, high numbers of barbicels and a high degree of overlap between barbules generate greater L and L:D ratios than younger wings with flexible, relatively symmetrical and less cohesive feathers. The gradual transition from immature feathers and drag-based performance to more mature feathers and lift-based performance appears to coincide with ontogenetic transitions in locomotor capacity. Younger birds engage in behaviors that require little aerodynamic force and that allow D to contribute to weight support, whereas older birds may expand their behavioral repertoire by flapping with higher tip velocities and generating greater L. Incipient wings are, therefore, uniquely but immediately functional and provide flight-incapable juveniles with access to three-dimensional environments and refugia. Such access may have conferred selective advantages to theropods with protowings during the evolution of avian flight.

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.

Effects of wing deformation on aerodynamic forces in hovering hoverflies

We studied the effects of wing deformation on the aerodynamic forces of wings of hovering hoverflies by solving the Navier-Stokes equations on a dynamically deforming grid, employing the recently measured wing deformation data of hoverflies in free-flight. Three hoverflies were considered. By taking out the camber deformation and the spanwise twist deformation one by one and by comparing the results of the deformable wing with those of the rigid flat-plate wing (the angle of attack of the rigid flat-plate wing was equal to the local angle of attack at the radius of the second moment of wing area of the deformable wing), effects of camber deformation and spanwise twist were identified. The main results are as follows. For the hovering hoverflies considered, the time courses of the lift, drag and aerodynamic power coefficients of the deformable wing are very similar to their counterparts of the rigid flat-plate wing, although lift of the deformable wing is about 10% larger, and its aerodynamic power required about 5% less than that of the rigid flat-plate wing. The difference in lift is mainly caused by the camber deformation, and the difference in power is mainly caused by the spanwise twist. The main reason that the deformation does not have a very large effect on the aerodynamic force is that, during hovering, the wing operates at a very high angle of attack (about 50 deg) and the flow is separated, and separated flow is not very sensitive to wing deformation. Thus, as a first approximation, the deformable wing in hover flight could be modeled by a rigid flat-plate wing with its angle of attack being equal to the local angle of attack at the radius of second moment of wing area of the deformable wing.

Differential pressure measurement using a free-flying insect-like ornithopter with an MEMS sensor

This paper presents direct measurements of the aerodynamic forces on the wing of a free-flying, insect-like ornithopter that was modeled on a hawk moth (Manduca sexta). A micro differential pressure sensor was fabricated with micro electro mechanical systems (MEMS) technology and attached to the wing of the ornithopter. The sensor chip was less than 0.1% of the wing area. The mass of the sensor chip was 2.0 mg, which was less than 1% of the wing mass. Thus, the sensor was both small and light in comparison with the wing, resulting in a measurement system that had a minimal impact on the aerodynamics of the wing. With this sensor, the 'pressure coefficient' of the ornithopter wing was measured during both steady airflow and actual free flight. The maximum pressure coefficient observed for steady airflow conditions was 1.4 at an angle of attack of 30 degrees . In flapping flight, the coefficient was around 2.0 for angles of attack that ranged from 25 degrees to 40 degrees . Therefore, a larger aerodynamic force was generated during the downstroke in free flight compared to steady airflow conditions.

Scaling for stress similarity and distorted-shape similarity in bending and torsion under maximal muscle forces concurs with geometric similarity among different-sized animals

When geometric similarity, or isometry, prevails among animals of different sizes their form and proportions are similar. Weight increases as the cube of the length dimension, while cross-sectional areas increase as its square, so in load-bearing structural elements the stress, caused by the body weight, increases in direct proportion to the length dimension, both for pure axial loads and for transverse bending and torsional loads. On this account, large body sizes would be expected to set up compensatory selection on the proportions of supporting structures, making them disproportionately thicker as required to maintain similar, size-independent safety factors against breakage. Most previous scaling theories have assumed that the strength of support elements has evolved with respect to loads due to the body weight. But then, from the arguments above, a scaling principle different from the geometric similarity rule would be required in order for safety factors to remain similar among different-sized animals. Still, most comparable animals of ‘similar kind’ scale in accordance with the geometric similarity rule. Here, we instead argue that muscle forces cause much larger loads on structural support elements during maximum performance events (such as during prey capture or escape from predators) than do loads dictated by the body weight (such as during cruising locomotion), and that structural strength therefore might evolve with respect to maximal muscle forces rather than to the body weight. We explore how the transverse and longitudinal lengths of structural support elements must scale to one another, and to muscle transverse length, in order to satisfy each of the following, functionally based, similarity principles for support elements placed in bending, or in torsion, by maximal muscle forces during locomotion: (1) similarity in axial stress, or (2) in torsional shear stress, and (3) similarity in bent shape, or (4) in twisted shape. A dimensional relationship that satisfies all four conditions actually turns out to be the geometric similarity rule. These functional attributes may therefore help to explain the prevalence of geometric similarity among animals. Conformance of different-sized species with the geometric similarity principle has not been directly selected for as such, of course, but may have arisen as a by-product of adaptation in morphological proportions, following upon selection, in each separate species-lineage, for adequate and similar safety factors against breakage, and similar optimal distorted shapes, of structural support elements placed in bending, or in torsion, by maximal muscle forces.

How wing compliance drives the efficiency of self-propelled flapping flyers

Wing flexibility governs the flying performance of flapping-wing flyers. Here, we use a self-propelled flapping-wing model mounted on a "merry go round" to investigate the effect of wing compliance on the propulsive efficiency of the system. Our measurements show that the elastic nature of the wings can lead not only to a substantial reduction in the consumed power, but also to an increment of the propulsive force. A scaling analysis using a flexible plate model for the wings points out that, for flapping flyers in air, the time-dependent shape of the elastic bending wing is governed by the wing inertia. Based on this prediction, we define the ratio of the inertial forces deforming the wing to the elastic restoring force that limits the deformation as the elastoinertial number N(ei). Our measurements with the self-propelled model confirm that it is the appropriate structural parameter to describe flapping flyers with flexible wings.

The importance of leading edge vortices under simplified flapping flight conditions at the size scale of birds

Over the last decade, interest in animal flight has grown, in part due to the possible use of flapping propulsion for micro air vehicles. The importance of unsteady lift-enhancing mechanisms in insect flight has been recognized, but unsteady effects were generally thought to be absent for the flapping flight of larger animals. Only recently has the existence of LEVs (leading edge vortices) in small vertebrates such as swifts, small bats and hummingbirds been confirmed. To study the relevance of unsteady effects at the scale of large birds [reduced frequency k between 0.05 and 0.3, k=(πfc)/U∞; f is wingbeat frequency, U∞ is free-stream velocity, and c is the average wing chord], and the consequences of the lack of kinematic and morphological refinements, we have designed a simplified goose-sized flapping model for wind tunnel testing. The 2-D flow patterns along the wing span were quantitatively visualized using particle image velocimetry (PIV), and a three-component balance was used to measure the forces generated by the wings. The flow visualization on the wing showed the appearance of LEVs, which is typically associated with a delayed stall effect, and the transition into flow separation. Also, the influence of the delayed stall and flow separation was clearly visible in measurements of instantaneous net force over the wingbeat cycle. Here, we show that, even at reduced frequencies as low as those of large bird flight, unsteady effects are present and non-negligible and have to be addressed by kinematic and morphological adaptations.

Resonance of flexible flapping wings at low Reynolds number

Using three-dimensional computer simulations, we examine hovering aerodynamics of flexible planar wings oscillating at resonance. We model flexible wings as tilted elastic plates whose sinusoidal plunging motion is imposed at the plate root. Our simulations reveal that large-amplitude resonance oscillations of elastic wings drastically enhance aerodynamic lift and efficiency of low-Reynolds-number plunging. Driven by a simple sinusoidal stroke, flexible wings at resonance generate a hovering force comparable to that of small insects that employ a very efficient but much more complicated stroke kinematics. Our results indicate the feasibility of using flexible wings driven by a simple harmonic stroke for designing efficient microscale flying machines.