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.     

Two-and Three-Dimensional Simulations of Beetle Hind Wing Flapping during Free Forward Flight

Aerodynamic characteristic of the beetle, Trypoxylus dichotomus, which has a pair of elytra (forewings) and hind wings, is numerically investigated. Based on the experimental results of wing kinematics, two-dimensional (2D) and three-dimensional (3D) computational fluid dynamic simulations were carried out to reveal aerodynamic performance of the hind wing. The roles of the spiral Leading Edge Vortex (LEV) and the spanwise flow were clarified by comparing 2D and 3D simulations. Mainly due to pitching down of chord line during downstroke in highly inclined stroke plane, relatively high averaged thrust was produced in the free forward flight of the beetle. The effects of the local corrugation and the camber variation were also investigated for the beetle's hind wings. Our results show that the camber variation plays a significant role in improving both lift and thrust in the flapping. On the other hand, the local corrugation pattern has no significant effect on the aerodynamic force due to large angle of attack during flapping.     

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.     

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.     

Measurement on Camber Deformation of Wings of Free-flying Dragonflies and Beating-flying Dragonflies

1　IntroductionNumerouskinematicparameters,includingwing beatfrequency ,wingorientation ,andbothspan andchord wisedeformation ,arerelevanttotheaerodynam icanalysisofinsectflight[1,2 ] .Althoughnearlyalltherecentstudiesofinsectflightaerodynamics[3,4 ] haveidentifiedthatthemechanismsrequireflowseparationattheleadingedge ,andcamberisnotexpectedtohaveanysignificantinfluenceonthemagnitudeoftheforcecoefficient,someinsects ,suchasdragonfliesandbut terflies,frequently glideusinglowanglesofattack ,lead…     

Wing flexibility enhances load-lifting capacity in bumblebees

The effect of wing flexibility on aerodynamic force production has emerged as a central question in insect flight research. However, physical and computational models have yielded conflicting results regarding whether wing deformations enhance or diminish flight forces. By experimentally stiffening the wings of live bumblebees, we demonstrate that wing flexibility affects aerodynamic force production in a natural behavioural context. Bumblebee wings were artificially stiffened in vivo by applying a micro-splint to a single flexible vein joint, and the bees were subjected to load-lifting tests. Bees with stiffened wings showed an 8.6 per cent reduction in maximum vertical aerodynamic force production, which cannot be accounted for by changes in gross wing kinematics, as stroke amplitude and flapping frequency were unchanged. Our results reveal that flexible wing design and the resulting passive deformations enhance vertical force production and load-lifting capacity in bumblebees, locomotory traits with important ecological implications.     

Artificial Cambered-Wing for a Beetle-Mimicking Flapper

In this paper, we have attempted to improve the aerodynamic force generation ability of an artificial wing by implementing initial wing camber in the flexible artificial wing. This initial camber is used to create passive wing camber during flapping motion. We modified original artificial wing by removing many minor vein structures in the wing and then placed the initial camber between two major veins. Stiffness measurements for the original artificial wing and the present wing with initial camber were conducted to compare the stiffnesses of the two artificial wings, and the similarities of the two wings are discussed. A flapping test was carried out using a previously-built flapper that can flap at higher than 25 Hz flapping frequency to verify the wing camber effect. Finally, a performance comparison between uncambered- and cambered-wings was also undertaken based on observations using a high-speed camera and force measurements from wired-flight tests and swing tests. The comparison showed that the cambered-wing could produce about 10% higher thrust than the uncambered-wing.     

Comparative characteristics of the wing apparatus and flight of Syrphid flies (Diptera: Syrphidae)

Comparative analysis of the wing apparatus and flight in nine species of flower flies (Syrphidae) has been performed. Data on the flight velocity, aerodynamic force, wing-beat frequency, stroke amplitude and stroke plane angle, wing area, body mass and volume, as well as correlations between these parameters at the intraspecific and family levels, have been obtained. Based on the obtained data, the subfamilies Syrphinae and Eristalinae have been compared.     

Simulating avian wingbeat kinematics

Inverse dynamics methods are used to simulate avian wingbeats in varying flight conditions. A geometrically scalable multi-segment bird model is constructed, and optimisation techniques are employed to determine segment motions that generate desired aerodynamic force coefficients with minimal mechanical power output. The results show that wingbeat kinematics vary gradually with changes in cruise speed, which is consistent with experimental data. Optimised solutions for cruising flight of the pigeon suggest that upstroke wing retraction is used as a method of saving energy. Analysis of the aerodynamic force coefficient variation in high and low speed cruise leads to the proposal that a suitable gait metric should include both thrust and lift generation during each half-stroke.     

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.     

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.     

Comparative description of the wing apparatus and flight of some flies (diptera, brachycera)

Comparative analysis of the wing apparatus and flight characteristics has been performed on members of five dipteran families (Bombyliidae, Syrphidae, Calliphoridae, Scathophagidae, and Sarcophagidae). We obtained data on flight velocity, aerodynamic force, stroke plane angle, stroke amplitude, wingbeat frequency, wing area, and body mass and volume. The relations between these parameters are analyzed. Characters distinguishing between species of the same genus, members of different genera of the same family, and members of different families have been determined.     

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.     

Effect of outer wing separation on lift and thrust generation in a flapping wing system

We explore the implementation of wing feather separation and lead-lagging motion to a flapping wing. A biomimetic flapping wing system with separated outer wings is designed and demonstrated. The artificial wing feather separation is implemented in the biomimetic wing by dividing the wing into inner and outer wings. The features of flapping, lead-lagging, and outer wing separation of the flapping wing system are captured by a high-speed camera for evaluation. The performance of the flapping wing system with separated outer wings is compared to that of a flapping wing system with closed outer wings in terms of forward force and downward force production. For a low flapping frequency ranging from 2.47 to 3.90 Hz, the proposed biomimetic flapping wing system shows a higher thrust and lift generation capability as demonstrated by a series of experiments. For 1.6 V application (lower frequency operation), the flapping wing system with separated wings could generate about 56% higher forward force and about 61% less downward force compared to that with closed wings, which is enough to demonstrate larger thrust and lift production capability of the separated outer wings. The experiments show that the outer parts of the separated wings are able to deform, resulting in a smaller amount of drag production during the upstroke, while still producing relatively greater lift and thrust during the downstroke.     

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).     

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.     

Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds

The wing kinematics of birds vary systematically with body size, but we still, after several decades of research, lack a clear mechanistic understanding of the aerodynamic selection pressures that shape them. Swimming and flying animals have recently been shown to cruise at Strouhal numbers (St) corresponding to a regime of vortex growth and shedding in which the propulsive efficiency of flapping foils peaks (St approximately fA/U, where f is wingbeat frequency, U is cruising speed and A approximately bsin(theta/2) is stroke amplitude, in which b is wingspan and theta is stroke angle). We show that St is a simple and accurate predictor of wingbeat frequency in birds. The Strouhal numbers of cruising birds have converged on the lower end of the range 0.2 < St < 0.4 associated with high propulsive efficiency. Stroke angle scales as theta approximately 67b-0.24, so wingbeat frequency can be predicted as f approximately St.U/bsin(33.5b-0.24), with St0.21 and St0.25 for direct and intermittent fliers, respectively. This simple aerodynamic model predicts wingbeat frequency better than any other relationship proposed to date, explaining 90% of the observed variance in a sample of 60 bird species. Avian wing kinematics therefore appear to have been tuned by natural selection for high aerodynamic efficiency: physical and physiological constraints upon wing kinematics must be reconsidered in this light.     

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.     

AUTOROTATION, SELF-STABILITY, AND STRUCTURE OF SINGLE-WINGED FRUITS AND SEEDS (SAMARAS) WITH COMPARATIVE REMARKS ON ANIMAL FLIGHT

• 1 A samara is a winged fruit or seed that autorotates when falling, thereby reducing the sinking speed of the diaspore and increasing the distance it may be transported by winds. Samaras have evolved independently in a large number of plants.
• 2 Aerodynamical, mechanical, and structural properties crucial for the inherent self-stability are analysed, and formulae for calculation of performance data are given.
• 3 The momentum theorem is applied to samaras to calculate induced air velocities. As a basis for blade element analysis, and for directional stability analysis, various velocity components are put together into resultant relative air velocities normal to the blade's span axis for a samara in vertical autorotation and also in autorotation with side-slip.
• 4 When falling, a samara is free to move in any sense, but in autorotation it possesses static and dynamic stability. Mainly qualitative aspects on static stability are pre sented. Simple experiments on flat plates at Reynolds numbers about 2000 as in samaras, showed that pitch stability prevails when the C. M. (centre of mass) is located 27–35 % of the chord behind the leading edge. The aerodynamic c.p. (centre of pressure) moves forward upon a decrease of the angle of attack, backward upon an increase. In samara blades the c.m. lies ca. one-third chord behind the leading edge, and hence the aerodynamic and centrifugal forces interact so as to give pitch stability, involving stability of the angles of attack and gliding angles.
• 5 Photographs show that the centre of rotation of the samara approximately coincides with its c.m.
• 6 The coning angle (blade angle to tip path plane) taken up by the samara is determined by opposing moments set up by the centrifugal and aerodynamic forces. It is essentially the centrifugal moment (being a tangent function of the coning angle, which is small) that changes upon a change of coning angle, until the centrifugal and aerodynamic moments cancel out at the equilibrium coning angle.
• 7 Directional stability is maintained by keeping the tip path plane horizontal whereby a vertical descent path relative to the ambient air is maintained. Tilting of the tip path plane results in side-slip. Side-slip leads to an increased relative air speed at the blade when advancing, a reduced speed when retreating. The correspondingly fluctuating aerodynamic force and the gyroscopic action of the samara lead to restoring moments that bring the tip path plane back to the horizontal.
• 8 Entrance into autorotation is due to interaction between aerodynamic forces, the force of gravity, and inertial forces (when the blade accelerates towards a trailing position behind the c.m. of the samara).
• 9 The mass distribution must be such that the c.m. lies 0–30 % of the span from one end. In Acer and Plcea samaras the C.M. lies 10–20% from one end, thereby making the disk area swept by the blade large and the sinking speed low.
• 10 The blade plan-form is discussed in relation to aerodynamics. The width is largest far out on the blade where the relative air velocities are large. The large width of the blade contributes to a high Re number and thus probably to a better L/D (lift/drag) ratio and a slower descent.
• 11 The concentration of vascular bundles at the leading edge of the blade and the tapering of the blade thickness towards the trailing edge are essential for a proper chord wise mass distribution.
• 12 Data are given for samaras of Acer and Plcea, and calculations of performance are made by means of the formulae given in the paper. Some figures for an Acer samara are: sinking speed 0.9 m/sec, tip path inclination 15°, average total force coefficient 1.7 (which is discussed), and a L/D ratio of the blade approximately 3.
• 13 The performances of samaras are compared with those of insects, birds, bats, a flat plate, and a parachute. They show the samara to be a relatively very efficient structure in braking the sinking speed of the diaspore.
• 14 In samaras the mass, aerodynamic, and torsion axes coincide, whereas in insect wings the torsicn axis often lies ahead of the other two. Location of the torsion axis in front of the aerodynamic axis in insects tends towards passive wing twisting and passive adjustment of the angles of attack relative to the incident air stream, the direction of which varies along the wing because of wing flapping.
• 15 Location of the mass axis behind the torsion axis may lead to unfavourable

     

Fuzzy Vorticity Control of a Biomimetic Robotic Fish Using a Flapping Lunate Tail

Vorticity control mechanisms for flapping foils play a guiding role in both biomimetic thrust research and modeling the forward locomotion of animals with wings, fins, or tails. In this paper, a thrust-producing flapping lunate tail is studied through force and power measurements in a water channel. Proper vorticity control methods for flapping tails are discussed based on the vorticity control parameters: the dimensionless transverse amplitude, Strouhal number, angle of attack, and phase angle. Field tests are conducted on a free-swimming biomimetic robotic fish that uses a flapping tail. The results show that active control of Strouhal number using fuzzy logic control methods can efficiently reduce power consumption of the robotic fish and high swimming speeds can be obtained. A maximum speed of 1.17 length specific speed is obtained experimentally under conditions of optimal vorticity control. The St of the flapping tail is controlled within the range of 0.4～0.5.