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In aircraft propellers that are used to propel aircraft forward at some speed, propeller blade twist is important to make the individual propeller 'wings' operate at a relatively constant effective angle of attack over the full span. Wing twist is sometimes also assumed to be essential in flapping flight, especially in bird flight. For small insects, it has however been shown that wing twist has little effect on the forces generated by a flapping wing. The unimportance of twist was attributed to the prominent role of unsteady aerodynamic mechanisms. These were recently also shown to be important in bird flight. It has therefore become necessary to verify the role of wing twist in the flapping flight of birds. The aim of the study is to compare the efficiency and the aerodynamic forces of twisted and non-twisted wings that mimic the slow-speed flapping flight of birds. The analyses were performed by using physical models with different amounts of spanwise twist (0°, 10°, 40°). The flow was mapped in three-dimensions using digital particle image velocimetry. The spanwise circulation, the induced drag, the lift-to-drag ratio and the span efficiency were determined. Twist and Strouhal number (St) both determine the local effective angles of attack of the flapping wing. Wings with low average effective angles of attack (resulting from high twist and/or low St) are more efficient, but generate significantly lower aerodynamic forces. High average effective angles of attack result in lower efficiency and high aerodynamic forces. Efficiency and the magnitude of aerodynamic forces are competing parameters. Wing twist is beneficial only in the cases where efficiency is most important-e.g. in cruising flight. Take-off, landing and maneuvering, however, require large and robust aerodynamic forces to be generated. The additional force comes at the cost of efficiency, but it enables birds to perform extreme manoeuvres, increasing their overall fitness.

In this study, the unsteady flow and acoustic characteristics of a three-dimensional (3D) flapping wing model of a Tibicen linnei cicada in forward-flight are numerically investigated. A single cicada wing is modelled as a membrane with a prescribed motion reconstructed from high-speed videos of a live insect. The numerical solution takes a hydrodynamic/acoustic splitting approach: the flow field is solved with an incompressible Navier-Stokes flow solver based on an immersed boundary method, and the acoustic field is solved with linearized perturbed compressible equations. The 3D simulation allows for the examination of both the directivity and frequency compositions of the flapping wing sound in a full space. Along with the flexible wing model, a rigid wing model that is extracted from real motion is also simulated to investigate the effects of wing flexibility. The simulation results show that the flapping sound is directional; the dominant frequency varies around the wing. The first and second frequency harmonics show different radiation patterns in the rigid and flexible wing cases, which are demonstrated to be highly associated with wing kinematics and loadings. Furthermore, the rotation and deformation in the flexible wing is found to help lower the sound strength in all directions.

Aerodynamic performance of biological flight characterized by the fluid structure interaction of a flapping wing and the surrounding fluid is affected by the wing flexibility. One of the main challenges to predict aerodynamic forces is that the wing shape and motion are a priori unknown. In this study, we derive an analytical fluid-structure interaction model for a chordwise flexible flapping two-dimensional airfoil in forward flight. A plunge motion is imposed on the rigid leading-edge (LE) of teardrop shape and the flexible tail dynamically deforms. The resulting unsteady aeroelasticity is modeled with the Euler-Bernoulli-Theodorsen equation under a small deformation assumption. The two-way coupling is realized by considering the trailing-edge deformation relative to the LE as passive pitch, affecting the unsteady aerodynamics. The resulting wing deformation and the aerodynamic performance including lift and thrust agree well with high-fidelity numerical results. Under the dynamic balance, the aeroelastic stiffness decreases, whereas the aeroelastic stiffness increases with the reduced frequency. A novel aeroelastic frequency ratio is derived, which scales with the wing deformation, lift, and thrust. Finally, the dynamic similarity between flapping in water and air is established.

This work presents a parametric study, using the unsteady blade element theory, to investigate the role of twist in a hovering flapping wing. For the investigation, a flapping-wing system was developed to create a wing motion of large flapping amplitude. Three-dimensional kinematics of a passively twisted wing, which is capable of creating a linearly variable geometric angle of attack (AoA) along the wingspan, was measured during the flapping motion and used for the analysis. Several negative twist or wash-out configurations with different values of twist angle, which is defined as the difference in the average geometric AoAs at the wing root and the wing tip, were obtained from the measured wing kinematics through linear interpolation and extrapolation. The aerodynamic force generation and aerodynamic power consumption of these twisted wings were obtained and compared with those of flat wings. For the same aerodynamic power consumption, the vertical aerodynamic forces produced by the negatively twisted wings are approximately 10%-20% less than those produced by the flat wings. However, these twisted wings require approximately 1%-6% more power than flat wings to produce the same vertical force. In addition, the maximum-force-producing twisted wing, which was found to be the positive twist or wash-in configuration, was used for comparison with the maximum-force-producing flat wing. The results revealed that the vertical aerodynamic force and aerodynamic power consumption of the two types of wings are almost identical for the hovering condition. The power loading of the positively twisted wing is only approximately 2% higher than that of the maximum-force-producing flat wing. Thus, the flat wing with proper wing kinematics (or wing rotation) can be regarded as a simple and efficient candidate for the development of hovering flapping-wing micro air vehicle.

Fruit flies have flexible wings that deform during flight. To explore the fluid-structure interaction of flexible flapping wings at fruit fly scale, we use a well-validated Navier-Stokes equation solver, fully-coupled with a structural dynamics solver. Effects of chordwise flexibility on a two dimensional hovering wing is studied. Resulting wing rotation is purely passive, due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. Hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift coefficient of 3.3 was obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing within the range of the current study, although the corresponding power required was also the highest. Optimal efficiency was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the water tunnel scale with water as the surrounding fluid instead of air, the resulting vortex dynamics and aerodynamic performance remained similar for the optimal efficiency motion, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the dimensionless shape deformation parameter γ. Moreover, the wing kinematics that resulted in the optimal efficiency motion was closely aligned to the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

In hovering flight, hummingbirds reverse the angle of attack of their wings through pitch reversal in order to generate aerodynamic lift during both downstroke and upstroke. In addition, the wings may pitch during translation to further enhance lift production. It is not yet clear whether these pitching motions are caused by the wing inertia or actuated through the musculoskeletal system. Here we perform a computational analysis of the pitching dynamics by incorporating the realistic wing kinematics to determine the inertial effects. The aerodynamic effect is also included using the pressure data from a previous three-dimensional computational fluid dynamics simulation of a hovering hummingbird. The results show that like many insects, pitch reversal of the hummingbird is, to a large degree, caused by the wing inertia. However, actuation power input at the root is needed in the beginning of pronation to initiate a fast pitch reversal and also in mid-downstroke to enable a nose-up pitching motion for lift enhancement. The muscles on the wing may not necessarily be activated for pitching of the distal section. Finally, power analysis of the flapping motion shows that there is no requirement for substantial elastic energy storage or energy absorption at the shoulder joint.

The relative importance of the wing's inertial and aerodynamic forces is the key to revealing how the kinematical characteristics of the passive pitching motion of insect flapping wings are generated, which is still unclear irrespective of its importance in the design of insect-like micro air vehicles. Therefore, we investigate three species of flies in order to reveal this, using a novel fluid-structure interaction analysis that consists of a dynamically scaled experiment and a three-dimensional finite element analysis. In the experiment, the dynamic similarity between the lumped torsional flexibility model as a first approximation of the dipteran wing and the actual insect is measured by the Reynolds number Re, the Strouhal number St, the mass ratio M, and the Cauchy number Ch. In the computation, the three-dimension is important in order to simulate the stable leading edge vortex and lift force in the present Re regime over 254. The drawback of the present experiment is the difficulty in satisfying the condition of M due to the limitation of available solid materials. The novelty of the present analysis is to complement this drawback using the computation. We analyze the following two cases: (a) The equilibrium between the wing's elastic and fluid forces is dynamically similar to that of the actual insect, while the wing's inertial force can be ignored. (b) All forces are dynamically similar to those of the actual insect. From the comparison between the results of cases (a) and (b), we evaluate the contributions of the equilibrium between the aerodynamic and the wing's elastic forces and the wing's inertial force to the passive pitching motion as 80-90% and 10-20%, respectively. It follows from these results that the dipteran passive pitching motion will be based on the equilibrium between the wing's elastic and aerodynamic forces, while it will be enhanced by the wing's inertial force.

Micro air vehicle-motivated aerodynamics in biological flight has been an important subject in the past decade. Inspired by the novel flapping wing mechanisms in insects, birds and bats, we have carried out a numerical study systematically investigating a three-dimensional flapping rigid wing with passively actuated lateral and rotational motion. Distinguishing it from the limited existing studies, this work performs a systematic examination on the effects of wing aspect ratio (AR = 1.0 to infinity), inertia (density ratio σ = 4–32), torsional stiffness (frequency ratio F = 1.5–10 and infinity) and pivot point (from chord-center to leading edge) on the dynamics response of a low AR rectangular wing under an initial zero speed flow field condition. The simulation results show that the symmetry breakdown of the flapping wing results in a forward/backward motion with a rotational pitching. When the wing reaches its stable periodic state, the induced pitching frequency is identical to its forced flapping frequency. However, depending on various kinematic and dynamic system parameters, (i.e. flapping frequency, density ratio and pitching axis), the lateral induced velocity shows a number of different oscillating frequencies. Furthermore, compared with a one degree of freedom (DoF) wing in the lateral direction only, the propulsion performance of such a two DoF wing relies very much on the magnitude of torsional stiffness adding on the pivot point, as well as its pitching axis. In all cases examined here, thrust force and moment generated by a long span wing is larger than that of a short wing, which is remarkably linked to the strong reverse von K´arm´an vortex street formed in the wake of a wing.

Previous research on the flexible structure of flapping wings has shown an improved propulsion performance in comparison to rigid wings. However, not much is known about this function in terms of power efficiency modification for flapping wing energy devices. In order to study the role of the flexible wing deformation in the hydrodynamics of flapping wing energy devices, we computationally model the two-dimensional flexible single and twin flapping wings in operation under the energy extraction conditions with a large Reynolds number of 106. The flexible motion for the present study is predetermined based on a priori structural result which is different from a passive flexibility solution. Four different models are investigated with additional potential local distortions near the leading and trailing edges. Our simulation results show that the flexible structure of a wing is beneficial to enhance power efficiency by increasing the peaks of lift force over a flapping cycle, and tuning the phase shift between force and velocity to a favourable trend. Moreover, the impact of wing flexibility on efficiency is more profound at a low nominal effective angle of attack (AoA). At a typical flapping frequency f * = 0.15 and nominal effective AoA of 10°, a flexible integrated wing generates 7.68% higher efficiency than a rigid wing. An even higher increase, around six times that of a rigid wing, is achievable if the nominal effective AoA is reduced to zero degrees at feathering condition. This is very attractive for a semi-actuated flapping energy system, where energy input is needed to activate the pitching motion. The results from our dual-wing study found that a parallel twin-wing device can produce more power compared to a single wing due to the strong flow interaction between the two wings.

In the present study, we conduct an experiment using a one-paired dynamically scaled model of an insect wing, to investigate how asymmetric strokes with different wing kinematic parameters are used to control the aerodynamics of a dragonfly-like inclined flapping wing in still fluid. The kinematic parameters considered are the angles of attack during the mid-downstroke (α(md)) and mid-upstroke (α(mu)), and the duration (Δτ) and time of initiation (τ(p)) of the pitching rotation. The present dragonfly-like inclined flapping wing has the aerodynamic mechanism of unsteady force generation similar to those of other insect wings in a horizontal stroke plane, but the detailed effect of the wing kinematics on the force control is different due to the asymmetric use of the angle of attack during the up- and downstrokes. For example, high α(md) and low α(mu) produces larger vertical force with less aerodynamic power, and low α(md) and high α(mu) is recommended for horizontal force (thrust) production. The pitching rotation also affects the aerodynamics of a flapping wing, but its dynamic rotational effect is much weaker than the effect from the kinematic change in the angle of attack caused by the pitching rotation. Thus, the influences of the duration and timing of pitching rotation for the present inclined flapping wing are found to be very different from those for a horizontal flapping wing. That is, for the inclined flapping motion, the advanced and delayed rotations produce smaller vertical forces than the symmetric one and the effect of pitching duration is very small. On the other hand, for a specific range of pitching rotation timing, delayed rotation requires less aerodynamic power than the symmetric rotation. As for the horizontal force, delayed rotation with low α(md) and high α(mu) is recommended for long-duration flight owing to its high efficiency, and advanced rotation should be employed for hovering flight for nearly zero horizontal force. The present study suggests that manipulating the angle of attack during a flapping cycle is the most effective way to control the aerodynamic forces and corresponding power expenditure for a dragonfly-like inclined flapping wing.

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.

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.

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.

Two styles of bird locomotion, hovering and intermittent flight, have great potential to inform future development of autonomous flying vehicles. Hummingbirds are the smallest flying vertebrates, and they are the only birds that can sustain hovering. Their ability to hover is due to their small size, high wingbeat frequency, relatively large margin of mass-specific power available for flight and a suite of anatomical features that include proportionally massive major flight muscles (pectoralis and supracoracoideus) and wing anatomy that enables them to leave their wings extended yet turned over (supinated) during upstroke so that they can generate lift to support their weight. Hummingbirds generate three times more lift during downstroke compared with upstroke, with the disparity due to wing twist during upstroke. Much like insects, hummingbirds exploit unsteady mechanisms during hovering including delayed stall during wing translation that is manifest as a leading-edge vortex (LEV) on the wing and rotational circulation at the end of each half stroke. Intermittent flight is common in small- and medium-sized birds and consists of pauses during which the wings are flexed (bound) or extended (glide). Flap-bounding appears to be an energy-saving style when flying relatively fast, with the production of lift by the body and tail critical to this saving. Flap-gliding is thought to be less costly than continuous flapping during flight at most speeds. Some species are known to shift from flap-gliding at slow speeds to flap-bounding at fast speeds, but there is an upper size limit for the ability to bound (~0.3 kg) and small birds with rounded wings do not use intermittent glides.

Unlike other flying insects, the wing motion of swallowtail butterflies is basically limited to flapping because their fore wings partly overlap their hind wings, structurally restricting the feathering needed for active control of aerodynamic force. Hence, it can be hypothesized that the flight of swallowtail butterflies is realized with simple flapping, requiring little feedback control of the feathering angle. To verify this hypothesis, we fabricated an artificial butterfly mimicking the wing motion and wing shape of a swallowtail butterfly and analyzed its flights using images taken with a high-speed video camera. The results demonstrated that stable forward flight could be realized without active feathering or feedback control of the wing motion. During the flights, the artificial butterfly's body moved up and down passively in synchronization with the flapping, and the artificial butterfly followed an undulating flight trajectory like an actual swallowtail butterfly. Without feedback control of the wing motion, the body movement is directly affected by change of aerodynamic force due to the wing deformation; the degree of deformation was determined by the wing venation. Unlike a veinless wing, a mimic wing with veins generated a much higher lift coefficient during the flapping flight than in a steady flow due to the large body motion.