Animal flight dynamics II. Longitudinal stability in flapping flight

Stability is essential to flying and is usually assumed to be especially problematic in flapping flight. If so, problems of stability may have presented a particular hurdle to the evolution of flapping flight. In spite of this, the stability of flapping flight has never been properly analysed. Here we use quasi-static and blade element approaches to analyse the stability provided by a flapping wing. By using reduced order approximations to the natural modes of motion, we show that wing beat frequencies are generally high enough compared to the natural frequencies of motion for a quasi-static approach to be valid as a first approximation. Contrary to expectations, we find that there is noting inherently destabilizing about flapping: beating the wings faster simply amplifies any existing stability or instability, and flapping can even enhance stability compared to gliding at the same air speed. This suggests that aerodynamic stability may not have been a particular hurdle in the evolution of flapping flight. Hovering animals, like hovering helicopters, are predicted to possess neutral static stability. Flapping animals, like fixed wing aircraft, are predicted to be stable in forward flight if the mean flight force acts above and/or behind the centre of gravity. In this case, the downstroke will always be stabilizing. The stabilizing contribution may be diminished by an active upstroke with a low advance ratio and more horizontal stroke plane; other forms of the upstroke may make a small positive contribution to stability. An active upstroke could, therefore, be used to lower stability and enhance manoeuvrability. Translatory mechanisms of unsteady lift production are predicted to amplify the stability predicted by a quasi-static analysis. Non-translatory mechanisms will make little or no contribution to stability. This may be one reason why flies, and other animals which rely upon non-translatory aerodynamic mechanisms, often appear inherently unstable.     

Morphological and kinematic basis of the hummingbird flight stroke: scaling of flight muscle transmission ratio

Hummingbirds (Trochilidae) are widely known for their insect-like flight strokes characterized by high wing beat frequency, small muscle strains and a highly supinated wing orientation during upstroke that allows for lift production in both halves of the stroke cycle. Here, we show that hummingbirds achieve these functional traits within the limits imposed by a vertebrate endoskeleton and muscle physiology by accentuating a wing inversion mechanism found in other birds and using long-axis rotational movement of the humerus. In hummingbirds, long-axis rotation of the humerus creates additional wing translational movement, supplementing that produced by the humeral elevation and depression movements of a typical avian flight stroke. This adaptation increases the wing-to-muscle-transmission ratio, and is emblematic of a widespread scaling trend among flying animals whereby wing-to-muscle-transmission ratio varies inversely with mass, allowing animals of vastly different sizes to accommodate aerodynamic, biomechanical and physiological constraints on muscle-powered flapping flight.     

Two-Dimensional Aerodynamic Models of Insect Flight for Robotic Flapping Wing Mechanisms of Maximum Efficiency

In the ＂modified quasi-steady＂ approach, two-dimensional （2D） aerodynamic models of flapping wing motions are analyzed with focus on different types of wing rotation and different positions of rotation axis to explain the force peak at the end of each half stroke. In this model, an additional velocity of the mid chord position due to rotation is superimposed on the translational relative velocity of air with respect to the wing. This modification produces augmented forces around the end of each stroke. For each case of the flapping wing motions with various combination of controlled translational and rotational velocities of the wing along inclined stroke planes with thin figure-of-eight trajectory, discussions focus on lift-drag evolution during one stroke cycle and efficiency of types of wing rotation. This ＂modified quasi-steady＂ approach provides a systematic analysis of various parameters and their effects on efficiency of flapping wing mechanism. Flapping mechanism with delayed rotation around quarter-chord axis is an efficient one and can be made simple by a passive rotation mechanism so that it can be useful for robotic application.     

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.     

Hovering and intermittent flight in birds

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.     

A two-dimensional aerodynamic model of freely flying insects

Possible free flights of insects by a single flapping motion were studied. It is well-known that insects utilize vortices generated by flapping, by which they generate larger lift than that evaluated by the ordinary aerodynamic theory. However, the effect of the motion of the center of mass (CM) of the insect on its flight has not been clarified. To clarify the effect, numerical simulation was performed for a simple model considering the coupling between the vertical CM motion and the separation vortices generated by flapping wing. As a result, it is shown that the flapping flight has the following interesting features. First, despite a single flapping motion, the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights are selected by the initial conditions even when all the parameters are the same. Second, at a certain critical parameter value, the steady flight loses its stability and undergoes an abrupt transition to the wandering flight. Interestingly, at this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple assumption. These results suggest the significance of the effect of CM motion.     

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.     

A wing-assisted running robot and implications for avian flight evolution

DASH+Wings is a small hexapedal winged robot that uses flapping wings to increase its locomotion capabilities. To examine the effects of flapping wings, multiple experimental controls for the same locomotor platform are provided by wing removal, by the use of inertially similar lateral spars, and by passive rather than actively flapping wings. We used accelerometers and high-speed cameras to measure the performance of this hybrid robot in both horizontal running and while ascending inclines. To examine consequences of wing flapping for aerial performance, we measured lift and drag forces on the robot at constant airspeeds and body orientations in a wind tunnel; we also determined equilibrium glide performance in free flight. The addition of flapping wings increased the maximum horizontal running speed from 0.68 to 1.29 m s?1, and also increased the maximum incline angle of ascent from 5.6° to 16.9°. Free flight measurements show a decrease of 10.3° in equilibrium glide slope between the flapping and gliding robot. In air, flapping improved the mean lift:drag ratio of the robot compared to gliding at all measured body orientations and airspeeds. Low-amplitude wing flapping thus provides advantages in both cursorial and aerial locomotion. We note that current support for the diverse theories of avian flight origins derive from limited fossil evidence, the adult behavior of extant flying birds, and developmental stages of already volant taxa. By contrast, addition of wings to a cursorial robot allows direct evaluation of the consequences of wing flapping for locomotor performance in both running and flying.     

Non-Jumping Take off Performance in Beetle Flight （Rhinoceros Beetle Trypoxylus dichotomus）

In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes offwithout jumping. In this study, we used 3-Dimensional （3D） high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be con- sidered as a main source of lift for heavy beetle.     

Normalized lift: an energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces

For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ?ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ?v(2). This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.     

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.     

Dynamic Modeling, Testing, and Stability Analysis of an Ornithoptic Blimp

In order to study omithopter flight and to improve a dynamic model of flapping propulsion,a series of tests are conducted on a flapping-wing blimp.The blimp is designed and constructed from mylar plastic and balsa wood as a test platform for aerodynamics and flight dynamics.The blimp,2.3 meters long and 420 gram mass,is propelled by its flapping wings.Due to buoyancy the wings have no lift requirement so that the distinction between lift and propulsion can be analyzed in a flight platform at low flight speeds.The blimp is tested using a Vicon motion tracking system and various initial conditions are tested including accelerating flight from standstill,decelerating from an initial speed higher than its steady state,and from its steady-state speed but disturbed in pitch angle.Test results are used to estimate parameters in a coupled quasi-steady aerodynamics/Newtonian flight dynamics model.This model is then analyzed using Floquet theory to determine local dynamic modes and stability.It is concluded that the dynamic model adequately describes the vehicle's nonlinear behavior near the steady-state velocity and that the vehicle's linearized modes are akin to those of a fixed-wing aircraft.     

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.     

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

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

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

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

Physical theory,origin of flight,and a synthesis proposed for birds

Neither flapping and running to take-off nor gliding from heights can be disproved as the assured evolutionary origin of self-powered flight observed in modern vertebrates. Gliding with set wings would utilize available potential energy from gravity but gain little from flapping. Bipedal running, important in avian phylogeny, possibly facilitated the evolution of flight. Based on physical principles, gliding is a better process for the origin of powered flight than the "ground-up" process, which physically is not feasible in space or time (considering air resistance, metabolic energy costs, and mechanical resistance to bipedal running). Proto-avian ancestors of Archaeopteryx and Microraptor probably flapped their sparsely feathered limbs synchronously while descending from leaps or heights, with such "flutter-gliding" presented as a synthesis of the two earlier theories of flight origin (making use of the available potential energy from gravity, involving wing thrusts and flapping, coping with air resistance that slows air speed, but effecting positive fitness value in providing lift and slowing dangerous falls).     

Characteristics of a Beetle's Free Flight and a Flapping-Wing System that Mimics Beetle Flight

In this work, we first present a method to experimentally capture the free flight of a beetle (Allomyrina dichotoma), which is not an active flyer. The beetle is suspended in the air by a hanger to induce the free flight. This flight is filmed using two high-speed cameras. The high speed images are then examined to obtain flapping angle, flapping frequency, and wing rotation of the hind wing. The acquired data of beetle free flight are used to design a motor-driven flapper that can approximately mimic the beetle in terms of size, flapping frequency and wing kinematics. The flapper can create a large flapping angle over 140° with a large passive wing rotation angle. Even though the flapping frequency of the flapper is not high enough compared to that of a real beetle due to the limited motor torque, the flapper could produce positive average vertical force. This work will provide important experience for future development of a beetle-mimicking Flapping-Wing Micro Air Vehicle (FWMAV).     

Flight physiology of migrating Urania fulgens (Uraniidae) moths: kinematics and aerodynamics of natural free flight

Summary Air speeds and wing kinematics were determined for the Neotropical moth Urania fulgens in natural migratory flight over Lake Gatun, Republic of Panama. Morphological parameters are presented for the same insects filmed in free flight. A quasi-steady aerodynamic analysis was used to show that unsteady mechanisms of lift generation are probably not necessary to produce the forces necessary for fast forward flight. Mechanical power requirements of forward flight were estimated from the biomechanical and morphological data. Over an airspeed range of 1.5 to 4.5 m/s, the mechanical power required to fly is predicted to increase dramatically with forward speed. A comparison of estimated metabolic rates with endogenous lipid reserves suggests that U. fulgens feeds extensively on flower nectar during migration from Central into South America.     

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’.     

On the Estimation of Time Dependent Lift of a European Starling (Sturnus vulgaris) during Flapping Flight

We study the role of unsteady lift in the context of flapping wing bird flight. Both aerodynamicists and biologists have attempted to address this subject, yet it seems that the contribution of unsteady lift still holds many open questions. The current study deals with the estimation of unsteady aerodynamic forces on a freely flying bird through analysis of wingbeat kinematics and near wake flow measurements using time resolved particle image velocimetry. The aerodynamic forces are obtained through two approaches, the unsteady thin airfoil theory and using the momentum equation for viscous flows. The unsteady lift is comprised of circulatory and non-circulatory components. Both approaches are presented over the duration of wingbeat cycles. Using long-time sampling data, several wingbeat cycles have been analyzed in order to cover both the downstroke and upstroke phases. It appears that the unsteady lift varies over the wingbeat cycle emphasizing its contribution to the total lift and its role in power estimations. It is suggested that the circulatory lift component cannot assumed to be negligible and should be considered when estimating lift or power of birds in flapping motion.