Hummingbird wing efficacy depends on aspect ratio and compares with helicopter rotors

Hummingbirds are the only birds that can sustain hovering. This unique flight behaviour comes, however, at high energetic cost. Based on helicopter and aeroplane design theory, we expect that hummingbird wing aspect ratio (AR), which ranges from about 3.0 to 4.5, determines aerodynamic efficacy. Previous quasi-steady experiments with a wing spinner set-up provide no support for this prediction. To test this more carefully, we compare the quasi-steady hover performance of 26 wings, from 12 hummingbird taxa. We spun the wings at angular velocities and angles of attack that are representative for every species and measured lift and torque more precisely. The power (aerodynamic torque × angular velocity) required to lift weight depends on aerodynamic efficacy, which is measured by the power factor. Our comparative analysis shows that AR has a modest influence on lift and drag forces, as reported earlier, but interspecific differences in power factor are large. During the downstroke, the power required to hover decreases for larger AR wings at the angles of attack at which hummingbirds flap their wings (p < 0.05). Quantitative flow visualization demonstrates that variation in hover power among hummingbird wings is driven by similar stable leading edge vortices that delay stall during the down- and upstroke. A side-by-side aerodynamic performance comparison of hummingbird wings and an advanced micro helicopter rotor shows that they are remarkably similar.     

On the quasi-steady aerodynamics of normal hovering flight part II: model implementation and evaluation

This paper introduces a generic, transparent and compact model for the evaluation of the aerodynamic performance of insect-like flapping wings in hovering flight. The model is generic in that it can be applied to wings of arbitrary morphology and kinematics without the use of experimental data, is transparent in that the aerodynamic components of the model are linked directly to morphology and kinematics via physical relationships and is compact in the sense that it can be efficiently evaluated for use within a design optimization environment. An important aspect of the model is the method by which translational force coefficients for the aerodynamic model are obtained from first principles; however important insights are also provided for the morphological and kinematic treatments that improve the clarity and efficiency of the overall model. A thorough analysis of the leading-edge suction analogy model is provided and comparison of the aerodynamic model with results from application of the leading-edge suction analogy shows good agreement. The full model is evaluated against experimental data for revolving wings and good agreement is obtained for lift and drag up to 90° incidence. Comparison of the model output with data from computational fluid dynamics studies on a range of different insect species also shows good agreement with predicted weight support ratio and specific power. The validated model is used to evaluate the relative impact of different contributors to the induced power factor for the hoverfly and fruitfly. It is shown that the assumption of an ideal induced power factor (k = 1) for a normal hovering hoverfly leads to a 23% overestimation of the generated force owing to flapping.     

Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio

Airplanes and helicopters use high aspect ratio wings to reduce the power required to fly, but must operate at low angle of attack to prevent flow separation and stall. Animals capable of slow sustained flight, such as hummingbirds, have low aspect ratio wings and flap their wings at high angle of attack without stalling. Instead, they generate an attached vortex along the leading edge of the wing that elevates lift. Previous studies have demonstrated that this vortex and high lift can be reproduced by revolving the animal wing at the same angle of attack. How do flapping and revolving animal wings delay stall and reduce power? It has been hypothesized that stall delay derives from having a short radial distance between the shoulder joint and wing tip, measured in chord lengths. This non-dimensional measure of wing length represents the relative magnitude of inertial forces versus rotational accelerations operating in the boundary layer of revolving and flapping wings. Here we show for a suite of aspect ratios, which represent both animal and aircraft wings, that the attachment of the leading edge vortex on a revolving wing is determined by wing aspect ratio, defined with respect to the centre of revolution. At high angle of attack, the vortex remains attached when the local radius is shorter than four chord lengths and separates outboard on higher aspect ratio wings. This radial stall limit explains why revolving high aspect ratio wings (of helicopters) require less power compared with low aspect ratio wings (of hummingbirds) at low angle of attack and vice versa at high angle of attack.     

Insect-like flapping wing mechanism based on a double spherical Scotch yoke

We describe the rationale, concept, design and implementation of a fixed-motion (non-adjustable) mechanism for insect-like flapping wing micro air vehicles in hover, inspired by two-winged flies (Diptera). This spatial (as opposed to planar) mechanism is based on the novel idea of a double spherical Scotch yoke. The mechanism was constructed for two main purposes: (i) as a test bed for aeromechanical research on hover in flapping flight, and (ii) as a precursor design for a future flapping wing micro air vehicle. Insects fly by oscillating (plunging) and rotating (pitching) their wings through large angles, while sweeping them forwards and backwards. During this motion the wing tip approximately traces a "figure-of-eight" or a "banana" and the wing changes the angle of attack (pitching) significantly. The kinematic and aerodynamic data from free-flying insects are sparse and uncertain, and it is not clear what aerodynamic consequences different wing motions have. Since acquiring the necessary kinematic and dynamic data from biological experiments remains a challenge, a synthetic, controlled study of insect-like flapping is not only of engineering value, but also of biological relevance. Micro air vehicles are defined as flying vehicles approximately 150 mm in size (hand-held), weighing 50-100g, and are developed to reconnoitre in confined spaces (inside buildings, tunnels, etc.). For this application, insect-like flapping wings are an attractive solution and hence the need to realize the functionality of insect flight by engineering means. Since the semi-span of the insect wing is constant, the kinematics are spatial; in fact, an approximate figure-of-eight/banana is traced on a sphere. Hence a natural mechanism implementing such kinematics should be (i) spherical and (ii) generate mathematically convenient curves expressing the figure-of-eight/banana shape. The double spherical Scotch yoke design has property (i) by definition and achieves (ii) by tracing spherical Lissajous curves.     

柔性扑翼气动性能的数值研究

国内外对扑翼飞行的气动特性进行了大量研究,这些研究大多基于简谐扑动的刚性翼,然而大量观察发现鸟或昆虫飞行时,翅膀存在明显的柔性变形,这种变形对其气动性能具有显著的影响。该文针对一简化的二维柔性扑翼模型,采用数值求解N-S方程并耦合扑翼柔性变形方程的计算方法,研究了扑翼柔性变形对其气动性能的影响。结果显示扑翼的柔性变形改变了扑翼周围的涡结构,从而影响扑翼的气动性能;适当的柔性变形能延迟前缘涡的脱落,从而有效地改善扑翼的推进效率,但同时减弱了扑翼在低雷诺数环境中产生高升力的尾迹捕捉机制。     

Predicting power-optimal kinematics of avian wings

A theoretical model of avian flight is developed which simulates wing motion through a class of methods known as predictive simulation. This approach uses numerical optimization to predict power-optimal kinematics of avian wings in hover, cruise, climb and descent. The wing dynamics capture both aerodynamic and inertial loads. The model is used to simulate the flight of the pigeon, Columba livia, and the results are compared with previous experimental measurements. In cruise, the model unearths a vast range of kinematic modes that are capable of generating the required forces for flight. The most efficient mode uses a near-vertical stroke–plane and a flexed-wing upstroke, similar to kinematics recorded experimentally. In hover, the model predicts that the power-optimal mode uses an extended-wing upstroke, similar to hummingbirds. In flexing their wings, pigeons are predicted to consume 20% more power than if they kept their wings full extended, implying that the typical kinematics used by pigeons in hover are suboptimal. Predictions of climbing flight suggest that the most energy-efficient way to reach a given altitude is to climb as steeply as possible, subjected to the availability of power.     

A new twist on gyroscopic sensing: body rotations lead to torsion in flapping,flexing insect wings

Insects perform fast rotational manoeuvres during flight. While two insect orders use flapping halteres (specialized organs evolved from wings) to detect body dynamics, it is unknown how other insects detect rotational motions. Like halteres, insect wings experience gyroscopic forces when they are flapped and rotated and recent evidence suggests that wings might indeed mediate reflexes to body rotations. But, can gyroscopic forces be detected using only changes in the structural dynamics of a flapping, flexing insect wing? We built computational and robotic models to rotate a flapping wing about an axis orthogonal to flapping. We recorded high-speed video of the model wing, which had a flexural stiffness similar to the wing of the Manduca sexta hawkmoth, while flapping it at the wingbeat frequency of Manduca (25 Hz). We compared the three-dimensional structural dynamics of the wing with and without a 3 Hz, 10° rotation about the yaw axis. Our computational model revealed that body rotation induces a new dynamic mode: torsion. We verified our result by measuring wing tip displacement, shear strain and normal strain of the robotic wing. The strains we observed could stimulate an insect''s mechanoreceptors and trigger reflexive responses to body rotations.     

Aerodynamic effects of flexibility in flapping wings

Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re ≈ 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.     

Wing‐kinematics measurement and flight modelling of the bamboo weevil C. buqueti

Insects are one of the most agile flyers in nature, and studying the kinematics of their wings can provide important data for the design of insect‐like wing‐flapping micro aerial vehicles. This study integrates high‐speed photogrammetry and three‐dimensional (3D) force measurement system to explore the kinematics of Cyrtotrachelus buqueti during the wing‐flapping flight. The tracking point at the wing tip of the hind wing was recorded using high‐speed videography. The lift‐thrust force characteristic of wing‐flapping motion was obtained by the 3D force sensor. Quantitative measurements of wing kinematics show that the wing‐flapping pattern of the hind wing of C. buqueti was revealed as a double figure‐eight trajectory. The kinematic modelling of the wing‐flapping pattern was then established by converting the flapping motion into rotational motion about the pivoting wing base in the reference coordinate system. Moreover, the lift force generated by C. buqueti during the wing‐flapping flight is sufficient to support its body weight without the need to use thrust force to compensate for the lack of lift force.Inspec keywords: video recording, force sensors, photogrammetry, kinematics, force measurement, aerospace componentsOther keywords: kinematic modelling, pivoting wing base, wing‐flapping flight, insect‐like wing‐flapping microaerial vehicles, high‐speed videography, 3D force sensor, Cyrtotrachelus buqueti, wing kinematics measurement, wing‐flapping motion pattern, lift‐thrust force characteristics, bamboo weevil C. buqueti, high‐speed photogrammetry, three‐dimensional force measurement system, 3D force measurement system, double figure‐eight trajectory     

An unsteady lifting-line theory

A lifting-line theory is developed for wings of large aspect ratio undergoing time-harmonic oscillations, uniformly from high to low frequencies. The method of matched asymptotic expansions is used to enforce the compatibility of two approximate solutions valid far from and near the wing surface. The far-field velocity potential is expressed as a distribution of normal dipoles on the wake, and its expansion near the wing span leads to an expression for the oscillatory downwash. The near-field flow is two-dimensional. A particular solution is obtained from strip theory and a homogeneous component is added to account for the spanwise hydrodynamic interactions. The compatibility of the inner and outer solutions leads to an integral equation for the distribution of circulation along the wing span. In the zero-frequency limit it reduces to that in Prandtl's lifting-line theory, and for high frequencies it tends to the two-dimensional strip theory. Lift computations are presented for an elliptic and a rectangular wing of aspect ratio A = 4.     

Ionic Polymer Metal Composite Flapping Actuator Mimicking Dragonflies

In this study, variational principle is used for dynamic modeling of an Ionic Polymer Metal Composite (IPMC) flapping wing. The IPMC is an Electro-active Polymer (EAP) which is emerging as a useful smart material for `artificial muscle' applications. Dynamic characteristics of IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens are analyzed using numerical simulations. An unsteady aerodynamic model is used to obtain the aerodynamic forces. A comparative study of the performances of three IPMC flapping wings is conducted. Among the three species, it is found that thrust force produced by the IPMC flapping wing of the same size as Anax Parthenope Julius wing is maximum. Lift force produced by the IPMC wing of the same size as Sympetrum Frequens wing is maximum and the wing is suitable for low speed flight. The numerical results in this paper show that dragonfly inspired IPMC flapping wings are a viable contender for insect scale flapping wing micro air vehicles.     

A dynamic mesh strategy applied to the simulation of flapping wings

A robust and efficient dynamic grid strategy based on an overset grid coupled with mesh deformation technique is proposed for simulating unsteady flow of flapping wings undergoing large geometrical displacement. The dynamic grid method was implemented using a hierarchical unstructured overset grid locally coupled with a fast radial basis function (RBF)‐based mapping approach. The hierarchically organized overset grid allows transferring the grid resolution for multiple blocks and overlapping/embedding the meshes. The RBF‐based mapping approach is particularly highlighted in this paper in view of its considerable computational efficiency compared with conventional RBF evaluation. The performance of the proposed dynamic mesh strategy is demonstrated by three typical unsteady cases, including a rotating rectangular block in a fixed domain, a relative movement between self‐propelled fishes and the X‐wing type flapping‐wing micro air vehicle DelFly, which displays the clap‐and‐fling wing‐interaction phenomenon on both sides of the fuselage. Results show that the proposed method can be applied to the simulation of flapping wings with satisfactory efficiency and robustness. Copyright © 2016 John Wiley & Sons, Ltd.     

Vortex wake,downwash distribution,aerodynamic performance and wingbeat kinematics in slow-flying pied flycatchers

Many small passerines regularly fly slowly when catching prey, flying in cluttered environments or landing on a perch or nest. While flying slowly, passerines generate most of the flight forces during the downstroke, and have a ‘feathered upstroke’ during which they make their wing inactive by retracting it close to the body and by spreading the primary wing feathers. How this flight mode relates aerodynamically to the cruising flight and so-called ‘normal hovering’ as used in hummingbirds is not yet known. Here, we present time-resolved fluid dynamics data in combination with wingbeat kinematics data for three pied flycatchers flying across a range of speeds from near hovering to their calculated minimum power speed. Flycatchers are adapted to low speed flight, which they habitually use when catching insects on the wing. From the wake dynamics data, we constructed average wingbeat wakes and determined the time-resolved flight forces, the time-resolved downwash distributions and the resulting lift-to-drag ratios, span efficiencies and flap efficiencies. During the downstroke, slow-flying flycatchers generate a single-vortex loop wake, which is much more similar to that generated by birds at cruising flight speeds than it is to the double loop vortex wake in hovering hummingbirds. This wake structure results in a relatively high downwash behind the body, which can be explained by the relatively active tail in flycatchers. As a result of this, slow-flying flycatchers have a span efficiency which is similar to that of the birds in cruising flight and which can be assumed to be higher than in hovering hummingbirds. During the upstroke, the wings of slowly flying flycatchers generated no significant forces, but the body–tail configuration added 23 per cent to weight support. This is strikingly similar to the 25 per cent weight support generated by the wing upstroke in hovering hummingbirds. Thus, for slow-flying passerines, the upstroke cannot be regarded as inactive, and the tail may be of importance for flight efficiency and possibly manoeuvrability.     

Flight efficiency is a key to diverse wing morphologies in small insects

Insect wings are hybrid structures that are typically composed of veins and solid membranes. In some of the smallest flying insects, however, the wing membrane is replaced by hair-like bristles attached to a solid root. Bristles and membranous wing surfaces coexist in small but not in large insect species. There is no satisfying explanation for this finding as aerodynamic force production is always smaller in bristled than solid wings. This computational study suggests that the diversity of wing structure in small insects results from aerodynamic efficiency rather than from the requirements to produce elevated forces for flight. The tested wings vary from fully membranous to sparsely bristled and were flapped around a wing root with lift- and drag-based wing kinematic patterns and at different Reynolds numbers (Re). The results show that the decrease in aerodynamic efficiency with decreasing surface solidity is significantly smaller at Re = 4 than Re = 57. A replacement of wing membrane by bristles thus causes less change in energetic costs for flight in small compared to large insects. As a consequence, small insects may fly with bristled and solid wing surfaces at similar efficacy, while larger insects must use membranous wings for an efficient production of flight forces. The above findings are significant for the biological fitness and dispersal of insects that fly at elevated energy expenditures.     

Span efficiency in hawkmoths

Flight in animals is the result of aerodynamic forces generated as flight muscles drive the wings through air. Aerial performance is therefore limited by the efficiency with which momentum is imparted to the air, a property that can be measured using modern techniques. We measured the induced flow fields around six hawkmoth species flying tethered in a wind tunnel to assess span efficiency, e_i, and from these measurements, determined the morphological and kinematic characters that predict efficient flight. The species were selected to represent a range in wingspan from 40 to 110 mm (2.75 times) and in mass from 0.2 to 1.5 g (7.5 times) but they were similar in their overall shape and their ecology. From high spatio-temporal resolution quantitative wake images, we extracted time-resolved downwash distributions behind the hawkmoths, calculating instantaneous values of e_i throughout the wingbeat cycle as well as multi-wingbeat averages. Span efficiency correlated positively with normalized lift and negatively with advance ratio. Average span efficiencies for the moths ranged from 0.31 to 0.60 showing that the standard generic value of 0.83 used in previous studies of animal flight is not a suitable approximation of aerodynamic performance in insects.     

扑动轨迹对扑翼气动特性影响的数值研究

国内外对扑翼飞行的气动性能进行了大量研究,这些研究大多针对特定运动轨迹下的扑翼,然而大量观察发现,昆虫在飞行时其翅膀会出现各种不同的运动形式,这些不同的翅膀运动方式必定对其气动性能产生重要影响。该文基于对昆虫的实验和数值模拟中常用的几种扑动轨迹模型分析,建立了三种具有相同准稳态气动力的扑翼扑动轨迹,并采用数值求解N-S 方程的方法,研究了前飞状态下不同扑动轨迹对扑翼气动特性产生的影响。结果显示扑动和转动均为简谐函数轨迹形式的扑翼具有较高的升举效率和推进效率。进一步通过对不同扑动轨迹扑翼流场分析得出,扑动轨迹不能改变扑翼产生的尾流性质,但可以影响涡的强度,从而使扑翼产生不同的气动性能。     

扑翼飞行器测力平台设计与振动特性仿真分析

扑翼飞行器是基于鸟类仿生学理论衍生出的新型无人飞行器,主要通过机翼周期性上下扑动来提供飞行器所需的升力和推力,在军用和民用飞行器领域均有广阔的应用前景。扑翼飞行器气动力测量作为样机气动性测试的重要手段,多维气动力的准确测量可为新型扑翼飞行器设计优化和飞控品质的提高提供试验数据支持。本文介绍了一种新型组合式多维小量程测力平台,可实现扑翼飞行器六维气动力和气动力矩的测量。考虑到扑翼飞行器机翼上下扑动过程动态测力需求,应用Ansys Workbench有限元分析软件对测力平台进行了模态分析和频响分析,获得在工作频率下的频率响应,仿真结果表明测力平台的振动特性满足设计要求。     

扑翼飞行器气动力测量技术研究进展与展望

扑翼飞行器是一种仿照鸟类飞行的新概念小型无人飞行器,区别于传统固定翼和旋翼飞行器,它主要通过机翼扑动与空气相互作用来提供飞行动力,从而实现飞行器的姿态变动。扑翼飞行器气动特性测试的实质是揭示在非定常流场环境下,扑翼飞行器气动力的产生机制,以及相关扑翼飞行器设计参数对气动特性的影响。通过气动试验方法为扑翼飞行器飞行控制和结构优化等研制工作提供数据支持,将对新型扑翼飞行器理论研究以及飞控品质的提升起到巨大的推动作用。     

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.