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

     

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.     

被子植物翅果的多样性及演化

翅果能够依靠风力进行传播, 可能是被子植物快速散布和物种分化的一个重要因素。狭义的翅果是指果皮延伸成翅且不开裂的干果; 广义的翅果则包括果皮、花被片或苞片形成果翅的所有果实。根据果翅形态及其生长方式的不同, 广义的翅果可分为单侧翅果、周位翅果(圆翅果与蝶翅果)、棱翅果、披针翅果、翼状萼翅果、叶状苞翅果6种类型, 其空中运动方式有自旋式(单侧翅果、翼状萼翅果)、波浪式(周位翅果、叶状苞翅果)、翻滚自旋式(周位翅果)、直升机式(披针翅果、翼状萼翅果)和滚筒式(棱翅果)。棱翅果与圆翅果在被子植物基部类群樟目就有发生, 并同时出现在单子叶植物和双子叶植物中, 可能是最早出现的翅果类型。翅果的演化过程呈现出果翅数量增加、果翅偏向单侧和果翅负荷(果实质量与果翅面积之比)降低的趋势, 以利于适应较小的风并增加传播距离。果翅除了促进果实与种子的风力传播外, 还具有物理防御、调节种子萌发和促进二次传播等作用。泛热带分布的金虎尾科有着极其丰富的翅果类型, 与其多次跨洋长距离扩散密切相关, 可以作为研究翅果适应与演化的一个模式类群。结合生态和演化-发育生物学方法, 研究不同类型翅果在适应风力传播方面的差异、萼片或苞片发育成翅的分子与遗传机制、翅果不同类型的演化历史及其对被子植物物种多样性的影响等是今后值得探讨的重要问题。     

Aerodynamic Interactions Between Wing and Body of a Model Insect in Forward Flight and Maneuvers

The aerodynamic interactions between the body and the wings of a model insect in forward flight and maneuvers are studied using the method of numerically solving the Navier-Stokes equations over moving overset grids. Three cases are considered, including a complete insect, wing pair only and body only. By comparing the results of these cases, the interaction effect between the body and the wing pair can be identified. The changes in the force and moment coefficients of the wing pair due to the presence of the body are less than 4.5% of the mean vertical force coefficient of the model insect; the changes in the aerodynamic force coefficients of the body due to the presence of the wings are less than 5.0% of the mean vertical force coefficient of the model insect. The results of this paper indicate that in studying the aerodynamics and flight dynamics of a flapping insect in forward flight or maneuver, separately computing (or measuring) the aerodynamic forces and moments on the wing pair and on the body could be a good approximation.     

Diversity and evolution of samara in angiosperm

翅果能够依靠风力进行传播, 可能是被子植物快速散布和物种分化的一个重要因素。狭义的翅果是指果皮延伸成翅且不开裂的干果; 广义的翅果则包括果皮、花被片或苞片形成果翅的所有果实。根据果翅形态及其生长方式的不同, 广义的翅果可分为单侧翅果、周位翅果(圆翅果与蝶翅果)、棱翅果、披针翅果、翼状萼翅果、叶状苞翅果6种类型, 其空中运动方式有自旋式(单侧翅果、翼状萼翅果)、波浪式(周位翅果、叶状苞翅果)、翻滚自旋式(周位翅果)、直升机式(披针翅果、翼状萼翅果)和滚筒式(棱翅果)。棱翅果与圆翅果在被子植物基部类群樟目就有发生, 并同时出现在单子叶植物和双子叶植物中, 可能是最早出现的翅果类型。翅果的演化过程呈现出果翅数量增加、果翅偏向单侧和果翅负荷(果实质量与果翅面积之比)降低的趋势, 以利于适应较小的风并增加传播距离。果翅除了促进果实与种子的风力传播外, 还具有物理防御、调节种子萌发和促进二次传播等作用。泛热带分布的金虎尾科有着极其丰富的翅果类型, 与其多次跨洋长距离扩散密切相关, 可以作为研究翅果适应与演化的一个模式类群。结合生态和演化-发育生物学方法, 研究不同类型翅果在适应风力传播方面的差异、萼片或苞片发育成翅的分子与遗传机制、翅果不同类型的演化历史及其对被子植物物种多样性的影响等是今后值得探讨的重要问题。     

THE TERMINAL VELOCITY AND DISPERSAL OF SPINNING SAMARAS

Strobe photographs were taken of over 200 spinning samaras from seven species of trees. These were used to measure the rate of descent, angular velocity, orientation, and other parameters of the samaras as they fell. These data were then used to compare the aerodynamic behavior of samaras, helicopters, and theoretical ideal rotors. Plotting morphological data for each samara against its rate of descent showed that this rate was highly correlated with the square root of the samara's wing loading (samara weight divided by wing-surface area). This plot demonstrated the existence of two distinct groups of samaras, distinguished by their morphology, spinning motion, and rate of descent. These results are of greatest use in characterizing local dispersal patterns.     

AERODYNAMICS,THERMOREGULATION, AND THE EVOLUTION OF INSECT WINGS: DIFFERENTIAL SCALING AND EVOLUTIONARY CHANGE

We examine several aerodynamic and thermoregulatory hypotheses about possible adaptive factors in the evolution of wings from small winglets in insects. Using physical models of Paleozoic insects in a wind tunnel, we explore the potential effects of wings for increasing gliding distance, increasing dispersal distance during parachuting, improving attitude control or stability, and elevating body temperatures during thermoregulation. The effects of body size and shape, wing length, number, and venation, and meteorological conditions are considered. Hypotheses consistent with both fixed and moveable wing articulations are examined. Short wings have no significant effects on any of the aerodynamic characteristics, relative to wingless models, while large wings do have significant effects. In contrast, short wings have large thermoregulatory effects relative to wingless models, but further increases in wing length do not significantly affect thermoregulatory performance. At any body size, there is a wing length below which there are significant thermoregulatory effects of increasing wing length, and above which there are significant aerodynamic effects of increasing wing length. The relative wing length at which this transition occurs decreases with increasing body size. These results suggest that there could be no effective selection for increasing wing length in wingless or short-winged insects in relation to increased aerodynamic capacity. Our results are consistent with the hypothesis that insect wings initially served a thermoregulatory function and were used for aerodynamic functions only at larger wing lengths and/or body sizes. Thus, we propose that thermoregulation was the primary adaptive factor in the early evolution of wings that preadapted them for the subsequent evolution of flight. Our results illustrate an evolutionary mechanism in which a purely isometric change in body size may produce a qualitative change in the function of a given structure. We propose a hypothesis in which the transition from thermoregulatory to aerodynamic function for wings involved only isometric changes in body size and argue that changes in body form were not a prerequisite for this major evolutionary change in function.     

A Quasi-Steady Lifting Line Theory for Insect-Like Hovering Flight

A novel lifting line formulation is presented for the quasi-steady aerodynamic evaluation of insect-like wings in hovering flight. The approach allows accurate estimation of aerodynamic forces from geometry and kinematic information alone and provides for the first time quantitative information on the relative contribution of induced and profile drag associated with lift production for insect-like wings in hover. The main adaptation to the existing lifting line theory is the use of an equivalent angle of attack, which enables capture of the steady non-linear aerodynamics at high angles of attack. A simple methodology to include non-ideal induced effects due to wake periodicity and effective actuator disc area within the lifting line theory is included in the model. Low Reynolds number effects as well as the edge velocity correction required to account for different wing planform shapes are incorporated through appropriate modification of the wing section lift curve slope. The model has been successfully validated against measurements from revolving wing experiments and high order computational fluid dynamics simulations. Model predicted mean lift to weight ratio results have an average error of 4% compared to values from computational fluid dynamics for eight different insect cases. Application of an unmodified linear lifting line approach leads on average to a 60% overestimation in the mean lift force required for weight support, with most of the discrepancy due to use of linear aerodynamics. It is shown that on average for the eight insects considered, the induced drag contributes 22% of the total drag based on the mean cycle values and 29% of the total drag based on the mid half-stroke values.     

绒毛白蜡二态型果实的扩散特征

多态型果实或种子的出现对植物种群的扩散具有重要的意义。绒毛白蜡(Fraxinus velutina)的果实具有二态型特征,主要表现在果翅数量上不同,分别定义为二翅型和三翅型果实,为了比较两类果实在风传扩散时的差异,研究了两类果实的形态、果翅结构和扩散距离及扩散时长。在大型封闭地下室内,以电扇在不同速度档位产生的气流作为风源,分别从2、1.5、1m处手动释放果实,对风速为0、4.6、6.5、7.3m/s时的果实扩散距离及扩散时长进行了比较;并在此基础上对果实的形态特征与扩散特征进行了线性相关分析。结果表明:在同一高度及相同风速下,三翅型果实的水平扩散距离都极显著的大于二翅型,但其相应的扩散时长都小于二翅型。在相同情况下,三翅型的果实沉降速度显著高于二翅型。两类果实随着释放高度的增加,其扩散距离和扩散时长都相应的增加;随着风速的升高,其扩散距离及扩散时长都相应的增加。三翅型果实质量显著高于二翅型,相反,三翅型果翅长与宽都显著小于二翅型。两种翅型的果翅细胞结构都一样,细胞内部都呈现气囊状,果翅表面沿纵轴方向有流线型的纵棱。通过直线相关分析发现,翅型是对扩散距离和扩散时长影响最显著的形态特征;与果实释放高度相比,风速是影响绒毛白蜡果实扩散距离与扩散时长最显著的环境因素。绒毛白蜡三翅型果实比二翅型果实传播的远,关键在于其具有三翅,三翅对阵风瞬间响应,使得沉降速度较二翅型高,可以在瞬时风的作用下,快速传播到较远的距离。三翅型与二翅型在扩散方式上的结合增强了绒毛白蜡的生存与定殖机会。     

Numerical investigation of the aerodynamic characteristics of a hovering Coleopteran insect

The aerodynamic characteristics of the Coleopteran beetle species Epilachna quadricollis, a species with flexible hind wings and stiff elytra (fore wings), are investigated in terms of hovering flight. The flapping wing kinematics of the Coleopteran insect are modeled through experimental observations with a digital high-speed camera and curve fitting from an ideal harmonic kinematics model. This model numerically simulates flight by estimating a cross section of the wing as a two-dimensional elliptical plane. There is currently no detailed study on the role of the elytron or how the elytron-hind wing interaction affects aerodynamic performance. In the case of hovering flight, the relatively small vertical or horizontal forces generated by the elytron suggest that the elytron makes no significant contribution to aerodynamic force.     

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.     

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.     

Effect of slotted wing tips on yawing moment characteristics

The aerodynamic yawing moment characteristics of bird wings with slotted tips are dealt with. Emphasis is placed on the effect of sweep which the separated feathers constituting the wing tips show and which can reach significant values. Reference is made to basic aerodynamic characteristics of wings with sweep which yields a stabilizing yawing moment significantly larger than that of unswept wings. Then, the yawing moment characteristics are determined for a wing, the features of which are considered as representative of bird wings with sweep in their slotted tips. A sophisticated aerodynamic procedure is used for obtaining results of high precision. It is shown that the sweep in the slotted wing tips yields a stabilizing yawing moment of significant magnitude, considerably increasing with the lift coefficient. To make the significance of wing tip sweep for the ability to generate yawing moments more perspicuous, a wing modification the slotted tips of which are unswept is considered for comparison. It turns out that this wing shows yawing moments which are substantially smaller. A physical insight into the effect of slotted wing tip sweep on the aerodynamic yawing moment characteristics is provided by showing the underlying mechanism. From the results presented in this paper it follows that the sweep in slotted wing tips provides a substantial contribution to the aerodynamic yawing moment and, thus, to yaw stability. It may be concluded that this is an essential reason why there is sweep in the slotted tips of bird wings.     

Falling with Style: Bats Perform Complex Aerial Rotations by Adjusting Wing Inertia

The remarkable maneuverability of flying animals results from precise movements of their highly specialized wings. Bats have evolved an impressive capacity to control their flight, in large part due to their ability to modulate wing shape, area, and angle of attack through many independently controlled joints. Bat wings, however, also contain many bones and relatively large muscles, and thus the ratio of bats’ wing mass to their body mass is larger than it is for all other extant flyers. Although the inertia in bat wings would typically be associated with decreased aerial maneuverability, we show that bat maneuvers challenge this notion. We use a model-based tracking algorithm to measure the wing and body kinematics of bats performing complex aerial rotations. Using a minimal model of a bat with only six degrees of kinematic freedom, we show that bats can perform body rolls by selectively retracting one wing during the flapping cycle. We also show that this maneuver does not rely on aerodynamic forces, and furthermore that a fruit fly, with nearly massless wings, would not exhibit this effect. Similar results are shown for a pitching maneuver. Finally, we combine high-resolution kinematics of wing and body movements during landing and falling maneuvers with a 52-degree-of-freedom dynamical model of a bat to show that modulation of wing inertia plays the dominant role in reorienting the bat during landing and falling maneuvers, with minimal contribution from aerodynamic forces. Bats can, therefore, use their wings as multifunctional organs, capable of sophisticated aerodynamic and inertial dynamics not previously observed in other flying animals. This may also have implications for the control of aerial robotic vehicles.     

Computational Aerodynamic Analysis of a Micro-CT Based Bio-Realistic Fruit Fly Wing

The aerodynamic features of a bio-realistic 3D fruit fly wing in steady state (snapshot) flight conditions were analyzed numerically. The wing geometry was created from high resolution micro-computed tomography (micro-CT) of the fruit fly Drosophila virilis. Computational fluid dynamics (CFD) analyses of the wing were conducted at ultra-low Reynolds numbers ranging from 71 to 200, and at angles of attack ranging from -10° to +30°. It was found that in the 3D bio-realistc model, the corrugations of the wing created localized circulation regions in the flow field, most notably at higher angles of attack near the wing tip. Analyses of a simplified flat wing geometry showed higher lift to drag performance values for any given angle of attack at these Reynolds numbers, though very similar performance is noted at -10°. Results have indicated that the simplified flat wing can successfully be used to approximate high-level properties such as aerodynamic coefficients and overall performance trends as well as large flow-field structures. However, local pressure peaks and near-wing flow features induced by the corrugations are unable to be replicated by the simple wing. We therefore recommend that accurate 3D bio-realistic geometries be used when modelling insect wings where such information is useful.     

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.     

Thermal impact of migrating birds’ wing color on their flight performance: Possibility of new generation of biologically inspired drones

The thermal impact of the birds’ color on their flight performance are investigated. In most of the large migrating birds, the top of their wings is black. Considering this natural phenomenon in the migrating birds, such as albatross, a thermal analysis of the boundary layer of their wings is performed during the year depending on the solar insulation. It is shown that the temperature difference between the bright and dark colored top wing surface is around 10 °C. The dark color on the top of the wing increases the temperature of the boundary layer over the wing which consequently reduces the skin drag force over the wing. This reduction in the drag force can be considered as one of the effective factors for long endurance of these migrating birds. This research should lead to improved designs of the drones by applying the inspired colors which can help drones increase their endurance.     

Aerodynamic yawing moment characteristics of bird wings

The aerodynamic yawing moments due to sideslip are considered for wings of birds. Reference is made to the experience with aircraft wings in order to identify features which are significant for the yawing moment characteristics. Thus, it can be shown that wing sweep, aspect ratio and lift coefficient have a great impact. Focus of the paper is on wing sweep which can considerably increase the yawing moment due to sideslip when compared with unswept wings. There are many birds the wings of which employ sweep. To show the effect of sweep for birds, the aerodynamic characteristics of a gull wing which is considered as a representative example are treated in detail. For this purpose, a sophisticated aerodynamic method is used to compute results of high precision. The yawing moments of the gull wing with respect to the sideslip angle and the lift coefficient are determined. They show a significant level of yaw stability which strongly increases with the lift coefficient. It is particularly high in the lift coefficient region of best gliding flight conditions. In order to make the effect of sweep more perspicuous, a modification of the gull wing employing no sweep is considered for comparison. It turns out that the unswept wing yields yawing moments which are substantially smaller than those of the original gull wing with sweep. Another feature significant for the yawing moment characteristics concerns the fact that sweep is at the outer part of bird wings. By considering the underlying physical mechanism, it is shown that this feature is most important for the efficiency of wing sweep. To sum up, wing sweep provides a primary contribution to the yawing moments. It may be concluded that this is an essential reason why there is sweep in bird wings.     

Note on the glide of a bird with wings bent downwards

This note considers the influence of the bending down of the wings of a bird on the performance of its glide. The induced drag of bent wings is compared with the induced drag of a corresponding straight wing. Numerical results are given.     

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.