Biomechanics and physiology of gait selection in flying birds

Two wing-beat gaits, distinguished by the presence or absence of lift production during the upstroke, are currently used to describe avian flight. Vortex-visualization studies indicate that lift is produced only during the downstroke in the vortex-ring gait and that lift is produced continuously in the continuous-vortex gait. Tip-reversal and feathered upstrokes represent different forms of vortex-ring gait distinguished by wing kinematics. Useful aerodynamic forces may be produced during tip-reversal upstroke in slow flight and during a feathered upstroke in fast flight, but it is probable that downstroke forces are much greater in magnitude. Uncertainty about the function of these types of upstroke may be resolved when more data are available on wake structure in different flight speeds and modes. Inferring from wing kinematics and available data on wake structure, birds with long wings or wings of high aspect ratio use a vortex-ring gait with tip-reversal upstroke at slow speeds, a vortex-ring gait with a feathered upstroke at intermediate speeds, and a continuous-vortex gait at fast speeds. Birds with short wings or wings of low aspect ratio use a vortex-ring gait with a feathered upstroke at all speeds. Regardless of wing shape, species tend to use a vortex-ring gait for acceleration and a continuous-vortex gait for deceleration. Some correlations may exist between gait selection and the function of the muscular and respiratory system. However, overall variation in wing kinematics, muscle activity, and respiratory activity is continuous rather than categorical. To further our understanding of gait selection in flying birds, it is important to test whether upstroke function varies in a similar manner. Transitions between lifting and nonlifting upstrokes may be more subtle and gradual than implied by a binomial scheme of classification.     

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.     

The Aerodynamic Cost of Head Morphology in Bats: Maybe Not as Bad as It Seems

At first sight, echolocating bats face a difficult trade-off. As flying animals, they would benefit from a streamlined geometric shape to reduce aerodynamic drag and increase flight efficiency. However, as echolocating animals, their pinnae generate the acoustic cues necessary for navigation and foraging. Moreover, species emitting sound through their nostrils often feature elaborate noseleaves that help in focussing the emitted echolocation pulses. Both pinnae and noseleaves reduce the streamlined character of a bat’s morphology. It is generally assumed that by compromising the streamlined charactered of the geometry, the head morphology generates substantial drag, thereby reducing flight efficiency. In contrast, it has also been suggested that the pinnae of bats generate lift forces counteracting the detrimental effect of the increased drag. However, very little data exist on the aerodynamic properties of bat pinnae and noseleaves. In this work, the aerodynamic forces generated by the heads of seven species of bats, including noseleaved bats, are measured by testing detailed 3D models in a wind tunnel. Models of Myotis daubentonii, Macrophyllum macrophyllum, Micronycteris microtis, Eptesicus fuscus, Rhinolophus formosae, Rhinolophus rouxi and Phyllostomus discolor are tested. The results confirm that non-streamlined facial morphologies yield considerable drag forces but also generate substantial lift. The net effect is a slight increase in the lift-to-drag ratio. Therefore, there is no evidence of high aerodynamic costs associated with the morphology of bat heads.     

Kinematic plasticity during flight in fruit bats: individual variability in response to loading

All bats experience daily and seasonal fluctuation in body mass. An increase in mass requires changes in flight kinematics to produce the extra lift necessary to compensate for increased weight. How bats modify their kinematics to increase lift, however, is not well understood. In this study, we investigated the effect of a 20% increase in mass on flight kinematics for Cynopterus brachyotis, the lesser dog-faced fruit bat. We reconstructed the 3D wing kinematics and how they changed with the additional mass. Bats showed a marked change in wing kinematics in response to loading, but changes varied among individuals. Each bat adjusted a different combination of kinematic parameters to increase lift, indicating that aerodynamic force generation can be modulated in multiple ways. Two main kinematic strategies were distinguished: bats either changed the motion of the wings by primarily increasing wingbeat frequency, or changed the configuration of the wings by increasing wing area and camber. The complex, individual-dependent response to increased loading in our bats points to an underappreciated aspect of locomotor control, in which the inherent complexity of the biomechanical system allows for kinematic plasticity. The kinematic plasticity and functional redundancy observed in bat flight can have evolutionary consequences, such as an increase potential for morphological and kinematic diversification due to weakened locomotor trade-offs.     

ON THE RECONSTRUCTION OF PTEROSAURS AND THEIR MANNER OF FLIGHT, WITH NOTES ON VORTEX WAKES

Classical pterosaur reconstructions are variants on a ‘bat-analogy’, whereby the wing is conceived as a simple membrane with no inherent bending strength, stretched between the arm and leg skeletons. The legs are considered to be splayed out to the sides, as in bats, so that the animal would have to adopt a quadrupedal stance on the ground, supported on its feet and the metacarpo-phalangeal joints. In recent years an alternative ‘bird-analogy’ has come to be generally accepted. This hypothesis, most elements of which are due to Padian (1983 a, b) calls for the animal to stand upright on its legs like a bird. The wings are independent of the legs, as in birds, are stiffened by skeletal fibres in the membrane, and have a very narrow, sharply pointed shape. There are difficulties in reconciling the bird-analogy with the evidence. The long-tailed rhamphorhynchs might conceivably have balanced their weight about their hip joints but this would not have been possible for the short-tailed pterodactyls. The bird pelvis shows modifications which permit bipedal standing in spite of the reduction of the tail, but no equivalent adaptations are seen in pterodactyls. Besides, all known pterosaur pelvises, except that of the giant pterodactyl Pteranodon were open ventrally, which would have precluded the legs from being brought to a parasagittal position, as required for bipedal walking. The notion that the wing was not attached to the legs is based on negative evidence, in that no clear impressions of the inner end of the wing membrane are preserved in the fossils. However one pterodactyl fossil shows a membrane edge approaching the ankle joint. In fossils that are preserved with the wings forward, the legs have been pulled forwards by the ankles. A tendon connecting the ankle to the wing tip is consistent with the evidence. The ‘fibres’ in the wing membranes are actually impressions of surface ridges, with no internal structure, and are better interpreted as surface wrinkles in the skin, caused by contraction of elastic fibres within the membrane. The bird analogy also results in a very unsatisfactory wing from an aerodynamic point of view. The structure of an animal wing is best understood in terms of the type of vortex wake it is adapted to generate. Hummingbirds, and insects capable of economical hovering, have wings that can be inverted on the upstroke, and when hovering, generate a wake consisting of two vortex rings per wingbeat cycle. The span of such wings is fixed, which implies that they create a ‘ladder wake’ in cruising flight, consisting of a pair of undulating wing-tip vortices, joined by a transverse vortex at each transition from downstroke to upstroke and back. Normal birds cannot invert their wings, and so are less efficient in hovering, but they can shorten the wing during the upstroke in cruising flight. This creates a ‘concertina wake’, with no transverse vortices. Hummingbirds show very limited migration performance, compared with normal birds, with the implication that a wing capable of creating a concertina wake is more economical in cruising flight than one creating a ladder wake, and is an essential adaptation for long-distance migration. A revised reconstruction of the pterosaur wing starts from the observations that, contrary to the currently popular bird-analogy, pterosaurs were not bipedal, their wings did not contain stiffening fibres but did contain elastic fibres, and the trailing edge of the membrane was supported by a tendon joining the tip of the wing finger to the ankle. A hypothetical arrangement of elastic fibres, that accounts well for the observed pattern of wrinkles in contracted wings, also allows the planform shape of the wing to be adjusted in much the same way as seen in birds, although using a completely different mechanism. It opens the possibility that pterosaurs could fly with a concertina wake, and thus could have been long-distance migrators like modern birds. Although this hypothetical wing is mechanically somewhat bat-like, it is not a return to the classical bat-analogy. It would not have the high degree of control over profile shape, which gives bats their outstanding manoeuvrability. On the other hand bats do not have the degree of control over their wingspan that is suggested here for pterosaurs, and consequently are not notable for migration performance.     

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.     

Contrasting patterns of elevational zonation for birds and mammals in the Andes of southeastern Peru

Abstract. To determine the generality of avian diversity patterns, we investigated patterns of elevational zonation shown by birds and mammals along the eastern slope of the Andes Mountains in southeastern Peru. The strong environmental gradient sampled, entirely within Peru's Manu National Park and Biosphere Reserve, supports highly diverse faunas. Elevational distributions of 901 bird species, 129 bat species, and twenty-eight species of native mice exhibit contrasting patterns in species richness, species composition, and species turnover. Birds and bats showed smooth declines of species richness with elevation, whereas the richness of mouse assemblages was unrelated to elevation. For all three groups, the greatest differences were between lowland and highland faunas, although cutoff points for this contrast varied among groups (≈ 500 m for birds, 750 m for bats, and 1000 m for mice). Differences in composition also separated bird and bat faunas on either side of c. 1400 m (the boundary between montance forest and cloud forest); for mice, this faunal transition may take place nearer to 2000 m. Bird and bat faunas lacked the more discrete zonations suggested for mouse assemblages, as indicated by elevational range profiles and nested subset analyses. Distinct highland assemblages are apparent in two-dimensional histograms of range limits of birds and mice, but not for bats. Highland bat species occupy broader elevational ranges than lowland bat species, but for both birds and mice, species at intermediate elevations had the broadest amplitudes. Finally, clumping of range maxima and minima along the gradient identified zones of pronounced species turnover in each group, but these were generally not strongly associated with the locations of ecotones. Differences in zonation of these groups appear to reflect their different biological attributes and phylogenetic histories. Such differences obviously complicate discussions of ‘general’ diversity patterns, and limit the usefulness of birds to forecast or predict diversity patterns in other more poorly known groups—other groups may show elevated diversity and endemism in areas where avian diversity patterns appear unremarkable. The pronounced contrasts between bats and mice, and the generally intermediate character of avian patterns, suggest that future analyses might profitably partition birds into finer, more homogeneous groups of historically and/or ecologically similar species. Group differences in zonation may ultimately prove explicable with information on both species-abundance patterns and resource distributions.     

Flow visualization and unsteady aerodynamics in the flight of the hawkmoth,Manduca sexta

The aerodynamic mechanisms employed durng the flight of the hawkmoth, Manduca sexta, have been investigated through smoke visualization studies with tethered moths. Details of the flow around the wings and of the overall wake structure were recorded as stereophotographs and high-speed video sequences. The changes in flow which accompanied increases in flight speed from 0.4 to 5.7 m s^-1 were analysed. The wake consists of an alternating series of horizontal and vertical vortex rings which are generated by successive down- and upstrokes, respectively. The downstroke produces significantly more lift than the upstroke due to a leading-edge vortex which is stabilized by a radia flow moving out towards the wingtip. The leading-edge vortex grew in size with increasing forward flight velocity. Such a phenomenon is proposed as a likely mechanism for lift enhancement in many insect groups. During supination, vorticity is shed from the leading edge as postulated in the ''flex'' mechanism. This vorticity would enhance upstroke lift if it was recaptured diring subsequent translation, but it is not. Instead, the vorticity is left behind and the upstroke circulation builds up slowly. A small jet provides additional thrust as the trailing edges approach at the end of the upstroke. The stereophotographs also suggest that the bound circulation may not be reversed between half strokes at the fastest flight speeds.     

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.     

Bats as prey of diurnal birds: a global perspective

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Agroforestry systems conserve species-rich but modified assemblages of tropical birds and bats

Although an increasing number of studies have shown that diverse, multi-strata agroforestry systems can contribute to the conservation of tropical biodiversity, there is still debate about how the biodiversity within agroforestry systems compares to that of intact forest and alternative land uses. In order to assess the relative importance of agroforestry systems for biodiversity conservation, we characterized bat and bird assemblages occurring in forests, two types of agroforestry systems (cacao and banana) and plantain monocultures in the indigenous reserves of Talamanca, Costa Rica. A total of 2,678 bats of 45 species were captured, and 3,056 birds of 224 species were observed. Agroforestry systems maintained bat assemblages that were as (or more) species-rich, abundant and diverse as forests, had the same basic suite of dominant species, but contained more nectarivorous bats than forests. Agroforestry systems also contained bird assemblages that were as abundant, species-rich and diverse as forests; however the species composition of these assemblages was highly modified, with fewer forest dependent species, more open area species and different dominant species. The plantain monocultures had highly modified and depauperate assemblages of both birds and bats. Across land uses, bird diversity and species richness were more closely correlated with the structural and floristic characteristics than were bats, suggesting potential taxon-specific responses to different land uses. Our results indicate that diverse cacao and banana agroforestry systems contribute to conservation efforts by serving as habitats to high numbers of bird and bat species, including some, but not all, forest-dependent species and species of known conservation concern. However, because the animal assemblages in agroforestry systems differ from those in forests, the maintenance of forests within the agricultural landscape is critical for conserving intact assemblages at the landscape level.     

Wing kinematics of avian flight across speeds

To test whether wing shape affects the kinematics of wing motion during bird flight, we recorded high-speed video (250 Hz) of four species flying in a variable-speed wind tunnel. The birds flew at intervals of 2 m s⁻¹, ranging from 1 m s⁻¹ up to their respective maximum flight speed, which varied from 14 to 17 m s⁻¹ depending on the species. Kinematic data obtained from two synchronized, high-speed video cameras were analyzed using 3D reconstruction. Three species with relatively pointed, high-aspect ratio wings changed wingbeat styles according to flight speed (budgerigar, Melopsittacus undulatus ; cockatiel, Nymphicus hollandicus ; ringed turtle dove, Streptopelia risoria ). These species used a wing-tip reversal upstroke, characterized by supination of the distal wing at mid-upstroke, at equivalent airspeeds ≤7 to 9 m s⁻¹. In faster flight, they used a swept-wing upstroke, without distal wing supination. At mid-upstroke at any speed, wingspan in these species was greater than wrist span. In contrast, at all steady flight speeds, the black-billed magpie Pica hudsonia with relatively broad, low-aspect ratio wings, used a flexed-wing, feathered upstroke in which wrist spans were equal to or greater than wingspans. Our results demonstrate that wing kinematics vary gradually as a function of flight speed, and that the patterns of variation are strongly influenced by external wing shape.     

Flapping tail membrane in bats produces potentially important thrust during horizontal takeoffs and very slow flight

Historically, studies concerning bat flight have focused primarily on the wings. By analyzing high-speed video taken on 48 individuals of five species of vespertilionid bats, we show that the capacity to flap the tail-membrane (uropatagium) in order to generate thrust and lift during takeoffs and minimal-speed flight (<1 m ^s−1) was largely underestimated. Indeed, bats flapped the tail-membrane by extensive dorso-ventral fanning motions covering as much as 135 degrees of arc consistent with thrust generation by air displacement. The degree of dorsal extension of the tail-membrane, and thus the potential amount of thrust generated during platform launches, was significantly correlated with body mass (P = 0.02). Adduction of the hind limbs during upstrokes collapsed the tail-membrane thereby reducing its surface area and minimizing negative lift forces. Abduction of the hind limbs during the downstroke fully expanded the tail-membrane as it was swept ventrally. The flapping kinematics of the tail-membrane is thus consistent with expectations for an airfoil. Timing offsets between the wings and tail-membrane during downstrokes was as much as 50%, suggesting that the tail-membrane was providing thrust and perhaps lift when the wings were retracting through the upstoke phase of the wing-beat cycle. The extent to which the tail-membrane was used during takeoffs differed significantly among four vespertilionid species (P = 0.01) and aligned with predictions derived from bat ecomorphology. The extensive fanning motion of the tail membrane by vespertilionid bats has not been reported for other flying vertebrates.     

Simulating avian wingbeat kinematics

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

Bats are Not Birds – Different Responses to Human Land‐use on a Tropical Mountain

Land‐use intensification has consequences for biodiversity and ecosystem functioning, with various taxonomic groups differing widely in their sensitivity. As land‐use intensification alters habitat structure and resource availability, both factors may contribute to explaining differences in animal species diversity. Within the local animal assemblages the flying vertebrates, bats and birds, provide important and partly complementary ecosystem functions. We tested how bats and birds respond to land‐use intensification and compared abundance, species richness, and community composition across a land‐use gradient including forest, traditional agroforests (home garden), coffee plantations and grasslands on Mount Kilimanjaro, Tanzania. Furthermore, we asked how sensitive different habitat and feeding guilds of bats and birds react to land‐use intensification and the associated alterations in vegetation structure and food resource availability. In contrast to our expectations, land‐use intensification had no negative effect on species richness and abundance of all birds and bats. However, some habitat and feeding guilds, in particular forest specialist and frugivorous birds, were highly sensitive to land‐use intensification. Although the habitat guilds of both, birds and bats, depended on a certain degree of vegetation structure, total bat and bird abundance was mediated primarily by the availability of the respective food resources. Even though the highly structured southern slopes of Mount Kilimanjaro are able to maintain diverse bat and bird assemblages, the sensitivity of avian forest specialists against land‐use intensification and the dependence of the bat and bird habitat guilds on a certain vegetation structure demonstrate that conservation plans should place special emphasis on these guilds.     

Scaling of body frontal area and body width in birds

By analyzing a homogenous dataset we show, in contradiction to a previous study, that the scaling of body frontal area (S(b)) with body mass (m(b)) does not differ between passerine and nonpasserine birds. It is likely that comparison of data collected from live passerines with data collected from frozen nonpasserines had led to the incorrect conclusion that the scaling of S(b) varied between the taxa. We suggest that body dimensions collected from frozen specimens, or specimens stored in alcohol, are not applicable to live birds, and that both the current equations presented in the literature for predicting S(b) from m(b) may lead to inaccurate estimates. Using data from preserved specimens, we found that S(b) scales isometrically with m(b) (S(b) proportional, variant m(b) (0.66)), and therefore we found no evidence for larger birds being more streamlined than smaller birds. S(b) scales with negative allometry against wingspan (b), however, and b scales with positive allometry against m(b), so larger birds have smaller S(b) relative to b. In addition, it appears that dorsoventral flattening of the body is a general characteristic of bird's bodies but that it is more pronounced in larger birds, suggesting perhaps a function in terms of increased lift during forward flight. It appears that bird's bodies obey the surface-to-area geometric scaling law, but bird body shape may vary in relation to aerodynamic function. We suggest that a large-scale study, simultaneously measuring S(b) and m(b) in live passerines and nonpasserines, is required to improve the predictive power of S(b) upon m(b) scaling equations, which play a key role in the estimation of mechanical power consumption in flight in birds. Furthermore, the relations between bird body shape and axial skeleton dimensions, with reference to aerodynamic adaptation, warrant further investigation.     

Parallel trends in the species diversity of west indian birds and bats

Summary In this paper I compare several biogeographic patterns of West Indian resident land birds and bats, including species-area and trophic diversity-area relationships, the number of islands inhabited per species and levels of endemism, trophic structure as compared with tropical mainland areas, and the degree of faunal simlarity between islands of similar sizes but different locations. In most respects, the bat and bird patterns are strikingly similar. Groups of birds that are conspicuously missing from the Antilles because of the absence of appropriate resources also have missing chiropteran counterparts. Plant-visiting bats and birds are better-represented in terms of relative number of species and, in birds, in biomass, on the Lesser Antilles than on the mainland (e.g. Panama). Small Antillean islands tend to share more species of birds and bats than do larger islands. Stochastic (sensu Simberloff 1978), deterministic, and interactive (e.g. competitive and trophic interactions) factors appear to underly these biogeographic trends. No evidence exists to suggest that Caribbean bats and birds have negatively affected each other's diversity.     

Flow Visualization of Rhinoceros Beetle (Trypoxylus dichotomus) in Free Flight

Aerodynamic characteristics of the beetle,Trypoxylus dichotomus,which has a pair of elytra (forewings) and flexible hind wings,are investigated.Visualization experiments were conducted for various flight conditions of a beetle,Trypoxylus dichotomus:free,tethered,hovering,forward and climbing flights.Leading edge,trailing edge and tip vortices on both wings were observed clearly.The leading edge vortex was stable and remained on the top surface of the elytron for a wide interval during the downstroke of free forward flight.Hence,the elytron may have a considerable role in lift force generation of the beetle.In addition,we reveal a suction phenomenon between the gaps of the hind wing and the elytron in upstroke that may improve the positive lift force on the hind wing.We also found the reverse clap-fling mechanism of the T.dichotomus beetle in hovering flight.The hind wings touch together at the beginning of the upstroke.The vortex generation,shedding and interaction give a better understanding of the detailed aerodynamic mechanism of beetle flight.     

A mechanical model of wing and theoretical estimate of taper factor for three gliding birds

We tested a mechanical model of wing, which was constructed using the measurements of wingspan and wing area taken from three species of gliding birds. In this model, we estimated the taper factors of the wings for jackdaw (Corrus monedula), Harris’ hawk (Parabuteo unicinctas) and Lagger falcon (Falco jugger) as 1.8, 1.5 and 1.8, respectively. Likewise, by using the data linear regression and curve estimation method, as well as estimating the taper factors and the angle between the humerus and the body, we calculated the relationship between wingspan, wing area and the speed necessary to meet the aerodynamic requirements of sustained flight. In addition, we calculated the relationship between the speed, wing area and wingspan for a specific angle between the humerus and the body over the range of stall speed to maximum speed of gliding flight. We then compared the results for these three species of gliding birds. These comparisons suggest that the aerodynamic characteristics of Harris’ hawk wings are similar to those of the falcon but different from those of the jackdaw. This paper also presents two single equations to estimate the minimum angle between the humerus and the body as well as the minimum span ratio of a bird in gliding flight.     

Wing design and scaling of flying fish with regard to flight performance

Fin and body dimensions of six genera of flying fish (Exocoetidae) were examined to study variation in morphological parameters in relation to aerodynamics performance. The fins are modified as wings for gliding flight. Fin area and fin span increase with increasing body mass, whereas the percentage of wing area contributed by the pectoral fins and the percentage of the caudal fin area contributed by the hypocaudal lobe remain constant. The aerodynamic design of flying fish approximates the monoplane-biplane classification proposed by Breder (1930). Scaling relationships for wing loading and aspect ratio indicate that wing morphology in the Exocoetidae is more similar to birds and bats than to other gliders. The flight performance of flying fish is a high-speed glide with a relatively flat trajectory. The wing, as indicated by the aspect ratio, is designed for high lift with low drag characteristics.