Flight speed of seabirds in relation to wind speed and direction

We studied flight speed among all major seabird taxa. Our objectives were to provide further insight into dynamics of seabird flight and to develop allometric equations relating ground speed to wind speed and direction for use in adjusting seabird density estimates (calculated from surveys at sea) for the effect of bird movement. We used triangulation at sea to estimate ground speeds of 1562 individuals of 98 species. Species sorted into 25 “groups” based on similarity in ground speeds and taxonomy. After they were controlled for differences inground speed, the 25 groups sorted into eight major “types” on the basis of response to wind speed and wind direction. Wind speed and direction explained 1664% of the variation in ground speed among seabird types. For analyses on air speed (ground speed minus apparent wind speed), we divided the 25 groups according to four flight styles: gliding, flap-gliding, glide-flapping and flapping. Tailwind speed had little effect on air speed of gliders (albatrosses and large gadfly petrels), but species that more often used flapping decreased air speed with increase in tailwinds. All species increased air speeds significantly with increased headwinds. Gliders showed the greatest increase relative to increase in headwind speed and flappers the least. With tailwind flight, air speeds were greatest among species with highest wing loading for each flight style except gliders, which showed no relationship. For headwind flight, species with higher wing loading had higher air speeds; however, the relation was weaker in flappers compared with species using some amount of gliding. In contrast, analyses for air speed ratio (i.e. difference between air speed in acrosswinds [with no apparent wind] and speed flown into headwinds, or with tailwinds, divided by speed acrosswind) revealed that among species using some flapping, and with lower wing loading (surface-feeding shearwaters, small gadfly petrels, storm petrels, phalaropes, gulls and terns), adjusted air speeds more than those with higher wing loading (alcids, “diving shearwaters”, “Manx-type shearwaters”, pelicans, boobies and cormorants). As a result, most flappers of low wing loading flew much faster than V_mr (the most energy efficient air speed per distance flown) when flying into headwinds. We suggest that better-than-predicted gliding performance with acrosswinds and tailwinds of large gadfly petrels, compared with albatrosses, resulted from a different type of “soaring” not previously described in seabirds.     

Morphology, Velocity, and Intermittent Flight in Birds

Body size, pectoralis composition, aspect ratio of the wing,and forward speed affect the use of intermittent flight in birds.During intermittent non-flapping phases, birds extend theirwings and glide or flex their wings and bound. The pectoralismuscle is active during glides but not during bounds; activityin other primary flight muscles is variable. Mechanical power,altitude, and velocity vary among wingbeats in flapping phases;associated with this variation are changes in neuromuscularrecruitment, wingbeat frequency, amplitude, and gait. Speciesof intermediate body mass (35–158 g) tend to flap-glideat slower speeds and flap-bound at faster speeds, regardlessof the aspect ratio of their wings. Such behavior may reducemechanical power output relative to continuous flapping. Smallerspecies (<20 g) with wings of low aspect ratio may flap-boundat all speeds, yet existing models do not predict an aerodynamicadvantage for the flight style at slow speeds. The behaviorof these species appears to be due to wing shape rather thanpectoralis physiology. As body size increases among species,percent time spent flapping increases, and birds much largerthan 300 g do not flap-bound. This pattern may be explainedby adverse scaling of mass-specific power or lift per unit poweroutput available from flight muscles. The size limit for theability to bound intermittently may be offset somewhat by thescaling of pectoralis composition. The percentage of time spentflapping during intermittent flight also varies according toflight speed.     

Scaling of Soaring Seabirds and Implications for Flight Abilities of Giant Pterosaurs

The flight ability of animals is restricted by the scaling effects imposed by physical and physiological factors. In comparisons of the power available from muscle and the mechanical power required to fly, it is predicted that the margin between the powers should decrease with body size and that flying animals have a maximum body size. However, predicting the absolute value of this upper limit has proven difficult because wing morphology and flight styles varies among species. Albatrosses and petrels have long, narrow, aerodynamically efficient wings and are considered soaring birds. Here, using animal-borne accelerometers, we show that soaring seabirds have two modes of flapping frequencies under natural conditions: vigorous flapping during takeoff and sporadic flapping during cruising flight. In these species, high and low flapping frequencies were found to scale with body mass (mass ^−0.30 and mass ^−0.18) in a manner similar to the predictions from biomechanical flight models (mass ^−1/3 and mass ^−1/6). These scaling relationships predicted that the maximum limits on the body size of soaring animals are a body mass of 41 kg and a wingspan of 5.1 m. Albatross-like animals larger than the limit will not be able to flap fast enough to stay aloft under unfavourable wind conditions. Our result therefore casts doubt on the flying ability of large, extinct pterosaurs. The largest extant soarer, the wandering albatross, weighs about 12 kg, which might be a pragmatic limit to maintain a safety margin for sustainable flight and to survive in a variable environment.     

Perch-hunting in insectivorous Rhinolophus bats is related to the high energy costs of manoeuvring in flight

Foraging behaviour of bats is supposedly largely influenced by the high costs of flapping flight. Yet our understanding of flight energetics focuses mostly on continuous horizontal forward flight at intermediate speeds. Many bats, however, perform manoeuvring flights at suboptimal speeds when foraging. For example, members of the genus Rhinolophus hunt insects during short sallying flights from a perch. Such flights include many descents and ascents below minimum power speed and are therefore considered energetically more expensive than flying at intermediate speed. To test this idea, we quantified the energy costs of short manoeuvring flights (<2 min) using the Na-bicarbonate technique in two Rhinolophus species that differ in body mass but have similar wing shapes. First, we hypothesized that, similar to birds, energy costs of short flights should be higher than predicted by an equation derived for bats at intermediate speeds. Second, we predicted that R. mehelyi encounters higher flight costs than R. euryale, because of its higher wing loading. Although wing loading of R. mehelyi was only 20% larger than that of R. euryale, its flight costs (2.61 ± 0.75 W; mean ± 1 SD) exceeded that of R. euryale (1.71 ± 0.37 W) by 50%. Measured flight costs were higher than predicted for R. mehelyi, but not for R. euryale. We conclude that R. mehelyi face elevated energy costs during short manoeuvring flights due to high wing loading and thus may optimize foraging efficiency by energy-conserving perch-hunting.     

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.     

Wing‐beat characteristics of birds recorded with tracking radar and cine camera

This study presents wing‐beat frequency data measured mainly by radar, complemented by video and cinematic recordings, for 153 western Palaearctic and two African species. Data on a further 45 Palaearctic species from other sources are provided in an electronic appendix. For 41 species with passerine‐type flight, the duration of flapping and pausing phases is given. The graphical presentations of frequency ranges and wing‐beat patterns show within‐species variation and allow easy comparison between species, taxonomic groups and types of flight. Wing‐beat frequency is described by Pennycuick (J. Exp. Biol. 2001; 204: 3283–3294) as a function of body‐mass, wing‐span, wing‐area, gravity and air density; for birds with passerine‐type flight the power‐fraction has also to be considered. We tested Pennycuick’s general allometric model and estimated the coefficients based on our data. The general model explained a high proportion of variation in wing‐beat frequency and the coefficients differed only slightly from Pennycuick’s original values. Modelling continuous‐flapping flyers alone resulted in coefficients not different from those predicted (within 95% intervals). Doing so for passerine‐type birds resulted in a model with non‐significant contributions of body‐mass and wing‐span to the model. This was mainly due to the very high correlation between body‐mass, wing‐span and wing‐area, revealing similar relative scaling properties within this flight type. However, wing‐beat frequency increased less than expected with respect to power‐fraction, indicating that the drop in flight level during the non‐flapping phases, compensated by the factor (g/q)^0.5 in Pennycuick’s model, is smaller than presumed. This may be due to lift produced by the body during the bounding phase or by only partial folding of the wings.     

Cross sectional geometry of the forelimb skeleton and flight mode in pelecaniform birds

Avian wing elements have been shown to experience both dorsoventral bending and torsional loads during flapping flight. However, not all birds use continuous flapping as a primary flight strategy. The pelecaniforms exhibit extraordinary diversity in flight mode, utilizing flapping, flap‐gliding, and soaring. Here we (1) characterize the cross‐sectional geometry of the three main wing bone (humerus, ulna, carpometacarpus), (2) use elements of beam theory to estimate resistance to loading, and (3) examine patterns of variation in hypothesized loading resistance relative to flight and diving mode in 16 species of pelecaniform birds. Patterns emerge that are common to all species, as well as some characteristics that are flight‐ and diving‐mode specific. In all birds examined, the distal most wing segment (carpometacarpus) is the most elliptical (relatively high I_max/I_min) at mid‐shaft, suggesting a shape optimized to resist bending loads in a dorsoventral direction. As primary flight feathers attach at an oblique angle relative to the long axis of the carpometacarpus, they are likely responsible for inducing bending of this element during flight. Moreover, among flight modes examined the flapping group (cormorants) exhibits more elliptical humeri and carpometacarpi than other flight modes, perhaps pertaining to the higher frequency of bending loads in these elements. The soaring birds (pelicans and gannets) exhibit wing elements with near‐circular cross‐sections and higher polar moments of area than in the flap and flap‐gliding birds, suggesting shapes optimized to offer increased resistance to torsional loads. This analysis of cross‐sectional geometry has enhanced our interpretation of how the wing elements are being loaded and ultimately how they are being used during normal activities. J. Morphol., 2011. © 2011 Wiley‐Liss,Inc.     

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.     

Hunting flight speeds of five southern African raptors

The flight speeds of hunting falconry birds were determined using global positioning system data loggers. Until now, the hunting flight speed of African raptors has not been directly measured. We predicted that hunting flight speeds would differ between species and that flight dynamics, such as altitude, and bird morphology, particularly wing surface area, would influence maximum and mean flight speeds. This study considered five African raptor species, which included two long-wing species, Lanner Falcon Falco biarmicus and Peregrine Falcon F. peregrinus, one short-wing species, Black Sparrowhawk Accipiter melanoleucus, and two broad-wing species, African Hawk-eagle Aquila spilogaster and Jackal Buzzard Buteo rufofuscus. Maximum and mean hunt speeds differed significantly between the long- and short-wing species. There was no difference in acceleration or deceleration rates between these species, but this could be due to small sample sizes. There was a significant positive correlation between maximum hunt speed and maximum flight height for the long-wing species. Maximum and mean flight speeds were significantly negatively correlated with wing area for all five species in this study. However, following phylogenetic correction, no significant relationship between wing area and maximum hunt speeds was found. This study presents baseline data of hunting speeds in African raptors and further highlights the importance of inter-species variation, which can provide accuracy to flight speed models and the understanding of hunting strategies.     

Precocial development of locomotor performance in a ground-dwelling bird (Alectoris chukar): negotiating a three-dimensional terrestrial environment

Developing animals are particularly vulnerable to predation. Hence, precocial young of many taxa develop predator escape performance that rivals that of adults. Ontogenetically unique among vertebrates, birds transition from hind limb to forelimb dependence for escape behaviours, so developmental investment for immediate gains in running performance may impair flight performance later. Here, in a three-dimensional kinematic study of developing birds performing pre-flight flapping locomotor behaviours, wing-assisted incline running (WAIR) and a newly described behaviour, controlled flapping descent (CFD), we define three stages of locomotor ontogeny in a model gallinaceous bird (Alectoris chukar). In stage I (1–7 days post-hatching (dph)) birds crawl quadrupedally during ascents, and their flapping fails to reduce their acceleration during aerial descents. Stage II (8–19 dph) birds use symmetric wing beats during WAIR, and in CFD significantly reduce acceleration while controlling body pitch to land on their feet. In stage III (20 dph to adults), birds are capable of vertical WAIR and level-powered flight. In contrast to altricial species, which first fly when nearly at adult mass, we show that in a precocial bird the major requirements for flight (i.e. high power output, wing control and wing size) convene by around 8 dph (at ca 5% of adult mass) and yield significant gains in escape performance: immature chukars can fly by 20 dph, at only about 12 per cent of adult mass.     

Interactive effects of body mass changes and species‐specific morphology on flight behavior of chick‐rearing Antarctic fulmarine petrels under diurnal wind patterns

For procellariiform seabirds, wind and morphology are crucial determinants of flight costs and flight speeds. During chick‐rearing, parental seabirds commute frequently to provision their chicks, and their body mass typically changes between outbound and return legs. In Antarctica, the characteristic diurnal katabatic winds, which blow stronger in the mornings, form a natural experimental setup to investigate flight behaviors of commuting seabirds in response to wind conditions. We GPS‐tracked three closely related species of sympatrically breeding Antarctic fulmarine petrels, which differ in wing loading and aspect ratio, and investigated their flight behavior in response to wind and changes in body mass. Such information is critical for understanding how species may respond to climate change. All three species reached higher ground speeds (i.e., the speed over ground) under stronger tailwinds, especially on return legs from foraging. Ground speeds decreased under stronger headwinds. Antarctic petrels (Thalassoica antarctica; intermediate body mass, highest wing loading, and aspect ratio) responded stronger to changes in wind speed and direction than cape petrels (Daption capense; lowest body mass, wing loading, and aspect ratio) or southern fulmars (Fulmarus glacialoides; highest body mass, intermediate wing loading, and aspect ratio). Birds did not adjust their flight direction in relation to wind direction nor the maximum distance from their nests when encountering headwinds on outbound commutes. However, birds appeared to adjust the timing of commutes to benefit from strong katabatic winds as tailwinds on outbound legs and avoid strong katabatic winds as headwinds on return legs. Despite these adaptations to the predictable diurnal wind conditions, birds frequently encountered unfavorably strong headwinds, possibly as a result of weather systems disrupting the katabatics. How the predicted decrease in Antarctic near‐coastal wind speeds over the remainder of the century will affect flight costs and breeding success and ultimately population trajectories remains to be seen.     

Body mass and locomotor habits of the smallest darter,Anhinga minuta (Aves,Anhingidae)

During the Neogene of South America, Anhingidae was represented by several species, mainly with greater sizes than the extant members. In the present contribution, body mass and locomotor habits of Anhinga minuta, the smallest known darter, were inferred. Body mass was estimated using two methods, one with measures of a tibiotarsus (the holotype) and the other, with measurements of a humerus; locomotor habits were inferred through muscular reconstructions and wing parameters (wing span, wing area and wing loading). Estimates of wing span and wing area were based on the length of humerus, assuming a condition of isometry with respect to Anhinga anhinga; wing loading was obtained through a relation formula between wing area and body mass. The results obtained indicate a body mass of about 729 g, a wing span of 0.958 m, a wing area of 0.117 m² and a corresponding wing loading of 61 N/m². These values and also the proximal insertion of the musculus pectoralis are consistent with those of a soaring bird but with more frequent flapping than extant anhingids. Furthermore, the inferred musculature for tibiotarsus indicates abilities for swimming, climbing and moving through the vegetation as in extant representatives.     

Wing size but not wing shape is related to migratory behavior in a soaring bird

Both wing size and wing shape affect the flight abilities of birds. Intra and inter‐specific studies have revealed a pattern where high aspect ratio and low wing loading favour migratory behaviour. This, however, have not been studied in soaring migrants. We assessed the relationship between the wing size and shape and the characteristics of the migratory habits of the turkey vulture Cathartes aura, an obligate soaring migrant. We compared wing size and shape with migration strategy among three fully migratory, one partially migratory and one non‐migratory (resident) population distributed across the American continent. We calculated the aspect ratio and wing loading using wing tracings to characterize the wing morphology. We used satellite‐tracking data from the migratory populations to calculate distance, duration, speed and altitude during migration. Wing loading, but not aspect ratio, differed among the populations, segregating the resident population from the completely migratory ones. Unlike what has been reported in species using flapping flight during migration, the migratory flight parameters of turkey vultures were not related to the aspect ratio. By contrast, wing loading was related to most flight parameters. Birds with lower wing loading flew farther, faster, and higher during their longer journeys. Our results suggest that wing morphology in this soaring species enables lower‐cost flight, through low wing‐loading, and that differences in the relative sizes of wings may increase extra savings during migration. The possibility that wing shape is influenced by foraging as well as migratory flight is discussed. We conclude that flight efficiency may be improved through different morphological adaptations in birds with different flight mechanisms.     

Flight mode affects allometry of migration range in birds

Billions of birds migrate to exploit seasonally available resources. The ranges of migration vary greatly among species, but the underlying mechanisms are poorly understood. I hypothesise that flight mode (flapping or soaring) and body mass affect migration range through their influence on flight energetics. Here, I compiled the tracks of migratory birds (196 species, weighing 12–10 350 g) recorded by electronic tags in the last few decades. In flapping birds, migration ranges decreased with body mass, as predicted from rapidly increasing flight cost with increasing body mass. The species with higher aspect ratio and lower wing loading had larger migration ranges. In soaring birds, migration ranges were mass‐independent and larger than those of flapping birds, reflecting their low flight costs irrespective of body mass. This study demonstrates that many animal‐tracking studies are now available to explore the general patterns and the underlying mechanisms of animal migration.     

Causes of variation in wing loading among Drosophila species

We examined influences on wing and body size in 11 species (12 strains) of Drosophila. Six measures of wing length and width were closely correlated with wing area and suggested little variation in wing shape among the species. Among ten species wing loading, an important factor in flight costs and manoeuvrability, increased as body mass increased at a rate consistent with expectations from allometric scaling of wing area and body mass to body length. Intraspecific variation in wing loading showed similar relationships to body mass. Density and temperature during larval development influenced wing loading through general allometric relations of body size and wing area. Temperature during the pupal stage, but not during wing hardening after eclosion, influenced wing area independently of body size. Wing area increased as growth temperature decreased. Individuals reared at cooler temperatures thus compensated for a potential allometric increase in wing loading by differentially enlarging the wing area during pupal development.     

Metabolic costs of avian flight in relation to flight velocity: a study in Rose Coloured Starlings (Sturnus roseus, Linnaeus)

The metabolic costs of flight at a natural range of speeds were investigated in Rose Coloured Starlings (Sturnus roseus, Linnaeus) using doubly labelled water. Eight birds flew repeatedly and unrestrained for bouts of 6 h at speeds from 9 to 14 m s⁻¹ in a low-turbulence wind tunnel, corresponding to travel distances between 200 and 300 km, respectively. This represents the widest speed range where we could obtain voluntarily sustained flights. From a subset of these flights, data on the wing beat frequency (WBF) and intermittent flight behaviour were obtained. Over the range of speeds that were tested, flight costs did not change with velocity and were on an average 8.17±0.64 W or 114 W kg⁻¹. Body mass was the only parameter with a significant (positive) effect on flight costs, which can be described as EE_f=0.741 M ^0.554. WBF changed slightly with speed, but correlated better with body mass. Birds showed both types of intermittent flight, undulating and bounding, but their frequencies did not systematically change with flight speed.     

Flight modes in migrating European bee-eaters: heart rate may indicate low metabolic rate during soaring and gliding

Background

Many avian species soar and glide over land. Evidence from large birds (m _b>0.9 kg) suggests that soaring-gliding is considerably cheaper in terms of energy than flapping flight, and costs about two to three times the basal metabolic rate (BMR). Yet, soaring-gliding is considered unfavorable for small birds because migration speed in small birds during soaring-gliding is believed to be lower than that of flapping flight. Nevertheless, several small bird species routinely soar and glide.

Methodology/Principal Findings

To estimate the energetic cost of soaring-gliding flight in small birds, we measured heart beat frequencies of free-ranging migrating European bee-eaters (Merops apiaster, m _b∼55 g) using radio telemetry, and established the relationship between heart beat frequency and metabolic rate (by indirect calorimetry) in the laboratory. Heart beat frequency during sustained soaring-gliding was 2.2 to 2.5 times lower than during flapping flight, but similar to, and not significantly different from, that measured in resting birds. We estimated that soaring-gliding metabolic rate of European bee-eaters is about twice their basal metabolic rate (BMR), which is similar to the value estimated in the black-browed albatross Thalassarche (previously Diomedea) melanophrys, m _b∼4 kg). We found that soaring-gliding migration speed is not significantly different from flapping migration speed.

Conclusions/Significance

We found no evidence that soaring-gliding speed is slower than flapping flight in bee-eaters, contradicting earlier estimates that implied a migration speed penalty for using soaring-gliding rather than flapping flight. Moreover, we suggest that small birds soar and glide during migration, breeding, dispersal, and other stages in their annual cycle because it may entail a low energy cost of transport. We propose that the energy cost of soaring-gliding may be proportional to BMR regardless of bird size, as theoretically deduced by earlier studies.     

THE FLYING ABILITY OF ARCHAEOPTERYX

Estimates for the wing span, mass and wing area of Archaeopteryx lithographica are provided, and these are used to derive certain of the flight parameters. From the data available on the lengths of skeletal components, amplified by examination of casts of the specimens and full-size enlargements of photographs, the wing span is estimated at 58–59 cm and the wing area as 479 cm2. To judge from animals of similar size, the mass was probably about 200 g. These figures give an estimated minimum flying speed of 7-6 m/sec and a wing loading of 0–42 gf/cm2. These figures are, and must be from their method of derivation, comparable with those of similar sized modern birds, These data are used to reconsider the possibility of flapping flight in this bird. It is suggested that the primitive anatomy of the pectoral skeleton has been somewhat over-emphasized, and it is shown that the pectoral crest on the humerus was relatively very large compared with modern birds. The power required to fly would require muscular physiology outside the range of mammalian (at least, human) capability, but well within the modern avian range. It is felt that Archaeopteryx was capable of flapping flight, but that it was probably not long sustained.     

Energy expenditure and wing beat frequency in relation to body mass in free flying Barn Swallows (<Emphasis Type="Italic">Hirundo rustica</Emphasis>)

Many bird species steeply increase their body mass prior to migration. These fuel stores are necessary for long flights and to overcome ecological barriers. The elevated body mass is generally thought to cause higher flight costs. The relationship between mass and costs has been investigated mostly by interspecific comparison and by aerodynamic modelling. Here, we directly measured the energy expenditure of Barn Swallows (Hirundo rustica) flying unrestrained and repeatedly for several hours in a wind tunnel with natural variations in body mass. Energy expenditure during flight (e _f, in W) was found to increase with body mass (m, in g) following the equation e _f = 0.38 × m ^0.58. The scaling exponent (0.58) is smaller than assumed in aerodynamic calculations and than observed in most interspecific allometric comparisons. Wing beat frequency (WBF, in Hz) also scales with body mass (WBF = 2.4 × m ^0.38), but at a smaller exponent. Hence there is no linear relationship between e _f and WBF. We propose that spontaneous changes in body mass during endurance flights are accompanied by physiological changes (such as enhanced oxygen and nutrient supply of the muscles) that are not taken into consideration in standard aerodynamic calculations, and also do not appear in interspecific comparison.     

Speed stability in birds

Solutions for the speed stability problem in bird flight at low speed are developed. Speed stability is usually considered not to exist in flapping flight at speeds below the speed of the minimum power required, and in gliding flight below the speed for maximum range. Approaches thus far for solving the speed stability problem are relating to a 1-degree-of-freedom model of the bird where the speed is regarded as the only motion variable involved. However, a speed deviation is inherently associated with a deviation in the height. In this paper, an expanded treatment with an appropriate mathematical model is presented. The expanded treatment is based on a 2-degree-of-freedom model of the bird. Thus, it is possible to account for the speed and the height changes. With this expanded treatment, it can be shown that there is speed stability in the gliding flight of birds, whether the speed is below the speed for maximum range or above. This also holds for flapping flight with regard to speeds below the speed of the minimum power required. Further, it is shown that there can be speed instability if the bird acts as a controller to suppress height deviations. For this purpose, a model of the bird acting as a controller is presented.