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.     

Flight reconstruction of two European enantiornithines (Aves,Pygostylia) and the achievement of bounding flight in Early Cretaceous birds

Intermittent flight through flap‐gliding (alternating flapping phases and gliding phases with spread wings) or bounding (flapping and ballistic phases with wings folded against the body) are strategies to optimize aerial efficiency which are commonly used among small birds today. The broad morphological disparity of Mesozoic birds suggests that a range of aerial strategies could have evolved early in avian evolution. Based on biomechanics and aerodynamic theory, this study reconstructs the flight modes of two small enantiornithines from the Lower Cretaceous fossil site of Las Hoyas (Spain): Concornis lacustris and Eoalulavis hoyasi. Our results show that the short length of their wings in relation to their body masses were suitable for flying through strict flapping and intermittent bounds, but not through facultative glides. Aerodynamic models indicate that the power margins of these birds were sufficient to sustain bounding flight. Our results thus suggest that C. lacustris and E. hoyasi would have increased aerial efficiency through bounding flight, just as many small passerines and woodpeckers do today. Intermittent bounding appears to have evolved early in the evolutionary history of birds, at least 126 million years ago.     

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 characteristics of birds:

This is the first part of a study on flight characteristics of birds and presents an annotated list of flight speeds of 139 western Palearctic species. All measurements were taken with the same tracking radar and corrected for wind influence according to radar-tracked wind-measuring balloons. Graphical presentation of the birds' air speeds emphasizes the wide variation of speeds within species and allows easy comparison between taxonomic groups, species, and types of flight. Unlike theoretical predictions, speeds increase only slightly with size. The larger species seem to be increasingly limited to speeds close to their speed of minimum power consumption V_mp',. Released birds, apparently reluctant to depart with migratory speed, fly at considerably lower speeds than migrating conspecifics. While large birds seem to be limited to speeds around V _mp', smaller birds seem to be capable of selecting between various speeds, approaching predicted V _mp, when tending to remain airborne at low cost, but flying at much higher speeds when tending to make best progress at low cost (around predicted speed of maximum range V _mr,). Predictions of air speeds by aerodynamic models proved to be too low for small birds because the models do not account for the gain in speed attained by the reduction in profile drag during bounding flight of small passerines. The models predict excessive speeds for large birds because the power output available for flight seems to decline much more with size than previously assumed.     

Bird maneuvering flight: blurred bodies, clear heads

While useful in describing the efficiency of maneuvering flight,steady-state (i.e., fixed wing) models of maneuvering performancecannot provide insight to the efficacy of maneuvering, particularlyduring low-speed flapping flight. Contrasted with airplane-analogousgliding/high speed maneuvering, the aerodynamic and biomechanicalmechanisms employed by birds at low flight speeds are violent,with rapidly alternating forces routinely being developed. Thesaltatory nature of this type of flight results in extreme linearand angular displacements of the bird's body; however, birdsisolate their heads from these accelerations with cervical reflexes.Experiments with pigeons suggest this ability to isolate thevisual and vestibular systems is critical to controlled flappingflight: birds wearing collars that prohibited the neck fromisolating the head from the angular accelerations of inducedrolls frequently exhibited (50% of flights) a loss of vestibularand/or visual horizon and were unable to maintain controlledflight.     

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.     

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.     

New modeling approach for bounding flight in birds

A new modeling approach is presented which accounts for the unsteady motion features and dynamics characteristics of bounding flight. For this purpose, a realistic mathematical model is developed to describe the flight dynamics of a bird with regard to a motion which comprises flapping and bound phases involving acceleration and deceleration as well as, simultaneously, pull-up and push-down maneuvers. Furthermore, a mathematical optimization method is used for determining that bounding flight mode which yields the minimum energy expenditure per range. Thus, it can be shown to what extent bounding flight is aerodynamically superior to continuous flapping flight, yielding a reduction in the energy expenditure in the speed range practically above the maximum range speed. Moreover, the role of the body lift for the efficiency of bounding flight is identified and quantified. Introducing an appropriate non-dimensionalization of the relations describing the bird’s flight dynamics, results of generally valid nature are derived for the addressed items.     

Flight speeds among bird species: allometric and phylogenetic effects

Flight speed is expected to increase with mass and wing loading among flying animals and aircraft for fundamental aerodynamic reasons. Assuming geometrical and dynamical similarity, cruising flight speed is predicted to vary as (body mass)^1/6 and (wing loading)^1/2 among bird species. To test these scaling rules and the general importance of mass and wing loading for bird flight speeds, we used tracking radar to measure flapping flight speeds of individuals or flocks of migrating birds visually identified to species as well as their altitude and winds at the altitudes where the birds were flying. Equivalent airspeeds (airspeeds corrected to sea level air density, U_e) of 138 species, ranging 0.01–10 kg in mass, were analysed in relation to biometry and phylogeny. Scaling exponents in relation to mass and wing loading were significantly smaller than predicted (about 0.12 and 0.32, respectively, with similar results for analyses based on species and independent phylogenetic contrasts). These low scaling exponents may be the result of evolutionary restrictions on bird flight-speed range, counteracting too slow flight speeds among species with low wing loading and too fast speeds among species with high wing loading. This compression of speed range is partly attained through geometric differences, with aspect ratio showing a positive relationship with body mass and wing loading, but additional factors are required to fully explain the small scaling exponent of U_e in relation to wing loading. Furthermore, mass and wing loading accounted for only a limited proportion of the variation in U_e. Phylogeny was a powerful factor, in combination with wing loading, to account for the variation in U_e. These results demonstrate that functional flight adaptations and constraints associated with different evolutionary lineages have an important influence on cruising flapping flight speed that goes beyond the general aerodynamic scaling effects of mass and wing loading.     

Regional and seasonal flight speeds of soaring migrants and the role of weather conditions at hourly and daily scales

Given that soaring birds travel faster with supportive winds or in good thermal soaring conditions, we expect weather conditions en route of migration to explain commonly observed regional and seasonal patterns in the performance of soaring migrants. We used GPS‐loggers to track 13 honey buzzards and four Montagu's harriers for two to six migrations each. We determined how tailwinds, crosswinds, boundary layer height (a proxy for thermal convection) and precipitation affected hourly speeds, daily distances and daily mean speeds with linear regression models. Honey buzzards mostly travel by soaring while Montagu's harriers supplement soaring with flapping. Therefore, we expect that performance of harriers will be less affected by weather than for buzzards. Weather conditions explained between 30 and 50% of variation in migration performance of both species. Tailwind had the largest effect on hourly speeds, daily mean speeds and daily travel distances. Honey buzzards travelled significantly faster and farther, and Montagu's harriers non‐significantly faster, under better convective conditions. Honey buzzards travelled at slower speeds and shorter distances in crosswinds, whereas harriers maintained high speeds in crosswinds. Weather conditions varied between regions and seasons, and this variation accounted for nearly all regional and seasonal variation in flight performance. Hourly performance was higher than predicted at times when we suspect birds had switched to intermittent or continuous flapping flight, for example during sea‐crossings. The daily travel distance of Montagu's harriers was determined to a significant extent by their daily travel time, which differed between regions, possibly also due to weather conditions. We conclude with the implications of our work for studies on migration phenology and we suggest an important role for high‐resolution telemetry in understanding migratory behavior across entire migratory journeys.     

Skylark optimal flight speeds for flying nowhere and somewhere

Flight is energetically very costly. For birds the mechanicalpower in relation to airspeed is characterized by a U-shapedfunction. From this function we can derive optimal flight speedsassociated with minimum power (V_mp), minimum cost of transport(V_mr) and minimum overall time of migration (V_mt). Since flightis energetically so costly, aerial displays and song flightcan potentially serve as signals reliably indicating the individualquality or resource potential of the signaler. In order to maximizethe amount of song flight produced, we expect V_mp during songflight, while during migration we rather expect V_mr or V_mv Wecompared flight speeds of skylarks (Alauda arvensis) duringsong flight and migration flight, respectively. In this speciespredicted V_mp = 5.5 m/s, V_mr = 10.5 m/s, and V_mt = 12.1 m/s.The preferred airspeed during song flight did not differ significantlyfrom the predicted V_mp, while airspeed during migration wassignificantly higher than V_mr and Vmp indicating that flightspeed is a flexible trait that birds adjust to different situations.Why the skylarks speed up so much on migration is still unclear,but it may be that due to the shape of the predicted power curve,variation in cost of transport at high speeds is relativelysmall.     

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.     

Gravity-defying Behaviors: Identifying Models for Protoaves

Most current phylogenetic hypotheses based upon cladistic methodologyassert that birds are the direct descendants of derived maniraptorantheropod dinosaurs, and that the origin of avian flight necessarilydeveloped within a terrestrial context (i.e., from the "groundup"). Most theoretical aerodynamic and energetic models or chronologicallyappropriate fossil data do not support these hypotheses forthe evolution of powered flight. The more traditional modelfor the origin of flight derives birds from among small arborealearly Mesozoic archosaurs ("thecodonts"). According to thismodel, protoavian ancestors developed flight in the trees viaa series of intermediate stages, such as leaping, parachuting,gliding, and flapping. This model benefits from the assemblageof living and extinct arboreal vertebrates that engage in analogousnon-powered aerial activities using elevation as a source ofgravitational energy. Recent reports of "feathered theropods"notwithstanding, the evolution of birds from any known groupof maniraptoran theropods remains equivocal.     

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.     

The evolution of vertebrate flight

Flight–defined as the ability to produce useful aerodynamic forces by flapping the wings–is one of the most striking adaptations in vertebrates. Its origin has been surrounded by considerable controversy, due in part to terminological inconsistencies, in part to phylogenetic uncertainty over the sister groups and relationships of birds, bats and pterosaurs, and in part to disagreement over the interpretation of the available fossil evidence and over the relative importance of morphological, mechanical and ecological specializations. Study of the correlation between functional morphology and mechanics in contemporary birds and bats, and in particular of the aerodynamics of flapping wings, clarifies the mechanical changes needed in the course of the evolution of flight. This strongly favours a gliding origin of tetrapod flight, and on mechanical and ecological grounds the alternative cursorial and fluttering hypotheses (neither of which is at present well-defined) may be discounted. The argument is particularly strong in bats, but weaker in birds owing to apparent inconsistencies with the fossil evidence. However, study of the fossils of the Jurassic theropod dinosaur Archaeopteryx , the sister-group of the stem-group proto-birds, supports this view. Its morphology indicates adaptation for flapping flight at the moderately high speeds which would be associated with gliding, but not for the slow speeds which would be required for incipient flight in a running cursor, where the wingbeat is aerodynamically and kinematically considerably more complex. Slow flight in birds and bats is a more derived condition, and vertebrate flapping flight apparently evolved through a gliding stage.     

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.     

Optimal flight behavior of soaring migrants: a case study of migrating steppe buzzards, Buteo buteo vulpinus

This article presents tests of the theoretical predictions onoptimal soaring and gliding flight of large, diurnal migrantsusing Pennycuick's program 2 for "bird flight performance."Predictions were compared with 141 observed flight paths ofmigrating steppe buzzards, Buteo buteo vulpinus. Calculationsof cross-country speed relative to the air included bird's airspeedsand sinking rates in interthermal gliding and climbing ratesin thermal circling. Steppe buzzards adjusted interthermal glidingairspeed . according to their actual climbing rate in thermalcircling. By optimizing their gliding airspeed, the birds maximizedtheir crosscountry performance relative to the air. Despitethis general agreement with the model, there was much scatterin the data, for the model neglects horizontal winds and updraftsduring the gliding phase. Lower sinking rates due to updraftsduring the gliding phases allowed many birds to achieve highercross-country speeds than predicted. In addition, birds reactedto different wind directions and speeds: in side and opposingwinds, the steppe buzzards compensated for wind displacementduring soaring and increased their gliding airspeed with decreasingtailwind component Nevenheless, cross-country speed relativeto the ground, which is the important measure for a migratorybird, was still higher under following winds. This study showsthat Pennycuick's program 2 provides reliable predictions onoptimal soaring and gliding behavior using realistic assumptionsand constants in the model, but a great deal of variation aroundthe mean is generated by factors not included in the model     

Maximal horizontal flight performance of hummingbirds: effects of body mass and molt

Hovering and fast forward flapping represent two strenuous types of flight that differ in aerodynamic power requirement. Maximal capabilities of ruby-throated hummingbirds (Archilochus colubris) in hovering and forward flight were compared under varying body mass and wing area. The capability to hover in low-density gas mixtures was adversely affected by body mass, whereas the capability to fly in a wind tunnel did not show any adverse mass effect. Molting birds that lost primary flight feathers and reduced wing area also displayed mass loss and loss of aerodynamic power and flight speed. This suggests that maximal flight speed is insensitive to short-term perturbations of body mass but that molting is stressful and reduces the birds' speed and capacity for chase and escape. Hummingbirds' flight behavior in confined space was also investigated. Birds reduced their speeds flying through a narrow tube to approximately one-fifth of that in the wind tunnel and did not display differences under varying body mass and wing area. Hence, performance in the flight tube was submaximal and did not correlate with performance variation in the wind tunnel. For ruby-throated hummingbirds, both maximal mass-specific aerodynamic power derived from hovering performance in low-density air media and maximal flight velocity measured in the wind tunnel were invariant with body mass.     

Flight speeds and climb rates of Brent Geese: mass-dependent differences between spring and autumn migration

Aerodynamic theories of bird flight predict that horizontal flight speed will increase with increasing load whereas vertical flight speed will decrease. Horizontal flight speed for birds minimizing overall time on migration is predicted to be higher than flight speed for birds minimizing energy expenditure. In this study we compare flight speeds of Brent Geese Branta b. bernicla recorded by tracking radar and optical range finder during spring and autumn migration in southernmost Sweden, testing the above-mentioned predictions. Geese passing Sweden in spring are substantially heavier than in autumn and there might also be a stronger element of time-selection in spring than in autumn. Recorded airspeeds were significantly higher in spring (mean 19.0 m s⁻¹) than in autumn (mean 17.3 m s⁻¹), the average difference being slightly larger than predicted due to the mass difference alone. The effects on airspeed of wind, vertical speed, flock size and altitude were also analysed, but none of these factors could explain the seasonal difference in airspeed. Hence, the results support the hypothesis of mass-dependent flight speed adjustment. The difference between the two seasons was not large enough to corroborate the hypothesis of a stronger element of time-selection in spring, but this hypothesis cannot be rejected. Vertical flight speeds were lower in spring than in autumn, supporting a negative effect of load on birds' flight power margin.     

FORELIMB POSTURE IN DINOSAURS AND THE EVOLUTION OF THE AVIAN FLAPPING FLIGHT-STROKE

Ontogenetic and behavioral studies using birds currently do not document the early evolution of flight because birds (including juveniles) used in such studies employ forelimb oscillation frequencies over 10 Hz, forelimb stroke-angles in excess of 130°, and possess uniquely avian flight musculatures. Living birds are an advanced morphological stage in the development of flapping flight. To gain insight into the early stages of flight evolution (i.e., prebird), in the absence of a living analogue, a new approach using Strouhal number     was used. Strouhal number is a nondimensional number that describes the relationship between wing-stroke amplitude ( A ), wing-beat frequency ( f ), and flight speed ( U ). Calculations indicated that even moderate wing movements are enough to generate rudimentary thrust and that a propulsive flapping flight-stroke could have evolved via gradual incremental changes in wing movement and wing morphology. More fundamental to the origin of the avian flapping flight-stroke is the question of how a symmetrical forelimb posture—required for gliding and flapping flight—evolved from an alternating forelimb motion, evident in all extant bipeds when running except birds.