The problems in understanding bird flight aerodynamics A complete, correct and/or detailed understanding of the aerodynamic mechanisms of importance in bird flight is complicated immensely by a number of factors. The most basic problem is that flight speeds are sufficiently slow (typical values for the mean forward speed, U, may range from 1-20·m·s -1 ) and the length scales are sufficiently small (mean chord, c, ranging from 1-10·cm), that the effects of viscosity are not ordinarily negligible. This fact can be written more formally by calculating a characteristic value for the dimensionless Reynolds number,where ν is the kinematic viscosity. For U=10·m·s -1 and c=5·cm, Re≈3×10 4 . This is an extremely inconvenient number. It lies well below typical values of 10 6 for small planes where viscous effects can safely be presumed to be restricted to thin, attached boundary layers, and it lies well above characteristic values of 10 2 where the flow over the body and in any wake is laminar and well-organised. On the contrary, even at moderate angles of attack, the flow over well-designed aerofoils veers notoriously between separated and nonseparated states, with dramatic differences in mean and instantaneous force coefficients as a result. Over and above treatments found in standard aerodynamics texts, one must also account for the fact that in animal flight the wings themselves are moving relative to the body, and furthermore that they are not rotating steadily like a propeller, but are beating up and down, accelerating and decelerating with each cycle. To this one adds the effects of flexible wing surfaces that not only have complex geometric descriptions, but also significantly change their shape during the wing beat cycle. Although it is straightforward to compile long lists of complicating factors, it is not clear which of them are important, and why and when. 2313The doi:10.1242/jeb.00423 In view of the complexity of the wing-beat kinematics and geometry, an important class of theoretical models for analysis and prediction of bird flight performance entirely, or almost entirely, ignores the action of the wing itself and considers only the resulting motions in the air behind the bird. These motions can also be complicated, but some success has previously been recorded in detecting and measuring relatively simple wake structures that can sometimes account for required quantities used to estimate aerodynamic power consumption. To date, all bird wakes, measured or presumed, seem to fall into one of two classes: the closedloop, discrete vortex model at low flight speeds, and the constant-circulation, continuous vortex model at moderate to high speeds. Here, novel and accurate quantitative measurements of velocity fields in vertical planes aligned with the freestream are used to investigate the wake structure of a thrush nightingale over its entire range of natural flight speeds. At most flight speeds, the wake cannot be categorised as one of the two standard types, but has an intermediate structure, with approxima...

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.

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The wakes of two individual robins were measured in digital particle image velocimetry (DPIV) experiments conducted in the Lund wind tunnel. Wake measurements were compared with each other, and with previous studies in the same facility. There was no significant individual variation in any of the measured quantities. Qualitatively, the wake structure and its gradual variation with flight speed were exactly as previously measured for the thrush nightingale. A procedure that accounts for the disparate sources of circulation spread over the complex wake structure nevertheless can account for the vertical momentum flux required to support the weight, and an example calculation is given for estimating drag from the components of horizontal momentum flux (whose net value is zero). The measured circulations of the largest structures in the wake can be predicted quite well by simple models, and expressions are given to predict these and other measurable quantities in future bird flight experiments.

An extensive set of experiments on the flight aerodynamics of a thrush nightingale Luscinia luscinia L. were described by Spedding, Rosén and Hedenström (2003a), giving detailed quantitative measurements of the wake. The wake structure was complex, but the gradual changes in circulation of crossstream or spanwise wake elements and inferred changes in three-dimensional (3D) wake topology supported an empirical model that was self-consistent and provided sufficient averaged vertical forces to balance weight in steady flight. Since no previous quantitative wake measurements have been reported at more than one flight speed for any particular bird (or bat) species, the observations of change in structure with flight speed as an independent, controllable parameter were new, interpolating some rather large gaps in the literature.A notable characteristic of aerodynamic studies using wake analysis is that the results do not depend on, or reveal anything directly about, the wing kinematics that create the disturbance. While observations of wake structure were new and extensive, they were related to the kinematics only by rather loose inference. The kinematic basis for flight in birds and bats has a long history of careful measurement (see, for example, Brown 1953;Norberg, 1976) for classic treatments of birds and bats, respectively). In turn, inferring aerodynamic quantities from kinematics alone is also difficult. In the absence of any better alternative, all such studies have been obliged to make strong assumptions about the quasi-steady (and 2D) aerodynamic properties of the wing sections as they accelerate and deform during the wingbeat. A more recent study by Hedrick et al. (2002) carried these calculations through to the point of estimating circulations of wing sections, but this process invoked exactly the same set of quasi-steady assumptions about how the wing motion and air flow are linked. Undoubtedly, much remains to be done to make this connection clearer. This paper is a small step in this direction, where a simple kinematic analysis is related to the measured wake flow. The flow on the wing itself is inaccessible to the flow experiments, but correlates of kinematic variation with wing speed and wake structure will be sought. The relationship between measured wake geometry and wingbeat kinematics can be qualitatively explained by presumed self-induced convection and deformation of the wake between its initial formation and later measurement, and varies in a predictable way with flight speed. Although coarse details of the wake geometry accord well with the kinematic measurements, there is no simple explanation based on these observed kinematics alone that accounts for the measured asymmetries of circulation magnitude in starting and stopping vortex structures. More complex interactions between the wake and wings and/or body are implied.