The Wake of a Kestrel (Falco Tinnunculus) in Gliding Flight

There have been a number of attempts to model aspects of bird flight of interest to both ecologists and aerodynamicists, aimed, on the one hand, at predicting the energetic cost of flight to the bird and attempting to understand its behaviour in this light (e.g. Pennycuick, 1969, 1978; Tucker, 1971; Greenewalt, 1975), and, on the other, trying to model with some degree of accuracy the unsteady or nonlinear terms in the aerodynamic model which arise as a consequence of the oscillation and/or irregular shape of the lifting surfaces (Lan, 1979; Phlips, East & Pratt, 1981). As can be readily appreciated from the above references, no model can be cast exclusively as one or other of these two types; energetic models, in order to be sufficiently general, make broad assumptions concerning the flow over the wings and the resulting aerodynamic forces, while the aerodynamic models must usually assume some simplified wing beat kinematics or wake geometry (Rayner, 1979a,b;,Phlips et al. 1981). All models assume that the wings of a bird operate in the same fashion as a conventional aerofoil, with various degrees of unsteadiness (typically measured by the reduced frequency Ω = cω/2U, where U is the freestream velocity, c is a streamwise length scale (such as the mean chord) and ω is the radian frequency of oscillation) caused by the flapping motion. In the limit of zero-reduced frequency, gliding flight, such an approach has met with some success in analysing the flight behaviour of large birds which depend on gliding as their primary means of transport (e.g. Pennycuick, 1971a,b, 1982). Flapping flight has also been studied in the light of model predictions (e.g. Pennycuick, 1975; Rayner, 1979b; Norberg, 1979) but the agreement with direct physiological measurements of oxygen consumption has been poor (Tucker, 1973; Torre-Bueno & Larochelle, 1978). In all cases, the model predictions assume, either implicitly or explicitly, that the wings behave as a conventional wing pair, operating at or near an optimum elliptical spanwise load distribution.

This paper is the first of two which use a previously reported flow visualization technique (Spedding, Rayner & Pennycuick, 1984) to analyse the wake of a bird flying at a moderate flight speed. The gliding flight results, reported here, enable some of the performance characteristics of the wings to be inferred from some simple wake measurements, and mark the first time that such results have been measured from a live, freely flying animal.

The apparatus was a portable version of that described by Spedding et al. (1984) and is shown schematically in Fig. 1. A rigid frame constructed of slotted angle iron (Dexion) supported a pair of 35 mm Nikon cameras in precisely defined positions so that the film planes were coplanar and equal in height from the floor and the lens axes were normal to this plane and parallel to each other. This frame was recessed in a doorway halfway down a 36 m corridor. Opposite the doorway a cloud of helium-filled soap bubbles was generated (Armstrong SAI Bubble Generator with Low Speed Head no. 2) in front of a plain dark background. A hand-trained kestrel was taught to fly from one operator (1) to another (2) at the opposite end of the corridor in order to receive his daily feed. The experiments were run at dusk for multiple flash photography and around 10 flights could be elicited each evening. As the kestrel flew across the field of view of the cameras, operator 2 closed a switch, opening the camera shutters and triggering the sequential firing of a series of four flash guns with flash intervals determined accurately by a purpose-built timer.

In the first series of flights, as shown in Fig. 1, the kestrel quickly built up speed after leaving operator 1 (approx. 1 m above ground) and then, dropping to a flying height of about 40cm, continued in a shallow glide before pulling up to land at operator 2, again about 1 m from the floor. Throughout the gliding phase, the wings were held fully outstretched with the primary feathers extended. Timed with a stopwatch, the average flight speed was 6ms⁻¹ and, allowing for acceleration from rest and deceleration at the end of the flight, the flight speed in the middle portion of the flight, including the initial gliding phase in front of the cameras, was estimated at 7 ms⁻¹. These rather crude measures of the flight pattern were not checked by high speed ciné film analysis owing to the limited time available for experiments, but should be sufficient for a first order analysis, bearing in mind the possible sources of error. Both the flight height and the flight speed through the bubbles may be checked directly from the multiple flash photographs.

A right-handed coordinate system is defined with X and Y parallel and normal to the direction of flight, and Z parallel to the camera lens axes, and the u, v and w components of velocity in X, Y and Z are defined following the usual conventions, as shown in Fig. 2. From those stereopairs which showed the wake structure in gliding flight, one was subjected to a full stereophotogrammetric analysis, as described in SpeddingeZ al. (1984). From the resulting three-dimensional velocity field, velocity profiles were taken in two-dimensional slices at appropriate locations across the wake and from these, estimates of the vorticity distribution and circulation of the vortices in the wake could be made.

Judging by an error analysis, as previously reported, together with reconstructions of a control object, it was estimated that velocities could be determined to within 13%.

Fig. 3 is a stereopair of the wake behind a gliding kestrel. The tip of the tail is visible in stereo and may be used to locate the flight path. Behind the port wingtip (closest to the cameras) a line of bubbles circulating in a corkscrew type of motion can be seen stretching behind the bird, inclined at a small angle to the horizontal. This pattern is quite consistent with all the photographs examined and indicates the presence of a single pair of wingtip trailing vortices such as those observed behind fixed-wing aircraft. Assuming, for the moment, that their formation follows the classical pattern, roll-up of the unstable vortex sheet initially shed from the wing trailing edges appears to take place within 4–5 chord lengths. A sketch of the wake appears in Fig. 6.

A reconstruction of the bubble field is shown in Fig. 4, where the line of flight calculated from the tail tip position is indicated by the dashed line and numbered and lettered segments mark the location of vertical slices made in the YZ and XY planes, respectively. Three of these sections are shown in Fig. 5A—C. Fig. 5A and 5B cut along the edge of the vortex core, parallel to the line of flight, roughly at the inner and outer edges of the vortex, whilst Fig. 5C is a plane section normal to the long axis of the vortex. Fig. 6 is a schematic interpretation of the gliding wake from stereopairs such as Fig. 3, consistent with the qualitative analysis of these wake sections.

Serial reconstruction of the wake in this fashion allows the core centre in YZ to be estimated at each section. w(Y) profiles were taken at a number of stations in Z, and Z_core, the Z location of the core centre, is that station with the greatest | ∂w/∂Y |. At Z_core, Y_core is the location of maximum | ∂v/∂Y | : The XZ location of the vortex core centre is plotted at seven downstream locations in Fig. 7. Slight oscillations of the wake vortices in Z may be discerned, but it is not clear whether this is due to limited experimental accuracy or to low-amplitude wing motions in flight. Measured from these data, the mean spanwise vortex separation, D, is 0·513 ± 0·015 m. Following roll-up, the diameter of the vortex core appeared to vary little with downstream distance in the wake, as far as could be told from the sparse data in some sections. The mean core diameter, d, was taken from the distance between w_max and w_mi_n in a plot of w(Y—Y_corc) for a number of downstream locations in the wake (Fig. 8). From this figure, the circulation, г, around the trailing vortex was estimated, assuming a circular core, from,

Classical aerofoil theory demonstrates that an optimum spanwise circulation distribution, in terms of minimizing the wake kinetic energy generated for a given amount of aerodynamic work, has the shape of a semi-ellipse for a fixed wing in steady flow. This wing loading distribution is reflected in the geometry of the wake and the results outlined above may be used for comparison. All quantities quoted for an elliptically loaded wing have been taken from Milne-Thompson (1966) in the following discussion.

If the wing is behaving like a classical aerofoil, an approximate check on the expected magnitude of the circulation may be made. Consider an elliptically loaded wing replaced by a lifting line with circulation which, together with the wake vortices, may be represented as a horseshoe vortex lengthening by ∂X in time ∂t (Fig. 9). The rate of change of momentum, Q̇, is

Assumptions concerning the value of e vary in the bird flight literature. Reviewing a range of studies, Greenewalt (1975) drew attention to this wide variation, noting aspects of experimental design which effectively lower the estimated value. He then postulated a rather low value of 0·5–0·7, based on just such data, albeit selected for self-consistency. Withers (1981) reported values ranging from 0·2 to 0’8 based on wind tunnel measurements of fixed wings. These wings were mounted away from the wind tunnel wall, which is likely to increase tip losses considerably, reflected in the low e estimates. While the value of e reported here is only for one case, the wing/body configuration of the kestrel is not thought to be exceptional in its aerodynamic characteristics. Neither does the value of 0·96 seem improbably high in view of Cone’s (1962) finding thate may rise above TO in non-planar lifting systems, such as branched wingtips. The value of e = 0·96 reported here suggests that it might normally be taken as close to 1·0, as assumed by Pennycuick (1968), Tucker & Parrott (1970) and Wood (1973), among others.

The aerodynamics of a kestrel in steady gliding flight seem to be well described by classical aircraft theory and a steady-state lifting line analysis of an elliptically loaded wing pair should provide accurate estimates of both the drag forces on the wings and the induced velocities in the wake. This is an encouraging basis on which to construct a general model of bird flight, but it is not immediately obvious whether these tenets may be retained in the flapping case. The following paper uses similar methods to examine the same kestrel in medium-speed flapping flight.

The author would like to thank Dr C. J. Pennycuick, who was academic supervisor during the course of this research, and who read an early version of the manuscript. Thanks are also due to Dr J. M. V. Rayner, for valuable advice and discussion, and Dr K. D. Scholey who performed the vital role of operator 1 in all experiments. The financial support of the Science and Engineering Research Council is gratefully acknowledged.