Aerodynamics of Gliding Flight of A Black Vulture Coragyps Atratus

Although aerodynamicists have used wind tunnels for over half a century, biologists have only recently studied the aerodynamics and physiology of live birds flying in tunnels (see Tucker & Parrott, 1970; Pennycuick, 1968; Greenewalt, 1960, for aerodynamic work; and Tucker, 1968, 1966; Eliassen, 1963, for physiological studies). The wind tunnel provides a controlled aerial environment that allows one to obtain aerodynamic data of known accuracy. In addition, the aerodynamic and gravitational forces of gliding can be simulated in a tunnel without the movement of a bird relative to an observer. Under these conditions measurement of glide angle (angle between horizontal and a bird’s glide path relative to air) is facilitated and a gliding bird can be studied over a selected range of air speeds and glide angles.

Prior to wind tunnel studies on live birds, aerodynamic data for gliding birds were obtained either from wind tunnel tests on frozen, stuffed or model birds (see e.g. Nayler & Simmons, 1921; Feldmann, 1944), or from field studies on naturally gliding birds (see e.g. Raspet, 1950; Pennycuick, 1960). Models may not simulate the surface features of a live bird and cannot assume the various configurations of a flying bird. Measurement of a bird’s glide angle under natural conditions is difficult because an observer on the ground must know both the motion of the bird relative to the ground and the motion of the air relative to ground to determine glide angle.

I have circumvented these difficulties by training a black vulture to fly freely in the working section of a wind tunnel. The black vulture is a common cathartid of the south-eastern United States, where it can often be seen soaring for many minutes on motionless wings.

I calculated body area by assuming that the vulture consisted of a cylinder (head and neck), a frustrum (thoracic region) and a cone (abdomen). Projected wing area was multiplied by 2·05 (this factor accounted for upper and lower surfaces and curvature of the wings) to obtain wetted wing area. Total wetted area was then calculated by adding wetted wing area to body and tail area and subtracting twice the intercepted area. Body area is probably accurate to only 20%, but because body area is about 10% of the total wetted area the latter is accurate to better than 10%.

The wind tunnel used for this study was of the open circuit, closed jet design and could be tilted from 0° to down from horizontal about a central pivot. The working section was 1·1 m high by 1·4 m wide by 2·3 m long and had a wire screen (0·013 m mesh) at the rear to prevent the bird from drifting close to the fan. The front of the working section opened without screen or obstruction into the entrance cone. A variable speed motor provided air speeds up to 16·8 m/s.

I calibrated the working section for air speed distribution, direction of air flow and turbulence (see Tucker & Parrott, 1970, for a description of the calibration techniques). Air speed, determined in the region where the bird usually flew, varied ± 5% from the mean.

Direction of air flow varied about 1° across the working section. The direction of air flow with respect to the working section was independent of tunnel tilt and air speed. Mean angles, accurate to ⁠, were used for calculations. Variation in direction of air flow resulted in drag measurements accurate to 11%.

Mean% turbulence was 0-4%, which corresponds to a turbulence factor of approximately 1-3 (Pope & Harper, 1966).

The black vulture was purchased from an animal dealer and its weight during the study was 17·5 newtons ± 2% (mass = 1·79 kg, g = 9·8 m/s²). The wing span to tunnel width ratio was 0·97 at maximum L/D.

A perch that could be raised and lowered (when lowered, the perch did not interfere with air flow) was mounted in the front of the working section. A capacitance-discharge shocking device was employed to give the bird mild shocks. A wire (1·5 × 10⁻³ m in diameter and 2·2 m long) was attached to each leg and a shock could be given whenever necessary. These wires also prevented the bird from entering the entrance cone.

The training procedure consisted of reward and punishment. Initially, the bird was placed on the perch and given a shock if it jumped from the perch to the tunnel floor. After a few shocks the bird learned to stay on the perch and rarely jumped to the floor. At this stage of the training I turned on the motor and lowered the perch. If the bird remained in the air for a few seconds no shock was given and the perch was raised. The bird was then rewarded by being allowed to sit on the perch for 15–30 s before the next flight. If the bird landed, instead of remaining in the air, a shock was given and the bird was placed back on the perch. By giving shocks whenever the bird landed and by gradually lengthening the time that the perch was lowered, the vulture was trained to glide for up to 30 min at a time. The entire training procedure took about 4 weeks with sessions at least every other day.

I was able to train the vulture to glide in the desired part of the working section by giving mild correctional shocks whenever the bird drifted back into the screen or bumped into the ceiling or side walls. Characteristically, the bird would drift back when the perch was lowered and then glide to the front portion of the section. After remaining nearly motionless there for 10–30 s, the vulture would slowly drift back about i m and then glide forward again.

At air speeds less than 13·9 m/s and glide angles greater than 6°, the vulture usually held its feet down perpendicular to the air flow. The feet were progressively retracted with increasing air speed and/or decreasing angle.

I photographed the vulture when it was in the region where the calibrations had been made and when neither of its wing tips was touching the side walls. Photographs were taken from above the working section through the Plexiglass ceiling with a motor-driven 35 mm camera that tilted with the tunnel. An electronic flash illuminated the bird from above.

Glide angle and air speed were systematically varied, and about six pictures were obtained for each combination of speed and angle. The normal procedure was as follows. The bird was flown for a few minutes until its flight pattern was consistent (the vulture usually flapped vigorously and was erratic at the beginning of each session). Then the tunnel was tilted down to and the tunnel speed set. After pictures were taken, the tunnel was tilted back and the bird was photographed at the new angle. This procedure was continued until an angle (minimum glide angle, θ_M) was found below which the bird would no longer maintain its position without flapping. I then tilted the tunnel to again and selected a higher speed.

Photographs were obtained over a range of air speeds and glide angles from 9·9 to 16·8 m/s and from 4·8° to 7·9°, respectively. Below 9·9 m/s the vulture would not remain airborne without flapping.

Wind tunnel boundaries cause the flow pattern around an object in a tunnel to differ from the pattern in free air and measurements may have to be corrected for this boundary interference (Pope & Harper, 1966).

The wake and solid blockage correction for lift and drag, horizontal buoyancy correction for drag and streamline curvature correction for lift were each about 1% or less and I did not correct data for these effects.

Wing span and wing area were linearly related (Fig. 1). Air speed and glide angle influenced wing area (Fig. 2). The variation of wing area with air speed depended on glide angle. At a given air speed wing area decreased as glide angle increased.

Lift coefficients calculated for the vulture ranged from 0·3 to 1·1. At a particular air speed, C_L was largest for a glide angle of 7·9° (Fig. 3). Maximum C_L for the vulture is smaller than that calculated for the falcon (Tucker & Parrott, 1970) and for the pigeon (Pennycuick, 1968), which have maximum C_L’s of 1·6 and 1·3, respectively. Raspet (1950) calculated a maximum C_L of 1·57 for the black vulture.

Minimum glide angle for the vulture was about 4·9° from 11 to At air speeds lower and higher than this range, θ_M increased (Fig. 4). Basic data at θ_M are summarized in Table 1.

The vulture’s sinking speed varied with air speed (Fig. 5). L/D for an aircraft in Fig. 5 can be found at any air speed by use of equation (5). The vulture had a maximum L/D of 11·6 at 13·9 m/s.

Parasite drag coefficients for the vulture at different Re ranged from 0·0113 to 0·0179 (Fig. 6). K values (as used in Tucker & Parrott, 1970) ranged from 1·9 to 2·8.

Raspet (1950) studied the gliding performance of black vultures in free air. He followed vultures with a sailplane and recorded their position and air speed relative to the plane. From this information he calculated the difference in sinking speed between the bird and plane. The plane’s sinking speed at various air speeds in still air was known and thus the vulture’s sinking speed at different air speeds could be computed.

Raspet reported maximum L/D’s of 23 and 21, respectively, for soaring and gliding vultures. The former had fully extended wings and were gaining altitude while circling. The latter had flexed wings and were descending along a fairly straight path. The vulture I studied in the tunnel had a continuously variable wing shape rather than the dichotomy described by Raspet.

Why is the maximum L/D (11·6) of the vulture in the wind tunnel so inferior to the values Raspet computed for vultures in free air ? An analysis of parasite drag reveals that Raspet’s vultures, at most values of Re, apparently have a C_Dp less than, or similar to, that for a flat plate (parallel to air flow) at the same Re with a laminar boundary layer. The coefficients for such a plate are, however, at a theoretical minimum and this leads one to conclude that the vulture’s maximum L/D is almost certainly not as large as that determined by the sailplane technique.

Parasite drag coefficients for the vulture, based on both Raspet’s data and mine, are shown in Fig. 6 as a function of Re. On the same figure are shown the drag co-efficients of a flat plate parallel to the air flow with a laminar boundary layer in one case and a turbulent one in the other. The values of C_Dp (usually called C_f for a flat plate) for the plate with laminar flow are, as mentioned previously, theoretically at a minimum (Goldstein, 1965).

Raspet (1960) presented ‘average skin friction coefficients’ for the vulture, none of which was below the line for a laminar plate, but he did not describe the method used to calculate the coefficients. The curves in Fig. 6 for soaring and gliding vultures were computed from Raspet’s values for L/D,b(1·44 m), W(22·5 N)and S_w (1·06 m²), using equations (7) and (8) and a M² of 0·9. In gliding flight the vulture’s minimum C_Dp is 17% above the line for a flat plate with a laminar boundary layer, while in soaring flight the minimum is 19% below the same line.

The curve calculated from tunnel data, by comparison, lies above the line for a turbulent flat plate and minimum C_Dp (which was reached at the same air speed as maximum L/D) for the vulture is 1·9 times as large as the for a turbulent plate at the same Re. Furthermore, bird-like airfoils with Re’s around 3·75 × 10⁵ have parasite drag coefficients that are 1·6 to 5·7 times as large as C_Dp for the turbulent flat plate at the same Re (see Tucker & Parrott, 1970, for airfoil data).

Tucker & Parrott (1970) stated that Raspet’s high L/D values were probably the result of the vultures’ using some form of atmospheric energy (such as vertical currents of air or changes in the velocity of air) which the larger sailplane could not utilize. They did not, however, analyse several other possible errors that could explain the discrepancy between Raspet’s data and mine: the effect of circling on sinking speed, tunnel interference effects and boundary layer transition effects.

The sinking speed of an aircraft in a turn is proportional to secant (β)^1·5 (Cone, 1964). Angle of bank (β) is the angle between a line perpendicular to the mean wing plane and the vertical direction (von Mises, 1959). Raspet’s data for soaring vultures were obtained when the bird and the plane were circling together and the fact that he did not correct data for the increase in sinking speed during a turn could account for the larger L/D he reported for soaring vultures. If C_L, total drag coefficient and wing loading (W/S) are the same as for level flight, then in a turn requiring a β of 30° (Raspet stated that the angle was usually less than 30°), the sinking speed of the plane and bird would be increased by about 25%. The difference in sinking speed between bird and plane would be 25% larger during a turn and the sinking speed calculated for the vulture would be 25% too small. This error does not, however, resolve the difference between my data and Raspet’s data for vultures gliding in a straight path.

Tunnel interference effects in this study do not seem large enough to explain the disparity between tunnel and sailplane data. Only down wash was significant and this effect caused the vulture’s apparent drag in the wind tunnel to be smaller than the actual drag. Neglecting down wash corrections entirely results in a maximum L/D of 13·6, a figure considerably lower than either of Raspet’s.

Transition of air flow from laminar to turbulent could explain the discrepancy if the air flow over the vulture’s wings in the tunnel had not undergone transition, while that over the wings of naturally flying vultures had. Schmitz (1952) worked at lower Re’s (approximate range: 0·2 × 10⁸ to 1·68 × 10⁶) than most aerodynamicists and showed that transition can double the L/D of an airfoil. This effect probably does not account for the disparity, however, since the vulture’s Re, the tunnel turbulence factor and the Re (around 7 × 10⁴) at which Schmitz observed a doubling of L/D for conventional airfoils all indicate that the wings of the vulture in the tunnel had a turbulent boundary layer.

Raspet concluded on the basis of low drag coefficients for the vulture that some form of boundary layer control must operate to keep the air flow over the wings laminar and the drag low. But Tucker & Parrott (1970) pointed out that, at a given C_L, the vulture would probably have a lower C_Dp with a turbulent boundary layer than with a laminar one over the wings. Furthermore, Schmitz’s data and the vulture’s Re again indicate that the wings of vultures in free air also have turbulent boundary layers.

The wind-tunnel data I have presented, coupled with values of C_Dp for conventional airfoils, strongly suggest that Raspet’s low drag coefficients and high values of L/D are explained by the vultures’ using atmospheric energy which the plane did not, rather than by control of the boundary layer.

Maximum L/D for the black vulture is the largest for birds thus far tested in wind tunnels. The falcon has a slightly smaller maximum L/D of 10, while that for the pigeon is only 6 (see Fig. 5). The L/D values for these birds are small compared to the maximum L/D of 38 for the sailplane in the same figure.

Although the falcon does not achieve an L/D as large as the vulture’s, it nevertheless has a lower minimum sinking speed. This is possible because sinking speed is a function of V and L/D (see equation 5) and the falcon’s lower air speed more than compensates for its smaller L/D.

The vulture’s air speed under natural conditions may be influenced by two possible objectives of an avian glider: covering distance over the ground toward a site and gaining altitude without flapping. In the wind tunnel the vulture achieves its minimum sinking speed at an air speed (ii’3 m/s) less than that for maximum L/D (13·9 m/s). Tucker & Parrott (1970) analysed the significance of L/D, V and time to maximizing the distance travelled or altitude gained by a naturally gliding aircraft under various aerial conditions. According to their analysis the vulture should glide at maximum L/D in still air to cover the greatest distance over the ground (from a given altitude). However, with a tail wind, the distance travelled would be maximized by gliding at minimum sinking speed. Furthermore, in an updraft greater than the vulture’s sinking speed, the greatest altitude would be gained by gliding at minimum sinking speed and remaining in the updraft as long as possible.

Data for the pigeon, falcon and vulture (present paper) show that wing area and wing span are linearly related at all air speeds and glide angles investigated.

At a given air speed the wing area of the falcon and vulture decreases as θ increases. At θ_M wing area of the pigeon and falcon decreases with increasing air speed. Wing area for the vulture, however, increases slightly at θ_M as air speed increases.

This study was supported by a National Institutes of Health Training Grant (No. HE 05219) and a Duke University Biomedical Sciences Support Grant (No. 303-3215) administered by V. A. Tucker.