## ABSTRACT

The basis used for estimating lift and drag coefficients is explained. A method of obtaining a photograph of a bird flying at known airspeed and rate of sink is described.

96 % of the speed measurements fall between 22 and 65 ft./sec., the average being 40 ft./sec.

A maximum lift coefficient of 1-8 can be achieved. Wing area is reduced with increasing speed.

The feet are used as airbrakes.

A comparison of the minimum drag coefficient (0·06) with the maximum estimated power output of the pectoral muscles leaves only a narrow margin of power available for climbing.

The performance diagram gives a minimum gliding angle of 1 in $812$, and a minimum sinking speed of just under 4 ft./sec.

The fulmar has apparently sacrificed the ability to soar dynamically over the sea in order to be able to fly slowly and thus utilize light upcurrents at cliff faces.

## INTRODUCTION

The fulmar petrel *(Fulmarus glacialis)* is one of the very few species of British breeding birds which can be watched in flight at close range, under natural conditions and without causing it any alarm. A qualitative account of its manner of flight and the control movements which it uses has been given by Pennycuick & Webbe (1959). The present paper presents a quantitative account of its performance in gliding flight.

## THEORY

*(C*

_{L}and

*C*

_{D}

*)*developed by fulmars in gliding flight. These were obtained from the usual formulae : where

*L*is the lift,

*D*the drag,

*p*the air density,

*V*the airspeed and S the wing area. The measurements of lift and drag are based on the following assumptions.

*W*is the weight,

*M*the mass, and

*a*

_{n},

*a*, are the accelerations normal to and in line with the direction of motion respectively. In practice the method of tracking did not lend itself to measuring the accelerations with the necessary accuracy, and so they were ignored. This is equivalent to assuming that all the birds were gliding in a straight line at constant speed, and although this is not in itself a good assumption a sufficient number of measurements was obtained to draw some reasonably solid conclusions from the resulting scatter.

_{1}## METHOD

The five quantities on the right-hand side of equations (5) and (6) were estimated as follows.

### Weight

No method has been hit upon for estimating the weights of individual birds without catching them. All the birds were therefore assumed to weigh 1.6 lb., from the average given in Fisher’s (1952) monograph.

### Air density

A value of 0·0024 slugs per cubic foot was used throughout.

### Wing area

This can be varied in flight. The outlines of Fig. 1 were obtained by holding a fulmar down on a piece of graph paper and drawing round it. Outline 1 with tail spread has about 1·9 times the area of outline 4 with tail furled. A photograph of each bird taken at the moment for which the speed was calculated, was compared with these outlines, and the prevailing wing area estimated therefrom.

### Airspeed and gliding angle

These were obtained by tracking the birds optically from a point on the cliff top. The tracking device was based on a camera mounted on a pan-tilt head, the azimuth and elevation movements of which were connected by Bowden cables to two pens writing in different colours on a moving paper chart. Attached to the camera was a rangefinder of 8 in. base whose ranging knob was connected by another Bowden cable to a third pen on the recorder.

The recorder was started when an approaching bird reached a range of about 65 ft., and the device was then kept trained on the bird with the rangefinder following its approach: the pen recorder thus produced a record of the bird’s azimuth, elevation and range from the camera position, in other words a plot of its position in polar co-ordinates as a function of time.

When the bird reached a distance of 35 ft., at which the camera was focused, an arm projecting from the ranging knob pressed a microswitch which tripped an electric shutter release and also operated a relay which marked the chart. The end product was thus a photograph of the bird for which its position was known in polar co-ordinates, and also the rates of change of these co-ordinates. From this information its vector groundspeed was calculated in rectilinear co-ordinates.

The vector windspeed was obtained from a whirling cup anemometer fitted with fins and mounted in gimbals on the end of a pole, so that it orientated itself into wind both horizontally and vertically. It was held in the region where the fulmars were flying, and the windspeed and the angles which the anemometer took up were noted, the operation being carried out before (or in the middle of) a series of observations, and the wind assumed constant. The information was converted into the three rectilinear components of windspeed, referred to the same axes as those of the bird’s groundspeed. The three components of airspeed were then obtained by subtracting the windspeed from the groundspeed, and hence the scalar airspeed and the angle of glide were calculated.

### Accuracy

The accuracy of the groundspeed measurements is thought to be about ±10%. To this must be added an unknown error due to variations in windspeed, since this was not continuously recorded; this error is at its worst in gusty conditions. Together with the doubt attaching to the weight and wing area, it is thought not unreasonable to claim an accuracy of ± 20 % for the calculated values of the coefficients, neglecting errors due to accelerations.

## RESULTS

### Range of speed

Fig. 2 shows the distribution of speed measurements grouped at intervals of 5 ft./sec. The average of the 111 measurements there represented is almost exactly 40 ft./sec., the greatest proportion (24%) falling between 35 and 40 ft./sec. Over 96 % of the measurements fall between 22 and 65 ft./sec.

### Range of lift coefficient

Fig. 3 shows the relation between lift coefficient and airspeed. The regularity of the curve is not surprising since the airspeed is used to calculate the lift coefficient, the scatter being mainly due to variations in wing area. The important feature of the diagram is that the main mass of measurements goes up to *C*_{L}*=* 1·8, above which there are only four scattered observations, no doubt representing birds in a stalled condition. If the maximum lift coefficient is taken to be 1-8, the stalling speed with maximum wing area would be about 23 ft./sec.

A maximum lift coefficient of 1·8 is rather high for the Reynolds number concerned (5 × 10^{4}), at which a maximum of 1·2 would be more likely according to glider practice (Welch, Welch & Irving, 1955). However, gliders are constructed for a much lower minimum drag coefficient than prevails in the fulmar. For a high lift, low speed wing, the figure of 1·8 is not unreasonable, and its achievement is doubtless facilitated by efficient slotting by the alula and splayed primaries, and a flap effect produced by spreading the tail. Lift coefficients over 2 can be obtained by these means in aircraft (Bairstow, 1939).

In this connexion it is of interest to note that, as in other birds (Schufeldt, 1890), the alula is supplied by a branch of the tendon of the extensor digitorum communis, so that when the wing is swept fully forward and spread for minimum speed, the alula would be extended automatically.

### Variation of wing area with speed

Although there is no rigid connexion between wing area and speed, there is a significant tendency to reduce wing area with increasing speed as shown in Fig. 4, thus reducing the range of variation of lift coefficient needed to effect changes of speed.

### Connexion between drag coefficient and foot positions

When fully retracted the feet are folded forwards and concealed under the flap of flank feathers which covers the leading edge of the wings when they are folded. They are then entirely invisible (position o). When the bird is manoeuvring near the cliff the feet are generally lowered, and if not required they are then carried close together with webs furled below the tail (position 1). From here they can be lowered, with webs spread, into the airstream. Up to 20° of lowering is position 2, more than 20°is position 3.

Fig. 5 shows the drag coefficients produced at these different foot positions. While the readings for position 0 are fairly well bunched, as soon as the feet are brought out from this position the scatter (whose causes have been considered) at once increases. This is explained by the observation that the feet are only kept fully retracted when the bird is gliding steadily along in smooth conditions, and as soon as gusty conditions are met with, or manoeuvres called for, the feet appear. Thus neglected accelerations are more likely to give rise to errors in foot positions 1–3 than in position 0.

In spite of the increased scatter, it is evident that the drag coefficient increases as soon as the feet appear, even though they be folded beneath the tail (position 1), and that lowering them produces further increases in drag. They are used, in other words, as airbrakes.

### Power required for level flight

Dickinson (1928) gives a value for the maximum power output for a short period by human muscle as 0·024 h.p./lb., using a bicycle ergometer. In continuous activity this is limited by the rate at which oxygen can be supplied to the muscles to 0·01 h.p./lb., if an oxygen debt is not to be incurred (Henderson & Haggard, 1925). Taking into account the more efficient ventilation to be expected in a bird’s lungs (Sturkie, 1954), 0·02 h.p./lb. seems a reasonable value to take for continuous activity. The three pectoralis muscles of both sides of a fulmar together weigh 0·19 lb., and if these are assumed to provide the power used in flapping flight, there will be 0·0038 h.p. available.

From the *C*_{D} measurements for foot position o shown in Fig. 5 it can be seen that there is a cluster of points around *C*_{D}*=* 0·06. If this is taken as the minimum drag coefficient, then with a wing area of 1 ·2 sq.ft, the speed attainable would be 29 ft./sec. This is well above the stalling speed, but seems rather low for cruising, and would leave little power in hand for climbing; on the other hand, fulmars do not seem to be capable of anything more than a very shallow climb in flapping flight. The result is of the right order of magnitude, but it should be borne in mind that the estimates of power required and of power available are both subject to some doubt.

### Performance diagram

Glider performance is often expressed in terms of a plot of sinking speed against airspeed. This curve is convex upwards and the minimum gliding angle can be found by drawing a tangent to the curve from the origin. In Fig. 6 the curve obtained for the fulmar is shown alongside that for a typical medium performance glider (after Welch *et al*. 1955). The fulmar curve has been obtained from the measurements on birds with their feet in position o, by averaging the speeds and rates of sink of all those between 20 and 29 ft./sec. to give the first point, likewise with observations between 30 and 39 ft/sec. for the second, and so on. The number of measurements averaged for each point is shown beside the point. The minimum gliding angle for the fulmar is thus about 1 in $812$, as against 1 in 25 for the glider, and its minimum rate of sink in nearly 4 ft./sec. as against just over $212$ ft./sec. for the glider. It should be remembered, however, that a gliding fulmar is not a glider but a powered aircraft with its motor idling, and in this context its performance is by no means contemptible.

## DISCUSSION

The overall picture which emerges is that of a craft adapted to low-speed flight which has accepted some sacrifice of gliding performance. The various observations fit together fairly well, and there are no serious anomalies to be explained. There is not, for example, any need to invoke laminar flow or other subtleties to explain the results, as was found necessary by Raspet (1950) to account for his measurements on the black buzzard *Coragyps atrata*.

A question which can be considered theoretically is whether or not the fulmar is capable of dynamic soaring (Lord Rayleigh, 1883), using the wind gradient over the surface of the sea as their larger relatives the albatrosses do (Idrac, 1924a). This method of soaring has been analysed quantitatively by Walkden (1925), who showed that if a bird is to climb into wind without losing airspeed there must be a certain minimum rate of change of windspeed with height, which can be calculated from the bird’s airspeed and gliding angle.

Using an airspeed of 35 ft./sec. and a gliding angle of 1 in $812$, and assuming the wind gradient to have the form given by Idrac (1924b), Walkden’s equations show that to soar over a height range of 20 ft. (selected as a reasonable minimum), the fulmar would require a windspeed of 105 ft./sec., or 62 knots, at the surface. Seamen seldom have much time to spare for bird watching under such conditions, and it may be that fulmars do soar in this way in winds of this strength. However, their normal mode of progression over the sea seems to be to climb sharply in the lift above a wave, bank steeply and dive down into the trough, flap the wings for a few strokes to reach the windward slope of the next wave, and so on.

The wandering albatross was found by Idrac to have a gliding angle of about 1 in 18 at speeds around 70 ft./sec., which allows it to soar easily in winds of 20 ft./sec. or so at the surface. The fulmar thus seems to have sacrificed the ability to soar in this way in order to be able to fly at low speeds and thus exploit the upcurrents formed on cliff faces in light winds. Indeed it is the fulmar’s extraordinary skill at, and predilection for, soaring in front of cliffs which makes it such a suitable object for study.

## ACKNOWLEDGEMENTS

I am very grateful to Mr Peter Davis, warden of Fair Isle Bird Observatory, Shetland, both for his personal help and for making available the facilities of the observatory, where this work was done. I am also indebted to Dr K. E. Machin for a great deal of help and advice, especially with the design and construction of the apparatus, and to Dr M. R. Head for allowing me to use a wind tunnel at the Engineering Laboratory, Cambridge, for calibrating the anemometer. Also Dr Machin and Dr R. H. J. Brown were kind enough to read the manuscript and made some valuable suggestions which have been incorporated. This work was carried out during the tenure of a D.S.I.R. Research Studentship.

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