Body drag, feather drag and interference drag of the mounting strut in a peregrine falcon, Falco Peregrinus

A complete analysis of avian aerodynamics divides a flying bird into its various parts and describes the aerodynamic forces on them. The first step in the analysis conventionally separates the wings from the rest of the bird – the ‘body’ in this study. The drag component of the aerodynamic force on a bird’s body is known as ‘body drag’ or sometimes ‘parasite drag’ because it is not associated with a significant lift component.

Recent studies of gliding flight (Tucker, 1987, 1988; Tucker and Heine, 1990) use body drag as one of the terms in a mathematical model that calculates the aerodynamic forces on a bird’s wings and predicts the bird’s gliding performance. These studies estimate body drag from an equation (Tucker, 1973) fitted to drag measurements on seven frozen, wingless bird bodies mounted on drag balances in wind tunnels. More recent studies of body drag (Prior, 1984; Pennycuick et al. 1988) report variable results and raise questions about interference drag on bodies mounted on drag balances and the effect of the feathers on the drag of frozen bodies.

This study reports drag measurements in a wind tunnel on the frozen, wingless body of a peregrine falcon and on an accurate, smooth-surfaced model of that body. It has two purposes: (1) to remedy technical problems in measuring body drag, and (2) to obtain an accurate estimate of the body drag of a Harris’ hawk (Parabuteo unicinctus, a bird of the same size as the falcon), whose gliding performance is described in an adjoining paper (Tucker and Heine, 1990).

Air moving past an object creates an aerodynamic force with components that are perpendicular and parallel to the flow direction. The perpendicular component (lift) is negligible in this study, but drag (the parallel component) varies with the size and shape of the object and with the speed, density and viscosity of the air. ‘Shape’ includes the orientation of the object relative to the air flow and its surface roughness. Air viscosity and density are constant in this study. I shall describe drag with two related quantities that are less dependent on size and speed: the equivalent flat plate area and the drag coefficient. More information on these quantities may be found in standard aerodynamic textbooks such as von Mises (1959), in an adjoining paper in this journal (Tucker and Heine, 1990) and in Vogel (1981) and Pennycuick (1989).

Body drag is the sum of skin friction drag and pressure drag. The following discussion summarizes relevant information from Goldstein (1965) and von Mises (1959).

An infinitely thin flat plate held parallel to the air flow illustrates pure skin friction drag. The air in contact with the plate sticks to the surface and, because air is viscous, this stationary layer influences the speed of the air in a boundary layer next to the plate. The air flow in the boundary layer may be either laminar or turbulent. Air in a laminar boundary layer flows in essentially the same direction as the air immediately outside the boundary layer. Air in a turbulent boundary layer flows in different directions.

Pure pressure drag arises on an idealized, infinitely thin flat plate held perpendicular to the flow direction. The pressure in the undisturbed flow, and in the theoretical wake behind the plate, is P. At the edges of the plate, air flow separates between the free stream flow and the wake. Air flow comes to a stop at the upstream face of the plate and exerts pressure P+0.5ρ V². The difference in pressure between the upstream face of the plate and the relatively low pressure wake is 0.5ρV², and the drag on the plate is 0.5ρV²S. 5 is the area of the upstream face of the plate, and the drag coefficient for the reference area S has a value of 1.

The condition of the boundary layer on a three-dimensional object influences the tendency of the air flow to separate from the object and, thereby, influences pressure drag. When the boundary layer is turbulent, air tends to cling to rounded eminences and flow around them rather than separating and leaving a low-pressure wake. The opposite is true of a laminar boundary layer. In contrast to skin friction drag, a turbulent boundary layer reduces pressure drag and a laminar boundary layer increases it. Whether the boundary layer on an object is laminar or turbulent depends on the shape of the object, its Reynolds number and the turbulence of the air before it flows over the object.

The drag coefficients of rounded objects may decrease sharply when the boundary layer in certain regions goes through the transition from laminar to turbulent. For example, the drag coefficient of a sphere with a laminar boundary layer at the point of separation may drop by half when the speed, and hence the Reynolds number, increases by 20%. The increase in Re causes the boundary layer to become turbulent, and the air flows further around the sphere before separating. The smaller wake reduces pressure drag.

Many birds fly at Reynolds numbers where rounded objects have significant areas of both laminar and turbulent boundary layers. The bird’s body surface can be seen as a mosaic of patches, some with separated air flow and others with laminar or turbulent boundary layers. The patches are in a delicate balance seemingly minor changes in the turbulence and speed of the air, and in the shape of the bird’s body, may change their sizes and locations. As a result, both skin friction and pressure drag may change markedly with the minor changes mentioned.

A shroud may be designed to cover all of the strut, in which case it extends to the bird body, or it may be lower and leave some of the strut exposed. If a shroud that extends to the body is lowered progressively at a particular air speed, the measured drag first decreases to a minimum and then increases (Fig. 1), for reasons explained below.

The shroud position on the flight balance in this study made D_I,sh negligible. To simplify nomenclature, the following discussion ascribes all of D_I to D_I,s.

The conventional method for determining interference drag uses combinations of multiple mounting struts (Gorlin and Slezinger, 1966; Pope and Harper, 1966). I used a new method in this study based on changing the drag of a single strut and extrapolating to zero. At a given speed, the drag of the isolated strut (D_s) can be made large or small by changing the cross-sectional shape of the strut. As D_s approaches zero, the interference drag also approaches zero; and the measured drag (D_m) of a body mounted on the strut approaches D₃ (Fig. 2). Although there is a mechanical limit to how small D_s can be, the curve relating it to D_m extrapolates to D_m=D_B at D_s=0.

The sum D_s+D₁ at speed V₀ may be expressed as an equivalent flat plate area and subtracted from an equivalent flat plate area for D_m to determine the equivalent flat plate area of the body (S_fP,B). Body drag and C_D,B can then be calculated for other speeds.

I measured the drag of a frozen falcon body and a model body mounted on a drag balance in a wind tunnel (described in Tucker and Parrott, 1970; and Tucker and Heine, 1990). The tunnel was set to air speeds equivalent to 10.0, 12.4 and 14.5 ms⁻¹ at sea level in the US standard atmosphere (air density=1.23 kg m⁻³, von Mises, 1959). When making measurements on the frozen body, I varied the speeds in alternating sequences of ascending and descending order.

The drag balance was a parallelogram type, similar to that shown in Fig. 6.65 of Gorlin and Slezinger (1966). A digital voltmeter measured the imbalance of four strain gauges connected in a bridge circuit and attached to the flexible beams of the parallelogram. I calibrated the balance by hanging a weight from a thread that attached to the bird body (or the strut, for measurements on an isolated strut) after running over a pulley on a ball-bearing. The ball-bearing (New Hampshire Bearing SR168) was specially constructed to have low starting torque, and it transferred the gravitational force on the weight to the balance with a change of less than 0.7%. The accuracy of this measurement system is shown in Table 1.

The drag balance was inside the wind tunnel, shielded from the wind by a wingshaped, streamlined shroud with a maximum aerofoil thickness of 2.5 cm where the mounting strut extended from the shroud. The chord of the shroud was 3.8 cm at this point and increased to a maximum of 24.3 cm at a level 13 cm lower. The maximum aerofoil thickness where the shroud covered the drag balance was 3.9 cm. The trailing edge of the shroud tapered from blunt where the chord was minimum to sharp where the chord was maximum.

The mounting strut had a streamlined cross-section with a maximum thickness of 3.2 mm and a chord of 12.7 mm. It was exposed to the airflow for 9 cm between the top of the shroud and the body mounted on it.

The US Fish and Wildlife Service provided the body of a peregrine falcon that in life had a mass of 0.713 kg. The wings had been cut off at mid-humerus to leave the proximal humeral feathers attached to the body. These feathers smoothly covered the stump of the humerus (which was folded back parallel to the body surface) and the region where each wing had been removed.

To mount the body on the strut of the drag balance, I froze a cylindrical wooden plug into a hole drilled in the ventral midline of the frozen body. The plug was 15.9mm in diameter, fitted flush with the skin and contained a threaded aluminium insert. A rod attached to the end of the strut screwed into the insert.

I trimmed the body for minimum drag by measuring its drag, then thawed the body just enough to make the neck and tail movable. I preened the feathers with tweezers and refroze the body on its back on a board after propping the head and tail in the desired positions with loose rolls of gauze tape. I measured body drag again and repeated the process to attain minimum drag. During all measurements, the sunken eyeballs were restored to lifelike contours with modelling clay, the feet were tucked up under the tail, and the angle of the entire body on the mounting strut was adjusted for minimum drag.

I was unable to preen the feathers to lie in the smooth, orderly, overlapping pattern that they assumed in a living Harris’ hawk in flight (Tucker and Heine, 1990). The feathers on a newly frozen body have gaps between them and flat spots where the body pressed down on them. Some feather shafts are misaligned and the barbs on the shafts tend to separate. By preening the body when it was slightly hawed rather than entirely thawed or frozen, I was able to remove the flat spots and most of the gaps in the feathers and improve the alignment of the feather shafts. The result was a body that looked smooth and unruffled.

The model was a light-weight casting of a plaster body sculpted around two armatures of laminated plywood. The armatures represented the feathered surfaces of the right and left halves of the frozen falcon body in its minimum drag configuration.

To construct the armatures, I measured 999 three-dimensional coordinates on one side of the frozen body with a digitizer (accuracy shown in Table 1). The digitizer arm ended in a needle point that could be placed anywhere in a horizontal plane. I mounted the body vertically in an apparatus that could be raised or lowered with a rack and pinion gear. I recorded coordinates of points around a cross-section at the base of the beak by touching the needle point to the feather surface at the dorsal midline and then moving the needle in steps to the ventral midline along the feather surface of half the circumference. Then I raised the body 7.93 mm with the rack and pinion and digitized the feather surface of the next (more posterior) half-circumference. The needle moved in up to 30 steps per halfcircumference, with smaller steps where the radius of curvature was small. The last half-circumference was 8 cm from the tip of the tail. A computer used the complete set of coordinates as data for a program that plotted a life-size contour map of one side of the body (Fig. 3).

The contour interval (5.77mm) on the map equalled the thickness of the plywood laminations plus the glued joint between them. For each contour line, I glued a copy of the map to two pieces of plywood held together with screws. I then sawed along the contour lines to form identical pairs of plywood laminations, one for each side of the body. I stacked the pairs in register and drilled two index holes through the entire stack. I then peeled the map from each pair, removed the screws, arranged the laminations for each side of the body in order, aligned them on dowels through the index holes, glued them together and completed the sculpture by filling the steps between laminations with plaster and sanding the plaster smooth.

I made plaster-of-Paris moulds of both sculptures and cast them in orthopaedic foam (Pedilen rigid foam, Otto Bock, Duderstadt, Germany). I glued the casts together after partially hollowing out their insides and attached balsa-wood carvings of the beak and tail feathers. The resulting model body had a mass of 0.2 kg and a surface with the texture of sanded plaster that duplicated the linear dimensions of the frozen body within 2 %.

I investigated the interference drag on the model body due to the shroud (see Theory) at a wind speed of 12.4 ms⁻¹ by measuring drag with the shroud at different heights from 23 mm to 14.6 cm below the body.

I determined interference drag on the frozen body due to the strut (see Theory) at a wind speed of 12.4 ms⁻¹ by using three struts: the unmodified strut and two modifications of it that increased its drag in steps. The modifications were strips of wood along both its sides and parallel to its long axis. The smaller strips had a circular cross-section with a diameter of 2.2 mm, and the larger strips had a halfround cross-section with a diameter of 12.7 mm. I then measured the drag (D_m) of the body mounted on the various struts, and the drag (D_s) of the struts alone.

The relationship between the position of the shroud on the drag balance and the measured drag conformed to the description in the Theory section and to equation 13. The interference drag due to the shroud (D_I,sh) in this study is negligible, since the point that describes the normal strut length (9 cm) and the measured drag of the model mounted on the strut falls on the ascending part of the curve that relates D_m to ds (Fig. 4). This part of the curve extrapolates to an intercept of D_m,0–D_s,0 at d_s=0, as expected.

Interference drag due to the shroud became negligible when the exposed strut length was three times the aerofoil thickness of the shroud. This factor is specific for the combination of drag balance and falcon body used in the present study, but it can serve as a starting point for evaluating the interference drag of other bodies and drag balances.

The measured drag (D_m) of the frozen body mounted on the different struts varied linearly with strut drag (Fig. 5), as in equation 14 (repeated here):

The values of k_1;k₂ and D_s,0 may be used with equations 14–23 to calculate other quantities related to interference drag. For example, the measured drag (D_m,0) for D_s,0 is 0.1573 N (equation 14), the strut drag is 5.2 % of measured drag (equation 20), the interference drag is 62.2 % of strut drag (equation 19) and the equivalent flat plate area of strut drag plus interference drag is 0.000142 m² (equation 17). I used this value for both the frozen body and the model.

I computed dimensions (Table 2) from the three-dimensional coordinates of the model, plus measurements on the balsa-wood beak and tail. These dimensions also describe the frozen body.

Drag coefficients of both the frozen body and the model varied in the same way with speed, but the values for the model were only about 60% of those for the frozen body (Fig. 6 and Table 3). Analysis of variance indicates that the differences between the mean C_DjB values at different speeds are highly significant.

The literature contains a wide range of values for the drag coefficients of wingless bird bodies (see Fig. 8). Some of the variation can be explained by differences among species but, where large variation is seen even between similar species, uncontrolled factors in the measurement process may be responsible. The results of the present study implicate shape factors – the smoothness of the feathers and the trim of the body – and the interference drag of the mounting system.

The feathered surface caused a large proportion of the drag on the falcon body in this study, since the drag of the model was only about 60 % of that of the frozen body (Table 2). The rougher surface of the feathered body compared with the model probably increased drag by thickening the boundary layer, and influenced the distribution of the laminar and turbulent boundary layers and separated flow. Feathers that flutter in the wind probably have high pressure drag, as do fluttering flags (Hoerner, 1965). The effects of the compliance and porosity of the feathered surface on drag are unknown.

Pennycuick et al. (1988) also noticed an effect of feathers on drag. The feathers on some bird bodies fluffed out as speed increased, and body drag did not return to its original value when speed decreased. The authors were able to reduce by 15 % the drag on a snow goose body by smoothing down the feathers and holding them in place with hair spray. In the present study, the feathers on the falcon body did not appear to fluff out, and the drag measurements were not affected by the direction of speed change.

‘Trim’ refers to the angles between head, torso and tail and the air flow. I could change the drag on the falcon body by 25 % by adjusting these angles through a range of lifelike configurations.

Interference drag can be significant if the drag of the isolated mounting strut (of struts) is a large proportion of the measured drag. For example, when the strut drag is 25 % of the measured drag, the body drag is only 79 % (Fig. 7) of the value usually reported as body drag (the difference between measured drag and strut drag). The curve in the figure is specific for the falcon body and mounting system used in this study, but it indicates the magnitude of the errors that can arise in other systems.

The body drag coefficients reported by various authors for wingless, frozen bodies of several bird species can be related to Reynolds number (Fig. 8). The figure also shows the measured drag coefficients of the falcon model and the drag coefficients the model would have if its drag were the same as that on a parallel plate of the same wetted area with a turbulent boundary layer (equation 10). I shall describe these data in more detail below and review the information provided by the authors on (1) how they smoothed the feathers, trimmed the body, and corrected for interference drag and (2) the accuracy (Eisenhart, 1968) of the measurement process.

Pennycuick measured the drag coefficients (circles at top left of Fig. 8) of a pigeon (1968) and an African vulture (1971). The pigeon was frozen with its head raised above the position that is typical for free flight. The vulture was frozen in a position judged typical for free flight with minimum drag.

These data (crosses at the top left of Fig. 8) come from equivalent flat plate areas for a budgerigar, sparrow, starling, falcon and a mallard. I converted them to drag coefficients by dividing by cross-sectional body areas from equation 6. My 1973 paper described the bodies as arranged in ‘natural flight attitudes’ but did not say whether they were trimmed for minimum drag (I did not systematically adjust the body parts) or how the feathers were preened (I smoothed them on the frozen bodies). The paper specified the accuracy of the measurement process.

I can estimate the interference drag on the 1973 falcon (a 0.571-kg laggar falcon, Falco jugger, similar to the peregrine falcon in the present study) from the original data. The drag of the mounting strut was 12% of the measured drag, and correcting for its interference drag reduces C_D,B from 0.40 to 0.36. The latter value in Fig. 8 is at the tip of the arrow that extends downwards from the uncorrected value.

Prior (1984) measured the drag on 30 frozen bodies of 17 species of water fowl ranging in size from small ducks to swans. Pennycuick et al. (1988) summarized Prior’s data with two curves (Fig. 8): one fitted to the lower boundary of the data and the other fitted above about 80% of the data. (The excluded data are markedly above the rest of Prior’s results.) I have fitted curves (Fig. 8) to Prior’s data for ducks, geese and swans for comparison with other body drag measurements on these groups.

Prior rotated the bodies in the wind tunnel to obtain minimum drag. He assumed that streamlined mounting struts caused negligible interference drag.

These authors measured body drag for a mallard, an eagle, a goose and a swan (curves at top right of Fig. 8) after smoothing the feathers on the frozen bodies. Although they did not correct for interference drag, they noted that the drag of the support system amounted to about 40 % of the total drag for the larger bodies, and that the support bar apparently caused the feathers in its wake to flutter. They expressed reservations about the accuracy of their measurements because the drag balance operated near the lower limit of its range where they could not determine the linearity or repeatability of its readings. Their drag coefficients were higher than those of Prior, and they suggested a compromise curve (dashed in Fig. 8) to describe drag coefficients as a function of Reynolds number.

One can use Fig. 7 to estimate the error introduced by interference drag in the results of Pennycuick et al. (1988). For the body and mounting system used in the present study, the corrected drag coefficient is 59 % of the uncorrected drag when the strut drag is 40% of the measured drag. However, these authors used a different mounting system with various bodies, and one might plausibly assume that the interference drag of their system was equivalent to that of the system in the present study when the strut drag equals 25% of measured drag. Then, corrected drag coefficients would be 79 % of those shown in Fig. 8.

The measurements made in this study yield a much lower estimate of the drag coefficient for a falcon than my 1973 measurements. I attribute this reduction to careful preening of the feathers on the partially thawed body, adjusting the body parts for minimum drag, and reducing interference drag and correcting for it.

Objects may be classified as streamlined or unstreamlined, depending on whether skin friction drag or pressure drag predominates. The drag of streamlined objects may be only 10 % more than the skin friction drag on a parallel plate of equivalent wetted area when the boundary layers on both objects are turbulent (Goldstein, 1965). Unstreamlined objects may have much greater pressure drag than skin friction drag. For example, a sphere with a laminar boundary layer up to the region of separation has a large pressure drag because of its large wake. The drag on the sphere may be 30 times the drag on a parallel plate of equivalent wetted area with a laminar boundary layer (Goldstein, 1965).

Bird bodies are relatively unstreamlined (Prior, 1984; Pennycuick et al. 1988). All the drag coefficients in Fig. 8 are more than twice what they would be if body drag were equal only to the skin friction drag on a parallel plate of equal wetted area with a turbulent boundary layer. Indeed, the pressure drags on bird bodies are even greater than comparisons with the curve for coefficients based on skin friction indicate. Birds fly at Reynolds numbers where significant areas of both laminar and turbulent boundary layers exist on rounded objects (Goldstein, 1965), and skin friction drag is less for a laminar than for a turbulent boundary layer.

The drag on bird bodies may be quite sensitive to changes in Reynolds number, surface roughness and air turbulence because transition from a laminar to a turbulent boundary layer can cause a large change in pressure drag (see Theory).

The preceding discussion shows that any estimate of a body drag coefficient for the Harris’ hawk based on body mass or Reynolds number will be controversial. Instead, I shall use the measurements on the falcon body and model in the present study. The intact falcon had nearly the same mass (0.713 kg) as the hawk (0.702kg), and their bodies had similar proportions. Although the drag coefficients for the falcon and the model are lower than those reported by others, the present study controlled factors that can generate high drag coefficients.

The drag coefficients for the Harris’ hawk are probably somewhere between those for the frozen falcon body and those for the model. The surface of the Harris’ hawk in flight was smooth, more like that of the model. However, the model did not accurately reproduce all the surface details of the frozen body -for example, the contours where the cere merged with the beak, the groove between the eyeball and the brow, and the individual toes of the retracted feet. Considering these factors, I shall use a drag coefficient of 0.18, the mean of the drag coefficients of the frozen body and the model at 12.4 ms⁻¹, for a Harris’ hawk gliding at its normal range of flight speeds. The corresponding equivalent flat plate area is 0.00120 m².

I am grateful to Mark Fuller, US Fish and Wildlife Service, for providing the falcon body, and to Carlton Heine for building the flight balance.

 
• C_D

  drag coefficient

 
• C_D,B

  body drag coefficient

 
• C_f,lam

  skin friction coefficient, laminar boundary layer

 
• C_f,tur

  skin friction coefficient, turbulent boundary layer

 
• D

  drag on an object

 
• D_B

  body drag

 
• D_B,_e

  erroneous body drag

 
• D_I

  interference drag

 
• D_I,0

  interference drag of a particular strut

 
• D_I,s

  interference drag of strut

 
• D_I,sh

  interference drag of shroud

 
• D_m

  measured drag of a body on a strut

 
• D_m,0

  measured drag of a body on a particular strut

 
• D_s

  strut drag

 
• D_s,0

  drag of a particular strut

 
• d

  reference length for Reynolds number

 
• d_B

  diameter of circle with area S_B

 
• d_s

  exposed length of strut

 
• d_s,0

  exposed length of a particular strut

 
• d_w

  length of body from beak to tail

 
• F₁

  correction factor for interference drag

 
• k₁, k₂

  slope and intercept, respectively, of equation 14

 
• k₃

  ratio of strut drag to measured drag

 
• M

  mean value of repeated measurements

 
• m

  body mass

 
• N

  sample size

 
• P

  air pressure

 
• Re

  Reynolds number

 
• r

  rate of change of strut drag with strut length

 
• S

  reference area

 
• S_B

  maximum cross-sectional area of a bird body

 
• S_fp

  equivalent flat plate area

 
• S_fp,B

  equivalent flat plate area of body

 
• S_fp,s+1

  equivalent flat plate area of strut drag plus interference drag

 
• S_w

  wetted area

 
• V

  air speed

 
• V₀

  a specified air speed

 
• μ

  viscosity of air

 
• π

  ratio of circumference to diameter of a circle

 
• ρ

  air density