Measuring Aerodynamic Interference Drag Between a Bird Body and the Mounting Strut of a Drag Balance

The aerodynamic drag on bird bodies is an important quantity in theoretical treatments of gliding and flapping flight (see review by Pennycuick, 1989). The usual method of measuring body drag involves mounting a frozen, wingless body on the strut of a drag balance in a wind tunnel (see Tucker, 1990). The drag of the body alone is taken to be the difference between the drag of the body on the strut and the drag of the strut alone.

However, this difference does not measure the drag of the isolated body, because the presence of the strut changes the air flow around the body and the strut and causes additional drag known as interference drag (Hoerner, 1965; Gorlin and Slezinger, 1966; Pankhurst and Holder, 1952; Pope and Harper, 1966). Interference drag may make up more than 20 % of the drag measured by the drag balance (Tucker, 1990).

Tucker (1990) described an extrapolation method suitable for measuring interference drag on bird bodies. The method establishes an empirical mathematical relationship between the drag of the body on a strut and the drag of the strut alone for different types of struts. It then extrapolates the relationship to find the drag of a body mounted on a strut with no drag, i.e. the drag of the isolated body. The interference drag is the drag of the body mounted on the strut minus the drag of the isolated strut minus the drag of the isolated body.

This study investigates how the relationship mentioned in the previous paragraph depends on the types of strut used to establish the relationship. The results show that the relationship is independent of strut size and shape for certain types of struts, that the relationship can be established with just two struts, and that the interference drag generated by a strut can be predicted from the drag of the isolated strut. The study demonstrates a practical method for measuring interference drag and confirms the value of the body drag coefficient found for a peregrine falcon (Falco peregrinus) in an earlier study (Tucker, 1990).

Two characteristics define a strut: length and cross-section. The length is the distance between the point where the strut exits from the shroud of the drag balance and the point where it contacts the body mounted on it. The cross-section (Fig. 1A) is the perimeter of the strut in a plane perpendicular to the length and is the same at all points along the length. The cross-section is symmetrical about an axis of symmetry parallel to the direction of air flow. The leading point is the intersection between the axis of symmetry and the blunter, upwind end of the cross-section. The trailing point is a similar point at the sharper, downwind end of the cross-section.

The chord is the distance from the leading to the trailing point. The thickness is the maximum width of the cross-section along an axis perpendicular to the axis of symmetry. The fineness is the chord divided by the thickness.

Cross-sections may have different shapes, defined by an equation or a table of dimensionless, standard x,y coordinates for a half of a standard cross-section. The coordinate system originates at the leading point of the standard cross-section, and x increases along the axis of symmetry to a value of 1 at the trailing point, y increases along a perpendicular axis to a value of 1 at the maximum width of the cross-section. The x and y coordinates of an actual cross-section equal the desired chord multiplied by the standard x coordinates, and half the desired thickness multiplied by the standard y coordinates, respectively.

Each standard cross-section defines a strut type. One type of strut may have a variety of sizes and shapes depending on its chord and thickness. For example, this study uses three struts of a circular type with different diameters, three struts of a streamlined type with different chords and thicknesses, and one strut of another streamlined type.

This assumption is probably not strictly correct. The drag per unit length of circular cylinders oriented with the cylinder axis perpendicular to the direction of air flow increases with length because of flow around the ends of the cylinders (Goldstein, 1965). However, the assumption will serve for present purposes since struts for bird bodies have a limited range of lengths and have one end shielded by the drag balance.

Conventional methods for measuring interference drag on aircraft use combinations of multiple mounting struts (Gorlin and Slezinger, 1966; Pope and Harper, 1966). The extrapolation method for bird bodies is novel (Tucker, 1990), and this section uses new terminology and derivations to describe it.

Investigators may find the extrapolation method useful for a variety of bodies arranged in different configurations and exposed to different air speeds. This paper does not attempt to predict hi and C_D under all conditions.

Instead, the measurement methods described herein should be used. A plausible first assumption is that neither h₁ nor C_D change appreciably with speed. It follows that C_D and h₁ can be determined at a particular speed and used with equations 2 and 9 to calculate D_s and D_t at other speeds.

I measured drag on the frozen body of a peregrine falcon (Falco peregrinus L.) and a model body mounted on a drag balance (Fig. 1B) in an open-circuit wind tunnel set to an equivalent air speed of 12.6 ms⁻¹. (The actual air speed produced the same dynamic pressure (q) as an air speed of 12.6 ms⁻¹ in the US standard atmosphere at sea level (von Mises, 1959).) The wind tunnel had a rectangular working section with a cross-sectional area of 1.5 m². Tucker and Parrott (1970) and Tucker and Heine (1990) give a more complete description of the tunnel and its calibration.

The frozen body was wingless, and its head, torso and tail were positioned for minimum drag. The model body was made of rigid plastic foam and was hollow. The shape of its smooth surface accurately duplicated the feathered surface of the frozen body. I used these same bodies in a previous study (Tucker, 1990), which describes them in more detail.

The mounting struts from the drag balance attached to the frozen body and the model at a point in the mid-ventral line, half-way from the anterior end of the sternum to the posterior end. Each strut ended in a threaded rod, 3.18 mm in diameter, that either screwed into a wooden insert frozen into the frozen body or passed through a hole in the model. A nut could be placed on the threaded rod inside the model through a larger hole in the mid-dorsal line. I covered this hole with tape when measuring drag. I rotated the frozen body and the model around the threaded rod to align their long axes with the direction of air flow.

The drag balance had three parts: a force transducer, mounts and a streamlined shroud (Fig. 3). The force transducer was of the parallelogram type described by Gorlin and Slezinger (1966). I milled it out of aluminium plate 6.35 mm thick, with arms 1.14 mm thick. Four strain gauges glued to the arms with cyanoacrylate cement formed a Wheatstone bridge.

A 5 V power supply excited the bridge, and an amplifier multiplied the voltage from the bridge by 100 to produce approximately 0.12 mV mN⁻¹ of drag. A digital voltmeter (Acculex model 950) displayed the voltage from the amplifier. The voltmeter reduced electrical noise by (1) using a dual-slope analogue-to-digital converter that integrated the analogue voltage over a 0.2 s conversion period, and (2) using a microprocessor that averaged eight successive digital conversions. The bridge was at least 1000 times more sensitive to drag than to a vertical force applied at right angles to the drag direction.

Aluminium mounts supported the force transducer, the strut and the streamlined shroud. A tapped hole in the transducer mount received the cut-down, threaded end of a steel rod 12.70 mm in diameter that extended through a hole in the floor of the wind tunnel from a tripod on the laboratory floor. The rod isolated the drag balance from the wind tunnel, and I tilted it to align the force transducer with the direction of air flow in the tunnel.

The strut mount clamped onto the end of the strut. I tilted the strut back and forth in the mount to align reference points on the beak and tail of the frozen body and the model to within 1mm of fixed heights above the tunnel floor. This adjustment minimized drag and ensured that the frozen body and the model had the same angle of attack in all experiments.

The streamlined shroud shielded the transducer and the mounts from the wind. I made the shroud by shaping an aluminium sheet 0.51mm thick to the crosssection of a Navy Number 1 strut type (see Table 1) with a thickness of 26.0 mm and a chord of 130.0mm. Two nuts held the shroud firmly to one of the shroud mounts, and tape held the trailing edges of the shroud together. This arrangement allowed the shroud to be lowered for access to the strut mount.

I calibrated the drag balance with weights hanging from the end of a thread that ran over a pulley with a low-starting-torque ball bearing (New Hampshire Bearing SR168). The other end of the thread attached to the tail of the frozen or model body, or to the top of the strut in experiments with isolated struts. The pulley changed the force transmitted from the weight to the drag balance by less than 1 mN (the bias of the drag balance). The voltage from the Wheatstone bridge was linearly related to weight within the imprecision of the drag balance. Imprecision, expressed as the standard deviation of repeated measurements of the same force, was less than 0.1 mN for the weights and less than 1.5 mN for the struts and bodies with the wind tunnel turned on.

I used several different types of struts, all of which extended 93 mm from the top of the shroud to the frozen or model bodies. This length eliminated interference drag between the shroud and the body, since measurements showed that a strut length of 80 mm minimized the measured drag of the model (see Tucker, 1990, for an explanation of shroud interference). The 80mm strut length is three times the thickness of the shroud cross-section, the same factor that minimized drag measured by another drag balance with a differently shaped shroud (Tucker, 1990).

Three struts of this type (Fig. 4A and Table 1), henceforth referred to as navy struts, all had a nominal fineness of 2.94, but chords of 6.35 mm, 12.70mm and 36.58mm. Navy struts with a fineness close to 3 had lower drag coefficients than any other known strut type at the time they were designed (Beisel and Diehl, 1923; Diehl, 1928). I machined the struts from aluminium, or steel in the case of the smallest one. The machining process began with a workpiece, typically a rod, mounted horizontally on the table of a vertical milling machine between an indexing head and a tail stock. The indexing head rotated the rod around its long axis in 20 angular steps. At each angle, I milled a flat surface along the length of the rod at a precise distance from its long axis (Fig. 4B and Table 2). The flat surfaces approximated the cross-section of the strut, and I filed down the corners between them to finish the strut. The actual fineness values of the struts varied from 2.58 for the smallest to 2.94 for the largest, because the smaller struts bowed away from the cutting tool during the milling process.

The end of the strut that fitted into the mount on the force transducer had flat sides, parallel to its plane of symmetry. I drilled and tapped the other end to receive the threaded rod that fitted into the frozen body or the model. The tapped end of the smallest strut was left rod-shaped to support the tapped hole. The rod-shaped portion fitted into a recess in the frozen body and the model, and was not exposed to the air flow.

This strut type can be made by a milling machine equipped with a vice instead of an indexing head, or by hand-filing. I investigated it to provide information on a strut that is easier to make than a standard navy strut, yet still is suitable for use with a drag balance.

A rectangular workpiece with four flats cut on it approximated the cross-section of a navy strut of fineness 3 (Fig. 4C). The flats served as guides for hand-filing the strut to its final form. I set the head of the milling machine to just two angles -20 and 45° -and cut all four flats by rotating the workpiece end-for-end in the vice. Alternatively, I could have filed the flats by hand between lines scribed on the four sides of the work piece. The simplified navy strut used in this study had a fineness of 2.95 and a chord of 12.0 mm.

I made this strut from streamlined aluminium tubing bought at a store that sold supplies for model aeroplanes. The cross-section of the tubing had a chord of 12.6 mm, a fineness of 2.05 and was thicker near the trailing point than a navy strut with the same chord (Fig. 4A).

These struts were steel or aluminium rods with circular cross-sections and diameters of 3.18, 4.76 and 6.35mm (Fig. 4A). The diameter of a circular strut equals its thickness and chord.

I made a special circular strut for investigating the effect of a gap between the strut and the model on interference drag. This strut was a threaded rod, 3.18 mm in diameter covered by a sleeve 6.35 mm in diameter. The rod supported the model, and the sleeve could be moved up and down the rod to adjust the size of the gap between the sleeve and the model.

A spoiled strut is a streamlined strut with a spoiler attached that increases the drag of the strut. The spoiler in this study was a grooved wooden rod that fitted over the entire leading or trailing edge of the smallest navy strut (Fig. 4A). I made the spoiler by milling a groove along the length of a wooden dowel 6.60 mm in diameter.

The measured drag values reported in the text or graphs for a body on a strut are means of 3–5 sequential measurements. The sequence began with a reading from the drag balance with the wind tunnel turned off, then with the tunnel turned on, and so forth for each measurement in the series. The paired readings compensated for any drift in the drag balance output. After three sequences, I calibrated the drag balance by reading it with the thread from the calibrating weight attached to the body or the strut and again with the thread detached.

I used the same sequential process to measure the drag of isolated struts. Strut drag values are grand means -means of 2–3 means of sequential measurements.

Relationship between strut drag and measured drag of the model body

(drag in mN, standard deviation around line=1.42, N = 21).

The spoiled struts produced measured drag values that fell above the line in Fig. 5. The spoiled strut with the spoiler pressed over the trailing edge had less drag than with the spoiler pressed over the leading edge. Combining the data for both spoiled struts yields a mean spoiled strut drag of 54.4 mN and a mean measured drag of the model on the spoiled struts of 166.4 mN.

The streamlined struts had lower drag coefficients than the circular ones (Fig. 6). The smaller navy struts, including the simplified type, had C_D values that were about 60 % of those of circular struts with the same thickness. The commercial strut was less effective at reducing drag. Its C_D was 74% of that of a circular strut of the same thickness.

Drag coefficients of both streamlined and circular struts are known to change with Reynolds number (Goldstein, 1965). Only the navy struts varied enough in size to show a marked dependence of C_D on Reynolds number. Some of the decrease in C_D for the largest navy strut may be due to its greater fineness.

Measured drag increased as the gap between the strut and the model increased from 0 to 6.4mm (Fig. 7).

The mean measured drag of the frozen body on the spoiled strut (spoiler on leading edge) was 239.6mN (N=2), and on the smallest navy strut was 171.2 mN (N=2). The mean strut drags of the spoiled and navy struts were 57.1 and 11.7 mN, respectively.

The struts used in this study fall into two categories, depending on the relationship between the drag of the strut and the measured drag of the model body mounted on it. Graphically, this relationship is a straight line for smooth struts. I shall call this line the smooth strut line. Smooth struts have a fineness of 1 or more and cross-sections that are everywhere outwardly convex. They comprise the navy, simplified navy, commercial and circular struts.

Data for spoiled struts fall above the smooth strut line. Spoiled struts have crosssections with discontinuities. They comprise the smallest navy strut with the spoiler pressed on either the leading or trailing edge.

The existence of this line greatly simplifies the determination of interference drag for the following reasons.

1. The equation of the line can be derived from measurements on just two struts (see Appendix for sample calculations). One of these struts (the standard strut) can be the strut ordinarily used with the drag balance. It should have low drag, i.e. it should be streamlined and as small as practical. The other (the calibration strut) must have greater drag.

2. Smooth struts need not have precisely defined cross-sections. Apparently any smooth cross-section will do, since struts with cross-sections ranging from streamlined to circular qualify as smooth struts. For example, the standard strut could be filed to shape by hand, and the calibration strut could be cut from a rod of circular cross-section. The cross-section should be symmetrical and constant along the strut length.

   The most convenient calibration strut is one made by attaching a spoiler to the standard strut. In this case, the standard strut becomes the calibration strut without disturbing the bird body on the drag balance. Although a spoiled calibration strut is not smooth, the error in estimating body drag can be made small and corrected for. I shall discuss this error in a later section.

3. A single interference length of 33.1mm describes all the smooth struts in this study, regardless of their type or chord, and hence drag coefficient. This value comes from substituting the slope of the smooth strut line into equation 13. The interference length also is independent of strut length and air speed, according to plausible assumptions (see Theory).

The single interference length for smooth struts suggests that the interference drag for all bodies mounted on smooth struts of any chord and length could be calculated from an interference length of 33.1mm (see Appendix for sample calculations). Such calculations may be accurate for bird bodies that are similar in size and shape to the model in this study and attach to the strut in the mid-ventral line. However, the interference length may depend on body size and shape, attachment point of the strut or struts, and orientation of the body to the air flow. Whether the surface of the body is feathered or rigid did not significantly affect the interference length in this study, as will be discussed in a later section.

A spoiled strut is particularly suitable as a calibration strut for frozen bodies, which steadily thaw. A spoiler may be attached to the standard strut quickly without ruffling the feathers or changing the position of body parts. However, the spoiled struts in this study generated more interference drag than the smooth struts. The extra interference drag causes an error in estimating body drag by the extrapolation method. This section shows how the error can be kept small and corrected for.

The measured drag of the model body mounted on a spoiled strut fell at a point above the smooth strut line. The extra interference drag is the distance between this point and the line. The spoiled strut line is the line between this point and the point on the smooth strut line for the standard strut drag (see Fig. 9). The spoiled strut line extrapolates to an erroneous body drag, which is less than that found by extrapolating the smooth strut line.

The error, however, is only a fraction of the extra interference drag. The fraction is the drag of the standard strut divided by the drag added to the strut by the spoiler, and it can be kept small by using a standard strut with low drag.

For example, the drag of the smallest navy strut was 0.21 of the mean drag added by the spoiler. (Mean drags in this section are means for the spoiler added to the leading edge and the trailing edge of the standard strut.) The mean measured drag of the model on the spoiled strut was 9.4mN above the smooth strut line. Thus, the body drag determined by extrapolating the spoiled strut line is 0.21×9.4=2.0mN less than the correct body drag determined by extrapolating the smooth strut line -a 2.4% error.

This error can be eliminated by using the extra interference length to calculate the position of the smooth strut line. The extra interference length is analogous to the interference length: it is the length of a spoiled strut that has the same strut drag as the extra interference drag. Continuing the analogy, I assume that a single extra interference length describes spoiled struts with different chords and lengths at different air speeds.

The extra interference length is the extra interference drag divided by the drag per unit length (r in equation 7) of the spoiled strut. It has a value of 16.1mm (see Appendix) for the model body on the spoiled strut. An example in the Appendix shows how to use the extra interference length to find the smooth strut line for the frozen body.

Tucker (1990) reported that the drag coefficient of the model body was only 59% of that for the frozen body at an air speed of 12.4 ms⁻¹, and attributed the difference to the drag of the feathers. In the present study, the drag coefficient of the model was 54 % of that for the frozen body.

Does the feathered surface of the frozen body rather than the rigid surface of the model influence interference length? The smallest navy strut supporting the frozen body had a smaller interference length (26.1 mm, from equations 13 and 18) than that (33.1 mm) for smooth struts supporting the rigid model. This difference is not significant, since the standard deviation of h₁ for the frozen body is 6 mm. This value comes from a propagation of error analysis (Ku, 1969, p. 331) of the imprecisions of the measured values used to calculate h₁.

These experiments show how the closeness of fit between the strut and the body affects interference drag. I adjusted the gap between the strut and the body by moving the sleeve of the special circular strut up and down the rod that supported the body. As the gap widened, the measured drag gradually decreased (Fig. 7).

A mathematical model (see Appendix) accounts for the effect of the gap by treating measured drag as the sum of several terms: the body drag, the interference drag from both the rod and the sleeve, and the non-interference drag from both the rod and the sleeve. The interference drag decreases as the gap widens because the interference drag of the rod exposed in the gap is less than that of the larger sleeve. Likewise, the non-interference drag decreases because the drag of the rod is less than that of the sleeve.

The model treats the interference drag of the rod and the sleeve as exponential functions of gap width. These functions fit the measured data reasonably well when 95 % of the interference drag arises from a region of the strut 15 mm long nearest the body (a space constant λ of 5 mm in Fig. 7). This length seems plausible; Hoerner (1965) also suggests a length of 15 mm (see Appendix). It should not be taken too seriously, because it depends on small changes in drag and on the exponential model for interference drag. Other models that fit the observations may give different lengths.

Example 1 shows how to use measurements from a smooth standard strut and a smooth calibration strut. Example 2 shows how to use measurements from a smooth standard strut and a calibration strut made by attaching a spoiler to the standard strut. Fig. 8 shows the smooth strut line and the variables described below.

D_s,std=drag of the standard strut.

D_s,_cal=drag of the calibration strut.

D_m,cal,sm⁼nteasured drag of a body on a smooth calibration strut.

D_m,cal,sp=measured drag of a body on a spoiled calibration strut.

Measure D_m,std, D_s,std, D_m,cal,sm and D_s,_cal. Calculate the slope and intercept with equations 20 and 21.

The extra drag (D_ex) is the sum of the interference drag and the strut drag, and subtracting it from measured drag yields body drag. Example 1 shows how to estimate D₁ and D_ex without measuring strut drag. Example 2 shows how to estimate both quantities if strut drag is measured.

Fig. 9 shows the variables described below.

D_s,_cal⁼mean drag of the smallest navy strut with the spoiler on its leading edge, and on its trailing edge

=54.4mN.

D_m,cal,sp =mean measured drag of the model mounted on the smallest navy strut with the spoiler on its leading edge, and on its trailing edge

= 166.4 mN.

D_m,cal,sm⁼157.0 mN (calculated by substituting D_s,_cal into equation 14 for the smooth strut line).

Given h_1,ex =16.1mm. Fig. 9 shows the variables described below.

D_s,std=drag of the smallest navy strut

=11.7mN.

D_s,_cal=drag of the smallest navy strut with the spoiler on the leading edge

=57.1 mN.

D_m,std =measured drag of the frozen body on the standard strut

= 171.2mN.

D_m,cal,sp =measured drag of the frozen body on the spoiled standard strut

=239.6 mN.

Drag/length (r) for the calibration strut (h=93mm) is 0.614 mN mm⁻¹, given by: .

where e is the base of the natural logarithms (2.718), G is the width of the gap and λ is the space constant. D_I,rod reaches 63.2% of its maximum value when G= λ, and 95.0% when G=3 λ.

Hoerner (1965, pp. 8–10), using a different method, estimated that interference drag arises from a length of the strut that is 16 % of the maximum diameter of the object mounted on the strut. (The objects were bodies of revolution.) Applying this percentage to the effective diameter of the model falcon body (92.3 mm, equation 15) yields a strut length of 14.8 mm -essentially the same as the value estimated from the space constant.

 
• C_D

  drag coefficient of strut

 
• C_D,_B

  drag coefficient of body

 
• C_D,_rod

  drag coefficient of rod of special circular strut

 
• C_D,_sl

  drag coefficient of sleeve of special circular strut

 
• c

  chord of strut

 
• D_B

  body drag

 
• D_ex

  extra drag (Ds+D_I)

 
• D_I

  interference drag

 
• D_I,ex

  extra interference drag (Dm,ca_l,Sp-Dm,cal,sm)

 
• D_I.rod

  interference drag from rod of special circular strut

 
• D_I.rod,max

  maximum value of DI,rod

 
• D_I.sl

  interference drag from sleeve of special circular strut

 
• D_I.sl,max

  maximum value of DI,sl

 
• D_I.0

  interference drag for a strut with drag Ds,0 and measured drag D_m,0

 
• D_m

  measured drag of a body on a strut

 
• D_m,cal,sm

  measured drag of a body on a smooth calibration strut

 
• D_m,cal,sp

  measured drag of a body on a spoiled calibration strut

 
• D_m,0

  measured drag of a body on a particular strut

 
• D_rod

  drag of rod of special circular strut

 
• D_s

  strut drag

 
• D_s,cal

  drag of calibration strut

 
• D_s,std

  drag of standard strut

 
• D_s,0

  drag of a particular strut

 
• D_sl

  drag of sleeve of special circular strut

 
• d_B

  diameter of circle of area SB

 
• e

  base of natural logarithms

 
• f

  fineness (c/t)

 
• G

  width of gap between sleeve of special circular strut and body

 
• h

  strut length

 
• h_I

  interference length

 
• h_I,ex

  extra interference length

 
• q

  dynamic pressure (0.5 ρV2)

 
• m

  mass of intact bird

 
• m

  mass of intact bird

 
• Re

  Reynolds number

 
• r

  strut drag per unit length of strut

 
• SB

  maximum cross-sectional area of body

 
• t

  strut thickness

 
• t

  rod thickness of rod of special circular strut

 
• t

  sl thickness of sleeve of special circular strut

 
• V

  air speed

 
• w

  corner dimension for simplified navy strut

 
• λ

  A space constant for interference drag

 
• μ

  viscosity of air

 
• π

  ratio of circumference to diameter of a circle

 
• ρ

  density of air

This study was partly supported by a grant (453-5969) from the Duke University Research Council, and by a Cooperative Agreement (14-16-0009-87-991) between Mark Fuller, US Fish and Wildlife Service and Duke University.