ABSTRACT
The aerodynamic properties of bird wings were examined at Reynolds numbers of 1·5 × 104 and were correlated with morphological parameters such as apsect ratio, camber, nose radius and position of maximum thickness. The many qualitative differences between the aerodynamic properties of bird, insect and aeroplane wings are attributable mainly to their differing Reynolds numbers. Bird wings, which operate at lower Reynolds numbers than aerofoils, have high minimum drag coefficients (0·03–0·13), low maximum lift coefficients (0·8–1·2) and low maximum lift/drag ratios (3–17). Bird and insect wings have low aerofoil efficiency factors (0·2–0·8) compared to conventional aerofoils (0·9–0·95) because of their low Reynolds numbers and high profile drag, rather than because of a reduced mechanical efficiency of animal wings.
For bird wings there is clearly a trade-off between lift and drag performance. Bird wings with low drag generally had low maximum lift coefficients whereas wings with high maximum lift coefficients had high drag coefficients. The pattern of air flow over bird wings, as indicated by pressure-distribution data, is consistent with aerodynamic theory for aeroplane wings at low Reynolds numbers, and with the observed lift and drag coefficients.
INTRODUCTION
The theory of animal flight can be better understood than the theory of many other aspects of animal energetics and locomotion, by making use of classical fluid dynamic and modem aerofoil theory. The fluid-dynamic basis for lift and drag applies equally to man-made and animal aerofoils, and our present understanding of bird flight is mostly derived from aerofoil theory with only some recourse to empirical data for birds (e.g. Pennycuick, 1969,1975; Tucker, 1968,1972,1973; Weis-Fogh, 1973,1976; Greenewalt, 1975; Rayner, 1979). However, aerofoil data cannot be extrapolated directly to avian and insect flight, but must be scaled according to the Reynolds number (Re). Bird wings generally operate at Re&s below a critical transition range (104–106), where lift and drag coefficients alter markedly (Von Mises, 1959; Hoemer, 1965; Hoerner & Borst, 1975)-Empirical studies of bird wings (Nachtigall & Kempf, 1971; Reddig, 1978; Nachtigall, 1979) and insect wings dramatically illustrate the aerodynamic consequences of a low Re (see also Nachtigall, 1977; Jensen, 1956; Vogel, 1966).
The primary objectives of the present study are to investigate the basic aerodynamic properties of isolated, fixed bird wings at their appropriate. Re, to determine how the aerodynamic properties are affected by wing morphology, and to compare their performance with that of conventional aerofoils (working at high Re) and insect wings (low Re). The basic aerodynamic measurements are: lift and drag coefficients at varying angles of attack, minimum drag coefficient, maximum lift coefficient, maximum lift/drag ratio, and aerofoil efficiency factor. The role of wing-tip slots, a complication due to bird wings being composed of many laminated feathers, is considered elsewhere (P. C. Withers, in preparation) but basic aerodynamic data for a single primary feather from a black vulture are presented here as a comparison for the data concerning complete wings.
METHODS
Bird wings
Bird wings, dried in an appropriate gliding position, were used. Wings were obtained from frozen birds or were borrowed from the ornithology collection of the Duke University Zoology Department. A brass rod was glued inside the humerus with epoxy resin, and the rod was mounted directly on a force transducer assembly. Separation of the primary feathers did not occur for any species at positive angles of attack. Only the hawk wing had wing-tip slots.
Wings from the following species were studied: European starling (Sturnidae; Sturnus vulgaris); common nighthawk (Caprimulgidae; Chordeiles minor); chimney swift (Apodidae; Chaetura pelagica)-, Leach&s petrel (Hydrobatidae; Oceanodroma leucorhoa); bobwhite quail (Phasianidae; Colinus virginianus); wood duck (Anatidae; Aix sponsa); American Woodcock (Scolopidae; Philohela minor)-, red-shouldered hawk (Accipitridae; Buieo lineatus). The tip of a primary feather from a black vulture (Coragyps atratus) was also studied. Body mass and wing loading of these species are: starling, 0·0850 kg, 4·3 kg m-2; nighthawk, 0·064 kg, 1·9kg m–2; chimney swift, 0·017 kg, 1·7 kg m–2; petrel, 0·027 kg, 1·1 kg m–2; quail, 0·150 kg, 9·2 kg m–2; wood duck, 0·590 kg m–2; woodcock, 0·200 kg, 5·6 kg m–2; hawk, 0·550 kg, 3·3 kg m-2 (Poole, 1938; Hartman, 1961).
Wind tunnel
A Kenney Engineering Corporation model 1057 closed-circuit wind tunnel (single return) was used. The working section was 0·26 × 0·30 m. The turbulence factor for the wind tunnel was determined by measuring the drag coefficient of ad sphere (0·1 m diam.) at different Re (Pope & Harper, 1966). The drag coefficient of the sphere declined markedly at Re = 1·6× 106, hence the turbulence factor is quite low, at about 2·4.
Wind velocity in the tunnel was measured by using a pilot tube (United sensor PAC-12-ki) and a Barocell electric manometer (sensitivity = 10−6 mmHg). The static and dynamic pressure heads measured with the pitot tube were converted to air velocity as described by Pope and Harper (1966).
Lift/drag measurement
Lift and drag forces were measured by using two rectilinear strain-gauge assemblies, with their movement axes mounted at 90°. Each assembly was composed of four strain-gauges for thermal stability. The strain-gauge assemblies were mounted under the floor of the tunnel, and could be rotated through an angle of about 100° with a motorized, rotating support. The lift and drag forces were calculated trigonometrically from the measured forces and the angle of rotation, since the whole strain-gauge assembly rotated. The gauges were operated with a Beckman RS Dynograph (type 462) with type 9802 strain-gauge couplers and 416 B pre-amplifiers. The output signals were time-averaged over about 5 s using a Heath Universal Digital Instrument EU-805. The strain-gauge assembly was calibrated daily by using a 0–0·1 N Pesola scale. Lift and drag measurements were repeatable to ± 0·002 N.
The bird wings were mounted vertically in the tunnel because the strain-gauge assembly was located under the floor of the tunnel. This attitude did not affect the aerodynamic properties of the wing to a significant extent, but meant that the mass of the wing was acting at 90° to its normal direction relative to the wing. However, the weight of the wing is generally small compared to the aerodynamic forces and can be ignored. The wings were not mounted with the root flush against the tunnel wall (as model aeroplane wings are) because of technical difficulties. The wing root hence shed a vortex wake, and the pattern of air flow around the wing root was atypical. This might increase CD,in, but would have little effect on minimum CD, or CL values. The most significant effect would be to underestimate aerofoil efficiency factor. However, the data obtained with this mounting system do not indicate any significant effects (see below). Standard wall interference factors for the wind tunnel were calculated for a close-circuit, rectangular tunnel (Pope & Harper, 1966), but no corrections were required except for the induced drag of the largest wing (redshouldered hawk) which was adjusted for the proximity of the ground-plane.
The local angle of attack of the wing was measured at mid-span with a protractor mounted on the top of the wind tunnel. Angle of attack varies along the wing, however, because of natural twist and aerodynamically induced bending.
PRessuRe distribution
RESULTS
Morphometries
The ranges of various morphological parameters for the wings studied are shown in Table 1. Most of the wings were approximately elliptical in planform, although the hawk wing was the most rectangular and the wood duck wing was the most tapered. The surface areas (&wetted& areas) of the wings were about 2 ·04 –2 ·14 times greater than the projected areas.
Lift/Drag
The absolute values of lift and drag (in Newtons) were dependent upon wind velocity although the general form of the lift-drag polar and the maximum lift/drag ratio were independent of velocity. All lift and drag data presented here are converted to the lift and drag coefficients (CL = 2L/(ρV2S); CD = 2D/(ρV2S)) to correct for variation in dynamic pressure head and wing surface area (S). The correction for dynamic pressure resulted in values of CL and CD which were independent of V over the narrow range of V used in this study. The aerodynamic forces all high wind speeds did not bend the wing sufficiently to alter the lift or drag coefficients. However, CL and CD would vary markedly over wider ranges of V (see Discussion).
The CL and CD of the various bird wings and the vulture primary feather altered markedly at differing angles of attack (α) at mid-span; the CD–CL curves, CL, CD and CT/CD data are summarized in Figs. 1–3. The value of a was arbitrarily measured only at mid-span, although the local α varied along the wing span because of inherent wing twist (see Table 1) and due to aerodynamic forces deforming (including twisting) the wing.
Aerodynamic parameters for the bird wings and vulture feathers were generally similar (Figs. 1–3; Tables 2, 3) although there were many qualitative differences. The relationship between CD and CL was generally U-shaped except at high α when CL levelled off or even declined. Quadratic, best-fit equations were fitted to the CD-CL data (excluding data at high α) since the relation is, in theory, parabolic. The curves were often quadratic rather than parabolic (i.e. parabolic but shifted from the origin since the minimum CD was not at zero lift; Figs. 1–3, Table 2). The CD varied with a in a parabolic fashion, and the quadratic best-fit equations are presented in Table 2. The CL was usually linear at intermediate a and relatively constant at lower and higher α. The best-fit linear equations for CL at intermediate a are summarized in Table 2.
The profile drag coefficient (ideally determined as the minimum drag which occurs at zero lift) was from 0·024 to 0·125 but generally did not occur at the zero lift angle. The maximum CL values varied from about 0·7 to 1·2 at α of 15–20° (Table 3). The CL/CD ratio was often quite variable, reflecting the errors involved in lift and drag measurement, but CL/CD always increased from negative values at low a to maximal values at a of 5–8°, then declined markedly at higher a. This is the expected form of the relation, but there is no theoretical equation so best-fit curves were obtained by using 10th degree polynomial equations to indicate the approximate relationship. The maximum values for CL/CD(= L/D) varied from 3·3 to 17 for the different wings and vulture feather.
The aerofoil efficiency factor (e) was calculated in two ways. Firstly, e was calculated from a regression of CD and CL since the theoretical slope of this relationship is 1/(πARe) and the intercept is the profile drag coefficient (Greenewalt, 1975). The values of e were also calculated from the (CL/CD)max value since e = 4CD, pro (CL/CD)2max/(πAR) (Greenewalt, 1975). The values of e were in reasonable agreement using the two different methods, and generally ranged from 0·3 to 0·8 (ignoring the unreasonable values 1).
PRessuRe distribution
The pressure distribution (expressed as P, corrected for dynamic-and static pressure head) over the mid-span of the nightjar wing altered markedly at differing a (Fig. 4). The values for CL and CD can be calculated from these distribution data (Pope & Harper, 1966). Only the pressure for the leading one-half of the wing section was measured, but this is the most important in terms of lift and drag, so approximate calculated values for CL and CD are presented in Table 4. These estimated CL and CD values are in general agreement with CL and CD values measured for the whole wing.
DISCUSSION
The lift and drag characteristics of bird wings and the vulture feather resemble, in general form, those of conventional (man-made) aerofoils (e.g. Von Mises, 1959; Hoerner, 1965; Pope & Harper, 1966; Hoerner & Borst, 1975), other bird wings (Nachtigall & Kempf, 1971; Reddig, 1978; Nachtigall, 1979) and insect wings (Jensen, 1956; Vogel, 1966; Nachtigall, 1976). However, there are significant quantitative differences between the aerodynamic performances of conventional aerofoils, bird wings, and insect wings. The following discussion relates how these differences are attributable to variation in wing morphometries and air-flow regime (i.e. Re).
Aerodynamic drag
The minimum drag coefficients measured here for the bird wings were from 0·03 to 0·13, with the primary feather tip of a black vulture having a drag coefficient of 0-024. These drag coefficients are similar to those measured for other bird wings, or parts of bird wings, or models of bird wings. Minimum drag coefficients for insect wings are similar or higher: locust forewing 0 ·024; locust hind wing, 0 ·06 (Jensen, 1956); Drosophila wing 0 ·3 (Vogel, 1966). These values for bird and insect wings are considerably higher than those for conventional aerofoils, which typically have minimum drag coefficients of less than 0·01. As will be shown below, these marked variations in minimum drag coefficient for insect, bird and man-made wings do not necessarily reflect different wing morphology or function but simply the Re at which they operate.
There are three basic components of aerodynamic drag: skin friction drag (drag coefficient = CD, f), pressure drag (CD,pre) and induced drag (CD, in). The first two drag terms are generally combined into a single term, profile drag (CD,pro).
The pressure drag coefficient is determined by the magnitude of the turbulent wake left behind an object, and hence is lowest for streamlined bodies with delayed separtion. The CD,pre is experimentally determined as CD, pro –CD, f. Pressure drag becomes relatively more important than skin friction to total drag at high Re since skin friction is reduced. Separation of air flow is delayed at high Re by boundary layer turbulence, and this is reflected by a dramatic decrease in CD, Pre (or CD pro) at Re above a critical level, about 108 (Fig. 6). Conventional aerofoils, which usually operate above this critical Re, have a much lower drag than bird and insect wings. However, third wings have higher drag coefficients (Fig. 7) than aerofoils at equivalent Re (below the critical range), perhaps reflecting the surface roughness of bird wings and the tendency of individual feathers to flutter and increase drag, or wing twist (see below).
The profile drag coefficient, although markedly influenced by Re, is also dependent upon the thickness of the wing, particularly at low Re when flow separation occurs immediately after the thickest or most cambered portion of the wing. This is clearly shown by the relationship between CD, pro and thickness (or camber) for bird wings and aerofoils at subcritical and supercritical Re (Fig. 7). The CD, pro of different bird wings was correlated with aspect ratio, camber and nose-radius (Table 5). Camber would be expected to have the same effect as thickness in determining the point of flow separation, the magnitude of the turbulent wake, and the drag coefficient. Indeed, camber was the morphological parameter which best predicted CD, pro using multiple linear regression analysis (Table 5).
Induced drag of wings is usually greater than calculated as CL2π AR even for elliptical, untwisted wings because a wing is not a perfectly efficient device. An aera
In summary, the drag of bird wings is considerably greater than that of conventional aerofoils for a variety of reasons. Skin friction drag is higher because of the lower Re, and whether air flow over bird wings is laminar or turbulent makes little difference to the value for skin friction drag. Pressure drag is high for bird wings because the Re is subcritical and so separation occurs immediately after the thickest part of the wing; it also appears to be high because bird wings are twisted. Feathers may also result in some additional drag compared to a smooth aerofoil. Induced drag appears to be greater for bird wings, which have lower aerofoil efficiency factors. Insect wings, which operate at lower Re than bird wings, have even higher drag coefficients despite their &cleaner& aerodynamic shapes, because of higher skin friction drag.
Aerodynamic lift
Lateral flow of air around wing tips is also of significance to aerofoils of low aspect ratio (< 5) such that dCL/d α. is higher (= 0·5 × AR up to a maximum of about 0·27; Hoerner & Borst, 1975). However, values for dCL/d α of the bird wings were usually less than or equal to o-i (Table 2). The dCL/da. for bird wings may have been underestimated slightly since the CL– α relationship often appeared to be S-shaped (sigmoidal) but a linear regression was used to estimate the mean slope.
The values of CLt max of bird wings measured in the wind tunnel were quite low (⦤ 1·2). Similar values of CL max for bird wings are reported elsewhere (Table 3). This is in marked contrast to calculated or estimated values of CL,max for birds or bird wings for gliding or flapping flight (Tucker & Parrott, 1970; Weis-Fogh, 1973; Norberg, 1975). However, Norberg (1976) calculates lower values which are more consistent with steady state for hovering bats, of about 1·4–1·6. Such high CL, max values are not consistent with steady-state aerodynamics, either for the measured bird wings or conventional aerofoils at low Re. The body and tail of birds probably contributes some lift (hence CL based only on wing projected area is overestimated). Separation of primary feathers during the wing stroke may increase the effective aerofoil area, hence use of the wing projected area would also overestimate the actual CL (see P. C. Withers, in preparation). Further, non-steady state aerodynamics have been shown to yield higher CL, max values in some instances (Weis-Fogh, 1973, 1976).
Morphological parameters, such as camber and leading-edge shape, can also affect CL, max The CL, max.. The CL, max of bird wings was correlated with the position of maximum thickness, such that wings with the point of maximum thickness near the leading edge had the lowest CL max. The CL, max of bird wings (but not the vulture primary feather tip) was also correlated with camber (r = 0·52), as would be expected.
The CL of conventional aerofoils decreases dramatically at high a, but this is not so for conventional aerofoils or bird wings at low Re. A high CL at large a is of significance to birds during landing, when the wing may be & stalled & at high a, with a consequently high drag to decelerate the bird, without reducing CL. No special properties of bird wings are required to explain this lack of wing stall at high a, although Vogel (1966) suggests that insect wings are specially adapted to maintain high CL after &stall&.
Lift/drag ratio
The CL of bird wings determines the angle of attack and wind velocity required for horizontal flight. The CD determines the power required for flight (power = drag force x velocity). The lift/drag ratio (CL/CD= L/D) reflects the performance of the aerofoil, i.e. its aerodynamic &cleanness& and glide angle. The CL/CD of bird wings was maximum at small, positive α (and at low CL values); (CL/CD)max ranged from 3·3 for the starling wing to about 17 for the swift wing and vulture primary feather. Conventional aerofoils typically have CL/CD ratios of 20 or more, at high Re, but (CL/CD) max is much lower at Re&s similar to those of the bird wings (Pope & Harper, 1966). The (CL/CD)max of moth, butterfly and Drosophila wings is even lower (2-4) than that of bird wings because of their very low Re (Vogel, 1966; Nachtigall, 1976), although it is about 8-10 for locust wings (Jensen, 1955). It is clear that the (CL/CD)max, like many other aerodynamic parameters, is markedly dependent upon Re.
Aerofoil efficiency factor
It proves to be much more difficult to determine e for a bird wing than for a conventional aerofoil, and the meaning is quite different. Greenewalt (1975) states that it is possible to determine both e and CD, pro by plotting Cl2/ πAR against CD, total since the result is a straight line whose slope is i/e and intercept is CD, pro. However, this assumes that CD, pro is independent of CL, CD and α. In fact, the relationship between CL2/ π AR and CD, total is clearly not linear and great care is required in selecting the range of CD, total used to estimate e since the slope is low (and e is high) at low a, and the slope is high (and e is low) at greater α.
Values of e calculated in this study by two different methods were generally from 0-3 to o-8, but some values were unreasonably high. Furthermore, values of e for bird wings, are not simply an efficiency factor for the following reason. CD, pro is a significant portion of total drag, for bird wings, and CD, pro will change at differing α. Thus, D, totalalters by more than the change in induced drag, and includes not only the mechanical efficiency term but also the change in CD, pro at differing a. This is not the situation for conventional aerofoils at high Re since D, pro is a less significant proportion of D, total and e more closely approximates a mechanical efficiency factor (D, pro changes with a for conventional aerofoils, but it is still relatively insignificant relative to CD, m)-Values of e for insect wings range from about 0·2 (Drosophila) to 0·5 (Schistocerca) (calculated from data of Jensen, 1956; Vogel, 1966). Similarly, the value of e for a flat plate at Re = 4 ×104 is low, at about 0·4 (calculated from data in Hoerner, 1965). It is therefore of little intrinsic value to calculate e for bird wings for this reason, except for the sake of having a value for substitution into various equations.
It is possible that the manner of mounting the wing used here (no end-plate or wall boundary as a reflecting plane) overestimated the CD at high α. However, the values of 1/ π ARe calculated for bird wings from other studies are also quite low (Table 3; 1/ π ARe could not be converted to e since AR was often not given). Furthermore, Nachtigall (1979) used a double end-plate system which approximates a wing of infinite span, so induced drag should be o (Von Mises, 1959). Nevertheless, there was clearly a marked increase in CD at high a, indicating that CD ln is a small fraction of the increase in Cn; CD, pro being the most important.
Pressure distribution
The pressure distribution over the nightjar wing (Fig. 4) was similar to that over a conventional aerofoil (Harper & Pope, 1966; Hoerner & Borst, 1975), with a pronounced suction peak forming on the upper, leading edge at a of 5–9°. This suction peak diminished at lower and higher a. A positive pressure developed on the lower wing surface at moderate to high a (⩾ 2°) whereas a suction pressure formed at lower a. The relative magnitude and sign of the pressure distribution indicated the development of negative lift at, maximum positive lift at moderate a, and a decline in lift at higher a. In fact, the actual lift and drag coefficients can be calculated from the pressure distribution (Pope & Harper, 1966). The calculations for the mid-span of the nighthawk wing, although only approximate, are consistent with the measured lift coefficients and with the pressure drag coefficient estimated from the measured CD (the pressure distribution allows the estimation on of the pressure drag coefficient, not skin friction drag or induced drag coefficient like deviation of the CL and CD pre values from measured CL and estimated CD, pre reflect not only potential experimental errors but also possible variation in CL and CD, pro along the wing span.
The pressure distribution not only enables the estimation of local CL and CD, pre, but also indicates the air flow pattern over the wing. Both the pressure distribution for the nighthawk wing and basic aerodynamic considerations (Schlicting, 1966) indicate a transition from laminar to turbulent flow immediately after the thickest part of the wing, and flow separation (Figs. 4, 8). Such a flow pattern is in marked contrast to that over a conventional aerofoil, where the higher kinetic energy of the air delays turbulence and separation to a point much closer to the trailing edge than the thickest part of the wing. This difference in flow pattern for wings at low and high Re results in the higher CD, pre for the former. Birds, by virtue of their small wings and low flight velocity, are generally restricted to Re less than about 105, although the largest flying birds may have Re&s into the transition zone and greatly benefit in terms of reduced drag and also increased lift coefficients. However, the flow pattern for a flapping bird wing may bear little resemblance to that measured in this study for a stationary wing. It would be of great interest to measure the pressure distribution or air flow of a flapping wing. Perhaps the standard boundary layer visualization techniques used for aerofoils could also be applied to bird wings.
Lift/drag relation
There is clearly an inverse correlation between the lift and drag performance of bird wings (Table 3). For example, the most streamlined wing (swift) had the lowest CDt pro and CLt max, and highest (CL/CD)max. The starling wing had the highest CD, pro, a high CL, max and the lowest (CL/CD)max. The morphology of the wings clearly contributed to these differing lift and drag performances (Table 5). The wing loading of the birds (kg m-2; from Poole, 1938, and Hartman, 1961) was not significantly correlated with CD, min, Cmax or (L/D)max but was significantly correlated with the lift curve slope (dCL/d α. = 0·086 − 0·004 (wing loading); P < 0·05). The aerodynamic performance of different bird species would seem to be determined by their wing morphology, which in turn would reflect many ecological and physiological constraints. The great variety of shape, size and aerodynamic performance of bird wings testifies to the differing trade-offs between lift and drag performance required by various bird species.
ACKNOWLEDGEMENTS
I am greatly indebted to E. Shaughnessy of the Engineering Department at Duke University for use of the wind tunnel, pitot tube and pressure sensor, and for valuable discussion. I thank P. L. O&Neill for valuable discussion. I also thank V. Tucker and K. Schmidt-Nielsen for loan of equipment.