mechanics of the avian propatagium: flexion-extension mechanism of the avian wing

JOURNAL OF MORPHOLOGY 225:91-105 (1995)

Mechanics of the Avian Propatagium: Flexion-Extension Mechanism of the Avian Wing

RICHARD E. BROWN, JULIAN J. BAUMEL, AND ROBERT D. KLEMM Department of Anatomy and Physiology, College of Veterinary Medicine, Kansas State University, Manhattan, Kansas 66506 (R.E.B., R.D.K.); Burke Museum, Division of Birds, University of Washington, Seattle, Washington 98195 (J.J.B.)

ABSTRACT The supporting elements of the avian propatagium were examined in intact birds and as isolated components, using static force-length measurements, calculated models, and airflow observations. The propatagial surface supported between Lig. propatagiale (LP) and brachium-antebrachium is equally resistant to distortion over the range of wing extension used in flight. The lengths LP assumes in flight occur across a nearly linear, low-stiffness portion of the force-length curve of its extensible pars elastica. In an artificial airflow, intact wings automatically extend; their degree of extension is roughly correlated with the airflow velocity. Comparisons between geometric models of the wing and the passive force-length properties of LPs suggest that the stress along LP balances the drag forces acting to extend the elbow. The mechanical properties (stiffness) of the LP vary and appear to be tuned for flight-type characteristics, e.g., changes in wing extension during flight and drag. Lig. limitans cubiti and LP combine to limit elbow extension at its maximum, a safety device in flight preventing hyperextension of the elbow and reduction of the propatagium's cambered flight surface. Calculations using muscle and ligament lengths suggest that M. deltoideus, pars propatagialis, via its insertions onto both the propatagial ligaments, controls and coordinates propatagial deployment, leading edge tenseness, and elbowlwing extension across the range of wing extensions used in flight. The propatagial ligaments and M. deltoideus, pars propatagialis, along with skeleto-ligamentous elbowlcarpus apparatus, are integral components of the wing's extension control mechanism. o 1995 Wiley-Liss, Ine.

In birds, "muscles supply the power for flight, while the wing and other areas are the foils with which the muscles operate" (Hart- man, '61). Although our knowledge of the flight muscles that act upon a bird's wing (Dial, '92a,b; Dial et al., '91) and avian aerodynamics (Spedding, '82, '86, '87a,b; Sped- ding et al., '84) is expanding, we understand little of how feathers, skin, ligaments, bones, muscles, and nerves are functionally com- bined, organized, and integrated within the bird's highly adaptable airfoil. Direct observations of birds in flight and those on slow motion film (Ruppell, '80) show that several parameters of the avian wing (e.g., extension, angle of attack, dihedral, and wing-beat) are varied during flight to produce controlled and maneuverable flight. Recently, Dial ('92b) has demonstrated that birds are capable of

sustained flight following the denervation of all muscles distal to the elbow. Such results indicate the existence of a high degree of automaticlpassive mechanical integration in the avian wing.

The literature dealing with the mechanisms that functionally integrate the anatomic components of the avian airfoil is limited to descriptions of the skeleto-ligamentous linkage between elbow and carpus (Sy, '36; Fisher, '57; Vasquez, '92, '94), comparative myologies of birds of numerous taxa, and descriptions of the anatomic components that integrate the flight feathers (largest projected area of the wing) with the other components of the wing (Robin and Chabry, 1884;

Richard E. Brown is now at Physiologj Program, Harvard School of Public Health, 665 Huntington Ave., Boston, MA 02115.

D 1995 WILEY-LISS, INC.

92 R.E. BROWN ET AL

Pelissier, ’23; Baumel, ’93). Elucidation of the mechanisms of avian flight and the evolution of birds and their flight depends on our understanding of the functional morphology of the avian airfoil per se. Here we examine the mechanics of the structures supporting the propatagium and their contributions to the function of the bird’s wing in flight.

MATERIALS AND METHODS Animals

The birds used during these experiments and their sources were: six pigeons (Columba Ziuia), six House sparrows (Passer domesti- cus), and six European starlings (Sturnus uulgaris) captured from local, wild popula- tions; six chickens (Gallus gallus) were pur- chased from a commercial source; three Blue- wing teal (Anas discours) were donated by D.K. Saunders; and birds were obtained from the Department of Clinical Sciences, College of Veterinary Medicine, Kansas State Univer- sity including six Great Horned Owls (Bubo uirginianus), four Red-tailed Hawks (Buteo jamaicensis), two Turkey Vultures (Cathartes auru), a Sharp-shinned Hawk (Accipiter striu- tus), a Coopers hawk (Accipiter cooperii), a Great Blue Heron (Ardea herodias), and two Kestrels (Falco sparuerius). All of the birds from the Department of Clinical Sciences had died or been euthanized because of irrepa- rable injuries that occurred in the wild. Live birds were killed with intravenous or intra- peritoneal pentobarbital-Na ( > 120 mglkg).

Terminology All terms of anatomical direction or rela-

tive position of one structure to another are based upon a bird in the “Standard reference position” in which the wings are fully ab- ducted and extended out and away from the body axis in the dorsal plane (Baumel et al., ’93). The anatomical nomenclature follows that of Baumel et al. (’93) and Brown et al. (’94a).

Mechanical testing Whole birds, intact wings, isolated propata-

gia, and support ligaments were examined in fresh specimens. To determine reference points and lengths for force-length analyses, intact birds were attached to a dissection board by one wing; a weight equal to = 3 times body weight was suspended from the contralateral wing, resulting in equal extension of both wings. This procedure elimi- nated postmortem contracture and produced

a configuration we refer to as the “maximum flying extension.’’ The maximum angle of elbow extension used in flight is reliably known only for starlings, in which it is reported to be 110” (Dial et al., ’91); our tech- nique produced a maximum angle of elbow extension of 112” in the starling. Isolated Lig. propatagiale

With both wings in maximum flying extension, the ventral propatagial skin was dis- sected away from underlying components; reference marks were applied directly to the structure(s) of interest, and lengths and angles were recorded. Tissues were kept moist with physiologic saline. Reference marks for the highly distensible central section of Lig. propatagiale (LP), i.e., its pars elastica (PE) (Fig. l), were located = 2 mm from its attachments to the collagenous portions of the ligament. The distance (L) between marks on the PE was measured (nearest 0.1 mm) as the upper limit to L in vivo (Lv, Figs. 2, 4). LP were then excised with attached bone, joint, and muscle tissues at each end, and un- stressed length (LO) of the PE was measured. Resting LO is the length of the PE when it is in a straight, flat configuration on a “wetted” ruler where the ligament is held in a flat configuration by surface tension.

The LP preparation (see above) was suspended by the proximal humerus, and a small plastic bag was sutured to the proximal stump of the manus. Weight (g) - length (0.1 mm) curves of the PE to the point of rupture (where L = L M ~ ) of the LP were made by addition of increasing weights to the bag; all weight was removed from the ligament between successive measurements. Finally the distal tissues and empty bag were weighed and summed with the added weights to give total weight at each L. For these long thin ligaments, we adopt the notion of nominal uniform uniaxial stress and strain: 1) Stress is the axial force per unit average cross- sectional area (see below) in the strained state; and 2 ) nominal strain is defined by E = (L - Lo)/Lo, where L is the strained length and Lo is the resting (unstrained) length. The tangent slope of the stress-strain curve is the strain-dependent stiffness of the mate- rial, i.e., hysteresis.

We determined average resting, cross- sectional area (AR) of comparable lengths from contralateral PE as V/Lo, where V is volume measured with precision syringes as the difference in saline volume required to fill a piece of small-bore plastic tubing to a refer-

FLEXION-EXTENSION OF THE AVIAN WING

1- Lig Propatagiale

TECR Fig. 1. Buteo jamaicensis. Diagrammatic anatomy of

the propatagial ligaments, dorsal view. Lig. propatagiale and Lig. limitans cubiti originate with a common aponeu- rosis (CA) from the deltopectoral crest and fibrous tissues directly attached to the crest. Lig. propatagiale is composed of a proximal collagenous segment, i.e., proximal pars fibrosa (PFp), a central distensible pars elastica, and a distal collagenous pars fibrosa (PFD). Lig. propatagiale inserts onto the fibrous capsules covering the distal radius, carpus, and carpometacarpus, and has a terminal

ence mark, with and without the specimen inside. We then calculated A of test specimens at any length as AL = AR/(E + 11, and nominal stress as u = WJAL (kg/cm2), where WL is the added weight at that length.

Propatagial deformation in intact wings To examine deformation of the intact

propatagium, the wing (attached to the bird) was supported in a horizontal position by a ring stand clamp attached to the proximal humerus and with the distal wing in the experimenter’s hand. Various weights were placed atop a triangular piece of paper, covering approximately half the area of the extended propatagium on its feathered surface, so that the load would be evenly distributed and the feathers could slide beneath the paper as the wing was flexed.

Wings of intact birds, with the proximal humerus supported by the experimenter’s hand in the axillary space, were observed under two conditions: 1) in the airflow from a large-volume pump (200 literstsec); and 2) suspended out from ( > 0.75 m) the side window of a moving vehicle. Vehicle speed was used as a measure of airflow velocity. Prevail-

DS

93

extension (LPT) continuing to and along the alular digit (AD), inserting into subcutaneous tissue. Lig. limitans cubiti inserts onto the tendon of origin (TECR) of M. extensor carpi radialis, caput dorsale (MECRD). The distal segment of Lig. limitans cubiti (DS) extends caudolaterally from the ligament’s insertion onto the tendon of origin of M. extensor carpi radialis, merging with the antebrachial fascia and ligaments supporting the secondary feathers. MECRV, M. extensor carpi radialis, caput ventrale.

ing winds if present were < 3 kmlhr and perpendicular to the road.

Propatagial ligaments and wing function Isolated wings (disarticulated at the shoul-

der) were used in determinations of the mechanical effects of the propatagial ligaments on the carpus, carpometacarpus, and alular digit. Each of these wings was supported by its radius mounted between strong pins (nails) imbedded in stiff rubber (tire) attached to the jaws of a vise. The pins securely supported the radius while allowing free movement of the humerus, ulna, and soft tissues around the pins. The propatagial skm had been removed so that forces could be applied to the LP. The wing was mounted in a vertical position so that its wrist and carpometacarpus was extended against gravity. A line attached to the proximal end of the LP was draped over a smooth metal rod, and weight was added to a bag attached to its free end, To ameliorate any starting friction between the smooth metal rod and the line attached to the wing from which we suspended weights, we gently wiggled or slightly vibrated the wing in the directions of ex-

94 R.E. BROWN ET AL.

STRESS (newtons) 18

16

14

12

10

8

6

4

2

0 0 0.5 1 1.5 2 2.5

STRAIN

Fig. 2. Force-strain mechanical properties of Lig. propatagiale, pars elastica. To compare the actual force necessary to elongate (strain) the leading edge ligament to its maximum flying extension (arrows) the force has not been converted to an equal cross-sectional area basis,

pected motion. That disturbance also elimi- nated the starting friction of the joint tissues or structures attaching to the joints in the dead birds under study.

RESULTS Supporting ligaments

Lig. limitans cubiti (elbow extension limiting ligament)

As the elbow of a bird's wing is extended, the elbow extension limiting ligament (LLC) (Fig. 1) remains slack, under no tension, until it reaches its full length (deltopectoral crest to proximal antebrachium), where it becomes taut, restricting further extension, i.e., "maximum flying extension": Cathartes and Ardea = 145"; Bubo and Buteo = 133"; pigeon ~ 1 2 5 " ; and Passer and Sternus = 112"). Force-length properties of isolated LLCs show an EMAX of less than 0.11. Sever- ing the Lig. propatagiale (LP, see below) (Fig. 1) and the leading edge of the propatagium that encloses it, in an extended wing maintained under tension (3 x bird's weight), per- mits less than a 5" increase in elbow extension. When the LLC, LP, and propatagium

i.e., stress. Note: In flight the Lig. propatagiale operates along the linear, low-stiffness portion of its force-strain relationship. GHO, Great Horned Owl (Bubo uirginianus); RTH, Red-tailed Hawk (Buteojamaicensis); TV, Turkey Vulture (Cathartes aura).

are severed, the bird's elbow can be easily (force < < < body weight) extended to > 175". Severing the LLC and LP (proximal and distal pars fibrosa, Fig. 1) through small incisions in the propatagium allows the elbow to be extended easily to = 180", at which point the propatagium then lies piled up against the brachium and antebrachium.

The distal segments of the LLC, caudola- teral to its attachments upon the tendon of origin of M. extensor carpi radialis and along the antebrachial fascia (Fig. l), tense when the ligaments proximal segment is tensed. The forces acting through the distal segment of the LLC, as it merges with the antebrachial fascia and directly connects to the follicles of the secondary feathers, assist in supporting the dorsal antebrachial fascia, postpatagium, and secondary feathers. This contribution appears to be secondary to that of the antebrachial fascia and interremigial ligaments within the postpatagium (Baumel, '93) supporting the secondaries.

The insertion of the LLC on the tendon of origin of caput dorsale of M. extensor carpi radialis (Fig. 1) passively tenses that muscle

FLEXION-EXTENSION OF THE AVIAN WING 95

STRESS (newton s/cm2) 1000

800

600

400

200

I I I I I I

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 STRAIN

Fig. 3. Stress-strain mechanical properties of Lig. propatagiale, pars elastica. Forces converted to an equal cross-sectional area basis, i.e., /em2. Cross-sectional area varies directly with body weight so that the differences between taxa are not just a function of a thicker ligament but are an inherent feature of the construction of the

when the LLC is taut at maximum flying extension in the intact wing. The degree of passive tension (elongation) produced within the M. extensor carpi radialis by the action of the taut LLC is variable among the examined taxa. In Cathartes and Ardea the dorsal head of M. extensor carpi radialis is displaced 3+ cm craniad by the taut LLC, at which point further elevation is limited by the muscle’s tendon or origin. Craniad displacement of M. extensor carpi radialis by the tensed LLC in Bubo, Columbia, and Passer is limited by strong connections between the muscle’s external fascia and the dorsal antebrachial fascia. The displacement of M. extensor carpi radialis both tenses the muscle and changes its orientation relative to the carpometacarpus, which it assists in extending, i.e., reduces the angulation between the axis of radius and carpometacarpus.

Lig. propatagiale (leading edge ligament) Mechanical descriptions of Lig. propata-

giale (LP) fall into two categories: 1) force- length properties of pars elastica (PE); 2)

pars elastica in different species. Note the range of stress- strain relationships for the different taxa. P, pigeon; GBH, Great Blue Heron; K, Kestrel; GHO, Great Horned Owl; HS, House sparrow; BWT, Blue-winged Teal; SSH, Sharp-shinned Hawk; S, starling.

ligament’s role in resisting flexion of the wrist and manus against drag.

Pars elastica. Force-length mechanical relationships of the PE of Lig. propatagiale have been determined from different birds representing a range of body sizes and flight styles; ten individuals are illustrated in Fig- ures 24.The reproducibility of those measurements among individuals of the same taxon, i.e., six specimens of Passer, is shown in Figure 5.

Force-length measurements for the PE con- tain three regions (Figs. 2,3,5): 1) initially a long, nearly horizontal linear portion with a low stiffness; 2) a transition zone, in which the stiffness rapidly increases; and 3) a third region in which the length of the ligament changes very little in response to greatly increased stress (high stiffness). The strain on the pars elastica at its “maximum flying length” occurs approximately at the junction of regions 1 and 2 (arrows in Figs. 2,4; note that Figure 4 shows only the lower third of the force-length relationships of the birds depicted in Fig. 3), so that we consider region


STRESS (newtons/cm2) 120

100

80

60

40

20

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

STRAIN

Fig. 4. Stress-strain mechanical properties of Lig. propatagiale, pars elastica across the range of lengths that occur in flight, same individuals as in Figure 3. Expanding the flying or physiologic range of the stress-

1 to represent the lengths encountered in flight. At the strain, EW, at which the LP ruptured, maximum strain of PE ranged from 1.4 (pigeon) to 3.2 (chicken).

Rupture of the LP at its EMAX most commonly occurred within its collagenous segments or at its insertions into the structures around the shoulder or wrist. Rupture occurred at local stresses that we calculate to be 300-400+ kg (weight)/cm2 (cross section of collagenous segments are 30% of that of the stretched PE at its b). Stresses on PE at EMAX were 35-70 kg (weight)/cm2 (Fig. 3). Permanent deformation of the PE occurred only at strains greater than 98% of EMAX.

If the propatagium were infinitely elastic, its leading edge would always describe a straight line from deltopectoral crest to carpus through the full range of elbow extension angles. Observations of flying birds and manipulation of fresh specimens showed that the leading edge forms a straight line only when the wing is near its maximal flying extension. The maximum mid-propatagial chord length, i.e., distance from leading edge to proximal antebrachium, is limited by fi-

strain curves of these species accentuates their species- specific mechanical properties and maximum flying strains (arrows).

brous connective tissue networks within the propatagium and the dermis (Brown et al., '94a); thus, as the elbow is flexed from its maximal flying extension, the leading edge assumes a progressively larger caudally directed arc. Comparison of the forces along the leading edge ligament relative to a range of elbow angles assumed to be used in flight between 1) the straight-line, deltopectoral crest to wrist distance and 2) the distance measured along the curved leading edge on an intact wing of Bubo reveals the following differences (Fig. 6). Higher forces, at elbow extension angles less than maximal, are maintained across the curved (i.e., in vivo) and thus longer propatagial leading edge length (Fig. 6). In the straight-line (deltopectoral crest to carpus) configuration of the leading edge, the force along the LP approaches zero when the elbow has been flexed to = 75" (60% of its maximum flying extension). The curved, and thus longer, length of the leading edge maintained by the fibrous networks within the propatagium prevented the stress along the leading edge from reaching zero, even in the fully flexed wing.

FLEXION-EXTENSION OF THE AVIAN WING

STRESS (newtons) 1.20

1 .oo

0.80

0.60

0.40

0.20

0.00 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

STRAIN

97

Fig. 5. Force-strain mechanical properties of Lig. propatagiale, pars elastica. Six House sparrows treated identically to show reproducibility of measurements from different individuals. Vertical bars indicate range of

Support by Lig. propatagiale of the distal wing

We hypothesized that the LP, along with its role of supporting the leading edge of the propatagium, performs another role in flight, that of acting to support the wing distal to the carpus against the forces of drag that are constantly working to push the wing caudad, concomitantly extending the elbow joint. To test that hypothesis, a theoretical model was constructed with the following assumptions (Fig. 7): 1) During flight the shoulder and/or humerus are held in a fixed position of cranial protraction by the shoulder musculature; 2) the elbow is free to flex and extend about its axis, within the maximum limit set by the Lig. limitans cubiti; 3) the automatic elbow-carpus extension mechanism (Sy, ’36; Fisher, ’57) supports the carpal joint in the extended position concurrent with elbow extension; and 4) the forces of drag are centered at the carpal joint. The model was used to calculate the tensile forces along the LP that would be necessary if the ligament were to support the wing distal to the elbow against the forces of drag acting to extend the elbow. We then compared our calculated “neces-

“maximum flying lengths” for all six birds. Not converted to an equal cross-sectional area basis (see legend to Fig. 3).

sary” tensile force with the actual measured stress across the LP, for Buteo and Cuthar- tes, stretched to its “maximum flyinglength.”

The actual drag forces on fully extended wings were calculated from glide speed and sink rate parameters reported in the literature (see Table l). The glide speed at which maximum forward movement is covered with the least loss of altitude (sink), i.e., the maximum glide, is achieved in a bird with a fully extended wing (Pennycuick, ’68; Tucker and Parrott, ’69). The relationship between drag, minimum glide speed, and the sink rate (loss of altitude) at that glide speed are given by the following equation:

Drag = Body weight (newtons) x sine

) sink rate (m/sec) glide speed (misec) m e r e 0 = arctan (

Of the total calculated drag force, 10% was considered to be due to profile and surface drag from the body (Pennycuick, ’68). The remaining drag was divided by two to yield the drag per wing (Table 1).


24 I I 500

400

T E N 300 s I 0 N

G M

200

100

0 85 90 95 100 105 110 115 120 125 130

ANGLE OF ELBOW EXTENSION

Fig. 6. Bubo uirginianus. Comparison of propatagial ligament lengths and tension acroas the Lig. propatagde for the Great Homed Owl in relation to the angle of elbow extension. Solid lines represent the leading edge length, deltopectoral crest to carpus, as if the leading edge always formed a straight line from deltopectoral crest to carpus (W and in the actual curved shape (*) that it assumes in intact wings at less than maximum flying

In our model (Fig. 71, the drag forces in the y-axis (Dy) must equal the tensile forces in the y-axis (TY) if the wing distal to the elbow is to be supported and the elbow maintained at a constant angle. The measured angle (a) between leading edge ligament and distal antebrachium, when the wing was extended to its maximum length configuration, was 17” in Buteo and 13” in Cathartes. The following relationship then exists between drag (D) and tensile (T) forces (Fig. 8): Elastic tensile force (T)

= Drag force (D) x cotci In Table 1 the calculated tensile force needed to support the wing distal to the elbow against drag is compared to the measured stress along the leading edge ligament stretched to its “maximum flying length” (full wing extension as in maximum glide). Terminal (postcarpal) segment of Lig. propatagiale

Three possible mechanical functions con- cerning the insertions of the LP upon the

extension. Dashed lines represent tension across Lig. propatagiale in relation to straight leading edge (W) and curved leading edge (*). Lowermost solid line represents the calculated length of a line from the deltopectoral crest to the site of insertion of Lig. limitans cubiti upon M. extensor carpi radialis as the elbow is flexed by M. deltoideus, pars propatagialis via its insertion upon Lig. limitans cubiti.

distal radius, carpus, and carpometacarpus and its terminal continuation along the alular digit (distal to the those insertions) were considered (Fig. 1): 1) tension on the ligament affecting the extension of the carpus; 2) flexion of the carpus affecting the tension across the LP by sliding the ligament distally across the distal radius; and 3) tension on the Iigament affecting the orientation of the alula.

In the following experiment we were interested in learning if the stress generated along the LP strained to its maximum flying length could extend the wrist and/or maintain the wrist in extension against the forces of drag. In these experiments we have disabled the input of the skeleto-ligamentous linkage on the extension of the wrist by allowing the humerus to hang free. It was necessary to apply medially directed tension to the LP at a level in excess of twice that measured in the isolated ligament extended to its maximum flying length configuration (Figs. 2, 4) to effect extension of the manus (with feathers) from a nearly fully flexed position against gravity (Table 2). There was not a propor-


. . . .' .* : . : . . , ... ,: .. : .._.. . . . . ._ . ... .. ...' .. . . .... .. .::.:. ....

Fig. 7. Theoretical model (see text for details) of Lig. propatagiale supporting the wing distal to the elbow against the forces of drag. Drag forces (open arrows) are considered to be centered at the carpus. Tensile force (T) across Lig. propatagiale is normal to the drag force (D) centered at the carpus. Assumptions of model Elbow is

tional correlation between applied force and extension of the manus. That is to say, the manus extends less than 10-20% of full extension until the force necessary for full extension is added to the proximal LP, a t which point the manus fully extends. Once the manus was fully extended, the force necessary to maintain the wrist in extension against gravity was approximately equal to the ten-

TABLE 1 . Values used to calculate the draglwing and the tensile forces on the Lig. propatagiale necessary to support the wing, distal to the elbow against drag in

Buteo and Cathartes, and comparison ofthe calculated and measured tensile forces along the Lig. propatagiale

in the maximally extended wing

Red-tailed hawk Turkey vulture Parameter Buteo iamaicensis Cathartes aura Body weight (Kg) 0.892 1.456 Glide speed (mls) 14.5' 13.g2

Total drag (Newtons) 0.979 1.26

Draglwing (Newtons) 0.44 0.57

Calculated tensile force (T)

Sink speed (mls) 1.6' 1.22

(Newtons) 1.44 2.47

force (Newtons) 1.94 3.66 Measured tensile

'Kerlinger ('89). *Parrott ('70: values for Black Vulture).

free to move about its axis of rotation in the plane of the wing; shoulder is supported in protraction by M. pectoralis and other muscles; manus is maintained in protraction by skeleto-ligamentous linkage between elbow- carpus. a, angle between antebrachium and Lig. propatagiale. See text for values.

sile force measured on the pars elastica at its maximum flying length. The protracted manus was very unstable when it was supported with the minimal necessary force; that is, only a slight additional force added to the manus resulted in almost complete flexion ke . , hangingvertically) of the wrist. Starting friction between the smooth metal rod and cord we used to apply forces to the proximal ligament and/or within or between the tissues of the dead wing may have been the source of the instability we observed in the above experiments.

We measured the length of the LP that was pulled caudolaterally about the distal radius (Fig. 1) when the carpus was flexed. Here we were interested in determining if increased stress-strain across the LP, i.e., elongation of the pars elastica, which was due to the ligament being pulled distally as the wrist was flexed, could assist in maintaining tension along the leading edge in a wing at less than maximum flying extension. Bubo and Buteo showed a = 2 mm extension of the LP that was due to flexion of the wrist when the wing was flexed from its maximum flying extension (= 130") to an elbow angle of = 20". A 2-mm extension of the ligament in the fully flexed wing represented only < 18 g increase


MDPP

MD

Fig. 8. Bubo virginianus. Details of muscles inserting on the propatagial ligaments, dorsal view. M. deltoideus, pars propatagialis (MDPP) inserts onto the common apo- neurosis (not visible in this view) and most proximal ends of Lig. propatagiale and Lig. limitans cubiti (multiple bands in Bubo; compare with Buteo in Fig. 1). M. pectoralis, pars propatagialis (dashed lines) on the ventral sur-

in ligament force, and with proportionally smaller changes in LP length across the range of elbow extension angles used during flight there is a smaller effect upon ligament tension.

The LP terminates within the loose subcutaneous tissues, i.e., external to periosteum and joint tissues, surrounding the alular digit (Fig. 1). The position of the alular digit was unaffected by any amount of tension, up to and including the rupture stress, across the LP. No changes in the configuration of the joint alignment between digitus alularis and digitus major that might affect automatic extension of the alula during flight were produced irrespective of the force applied to the proximal LP.

Propatagial surface In the following analysis, propatagial defor-

mation was considered to be a change in propatagial profile produced by its covering

TABLE 2. Force, applied to the Lig. propatagiale in a proximal direction, necessary to extend the narnus with

attached feathers against mavitv'

Force on LP Force necessary at max. flying to extend

Species length (em) manus (gm)

House sparrow 11.5 26-29

Pigeon 64 135-142 Great horned owl 398 865-925

Starling 24 51-54

'Wings of tested species were supported by their radii.

face of the wing extends from the cranio-lateral surface of M. pectoralis and inserts, via its own tendon, onto the proximal collagenous portion of Lig. propatagiale (PFp) and not onto pars elastica (PE). M. deltoideus (MD) inserts onto the deltopectoral crest and proximal shaft of humerus.

of feathers. Across the range of elbow extensions we assume are used in flight (=80 to = 130", not counting full flexion of the wing used for the upstroke in some birds), there were no observed changes in the shape of the propatagium until enough weight had been added onto the dorsal or ventral surface to deform the propatagium of a fully extended wing: Accipiter 17-33 g, Bubo 59-119 g, Ardea 162-224 g. Any amount of weight less than that did not produce propatagid deformation as the elbow was flexed and extended. The position of the weights on the paper platform (see Materials and Methods) and the position of the paper platform itself upon the propatagium affected how much total weight the propatagium was capable of supporting, but the observation of constant stiffness across a range of elbow extension was not compromised.

The propatagial surface is more compliant than its leading edge. When sufficient weight had been added to the propatagial surface to produce distortion of propatagial contour in an extended wing the leading edge remained straight and undistorted. Although it was sensitive to the position of the paper platform upon the propatagium, more than double the loading that produced deformation of the surface could be added without distorting the leading edge and enclosed LP.

Intact wing in an airflow We observed the wings of intact birds (Bubo

and Cathartes): 1) suspended in the airflow


from a large-volume air pump (200 liters/ sec) and 2) suspended out and away from (> .75 m) the window of a moving vehicle. The results were similar whether we used the air pump or when we suspended the wing from the moving vehicle's window; however, the vehicle allowed use of a calibrated (vehicle speed), streamlined airflow that covered the entire span of the wing.

At =8 km/hr the wing (angle of attack = 5"), both elbow and carpal joints, smoothly extends from a nearly fully flexed position to = 80% of its maximum flying extension. Accel- erating up to speeds of -25 km/hr brings about a slow increase in extension of both elbow and carpal joint to the fully extended position. From 25 to 40 km/hr there was no further increase in wing extension. At none of the speeds of the airflow were changes in the profile of the propatagium or its leading edge observed.

At a constant airflow velocity (25 km/hr) the wing's angle of attack was varied from 0" to 20" with no changes in the degree of elbow/ wing extension. It was not possible to control the wing above an angle of attack of ~ 2 0 " (speed >15 kmlhr). No visible changes in propatagial shape took place as the angle of attack was adjusted. When the wing was pro- nated to a negative angle of attack a sudden reduction of elbow/wing extension occurred, resembling that when the airflow was < 8 km/hr.

To examine the behavior of a wing in an airflow without the influence of the skeleto- ligametous linkage of elbow and carpus, a =l-cm section of the central ulna was crushed, and the soft tissues immediately surrounding the bone were severed. Follow- ing this manipulation the moving vehicle experiments were repeated. At a speed of 15 kmlhr the elbow joint extended to approximately 50-60% of what was considered to be full extension in the intact wing, while the manus and primary feathers assumed an alignment in parallel with the airflow over the wing. Increasing the airspeed did not produce an increase in elbow or wrist extension.

DISCUSSION

The mechanical experiments reported here were performed under static conditions. For clarity the following discussion will examine those results in light of gliding flight or in flight in which wing extension changes rather slowly. Yet we consider these results broadly applicable to dynamic flight modes, e.g., when the wing is flapped. Elastin-rich tissues such

as the pars elastica of the Lig. propatagiale and the elastic network supporting the propatagial surface are not strain-rate sensitive (Mijailovich et al., '94; Brown et al., '94b). Using a dynamic force-length (tensile) apparatus, the mechanical properties of Lig. propatagiale from pigeons, starlings, geese, and chickens were examined across a wide range of strains (up to E > 21, cyclic ampli- tudes (up to 1.2 cm peak to peak), and fre- quencies of oscillation (.1 Hz to 30 Hz) (Mijai- lovich et al., '94; Brown, '94b; and data not reported here). Hysteresis (the tangent of the phase angle of the force-length loop) was always less than 0.05 and commonly less than 0.02. As such, the pars elastica is me- chanically almost purely elastic and not strain-rate sensitive. Thus, the static mechanical experiments reported here are applicable to dynamic conditions.

Mechanics of the propatagial surface Skin is a supple, compliant tissue and in

birds maintains feather alignment. Without proper support, the projected area of the propatagium (skin fold and imbedded feathers) could balloon out, and the cambered contour it adds to the wing, shoulder to wrist (Brown et al., '94a), would be distorted in flight. Such deformation would elevate drag, decrease lift, and diminish control of flight path. The propatagial surface, braced by fibrous networks of collagen and elastic tissue suspended between leading edge ligament and antebrachium (Brown et al., '94a) is passively and automatically supported across the range of elbow angles, i.e., propatagial deployment, used in flight. Further, decrease in stress across the Lig. propatagiale (LP) and its pars elastica (PE) with elbow flexion did not influence the ability of the propatagium to bear a load. The lack of deformation of the propatagial surface, i.e., feathers, in intact wings of dead birds either with an airflow or with static loading across a range of elbow extension indicates that propatagial support is independent of muscular input.

The stagnation point of an airflow over a wing occurs at its leading edge and exposes that surface to a force equal to the dynamic pressure, % p V , of the airflow. Static loads twice that necessary to deform the propatagial surface did not distort the course or shape of its leading edge and enclosed LP. Moreover, we did not observe deformations of the propatagium's leading edge in wings of dead (these experiments) or anesthetized chickens (Brown and Fedde, '93) subjected to an airflow of 25+ kmlhr. We consider the


passive stresses across the LP, with the wing in a flying configuration, to be in excess of what is needed by the propatagial surface or its leading edge, and suggest that the force- length mechanics of the LP and its pars elas- tics have evolved to support the wing distal to the elbow against drag (see below).

Mechanics of the propatagial ligaments Limiting maximum elbow extension

The wing functions in a semiflexed configuration. An angle <175” between humerus and radius, the space occupied by the propatagium, must be maintained; otherwise this integral component of the flight surface would disappear. Lig. propatagiale and Lig. limitans cubiti (LLC) (Fig. 1) operate together to limit elbow extension. If the elbow were allowed to extend to 180”, the projected area of the propatagium and the cambered profile it produces would decrease nearly to zero, folding up against the cranial surface of brachium and antebrachium. Further, if the wing elements were allowed to outstretch completely in a straight line the wing would be more difficult to control (pronation-supination) than when it is partially flexed. Lig. propatagiale and LLC are the major structures that function as a passive “stop” or stay apparatus, not only to limit maximum elbow extension but also to prevent the elbow/carpus linked flexion-extension mechanism described by Sy (’361, Fisher (’571, and Vasquez (’94) from overextending.

Coordinated wing extension and support mechanism

Wing extension along with angle of attack and various flapping parameters are mechanisms by which birds control the lift production of their wings. The results, models, and calculations included in this paper indicate that the skeleto-ligamentous linkage of elbow/carpus is only a portion of the anatomical mechanism that automatically coordinates and simplifies wing operation, i.e., flexion- extension organized with aerodynamic support against drag. Here we have used the passive stress-strain properties of the leading edge ligament (Fig. 1) to examine some of the features of whole wing mechanics (Figs. 2-5). Experiments using simultaneous in vivo mea- surement of stresses across the propatagial ligaments and EMGs of muscles associated with those ligaments, i.e., the propatagial parts of M. deltoideus and M. pectoralis (Fig. 81, would further define the mechanism by

which the bird coordinates the action of its wing.

The model (Fig. 7; Table 1) presented shows a close agreement between the actual stress along the leading edge ligament and the calculated stress necessary to allow the wing distal to the elbow to resist drag forces working to hyperextend the elbow. These data indicate that the force-length properties of the LP have evolved for passive support of the distal wing against drag across the range of wing extensions used in flight. It is surprising that the measured stress on the leading edge ligament is in excess of the calculated force necessary to support the distal wing in the maximum flying extension (Table 1). Such a condition indicates that a bird would need to use continuous muscle energy (M. triceps) to maintain its wing in extension during flight, a muscular duty-cycle not seen during the wing beat in flying starlings (Dial et al., ’91) or pigeons (Dial, ’92a,b). In this theoretical analysis we have assumed that drag forces are centered at the carpus. In Buteo the com- bined length of the manus and primary feathers represents over twice the length of the antebrachium, and in Cathartes the manus and attached primaries are approximately three times the length of the antebrachium. When in both birds more than two-thirds of the wing (length) distal to elbow extends beyond the carpus, the assumption that the center of the drag forces is at the carpus may not be valid. If the actual center of the drag forces was distal to the carpus (longer lever arm for drag forces to work through), higher tensile forces across the LP than those calculated would be needed to support the distal wing.

Observations of intact wings (dead birds) in an airflow further substantiate the passive input of the LP’s stress-strain mechanics to the operation of the wing. Wing extension and airflow velocity both directly influence the level of drag forces acting to hyperextend the elbow. Increased airflow velocity, 8 to 25 kmlhr, across the wing resulted in increased wing extension, and thus elongation of the LP’s pars elastica; the increased strain of pars elastica supplies increased force to support the distal wing against drag. Thus it appears that the force-length properties of the LP (Figs. 2-5), operating in a wing that automatically extends in an airflow, are tuned to balance the drag forces across the distal wing over a range of wing extensions.

Disabling the skeletal elbow-carpus linkage, i.e., severed ulna and surrounding soft


tissue, prevented protraction of the manus (and attached primary feathers) with elbow extension; now the manus trails the proximal wing, aligned with the airflow. In the absence of the increased drag resulting from an extended manus and its attached primary feathers, maximum elbow extension of a wing in an airflow was ~ 6 0 % of maximum flying extension. Sixty percent of maximum flying elbow extension results in lower stress-strain along the LP (Figs. 2, 4-6). Without the increased drag force resulting from an extended manus, insufficient stress across the LP is produced to strain its pars elastica and fully extend the elbow. These results were predicted by the theoretical model of the LP, i.e., the leading edge ligament's stress-strain properties are tuned to function as a support of the distal wing against drag.

Mechanics of the propatagial musculature Whereas the above descriptions have exam-

ined the passive mechanical functions of the propatagial ligaments, the following consider- ations examine the possible functions of the muscles inserting upon the propatagial ligaments and their active contributions t o wing control (Fig. 8).

Pars propatagialis of M. pectoralis (MPP) (in the taxa in which this muscle is present) appears as a group of fasciculi protruding from the cranio-lateral surface of the main mass of M. pectoralis, parallel to and inserting on the proximal leading edge ligament (Brown et al., '94a) (Fig. 8). No fascial lami- nae separate the fasciculi of MPP from the main part of M. pectoralis. The length of MPP in Bubo external to the main mass of M. pectoralis is 1.85 cm (average of 6 birds), and would produce a 0.4-cm change in length across its optimal range of shortening (22% in avian muscle; Cutts, '86). That 0.4-cm shortening translates into a 1.7% change in length of the LP, and a 3.1% change in the length of its PE. When the PE is extended to its maximum flying length, a 0.4-cm increase in strain via contraction of MPP produces a =65 g/cm2 increase in stress. Under the assumption that pars pectoralis contracts con- currently with M. pectoralis during the downstroke, when lift and drag forces are highest (Spedding, '82, '86, '87a,b; Spedding et al., '84), then the increased stress across the leading edge ligament produced by contraction of MPP would compensate for the increased drag forces acting on the wing. M. pectoralis is active only during the first 50+% of the downstroke (Dial, '92a,b; Dial et al.,

'91). Thus, under our assumption of simultaneous activity of M. pectoralis and MPP, increased stress across the LP to counteract drag may be necessary only during that portion of the wingbeat. At wing extensions below maximum flying extension, a configuration not seen in flapping flight, reduced lift and drag production would eliminate the need for active increases in stress along the leading edge.

Contraction of M. deltoideus, pars propatagialis (MDPP) (Fig. 8) can produce two, possi- bly separate, actions: 1) flexion of the elbow through its insertion onto the proximal LLC and 2) increase in the stress-strain relationship of the pars elastica via its insertion onto the proximal LP. The anatomy of the propatagial musculature varies in different taxa; here we are concerned with the anatomical ar- rangement in Bubo (Brown et al., '94a), Bu- teo, or Cathartes, i.e., the presence of one muscular head, which is similar to that seen in the majority of avian orders (Furbinger, 1888; Brown, '92). Those taxa with a single head for MDPP show a parallel-fibered muscle with no obvious separation between the fasciculi destined for their insertions upon the propatagial ligaments; further, most of the fasciculi insert upon the aponeurotic, common proximal end of the ligaments (Brown, '92; Brown et al., '94a). Although there is evidence that birds are capable of neuromus- cularly partitioning this otherwise undivided muscle (Meyers, '91, in Falco sparuerius), the fact that its insertion is primarily onto the ligaments' common proximal aponeuro- sis leaves little possibility for separate actions upon the two propatagial ligaments.

The insertion of the LLC on the antebrachium being distal to that of M. biceps brachii (2-5 times elbow to insertion point) in a wide range of birds (Brown, '92) gives the propatagial part of M. deltoideus a mechanical advan- tage in flexing and/or maintaining the elbow and distal wing in less than maximal flying extension against drag forces. The shorter length of MDPP versus that of M. biceps and its insertion reduces the range of elbow angles (relative to the biceps) across which pars propatagialis would be effective. During the phase of the wing-beat when the wing is being flexed for the upstroke, MDPP is inac- tive while M. biceps is activated (Dial, '92a,b; Dial et al., ,911.

Figure 6 shows the relationships between the angle of elbow extension and 1) strained length of Lig. propatagiale, deltopectoral crest to carpus, and 2) distance from deltopectoral

104 R.E. BROWN ET AL

crest to insertion of Lig. limitans cubiti. In Bubo (average of six birds) the length of the belly of MDPP, 6 cm, represents 27% of the elongated LP (22.7 cm deltopectoral crest to carpus) and 49% of the PE strained to the maximum flying length (12.7 cm). The working range of MDPP (22% shortening, Cutts, ’86) is 1.3 cm. Starting from the maximum angle of elbow extension in Bubo, i.e., 130°, a 1.3-cm “shortening” of the LLC by MDPP would result in a new angle of elbow extension of 87”. That change in the angle of elbow extension translates into a 23% reduction in the length of a straight line connecting shoulder and carpus. Pennycuick (’68) and Tucker and Parrott (’69), in wind tunnel studies of gliding birds, demonstrate that the range of lengths of the leading edge, straight-line shoulder to carpus, across the various wing configurations varied by = 24% (measured from published illustrations). Thus, it appears that the MDPP is capable of controlling wing extension across the range actually used in flight.

When wing extension is sustained at 130” by the LLC the length of the LP is 22.7 cm. Shortening MDPP by 1.3 cm, via its insertion on LLC, reduces the length of the leading edge to 17.5 cm. If the leading edge always described a straight line from the deltopectoral crest to the carpus across the range of extension angles in question, the reduction in strain on Bubo’s LP (22.7 to 17.5 cm) would produce a reduction in stress from approximately 400 g/cm2 to 40 g/cm2, a 90% reduction. The actual curved length of the leading edge of the propatagium in the flexed wing makes the actual changes in the range of stresses approximately 400 to 150 g/cm2 when the elbow is flexed, a 62% reduction (Fig. 6). A 1.3 cm shortening of MDPP would simultaneously restore a portion of stress along the ligament’s pars elastica and the resultant loss of stress is then only 400 to 250 g/cm2, a reduction of 37.5%. Tucker and Parrott (’69) calculated that across the range of elbow extensions they observed in their gliding falcon (identical anatomical arrange- ment to Bubo) there was a 36% change in the drag forces acting on the bird’s wing, whereas Pennycuick (’68) calculated a 50% change in drag forces acting on a gliding pigeon. The stress-strain mechanics of the pigeon’s pars elastica, across the lengths it assumes in flight, had the highest elastic modulus of any bird measured, which agrees with the higher changes in drag with wing flexion as calcu-

lated by Pennycuick (’68). That is to say, the identical percentage reductions in leading edge length measured in the gliding falcon (Tucker and Parrott, ’69) and pigeon (Penny- cuick, ’68) would result in the largest reduction of stress across the leading edge in the pigeon and, thus, the largest reduction in support of the distal wing (Figs. 2,4). Thus, although the MDPP plays a role in the control of stress across the LP and its support of the wing distal to the elbow against drag, the passive force-length properties of the pars elastica (Figs. 2-4) appear to be “tuned” for each species’ flight mechanics and flight style.

CONCLUSIONS

1. Support for the bird’s propatagium, the skinfold that forms the cambered shape of the wing shoulder to wrist (Brown et al., ’94a), is supplied by the passive stress-strain mechanics of Lig. propatagiale and its distensible pars elastica and the fibrous networks within the fold. Sufficient support to prevent deformation of the propatagial contour by the forces of lift and drag appears to be independent of muscular input.

2. Lig. propatagiale provides passive support to the wing distal to the elbow, across a range of elbow extension angles, against the forces of drag acting to hyperextend the elbow. The stress-strain mechanics of the Lig. propatagiale appear to be tuned to a taxon’s aerodynamic requirements, i.e., drag forces versus wing extension.

3. The propatagial ligaments, Lig. propatagiale and Lig. limitans cubiti, and M. deltoideus, pars propatagiale, along with the skel- etoligamentous linkage between elbow and carpus form an integrated “wing extension- flexion control mechanism.”

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mechanics of the avian propatagium: flexion-extension mechanism of the avian wing

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