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First published online May 8, 2007
Journal of Experimental Biology 210, 1663-1671 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.000307
Commentary |
Sailing the skies: the improbable aeronautical success of the pterosaurs
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
e-mail: mtw21{at}cam.ac.uk
Accepted 28 February 2007
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Summary |
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 TOP Summary IntroductionConclusionsReferences |
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Key words: actinofibrils, aerodynamics, aeroelasticity, propatagium, pteroid, pterosaur flight, sails, wing membrane
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Introduction |
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TOPSummaryIntroductionConclusionsReferences |
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). The great
comparative anatomist and father of vertebrate palaeontology Georges Cuvier,
the man who correctly identified the first documented specimen, affectionately
wrote that it resembled more "le produit d'une imagination malade
plutôt que des forces ordinaries de la nature" (the product
of a sick imagination rather than the ordinary forces of nature)
(Cuvier, 1824). Pterosaurs
(formally the Pterosauria) are conveniently divided into two groups: a
paraphyletic assemblage of basal forms that spanned the Late Triassic and
Jurassic periods called the `Rhamphorhynchoidea', characterised by their long,
stiff tails (with the exception of the short-tailed anurognathids), and a
monophyletic group called the Pterodactyloidea that arose some time in the
Jurassic and continued until the end of the Cretaceous period
(Wellnhofer, 1991a). These all
had short tails, and generally had longer skulls and necks than the
`rhamphorhynchoids'. We currently recognise about 100 species
(Unwin, 2003), many of these
being putative piscivorous forms (e.g. the toothed `rhamphorhynchoid'
Rhamphorhynchus and toothless pterodactyloid Pteranodon),
but also including some apparently adapted for insect feeding (e.g.
Anurognathus), filter-feeding (e.g. the pterodactyloid
Pterodaustro), and for crushing the hard shells of molluscs and/or
crustaceans (e.g. the pterodactyloid Dsungaripterus)
(Wellnhofer, 1991a).
With regard to terrestrial locomotion, there is a consensus that the
smaller pterosaurs were habitually quadrupedal, thanks to a large number of
trackways consisting of both hand- and footprints that are unquestionably
pterosaurian in origin on account of certain diagnostic characteristics: e.g.
in many cases the left and right handprints are more widely spaced than the
footprints (Mazin et al.,
2003). The mode of terrestrial locomotion of the larger
pterodactyloids is still debated: it has been argued that these could not have
used quadrupedal locomotion because of the great disparity in length between
the fore- and hindlimbs, and it has been suggested instead that these forms
adopted an erect, upright, bipedal posture
(Bennett, 1990;
Bennett, 2001). This stance
would have circumvented problems of front-heaviness that would have arisen if
the vertebral column were horizontal or near-horizontal due to the (usually)
large skull and long neck. It would, however, have rendered these pterosaurs
top-heavy with only marginal postural stability due to the relatively small
legs, which would have defined a very small polygon of support. Additionally,
quadrupedal trackways made by large pterosaurs have been found
(Hwang et al., 2002), whereas
there are no known bipedal pterosaur trackways.
The chief skeletal adaptation for flight in the pterosaurs was the greatly
elongated fourth finger of each hand which, together with the proximal arm
bones, constituted a spar that supported a sail-like wing membrane or
cheiropatagium (Fig. 1). This
membrane is superbly preserved in several specimens
(Padian and Rayner, 1993), and
a number of recent finds indicate that its trailing edge ran from the wingtip
to the distal end of the lower leg, probably in all pterosaurs
(Unwin and Bakhurina, 1994;
Lu, 2002;
Frey et al., 2003). There are
no other rigid or semi-rigid support structures in the cheiropatagium, in
marked contrast to bird and bat wings, with their keratinous feather shafts
and additional elongated digits, respectively. Nevertheless, despite the
superficial simplicity of their wings, pterosaurs successfully exploited the
aerial environment for 150 million years, and the pterodactyloids became,
during the Cretaceous period, the largest flying animals that have ever lived.
Quetzalcoatlus northropi, one of the last of its kind, had a wingspan
estimated at about 12 m (Lawson,
1975; Wellnhofer,
1991a). Incidentally, it is now almost universally accepted that,
while these later, giant forms were secondarily adapted for soaring
(Hankin and Watson, 1914;
Bramwell and Whitfield, 1974;
Brower, 1983), the
`rhamphorhynchoids' and smaller pterodactyloids were fully capable flapping
flyers (Padian, 1983;
Padian and Rayner, 1993).
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Without rigid supports, it is likely that the high aspect ratio
cheiropatagium was subject to significant deformation in flight, particularly
flapping flight. The problems that this may cause were made starkly apparent
in a wind tunnel study of a life-size model of a wing of the Late Jurassic
pterosaur Pterodactylus, with a wing semi-span of 0.27 m
(Sugimoto, 1998). The model
consisted of a metal spar and a latex rubber membrane with an unloaded tension
of zero. As a fixed wing, the model performed very badly, fluttering severely
at relative air velocities above 3 m s–1, and achieving
maximum lift:drag ratios of only 1.6–1.7. These compare unfavourably
with measured lift:drag ratios of birds: for instance, the highest reported
value for bird wings is 36.3, calculated from wind tunnel data of a live
lagger falcon and black vulture (Tucker,
1987). In fact, a best lift:drag ratio of 1.6–1.7 is roughly
equivalent to that of some gliding mammals (i.e. entire gliding mammals, not
just the gliding membranes) (Jackson,
1999), despite the fact that the flight surfaces in these forms
have much lower aspect ratios than pterosaur wings, and also that the
pterosaur lift:drag ratios were derived from tests of the wings alone, and do
not account for the additional `parasite drag' caused by the body. When the
model Pterodactylus wing was flapped the deformation was so extreme
– the wing membrane turned inside out during the downstroke – that
the lift coefficient, averaged over the wingbeat, was negative unless the
angle of attack at the base of the wing exceeded 10°.
The severity of the problems apparent in these wind tunnel tests stems
mainly from the fact that the model wing membrane was initially slack, in all
likelihood an unrealistic state (Bramwell
and Whitfield, 1974;
Pennycuick, 1988). For a
membranous wing to be at equilibrium, the aerodynamic forces must be balanced
by tension in the membrane. If the unloaded tension is zero, the strain (i.e.
deformation) of the wing membrane must be large for this condition to be met
unless the Young's Modulus is very high, i.e. the elasticity very low, which
is certainly not the case for latex rubber. In addition, the model did not
include any representation of a trailing edge tendon, for which there is now
tentative fossil evidence (Frey et al.,
2003), which may have constrained deformation. The poor
performance of the model wings may therefore be partly regarded as a result of
unrepresentative material properties. There are, however, several problems
unique to sail-like wings that a simple tensioning of the membrane would not
have alleviated.
Firstly, unless membrane tension were infinite, the trailing edge of the
cheiropatagium would have lifted when an aerodynamic load was applied (either
in gliding or flapping flight), and the membrane, being strongly tapered,
would therefore have twisted in a nose-down sense from root to tip, a
morphology known as geometric wash-out. This would not have been entirely
detrimental. By reducing the angle of attack at the wingtips, the wash-out
would have reduced the risk of tip stall, a particular problem for highly
tapered wings (Simons, 1978;
Marchaj, 1996). A geometric
wash-out is also important for optimising the angle of attack along the wing
during the downstroke of flapping flight
(Norberg, 1990). However,
excessive twist is undesirable, as it diminishes the maximum lift coefficient
and the lift:drag ratio (Marchaj,
1988). Indeed, it was probably this factor more than any other
that caused the poor performance of the model Pterodactylus wing
described above. Some workers have therefore suggested that the shape of the
wing spar limited membrane wash-out in pterosaurs. Three-dimensionally
preserved fossil material shows that the wing-finger curved posteriorly and
ventrally from root to tip (Bramwell and
Whitfield, 1974; Wellnhofer,
1991a; Bennett,
2001). It has been argued that the ventral curvature of the spar
could have approached that of the trailing edge of the cheiropatagium, thus
reducing twist (Short, 1914;
Brower, 1983;
Bennett, 2000). Experiments on
spar-and-membrane parawings, precursors of the first hang gliders, have indeed
demonstrated the benefit in terms of the lift:drag ratio of curving the spar
in this fashion (Polhamus and Naeseth,
1963). However, it must be remembered that the pterosaur
wing-finger was not as rigid as the tubular metal leading edges of these
parawings. The wing-finger phalanges were slender, somewhat dorso-ventrally
flattened bones separated by synovial joints. These joints are widely believed
to have been immobile, i.e. not under muscular control, largely because the
joints are buttressed in the plane of the wing, which is also the plane in
which flexion and extension of the phalanges would be expected to occur
(Bramwell and Whitfield, 1974;
Wellnhofer, 1991b;
Bennett, 2001). Nevertheless,
given the low rigidity of the joint capsule connective tissue in comparison
with bone, they probably could not have prevented interphalangeal bending when
the wing was loaded, and of course they could not have prevented bending of
the bones themselves. It thus seems quite likely that the wing-finger would
have curved dorsally in flight, not ventrally, and the shape of the wing spar
would in reality have done relatively little to reduce excessive twist in the
cheiropatagium.
Secondly, theoretical and experimental work on sail profiles
(Thwaites, 1961;
Nielsen, 1963;
Greenhalgh et al., 1984;
Newman and Low, 1984;
Newman, 1987;
Sugimoto and Sato, 1991) has
shown that, owing to the mutual interdependence of shape and aerodynamic
loading, multiple profile shapes are simultaneously possible at low angles of
attack, a phenomenon that can cause serious instabilities
(Fig. 2). At high angles of
attack only a simple convex shape is possible
(Fig. 2, shape 1); as incidence
is reduced, the only significant effect at first is a rearward migration of
the chordwise position of maximum camber. Eventually, a specific angle of
attack is reached at which the incoming flow attaches smoothly to the profile,
i.e. the dividing streamline runs to the leading edge. This is termed the
ideal incidence (Theodorsen,
1930), at which the sail profile has fore-and-aft symmetry about
the mid-chord (Fig. 2, shape
2). It should theoretically occur at an angle of attack of zero
(Thwaites, 1961;
Nielsen, 1963). In reality,
however, ideal incidence is usually slightly positive, and increases in
magnitude with sail camber, because of flow separation ahead of the trailing
edge (Newman and Low, 1984;
Cyr and Newman, 1996). If the
angle of attack is reduced below ideal incidence, a point of inflexion appears
at the leading edge that migrates rearward as the angle of attack is reduced
(Fig. 2, shape 3). While the
sail is in this state it becomes susceptible to a frequently severe fluttering
instability called luffing (Greenhalgh et
al., 1984; Newman and Low,
1984; Newman,
1987; Sugimoto and Sato,
1991). The lift is still positive at this stage, but if incidence
is reduced still further, a point is eventually reached when an S-shaped
profile is no longer tenable, and the sail `pops through', adopting an
entirely convex shape, but lying beneath the chord line
(Fig. 2, shape 4).
Unsurprisingly, the lift is now negative. This pop-through generally occurs at
a small negative angle of attack, the precise value depending on camber and
the extent of flow separation (Greenhalgh
et al., 1984; Newman,
1987). If the angle of attack of the upside-down sail is now
increased, the profile will not cross the chord line again instantly, but must
once again pass through ideal incidence and an S-shaped phase
(Fig. 2, shape 5) before it
pops through and attains positive camber once more. In other words, sail
profiles exhibit hysteresis behaviour around ideal incidence
(Greenhalgh et al., 1984;
Newman, 1987;
Sugimoto and Sato, 1991).
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It is important to note that the behaviour described above concerns
inextensible sail profiles with constant slackness, in all likelihood quite
different to pterosaur wing profiles which, as has already been argued, would
probably have been elastic and pre-tensioned. For such profiles, membrane
camber increases with the angle of attack, all other factors being equal.
Should membrane camber disappear at an angle of attack of zero, such that the
profile becomes a flat plate, there would logically be no S-shaped profile
solution and no hysteresis, and the membrane would undergo a smooth transition
between positive and negative camber. It must be remembered, however, that in
flight, all other factors bar the angle of attack are not equal. Taking the
simple case of equilibrium gliding, for example, a reduction in the angle of
attack is accompanied by an increase in the relative airspeed, such that the
total aerodynamic force remains constant: equal and opposite to body weight
(Norberg, 1990). If one
ignores changes in the spanwise lift distribution, one could therefore argue
that the excess length of a profile at a given spanwise station of the wing
would in fact remain constant in this case unless the material properties of
the membrane were altered. The situation is different for flapping flight, in
which the magnitude of the aerodynamic forces is time-variant: in this case
the elasticity of the wing may have been important in avoiding luffing and
camber-reversal if the angle of attack was reduced during the upstroke, as is
the case in birds and bats (Norberg,
1990). Clearly, however, membrane elasticity did not prevent these
occurring during flapping of the model Pterodactylus wing
(Sugimoto, 1998), as described
above. Inextensible sail profiles therefore seem to be reasonably good models
for pterosaur wing profiles, at least to a first approximation. Needless to
say, their tendency to luff or turn inside out, and then remain inside out
even at small positive angles of attack, could have had disastrous
consequences. Indeed, the notorious unrecoverable `luffing dive' has been
known to cause fatal hang glider crashes
(LaBurthe, 1979;
Kroo, 1981).
A final potential drawback of sail-wings is that they offer relatively
little scope for control. Significant flexion at any of the forelimb joints,
as used by birds and bats to adjust wing span and area in gliding flight to
alter the equilibrium gliding speed
(Tucker and Parrott, 1970;
Pennycuick, 1971), or in
flapping flight to reduce the magnitude of the aerodynamic forces generated
during the upstroke in order to maximise net positive thrust
(Norberg, 1990), would have
caused a drop in tension in the cheiropatagium and a concordant increase in
the geometric twist. Furthermore, pronation or supination of the wing spar at
the shoulder would have had only a minor effect on the angle of attack because
there were no rigid members linking the spar to the trailing edge. Elevation
and depression of the leg would have been more effective in this regard.
However, given the high aspect ratio, the legs would only have been able to
modify the angle of attack of the proximal part of the wing.
On the evidence of the foregoing discussion one could get the impression
that pterosaurs were barely capable of flight at all, with excessively
twisted, unstable, scarcely controllable wings. The fact that this was
manifestly not the case reveals the degree to which they were able to escape
the historical constraints of their simple wing form. It should be noted at
this juncture that modern sails and hang gliders are not good analogies for
pterosaur wings, as they are generally made of nearly inextensible fabric
supported by rigid spars, and are provisioned with battens, high-tension wires
and other structures to limit deformation as much as possible
(Kroo, 1981;
Marchaj, 1988;
Marchaj, 1996;
Gratton, 2001). The
pterosaurian solution was necessarily quite different and is currently poorly
understood: investigations into the aerodynamics and aeroelasticity of
pterosaur wings are still in their infancy. Nevertheless, recent
palaeontological and aeronautical studies have highlighted a number of
anatomical features that may have been of critical importance in rendering the
pterosaurs airworthy.
Firstly, the cheiropatagium was not the only pterosaur wing membrane. There
was also a membrane between the legs called the uro- or cruropatagium and one
in front of the proximal region of the arm called the propatagium
(Fig. 1). The role of the
cruropatagium is poorly understood, and is not relevant to the present
discussion, but the propatagium is likely to have been a vitally important
component of the wing. It was supported by a modified wrist bone called the
pteroid, whose function is a controversial topic. For many years it was widely
believed that the pteroid was simply a passive element that pointed towards
the body, forming the distal part of the leading edge of the propatagium
(Bramwell and Whitfield, 1974;
Wellnhofer, 1985;
Wellnhofer, 1991a). This is
indeed how the bone appears to be oriented in several articulated (but
flattened) fossils (Padian and Rayner,
1993). However, my analysis, with colleagues, of exceptionally
well preserved three-dimensional wrist bones from the Santana Formation (Lower
Cretaceous) of Brazil indicated otherwise
(Wilkinson et al., 2006). We
proposed instead, on the basis of the 3D morphology of the supposed articular
surfaces of the relevant bones, that the pteroid pointed forwards in flight,
and could be depressed through a wide arc before swinging towards the body,
eventually coming to lie within a transverse vertical plane, but deflected
beneath the horizontal (Fig.
3A) (n.b. in the traditional reconstruction the pteroid is
typically oriented horizontally). The propatagium would thus have acted as a
ventrally deflectable leading edge flap that could have been conveniently
furled away when the pterosaur was on the ground
(Fig. 3B,C). We argued that it
is this furled configuration that is visible in articulated fossils
(Wilkinson et al., 2006).
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). In many such
fossils, a small oval sesamoid bone is located there instead, which has been
regarded by Bennett (Bennett,
2001; Bennett,
2006) as evidence that the fovea was not a true articular surface
at all, but a groove for a tendon, specifically the wing-finger metacarpal
extensor tendon. The sesamoid would in this case have developed within this
tendon at the point where it passed through the fovea, and the pteroid would
have articulated on the medial side of the medial carpal
(Fig. 4C), and would thus have
pointed towards the body. It would not, however, have necessarily been a
passive element: it would instead have been free to elevate and depress, and
therefore could still have enabled the propatagium to act as a leading edge
flap (Bennett, 2006), although
considerably narrower than in our alternative reconstruction
(Wilkinson et al., 2006).
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I find the reconstruction of Bennett
(Bennett, 2001;
Bennett, 2006) a little
difficult to accept, mainly because there is no obvious articular surface on
the side of the medial carpal (Wilkinson
et al., 2006). It is instead possible that the sesamoid was
embedded within a pteroid extensor tendon, and was closely associated with the
pteroid–carpal joint (Fig.
4D). It could thence have been pulled into apparent articulation
with the fovea of the medial carpal during post-mortem dislocation of
the pteroid, just as the sesamoids of the human hand and foot can be pulled
into their associated joint capsules following dislocation
(Del Rossi, 2003).
Nevertheless, the current lack of a known specimen in which the pteroid is
preserved in articulation with the fovea of the medial carpal is a significant
blow to the idea of a broad propatagium, and it thus seems safest at this
juncture to focus on the common aspects of the two opposing reconstructions:
the dorso-ventral mobility of the pteroid and concordant potential for
deflection of the propatagium.
A ventrally deflected propatagium would have had a number of important
benefits. Given that it extended only part-way along the semi-span, probably
terminating at the knuckle (Wilkinson et
al., 2006), it would have reduced the angle of attack of the
proximal wing with respect to that of the distal wing, more so for a given
pteroid deflection angle if the propatagium were broad. This twist in a
nose-up sense from root to tip is opposite to the wash-out described above,
and is termed a geometric wash-in. This arrangement would have partly
cancelled the inherent wash-out of the cheiropatagium.
Secondly, wind tunnel tests of sail profiles with and without a broad
propatagium indicate that it would also have acted as a very effective high
lift device (Wilkinson et al.,
2006). Deflection of the broad propatagium caused the flow to
remain attached near the leading edge even at an angle of attack of 20°
(the maximum attainable with the experimental set-up). By preventing stall in
this way, the maximum section lift coefficient was increased by nearly 45% to
2.4 (Fig. 5). Of key importance
is the fact that a movable propatagium can set the profile's entry angle (the
angle between the chord line and the tangent at the profile's leading edge).
In standard sail profiles the entry angle is a function of the camber and the
position of maximum camber, and the latter cannot be directly controlled. To
achieve high entry angles on such a profile, the camber would have to be very
large indeed. On the evidence of previous wind tunnel tests of slack sail
profiles (Greenhalgh et al.,
1984; Newman and Low,
1984; Sugimoto and Sato,
1991), excessive flow separation would probably prevent the
attainment of very high lift in this case. As yet, there are no wind tunnel
data available for a deflected narrow propatagium, but given that this
configuration would also increase the entry angle of the profile, the
possibility remains that the high lift effect would also occur in this case.
Wind tunnel tests of profiles with an undeflected narrow propatagium performed
very badly, such that its removal increased the best lift:drag ratio and the
maximum lift coefficient (Wilkinson et
al., 2006). It therefore appears that it would have been
detrimental for the pteroid to have been directed horizontally in flight.
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The high lift function of the propatagium would have been of great benefit
to the giant pterosaurs when taking off or landing. These manoeuvres are
generally problematic for large flying animals thanks to the well-known
adverse scaling of the minimum gliding speed with mass
(Alexander, 1998). Wing loading
(weight divided by wing area) generally increases with size because, while
mass scales with the cube of the linear dimension, wing area scales only with
the square of the linear dimension. Hence large flying animals are expected to
be, relative to their mass, less well endowed with lift-generating flight
surfaces, and must fly faster to support their weight, as indicated by the
following equation derived from classical aerodynamics:
 |
is air density [currently about 1.2 kg
m–3 at sea level but a little higher in Late Cretaceous times
(Dudley, 1998)] and
CL,max is the maximum lift coefficient.
The essential outcome of this line of reasoning is that, as size and wing
loading increase, it becomes progressively more difficult to achieve
sufficient relative airspeed to take off or to avoid mortal injury upon
landing. The disproportionately large wings and ultra-lightweight skeletons of
the giant pterosaurs would have partially offset the trend in wing loading
(Bramwell and Whitfield, 1974;
Alexander, 1998), but the very
high CL,max that on current evidence was provided by the
propatagium was clearly advantageous, particularly for Quetzalcoatlus
northropi, the largest known pterosaur. Unlike most other large
pterosaurs that have been found in marine deposits, its remains were found far
from contemporary seas (Lawson,
1975). This suggests that, while its ocean-going relatives were
able to use gravity-assisted take-offs from cliffs, Quetzalcoatlus
was land-based and may have had to take off from more-or-less level ground.
Furthermore, a fast running take-off would have been extremely problematic,
regardless of whether large pterosaurs were habitually quadrupedal or bipedal:
all pterosaurs must have become transiently bipedal to enable deployment of
the wings prior to take-off. The chief problem is that the cheiropatagia were
attached to the legs, which means that running would have caused the angle of
attack and camber of the inner wings to oscillate asymmetrically as the legs
moved back and forth, with concordant stability problems. A means of
substantially reducing the minimum relative airspeed for flight in these
giants must therefore have been vital.
In wind tunnel tests, the broad, deflected propatagium was shown to be useful not only as a high-lift device. It also greatly improved profile stability at low angles of attack. Without a propatagium, the model profile luffed severely at angles of attack below 2°, such that force measurements could not be taken. If the propatagium was present, positive lift was still obtained at an angle of attack of –2° (Fig. 5). This stabilising effect was a simple geometric consequence of there being a deflected forewing: its presence meant that the point where the membranes were anchored to the spar always lay above the chord line, which made a full pop-through physically impossible and ameliorated luffing.
Finally, the propatagium would have acted as a useful control surface. If
pteroid depression were coupled with leg depression, the result would have
been an increase in camber of the inner wing and a concordant increase in
lift. If, however, the pteroid were depressed alone, the increase in camber
would have been coupled with a decrease in the angle of attack, which may have
caused only an increase in drag. Used asymmetrically, the propatagia could
therefore have controlled roll or yaw by respectively increasing either the
lift or drag of one wing. Qualitatively, these conjectures should hold
regardless of whether the reconstructions of Bennett
(Bennett, 2001;
Bennett, 2006) or Wilkinson et
al. (Wilkinson et al., 2006)
prove to be correct, as both treat the pteroid as a mobile element, capable of
altering the ventral deflection angle of the propatagium.
The propatagium, thanks to the function of the pteroid, was undoubtedly a
tremendously important feature, and its absence from the distal part of the
wing could be regarded as a drawback, especially as the local angle of attack
was likely to have been lower here due to twist, and the membrane consequently
more susceptible to luffing and pop-through. However, the distal part of the
cheiropatagium was qualitatively different from its proximal part. It was
invested with a system of long, thin, closely spaced fibres or actinofibrils,
probably composed of either collagen or keratin
(Bennett, 2000), that ran
almost parallel to the wing spar near the bones, but radiated
postero-distally, curving to meet the trailing edge at a high angle
(Padian and Rayner, 1993;
Bennett, 2000). Fibres of
similar apparent histology are present in the proximal cheiropatagium, but
they are much shorter and diffusely scattered
(Unwin and Bakhurina, 1994).
It has been suggested that the actinofibrils of the distal cheiropatagium were
stiff structural elements, able to transfer aerodynamic loads directly to the
wing bones or to spread the distal cheiropatagium in the chordwise direction
when the wing was extended (Padian and
Rayner, 1993; Bennett,
2000). However, it seems most unlikely that the actinofibrils,
which had an average diameter of 0.05 mm
(Padian and Rayner, 1993),
possessed sufficient bending stiffness or compression resistance to have had
these functions, quite apart from the fact that the fibrils make no direct
contact with the wing bones (Bennett,
2000). Tension in the cheiropatagium was responsible for the
transfer of aerodynamic loads, and the putative trailing edge tendon
(Frey et al., 2003) could have
prevented its excessive chordwise contraction.
The form and likely composition of the actinofibrils strongly suggests that they were resistant neither to bending nor to compression, but to extension. They would thus have altered the equilibrium of profile shape and aerodynamic loading in the distal cheiropatagium. At the very least, the fibrils would have limited the strain of the membrane and therefore reduced camber along their respective lengths relative to that of a fibril-less membrane. Due to the radiating pattern of the fibrils, this constraining action would have occurred more in the chordwise direction proximally, but more in the spanwise direction distally. Near the tip, the fibrils may therefore have limited the deflection of the trailing edge and thus reduced the overall geometric twist.
Additionally, the diminishing chordwise constraint of membrane excess
length towards the tip could have caused a spanwise increase in profile
camber. This would have caused the local zero-lift angle of attack to decrease
from root to tip, thereby giving rise to an aerodynamic wash-in (a nose-up
twist of the angle of attack as measured from the zero-lift angle) that would
have opposed the geometric wash-out of the cheiropatagium and improved the
spanwise lift distribution (Simons,
1978). Finally, in limiting the deformation of the distal
cheiropatagium as a whole, the fibrils would have narrowed the range of angles
of attack within which there are multiple profile solutions, and could thus
have reduced the risk of luffing. The fibrils may therefore have fulfilled the
roles that one would expect, bearing in mind the potential problems of
sail-like wings, but it will take physical models or a coupled finite
element/computational fluid dynamic analysis to confirm these suppositions. As
a further complication, it is known that the cheiropatagium contained muscle
fibres, following the discovery and subsequent study with a scanning electron
microscope of a three-dimensionally preserved wing membrane fragment from the
Santana Formation of Brazil (Martill and
Unwin, 1989), but as yet the global distribution of these muscles
within the cheiropatagium is largely unknown, as is the likely effect of their
contraction on the shape of the membrane.
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Conclusions |
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TOPSummaryIntroductionConclusionsReferences |
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Acknowledgments |
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References |
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TOPSummaryIntroductionConclusionsReferences |
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