Zoological Journal of the Linnean Society, 2008, 154, 27–69. With 30 figures
Three-dimensional geometry of a pterosaur wing
skeleton, and its implications for aerial and
terrestrial locomotion
MATTHEW T. WILKINSON*
Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, UK
Received 21 September 2007; accepted for publication 17 September 2007
This study reports on the three-dimensional spatial arrangement and movements of the skeleton of Anhanguera
santanae (Pterodactyloidea: Ornithocheiridae), determined using exceptionally well-preserved uncrushed fossil
material, and a rigid-body method for analysing the joints of extinct animals. The geometric results of this analysis
suggest that the ornithocheirids were inherently unstable in pitch and yaw. As a result, pitch control would
probably have been brought about by direct adjustment of the angle of attack of the wing, by raising or lowering
the trailing edge from the root using the legs if, as is indicated in soft-tissue specimens of a number of unrelated
pterosaur species, the legs were attached to the main wing membrane, or by using long-axis rotations at the
shoulder or wrist to raise and lower the trailing edge from the wingtip. An analysis of the three-dimensional
morphology of the wrist lends support to the idea that the pteroid – a long, slender wrist bone unique to pterosaurs
that supported a membranous forewing – was directed forwards in flight, not towards the body. As a result, the
forewing could have fulfilled the function of an air-brake and high-lift device, and may also have had an important
role in pitch, yaw, and roll control. The joint analysis is consistent with a semi-erect quadrupedal model of
terrestrial locomotion in the ornithocheirids. © 2008 The Linnean Society of London, Zoological Journal of the
Linnean Society, 2008, 154, 27–69.
ADDITIONAL KEYWORDS: Aerodynamics – arthrology – biomechanics – flight – functional morphology –
morphometrics – Ornithocheiridae – pteroid – Pterosauria.
INTRODUCTION
It is now generally accepted that pterosaurs – the
winged reptiles of the Mesozoic Era – were fully
capable flyers (Padian, 1983; Padian & Rayner, 1993),
although the larger species were almost certainly
secondarily adapted for soaring (Hankin & Watson,
1914; Bramwell & Whitfield, 1974; Brower, 1983;
Padian & Rayner, 1993). Nevertheless, controversy
and uncertainty still surround many aspects of pterosaur locomotion, including their terrestrial ability
(Bennett, 1997a, b; Unwin, 1997; Henderson &
Unwin, 1999; Unwin & Henderson, 1999; Bennett,
2001; Chatterjee & Templin, 2004), the precise shape,
aerodynamic behaviour, and possible control movements of their wings, and how the giant forms – the
*E-mail: [email protected]
largest flying animals that have ever lived – took off
and landed (Alexander, 1998). In order to address
these issues, an understanding of the functional morphology of the joints is vital in providing information
about the range of movement and degrees of freedom
of the limbs, and important flight parameters such
as wing planform, span, and area. Unfortunately,
because most pterosaurs had extremely thin-walled
bones (Heptonstall, 1971; Bramwell & Whitfield,
1974; Wellnhofer, 1985, 1991a; Fastnacht, 2005), preserved skeletal remains are nearly always found in a
crushed, flattened state. Clearly, such fossils cannot
be used to reconstruct joint function or skeletal geometry with any real degree of accuracy: if bones are to
be correctly articulated, they must be in their original
three-dimensional condition. On a few rare occasions,
however, pterosaur fossils in this exceptional state
of preservation have been found. Notable among
these are the thousands of pterosaur bone fragments
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
27
28
M. T. WILKINSON
from the Cambridge Greensand (Lower Cretaceous)
(Seeley, 1870; Hooley, 1914). These specimens were
used as the basis of functional morphological studies
by Hankin & Watson (1914) and Bramwell & Whitfield (1974), who manipulated incomplete articular
ends of limb bones to determine the range of movement of the various joints of the wings.
Unfortunately, owing to considerable post-mortem
disturbance of the Cambridge Greensand material, its
fragmentary nature, and the large number of individuals represented in the collection, it is almost
certain that these attempts to directly articulate the
joints used fragments from different individuals,
probably of different size, and even of different species
in some cases. In addition, because the shafts of the
limb bones are missing, it is difficult to establish
exactly how the orientation of the proximal end of a
bone relates to that of its distal end, with the result
that the three-dimensional spatial arrangement and
range of movement of the whole wing skeleton cannot
be determined with certainty.
This limiting situation changed with the discovery
of three-dimensionally preserved fossilized limb bones
of single pterosaur individuals in calcareous nodules
of the Santana Formation (Aptian–Albian) in the
Chapada do Araripe, Ceará, Brazil (Price, 1971;
de Buisonjé, 1980; Wellnhofer, 1985, 1991b; Kellner &
Tomida, 2000; Veldmeijer, 2002, 2003). Most of these
specimens have been assigned to the Ornithocheiridae sensu Unwin (2003), one of the dominant pterosaur groups of the Early Cretaceous (Wellnhofer,
1991a). Additionally, three-dimensionally preserved
specimens of the Late Cretaceous azhdarchid pterosaur Quetzalcoatlus have been discovered in the Javelina Formation, Big Bend National Park, West Texas
(Lawson, 1975; Padian, 1984). Wellnhofer (1985,
1991b), Hazlehurst & Rayner (1992), and, to a limited
extent, Bennett (2001) used ornithocheirid fossils
from the Santana Formation in their studies of the
pterosaur wing skeleton, but manipulated, for the
most part, incomplete bones when articulating joints.
Thus, although the individual joints considered by
these authors could be reconstructed with a far
greater degree of confidence than was possible with
the Cambridge Greensand material, the spatial
arrangement and degrees of freedom of the complete
wing could still not be accurately determined. In the
last few years, however, a small number of nearcomplete skeletons have been discovered, offering
an unprecedented opportunity for a comprehensive
analysis of the functional morphology of the ornithocheirid pterosaurs. Chatterjee & Templin (2004)
used one such skeleton in their study of pterosaur
posture and locomotion, but went no further
than previous authors, treating most of the joints in
isolation.
This study reports a thorough investigation of the
range of movement, degrees of freedom, and spatial
arrangement of the ornithocheirid wing skeleton,
using the most complete three-dimensional specimens
from the Santana Formation, and discusses the implications of this geometric information for aerial and
terrestrial locomotion in this group. It is hoped that
the techniques developed here will also provide a
methodological basis for future studies of the joints of
extinct animals.
MATERIAL AND METHODS
FOSSIL MATERIAL
Ten three-dimensionally preserved ornithocheirid
skeletons from the Santana Formation were used in
the present analysis (for a list of the institutional
abbreviations, see Appendix 1): Anhanguera santanae
(AMNH 22555) (Wellnhofer, 1991b); Anhanguera sp.
(IMCF 1053, SMNK 1136PAL); Brasileodactylus sp.
(AMNH 24444); Coloborhynchus robustus (NSM-PV
19892) (Kellner & Tomida, 2000), originally classified
as Anhanguera piscator, and reassigned by
Unwin (2003), although two authors have implicitly
rejected this reassignment (Codorniú & Chiappe,
2004; Kellner, 2004); C. robustus (SMNK 1133);
Ornithocheiridae indet. (SMNK 1134PAL, SMNK
1135PAL); Santanadactylus pricei (AMNH 22552)
(Wellnhofer, 1991b); and ?Santanadactylus sp.
(SMNK 1250PAL). The wing skeletons of four of these
specimens: Anhanguera sp. (SMNK 1136PAL), C.
robustus (NSM-PV 19892, SMNK 1133) and S. pricei
(AMNH 22552) are nearly complete, and provided the
bulk of the morphological and arthrological information. Additional morphometric data were obtained
from the crushed, near-complete articulated skeleton
of the putative ornithocheirid Arthurdactylus conandoylei (SMNK 1132PAL) from the Crato Formation
(Lower Cretaceous) of Brazil (Frey & Martill, 1994),
and from the published description of the Santana
ornithocheirid Coloborhynchus spielbergi (RGM 401
880) (Veldmeijer, 2003).
MORPHOMETRIC
ANALYSIS
The specimens listed above include the most complete
three-dimensionally preserved pterosaur skeletons
yet discovered. Nevertheless, no single complete
specimen exists. The available material was therefore
used to determine the dimensions of a composite
ornithocheirid, scaled to the size of A. santanae
(AMNH 22555). This is the only specimen examined
in which the vertebral column is preserved in its
entirety. Hence, the dimensions of the axial skeleton
can be determined by direct measurement. However,
no complete long bones are preserved, so the dimen-
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
sions of the limb elements were estimated from measurements of the remaining specimens.
Bones were measured in accordance with Bennett’s
(2001) convention: the tubercula of the distal
humerus, distal ulna, and proximal wing metacarpal
were not included, and neither was the extensor
tendon process of the first phalanx of the wing finger.
The only element for which it was not possible to
obtain an exact length measurement was the pteroid:
where present, the bone was always broken, and the
tip lost. The pteroid of C. robustus (SMNK 1133PAL)
was the most complete of those examined, so its
length was estimated on the assumption that only the
very tip had broken off.
With the exception of A. santanae (AMNH 22555),
the ulna is preserved in all of the specimens examined.
Log (bone length) was plotted against log (ulna length)
to obtain linear scatter plots for each long bone, and
a major axis regression analysis was carried out to
determine their allometric relationships. An isometric
relationship was assumed for any bone represented by
only one specimen. The scapulae are complete in A.
santanae (AMNH 22555), so the relative dimensions of
the limb bones, expressed in terms of ulna length, were
converted into expressions in terms of scapula length,
and the skeletal dimensions of the composite A. santanae were estimated accordingly.
JOINT
ANALYSIS
Three specimens were used in the joint analysis: C.
robustus (NSM-PV 19892, SMNK 1133PAL) and S.
pricei (AMNH 22552). These are largely free of any
matrix and are the most complete three-dimensional
skeletons that can be directly articulated. All the
major joints of the wing skeleton, including those of
the legs, are represented among them.
When articulating fossil bones it is important
to allow for an appropriate thickness of cartilage
between them, for without this allowance the range of
movement at a joint will be substantially underestimated. As a rule, the bone surfaces of articulating
elements are not perfectly matched: typically, the
radius of curvature of convex surfaces is less than
that of the corresponding concave surfaces. However,
the cartilage is usually moulded to the underlying
bone in such a way that the true joint surfaces are
congruent in at least one position – the so-called
‘close-packed’ position, which for hinge joints usually
occurs at one end of the habitual articular movement,
e.g. at the full extension of the human knee (Williams
et al., 1989). Hence, in most cases, the thickness of
cartilage should be equal to the difference between
the radii of curvature of the corresponding bone surfaces when in the close-packed position. This difference can therefore be used to estimate the extent of
29
cartilage in fossil joints. For instance, a very close fit
of the fossilized surfaces indicates that the layers of
cartilage would have been very thin; conversely, if the
curvatures of corresponding articular surfaces are
very dissimilar, one can postulate that there may
have been a greater thickness of cartilage between
them in life. This is not always the case: in some
joints, such as the knee joint of many large mammals,
the curvatures of the articular surfaces differ radically, and an unfeasibly thick layer of cartilage would
be required in order to make them congruent. Needless to say, such a thickness of cartilage is not actually
observed, and full congruence is not attained at any
stage of articular motion. Fortunately, the radii of
curvature of the corresponding surfaces of all joints of
the ornithocheirid wing skeleton are similar enough
to permit the estimation of cartilage thickness by the
method just described with a fair degree of confidence.
The constraining actions of other soft tissues, such
as the fibrous joint capsule, accessory ligaments, and
muscles, are more difficult to ascertain in fossils than
the thickness of cartilage. One must always bear in
mind that the range of movement deduced from
articular geometry alone is the maximum possible
range: the range of movement in the living animal
may have been more restricted. The task is made
easier if there are bony stops that define one end of an
articular excursion, such as the olecranon process of
the ulna in the human elbow joint. In addition, joint
surfaces occasionally show signs of pathological
grooving associated with osteoarthritis (Bennett,
2001, 2003). The curvature and arc lengths of such
grooves give a direct measure of the extent of articular movement that occurred, although these indicate
pathological movements that may not be representative of normal joint function (Padian, 1984).
The joint analysis procedure was as follows. To
begin, each joint was classified by direct manipulation
as immobile, uniaxial (with a single axis, e.g. hinge
joints), biaxial (with two mutually perpendicular axes,
e.g. saddle joints), or multiaxial (with three orthogonal
axes, e.g. ball-and-socket joints). Long-axis rotations
were additionally classified as either adjunct, i.e. independent of angulation (swinging motion), or conjunct,
i.e. indissociable from angulation. Joint motion was
then analysed further to identify the positions and
orientations of the various joint axes. In clinical biomechanics, the analysis of articular motion classically
involves placing markers on the fixed and moving limb
elements, taking photographs or radiographs before
and after angulation, and geometrically analysing the
marker positions so obtained to find the axes of rotation and the range of movement around these axes.
The analysis can either be two-dimensional, in which
case a single camera is used (Frankel, Burstein &
Brooks, 1971; Walker, Shoji & Erkman, 1972; Smidt,
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
30
M. T. WILKINSON
1973), or three-dimensional, in which case at least
two cameras are used to give stereoscopic images
(Blankevoort, Huiskes & de Lange, 1988; Boyd &
Ronsky, 1998; Leardini et al., 1999). For the present
study, a two-dimensional method was used.
The procedure is illustrated using a simple hypothetical hinge joint, with a single degree of freedom
and no conjunct rotation (Fig. 1). The proximal
element of the joint was fixed and the distal element
remained mobile. The elements were set up with
respect to a single camera such that the joint axis was
perpendicular to the photographic film. In the plane
of the film, the axis was therefore manifest as a point
– the centre of rotation (CR). A single marker – O –
was placed on the proximal element to define the
origin of an arbitrary three-dimensional Cartesian
coordinate system. In Figure 1, the joint set-up is
viewed in the y–z plane, and the joint axis lies parallel to the x-axis. At least two further markers – A
and B – were placed on the distal element. The joint
set-up was then photographed at least twice: once
with the distal element at maximum extension
(usually corresponding to the close-packed position),
and a second time with the distal element at
maximum flexion.
z
A number of methods exist for finding the CR from
these marker coordinates. The method used here is
the rigid-body method developed by Spiegelman &
Woo (1987). This method is more accurate than older,
graphical methods, whilst having fewer constraints in
the placement of the markers (Panjabi, 1979; Panjabi,
Goel & Walter, 1982). It uses rigid-body equations to
find a clockwise rotation matrix M describing motion
around the CR, and a translation vector c defining
the position of the CR relative to the arbitrary origin
located at marker O.
The two markers on the moving bone – A and B –
are denoted A′ and B′ after rotation of magnitude q
(Fig. 1). Points A, A′, B, and B′ are defined by the
position vectors p1, p2, p3, and p4, respectively:
p1 = y1 j + z1 k,
(1)
p2 = y2 j + z2 k,
(2)
p3 = y3 j + z3 k,
(3)
p4 = y4 j + z4 k,
(4)
where j and k are unit vectors along the y- and z-axes,
respectively.
The angle of rotation q is given as follows:
s′ s + t ′t
q = cos −1⎛ 2 2 ⎞ ,
⎝ s +t ⎠
A'
(5)
where
θ
B'
B
O
c
A
CR
s = z1 − z3,
(6)
s′ = z2 − z4,
(7)
t = y1 − y3,
(8)
t ′ = y2 − y4.
(9)
The position of the CR is given by:
y
Cz = z1 +
Cy = y1 −
Figure 1. A pair of articulating elements with a single
joint axis, set up so that the axis runs perpendicular to the
viewing plane, and is perceived as a point – the centre of
rotation (CR). The proximal element is fixed and has a
single marker O, defining the origin of an arbitrary coordinate system. The distal element is mobile and bears two
markers A and B, denoted A′ and B′ after a rotation of
magnitude q. The positions of the markers before and after
angulation in the arbitrary coordinate system can be used
to determine the position vector c of the CR, and the
magnitude of rotation q. See text for details.
( y2 − u)
sin q
( z2 − v)
sin q
−
cos q ( y1 − u)
,
sin q
(10)
+
cos q ( z1 − v)
,
sin q
(11)
where
u=
sin q ( z1 − z2 ) y1 + y2
,
+
2 (1 − cos q )
2
(12)
v=
z1 + z2 sin q ( y1 − y2 )
−
.
2
2 (1 − cos q )
(13)
This process requires a minimum of two markers
(A and B) to compute the angle of rotation q and the
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
position of the CR, but more were used in practice,
and mean values of the parameters were calculated to
improve the accuracy.
For most uniaxial joints, the rigid-body method was
used in an unmodified form. The method was appropriate, even if the distal element underwent a conjunct rotation, provided the moving bone underwent a
cardinal angulation, i.e. remained within a single
plane. This is not always the case: conjunct rotation is
often accompanied by rotation of the joint axis with
respect to the proximal element, which causes the
distal element to swing out of a single plane (Fig. 2).
Such angulations are termed arcuate. The analysis of
arcuate motion is described below.
The analysis of biaxial joints was similar to that of
uniaxial joints: each component axis was simply
treated separately. In such joints, angulation occurs
around two mutually perpendicular axes, primary
and secondary, such that the maximum range of
movement is not simply an angle, but a virtual cone.
The shape of this cone is defined by the maximum
ranges of angulation around the two axes. Here, the
primary axis was defined as that around which the
greatest range of angulation took place. The secondary axis was perpendicular to the primary axis. The
CRs of these two axes and the ranges of angulation
around them were found as described above.
The long-axis rotation of a bone, whether conjunct
or adjunct, was also measured using the rigid-body
method. In this case, the bone in question was photographed in distal view, and markers were placed
on the distal surface. Because the static proximal
element was generally not in the field of view in this
31
case, another static element was placed near the
distal surface of the rotating bone, and a marker was
fixed to it in order to define the arbitrary origin, as
before. Multiaxial joints were analysed using the
methods employed for biaxial joints and long-axis
rotations.
As described above, arcuate swings occur if a joint
axis itself rotates during the angulation of a bone.
Arcuate motion was analysed by fixing the hinge
axis, such that the distal element underwent a
normal cardinal angulation. During angulation of
the distal element, the proximal element was therefore rotated in order to maintain articular contact.
This rotation – equal and opposite to that of the
hinge axis, with respect to the proximal element –
was measured using the rigid-body method by
marking and photographing the proximal element in
the usual way.
Immobile joints were set up so that both elements
were in the same plane, perpendicular to that of the
photographic film, as before. The joint was then photographed in its life position and in a reference position, with proximal and distal elements in line. The
CR and rotation angle q between this reference position and the life position were then calculated using
the rigid-body calculations. Essentially, immobile
joints were treated as if they were uniaxial, the life
and reference positions corresponding to the limits of
articular movement of a uniaxial joint.
The various joint axes, found in isolation, were
then placed in a single, common frame of reference,
this being a three-dimensional Cartesian coordinate
system, with its origin in the plane of symmetry of
Figure 2. Diagrammatic representation of an articulating element undergoing a cardinal angulation (A) and an arcuate
angulation (B). During a cardinal angulation, the joint axis remains fixed and the moving bone remains in a single plane.
During an arcuate angulation, the joint axis rotates and the bone moves out of the plane.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
32
M. T. WILKINSON
A
wf
pt
ul
ra hu
co
sc
wm
tt
il
fe
B
y
x
C
z
y
Figure 3. Reconstruction of the axial skeleton and left wing of Anhanguera santanae in dorsal view (A), and a virtual
fleshed-out reconstruction of the axial skeleton and right wing in ventral (B), and anterior (C) views. Principal limb bones
are laid out end-to-end. For a list of anatomical/arthrological abbreviations, see Appendix 1. Scale bar: 500 mm.
the pterosaur body. In order to visualize the threedimensional wing, a computer model was constructed to represent the reconstructed, fleshed-out
skeleton of the composite A. santanae (AMNH
22555). Model dimensions were obtained from the
morphometric analysis described above. The virtual
limb elements were initially laid out end to end,
along straight lines projecting from the shoulder
and hip joints (Fig. 3). The x-axis passed through
the plane of symmetry fore to aft, subparallel to the
vertebral column; the y-axis ran left to right; and
the z-axis ran ventral to dorsal.
The procedure for placing and orienting the joints
axes made use of the facts that: (1) in the analyses of
the isolated joints, the joint axes were always oriented perpendicular to the photographic film, and (2)
two consecutive joints along the arm or leg share a
common skeletal element. This shared element generally had to be adjusted between joint set-ups in
order to align the subsequent joint axis with the
horizontal. The relative orientation of consecutive
joint axes was found by quantifying the magnitude of
this angular adjustment. By carrying out this procedure for each consecutive pair of joints, moving from
root to tip, the orientation of all the joint axes was
found relative to the body axis system. The joint axes
were then mapped onto the limbs in locations corresponding to their respective CRs. Rotation matrices
were used to rotate each limb element around the
relevant CR within their respective ranges of angulation, working from tip to root. Moving the elements
within their calculated ranges could generate any
possible limb configuration.
SKELETAL PROPORTIONS
Bone dimensions are given in Appendix 2. The linear
scatter plots of log (bone length) plotted against log
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
B
C
2.50
2.65
2.15
2.45
2.60
2.10
2.05
2.00
1.95
1.90
1.85
2.40
2.45
2.50
2.55
2.60
2.40
2.35
2.30
2.25
2.20
2.15
2.35
2.65
2.40
Log ulna length (mm)
2.45
2.50
2.55
2.60
2.40
2.35
2.30
2.25
2.20
2.50
2.55
2.60
2.65
2.80
2.75
2.70
2.65
2.60
2.55
2.50
2.35
2.40
2.50
2.55
2.60
2.65
2.50
2.45
2.40
Log tibiotarsus length (mm)
2.55
2.40
2.30
2.20
2.10
2.35
2.45
2.50
2.55
2.60
2.65
2.50
2.55
2.60
2.65
2.60
2.65
2.60
2.65
2.80
2.75
2.70
2.65
2.60
2.55
2.50
2.45
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.60
2.45
Log ulna length (mm)
2.50
Log ulna length (mm)
2.40
I
2.70
Log femur length (mm)
Log wing-finger phalanx 3 length (mm)
2.45
H
G
2.40
2.35
Log ulna length (mm)
Log ulna length (mm)
2.30
2.35
2.40
F
Log wing-finger phalanx 1 length (mm)
Log wing-metacarpal length (mm)
2.45
2.45
2.45
Log ulna length (mm)
E
2.50
2.40
2.50
Log ulna length (mm)
D
2.15
2.35
2.55
2.30
2.35
2.65
Log wing-finger phalanx 2 length (mm)
1.80
2.35
Log radius length (mm)
2.20
Log humerus length (mm)
Log scapula length (mm)
A
33
2.00
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.50
2.40
2.30
2.20
2.10
2.35
2.40
Log ulna length (mm)
2.45
2.50
2.55
Log ulna length (mm)
Figure 4. Linear scatter plots of log-transformed length measurements of the long bones of selected ornithocheirid
specimens from the Santana Formation. A, scapula. B, humerus. C, radius. D, wing-metacarpal. E, wing-finger phalanx
1. F, wing-finger phalanx 2. G, wing-finger phalanx 3. H, femur. I, tibiotarsus.
(ulna length) are shown in Figure 4A–I. As Frey &
Martill (1994) found in their morphometric analysis
of the ornithocheirids, there was no significant departure from isometry for any of the long bones (regression ANOVA, P > 0.05). This can be seen clearly in
Figure 5, which shows the relative lengths of all of
the long bones, presented as percentages of the length
of the ulna, plotted against the ulna length. There is
no significant change in the relative length of any
element with increasing size. This demonstrates
that the ornithocheirids as a group were remarkably
homogenous: despite differences in the size, taxonomic status, and ontogenetic stages of the specimens
examined, the skeletal proportions remained essentially the same. Table 1 shows the relative lengths of
the limb bones expressed in terms of ulna length and
scapula length, and the estimated bone lengths of
A. santanae.
JOINT FUNCTIONAL MORPHOLOGY
Table 2 lists the joints of the ornithocheirid wing
skeleton, which specimens were used to analyse each
joint, and how they were classified. Each is described
below, and the reconstructions are compared with
those of other workers. Only limited morphological
information is given here – further details are given
by Wellnhofer (1985, 1991b), Kellner & Tomida
(2000), and Veldmeijer (2003).
SCAPULA–NOTARIUM
JOINT
In the ornithocheirids, as in many large pterodactyloids, the scapula is directed medially, and articulates with a facet on the neural spine of the fourth
dorsal vertebra, which in skeletally mature specimens is fused into the notarium, formed by the first
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
34
M. T. WILKINSON
160
sc
hu
ra
wm
wf-ph1
wf-ph2
wf-ph3
fe
tt
Relative bone length (%ulna length)
140
120
100
80
60
40
20
0
220
240
260
280
300
320
340
360
380
400
420
Ulna length (mm)
Figure 5. Relative lengths of the long bones of ten selected ornithocheirid specimens, expressed as a percentage of the
ulna length. The collection of points at each value of absolute ulna length represents measurements taken from a single
specimen.
Table 1. Allometric expressions for the lengths of the principal limb bones of ornithocheirid pterosaurs in terms of ulna
length (ul) and scapula length (sc), and the estimated lengths of the corresponding limb bones of Anhanguera santanae
(AMNH 22555). The number n of specimens used to derive each expression is indicated
Bone
n
Length w.r.t. ulna
Length w.r.t. scapula
Estimated bone
lengths of A. santanae
(AMNH 22555) (mm)
sc
hu
ul
ra
wm
wf-ph1
wf-ph2
wf-ph3
wf-ph4
pt
fe
tt
8
10
12
6
8
7
3
4
1
1
4
2
0.13(ul)1.16
0.51(ul)1.05
–
1.00(ul)1.00
0.98(ul)0.94
1.20(ul)1.03
0.71(ul)1.11
0.30(ul)1.22
0.88(ul)1.00
0.47(ul)1.00
0.04(ul)1.49
0.04(ul)1.53
–
3.34(sc)0.91
6.03(sc)0.87
6.02(sc)0.86
5.29(sc)0.81
7.73(sc)0.90
5.23(sc)0.96
2.68(sc)1.05
2.82(sc)1.00
1.50(sc)1.00
0.51(sc)1.29
0.57(sc)1.32
90
198
296
293
205
435
395
308
254
136
170
216
five dorsal vertebrae and sometimes by the last cervical (Wellnhofer, Buffetaut & Gigase, 1983; Veldmeijer, 2003). This arrangement firmly braced the
shoulder girdle on the vertebral column, creating a
rigid base for the wing. The articular surfaces of the
scapula–notarium joint are rather flat in the orni-
thocheirids, being slightly concave on the notarium
and convex on the scapula. In side view, the facets
are roughly oval. The corresponding surfaces can be
brought into near-congruence, indicating that there
was only a thin layer of cartilage between them
in life.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
35
Table 2. Characterization of the principal joints of the ornithocheirid fore- and hindlimbs, and the specimens used to
analyse each joint
Joint
Specimens used
Joint type
Degrees of
freedom
scno
stco
sh
el
ruc
is
mc
cpt
cm
knu
ip
hp
kne
NSM-PV 19892 – left
NSM-PV 19892 – right
NSM-PV 19892 – left + SMNK 1133PAL – right
SMNK 1133PAL – right
SMNK 1133PAL – right
SMNK 1133PAL – right
SMNK 1133PAL – right
SMNK 1133PAL – right
SMNK 1133PAL – right
NSM-PV 19892 – left + SMNK 1133PAL – left
AMNH 22552 – right
NSM-PV 19892 – right
NSM-PV 19892 – right
Immobile
Constrained saddle
Multiaxial
Uniaxial hinge
Uniaxial hinge with conjunct rotation
Uniaxial hinge
Uniaxial hinge
Uniaxial hinge with conjunct rotation
Uniaxial pivot
Uniaxial hinge with conjunct rotation
Immobile
Ball-and-socket
Uniaxial hinge
1
1
3
1
1
1
1
1
1
1
0
3
1
The opinion here is that the scapula–notarium
joint was essentially immobile: i.e. that the joint did
not permit muscle-controlled movements, but that it
may have had a limited degree of flexibility (if no
movement were permitted at all, one would
expect fusion to have occurred). The flatness of the
articular surfaces would, in my opinion, permit a
maximum range of fore-and-aft angulation of only
about 10° (incidentally, the curvature of the joint
surfaces is similar to that of the interphalangeal
joints, which are universally regarded as immobile,
in the sense that they would not have permitted
muscle-controlled movements – see below), and the
proximity of the transverse processes of the vertebrae and the elongate shape of the facets would
have prohibited significant long-axis rotation. The
scapulocoracoids were additionally constrained by
their articulations with the sternum (see below),
which would have prohibited elevation or depression. Bennett (2001) and Wellnhofer (1991b) provided alternative interpretations to those just
stated, proposing that significant voluntary movement was possible at the scapula–notarium joint.
This is here regarded as unlikely, not only because
the degree of movement suggested by these authors
would have caused disarticulation, but also because
the joint presumably evolved in order to provide
a stable base for the humerus: a high degree of
mobility would have been incompatible with this
function.
The orientation of the scapulocoracoid in life is
indicated in Figure 6. The glenoid was unusually high
in the ornithocheirids – nearly co-planar with the
vertebral column, as has been noted before (Wellnhofer, 1991b; Frey, Buchy & Martill, 2003a).
sc
no
gl
co
stp
cs
Figure 6. Diagrammatic anterior view of the left pectoral
girdle of a typical ornithocheirid. For a list of anatomical/
arthrological abbreviations, see Appendix 1.
STERNOCORACOID
JOINT
The articulation between the coracoid and the
sternum, at the rear of the cristospine, is a saddle
joint, concave in the fore-and-aft direction, but convex
in the mediolateral direction. Such joints are usually
biaxial; however, rotation of the sternum about a
fore-and-aft axis would usually be prevented by the
presence of the other coracoid, and hence rotation can
generally only occur about a transverse axis. It is
possible that asymmetric angulations of the left and
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
36
M. T. WILKINSON
right scapulocoracoids, which could have occurred
passively during walking for instance, may have
caused small rotations of the sternum about a vertical
axis passing between the two sternocoracoid joints,
but it is unlikely that such a movement would have
had functional significance. Rotation about a transverse axis causes the sternal plate to tilt up and
down. The sternum of birds moves in a similar
fashion during the ventilation cycle to expand and
contract the air sacs (Zimmer, 1935), and it is possible
that the movement of the sternum in pterosaurs had
a similar ventilatory function, a view shared by
Bennett (2001). Conversely, it has been suggested
that the ribcage lacked sufficient mobility for such
movement, and that pterosaurs instead used movements of the pelvis and abdominal wall, or maybe
a crocodilian-type hepatic piston, for ventilation
A
sc
SHOULDER
The ornithocheirid shoulder joint is a deceptively
complex structure. The glenoid fossa – the contribution of the scapulocoracoid to the shoulder joint –
consists of a shallow, largely biconcave scapular part,
which faces laterally, and a saddle-shaped coracoid
part, which faces dorsolaterally and a little to the rear
(Fig. 7A). The coracoid part is convex in the fore-andaft direction and concave in the mediolateral direction. The scapular part can itself be divided into a
small anterior region and a large posterior region,
with the two being separated by a shallow ridge. The
posterior region extends aft beyond the articular
B
ri
scgl
cogl
(Carrier & Farmer, 2000; Ruben, Jones & Geist, 2003;
Claessens, Unwin & O’Connor, 2006).
1ax
2ax
1ax
gl
2ax
3ax
dpcr
co
C
hu
1ax
co
dpcr
D
2ax
hu
sc
sc
dpcr
Figure 7. A, reconstructed articular surfaces of the right shoulder joint of Coloborhynchus robustus (SMNK 1133PAL).
Elements are oriented as if articulated in their close-packed position: scapulocoracoid in lateral view and humerus in
medial view. Scale bar: 50 mm. B, diagrammatic representation of (A), showing contact areas in the close-packed position
(shaded) and the joint axes. C, right scapulocoracoid and humerus in the close-packed position in anterior aspect, viewed
along the primary axis. D, (C) in dorsal aspect, viewed along the secondary axis. For a list of anatomical/arthrological
abbreviations, see Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
surface of the coracoid by a distance equal to a little
less than one half of the total width of the glenoid
fossa.
The head of the humerus is biconvex and slightly
elongate in the fore-and-aft direction (Fig. 7A). In
medial aspect it is bean-shaped, with a deeply excavated ventral border. The articular surface is asymmetrical, with a narrow anterior region, but expanded
posterior region, corresponding to the similar asymmetry of the scapular part of the glenoid. In some
specimens (e.g. SMNK 1133PAL, but not NSM-PV
19892) this articular surface is clearly delineated
dorsally by a ridge of bone.
The shoulder joint is multiaxial, but is not a true
ball-and-socket joint, thanks to the partially saddleshaped glenoid fossa and the elongate nature of
the head of the humerus, which restricts the range
of protraction and retraction (nominal fore-and-aft
angulation). In the close-packed position, the ridge on
the head of the humerus (if present) closely follows
the dorsal outline of the glenoid, and its ventral
concavity fits closely around the articular surface of
the coracoid. The estimated thickness of cartilage of
specimen NSM-PV 19892 is 3 mm – about 7.5% of the
width of the humeral articular surface. When in the
close-packed position, and when the scapulocoracoid
is oriented as in life, the shaft of the humerus lies in
a horizontal plane and is directed backwards by about
10°. The contact areas in the close-packed position are
shown in Figure 7B.
The principal movement at the shoulder joint is a
nominal elevation/depression of the humerus, with
an estimated maximum range (that may have been
reduced in life) of 95°. The primary axis passes
through the head of the humerus, and is tilted back
from the horizontal by about 35° (Fig. 7B, C), with
the result that the humerus swings backwards a
little when it is elevated, and forwards when it is
depressed. The estimated maximum elevation from
the horizontal is 70°. During elevation, the smaller,
anterior part of the head of the humerus moves
wholly onto the articular surface of the coracoid,
whereas the larger posterior region of the head of
the humerus rolls across the posterior region of the
articular surface of the scapula. There is an indication that the humerus would usually have undergone a conjunct supination (backward long-axis
rotation) of about 20° as it approached the closepacked position from above, as slight pronation
(forward long-axis rotation) of the humerus during
elevation maintains a greater area of articular
contact. The humerus can also be depressed from its
close-packed position by 25°, at which point the
proximal end of the humeral shaft abuts onto the
articular surface of the coracoid, preventing further
angulation.
37
The secondary axis of the shoulder is at 90° to the
primary, but is located medial to it, passing through
the scapulocoracoid (Fig. 7B, D). Angulation around
the secondary axis is predominantly manifest as
protraction/retraction, but, thanks to the 35° backward tilt of the axis with respect to the vertical
(corresponding to the equivalent tilt of the primary
axis with respect to the horizontal), protraction is
accompanied by a slight elevation, and retraction is
accompanied by a slight depression. The scapular
part of the glenoid is shallow in the fore-and-aft
direction, and, as a result, the maximum range of
angulation about the secondary axis is more limited
than that about the primary axis: the humerus can be
retracted from the close-packed position by no more
than 40°, and can be protracted by only 10°. This
asymmetry is caused by the nature of the fore-and-aft
curvature of the coracoid part of the glenoid. Specifically, the radius of curvature progressively decreases
from front to back. Hence, the congruence between
the deeply curved ventral excavated region of the
humeral head and the coracoid remains high throughout retraction. Beyond 40° retraction, contact with
the coracoid is lost, and the contact area between the
scapula and the humeral head is reduced nearly to
zero. Because of the comparatively shallow curvature
of the anterior region of the coracoid part of the
glenoid, any substantial degree of protraction from
the close-packed position causes the congruence
between the articulating surfaces to diminish rapidly.
The above description of secondary angulation
applies only when the humerus is horizontal or nearhorizontal. The situation is different if the humerus is
elevated. In this latter configuration the ventral excavated region of the head of the humerus is clear of the
coracoid, allowing the humeral head to roll freely
across it when protracted or retracted. The curvature
of the coracoid part of the glenoid in the fore-and-aft
direction is much deeper than that of the scapular
part, so a greater range of angulation is possible from
this position: up to 30° protraction and 50° retraction.
In addition to the angulations described above, the
humerus can also be rotated about its long axis. In
medial aspect this axis is located very close to the
centre of curvature of the ventral concavity of the
humeral head (Fig. 7B). Hence, during long-axis
rotation away from the close-packed position, the
humerus does not simply spin in place, but slides
around the articular surface of the coracoid. The
estimated maximum range of supination is 50°, and
the maximum range of pronation is 30°. Supination of
the humerus from the close-packed position is topologically equivalent to elevation, followed by retraction, followed by depression back to the close-packed
position (this phenomenon – known as a diadochal
movement – can be demonstrated by raising one’s
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
38
M. T. WILKINSON
Rayner, flapping could only have involved alternate
supination and pronation, without the usual dorsoventral angulation. However, the specimen used by
these authors – Santanadactylus brasilensis (M4894),
housed in the Geological Institute of the University of
Amsterdam, the Netherlands (de Buisonjé, 1980) – is
incomplete, missing a large part of the scapular part
of the glenoid. One must therefore conclude that
contact areas, and therefore ranges of movement,
were significantly underestimated in their study.
arm to the side, swinging it forward, then depressing
it: the arm will have been pronated by 90°).
The reconstruction presented above is broadly in
agreement with published accounts: most workers
accept that the principal motion at the shoulder was
elevation/depression, and that the range of elevation
of the humerus above the horizontal was much larger
than the range of depression below it (Hankin &
Watson, 1914; Bramwell & Whitfield, 1974; Wellnhofer, 1985, 1991b). These authors have reconstructed
a smaller range of secondary angulation than that
presented here, but Bramwell & Whitfield (1974)
noted that the range of protraction/retraction was
greatly increased as the humerus was elevated.
Bennett (2001), in contrast, believed that the
humerus could be retracted to 65° behind the transverse axis, even at the bottom of the downstroke. I
believe that this degree of retraction is possible, but
only if the humerus is first supinated, in which case
nominal retraction is actually an angulation around
the primary axis, not the secondary. Retraction of the
humerus by 65° from the close-packed position, as
stated above, causes the humerus and coracoid to
separate completely, and greatly reduces contact with
the scapula.
The only study in which the conclusions differ substantially from those presented above is an analysis
of an isolated shoulder joint by Hazlehurst & Rayner
(1992). It was concluded that the only possible movement at this joint was rotation around the humeral
long axis, in marked contrast to the results of other
workers, including myself. According to Hazlehurst &
A
rufac
dpr
ra
ELBOW
The elbow joint is uniaxial. Concave facets (shallow
surfaces) and cotyles (deeper depressions) on the
radius and ulna articulate with convex facets, and
condyles, on the anterior side of the distal humerus
(Fig. 8A). The axis is oriented 20° forward of the
vertical (Fig. 8B), so that when flexed, the forearm
swings forwards and a little downwards. At maximum
extension (the close-packed position), a ridge on the
proximal surface of the ulna fits into a groove in the
distal surface of the humerus, and prevents further
extension (Fig. 8A, B). In this position, the radius/
ulna and humerus make an angle of 160°, which
agrees reasonably well with other estimates for
the Ornithocheiroidea sensu Unwin (2003): 150° for
Santanadactlyus (Wellnhofer, 1985) and Pteranodon
(Bennett, 2001), and 145° for the basal ornithocheiroid Istiodactylus (Bramwell & Whitfield,
1974). There is considerable disagreement in the literature regarding the maximum range of flexion at
B
hufac
pn
ul
hu
racon
gr
ulcon
C
ri
hucot
ax
ax
ax
hu
ul
ra
dpcr
Figure 8. A, reconstructed articular surfaces of the right elbow joint of Coloborhynchus robustus. Elements are oriented
as in Fig. 7: humerus in lateral view, and radius and ulna in medial view. Scale bar: 50 mm. B, diagrammatic
representation of (A), showing contact areas in the close-packed position and the joint axis. C, right humerus, radius, and
ulna in the close-packed position in dorsal aspect, viewed along the joint axis. For a list of anatomical/arthrological
abbreviations, see Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
the distal syncarpal and the wing-finger metacarpal.
When analysing the radioulnocarpal joint, the proximal syncarpal was temporarily fixed with adhesive
putty to the distal syncarpal, which was in turn
fixed to the wing metacarpal, with the intersyncarpal and carpometacarpal joints placed in their
close-packed positions. The joint axis and range of
movement could then be more accurately determined thanks to the greater lengths of the articulating elements. Similarly, when analysing the
intersyncarpal joint, the proximal syncarpal was
fixed to the radius/ulna, and the distal syncarpal
was fixed to the wing metacarpal. There are three
additional splint-like metacarpals upon which the
three short, clawed digits I–III articulate, but the
arrangement of these bones has little bearing on
the three-dimensional geometry of the wing.
the elbow for the ornithocheiroids: estimates range
from 30° (Bramwell & Whitfield, 1974) to 120°
(Bennett, 2001); in other pterosaurs the morphology
of the elbow joint is very different, and the maximum
range of flexion is considerably greater (Wellnhofer,
1991a). The most likely cause of the large discrepancy
is the different estimates of the extent of cartilage in
the joint. I estimate that the thickness of cartilage
in the elbow of C. robustus (SMNK 1133PAL) was
approximately 5 mm – i.e. 6.5% of the width of the
distal humeral articular surface. Taking this into
account, the maximum range of flexion was estimated
at 90°.
WRIST
The pterosaur wrist comprises four elements: the
proximal syncarpal, formed by the fusion of the two
proximal carpals (Bennett, 1993); the distal syncarpal, formed by the fusion of three distal carpals
(Bennett, 1993); the block-like medial carpal
(Padian, 1984), also termed the distal lateral (Wellnhofer, 1985) and preaxial carpal (Bennett, 2001);
and the long, slender pteroid, which in life supported a membranous propatagium (forewing) in
front of the arm (Wellnhofer, 1991a). There are five
wrist joints: (1) the radioulnocarpal joint between
the radius/ulna and the proximal syncarpal; (2) the
intersyncarpal joint between the proximal and distal
syncarpals; (3) the medial carpal joint between the
distal syncarpal and the medial carpal; (4) the carpopteroid joint between the medial carpal and the
pteroid; and (5) the carpometacarpal joint between
A
ul
psfac
rafac
Radioulnocarpal joint
The proximal surface of the proximal syncarpal bears
two concave facets, which receive the convex facets of
the radius and ulna, and a hemispherical tuberculum,
which fits into a circular depression (fovea) in the
distal surface of the ulna (Fig. 9A, B). The radioulnocarpal joint is uniaxial. As other workers have noted,
flexion of the elbow automatically flexes the radioulnocarpal joint (Hankin & Watson, 1914; Bramwell &
Whitfield, 1974). As the elbow is flexed, the radial
facet and condyle on the distal humerus push against
the radius, causing it to slide along the ulna. This
movement is constrained to longitudinal translation
by a pronounced ridge on the anterior surface of the
ulna, near its proximal end, and another at its distal
B
ulfac
ra
psfac
39
ax
ax
ps
tu
fov
C
crax
wm
ul
ax
ra
ds
ps
Figure 9. A, reconstructed articular surfaces of the right radioulnocarpal joint of Coloborhynchus robustus. Elements are
oriented as in Fig. 7: radius and ulna in lateral view, and proximal syncarpal in medial view. Scale bar: 50 mm. B,
diagrammatic representation of (A), showing contact areas in the close-packed position, the joint axis, and the conjunct
rotation axis. C, right radius, ulna, syncarpals, and wing metacarpal in their respective close-packed positions in
posterodorsal aspect, viewed along the radioulnocarpal joint axis. For a list of anatomical/arthrological abbreviations, see
Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
40
M. T. WILKINSON
Intersyncarpal joint
The intersyncarpal joint is a sliding articulation.
The articular surface of the proximal syncarpal bears
a prominent ridge that runs anteroventrally, with
concave facets to either side, resembling a short
section of a left-handed corkscrew in the right-hand
limb (Fig. 10A). The corresponding articular surface
of the distal syncarpal fits very closely when the
radius/ulna and wing metacarpal are in line, indicating that only a thin layer of cartilage was present.
The joint axis is tilted back from the vertical by 40°,
and the maximum range of angulation is about 25°.
Flexion of the joint retracts the wing metacarpal by
20°, and depresses it by 15°, and is accompanied by a
slight posteroventral translation of the distal syncarpal with respect to the proximal.
The very tight fit between the proximal and distal
syncarpals has led many workers to believe that
it was incapable of muscle-controlled movement
(Hankin & Watson, 1914; Bramwell & Whitfield,
1974; Padian, 1984). In this case, the joint would have
functioned as a shock absorber, reducing the risk of
breakage of the wing in turbulent conditions, for
example. Opponents of this idea (Unwin, 1988;
Bennett, 2001) have argued that the range of permitted movement is too large to be accounted for solely
by nonvoluntary movement. The maximum theoretical range of 25° estimated for the intersyncarpal joint
here would indeed be large for a passive joint, but it
must be remembered that this range may have been
restricted in life by the presence of ligaments. The
evidence from the bones alone is clearly inconclusive,
end, that together support the radius ventrally. As the
radius slides along the ulna, its distal articular
surface pushes on the radial facet of the proximal
syncarpal, causing the latter to pivot around the
tuberculum, thus flexing the joint. The radial facet
occupies an anterodorsal position on the surface of the
proximal syncarpal, above and slightly in front of the
tuberculum, so that a push on the radial facet causes
the wing metacarpal to swing backwards and downwards. Hence, the joint axis is tilted back from the
vertical by 60° (Fig. 9B). As the proximal syncarpal
pivots about the tuberculum, the ulnar facet – located
behind the radial facet – slides across the convex
articular surface of the ulna, causing the syncarpal to
undergo a conjunct supination of 20° about the tuberculum over the full course of flexion. This conjunct
rotation, which has been noted by other workers
(Hankin & Watson, 1914; Bramwell & Whitfield,
1974), does not cause an equivalent rotation of the
joint axis, which remains fixed relative to the ulna
throughout flexion. At maximum extension – i.e. at
maximum extension of the elbow – the angle between
the radius/ulna and wing metacarpal is 175°. There is
no evidence that the wrist could be hyperextended
(i.e. angulated forwards beyond 180°), as suggested by
Bramwell & Whitfield (1974). The maximum range of
flexion is 50°, beyond which the radius fails to make
contact with the radial facet of the proximal syncarpal. At maximum flexion, and with the radius/ulna
oriented parallel to the transverse axis, the wing
metacarpal is directed backwards by 35° and downwards by 50°.
A
gr
dsfac
ps
B
mcfac
ax
ds
ri
pn
ax
psfac
ax
C
ul
wm
ds
ps
ra
Figure 10. A, reconstructed articular surfaces of the right intersyncarpal joint of Coloborhynchus robustus. Elements are
oriented as in Fig. 7: proximal syncarpal in lateral view and distal syncarpal in medial view. Scale bar: 50 mm. B,
diagrammatic representation of (A), showing contact areas in the close-packed position and the joint axis. C, right radius,
ulna, syncarpals, and wing metacarpal in their respective close-packed positions in posterodorsal aspect, viewed along the
joint axis. For a list of anatomical/arthrological abbreviations, see Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
wm
ds ps
ten
Figure 11. A, reconstructed articular surfaces of the right
medial carpal joint of Coloborhynchus robustus. Elements
are oriented as in Fig. 7: distal syncarpal in anterior view
and medial carpal in posterior view. Scale bar: 25 mm. B,
diagrammatic representation of (A), showing contact areas
in the close-packed position and the joint axis. For a list of
anatomical/arthrological abbreviations, see Appendix 1.
and until a detailed reconstruction of these soft
tissues is carried out, a definitive pronouncement on
this matter cannot be made. Such a reconstruction is
beyond the scope of this paper.
Medial carpal joint
The articular surfaces of the medial carpal joint are
elliptical – i.e. are elongated in the dorsoventral direction (Fig. 11). The facet on the medial carpal is biconcave, and that on the distal syncarpal is biconvex. The
joint permits a small range of movement (about 20°)
in the mediolateral direction, but this movement may
not have been under voluntary control. The facet of
the medial carpal is nearly symmetrical about its
dorsoventral and transverse axes, which makes it
difficult to tell which way up the medial carpal should
be articulated. This is important, because it affects
the orientation of the concave distal cotyle of the
medial carpal, within which the pteroid may have
articulated (see below). In one restoration, the cotyle
is directed anterodorsally (Wellnhofer, 1985; Bennett,
2001), in the other it points anteroventrally (Padian,
1984; Wellnhofer, 1991b). These two reconstructions
have radically different implications for the function
of the pteroid, which will be discussed further below.
Carpopteroid joint
The nature and function of the carpopteroid joint are
highly contentious. Until relatively recently, there
was a general consensus that the pteroid articulated
in the distal cotyle of the medial carpal, and that it
was directed medially, i.e. towards the body (Bramwell & Whitfield, 1974; Padian, 1984; Wellnhofer,
1985, 1991a). Both of these assertions have been
questioned of late. Bennett (2001, 2006) pointed out
that in many three-dimensionally preserved specimens a small oval sesamoid (sesamoid A) is located
within the distal cotyle of the medial carpal, and that
in no specimen is the pteroid preserved in articulation
ses
mc
ul
41
ra
pt
Figure 12. Reconstruction of the right wrist of Coloborhynchus robustus in dorsal view according to descriptions
provided by Bennett (2001, 2006), with a sesamoid bone
within the distal cotyle of the medial carpal, and the
pteroid articulating on the side of the medial carpal. The
postulated trajectory of the wing-finger metacarpal extensor tendon, in which the sesamoid is embedded, is also
shown. For a list of anatomical/arthrological abbreviations, see Appendix 1. Scale bar: 50 mm.
there (Bennett, 2006). A sesamoid usually lies within
a tendon at a point where it passes over a bony
protuberance proximal to its insertion, and serves to
increase the length of the tendon’s moment arm and
to improve its mechanical advantage. Bennett concordantly argued that sesamoid A was embedded in the
tendon of a wrist extensor muscle, where it ran
through the distal cotyle of the medial carpal proximal to its insertion on the wing metacarpal, and that
the pteroid articulated on the medial side of the
medial carpal (Fig. 12). In this reconstruction, the
medial carpal is oriented such that the cotyle faces
anterodorsally. The sesamoid would have been essentially fixed with respect to the medial carpal, so that
both would have acted as a single unit roughly analogous to the pisiform bone of the wrist of mammals
and reptiles (Romer, 1970).
I have two objections to this reconstruction. Firstly,
although there are suggestive depressions and grooves
on the medial side of the medial carpal of the
azhdarchid Quetzalcoatlus (J. R. Cunningham, pers.
comm.), there is no indication of an articular facet on
the equivalent surface of any three-dimensionally preserved ornithocheirid medial carpals. The surface is
nearly flat, and is therefore incongruent with the
convex head of the pteroid. Secondly, Bennett’s proposed arrangement, in which the sesamoid is lodged
within a deep concavity and is not directly associated
with a joint, is to my knowledge unique and quite
unlike equivalent systems in extant vertebrates,
despite the fact that the proposed function of the
sesamoid is typical of such bones. I propose instead
that sesamoid A was embedded within the tendon of a
pteroid extensor or flexor muscle, and that, as is
generally the case with sesamoids, it was closely
associated with a joint, i.e. the carpopteroid joint.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
42
M. T. WILKINSON
I suggest that the common presence of the bone within
the distal cotyle of the medial carpal is the result of
post-mortem dislocation of the pteroid, which could
have pulled sesamoid A into apparent articulation with
the medial carpal, just as the sesamoids of the human
hand and foot are sometimes pulled into their associated joint capsules by dislocation of the fingers or toes
(Wood, 1984; Del Rossi, 2003). This raises the question
of why such a dislocation of the pteroid is universally
seen in three-dimensionally preserved specimens. One
possibility relates to the fact that the pteroid points
ventrally to some extent throughout its articular
excursion, such that the pteroid tip is always some
distance below the arm. Contact with the substrate
following death would therefore push the tip of the
pteroid dorsally, and could conceivably prise the bone
out of the distal cotyle of the medial carpal. Contraction of the propatagium proximal to the wrist could
bring about the same effect.
I conclude from the above that the pteroid did
articulate in the distal cotyle of the medial carpal, but
I disagree with the prevailing opinion that the pteroid
pointed towards the body, owing to the form of the
corresponding joint surfaces. These are complex
(Fig. 13). The cotyle of the medial carpal is shaped
like a portion of the interior surface of a cone, and if
the medial carpal is oriented such that the cotyle
faces anteroventrally, as I believe is the case, for
reasons given below, the apex of the cone points
lateroventrally. The convex articular surface of the
pteroid is elongated medially, and is similarly asymmetrical, with a broad, subtriangular medial condyle,
and a narrow, roller-like lateral condyle. The head of
the pteroid is offset ventrally from the shaft by 40°.
Further details of pteroid morphology are given by
Unwin et al. (1996).
The following description of the functional morphology of the carpopteroid joint proceeds from the
assumption that the pteroid articulated in the distal
cotyle of the medial carpal. The joint is uniaxial in the
ornithocheirids. Articular movement is illustrated in
Figure 14. At maximum extension (Fig. 14A–C), the
articular head of the pteroid is oriented horizontally,
such that its shaft points anteroventrally, 15° beneath
the horizontal plane. It is this configuration that
defines what I believe to be the correct orientation of
the medial carpal: flipping the medial carpal upside
down, as in Bennett’s (2001, 2006) reconstruction,
causes the pteroid to be directed anterodorsally.
Given that the pteroid supported the propatagium,
this orientation would have given the wing negative
camber: a wholly unfeasible shape. At maximum
extension, a shallow semicircular facet on the dorsal
surface of the pteroid, just distal to the articular head
(Unwin et al., 1996), fits tightly against the upper
part of the articular surface of the medial carpal,
which acts as a bony stop, preventing further elevation. As the joint is flexed, the large medial condyle of
the head of the pteroid slides dorsally around the
medial edge of the articular cotyle of the medial
carpal, whereas the narrow, lateral condyle rolls in
place. If one imagines that the cotyle of the medial
carpal is a portion of the inside of a cone, the articular
head of the pteroid sweeps the surface of this cone,
such that the medial edge circumscribes its base, and
the lateral edge is held in its apex. The 95° range of
flexion is therefore accompanied by a conjunct lateral
rotation of the joint axis by 55°, with the sense being
anticlockwise for the right wrist if viewed from the
front (Fig. 13B). This causes the pteroid to undergo
an arcuate swing, with an initial depression
(Fig. 14D–F), giving way to adduction as the limit of
flexion is approached. At maximum flexion (Fig. 14G–
I), the shaft of the pteroid points ventromedially 25°
beneath the horizontal, and also posteriorly 5° behind
the transverse axis. Further flexion is prevented by
the ventral lip of the articular cotyle of the medial
carpal, which acts as another bony stop.
The above reconstruction of the carpopteroid joint
is controversial, and will be discussed further below,
Figure 13. A, reconstructed articular surfaces of the right carpopteroid joint of Coloborhynchus robustus. Elements are
oriented as in Fig. 7: medial carpal in anterior view and pteroid in posterior view. Scale bar: 25 mm. B, Diagrammatic
representation of (A), showing contact areas in the close-packed position and the joint axis. The axis rotates with respect
to the medial carpal during angulation of the pteroid, and is indicated at maximum extension (ext) and maximum flexion
(flex). For a list of anatomical/arthrological abbreviations, see Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
but for the moment it will be noted that, although a
pure medial orientation of the pteroid (with the shaft
parallel to the transverse axis) is possible, if the
pteroid articulates in the distal cotyle of the medial
carpal, articulating the bones in this way uses only a
fraction of the available joint surfaces, primarily the
medial condyle of the pteroid and the ventral region
of the cotyle of the medial carpal.
Carpometacarpal joint
The carpometacarpal joint is uniaxial, permitting
only long-axis rotation of the wing metacarpal. Rotation occurs about a point a short distance dorsal to
the centre of a tuberculum, located midway along the
medial border of the proximal end of the wing metac-
A
mc
43
arpal, which fits into a deep, well-defined fovea in the
distal syncarpal (Fig. 15A, B). Behind and above the
tuberculum are two shallow facets, separated by a
step-like groove. These facets articulate in a sliding
fashion with corresponding surfaces on the distal
syncarpal. In the close-packed position, when the
articular facets are completely congruent, the tuberculum of the wing metacarpal abuts onto the posterior border of the fovea in the distal syncarpal,
preventing pronation of the metacarpal. From this
position the wing metacarpal can be supinated by 20°,
at which point the step between the facets on the
distal syncarpal locks with the corresponding step on
the distal surface of the wing metacarpal, and the
tuberculum of the metacarpal makes contact with the
D
G
E
H
F
I
pt
ax
ds
B
wm
ds
ul
mc
ra
ps
pt
C
wm
mc
ds
ps
ra
ul
pt
Figure 14. Articular movement of the pteroid. A, lateral view of the right distal syncarpal, medial carpal, and pteroid
of Coloborhynchus robustus, with the carpopteroid joint positioned at maximum extension (pteroid at maximum
elevation), showing the position of the joint axis. The pteroid points forwards and downwards 15° below the horizontal.
B, (A) in dorsal view, also showing the radius, ulna, proximal syncarpal, and wing metacarpal, with all joints in their
respective close-packed positions. C, (A) in anterior view. D, lateral view of the wrist, with the carpopteroid joint partially
flexed (pteroid at maximum depression). The pteroid points downwards 50° below the horizontal. E, dorsal view of (D).
F, anterior view of (D). The pteroid is beginning to swing medially, towards the body. G, Lateral view of the wrist, with
the carpopteroid joint at maximum flexion. H, dorsal view of (G), with the pteroid apparently pointing medially. I, anterior
view of (G), showing the true ventromedial orientation of the pteroid at maximum flexion. The pteroid points downwards
25° below the horizontal. For a list of anatomical/arthrological abbreviations, see Appendix 1.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
44
M. T. WILKINSON
Figure 15. A, reconstructed articular surfaces of the right carpometacarpal joint of Coloborhynchus robustus. Elements
are oriented as in Fig. 7: distal syncarpal in lateral view and wing metacarpal in medial view. Scale bar: 50 mm. B,
diagrammatic representation of (A), showing contact areas in the close-packed position and the joint axis. For a list of
anatomical/arthrological abbreviations, see Appendix 1.
anterior border of the fovea in the distal syncarpal.
Both contacts prevent further supination. The range
of movement estimated here closely matches an estimate made by Bennett (2003) on the basis of pathological concentric grooves, indicating osteoarthritis,
on the articular surfaces of an ornithocheirid distal
syncarpal from the Cambridge Greensand.
As with the intersyncarpal joint, there is some
disagreement as to whether the carpometacarpal joint
was under direct muscular control (Bramwell & Whitfield, 1974; Bennett, 2001) or merely functioned to
absorb sudden transient loads, in this case torsional loads (Padian, 1984). Again, the osteological
evidence cannot categorically support either of these
interpretations.
KNUCKLE
The knuckle joint of pterosaurs has a very characteristic form, often described as ‘pulley-like’. The distal
end of the metacarpal bears two wheel-like condyles
that fit into corresponding cotyles in the first phalanx
of the wing finger (Fig. 16A, B). The ventral condyle is
approximately circular, whereas the dorsal condyle is
slightly elongate in the fore-and-aft direction. The
close-packed position is attained at maximum extension. Hyperextension of the joint is prevented by the
prominent process for the insertion of the wing-finger
extensor tendon. In the extended position, the first
phalanx of the wing finger and the wing metacarpal
make an angle of 180° (Fig. 16C). The joint is
uniaxial, with a flexural range of 160° (Fig. 16C, D).
The joint axis is oriented vertically, and passes
through the centre of curvature of the ventral distal
condyle of the wing metacarpal (Fig. 16B). The wing
finger undergoes a conjunct pronation of 20° over the
full course of flexion, which allows the posterior part
of the dorsal cotyle of the first phalanx to clear the
metacarpal when the limit of flexion is approached
(Fig. 16E, F). During this movement, the dorsal
articular surfaces pull away from each other, whereas
the ventral surfaces remain in close contact. Because
the joint axis remains fixed relative to the ventral
distal condyle of the wing metacarpal, angulation of
the wing finger is cardinal, not arcuate. This interpretation of the knuckle joint agrees very closely with
Bennett’s (2001) description of the knuckle joint of
Pteranodon.
INTERPHALANGEAL
JOINTS
The interphalangeal joints are almost universally
believed to have been immobile, i.e. they were not
under muscular control, but permitted passive deflection. This interpretation results mainly from the
shallow nature of the simple articular surfaces. These
are oval in outline, apart from the surfaces at the
distal end of phalanx 3 and the proximal end of
phalanx 4, which are circular. The distal articular
surfaces of the phalanges are convex; the proximal
surfaces are concave. The articular surfaces of all but
the most distal interphalangeal joint are expanded
posteriorly, which would have increased joint stiffness
in the fore-and-aft direction.
The angles between the life position and reference
position of the first, second, and third interphalangeal
joints (counting from root to tip) are, respectively, 6°,
4°, and 16°, and the corresponding axes about which
this virtual rotation occurs are supinated from the
vertical by 30°, 30°, and 40°. This backward tilt of the
virtual axes means that successive phalanges are
angled backwards and downwards, resulting in an
overall backward sweep and downward curvature of
the wing finger when the other joints of the arm are
in their respective close-packed positions, as several
other workers have noted previously (Short, 1914;
Brower, 1983; Bennett, 2000, 2001).
HIP
The ornithocheirid hip is a standard multiaxial
ball-and-socket joint, permitting elevation/depression,
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
45
Figure 16. A, reconstructed articular surfaces of the right knuckle joint of Coloborhynchus robustus. Elements are
oriented as in Figure 7: wing metacarpal in lateral view and wing-finger phalanx 1 in medial view. Scale bar: 50 mm. B,
diagrammatic representation of (A), showing contact areas in the close-packed position and the joint axis. C, right wing
metacarpal and wing-finger phalanx 1 in the close-packed position in dorsal aspect, viewed along the joint axis. D, Right
wing metacarpal and wing-finger phalanx 1 at maximum flexion in dorsal aspect, viewed along the joint axis, which
remains fixed with respect to the wing metacarpal throughout flexion. E, cross section X–X′ of the wing metacarpal viewed
medially, with the proximal end of wing-finger phalanx 1 behind, and with the knuckle joint at maximum extension. F,
Cross section X–X′ of the wing metacarpal viewed medially, with the proximal end of wing-finger phalanx 1 viewed from
behind, with the knuckle joint at maximum flexion. The broken line indicates the position that wing-finger phalanx 1
would take if no conjunct rotation took place during flexion: this position is impossible, as the posterior part of the
articular head of wing-finger phalanx 1 would overlap the shaft of the wing metacarpal. For a list of anatomical/
arthrological abbreviations, see Appendix 1.
protraction/retraction,
and
supination/pronation
about three mutually perpendicular axes that meet at
the centre of the head of the femur. This head is
nearly hemispherical, but not perfectly so, being
slightly elongate in a direction perpendicular to the
axis of the knee joint (see below). The acetabulum is
similarly elongate, predominantly in the horizontal
direction. Hence, one can define a close-packed orientation of the head of the femur about its long axis,
when it fits most comfortably within the acetabulum.
The primary axis of the hip (the joint axis around
which the greatest range of angulation takes place) is
oriented vertically, whereas the secondary axis (perpendicular to the primary) is oriented horizontally.
Primary angulation is therefore equivalent to
protraction/retraction, and secondary angulation is
equivalent to elevation/depression. Without taking
account of the constraining action of the soft tissues of
the hip, the reconstruction of which is beyond
the scope of this paper, the femoral shaft can be
protracted 40° forward of the transverse axis, and
retracted 70° behind it, and can be depressed
60° beneath the horizontal plane, and elevated 20°
above it.
There has been some disagreement in the literature
as to the habitual orientation of the femur in flight.
Bramwell & Whitfield (1974) and Wellnhofer (1985,
1991b) believed that the femur was usually directed
back from the transverse axis by about 60°. Bennett
(2001) noted that this orientation of the femur is very
close to its limit of retraction, and he argued that
habitually holding the femur at one end of its range
would have restricted its ability to manipulate the
wing membrane. He therefore postulated that the
femur was usually held at a shallower angle from
the transverse axis: between 25° and 30°. When the
femur is so oriented, and additionally held at 20°
below the horizontal, it is in its close-packed position,
and is near the middle of its range of not only
protraction/retraction but also elevation/depression.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
46
M. T. WILKINSON
From this position, the leg would therefore have the
maximum degree of control over the wing: evidence
that this position was habitual. This line of reasoning
presupposes, of course, that the main wing membrane
was attached to the leg. This controversial aspect of
pterosaur reconstruction will be discussed below.
The maximum degree of depression of the femoral
shaft from the horizontal has been the subject of
considerable debate, thanks to the importance of this
aspect of hip functional morphology in discussions of
terrestrial locomotion. The range of depression is
determined by two factors: the orientation of the
acetabulum, which itself depends partly on the orientation of the pelvis on the vertebral column, and the
range of angulation of the femur with respect to the
pelvis. The controversy surrounding the orientation of
the acetabulum has now been largely resolved, at
least for the ornithocheiroids: three-dimensional
pelvic material from the Santana Formation indicates
that the acetabulum was directed posterolaterally
(Bennett, 1990), not dorsolaterally, as suggested by
Wellnhofer (1988). However, there is still some disagreement as to the maximum range of movement of
the femur. As stated above, my estimate of the extent
of femoral depression is 60°, because further angulation causes the head of the femur to begin to slide out
of the acetabulum. I believe it is unlikely that the
area of contact between the femoral head and the hip
socket would be reduced in this way at the very time
when adequate support for the pelvic girdle was most
vital.
Bennett (1997a, b) proposed that the femur could
be depressed much further than 60°, perhaps even
beyond the vertical. This inference was based partly
on the type specimen of Dsungaripterus weii, in
which the femora are preserved in articulation with
the acetabula, and are adducted to such an extreme
degree that their distal ends cross beneath the
pelvis (Bennett, 1997a, 2001). I do not believe that
this specimen provides useful information regarding
this debate, because it only indicates that the bone
geometry of the hip joint permits a very wide range
of depression. This maximum range would have
been reduced in life because of the presence of ligaments and the joint capsule. There are many
instances in which fossil bones are preserved in an
unnatural state of articulation precisely because the
soft tissues of the joints had begun to rot away prior
to burial, and there is no way to show conclusively
that the hip of the type specimen of D. weii is
not one of these cases. A study of a second wellpreserved pelvis and associated femora of a dsungaripterid from Oker, Germany (Upper Jurassic),
indicated that the maximum degree of femoral
depression was only 40°: any more caused disarticulation (Fastnacht, 2005).
Bennett (1997a) also argued that poor joint contact
at the hip would not necessarily have been problematic, citing the human shoulder as an example of a
loose articulation that is stabilized with muscles and
ligaments. This is indeed the case, but the human
shoulder is not usually a weight-bearing joint
(although it may be transiently used for this purpose
by gymnasts, for example). In the vast majority of
the terrestrial tetrapod skeletons I have examined,
weight-bearing joints (specifically, joints where the
weight is borne in compression, not tension as in
brachiating primates) have good articular contact
where the weight is transmitted from body to limb.
In addition, the ornithocheirid hip was clearly not a
loose joint: extensive contact was maintained between
the femoral head and the acetabulum over a wide
range of motion. Furthermore, Fastnacht (2005)
argued that partial displacement of the hip throughout terrestrial locomotion, as proposed by Bennett
(1997a, b), was highly unlikely from a consideration
of the mechanical stability of the joint.
Finally, Bennett (1997a, b, 2001) pointed out that
the pterosaur knee and ankle joints would not have
permitted a significant level of long-axis rotation, and
therefore argued that the hindlimbs must have been
swung back and forth parasagittally, and that
the femora must have been nearly fully depressed
(i.e. erect) in order to do so, as originally proposed by
Padian (1983). I agree that the tibiotarsi would have
moved in parasagittal or near-parasagittal planes, and
that the distal end of the femur would have remained
at an approximately constant distance from the
midline throughout. However, this does not necessarily
require the femora to have been completely erect. Even
with a semi-erect posture, which is more in line with
my estimate of the maximum degree of femoral depression, the hindlimbs could have moved parasagittally
without the need for rotation at the knee or the ankle.
The reasoning is as follows: for sprawling tetrapods,
retraction of the femur is typically coupled with an
equal-magnitude conjunct lateral rotation (technically
supination) of the crus with respect to the pes, such
that the knee axis rotates from an orientation roughly
perpendicular to the direction of motion, to an orientation parallel to the direction of motion (Rewcastle,
1981). If the femur is adducted into a semi-erect
stance, as in many lizards, this conjunct rotation is
reduced in magnitude, and it can theoretically be
eliminated altogether if the femur undergoes an equal
and opposite adjunct medial rotation (Rewcastle,
1981). This holds the knee axis perpendicular to the
direction of travel throughout hindlimb movement,
and no ankle rotation is necessary. Considering the
bones alone, this movement, hence a parasagittal
hindlimb gait, would have been possible for pterosaurs, but further work will be necessary to assess
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
whether the hindlimb muscles were capable of executing the required rotations.
KNEE
The knee is a simple, uniaxial hinge joint. When the
femur is in its close-packed orientation, the knee axis
is oriented vertically. At maximum extension, the
tibiotarsus and femur make an angle of 175°, and the
range of angulation from this position is about 110°.
THREE-DIMENSIONAL CONFIGURATION
OF THE WING
The ornithocheirid joint axes of the right arm and
leg, mapped onto the virtual reconstruction of A.
santanae, are shown in Figure 17 (humeral/femoral
47
long axes and the carpometacarpal axis have been
omitted for clarity). The limbs are arranged along
straight lines projecting from the shoulder and hip:
this is obviously an unrealistic configuration, but is
presented here to show with greater clarity the orientation of the joint axes, without any rotation having
taken place around said axes. Table 3 shows the orientation of each joint axis when projected onto the xz
(sagittal) plane and the yz (vertical frontal) plane
when the limbs are arranged in straight lines, as in
Figure 17, and gives the limits of articular movement
of respective distal elements about each axis. In most
cases, the joint axes lie in planes that are parallel to
the xz plane (sagittal plane). The carpopteroid joint
axis, carpometacarpal axis, and the long axes of the
humerus and femur are the exceptions to this case:
these lie parallel to the y-axis.
Table 3. Orientations of the principal joint axes of the ornithocheirid fore- and hindlimbs when projected in the sagittal
(xz) and vertical frontal (yz) planes, and the range of movement of the respective distal elements about each axis. Axis
orientation angles denote anti-clockwise rotations from the x-axis in lateral view for the xz projection, or anti-clockwise
rotations from the y-axis in anterior view for the yz projection, for the right limbs. An orientation angle is not given where
the projected axis is a single point. Ranges of movement are given with respect to the straight-limbed configuration shown
in Figures 3 and 16. Positive angles denote predominantly backward and/or downward angulation or supination of the
relevant distal element, and negative angles denote forward and/or upward angulation or pronation of the distal element.
Only a single value is given for immobile joints, for which the joint axis is a virtual axis. Angles in parentheses for the
secondary axis of the shoulder (sh2) refer to the range of angulation when the humerus is fully elevated. Movement about
a conjunct rotation axis (crax) is indissociably tied to the angulation about the relevant joint axis, so the articular limits
of the former correspond to those of the latter
Axis orientation
Joint axis
xz projection
yz projection
Range of movement
scno
sh1
sh2
sh3
el
ruc
ruc crax
is
mc
cpt
cpt crax
cm
knu
knu crax
ip1
ip2
ip3
hp1
hp2
hp3
kne
90°
35°
125°
–
70°
150°
–
130°
110°
–
0°
–
90°
–
120°
120°
130°
90°
0°
–
90°
90°
90°
90°
0°
90°
90°
0°
90°
90°
0°
–
0°
90°
0°
90°
90°
90°
90°
–
0°
90°
10°
-70°
-10°
-30°
-20°
5°
0°
0°
-10°
15°
0°
0°
0°
0°
6°
4°
16°
-40°
-20°
?
5°
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
to 25°
(-30°) to 40° (50°)
to 50°
to -110°
to 55°
to 20°
to 25°
to 10°
to 110°
to 55°
to 20°
to 160°
to -20°
to 70°
to 60°
to 115°
48
M. T. WILKINSON
The entire wing, configured with all joints in their
close-packed positions except the knee, is shown
in Figure 18. In this configuration the wingspan
is 4.3 m, which is slightly higher than the 4.15-m
estimate of the wingspan of A. santanae made by
Figure 17. Three-dimensional
virtual
model
of
Anhanguera santanae, showing the positions and orientations of the principal joint axes of the limbs. For a list of
anatomical/arthrological abbreviations, see Appendix 1.
Wellnhofer (1991b). Various outlines of the wing
membranes have been added. Three possible trailing
edges of the cheiropatagium are shown that differ in
their proximal attachment position: at the distal end
of the crus, near the proximal end of the crus, and the
hip. There is now abundant evidence from fossilized
wing membranes and wing membrane impressions
that the trailing edge of the cheiropatagium ran to
the distal end of the crus in a number of unrelated
pterosaur species (Wellnhofer, 1987; Unwin & Bakhurina, 1994; Lu, 2002; Wang et al., 2002; Frey et al.,
2003b). Figure 18 would appear to bear out this
inference: a hip attachment results in an unfeasibly
narrow cheiropatagium, which would give (1) very
high minimum flight speeds owing to the small wing
area, and (2) poor lift : drag ratios, on account of the
large diameter of the wing spar when compared with
the width of the cheiropatagium. The Vienna
specimen of Pterodactylus kochi appears to show the
trailing edge attaching directly to the femur, but
Wellnhofer (1987) has convincingly argued that this
apparent relationship is illusory: if the trailing edge
of the cheiropatagium had indeed attached to the
thigh, one would expect its fossilized impression to
stop short some distance from the femur, because of
the presence in life of the overlying musculature of
the thigh. Wellnhofer (1987) proposed instead that
the trailing edge of the cheiropatagium ran further
down the leg, and that at the time of fossilization the
Figure 18. Three-dimensional virtual model of Anhanguera, with all limb joints in their respective close-packed
positions, except the knee, which is shown partially flexed so that the tibiotarsus is directed backwards. A, ventral view,
with flight membranes. Three possible trailing edges of the cheiropatagium are shown: running from the wingtip to the
distal end of the crus (solid line), the proximal end of the crus (broken line), and the hip (dotted line). Two possible leading
edges of the propatagium are shown, corresponding to an anteroventral orientation of the pteroid (solid line) and a medial
orientation of the pteroid (broken line – pteroid itself omitted in this case for clarity). Two possible trailing edges of the
cruropatagium are shown: running from the tip of the tail to the distal end of the crus (solid line), and to the proximal
end of the crus (broken line). See text for further explanation. B, anterior view, membranes omitted for clarity. For a list
of anatomical/arthrological abbreviations, see Appendix 1. Scale bar: 500 mm.
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3D PTEROSAUR WING SHAPE
most proximal part of the cheiropatagium was folded
underneath the crus, an idea developed further by
Pennycuick (1988). Precisely the same arrangement
is often seen in the folded wings of bats: in dorsal
view, the trailing edge of the plagiopatagium can
appear to run to the thigh, when in reality it runs to
the ankle (Wellnhofer, 1987). Without direct evidence
to the contrary in any pterosaur, it is most parsimonious to conclude that the trailing edge of the cheiropatagium ran at least part-way down the crus in the
ornithocheirids.
Two possible cruropatagium outlines are shown in
Figure 18: the first shows the trailing edge running
from the tail to the ankle, after Unwin (1999); the
second shows the trailing edge running from the
tail, embedded within the cruropatagium, to the
knee joint, after Bennett (2001), who argued that
removing the crura from the cruropatagium in
pterodactyloids would have allowed the membrane
to be more easily manipulated independently of the
legs by the tail (Bennett, 2001). This condition contrasts sharply with that displayed by the ‘rhamphorhynchoid’ Sordes pilosus, in which the tail was free
of the cruropatagium and situated dorsal to it
(Unwin & Bakhurina, 1994). This does not necessarily mean that Bennett’s (2001) reconstruction is
incorrect: within bats there is great variation in the
extent of contact between the tail and the uropatagium, equivalent to the pterosaur cruropatagium
(Hill & Smith, 1984).
Two propatagium outlines are shown in Figure 18,
corresponding to the two prevailing ideas regarding
the orientation of the pteroid discussed above:
forward-pointing and inward-pointing. In both reconstructions, it was assumed that the leading edge of
the propatagium ran from the lower neck, as indicated in the Vienna and Munich specimens of P. kochi
(Broili, 1938; Wellnhofer, 1987), to the knuckle.
In accordance with published reconstructions, a
medially-directed pteroid was assumed to form part of
the leading edge of the propatagium itself, whereas a
forward-pointing pteroid was assumed to intercept
the leading edge only at its tip. These reconstructions
of the propatagium will be discussed further below.
Video sequences showing the possible joint movements of the three-dimensional reconstruction of
A. santanae are available online (see Supporting
Information).
DISCUSSION
The reconstructed three-dimensional geometry of
the ornithocheirid wing presented above enables a
number of inferences to be made about the group,
particularly with regard to aerial and terrestrial
locomotion. Much has been written on this subject
49
(e.g. Hankin & Watson, 1914; Short, 1914; von Kripp,
1943; Bramwell, 1971; Heptonstall, 1971; Bramwell &
Whitfield, 1974; Brower, 1983; Pennycuick, 1988;
Wellnhofer, 1988; Alexander, 1989; Padian & Rayner,
1993; Bennett, 1997a, b; Unwin, 1997; Bennett, 2000,
2001), and in some cases the present study merely
confirms what has previously been supposed. This
discussion will therefore be largely confined to the
presentation of ideas that differ from those of previous accounts, or that clarify areas of disagreement or
uncertainty, and will cover matters arising from the
reconstruction of the pteroid: stability and control in
gliding flight, and terrestrial locomotion. Flapping
flight will not be covered, partly because so little is
known about the wingbeat kinematics, or the material properties of the wing membrane, that only
a cursory discussion can be attempted at present,
but also because the ornithocheirids seem to have
been predominantly adapted for oceanic soaring, on
account of their large size and high aspect ratio wings
(Hankin & Watson, 1914; Bramwell & Whitfield,
1974; Brower, 1983). Furthermore, the inferences
presented about stability and control should not be
regarded as anything more than a working hypothesis
at this stage. Further progress can be made only by
carrying out wind tunnel and flight tests of accurate
scale models, or computational fluid dynamic tests of
accurate virtual models. The three-dimensional geometric data presented here can be regarded as a
necessary first step towards this goal. Only limited
aerodynamic background information is given here.
Further details can be found in, for example, Prandtl
& Tietjens (1957), Simons (1978), Vogel (1981),
Norberg (1990), Barnard & Philpott (1995), and Etkin
& Reid (1996).
THE
PTEROID AND PROPATAGIUM
Three possible reconstructions of the carpopteroid
joint were described above: in the first, the pteroid
points towards the body, and articulates on the
medial side of the medial carpal (Bennett, 2001,
2006); in the second, traditional reconstruction, the
pteroid also points medially, but articulates in the
distal cotyle of the medial carpal (Bramwell & Whitfield, 1974; Padian, 1984; Wellnhofer, 1985, 1991a); in
the third, the pteroid articulates in the distal cotyle of
the medial carpal, but can swing from an anteroventral orientation to a ventromedial orientation (Unwin
et al., 1996; Wilkinson, Unwin & Ellington, 2006).
Although controversial, it is the latter reconstruction
that is preferred here for reasons that were given
above. A forward-pointing orientation of the pteroid
was previously suggested by Hankin (1912), Frey &
Riess (1981), and Pennycuick (1988), but the idea was
treated unfavourably, partly because, in many com-
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50
M. T. WILKINSON
plete, articulated fossils, the pteroid points medially
(Padian, 1984; Wellnhofer, 1985). I suggest that
this orientation is a taphonomic artefact: if the bone
were fully flexed at death, it could easily have been
elevated from its nominal ventromedial orientation to
a fully medial orientation while remaining in contact
with the substrate. As argued above, the same postmortem process, perhaps coupled with contraction of
the propatagium proximal to the wrist, could have
been responsible for the separation of the pteroid
from the distal cotyle of the medial carpal, and the
presence therein of sesamoid A (Bennett, 2006).
In carrying out the full reconstruction of the wing,
shown in Figure 18, I have assumed that the propatagium was attached to the entire length of the
pteroid. It could be argued that this was not necessarily the case. The leading edge of the propatagium
could conceivably have run from the shoulder to the
wrist, excluding the pteroid or part of the pteroid, just
as the bat forewing excludes the thumb. This is
unlikely for two reasons. Firstly, propatagium impressions of articulated fossils, particularly those from the
Solnhofen Limestone, clearly demonstrate its association with the pteroid: the tip of the bone often intercepts the leading edge of the propatagium precisely
(Wellnhofer, 1970; Padian & Rayner, 1993). This
would be most unlikely if there were no physical
connection between the two. Secondly, it is difficult to
envisage a function for the pteroid if it did not
support the propatagium. It is true that bats can use
their thumbs to climb, crawl, handle food, or jump
(Hill & Smith, 1984; Schutt et al., 1997), but this is
only possible because the thumb is clawed and robust:
the slender pteroid would not have been suited to
these activities.
In reconstructing the propatagium associated with
a forward-pointing pteroid, I have assumed that its
leading edge ran distally from the tip of the pteroid to
the knuckle. My reasons for doing so were as follows:
firstly, if the propatagium had not continued beyond
the pteroid there would have been a very abrupt
reduction in the wing chord (the distance between the
leading and trailing edges at the same spanwise
station) at this point. This would have caused the
creation of a longitudinally aligned vortex, of a kind
usually seen only at the wingtips, part-way along the
wing, created by the flow of air around the pteroid
from the high-pressure region beneath the propatagium to the low-pressure region above it. This itself
would have caused an increase in drag and a disruption of the airflow over the cheiropatagium immediately behind the propatagium. Secondly, if there was
no membrane distal to the pteroid, tension in the
propatagium proximal to the pteroid would have
induced a severe bending moment at the carpopteroid
joint, and there is no evidence that the distal cotyle of
the medial carpal was buttressed to resist such
loading. Some authors have argued that there is no
evidence for a propatagial membrane distal to the
wrist, but this claim is incorrect: the ‘Zittel wing’,
assigned to Rhamphorhynchus, from the Solnhofen
Limestone (Upper Jurassic) (von Zittel, 1882), and an
azhdarchoid from the Crato Formation (Lower Cretaceous) of Brazil (Frey & Tischlinger, 2000) both bear
traces of membrane distal to the wrist. The apparent
lack of a distal propatagium in other Solnhofen specimens may be another taphonomic artefact: given that
the pteroid is fully flexed in these fossils, the membrane distal to the wrist would have become tightly
folded against the metacarpus, where it could easily
have been obscured by the skeleton or removed
during preparation. Frey & Riess (1981) argued that
the distal propatagium extended even further along
the wing than shown in Figure 18A, terminating near
the second interphalangeal joint, and enveloping the
short, clawed fingers. However, there is no evidence
for a membrane associated with the fingers, even in
those specimens with good soft-part preservation
(Wellnhofer, 1985, 1987), so a more limited extent is
preferred here. Indeed, extending the propatagium to
the short digits would have had only a minor influence on its shape, given the small size of these digits
in comparison with the pteroid (Fig. 18A). Nevertheless, a greater spanwise extent of the propatagium,
with or without involvement of the clawed digits,
would have led to a reduction in the compressive load,
borne by a forward-pointing pteroid, and may in the
fullness of time prove to be the correct reconstruction.
An additional possibility is that there was a propatagial membrane distal to the wrist that terminated
only part-way along the metacarpus. However,
although the currently available soft tissue fossil evidence is of insufficient quality to identify the exact
spanwise limit of the propatagium, a narrow distal
section is unlikely within the paradigm of a forwardpointing pteroid, because of the concordant increased
compressive loading of the pteroid and the rapid
reduction of the chord, alluded to above. These arguments would not apply if the pteroid was directed
medially.
A comparison of Figure 14A–C and Figure 14G–I,
which show the limits of angulation of the pteroid
presuming it articulated within the distal cotyle of
the medial carpal, appears to indicate that the tip of
the pteroid moves a very substantial distance when
the carpopteroid joint is fully flexed. This would
require rather peculiar material properties of the
propatagium, particularly the leading edge of the
distal propatagium, for the membrane would have to
retain sufficient tension in flight, but also be sufficiently elastic to permit furling. This requirement
could be regarded as evidence against a forward-
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3D PTEROSAUR WING SHAPE
pointing pteroid, for such properties would not be
necessary if the pteroid pointed medially. However,
measurements taken directly from the threedimensional virtual model show that the distance
between the tip of the pteroid and the presumed
distalmost point of the leading edge of the propatagium increases by only 16% when the carpopteroid
joint is flexed from an anteroventral to a ventromedial orientation, i.e. the maximum strain of the
leading edge of the distal propatagium was only 16%.
This figure would be reduced if the maximum range of
flexion of the pteroid were smaller. Nevertheless, it
would still be an important stipulation of this reconstruction that propatagial tension was adjustable,
which could have been realized by the existence of
intrinsic propatagial muscle fibres, although there is
as yet no evidence for such fibres in the propatagium.
In functional terms, the chief difference between
the reconstructions stipulating medially and anteroventrally oriented pteroids is the size of the propatagium. Clearly, it is much larger if the pteroid
points forwards, with important consequences for the
overall wing loading (weight divided by total wing
area), and hence for speed: low wing loading gives
lower gliding speeds. In all three reconstructions the
pteroid would have had some ability to alter the
chordwise camber in the proximal region of the wing
(although this ability would be more definitely
constrained within the forward-pointing paradigm,
because the carpopteroid joint in this case would have
had only a single degree of freedom). Hence, regardless of the reconstruction, the propatagium could have
acted as a control surface for a number of flight
manoeuvres (see below). Additionally, in the forwardpointing reconstruction paradigm, the pteroid can
swing into a ventromedial orientation when fully
flexed. It is possible that this latter state was the
habitual orientation of the pteroid, and that the
anteroventral orientation was only used to increase
wing area, and hence to reduce wing loading during
take-off, landing, or other manoeuvres requiring slow
flight speeds, in a similar way to that proposed by
Pennycuick (1988). Alternatively, the ventromedial
orientation may only have been used to furl the
propatagium when the pterosaur was on the ground.
FLIGHT
STABILITY
Stability is defined here as the tendency to return to
a given flight path, attitude, and velocity without
active control, following a disturbance of one or more
of these factors, e.g. by a gust. It has often been
assumed that all pterodactyloids were inherently
unstable, simply because they lacked any equivalent
of the tailplane or tailfin of a conventional aircraft
(Bramwell & Whitfield, 1974; Brower, 1983) [the situ-
51
ation is somewhat different for the ‘rhamphorhynchoids’, as they possessed long tails furnished with
a vertically-oriented membrane at the tip (Marsh,
1882), but these will not be considered here]. This
makes some sense from an evolutionary perspective:
stability opposes control, so a high degree of manoeuvrability and a high degree of stability are mutually
exclusive (Maynard Smith, 1952; Thomas & Taylor,
2001). The means of acquiring stability also tend to
incur a drag cost, and can therefore reduce an
aircraft’s aerodynamic efficiency (Thomas & Taylor,
2001) and maximum lift (Maynard Smith, 1952).
However, tailless aircraft can be made to fly stably
without active control (Weyl, 1945; Pennycuick,
1971a; Nickel & Wolfahrt, 1994), and the same may
have been true of the pterodactyloids. Furthermore,
pterodactyloids may not have required a high degree
of manoeuvrability, and the neurological and
mechanical costs of the continuous maintenance of a
given flight attitude may have outweighed the drag
saving associated with instability. Clearly, these
cursory arguments are insufficient for providing any
kind of understanding of stability in pterosaurs.
A thorough assessment would require a complete
dynamic analysis, which is beyond the scope of this
paper. However, a qualitative appraisal of the 3D
shape of the ornithocheirid wing does allow a number
of important conclusions to be drawn. This section
will only consider the stability of certain fixed-wing
configurations, mainly the fully extended configuration shown in Figure 18: wing adjustments will be
considered under flight control below.
Pitch stability
Pitch (longitudinal) stability is usually achieved by
situating the centre of gravity (c.g.) ahead of the
mean aerodynamic centre (m.a.c.) – this being the
point through which the aerodynamic forces are conventionally taken to act; it usually lies roughly a
quarter of the length of the mean chord from its
anterior extent (Fig. 19A). The reasoning is simple to
understand: a pitching motion in the nose-up sense
(a positive moment) increases the angle of attack, and
therefore increases the lift. Because this lift acts
behind the centre of gravity, the result is a nose-down
(negative) moment that restores the original attitude.
Technically, this is static pitch stability: the restoring
moment may cause the aircraft to overshoot its original attitude, leading to an oscillating motion that,
if insufficiently damped, will render the aircraft
dynamically unstable. Dynamic stability will not be
considered here. For a statically unstable aircraft, the
c.g. usually lies behind the m.a.c. The increased angle
of attack caused by a nose-up disturbance therefore increases the pitching moment. Without active
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52
M. T. WILKINSON
wing lift
A
A
weight
B
wing lift
tail lift
weight
Figure 19. A, Stable but unbalanced wing profile, with
the centre of gravity (c.g.) situated ahead of the mean
aerodynamic centre (m.a.c.). B, stable and balanced configuration, with a small tailplane set at a negative incidence with respect to the main wing.
control, the aircraft would diverge from its original
attitude, and flight would be impossible.
Although placing the c.g. ahead of the m.a.c.
renders an aircraft statically stable, this is not in
itself sufficient for flight. This is because positive lift
in this case always gives rise to a nose-down pitching
moment about the c.g. In fact, positively cambered
wings (convex surface upwards) are inherently unbalanced: they always generate a nose-down pitching
moment about the aerodynamic centre, regardless
of the angle of attack (e.g. Simons, 1978; Nickel
& Wolfahrt, 1994; Barnard & Philpott, 1995; Etkin
& Reid, 1996; Thomas & Taylor, 2001). For these
reasons, conventional stable aircraft typically require
a second lifting surface to generate a nose-up moment
to compensate. A small tailplane is the most common
type. Being situated behind the main wing, the tailplane must generate negative lift to provide balance,
and it is therefore set at a negative angle of attack,
with respect to the main wing (Fig. 19B). The tailplane decreases the overall lift of an aircraft, but
increases its drag; hence, aerodynamic efficiency is
diminished in this case. In unstable aircraft, the
nose-down moment of the cambered wings can be
balanced by the aft position of the c.g. with respect to
the m.a.c. In this case the lift provides a balancing
nose-up moment directly.
There are a number of ways in which a stable
tailless aircraft can be made to generate a balancing
B
Figure 20. Methods of achieving longitudinal balance
and positive stability without a tail. A, sweepback coupled
with washout. The aft-situated tips are at a negative
incidence with respect to the forward-situated wing root.
B, reflex camber.
nose-up pitching moment. If the wings are twisted
such that the angle of attack of each wing decreases
from root to tip – a geometry known as washout –
and are additionally swept back, the aft-situated
wingtips can fulfil the balancing function of the tailplane (Fig. 20A). The same effect can be achieved by
sweeping the wings forward and twisting them so
that the angle of attack increases from root to tip –
a geometry known as washin. Alternatively, the
wings can be reflex cambered, i.e. deflected upwards
near the trailing edge (Fig. 20B), which reduces the
magnitude of the inherent nose-down moment
about the m.a.c. Evidence of these features in ornithocheirid wings could indicate that they were statically stable in pitch, whereas their absence would
suggest static instability.
It is impossible to tell directly whether or not
the ornithocheirid wings were reflex cambered. The
distal region of bat wings have been observed to be
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3D PTEROSAUR WING SHAPE
upturned near the trailing edge in gliding flight (Pennycuick, 1971a), but this is due to upward deflection
of the fourth and fifth digits, for which there is no
analogue in pterosaur wings. However, bats can also
facultatively reflex the inner panel of the wing membrane (the plagiopatagium) by contracting longitudinally arranged muscles there (Pennycuick, 1971a). It
is possible that pterosaurs could do the same thing,
for there is tentative evidence of muscles within the
cheiropatagium (Frey & Tischlinger, 2000; Frey et al.,
2003b). It is unlikely, however, that the wings were
habitually reflex cambered, simply because the lift in
this case would have been substantially reduced relative to that generated by positively-cambered wings
of the same area. Hence, a larger area would be
required to generate the same lift, which would also
increase the drag and diminish the lift : drag ratio
(Thomas & Taylor, 2001).
Another way that static pitch stability could have
been achieved was by using sweepback coupled with
washout or sweepforward coupled with washin. It is
most likely that the second of these options would not
have been feasible, for there is no doubt that the
pterosaur cheiropatagium was twisted in a nose-down
sense from root to tip in flight: the aerodynamic load
would have lifted the flexible trailing edge of the
cheiropatagium until it was balanced by its spanwise
tension. Furthermore, as Brower (1983) pointed out,
this geometry would have been important for safe
flight, because without it the tapered shape of the
wings would have caused the aerodynamic angle of
attack to increase from root to tip, thereby increasing
the likelihood of a potentially dangerous tip stall (e.g.
Simons, 1978; Marchaj, 1988; Chatterjee & Templin,
2004). Pitch stability in the ornithocheirids would
therefore have depended on the wings being sufficiently swept back. Having said this, depression of
the propatagium by the pteroid, if possible, would
have reduced the angle of attack of the proximal part
of the wing, and could therefore have conceivably
caused washin, although this effect may have been
cancelled out by the washout of the cheiropatagium.
However, it is most unlikely that a strongly deflected
propatagium was used habitually, as deflection of a
leading edge flap at the relatively low angles of attack
associated with cruising flight would have caused
substantial leading-edge flow separation on the lower
surface of the wing (Fullmer, 1947; Wilkinson et al.,
2006).
In the fully extended configuration depicted in
Figure 18, the wing is slightly swept forward, which
suggests pitch instability, based on the reasoning
given above. However, it must be remembered that
Figure 18 represents only one possible wing configuration that may not have been habitual. In fact, the
knuckle joint could certainly not have been extended
53
to its full limit in flight, for the drag force acting on
the wing finger would have caused some passive
flexion. The greater the typical degree of flexion, the
more likely it is that the ornithocheirids were habitually stable in pitch. I am of the opinion that the usual
degree of knuckle flexion in flight was quite small,
because the habitual position of a joint is usually very
near its close-packed position (Williams et al., 1989),
which is the position of full extension in this case.
This would give only a small degree of sweepback, if
any, which would require a rather extreme washout to
achieve balance with stability. As with reflex camber,
I believe that such a geometry would have compromised aerodynamic efficiency to an unacceptable
level.
The evidence therefore tentatively suggests that
ornithocheirids were habitually unstable in pitch,
which has a number of consequences for flight control
(see below). Further work could assess whether estimates of the relative positions of the c.g. and m.a.c.
support this statement: the prediction is that the
m.a.c. was usually located in front of the c.g. (movements of the wings fore and aft could of course alter
the relative positions of these points: such adjustments are discussed further below). It should be
noted, however, that the inference that the ornithocheirids were unstable in pitch is based purely on
a geometric consideration of the wing as a rigid structure. This is clearly an oversimplification: the pterosaur patagia were complex composite membranes.
The limited literature on the stability of such wings
indicates that compliance enhances pitch stability
without the usual trade-off with aerodynamic efficiency (Fink, 1969; Sneyd, Bundock & Reid, 1982;
Sneyd, 1984; Krus, 1997). Assessing the degree to
which this effect applied to pterosaurs would require
a coupled analysis of membrane mechanics and fluid
flow. Such an analysis is beyond the scope of this
paper. The remainder of this discussion will follow
from the assumption that the ornithocheirids were
habitually unstable in pitch.
Roll stability
Roll stability is generally obtained using dihedral: an
upward tilt of the wings about the longitudinal axis.
When an aircraft or flying animal with this geometry
is disturbed about the roll axis, an opposing moment
is generated that restores a level attitude (e.g.
Simons, 1978; Nickel & Wolfahrt, 1994; Barnard &
Philpott, 1995; Etkin & Reid, 1996; Thomas & Taylor,
2001). The anterior view of the extended configuration (Fig. 18B) shows that the dihedral angle was
negative if the joints were in their respective closepacked positions: the wings exhibit a downward
deflection or anhedral, which would reinforce a roll
disturbance. By this criterion, one would conclude
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54
M. T. WILKINSON
that the ornithocheirids were unstable about the roll
axis when in this configuration. However, Figure 18B
shows the wings in an unloaded condition. The dorsoventral stiffness of the wing spar is unknown, but it
is likely that an aerodynamic load would cause an
upward deflection of the distal wing-finger phalanges
about the interphalangeal joints, particularly
given the lack of any dorsoventral buttressing of
these joints. A pronouncement regarding roll stability
should therefore be postponed until a mechanical
analysis of the wing spar is carried out. Elevating or
depressing the wings using primary angulation of the
shoulder could, of course, have been used to increase
or decrease dihedral and roll stability in a facultative
manner. Sweeping the wings back could also have
conferred roll stability (e.g. Weyl, 1945; Nickel &
Wolfahrt, 1994; Barnard & Philpott, 1995; Thomas &
Taylor, 2001).
Yaw stability
Yaw stability is conventionally provided by situating
a vertical tailfin some distance behind the c.g. A yaw
in one direction inclines the fin with respect to the
airflow, such that it generates an opposing moment
about the c.g., restoring the original attitude. Neither
the ornithocheirids nor any other pterodactyloids had
such a surface. The head may have acted in a similar
way to a fin (this would certainly have been the case
for elaborately crested forms), but because it was
situated ahead of the c.g., a sideforce produced in
response to a yaw would have been destabilizing.
A second means of achieving yaw stability is to
deflect the wingtips downward about an oblique axis,
so that they act in a similar way to wingtip fins (Weyl,
1945; Pennycuick, 1971a). These so-called diffuser
wingtips can generate small sideforces to oppose a
yaw disturbance. The washout of the cheiropatagium
would have given a similar geometry, and the greater
the degree of twist in the membrane, the more
significant this effect would have been. In terms of
performance, however, an excessively twisted membrane would have been disadvantageous, and for this
reason the diffuser wingtip effect may not have
been important. In addition, the effect would have
depended on there being only a small degree of
aeroelastic deflection of the distal wing finger, which
may not have been the case.
FLIGHT
CONTROL
The extended configuration shown in Figure 18 represents only one of many possible wing configurations
that would have been used during gliding or soaring
flight to turn, adjust the flight speed, or change the
angle of descent. Additionally, adjustments would
have been required in order to respond to routine
changes of mass, and the position of the centre of
mass, such as those caused by feeding. Furthermore,
given that the ornithocheirids were probably unstable
in pitch and yaw, any such deviation caused by an
atmospheric disturbance would have to have been
corrected actively. The following section will describe
the basic requirements for flight control, and examine
how these requirements may have been realized by
the ornithocheirids, given the geometric constraints of
their wing skeleton.
Speed/pitch control
During steady (i.e. equilibrium) flight, the weight
must be balanced by the total aerodynamic force
produced by the wings and tailplane (if present). To a
first approximation, the magnitude of the resultant
aerodynamic force of the wings depends on their
angle of attack, camber, and area, and also on the
relative airspeed. Hence, by altering one or more of
the wing configuration factors symmetrically (i.e.
identically for both wings), a new equilibrium will be
assumed with an aerodynamic force of the same magnitude, but at a different speed. A discussion of speed
control in the ornithocheirids is therefore a discussion
of how wing camber, area, and angle of attack could
be altered in order to establish a new equilibrium.
The equilibrium angle of attack – i.e. the angle of
attack at which the overall pitching moment about
the c.g. is zero – essentially depends on two factors:
the pitching moment when the lift is zero, M0, and the
change in pitching moment with angle of attack,
dM/da. Stability requires that dM/da must be negative, and hence M0 must be positive (nose up) for M to
be zero at a positive angle of attack; when unstable,
dM/da is positive and M0 must be negative (nose
down) to balance at a positive angle of attack
(Fig. 21A). The sign and magnitude of dM/da depends
on the separation of the c.g. and m.a.c.: it increases as
the m.a.c. moves forwards with respect to the c.g., and
is positive if the m.a.c. lies ahead of the c.g. (dM/da
also depends on the flexibility of the wing, but this
phenomenon will not be considered here). M0 depends
partly on wing camber: as camber increases, M0
decreases, i.e. becomes increasingly negative, as a
result of the increased inherent nose-down moment of
the wing profile. Conversely, M0 is increased by the
addition of a negative-incidence tail, washout with
sweepback, etc. The stability paradigm has a profound influence on pitch control, as the following
example will illustrate. For conventional, stable
aircraft, the equilibrium angle of attack is usually
increased by raising the elevators, situated on the
tailplane, which increases M0, thereby causing a
nose-up pitching moment that brings the aircraft to
the new equilibrium (Fig. 21B). For unstable aircraft,
raising the elevators still increases M0, but this
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3D PTEROSAUR WING SHAPE
A
A
M
unstable
55
M
1
2
α
α
stable
B
B
M
M
2
1
1
α
C
M
2
1
α
Figure 21. A, typical plots of pitching moment M against
angle of attack a (measured with respect to the zero-lift
angle of attack) for stable and unstable aircraft. Both
aircraft are shown balancing at the same equilibrium
angle of attack, at which point the pitching moment is
zero. B, the effect of raising the elevators (1) on the
longitudinal balance of a stable aircraft: the pitching
moment is increased, as is the equilibrium angle of attack,
so the aircraft pitches up (2) until equilibrium is restored.
C, the effect of raising the elevators (1) on the longitudinal
balance of an unstable aircraft: the pitching moment is
increased, but the equilibrium angle of attack is reduced,
so the aircraft now pitches up away from equilibrium (2).
causes a decrease in the equilibrium angle of attack,
giving rise to a nose-up moment (Fig. 21C): a new
equilibrium is set, but cannot be reached using the
elevators alone.
For the ornithocheirids, the equilibrium angle of
attack could have been adjusted by shifting the m.a.c.
with respect to the c.g., which would have altered
dM/da, or by changing the camber of the wings, which
would have altered M0. For example, sweeping the
wings backwards would have decreased dM/da
(Fig. 22A), and increasing the camber would have
decreased M0 (Fig. 22B). The situation is actually
2
α
Figure 22. Increasing the equilibrium angle of attack of
an unstable aircraft can be brought about by decreasing
the derivative dM/da, where M is the pitching moment
and a is the angle of attack, by sweeping the wings back
(A), or by decreasing the zero-lift pitching moment M0, by
depressing the pteroids for example (B). These adjustments can theoretically be used in response to an unstable
nose-up pitch (1), thus establishing a new equilibrium (2).
more complicated than this thanks to the washout of
the wings: sweeping the twisted wings backwards
would increase M0 as well as decrease dM/da; also,
the magnitude of twist itself may have been affected
by the sweep, camber, and camber distribution, but
these effects will not be considered yet. Assuming
pitch instability, a decrease in dM/da and M0 would
have increased the equilibrium angle of attack, as
shown in Figure 22. However, neither would have
brought the pterosaur to the new equilibrium – in
fact, both would have given rise to a nose-down
moment. In order to pitch up, the wings could have
been swept forwards, but this would have led to a
decrease in the equilibrium angle of attack, and a
consequent loss of balance (this could have been
useful for certain transitory manoeuvres, such as
landing, but would have been inappropriate for
steady flight). Alternatively, the angle of attack of the
wings could have been increased directly. This direct
control of the angle of attack would not be effective in
a stable paradigm, for any increase in the angle of
attack would be followed by a nose-down pitch: only
when unstable does an increased angle of attack
increase the pitching moment.
In birds and bats, the angle of attack of the entire
wings can be adjusted by pronation or supination at
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56
M. T. WILKINSON
the shoulder. This is only possible, however, because
there are rigid beams cantilevered on the wing spar
that run aft to the trailing edge, these being the
elongate fourth and fifth digits in bats, and the
feather shafts of birds. Pterosaur wings possessed no
such structures. There was a system of fine structural
fibres (actinofibrils) within the distal cheiropatagium
that radiated in a posterodistal pattern, but these did
not attach to the wing spar, and had insufficient
bending stiffness to act as cantilevers (Bennett, 2000).
Nevertheless, because the wing finger is curved backwards, supination at either the shoulder or the carpometacarpal joint (if possible) would have caused
depression of the trailing edge near the wingtip, and
would therefore increase the angle of attack there.
The magnitude of this effect, and the extent to which
it propagated towards the root, would have depended
on the stiffness and tension of the actinopatagium,
the latter being controllable to an extent through
wing retraction.
Another means of altering the angle of attack
was elevation and depression of the leg at the hip
(Fig. 23A, B). This may only have affected the inner
wing: given the high aspect ratio, the actinopatagium
may have been too remote to be controlled in this
fashion. If the trailing edge of the cheiropatagium ran
to the ankle, the angle of attack of the inner wing
could also have been adjusted by pronation and supination of the femur (Fig. 23A, C), because these movements would have elevated and depressed the distal
end of the tibiotarsus, respectively. Because the tibiotarsus projects backwards further than the femur,
this would have had a more significant effect on the
angle of attack than femoral elevation or depression.
Interestingly, pterosaurs appear to have had almost
independent control of the angle of attack of the
proximal and distal regions of the wings: the legs
could have controlled the former, whereas pronation
or supination of either the entire wing spar or the
wing finger and metacarpus would have controlled
the latter.
Directly altering the angle of attack of the wings
would have resulted in a loss of balance in an
unstable paradigm, and its restoration would have
Figure 23. Methods of changing the angle of attack of the inner wing. A, left lateral view of Anhanguera configured as
in Fig. 18. The broken line indicates the chord line. The angle of attack of the section is zero. B, as in (A), but with the
left leg depressed at the hip by 30°. The geometric angle of attack a is indicated. C, as in (A), but with the leg supinated
at the hip by 30°. The leg movements shown in (B) and (C) increase both the angle of attack and the camber of the inner
wing.
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3D PTEROSAUR WING SHAPE
depended upon the establishment of a new equilibrium angle of attack. The pitch derivative dM/da
could have been decreased to increase the equilibrium
angle of attack in response to a nose-up pitch by
sweeping the wings backwards (Fig. 22A), using secondary angulation at the shoulder or flexion at the
intersyncarpal joint or knuckle, perhaps coupled with
a compensatory retraction of the leg to preserve membrane tension. The opposite movements could have
decreased the equilibrium angle of attack in response
to a nose-down pitch. However, a cautionary note
should be sounded, because, as mentioned above, the
washout of the wings complicates matters considerably: a backward sweep increases M0, whereas a
forward sweep decreases M0, which would have had
the opposite effect on the equilibrium angle of attack
to the corresponding changes in dM/da. Furthermore,
sweeping the wings back may have increased the
washout resulting from a reduction of spanwise
tension that, if uncompensated for, would have
increased M0 still further. Without quantitative windtunnel data, it is therefore very difficult to predict the
net effect of sweeping the wings backwards or forwards, but the use of these movements in the way
just described is counter-intuitive. One would expect
a protraction of the wings to be used to pitch up
(albeit in an unbalanced fashion), and not to respond
to a pitch down.
Alternatively, M0 could have been decreased in
order to establish a higher angle of attack in
response to a pitch up (Fig. 22B), by depressing the
cruropatagium using the tail and/or increasing the
camber of the wings. Conveniently, this would also
have increased the maximum lift, thereby contributing directly to the speed reduction brought about by
the increased equilibrium angle of attack. A camber
57
increase would in fact have occurred automatically if
depression of the legs were used to increase the angle
of attack, because the leading edge was fixed by
the presence of the propatagium (Fig. 23B, C). An
increase in wing camber could also have been readily
achieved by depressing the pteroid at the carpopteroid joint (Fig. 24). It is important to bear in
mind that this movement would not only have
increased the camber: the accompanying depression
of the leading edge of the inner wing with respect to
its trailing edge would also have decreased its angle
of attack relative to the incoming airflow (Fig. 24B).
By this token, one might presume that depressing
the pteroid alone was not an effective means of
reducing speed. However, the increased camber
caused by pteroid depression would also have
decreased the zero-lift angle of attack: hence the
effective angle of attack, measured relative to the
zero-lift angle, might have been increased by this
movement (a more rigorous analysis is required to
say for sure, but this is beyond the scope of the
present work). The possibility also exists that the
increased drag force associated with deflection of the
propatagium could have caused a nose-up moment, if
it acted above the c.g. Nevertheless, control authority
would doubtless have been improved if pteroid
depression were coupled with or preceded by leg
depression. As a further complicating factor, propatagium deflection alone would have decreased the
washout of the wing, for the resulting decrease in
the angle of attack would only have occurred in the
proximal part of the wing, because the propatagium
was absent from the distal part. It is possible,
however, that the accompanying leg depression,
which would have increased the angle of attack of the
proximal part of the wing, negated this effect.
A
B
α
Figure 24. Effects of pteroid depression. A, left lateral view of Anhanguera as in Fig. 23. B, as in (A), but with the left
pteroid depressed by 30°. The camber is increased and the angle of attack, a, is reduced by this movement.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
58
M. T. WILKINSON
Camber may also have been increased by retracting
the femur, as suggested by Bennett (2000), and/or
flexing the tibiotarsus (if the cheiropatagium ran to
the crus). Both of these movements would have
shifted the rear proximal margin of the cheiropatagium medially. The distance between the hip and
the wingtip would, however, have remained constant
(assuming, for the sake of simplicity, no other wing
adjustments took place): hence, the spanwise strain
would have increased from the mid-chord region to
the trailing edge. Because the increased spanwise
tension would have been largely limited to the posterior part of the cheiropatagium, the result would have
been a decreased washout and increased camber [this
latter point was not noted by Short (1914), who
believed that leg retraction would have decreased the
camber]. However, the reduced washout may also
have increased the risk of tip stall, because tapered,
untwisted wings exhibit a spanwise increase in the
effective angle of attack caused by diminished downwash at the tips. Hence, this method of camber
control may not have been used. It is more likely that
leg retraction and protraction were used in a compensatory manner in response to secondary angulation at
the shoulder, as described above.
Flight speed could have been increased by flexing
the elbow, wrist, and knuckle to reduce the area of the
wings. Such an adjustment has been documented in
birds (Pennycuick, 1960, 1988; Parrott, 1970; Tucker
& Parrott, 1970; Pennycuick, 1971b; McGahan, 1973;
Tucker & Heine, 1990; Rosén & Hedenström, 2001)
and bats (Pennycuick, 1971a), but the degree to which
it could have been used by pterosaurs is uncertain. In
birds, wing flexion is straightforward because the
feathers can overlap; hence, a significant reduction in
area is possible with no disruption of the flight
surface. Bats cannot flex their wings to the same
degree in flight (Pennycuick, 1971a), because the
elastic wing membranes would slacken and flutter,
making flight impossible, or at least very inefficient.
Hence, the minimum wingspan in flight is no less
than about 85% of the maximum (Pennycuick, 1971a).
Without the additional membrane-supporting digits
of bat wings, it is logical to conclude that pterosaurs
were even more restricted in this regard, although the
stiffening actinofibrils, acting in conjunction with the
contraction of intrinsic membrane muscles, may have
offered some scope for wing flexion (Bennett, 2000).
However, it is unlikely that the maximum degree of
wing retraction in pterosaurs was greater than that
in bats, for the reasons given above. I therefore
regard the bat limit of 85% as a minimum estimate of
the ornithocheirid limit. Flexion of the elbow, radioulnocarpal, and knuckle joints all by 25° brings the
wingspan to this value (Fig. 25).
It has been suggested that the pteroid (on the
assumption that it articulated in the distal cotyle
of the medial carpal) could ‘snap’ from a medial
orientation to an anteroventral orientation, thereby
transforming the wing from a shallow-cambered,
small-area state to a deep-cambered, large-area state
(Pennycuick, 1988). This switch would have instantly
changed the wing from a high-speed to a low-speed
configuration. However, this adjustment is not supported by the fossil evidence. As stated above, when
fully flexed (and articulating in the distal cotyle of the
medial carpal) the pteroid points ventromedially, not
medially. The pteroid must first be disarticulated to
permit a medial orientation. Therefore, this rather
abrupt form of speed control could not have been
used.
To summarize, an increase in speed could have
been brought about by elevating the legs and pronating the wing spar at the shoulder, and/or carpometacarpal joint, to decrease the angle of attack, and by
raising the pteroid to decrease the camber of the
wings – an effect augmented by the elevated legs – to
establish a new equilibrium. Alternatively, or additionally, the wing area could have been reduced by
flexion at the elbow, wrist, and knuckle. Sweeping the
Figure 25. Ventral view of Anhanguera, with the elbow, radioulnocarpal, and knuckle joints flexed by 25° from their
close-packed positions. The wingspan is 85% of the maximum. Scale bar: 500 mm.
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3D PTEROSAUR WING SHAPE
wings backwards would have caused a nose-down
moment and a concordant increase in speed, but in an
unbalanced fashion, unless the decrease in dM/da
caused by the sweep-back alone was more than compensated by an increase in M0 caused by the sweepback plus washout, or decreased camber. A decrease
in speed was probably effected by lowering the legs
and cruropatagium (using the tail), supinating the
wing, and depressing the pteroid. Sweeping the wings
forwards would have caused a nose-up moment, but,
again, balance would have been lost unless M0 was
decreased to compensate.
When coming in to land, the angle of attack must
have been very high, because the legs would have been
held quite far below the wing spar in order to contact
the ground (Fig. 26). At such a time, the pteroid
(assuming it articulated with the distal cotyle of the
medial carpal) could have been depressed to align the
propatagium with the airflow, like a leading edge flap.
Wind-tunnel tests of model wing profiles that incorporated a broad propatagium demonstrated that the
angle of attack at which stalling took place could be
increased by this means (Wilkinson et al., 2006). As a
result, the maximum lift coefficient (the lift force
standardized with respect to relative air velocity and
wing area) was greatly increased, which, coupled with
the increased area of the broad propatagium, would
have substantially reduced the pterosaur’s minimum
flight speed. The high-lift effect associated with a
forward-pointing pteroid may have been important in
facilitating landing in giant pterosaurs. It should be
noted that the wind-tunnel model from which high lift
coefficients were obtained, some 45% higher than for a
model without a propatagium, was not a model of the
Figure 26. Left lateral view of Anhanguera in a possible
landing configuration. The body is pitched up by 20°, the
femur is supinated by 30° and depressed by 30°, and the
pteroid is depressed by 30°. The geometric angle of attack
of the wing section is 40°.
59
entire wing, but of a cross section taken between the
wrist and knuckle (Wilkinson et al., 2006). Nevertheless, the high-lift effect would still have been significant for the complete wing, because, as explained
above, the propatagium probably extended from the
wing root to the knuckle, a region of the wing that, in
ornithocheirids, represented over half its projected
wing area (Wilkinson, 2002).
The wind-tunnel tests described above also indicated that the drag coefficient was very high when in
a landing configuration (Wilkinson et al., 2006), but
this would have been a distinct advantage, as the
high drag would have decelerated the pterosaur and
steepened the approach path, thereby allowing a
safer, more controlled touchdown. Indeed, it is known
that vultures lower their legs when coming in to land
for precisely this purpose (Pennycuick, 1971c; Tucker,
1988). Essentially, the forward-pointing pteroid, if
achievable, would have enabled the propatagium to
act not only as a very effective leading-edge flap, but
also as an air brake.
The need to attain very high angles of attack when
landing is perhaps the most persuasive argument
against inherent pitch stability in the ornithocheirids,
and possibly in all pterodactyloid pterosaurs. If
stable, any attempt to lower the legs directly without
other adjustments would have led to an immediate
nose-down pitch, so an alternative means of increasing the equilibrium angle of attack would have been
required. Increasing the camber of the wings would
have been useless (in fact, detrimental) for this
purpose, as the resulting decrease in M0 would have
caused the equilibrium angle of attack to decrease in
a stable paradigm. Given sufficient washout, sweeping the wings far back may have been helpful, as this
adjustment would have increased M0, and with it the
equilibrium angle of attack, but it would also have
decreased dM/da, which would have had the opposite
effect. The substantial washout would also have compromised lift production. Finally, one might suppose
that the cruropatagium and tail could have been used
as an elevator. According to Bennett (2001), the tail
was embedded within the cruropatagium, and so
could indeed have elevated the membrane to increase
M0, although the control authority of this small membrane, situated as it was very close to the c.g. and in
the wake of the body, cannot have been great. If, in
contrast to Bennett (2001), the tail was not embedded
within the cruropatagium, but instead lay dorsal to it,
as in the ‘rhamphorhynchoid’ S. pilosus (Unwin &
Bakhurina, 1994), the tail could only have been used
to lower the membrane, and thus decrease M0.
Roll control
In order to turn in flight, the wings must be banked
so that the lift has a horizontal component to provide
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60
M. T. WILKINSON
the required centripetal force. The animal must
therefore roll in the direction of the turn until the
correct angle of bank is attained. This could have
been achieved in the ornithocheirids by increasing the
lift of the outside wing by depressing the leg, supinating the wing at the shoulder and/or carpometacarpal joint (if possible), and depressing the pteroid
(if possible), and/or decreasing the lift of the inside
wing by elevating the leg, pronating the wing, or
flexing the elbow, wrist, and knuckle, as described
above. The most effective means of generating a large
rolling moment would have been by using the distal
parts of the wings, as these were furthest from the
c.g. Hence, the carpometacarpal joint, which could
have pronated or supinated the outer wing largely
independently of the inner wing, may have been particularly useful for this purpose.
Yaw control
Yawing rotations are not usually required for the
direct initiation of a turn: as described above, a
change of direction in flight is always preceded by a
roll, unless manoeuvring very close to the ground or
water, when banking could cause one wing to collide
with the surface. Yaw control is still important for
normal turning flight, however, because roll and yaw
are coupled, and any undesirable yaw movements
caused by a roll (adverse yaw) would need to have
been corrected. Specifically, the increased lift of the
ascending wing would have been accompanied by an
increased drag on the same wing, which if uncorrected would have caused the pterosaur to yaw in the
opposite direction to the roll.
There are two ways by which an ornithocheirid
pterosaur could have produced a yaw moment: by
turning its head or increasing the drag of one wing
with respect to the other. Even though the ornithocheirids lacked the bizarre sail-like crests of some
Cretaceous pterosaurs (Frey & Tischlinger, 2000;
Frey et al., 2003b), their heads would still have produced significant sideforces when inclined to the
flight path, as suggested by Bramwell & Whitfield
(1974). Because the head was situated ahead of the
c.g., turning it to the left would have caused a yaw to
the left. Hence, a pterosaur may have been able to
correct an adverse yaw during a roll simply by looking
where it was going. Failing this, a yaw moment could
have been produced by carefully manipulating the
angle of attack and camber of the proximal wing in
opposite directions using the leg and pteroid, which
could conceivably have caused the lift on the downgoing wing to be held constant but the drag to
be increased. Alternatively, if a roll were initiated
by retraction of one wing at the elbow, wrist,
and knuckle to decrease its lift, the accompanying
decrease in spanwise tension would, if left uncompen-
sated, have increased the drag of the same wing
through increased twist, and maybe even aeroelastic
flutter. In this latter case, adverse yaw would
have been immediately addressed without additional
control movements.
TERRESTRIAL
LOCOMOTION
The way pterosaurs moved on the ground has been
one of the most contentious aspects of their palaeobiology for many years (e.g. Padian, 1983; Wellnhofer,
1988; Padian, 1991; Bennett, 1997a, b; Unwin, 1997;
Bennett, 2001). We are now approaching a consensus
with regard to the terrestrial locomotion of smaller
pterodactyloids, thanks mainly to the discovery of
many well-preserved trackways, assigned to the ichnogenus Pteraichnus, that are stratigraphically and
morphologically consistent with this kind of pterosaur
(Stokes, 1957; Lockley et al., 1995; Mazin et al., 1995,
1997, 2003; Bennett, 1997b; Unwin, 1997). These
show that the pterosaur trackmakers were quadrupeds with plantigrade pedes, digitigrade manus, and
erect/semi-erect hindlimbs.
Unfortunately, the track record for large pterodactyloids is much less extensive than that for the
smaller forms. The best-preserved traces, from the
Purbeck Limestone Formation (Lower Cretaceous) of
southwestern England (Wright et al., 1997) and the
Uhangri Formation (Upper Cretaceous) of southwestern Korea (Hwang et al., 2002), have been assigned,
respectively, to two ichnotaxa: Purbeckopus and Haenamichnus, although the pterosaurian origin of the
first of these has been called into question (Padian,
2003). These trackways, like Pteraichnus, show that
the makers were moving quadrupedally.
From this limited ichnological evidence one would
conclude that large pterosaurs, like their smaller
relatives, were predominantly erect/semi-erect plantigrade quadrupeds, excepting the period immediately
after landing, when a bipedal posture must have been
transiently adopted while the forelimbs were still
deployed for flight, as has now been confirmed by a
trackway (Padian, Mazin & Billon-Bruyat, 2003), and
possibly before take-off when the same may have been
true. However, the precise nature of the quadrupedal
stance is still under debate. Wellnhofer (1988) proposed that the limbs were semi-erect, and that as a
result the hands were more widely separated than the
feet. This model is qualitatively consistent with
the Purbeckopus tracks, in which the manus prints
often lie outside the pes prints (Wright et al., 1997),
although these tracks may not be pterosaurian
(Padian, 2003). This is not the case for Haenamichnus, however: in these trackways the manus and pes
prints are nearly in line (Hwang et al., 2002). This
latter track morphology is consistent with recent
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3D PTEROSAUR WING SHAPE
models of quadrupedal locomotion developed by
Henderson & Unwin (1999) and Chatterjee & Templin
(2004). In these, both fore- and hindlimbs are held
nearly erect, and swing back and forth parasagittally.
The reconstruction of Chatterjee & Templin (2004) is
rather similar to a model developed for small pterodactyloids on the basis of the Crayssac tracks (Mazin
et al., 2003): the spine is held at an angle of about 45°
to the horizontal, and the humeri are directed downwards. By contrast, Henderson & Unwin (1999)
propose that the spine was elevated to a greater
degree, and that the humeri were retracted, not
depressed. All three of the quadrupedal models
described above were developed using ornithocheirid
material, and it would therefore be instructive to see
which are supported by the three-dimensional reconstruction of the present work.
Two possible quadrupedal stances of A. santanae,
both consistent with the limitations imposed by its
joints, are shown in Figures 27 and 28. In both postures the elbow, radioulnocarpal, and knuckle joints
are at their respective limits of flexion, the intersyn-
61
carpal joints are extended, and the carpometacarpal
joints are fully supinated. The femora are depressed
by 60°, and the pedes are separated by c. 0.2 m. In
Figure 27 the shoulders are close-packed, whereas in
Figure 28 the humeri are maximally depressed and
protracted, which has the effect of reducing the
manus separation from c. 0.6 m (3 ¥ pes separation)
to c. 0.3 m (1.5 ¥ pes separation). Of the two postures,
I regard Figure 27 as the more feasible, because
adduction of the forelimbs as shown in Figure 28
causes the wing fingers to splay outwards, which
would have made them more vulnerable to damage. It
is therefore likely that the manus were usually quite
widely separated, although an intermediate degree of
adduction cannot be definitely ruled out. Pronation at
the carpometacarpal joints has a similar effect on the
position of the wing fingers as depressing and protracting the humeri.
Of the three quadrupedal models described above,
the semi-erect model presented by Wellnhofer (1988)
is the most similar to that presented here, in that the
manus are widely separated and the spine subhori-
Figure 27. Dorsal (A), anterior (B), and left lateral (C) views of Anhanguera in a semi-erect quadrupedal stance. The
shoulder and intersyncarpal joints are in their close-packed positions, the carpometacarpal joints are supinated, and the
elbow, radioulnocarpal, knuckle, and carpopteroid joints are maximally flexed. The femora are depressed by 60°. Scale bar:
500 mm.
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62
M. T. WILKINSON
zontal. The models of Chatterjee & Templin (2004)
and Henderson & Unwin (1999), are problematic from
an osteological perspective. Chatterjee & Templin
(2004) thought that the humerus could be depressed
below the horizontal by 60°, but an angulation of
this magnitude causes complete disarticulation of
the joint. The fully retracted position of the humerus
reconstructed by Henderson & Unwin (1999), on the
other hand, lies within the range of shoulder motion
proposed in the present work. However, the humerus
can only take this position if it is supinated, which
also supinates the elbow axis. When the elbow is
flexed, the forearm therefore points in entirely the
wrong direction for manus–ground contact (Fig. 29).
This emphasizes the importance of correctly assessing
how the orientations of neighbouring joint axes relate
to each other when carrying out whole-skeleton
reconstructions.
It would be useful to compare the reconstructed
terrestrial stance with the ichnological evidence.
Unfortunately, the dimensions of the prints of Purbeckopus, even if these are pterosaurian, and Haenamichnus are not consistent with an ornithocheirid
trackmaker. Of particular importance in drawing this
conclusion is the small size of the ornithocheirid
pedes. Of the specimens I examined, C. robustus
(NSM-PV 19892) has the best-preserved pes, with
complete digits II and III, and their respective metatarsals. The estimated pes length is only 100 mm,
which is very small given the estimated wingspan of
5.7 m (assuming it was geometrically similar to A.
santanae, as the morphometric analysis indicates: see
Appendix 2). The pes is also smaller than the manus:
in C. robustus (NSM-PV 19892) manual digit III alone
is 10 mm longer than the entire pes. The largest pes
prints of Purbeckopus and Haenamichnus measure
225 mm and 350 mm in length, respectively. If it is
assumed that these prints were roughly similar in
length to the pedes that made them, ornithocheirid
trackmakers geometrically similar to A. santanae
would have had wingspans of 13 and 20 m, respectively, which seem excessive. In addition, the manus
prints of Purbeckopus and Haenamichnus are usually
similar in length or slightly shorter than associated
pes prints (Wright et al., 1997; Hwang et al., 2002):
the manus prints of an ornithocheirid track would be
expected to be significantly larger than the pes prints.
I would therefore argue that, in all likelihood, verifiable ornithocheirid tracks have yet to be discovered.
The idea that different pterosaur taxa could have
Figure 28. As in Fig. 27, but with the humeri at the limit of depression and protraction, and the elbows set 10° short
of the limit of flexion. Scale bar: 500 mm.
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3D PTEROSAUR WING SHAPE
63
Figure 29. Dorsal (A), anterior (B), and left lateral (C) views of Anhanguera in an upright bipedal stance. The humeri
are retracted by 65°, requiring a maximal supination of 50°, and the other arm joints are maximally flexed.
made tracks of different gross form is interesting, and
demonstrates that care must be taken when attempting to fit three-dimensional reconstructions to
trackways.
It is not universally accepted that large pterosaurs
were habitually quadrupedal. Some workers, most
notably Bennett (1990, 1997b, 2001), have argued
that the great disparity between the forelimb and
hindlimb lengths in large forms would have precluded
quadrupedal locomotion. Bennett (1990) therefore
proposed that large pterodactyloids were bipedal with
erect hindlimbs, as had been argued in the heyday of
the bird-like/bat-like controversy (Padian, 1983,
1991). Additionally, Bennett (1990) suggested that the
spine was elevated 60° from the horizontal, arguing,
as had Pennycuick (1988), that if the spine had been
subhorizontal as suggested by Padian (1983), the long
neck and skull typical of large pterodactyloids would
have caused them to topple forwards. Figure 30
shows A. santanae in such a posture, with bird-like
subhorizontal femora, the shoulders in their closepacked positions, the elbow, radioulnocarpal, and
knuckle joints at their respective limits of flexion, the
intersyncarpal joints extended, and the carpometacarpal joints fully supinated. The objections raised by
Pennycuick (1988) and Bennett (1990) are borne out:
the pterosaur would be markedly front-heavy in this
posture.
The upright bipedal model proposed by Bennett
(1990) is of course inconsistent with trackways that
indicate quadrupedal locomotion, although this ichnological evidence only indicates that certain large
pterosaurs were quadrupedal some of the time, and
not all pterosaurs all of the time. Bennett’s (1990,
1997b, 2001) chief objection may also be unfounded: it
does not necessarily follow that a disparity in length
between the fore- and hindlimbs should make quadrupedal locomotion prohibitively difficult. There are
or were quadrupeds with longer forelimbs than hindlimbs (the sauropod Brachiosaurus and small pterodactyloids, for example), and a human with a pair of
crutches can walk quadrupedally quite easily, despite
the great difference between the lengths of crutch and
leg. Most importantly, however, the full retraction of
the wings indicated in the bipedal models of Padian
(1983, 1991) and Bennett (2001) is unfeasible, as
Figure 29 clearly shows. The wings could not have
been fully furled against the body, making habitual
bipedal progression awkward.
CONCLUSIONS
On the basis of my analysis of the three-dimensional
geometry and range of movement of the ornithocheirid skeleton, I propose that:
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
64
M. T. WILKINSON
or some other camber-adjustment mechanism.
Sweeping the wings fore and aft at the shoulder
and/or knuckle would also have pitched the pterosaur up and down, respectively, but in an unbalanced fashion. Additionally, speed could have been
increased by flexing the wing at the elbow, wrist,
and/or knuckle.
4. Roll control was probably brought about by altering the angle of attack of the distal part of one
wing by rotating at the shoulder and/or carpometacarpal joint, and/or changing the area of
one wing using flexion/extension at the elbow,
wrist, and knuckle joints.
5. Yaw control was probably achieved by turning the
head, or by careful manipulation of the pteroid and
hindlimb or membrane tension to cause a drag
asymmetry.
6. When on the ground, it is likely that the ornithocheirids adopted a semi-erect quadrupedal
posture, with subhorizontal spine and humeri.
Typical manus separation is predicted to be about
three times the pes separation.
ACKNOWLEDGEMENTS
Figure 30. Left lateral view of Anhanguera in a bird-like
bipedal posture, with subhorizontal femora. The shoulder
and intersyncarpal joints are in their close-packed positions, the carpometacarpal joints are supinated, and the
elbow, radioulnocarpal, knuckle, and carpopteroid joints
are maximally flexed. The femora are depressed by 60°.
Scale bar: 500 mm.
1. The pteroid was directed forwards in flight, not
towards the body. The propatagium would therefore have functioned as an adjustable leading edge
flap and high-lift device, delaying aerodynamic
stall during landing, when the angle of attack was
unavoidably high because of the attachment of the
main wing membrane to the legs.
2. The ornithocheirids were, in all likelihood, inherently unstable in pitch and yaw, largely because of
the minimal backward sweep or even slight
forward sweep of the wings when extended, and
also because of the need to attain very high angles
of attack when landing.
3. Pitch and therefore speed control were probably
brought about by changing the angle of attack of
the inner region of the wings, using the hindlimbs
and/or the outer region of the wings, using pronation and supination of the shoulder and carpometacarpal joints. Increasing and decreasing the
angle of attack would have caused a nose-up and
nose-down pitch, respectively. Following such an
adjustment, longitudinal balance could have been
restored using depression/elevation of the pteroid,
I thank Makoto Manabe (NSM), Satoru Nabana
(IMCF), Yuji Takakuwa (Gunma Prefectural Museum,
Japan), Eberhard ‘Dino’ Frey (SMNK), Mark A.
Norell, and Eugene Gaffney (AMNH) for granting
access to the fossil material, and further thank
M. Manabe, E. Frey, and David M. Unwin (Museum
für Naturkunde der Humboldt-Universität, Berlin,
Germany) for the loan of specimens and casts. I also
thank the above, and additionally Yoko Kakegawa,
Hiroya Ogata, and Yukimitsu Tomida of the NSM,
and Steve Salisbury, Alex Anders, and Rene Kastner
of the SMNK for their generous assistance during my
museum visits, and also the Perez family for providing accommodation for the duration of my stay in
New York. I am also very grateful to Charles P.
Ellington, D. Unwin, Colin Palmer, and James Cunningham for their helpful comments on the manuscript, and for many interesting discussions about
pterosaur functional morphology and flight. Funding
for the research and travel was provided by the Biotechnology and Biological Sciences Research Council
(BBSRC), Queens’ College, University of Cambridge
and Clare College, University of Cambridge. I am
currently supported by a Junior Research Fellowship
at Clare College, University of Cambridge.
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APPENDIX 1
Institutional
abbreviations:
AMNH,
American
Museum of Natural History, New York, USA; IMCF,
Iwaki Coal and Fossil Museum, Iwaki, Japan; NSM,
National Science Museum, Tokyo, Japan; RGM,
National Natuurhistorisch Museum, Leiden, the
Netherlands; SMNK, Staatliches Museum für
Naturkunde, Karlsruhe, Germany; SMNS, Staatliches Museum für Naturkunde, Stuttgart, Germany.
Anatomical/arthrological abbreviations: (1,2,3)ax,
(primary, secondary, tertiary = long) axis; ch, cheiropatagium; cm, carpometacarpal joint; co, coracoid;
cogl, coracoid part of the glenoid fossa; cpt, carpopteroid joint; cr, cruropatagium; CR, centre of rotation; crax, conjunct rotation axis; cs, cristospine; dpcr,
deltopectoral crest; dpr, dorsal process; ds, distal syncarpal; dsfac, distal syncarpal facet; el, elbow joint;
etpr, extensor tendon process; ettr, extensor tendon
track; fe, femur; fov, fovea; gl, glenoid fossa; gr,
groove; hp(1,2,3), hip joint (primary axis, secondary
axis, tertiary = long axis); hu, humerus; hucot,
humeral cotyle; hufac, humeral facet; il, ilium;
ip(1,2,3), (first, second, third) interphalangeal joint;
is, intersyncarpal joint; kne, knee joint; knu, knuckle
joint; lcon, lateral condyle; mc, medial carpal/medial
carpal joint; mcfac, medial carpal facet; mcon, medial
condyle; no, notarium; phcon, phalangeal condyle;
phfac, phalangeal facet; pn, pneumatic foramen; pro,
propatagium; ps, proximal syncarpal; psfac, proximal
syncarpal facet; pt, pteroid; ptcot, pteroid cotyle; ra,
radius; racon, radial condyle; rafac, radial facet; ri,
ridge; ruc, radioulnocarpal joint; rufac, radial/ulnar
facet; sc, scapula; scgl, scapular part of the glenoid
fossa; scno, scapulonotarium joint; ses, sesamoid;
sh(1,2,3), shoulder joint (primary axis, secondary
axis, tertiary = long axis); stco, sternocoracoid joint;
stp, sternal plate; ten, tendon; tt, tibiotarsus; tu,
tuberculum; ul, ulna; ulcon, ulnar condyle; ulfac,
ulnar facet; wf, wing finger; wf-ph(1,2,3,4), (first,
second, third, fourth) wing-finger phalanx; wm, wing
metacarpal; wmcot, wing-metacarpal cotyle; wmfac,
wing-metacarpal facet.
Other abbreviations: a, angle of attack; c.g., centre
of gravity; M, pitching moment; M0, zero-lift pitching
moment; m.a.c., mean aerodynamic centre.
APPENDIX 2
Bone measurements (in mm) of selected ornithocheirid specimens from the Santana Formation and Crato
Formation (in the case of SMNK SMNK 1132PAL) of Brazil, given to the nearest mm, with estimated wingspans
(WS) in m. Each specimen represents a single individual. Asterisks indicate measurements taken from the
literature. Parentheses indicate an incomplete element. Wingspans were estimated on the assumption that the
ornithocheirid specimens were geometrically similar, with wingspan : ulna length ratios equal to those estimated for A. santanae.
Specimen
sc
co
hu
ul
ra
ps+ds
pt
wm
wf–ph1
wf–ph2
wf–ph3
wf–ph4
fe
tt
WS
AMNH 22552
AMNH 22555
AMNH 24444
IMCF 1053
NSM–PV 19892
RGM 401 880*
SMNK 1132PAL
SMNK 1133PAL
SMNK 1134PAL
SMNK 1135PAL
SMNK 1136PAL
SMNK 1250PAL
–
90
73
–
106
130
80
137
–
96
112
122
–
126
90
151
–
175
115
185
–
121
158
–
170
–
–
220
254
290
230
295
–
172
225
230
243
–
242
341
390
410
312
397
241
263
380
353
240
–
–
–
385
401
–
391
238
–
380
–
20
–
25
–
41
–
–
47
37
–
–
–
–
–
–
–
–
–
–
(178)
–
–
–
–
172
–
170
–
255
–
227
–
165
179
254
248
355
–
353
–
–
–
445
–
357
383
577
515
324
–
–
–
–
–
402
–
–
–
532
–
252
–
–
–
–
–
312
470
–
–
393
–
–
–
–
–
–
–
275
–
–
–
–
–
–
–
–
–
234
285
190
271
–
–
–
–
–
–
–
–
–
355
234
–
–
–
–
–
3.5
4.3
3.5
5.0
5.7
6.0
4.5
5.8
3.5
3.8
5.5
5.1
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69
3D PTEROSAUR WING SHAPE
69
SUPPORTING INFORMATION
Additional Supporting Information may be found in the online version of this article:
Video clips S1–S3. AVI films of a three-dimensional reconstruction of Anhanguera santanae, showing the
overall effects of full flexion at the elbow, radioulnocarpal, carpopteroid, and knuckle joints: the movements that
would have been used to furl the wing. Flexion of the elbow joint was indissociably coupled with that of the
radioulnocarpal joint, but the movements at the other joints could have occurred independently. These films also
show movement of the hindlimb from its close-packed position (20° below and 30° behind the transverse y-axis)
to a position suitable for a terrestrial stance (60° below and 20° ahead of the the transverse y-axis). The
trajectory of the hindlimb shown is one of very many possibilities. The relevant joints axes are indicated in red.
Video clip S1, dorsal aspect. Video clip S2, anterior aspect. Video clip S3, anterodorsolateral aspect. Gridlines
are spaced at intervals of 500 mm.
Video clips S4–S6. AVI films of the same sequence of movements shown in Video clips S1–S3, with the
addition of full flexion of the intersyncarpal joint. Video clip S4, dorsal aspect. Video clip S5, anterior aspect.
Video clip S6, anterodorsolateral aspect.
Video clips S7–S9. AVI films showing the various possible shoulder movements in the following sequence: (A)
elevation/retraction of 25° about the primary axis from the position of maximum depression to the close-packed
position; (B) supination of 50° about the tertiary axis; (C) primary angulation of 70°, manifest as almost pure
retraction caused by the supination of the primary axis in step (B); (D) protraction/elevation of 80° to the
position of maximum elevation, with no angulation about the primary axis; (E) depression of 70° about the
primary axis, following which the arm is maximally pronated as a result of diadochal movement that occurred
in step (D); (F) supination of 30° about the tertiary axis to the close-packed position; (G) positive secondary
angulation of 10°, manifest predominantly as protraction, but also elevation resulting from the 35° tilt of the
secondary axis; (H) negative secondary angulation of 50°, manifest predominantly as retraction, but also as
depression. These video clips do not illustrate realistic wing kinematics, but show the maximum theoretical
range of movement about the different shoulder joint axes estimated from a consideration of the bones alone.
Video clip S7, dorsal aspect. Video clip S8, anterior aspect. Video clip S9, antero-dorso-lateral aspect.
Please note: Blackwell Publishing are not responsible for the content or functionality of any supporting
materials supplied by the authors. Any queries (other than missing material) should be directed to the
corresponding author for the article.
© 2008 The Linnean Society of London, Zoological Journal of the Linnean Society, 2008, 154, 27–69