Bio1.J. Linn. SOC.,3,pp. 313-328. With 12figures
December 1971
Aerodynamics of Pteranodon
CHERRIE D. BRAMWELL
Department of Geology, University of Reading, Whiteknights, Reading
Acceptedfor publicutionJunuury 1971
A computer program originally designed to test glider performance was adapted and used
to study the flight behaviour of Pterunodon. A drag polar was determined for the membranous
wing, giving a cambered plate profile. Results of the program described the straight flight
performance, the turning ability and circling within thermals. Pteranodon was found to have
a very low sinking speed, a similar lift/drag ratio to gliding birds, to be capable of staying aloft
at extremely low speeds and a very small turning circle. The stress involved while turning was
calculated and found to be low. It is suggested that a change from settled light-wind weather
to more turbulent conditions could have brought about the extinction of this highly specialized
animal.
CONTENTS
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.
Introduction
Information
Results
Discussion
Acknowledgements
References
Appendix.
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PAGE
313
314
317
325
326
326
327
INTRODUCTION
T h e Cretaceous pterosaur, Pteranodon, was the largest flying animal known to have
existed in vertebrate history, with a wing span up to 27 feet. Aerial locomotion can only
be achieved by active flapping flight or by gliding, which is the ability to remain aloft
without expending energy in flapping the wings. Gliding birds manage this in two ways.
In static soaring the bird maintains or gains altitude by gliding in air that has an upward
velocity greater than its sinking speed. This can occur when the air stream is deflected
upwards from obstacles such as cliffs, or rises as thermal bubbles and columns from
differential heating of the land surface. T h e second method of gliding, dynamic soaring,
is that in which the bird uses changes in the horizontal wind-gradient to stay aloft.
These two methods of gliding require different aerodynamic adaptations. If the
aerodynamic characteristics of a flying animal are known, its performance can be
determined. This performance will then indicate the characteristic mode of gliding of
the animal.
Flight performance is extremely difficult to calculate for flapping flight, which
involves much non-steady hydrodynamic theory, but considerably simpler for gliding.
313
314
C. D. BRAMWELL
This paper only considers Pteranodon as a gliding animal, for which it was superbly
adapted (Hankin & Watson, 1914). Gliding performance in birds has recently been
measured directly for the pigeon CoZumba Ziwia (Pennycuick, 1968) and the lagger
falcon (Tucker & Parrott, 1970). I n these experiments the birds were trained to glide
freely in wind tunnels. Such a method is obviously impossible for an extinct animal.
However, it has recently been possible to make use of a computer program, originally
developed to measure glider performance, to do the same job for Pteranodon. The
program was written by Rear-Admiral H. C. N. Goodhart and has been in use for some
time in the Applied Physical Sciences Department of this University. It was run on
the ICL 1905 computer at the College of Aeronautics, Cranfield. (The Appendix gives
details of the program calculations.)
INFORMATION'
An animal gliding at constant velocity along a straight path is in equilibrium between
its weight (W) and the lift (L) and drag (D) forces acting on it (see Fig. 1). If 8 is the
L
W
Flight path
\
/-
I
L = wcos e
D=~sin8
FIGURE
1. Forces acting on Pteranodm during steady glide. The glide path is inclined at angle
to the horizontal. The weight, W, is balanced by two forces, the lift L, acting perpendicularly
to the flight path and the drag, D , acting parallel to it.
angle between the downward flight path and the horizontal (the glide angle) then,
L = wcos 8,
(1)
D = Wsin 8.
(2)
The glide angle may be expressed as the glide ratio, which compares the distance
travelled forwards to the height lost. Thus a glide ratio of 8.0 would mean that the
animal had moved eight units along its glide path while losing one unit of height. From
Fig. 1 and equations (1) and (2) it can be seen that :
and
cotan 8 = glide ratio = LID.
(3)
The conversions into metric units are approximate and are solely for the convenience of the reader
unfamiliar with English units.
AERODYNAMICS OF PTERANODON
315
Lift and drag are usually expressed as the non-dimensional coefficients C, and CD
from the equations :
= 2L/(pSV2),
(4)
c,
c, = 2D/(pSV2),
(5)
where p is air density (at sea level), S is the surface area of the wings and V is the air
speed.
T h e Reynolds number (Re) varies with the speed and size. It is non-dimensional
and is defined as :
Re = pVc/y
(6)
where c is the chord and y is the viscosity of air. From this it can be calculated that
Pteranodon worked within the range of Re 90,000 to 890,000.
and
Table 1. Pteranodon data. Program FOlC
Wing configuration A
Metric
Imperial
Span
Wing area
Aspect ratio
Weight
Wing loading
Co head
Misc. drag (body)
K cruise
K climb
CL at max
8.2 rn
5.8 mz
11.7
18 kg
3.1 kg/mz
0.12
2.0
1.15
1-30
1.20
27.0 ft
62-4 ft2
11.7
40 lb
0.64 lb/ftZ
0.12
2.0
1.15
1.30
1.20
Wing configuration B
Metric
Imperial
6.0 m
4.5 m2
8.1
18 kg
4.1 kg/mz
0.12
2.0
1-15
1.30
1.20
19.7 ft
48.0 ftz
8.1
40 Ib
0.83 lb/ftZ
0.12
2.0
1.15
1.30
1-20
The information used by the program is listed in Table 1. T h e program was run for
two wing configurations, designated A and B. I n configuration A the wings were fully
outstretched while in configuration B they were partially swept back by bending at the
metacarpal/phalangeal joint. T h e angle formed between these two bones in position B
is 100". This joint, the knuckle, was in fact capable of a wide range of movement, from
fully extended to folded back to form an acute angle (Hankin & Watson, 1914). T h e
planiform change between A and B configurations results in a reduction of the wing
span from 27.0 to 19.7 ft (8.2 to 6.0 m). T h e wing area is reduced from 62.4 to 48-0ft2
(5.8 to 4.5 m2). Wing area in both cases was measured to include a piece of body
between the wings, in accordance with aeronautical engineering convention. T h e
aspect ratio is 11.7 in configuration A and 8-1 in configuration B.
T h e weight of Pteranodon used in these calculations was estimated as 40 lb (18 kg).
This was deduced by several methods including extrapolation from gliding birds
weights and wing spans and a geometrical analysis that involved calculating the
volume and specific gravity of Pteranodon. Previous estimates of the weight vary from a
minimum of 20 lb (9.0 kg) (Brown, 1943) to a maximum of 55 lb (25 kg) (Kripp, 1943).
Pteranodon's large size and light weight gave it a remarkably low wing loading, this
being only 0.64 lb/ft2(3.1 kg/m2) and 0.83 lb/ft2 (4.1 kg/m2)in configurations A and B
respectively. This compares with 1.63 lb/ft2(8 kg/m2) for the vulture Corygyps atratus,
C. D. BRAMWELL
316
3.24 lb/ft2(15.8 kg/m2)for the albatross Diomedu melunophrys and a minimum of 4.0 lb/
ft2(19.5 kg/m2) in a man made glider (e.g. the Olympia).
The factor C, head is the coefficient of drag for the head of Pterunodon. This replaced
tail drag in the program when it was used for conventional gliders. Miscellaneous drag
takes the body into account. K cruise and K climb are factors which allow for the inefficiency of the wing in relation to lift. This is mainly due to the tendency of the wing,
which is a membranous structure only supported by a strut at the leading edge, to twist
during flight, A cambered plate wing section was used in the calculations, as the wings
obviously do not have a conventional aerofoil section (see Fig. 2). Schimtz (1960) has
B
A
FIGURE
2. Wing profiles. A, Conventional airfoil profiles; B, cambered plate profile.
I
0
002
I
I
I
004 006 0 0 0
I
I
I
010
0.12
014
CD
FIGURE
3. Ptmanodon, wing section profile drag polar. C, is the coefficient of drag and CL,
the coefficient of lift.
compared the merits of various aerofoil profiles at high and low Reynolds numbers.
He found that at a low Reynolds number of 42,000 the cambered plate profile gave the
best lift coefficient and maximum lift/drag ratio when compared with a traditional
aerofoil. The latter performs very poorly at lower Reynolds numbers, becoming
inefficient somewhere in the range 60,000 to 150,000. At low speeds Pterunodon falls
within this range so its cambered plate profile is an advantage. At higher speeds there
would have been a slight advantage in possessing a conventional aerofoil profile, but this
would have added an enormous amount of weight, even if such a design were possible
within the biological structure. The wing section drag polar is shown in Fig. 3. The
maximum lift coefficient is 1.5 and the maximum lift/drag ratio is 13:1 ;this occurs at
C, 1.2, hence the last piece of information reads C, 1.2.
AERODYNAMICS OF PTERANODON
317
RESULTS
Pteranodon's straight flight results from both wing configurations are plotted in
Figs 5 and 6. The maximum lift coefficient is 1.5 ;at higher lift coefficients laminar flow
is lost, leading to stalling. 1.5 is a typical maximum value for highly cambered wing
sections. Some maximum lift coefficients are listed in Table 2.
Without special anti-stalling devices ordinary airfoils will not develop lift coefficients
much above these. The alula of the birds' wing acts as a leading edge slot, allowing the
development of higher lift without stalling at low speeds. I have suggested (Bramwell,
1970) that the small pteroid membrane at the front of the pterosaur wing could have
acted as an anti-stalling device, but as this has not yet been tested quantitatively, its
possible effect on maximum CLhas been ignored in this study. At low speeds a high
Table 2
Animal or aircraft
Maximum CL
Falcon
Pigeon
Pteronodon
Skylark sailplane
Flapped sailplane
Light aircraft without flaps
Light aircraft with flaps
1 *6
1 *3
1*5
1 *3
1.6
1.4
1 *8
degree of camber gives higher lift coefficients, but at high speeds lift can be obtained
with less drag if the camber is not too great. Nachtigall & Wieser (1966), working on the
pigeon wing, have shown that with increased speed camber was decreased automatically
by the air flow bending back the rear of the wing, giving a flattening effect. This may
possibly have happened in the pterosaur wing; at higher speeds the centre of pressure
moves backwards-this effect acting on an elastic membrane would in itself lead to
some reduction of camber. The relationship between degree of camber, velocity and
drag is at present being investigated in a wind tunnel.
Figure 4 is a plot of lift coefficient against velocity. From its maximum of 1.5, the lift
coefficient decreases with increasing airspeed at all glide angles and for both wing
configurations. Its lowest value is 0.2, giving a top speed of 30.7 knots (16.1 m/sec) in
wing position A and 35.0 knots (18.0 m/sec) in wing position B. Higher speeds are
unobtainable as the wing stalls. Higher speeds are achieved in position B for the same
lift by the reduction in drag due to the altered wing shape.
The glide angle is plotted against velocity in Fig. 5 . The minimum glide angle is
found at the lower end of the speed range, increasing rapidly with increased velocity.
It is at a minimum of 4.3"at 13 knots (6.7 m/sec) in configuration A and 5.5" between
14 and 16 knots (7.2-8.2 m/sec) in configuration B.
C.D. BRAMWELL
318
15-
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\ I t , [
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\ ;
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\ '\
I413-
I2-
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0 9-
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Configuration B
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070 6-
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18 20 22
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---------
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Configuration A
\
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IO-
1
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4 26 28 30 32 3 4 36
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FIGURE
4. Pterunodon, lift coefficient and airspeed. C, is the lift coefficient.
2 8 - ,
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1
.
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1
26 -
1
1
1
24 22 20 -
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- -------
Configuration A
Configuration 8
18 -
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16-
/
14-
-
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0)
p0
12-
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0"
10-
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5
4
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8
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10 12 14 I6
a
10
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0
20 22 24 26 28 30 32 34 36 38
AERODYNAMICS OF PTERANODON
319
The performance of Pteranodon in a straight glide in still air is expressed in the conventional aeronautical manner in Fig. 6. In this the sinking speed is plotted against the
airspeed. As sink equals V/(L/D),points representing a given LID value fall among a
straight line that passes through the origin. T h e maximum LID ratio for configuration
A is 13 and drops to 10.4 for configuration B. The cross-over of the two curves shows
that it is an advantage to change to configuration B at speeds above 16 knots (8.2 mlsec).
As sinking speed is a measure of the energy lost in gliding, it can be said that partially
folding the wings conserves the energy expended on overcoming drag at higher velocities. It can be assumed that Pteranodon gradually reduced its wing span as it glided
(rnhec)
Airspeed (knots)
5-1
10
0
10.3
20
15 4
30
*%?
05 1 10 2 -
1 5 3-
--
5:
24-€5
f 265v)
31 6-
3 6 74 I 8-
FIGURE
6. Pterunodon, flight performance in still air.
faster, in a similar way to birds. This variability in wing shape gives living flying
machines a great advantage over man made gliders, allowing the animal to adjust its
LID ratio to the maximum possible for any particular velocity. Designing a continually
variable wing mechanically involves such an increase in weight that it negates the
advantage obtained.
The performance curve of Pteranodon is compared with those of various gliding
birds and a sailplane in Fig. 7. Pteranodon shows up as an extremely slow glider, performing best in the range 11 to 15 knots (5.7 to 7-7 m/sec), while all the others do not
fly at all at speeds below 15 knots. When flying at 13 knots (6.7 m/sec) Pteranodon has
a very low sink of only 1 knot (0.5 mlsec). This low sink is not achieved by any of the
birds, but is approached most closely by the sailplane, which has a sink of 1.2 knots
(0.61 mlsec).
22
C. D. BRAMWELL
320
T h e LID ratio of 13 for Pteranodon is slightly higher than that of most gliding birds
so far tested, but much lower than that of a sailplane. T h e pigeon has the lowest LID
of any of the birds shown in Fig. 7 at only 4.1 (Pennycuick, 1968). Pennycuick has also
determined the maximum LID of the fulmar as 8.3. Tucker & Parrott (1970) have shown
the falcon Falco jugger has a maximum LID of 10. T h e vulture Corugyps atratus
shown in Fig. 7 has a very high LID of 23. This curve was determined by Raspet (1960),
who explained this high figure as being due to extremely low drag, achieved by a special
property of feathers which gave laminar flow over the entire surface of the bird. These
results have been criticized by Tucker & Parrott (1970). Most modern sailplanes have
(rn/sec)
Airspeed (knots)
0
26 51 7 7 103 129 154 180206232257283309335360386412
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
\
\
"I
1'
Pteranodon\
\
I
\ \
FIGURE
7. The performance curve of Pterunodon compared with those of various gliding birds
and a sailplane.
good maximum LID values in the 35 to 40 range. Although the LID ratio of Pteranodon
is not as good as that of a sailplane, its lower flying speed cancels this out to give a lower
rate of sinking. This is because staying aloft depends on velocity as well as the LID ratio,
as sinking speed is governed by the relationship sink equals V / ( L / D ) .
So far Pteranodon has only been considered while gliding in a straight line in still air.
However, the program also calculated its turning ability. T h e results are shown in
Table 3.
Manoeuvring is an important aspect of an animal's flight as it may have to pursue or
avoid enemies while on the wing. As Maynard Smith (1952) has pointed out, flying
animals evolve to become aerodynamically unstable as this gives them greater manoeuvrability; less force is needed to turn an unstable animal from a straight flight path.
AERODYNAMICS OF PTERANODON
321
Table 3. Turning performance in climb configuration based on a level flight speed of 12.5
knots and sink of 0.91 1 knots (ConfigurationA) and 14.3 knots and 1.48 knots (Configuration B)
Radius of
turning
circle
(ft)
(m)
Sink
(knots)
(mlsec)
Angle of bank
(degrees)
(knots)
11.0
10.1
9.1
8.5
7.9
7.6
7.0
6.7
6.4
6.1
5.8
5.8
5.5
5.5
5.2
5.2
1.03
1.06
1.09
1.13
1.17
1.31
1.27
1.33
1-40
1.47
1.56
1.67
1.79
1.93
2.09
2.29
0.53
0.54
0.56
0.58
0.60
0.62
0.65
0.67
0.72
0.76
0.80
0.85
0.92
0.99
1*07
1.17
22.9
25.2
27.5
29.8
32.1
34.4
36.7
39.0
41.3
43.5
45.8
48.1
50.4
52.7
55-0
57.3
13-1
13.2
13-5
13-5
13.6
13.8
14.0
14.2
14.5
14.7
15.0
15.4
15.7
16.1
16.6
17.1
6.73
6.78
6.87
6-94
6.99
7.09
7.21
7.39
7.47
7.57
7.72
7-93
8.08
8.30
8.55
8.80
14.3
13.1
11.9
11.0
10.4
9.7
9.1
8.8
8.2
7.9
7.6
7.3
7.3
7.0
6.7
6.7
1.52
1.57
1.61
1*67
1.73
1-80
1.87
1a96
2.06
2.18
2.31
2.47
2.64
2.85
3.10
3.38
0.78
0.81
0.83
0.85
0.89
0.93
0.96
1.oo
1.06
1.12
1.18
1*26
1.36
1-47
1.59
1.73
22.9
25.2
27.5
29.8
32.1
34.4
36.7
39.0
41.3
43.5
45.8
48.1
50.4
52.7
55.0
57.5
14-9
15.0
15.2
15.4
15-5
15.7
16.0
16.2
16-5
16.8
17.1
17.5
17.9
18.4
18.9
19.5
7.67
7.72
7.84
7.93
7.98
8.08
8.24
8.34
8.51
8.65
8.80
9.00
9.20
9.45
9-73
10.02
Speed
(mlsec)
Configuration A
36
33
30
28
26
25
23
22
21
20
19
19
18
18
17
17
Configuration B
47
43
39
36
34
32
30
29
27
26
25
24
24
23
22
22
This evolutionary tendency is limited by the degree of control that the nervous system
can exert.
Figure 8 shows the forces acting on Pteranodon during a horizontal turn.
T h e velocity of a body travelling in a circle is not constant in direction and this tends
to make it fly off at a tangent. A force acting towards the centre of the circle is needed
to prevent this; it is known as the centripetal force. I n Fig. 8 the lift, L is shown to be
balanced by the weight, W, and the centripetal force, C. T h e actual forces acting on
Pteranodon when it is banking at an angle of 57.3",inwing configuration A are inserted in
brackets. They are calculated from the formulae:
and
L = Wlcos 6,
C = L/sin 6,
(7)
(8)
C. D. BRAMWELL
322
where 0 is the angle of bank. Pteranodon is shown in Fig. 8 turning in its minimum
circle of radius 17 ft (5.2 m). Figure 9 compares the radius of turn and velocity for both
wing positions. This shows that to make its sharpest turn Pteranodm flew with its
wings fully extended. This is due to the fact that the lowest flying speeds are achieved
FIGUR~
8. Forcm acting upon Pteranodon during horizontal tlight, when turning in its minimum
circle of radium 17 ft (5.2 m).
15.2
50-
13.7
45
I
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-
c
9.1
30-
Y)
xa
I
--7
------
I
\
\
\
10.7
35-
E
L
I
Confqumtion A
Configuration B
\
'$8 -=
5,
I
I
I
7.6
25
6.1
20 4.6
15
\
\
',
\
\
\
\
\
\
\
\
\
'-.-.-.---__-
.---
'\
3.1
10
FIGURE
9. Pteranodon, comparison of turn and velocity for both wing positions.
AERODYNAMICS OF PTERANODON
323
Table 4. Performance in thermals
Velocity of thermals
(knots)
(mlsec)
Radius of thermal
(ft)
(m)
Rate of climb Angle
of Pteranodon of bank
(knots)
(degrees)
Velocity of Pteranodon
(knots)
(mlsec)
Configuration A
12
12
12
12
12
10
10
10
10
10
8
8
8
8
8
6
6
6
6
6
4
4
4
4
4
6.2
6.2
6.2
6.2
6.2
5.1
5.1
5.1
5.1
5.1
4.1
4.1
4.1
4.1
4.1
3-1
3.1
3.1
3.1
2.1
2.1
2.1
2.1
2.1
1000
700
500
400
300
1000
700
500
400
300
1000
700
500
400
300
lo00
700
500
400
300
lo00
700
500
400
300
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
10.95
10.94
10.91
10.87
10.80
8.96
8.94
8.92
8.89
8-83
6.96
6.95
6.93
6.91
6.86
4.96
4.95
4.94
4.92
4.88
2.96
2.96
2.95
2.94
2.91
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13-1
13.1
13.1
13.1
13-1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
6.74
6-74
6.74
6.74
6.74
6.74
6.74
6.74
6.74
6.74
6-74
6-74
6.74
6.74
6.74
6.74
6-74
6.74
6.74
6.74
6-74
6.74
6.74
6.74
6.74
6.2
6.2
6.2
6.2
6.2
5.1
5.1
5.1
5.1
5.1
4.1
4.1
4.1
4.1
4.1
3.1
3.1
3.1
3.1
3.1
2.1
2.1
2.1
2.1
2.1
lo00
700
500
400
300
lo00
700
500
400
300
lo00
700
500
400
300
lo00
700
500
400
300
lo00
700
500
400
300
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
305
213
152
122
91
10.45
10.42
10.37
10.31
10.19
8.45
8-43
8.39
8.34
8.24
6.46
6.44
6.41
6-37
6.28
4.46
4.45
4.42
4-39
4.33
2.47
2.46
2.44
2.42
2.38
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
14.9
14.9
14-9
14.9
14-9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14.9
14-9
14.9
14.9
14-9
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
7-67
7.67
7.67
7.67
7.67
7.67
7.67
7.67
3.1
Conjiguration B
12
12
12
12
12
10
10
10
10
10
8
8
8
8
8
6
6
6
6
6
4
4
4
4
4
3 24
C . D.BRAMWELL
in this position. The minimum turning circle of radius 17 ft (5.2 m) is extremely small
for an animal with a 27 ft (8.2 m) wing span. Pennycuick (1966) has calculated the
minimum turning circle of a pigeon; it had a wing span of only 2.2 ft (0.67 m), yet
needed a minimum turning circle of radius 11.2 ft (3.4 m). The very small turning
circle possible in Pteranodon is a further consequence of its ability to glide remarkably
slowly. When travelling in a circle of radius 17 ft at a bank of 57.2" the inner wing of
Pteranodon prescribes a small circle of radius only 9 f t (2.7 m). The tip of the inner wing
is moving very slowly and any further reduction in the radius of turn leads to it stalling.
The greatest stresses acting on an aircraft or glider occur during rapid manoeuvring.
Very strong small aircraft can be constructed to withstand forces up to 8 g, while most
gliders do not go beyond 4 g. The pigeon can also withstand 4 g while making its
sharpest turn (Pennycuick, 1966). The stress acting on Pteranodon in its sharpest turn
may be calculated from the formula:
where A equals the acceleration in turning, V the velocity, Y the radius of the circle and
g the acceleration due to gravity. From this it is found that Pteranodon only had to
withstand 1.47 g even in its sharpest and fastest turn. This is very lucky in view of the
animal's rather fragile structure. How well Pteranodon could stand up to the forces
that its flight involved is under investigation.
A thermal is a mass of air which ascends because it is warmer and therefore less dense
than the air around it. In hot climates the thermals take the form of long columns, but in
cooler climates they are of bubble shape. In either case, the rising air may be used by
soaring birds or sailplanes to gain altitude, often prior to setting off on a long crosscountry glide. Height gain is possible only if the air in the thermal is rising at a faster rate
than the animal's sinking speed : and the thermal must be large enough for the animal
to circle within it. In view of this, the two flight adaptations most useful for thermalling
are a low sinking speed and a small turning circle. As it has been found that Pteranodon
has achieved both of these, it was decided to use the program to test its performance
in thermals. Pteranodon was an ocean flying fish-eater, but as thermals occur over
the sea as well as the land (Storer, 1952), it may have made use of them.
The thermalling results are shown in Table 4, which is a list of thermals of various
sizes and speeds, and the rate of climb, angle of bank and velocity of Pteranodon in
each one. As might be expected, climb is faster in configuration A as the sinking speed
is lowest in this wing position (see Fig. 10). Pteranodon was so lightly loaded that it was
carried up at only 1 to 2 knots (0.5 to 1.0 m/sec) less than the speed of the thermal. Most
thermals last for about five minutes (Piggott, 1958). In this length of time Pteranodon
circling in a thermal of 500 f t (152 m) radius rising at 8 knots (4.1 mlsec), would have
gained over half a mile in altitude.
All the air in a thermal is not rising at the same rate. The cooler outer layers are slower
than the faster moving central core and this is shown in Fig. 11. While circling the sailplane or animal may drift away from the central core into the slower outer layers.
Pteranodon has such a small turning circle that it was probably able to stay within the
core even in small thermals.
AERODYNAMICS OF PTERANODON
325
5.7
II
I
r
8
"
'
i
"
I
"
I
"
~
'
i
#
'
---A
'
_-----------
8-
----_____------
55 3 6 -
s
-
"
A_---
41
0
i
7
e
_----
265
------------
21
4-
15
3-
lo
2.a
I
I
3
1
-------------
Configuration A
----___----------
Configuration B
3
1
1
I
I
I
I
I
3
4
I
I
1
I
I
I
I
*
I
I
FIGURE
10. Pteronodon, rate of climb in a thermal.
FIGURE
11. Variation in speed of rising air within a thermal.
DISCUSSION
Success in gliding may be judged from several viewpoints. One is the ability to cover
ground towards some objective-in living creatures this may be while hunting food or
during migration. Perhaps most important is being able to stay aloft at all, making the
maximum use of any lift available. Suitable soaring conditions do not occur at all times
and the ability to make use of even weak upcurrents increases the time that can be spent
flying. A further important criterion is good manoeuvrability, on the whole more vital
to a living animal than a man made machine.
326
C. D. BRAMWELL
Pteranodon did not excel in any aspect of performance that called for high speed flight.
It was adapted to glide extremely slowly, being airborne at speeds lower than is possible
for present day soaring birds. As Pteranodon had a low rate of sinking and could make
use of weak thermals, it could indeed cover distance if the need arose, but this could not
be done fast. Long distance migrations of thousands of miles would have taken many
days.
Where Pteranodon had become extremely successful was in its ability to stay aloft in
weather conditions that would defeat modern gliding birds. The most striking feature
seen in pterosaur evolution is the progressive lightening of the body coupled with increase in size. Pteranodon is the end product of this trend. Its heavy tail and teeth had
been lost and the bony skeleton reduced to paper-like thinness, while the fourth finger
had elongated to support wings of enormous area. As the results have shown, the outcome was a very low wing loading, giving small sink and slow flight without stalling.
This particular adaptation suggests that the animal had to make use of weak air currents
at the time it lived. Possibly Pterunodon was adapted for crest soaring off waves rather
than the fast dynamic soaring used by present day sea-going birds.
The slow flight adaptation is important in several other ways. It makes take-off and
landing, always a problem for large flying animals, far easier (Bramwell & Whitfield,
1970). The small turning circle is a direct result of low velocity, as can be seen from
equation (9). Pteranodon turned slowly but sharply, without causing great stress to its
body. As Pteranodon had evolved to become basically unstable, this also acted to
improve the turning circle. The same trend is seen in bird evolution, and also in small
fighter planes, which are designed to be unstable so that they can take rapid evasive
action, yet must still be stable enough to be controlled by the human pilot.
The slow gliding that Pteranodon has become so perfectly adapted for meant that all
manoeuvres-take-off, landing, thermalling, altering course-caused little stress to the
framework. In one sense Pteranodon was able to manoeuvre gently only because it was
large and light, yet it was the result of evolving to be so fragile that demanded this slow
speed performance. Once set on this course of flight adaptation Pteranodon could not
go back to smaller size and stronger structure, and like many very specialized animals
it eventually became extinct. A change to rougher weather conditions at the close of the
Cretaceous could have brought this about.
ACKNOWLEDGEMENTS
I wish to thank Rear Admiral Goodhart for kindly allowing me to adapt his glider
program for use with pterosaurs and the College of Aeronautics for computer facilities.
I am greatly indebted to the staff of the Applied Physical Sciences of this University
for many interesting discussions and help with the mathematics involved.
REFERENCES
BRAMWELL,
C. D., 1970. The first hot-blooded flappers. Spectrum. No. 69.
G. R., 1970. Flying speed of the largest aerial vertebrate. Nuture,
BRAMWLL,
C. D. & WHITFIELD,
Lond. 225: 660-661.
BROWN,B., 1943. Flying Reptiles. BUN.Am. Mu.not. Hist., 52: 104-111.
AERODYNAMICS OF
PTERANODON
327
HANKIN,E. H. & WATSON,
D. M. S., 1914. On the fight of pterodactyls. Aeronaut.J., 18: 324335.
KRIPP,D. VON,1943. Ein Lebensbild von Pteranodon ingens auf flugtechnischer Grundlage. Nova
Acta Leopoldina, 83: 217-246.
NACHTICALL,
W. &WISER, J., 1966. Profilmessungen am Taubenflugel. Z . uergl. Physiol., 52: 333-346.
PENNYCUICK,
C. J., 1960. Gliding flight of the fulmar petra1.J. exp. B i d , 37: 330-338.
PENNYCUICK,
C. J., 1967. The strength of the pigeon’s wing bones in relation to their functi0n.J. exp.
Biol.,46: 219-233.
PENNYCUICK,
C. J., 1968. A wind-tunnel study of gliding flight in the pigeon Columba livia. J. exp.
B i d , 49: 509-526.
PIGWTT,D., 1958. Gliding: a handbook of Soaring Flight, 2nd ed., 263 pp. London: Adam & Charles
Black.
RASPET,A., 1960. Biophysics of bird flight. Science, N . Y. 132: 191-200.
SCHNITZ,
F. W., 1960. Aerodynamik des Flugmodells, 4th ed. Duisburg: Lange.
SMITH,J. M., 1962. The importance of the nervous system in the evolution of animal flight. Evolution,
Lancarter, Pa.,6 : 127-1 29.
STORER,
J. H., 1952. Bird aerodynamics. Scient. Am., 186: 24-29.
TUCKER,
V. A. & PARROT,
G. C., 1970. Aerodynamics of gliding flight in a falcon and other birds.J. exp.
Biol., 52: 345-367.
APPENDIX.
PROGRAM FOlC
The computer program, originally developed for assessment of high performance sailplanes
consists of three procedures:
(1) Assessment of straight flight performance.
(2) Assessment of turning performance.
(3) Calculation of sustained cross country speeds in given meteorological conditions using
the optimum combination of (1) and (2).
In the present paper we are concerned principally with the first two operations.
(1) Straight fZight performance
This is assessed basically on an equation of the form:
where CDo= profile drag coefficient,
CL
= lift
coefficient,
A R = vehicle aspect ratio = b2/S,
b = wing span,
S = surface area of wings.
In the program CDois estimated, at each of the lift coefficients considered, from imput data
consisting of:
(a) Profile drag data relating to the vehicles wing section. This is fed in as digitized drag
curves and has a facility for interpolation between curves of differing Reynolds number.
(b) Profile drag and trim drag relating to vertical and horizontal control surfaces.
(c) An additional figure to account for non-lifting elements, (i.e. bodies etc.) and skin
friction drag due to excrecencies.
The data is completed by the insertion of K , the induced drag factor predetermined after
consideration of the vehicles planform.
C. D. BRAMWELL
328
Speeds, sink rates and lift/drag ratios are then calculated from functions of the form:
I / = - -CLS
-2w '
-
v3s
-.c
u = 247
DIOI
and
L / D = v/u
where V = velocity,
W = weight,
u=sink rate.
(2) Turning performance
In turning flight, flight parameters are related to a pre-determined level flight lift coefficient,
and drag cofficients are determined from that coefficient,corrections may be applied to account
for changes in the spanwise lift distribution and its effect on both profile and induced drags.
Account can also be taken for changes of geometry such as variations of wing area, camber
etc. Following this circling conditions corresponding to various bank angles 4, are computed
as follows:
F
v -- (cosV Lr#)1'2'
VLF
uT = (cos 4 ) 3 ' 2
where subscript T = turn conditions,
LF = level flight datum condition.
Finally for turn radius
R:
(3) Thermalling performance
Having established, in (2), the still air turn performance it is now possible to estimate
the climb rate achieved in circling flight in a thermal. A thermal is considered in the program
to be a column of rising air characterized by two parameters, a centre strength, and an effective
radius. The vertical air movement within the thermal is assumed to vary in a square law
nature, see Fig. 12. The vehicles climb rate is optimized with respect to bank angle so that a
I
I
I
I
I
+-
Effective
-~
radius
I
I
FIGURE
12. Vertical air movement within a thermal.
maximum climb rate is obtained. The optimum speed to fly between such thermals is then
also computed, and an overall speed evaluated. The program carries out this process for a
number of thermal of different sizes and strengths, based of knowledge of real thermals.