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From damselflies to pterosaurs: How burst and sustainable flight performance scale with size



Recent empirical data for short-burst lift and power production of flying animals indicate that mass-specific lift and power output scale independently (lift) or slightly positively (power) with increasing size. These results contradict previous theory, as well as simple observation, which argues for degradation of flight performance with increasing size. Here, empirical measures of lift and power during short-burst exertion are combined with empirically based estimates of maximum muscle power output in order to predict how burst and sustainable performance scale with body size. The resulting model is used to estimate performance of the largest extant flying birds and insects, along with the largest flying animals known from fossils. These estimates indicate that burst flight performance capacities of even the largest extinct fliers (estimated mass 250 kg) would allow takeoff from the ground; however, limitations on sustainable power output should constrain capacity for continuous flight at body sizes exceeding 0.003-1.0 kg, depending on relative wing length and flight muscle mass.
266:1077-1084, 1994. Am J Physiol Regulatory Integrative Comp Physiol
J. H. Marden
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, August 1, 2002; 205 (15): 2153-2160. J. Exp. Biol.
G. N. Askew and R. L. Marsh
Muscle designed for maximum short-term power output: quail flight muscle
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From damselflies to pterosaurs: how burst and
sustainable flight performance scale with size
of Biology, Pennsylvania State University, University Park, Pennsylvania 16802
Marden, James H. From damselflies to pterosaurs: how burst and
sustainable flight performance scale with size. Am. J. PhysioZ. 266
(Regulatory Integrative Comp. Physiol.
35): R1077-R1084, 1994.-
Recent empirical data for short-burst lift and power production of flying
animals indicate that mass-specific lift and power output scale indepen-
dently (lift) or slightly positively (power) with increasing size. These
results contradict previous theory, as well as simple observation, which
argues for degradation of flight performance with increasing size. Here,
empirical measures of lift and power during short-burst exertion are
combined with empirically based estimates of maximum muscle power
output in order to predict how burst and sustainable performance scale
with body size. The resulting model is used to estimate performance of the
largest extant flying birds and insects, along with the largest flying animals
known from fossils. These estimates indicate that burst flight performance
capacities of even the largest extinct fliers (estimated mass 250 kg) would
allow takeoff from the ground; however, limitations on sustainable power
output should constrain capacity for continuous flight at body sizes
kg, depending on relative wing length and flight
muscle mass.
allometry; muscle physiology; birds; bats; insects; lift; power; locomotion
defined as the capacity to generate
lift, to accelerate and maneuver, and to do so over a
broad range of speeds, appears to degrade with increas-
ing size in flying animals. Most insects, along with many
small birds and bats, are capable of flying vertically,
hovering for extended periods of time, changing speeds
rapidly, and maneuvering in a highly controlled and
precise fashion. In contrast, most of the largest flying
animals (birds with body mass >
kg) appear to have
difficulty becoming airborne, are incapable of more than
momentary hovering, and fly over a limited range of
speeds. Detailed mechanistic models, based on a combi-
nation of empirically and theoretically derived aerody-
namic and muscle physiology parameters, have been
presented to explain this pattern of declining perfor-
mance with increasing size
Recent empirical studies (8, 20,
contradict these
observations and models, showing instead that flight
performance for a wide range of insects, birds, and bats
is independent of size. However, these data are based
solely on maximum flight performance during short-
burst activity, and no effort has yet been made to
determine how these results relate to the scaling of
sustainable performance. The study presented here
combines empirical measures of short-burst flight perfor-
mance with estimates for upper limits of burst and
sustainable muscle power output in order to construct a
general model for the scaling of flight performance. This
model is then used to estimate flight performance
capacities of the largest extant and extinct flying ani-
mals, including the largest flying species known from
Short-burst vs. sustainable performance. The North
American wild turkey (Meleagris gallopavo) is one of
the largest extant flying animals (body mass reaches
kg; Ref.
When flushed at close range, this species
achieves a near-vertical takeoff from a standing start
(personal observation). Such flights are invariably brief
and are probably powered by anaerobic metabolism.
Breast muscle from another fowl, the pheasant (Pha-
sianus colchicas), possesses one of the highest levels of
lactate dehydrogenase (the terminal enzyme in anaero-
bic glycolysis) activity measured from a terrestrial verte-
brate (5). Another galliform, the ruffed grouse (Bonasa
umbellus), is an explosive short-burst flier but is ren-
dered unable to fly and can be captured by hand after a
repeated series of flushes (personal observation). These
observations demonstrate that large flying animals are
capable of at least some of the aspects of flight that we
consider to be high performance, yet there are no
examples where they sustain these levels of perfor-
mance. Thus the problem of scaling of flight perfor-
mance needs to be approached by distinguishing be-
tween levels of performance that are sustainable and
0363-6119/94 $3.00 Copyright c 1994 the American Physiological Society
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performance that can be achieved only during short
bursts of maximal effort.
Upper limits of muscle power output. Differences
between short-burst and sustainable flight performance
can be modeled by combining estimates of the upper
limits of aerobic and anaerobic muscle power output
with empirical data relating power output to lift produc-
tion and morphology.
Ellington (7, 8) reviewed a large body of empirical
studies and concluded that the maximum muscle mass-
specific power output of insect flight muscle is -
which represents
strictly aerobic power because
insect flight muscle has little or no anaerobic capacity
This est imate agrees nicely with the value obtained
from a starling’s pectoralis muscle during steady horizon-
tal flight in a wind tunnel
W/kg; Ref. 3), similarly
obtained data for various modes of flight in pigeons
W/kg; Ref. 6), and estimates based on meta-
bolic rates and aerodynamic analyses of hovering hum-
W/kg; Ref. 40).
and R. D. Stevenson and T. M. Casey
(personal communication) have recently reviewed data
for isolated muscle preparations undergoing imposed
oscillation, with maximum power output determined by
the workloop method
From these data, they con-
cluded that muscle stress and strain during cyclic con-
traction vary inversely with contraction frequency. Con-
workloop area
net work per cycle)
increases with decreasing
contraction frequency, just
sufficiently so that power output (the product of net
work per cycle and cycle frequency) scales independently
of cycle frequency, with a fairly consistent upper limit of
aerobically sustainable power output at -
Thus data from a number of sources and methodologies
all suggest that the upper limit of aerobically sustain-
able mass-specific power output is -
W/kg flight
muscle and is size independent.
Maximum anaerobic power output is less certain, but
estimates for birds are roughly Z-2.5 times the aerobic
limit (i.e., 200-250 W/kg; Ref. 30), which corresponds
with the highest value of specific power output that has
been estimated from short-burst flight performance
experiments (245 W/kg; Refs.
Avian flight muscle contains a mixture of fast glyco-
lytic (FG) and fast oxidative glycolytic fibers, a func-
tional compromise that permits both burst and sustain-
able locomotion. In comparison, skeletal muscles of
lizards and snakes consist primarily of FG fibers special-
ized for burst locomotion, capable of power outputs
averaging 450 W/kg (30). Thus limits of both aerobic
and anaerobic power output are likely to vary according
to muscle fiber-type composition, and the models pre-
sented here should be interpreted as
central tendency rather
than inviolable
an indication of
How limitations on power output affect lift. The most
basic level of flight performance, becoming airborne, is
strictly a matter of producing sufficient lift (here lift
refers to the net upward force experienced by the
animal’s body, rather than the more typical usage that
refers to forces experienced along the surface of an
airfoil). Similarly, the ability to accelerate a body through
air depends on the ratio of force to body mass. Thus net
force production is the primary determinant of aerial
performance as defined here, and muscular power out-
put is indicative of performance only to the extent that it
affects the net force on an animal’s body. Scaling of
aerial performance therefore depends on how force
production varies with body size. Measures of short-
burst lift production in insects, birds, and bats spanning
nearly five orders of magnitude in size (18mg damself-
lies to a 920-g hawk; Refs. 20, 21) show that maximum
lift production is a surprisingly invariant, isometric
function of flight muscle mass (means for various taxa =
54-86 N/kg muscle; this range of lift values is reduced
further by distinguishing between “fling” and conven-
tional wingbeat kinematics among the insects; Fig. lA).
As a result of the nearly constant relationship be-
tween muscle mass and maximum force production,
animals of all taxa and size require nearly the same
minimal amount of flight muscle mass relative to body
mass to achieve takeoff ( - 0.16; termed the “marginal
flight muscle ratio”), and increases in flight muscle ratio
(FMR) above th e marginal level result in a nearly
constant increase in aerial performance.
Measures of maximum lift production can be used to
estimate induced power output (the predominant compo-
nent of total muscle power output for maximally loaded
animals at takeoff; Ref. 8) with the use of the actuator
disk equation for hovering flight (21). Ellington (8) has
proposed that these calculations overestimate induced
power by - 20% because of ground effect but underesti-
mate induced power by a similar amount because of the
assumption of 180” beat amplitude rather than the more
realistic approximation of 120”. The net result of these
considerations is that the two errors cancel. Adjusting
induced power upward by 25% to account for profile
power (8) reveals that muscle mass-specific power out-
put during short-burst flight scales consistently among
taxa according to body mass raised to an exponent of
0.13 (kO.02; 95% confidence limits).
Because muscle mass-specific lift is nearly constant
(Fig. LA), while muscle mass-specific power output
scales positively with body mass (Fig. IB), larger ani-
mals generate less lift per muscle power output (Fig 24).
In other words, larger animals must generate more
power to achieve the same lift. As body size increases
above 1 kg (the largest body mass for which burst
performance has been measured), upper limits of muscle
power output should eventually constrain lift produc-
tion capacity. In contrast, at the lower end of the size
spectrum, many small animals apparently cannot in-
crease their muscle power output up to the typical
aerobic limit (100 W/kg), for if they did, they would
generate lift greater than the observed values of 54-86
N/kg. For example, lift capacity in Sympetrum dragon-
flies averages 57 N/kg (20), which requires a muscle
power output of only 50 W/kg. Thus, for reasons as yet
unknown, over the spectrum of body sizes of flying
animals, there are different factors that limit flight
performance. For most insects, performance is appar-
ently limited by an upper bound of lift, whereas perfor-
mance in the largest flying animals is likely to be limited
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AA fi
100 15 0 200
Muscle mass-specific
Sphinx moth
o* l a
Harris’ Hawk
Fig. 1. A: maximum lift per muscle mass remains nearly
constant (9 = 0.00) across 7- to &fold increase in muscle
mass-specific power output. l , Insects with “fling”
wingbeat mechanism (butterflies, moths, damselflies); 0,
insects with conventional wingbeats (wide variety of taxa
listed in Ref. 20); +, bats; n, birds. B: scaling of muscle
mass-specific power output (P,,,) with body size. Sym-
bols as in A. Data in A and B are from Ref. 20. Power
output has been estimated from maximum lift data
according to helicopter theory (21) with correction for
additional profile power (8). A, 2 independently derived
measures of maximum P,,, for flight muscle: sphinx
moth for insect flight muscle undergoing sinusoidal
contraction (32), and Harris’ hawk for hawk flight
muscle during climbing flight (28). These data show that
estimates of power output derived from lift data agree
closely, in value and scaling slope, with independent,
empirically derived estimates of maximum power output.
-4 -2
Loibody mass (Kg)
by their muscle power output capacity, which can be
further differentiated into burst and sustainable capaci-
The relationship between muscle power output and
aerial performance can be quantified by the lift-to-power
ratio (L/P), obtained by dividing maximum lift produc-
tion by the muscle power output required to generate
that lift (Fig. 2A). Much of the scatter in the scaling of
L/P can be explained by considering wing length in
addition to mass because animals with relatively longer
wings generate a given lift at a lower muscle power
output (Fig. 2B; data from Refs. 20 and 21 corrected for
profile power according to Ref. 8).
A general model for flight performance. Observed
values of L/P (Fig. 2) can be used in combination with
limits on lift and/or muscle power output to estimate
flight performance of animals of various sizes. Flight
performance, defined as the ratio of net lift to body
mass, can be estimated from the following equation
Lift/body mass (N/kg) = FMR
L/P (1)
where FMR is the ratio of flight muscle mass to total
mass, PoJn
is the muscle mass-specific power output
(W/kg flight muscle), and L/P is in units of newtons per
watt. The right side of the equation must equate to at
least 9.8 N/kg for the animal to achieve flight. The
utility (and novelty) of this model is that different values
for upper limits to muscle power output (i.e., aerobic vs.
anaerobic limits) can be used to estimate differences in
burst and sustainable performance. Such an exercise is
presented below, with an emphasis on how burst and
sustainable performance scale with body size.
Maximum aerobically sustainable performance can be
calculated using lift, power, and morphometric data (20,
21) with Eq. 1. These data constitute short-burst lift and
power production capacity; thus the vertebrates in these
experiments were probably using some amount of an-
aerobic power output. This anaerobic contribution can
be factored out by assuming an upper limit of 100 W/kg
for P, m. For animals where the observed value of P,,, is
< 100’ W/kg (mostly insects), there is no reason to
impose an upper limit to P,,, and thus the observed
value is retained. Selected ‘large insects, birds, and
pterosaurs (Table 1) are included in this analysis by
estimating their L/P value from the multivariate regres-
sion of L/P on muscle mass and wing length (Fig. 2B)
and assuming PO,, of 100 W/kg. The goal here is to
determine how performance varies with size for animals
that have a common upper limit of aerobically sustain-
able specific power output.
To compute maximum performance during anaerobi-
cally supplemented flight attempts, I used observed
values for PO,,, along with dimensional data from se-
lected large insects, birds, and pterosaurs (Table l), for
whom L/P was estimated as described above, and P,,
was set at 225 W/kg. From these two approaches, we can
compare levels of performance that various-size
can achieve usi .ng aerobic vs. anaerobic power.
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-5 -4 -3
Log Body Mass (Kg)
Log Lift/Power (NM/)
Fig. 2.
decline in lift per muscle power output in insects, bats, and
birds spanning nearly 5 orders of magnitude in body mass. 0, Bats;
other symbols as in Fig.
same data as in A, plotted in 3
dimensions, showing how lift-to-power ratio (L/P; in units of N/W)
varies depending on body mass and wing length. Least-squares
multivariate regression equation for this relationship is logloL/P =
-0.44010glomuscle mass (kg) + 0.845loglowing length (cm) - 2.239
(rz = 0.97). Data are from Refs. 20 and 21, corrected for profile power
Scaling of sustainable vs. burst performance. If one
assumes an upper limit of aerobically sustainable muscle
power output of 100 W/kg, the model shows that lift
first dips below 9.8 N/kg (the minimum needed for
takeoff or hovering) at a body mass of - 3 g (Fig 3A).
This indicates that 3 g is the largest body mass at which
animals with the shortest relative wing length can
sustain hovering flight. Below 3 g body mass, even the
shortest-winged animals can sustain hovering, whereas
above this point, relatively longer wings are needed.
This may explain why 3 g body mass is the approximate
lower size limit for flying animals possessing significant
anaerobic capacity (i.e., the smallest birds and bats) and
is near the upper size limit for insects, who are thought
to universally lack significant anaerobic capacity. Beetles
and moths weighing more than 3-5 g are common in the
tropics, yet the proportion of insect species whose body
mass exceeds 3-5 g is vanishingly small. An estimate of
flight capacity for one of the heaviest flying insects, the
elephant beetle (Megasoma elephans; body mass 40 g),
falls very near (actually just below) the 9.8 N/kg limit,
suggesting that these giant beetles may actually need a
small anaerobic supplement. Certain fossil dragonflies
are also quite large, but these insects possessed long
wings, which increases their L/P value and changes
their performance estimate drastically. The largest fos-
sil dragonfly, Meganeura monyi, with an estimated body
mass of 18 g and wing length of 30 cm (22), should have
been able to generate a lift force of - 18 N/kg body mass
at a muscle power output of only 56 W (the muscle
power output required to achieve the 60 N/kg lift limit
exhibited by dragonflies). Similarly, the largest hum-
mingbird, Patagonia gigas, has a body mass of 19.1 g
and wing length of 11.7 cm (17); it should be capable of
producing a lift force of 13.4 N/kg body mass at a power
output of 100 W/kg muscle.
Estimates of performance capacity for examples of the
largest extant flying birds (albatross, swan, bustard,
turkey; Table 1) show that they should be capable of
takeoff using anaerobic metabolism (Fig. 3B) but that
they cannot sustain this level of performance aerobically
(Fig. 3A). Alb a t rosses are certainly capable of continu-
ous flight, but they do so by soaring and they rarely flap.
Swans maintain flapping flight for long distances during
migration, which according to this model is possible only
if their sustained power output is well above 100 W/kg
or if their power requirement during steady horizontal
flight is less than that during takeoff (i.e., they require
less power to generate the required amount of lift during
steady forward flight; thus a higher L/P value in the
terms of the present model). Hedenstrom and Alerstam
(12) have estimated sustained P, m of migrating mute
swans as 144 W/kg, a figure substantially higher than
the 100 W/kg limit assumed here, but which improves
their performance estimate to only 6.5 N/kg. Thus the
only remaining possibility is that power requirements of
swans and other large continuous fliers vary as a
function of forward speed, i.e., the long-held notion of a
U-shaped power curve (e.g., Refs. 10, 25, 36), where
flight at an intermediate speed requires less power than
takeoff or maximal speed. Empirical support for a
U-shaped power curve is weak; studies of small- to
medium-sized insects, birds, and bats flying in wind
tunnels mostly show a fairly flat relationship of power
vs. forward speed (8). Perhaps the shape of the power
curve scales allometrically with size, becoming more
U-shaped in larger animals.
A striking result of these calculations is that the lower
bound of the burst performance curve is asymptotic
with 9.8 N/kg at body masses greater than - 10 g (Fig.
3B). Thus the problem of takeoff for the largest known
flying dinosaur, Quetzalcoatlus northropi, with an esti-
mated mass of 250 kg (23, 24), is not vastly different
than takeoff for a l-kg vulture. Both should be able to
take off via anaerobically powered flapping but need to
reduce their power requirement, either by soaring or by
flying at a forward speed where power requirements are
below the level that can be sustained aerobically. In
terms of ability to sustain flight, QuetzaZcoatZus does not
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Table 1. Dimensional data, estimated LIP values, aerobic flight performance estimate, and muscle mass-specific
power required to achieve standing takeoff for selected birds, pterosaurs, and large insects
Mass, kg
Flight Muscle
Mass, kg
Wing Length,
N/kg body wt
Muscle Power
Output Required
for Standing
Takeoff, W/kg
0.0191 0.00573 11.7 0.445-0.446 13.38 73
10 2 168 0.322-0.323 6.47 152
10 3 80 0.144-0.145 4.34 226
10 2 100 0.208-0.209 4.17 235
10 2.2 110 0.216-0.217 4.77 206
Patagonia gigas
60 520
0.187-0.190 4.52 217
0.2 0.014 28 0.629-0.630 4.41
Wandering albatross
Kori bustard
Fossil birds and pterosaurs
Quetzalcoatlus northropi
Archaeopteryx lithographica
Megasoma elephans
Meganeura monyi
0.04 0.014 9.5 0.252-0.253 8.84 111
0.018 0.0063 30 0.947-0.949 18.58 30
Dimensional data for large birds are approximations based on data from a number of sources (e.g., Ref. 10); Patagonia gigas data are from Ref.
17; Quetzalcoatlus northropi data are from Refs. 23 and 24; Archaeopteryx data are from Refs. 42 and 30; Meganeura monyi data are from Ref.
22; Megasoma elephans data are my own unpublished measurements. Lift-to-power ratio (L/P) values are confidence intervals for predictions
from equation in Fig. 2B.
appear to face problems any more severe than those for Ruben (30) has made estimates of flight capacity for
swans, except that it may need a somewhat higher the earliest known fossil bird, Archaeopteryx, assuming
aerobic scope (see Constraints imposed by limitations on reptilian levels of anaerobic capacity (P, m = 450 W/kg),
the rate ofpower input). and concluded that Archaeopteryx could have achieved
1 J&&$3
-- &J
Swan- Bustard
000 A A
CL ---mm-- --
-d-&&; a---------- w-w ------ 9.8N/Kg
Fig. 3. A: scaling of aerobically sustainable
flight performance with body size, assuming
maximum sustainable PO,, I 100 W/kg. Hori-
zontal dashed line, minimum lift needed to
overcome gravity; 0, bats; O, animals in Table
1 whose performance capacity was calculated
as described in text; other symbols as in Fig. 1.
Error bars [based on 95% confidence intervals
(CI) for predictions of L/P from regression
equation in Fig. 2B] are narrower than sym-
bols and have been omitted. Curve shows
maximum performance that would result from
limitations on rate of power input (see Fig. 4);
dotted curves show 95% CI limits for data
points. B: same as A, but assuming maximum
P s 225 W/kg, i.e., approximate upper
lim!t of anaerobically generated power in avian
muscle. Note that much of curvature of data
in A and B is result of size-independent fac-
tors. High performance values for insects (lift
>20 N/kg) result primarily from 1) use of
fling wingbeat kinematics that enhance spe-
cific lift (20), and 2) high flight muscle ratios
in certain species (FMRs = 0.4-0.6) that far
exceed highest FMRs found in vertebrates
(FMR I 0.31 for all vertebrates shown here).
on Pi constraints
I/ Meganeura
-2 0
Log Body Mass (Kg)
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powered takeoff from the ground. Estimates for Ar-
chaeopteryx shown here (Fig. 3B), using Ruben’s esti-
mate of a 7% ratio of flight muscle mass to body mass
(i.e., FMR =
0.07), suggest marginal powered takeoff
ability, even if Archaeopteryx had a burst capacity no
greater than that of birds (-225 W/kg). This is a
surprising result given that birds need a FMR of at least
0.16 to achieve a standing takeoff (20). However, the
model given by Eq. 1 may have yielded an artifactually
high estimate of L/P for Archaeopteryx. L/P estimates
for the animals in Table 1 were calculated from a
multiple regression equation that used muscle mass and
wing length as independent variables (Fig. 2B). Archaeop-
teryx was essentially treated as a small animal (low flight
muscle mass) relative to its wing length, which resulted
in a L/P value that is very high for its actual body and
wing size.
Constraints imposed by limitations on the rate of
power input. Estimates of aerobically sustainable flight
performance derived from Eq. 1 assume that animals of
all sizes are capable of sustaining muscle mass-specific
power output of 100 W/kg. This can be true only if the
rate of power input to the muscle is sufficient to allow
100 W/kg power output, which may be a problem given
that aerobic scope (ratio of maximum metabolic rate to
resting metabolic rate; typically lo- 15) scales indepen-
dently of body size, while resting metabolic rate in birds
scales approximately as mass to the 0.75 power (re-
viewed in Ref. 29). Thus a size-invariant lo- to 15fold
increase above resting should also scale as the 0.75
power of mass, such that maximum mass-specific power
input decreases with increasing body mass. How does
this limitation of power input alter estimates of sustain-
able flight performance shown in Fig. 3A? The first step
in addressing this question is to derive a scaling equa-
tion for the maximum rate of muscle mass-specific
power input. If we assume that muscle accounts for 96%
of a flying animal’s total energy consumption during
flight (as does human muscle during heavy exercise; Ref.
9), and further assume an aerobic scope of 15, then
using Zar’s (42) equation for resting metabolism in
birds, a scaling equation for maximum sustainable
muscle mass-specific power input during flight is as
maximum muscle metabolic rate (W/kg)
= (0.96 x 15 x 3.76M;.73g)/M,
where Mb and M, are body and flight muscle mass,
respectively. Multiplying this result by the efficiency of
conversion of power input to power output, traditionally
thought to be - 20% in vertebrates, yields an estimate
for maximum muscle mass-specific power output. This
figure can be substituted for P,, in Eq. 1 to yield an
estimate of maximum sustainable performance, as lim-
ited by metabolic scope. [Note, however, that recent
empirical estimates of efficiency in flying animals sug-
gest an increase in efficiency with increasing body size
(4). Thus the model presented here represents a worst-
case scenario, where efficiency remains constant with
size. Relationships for scaling of muscle efficiency can be
inserted into this model when they become available.]
To complement estimates of limitations based on the
assumption of constant aerobic scope, I have used
empirical data for maximum metabolic rates measured
from birds flying in wind tunnels (2, 14, 33-35), along
with estimates of flight muscle mass based on data from
the same or similar species (1 l), to derive the following
formula for scaling of maximum muscle mass-specific
metabolic rate during flight
maximum muscle metabolic rate (W/kg)
= (0.96 x 49.09M;.605)/M,
As in Eq. 2, it is assumed that muscle consumes 96% of
total energy consumption during flight. Multiplying this
result by a size-independent conversion-efficiency factor
of 0.20 yields an estimate of the power output of flight
muscle during maximum sustainable exertion, which
can be substituted for PO,, in Eq. 1.
The resulting estimates of performance limitations
for a sample of birds and pterosaurs are shown in Fig. 4.
The constant aerobic scope estimates agree closely with
those derived from empirical measures of maximum
flight metabolism, except at low body mass ( ~0.05 kg).
However, at body mass below 0.05 kg, the curve based
on maximum metabolic rate would require muscle power
output in excess of 100 W/kg muscle, so we can disre-
gard that portion of the graph, whereupon we are left
with essentially a single curve that describes limitations
on power input, as calculated by either method. By
superimposing this curve onto Fig. 3A, we can see how
performance limited by power input (based on the
assumption of constant efficiency) compares with perfor-
x 5
l Performance limited by
scaling of maximum
0 metabolic rate
0 Performan ce limited by
aerobic SC ope = 15
0. 0
-3 -2 -1 0
Log Body Mass (Kg)
2 3
Fig. 4. Flight performance limitations imposed by scaling of metabolic
power input. Estimates are applied to birds sampled in Ref. 20 and
other birds and pterosaurs in Table 1. 0, Estimates based on assump-
tion of constant factorial aerobic scope of 15.
, Estimates based on
observed scaling of maximum flight metabolism in birds. Details of
these calculations are given in text. At body mass < 0.05 kg (arrow on
graph), performance values would require P,,, > 100 W/kg (the
limiting sustainable power output); this region has been omitted from
curve representing these estimates that is superimposed on Fig. 3A.
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mance limited by sustainable power output (100 W/kg
muscle). At body masses below 1 kg, there is a fairly
close match between constraints imposed by limited
power input and constraints imposed by limited power
output. At larger body masses, power input might
become more limiting than power output. This conclu-
sion may not be valid, however, given that efficiency may
increase with size (4) and that certain species can
achieve levels of power input far above what would be
predicted from scaling equations. For example, a prong-
horn antelope with a body mass of 32 kg has a maximum
metabolic rate equal to that expected for a 10-g mouse
(19). Large, continuous-flying animals are likely to have
similarly deviant respiratory capacities; therefore power
input may not be a limiting factor. Upper limits of
muscle power output are likely to be less flexible and
therefore more constraining than energy input rate.
In conclusion, it appears that the degradation in aerial
performance of large flying animals is caused by a
combination of unfavorable scaling of L/P (i.e., the
amount of lift generated per unit power output) and
size-independent upper limits on sustainable muscle
power output. Mass-specific burst power output in-
creases with body mass at a rate sufficient to offset the
reduced L/P value for animals of sizes up to the largest
birds for which we presently have measures of maxi-
mum performance (a 920-g Harris’ hawk; Refs. 21, ZS),
which has led to the conclusion that flight performance
does not vary with body size (8,20,21). Ellington (8) has
posed that we should look for aerodynamic peculiarities
of larger animals to explain their poor performance;
however, the model presented here shows that upper
limits of sustainable power output, in combination with
scaling of L/P, may be sufficient to explain size-
dependent degradation in animal flight performance.
However, even the largest flying animals (including
fossil pterosaurs) should be capable of anaerobically
fueled takeoff from a standing start because the degrada-
tion in predicted burst performance levels off at a value
just above 9.8 N/kg body mass.
A prominent unanswered question regarding perfor-
mance of large fliers is how they can maintain continu-
ous flapping flight, as swans clearly do during migration.
It appears that the most likely explanation for continu-
ous flapping flight in these birds is a U-shaped curve of
power required vs. forward velocity, despite the appar-
ent flatness of the power curve that has been observed in
most empirical studies of smaller birds, bats, and insects
(8). In addit’ ion, birds of this size also face potential
problems in supplying energy at a rate sufficient to meet
expenditure, unless they are substantially more efficient
and/or have respiratory exchange capacities that are
well above rates predicted by scaling relationships. Thus
a foremost opportunity for advancing our understand-
ing of the scaling of flight performance is a detailed
study of the physiology of continuous flight in large,
migratory birds such as swans.
I thank R. D. Stevenson, C. P. Ellington, and two anonymous
reviewers for helpful critiques of the manuscript.
This research was supported in part by National Science Founda-
tion Grants BSR-8803015 and IBN-9317969.
Address for reprint requests: J. H. Marden, Dept. of Biology, 208
Mueller Labs, Pennsylvania State Univ., Univ. Park, PA 16802.
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... m (settled on 11.43 m) (Brower and Veinus, 1981), 11.6-12.2 m (Padian, 1984a), 11-12 m (Langston, 1986;Busbey and Lehman, 1989;Murry et al., 1991;Wellnhofer, 1991b), 10.4 m (Marden, 1994), 12 m (Shipman, 1998), 10.39 m (Chatterjee and Templin, 2004), 10-11 m (Witton, 2007), and 9.64 m (Witton, 2008). A similar set of discrepancies developed for the mass estimates of Q. northropi, ranging from an anorexic 30 kg (Greenewalt, 1975) to an obese 544 kg (Henderson, 2010), but with the trend converging on larger masses over time: 30-440 kg (Greenewalt, 1975), 75 kg (Brower and Veinus, 1981), 86 kg (Langston, 1981;Wellnhofer, 1991b), 65 kg (Padian, 1984c), 64 kg (MacCready, 1985), 113 kg (Paul, 1987), 200 kg (Paul, 1991), 250 kg (Marden, 1994;Paul, 2002), 127 kg (Shipman, 1998), 63-77 kg (Atanassov and Strauss, 2002), 70 kg (Chatterjee and Templin, 2004), 50 kg (Unwin, 2006), 70-85 kg (Witton, 2007), 259 kg (Witton, 2008), 276 kg (Sato et al., 2009), 200-250 kg (Witton and Habib, 2010), 544 kg (Henderson, 2010), at least 350 kg , and 150 kg (Padian et al., 2021). ...
... m (Padian, 1984a), 11-12 m (Langston, 1986;Busbey and Lehman, 1989;Murry et al., 1991;Wellnhofer, 1991b), 10.4 m (Marden, 1994), 12 m (Shipman, 1998), 10.39 m (Chatterjee and Templin, 2004), 10-11 m (Witton, 2007), and 9.64 m (Witton, 2008). A similar set of discrepancies developed for the mass estimates of Q. northropi, ranging from an anorexic 30 kg (Greenewalt, 1975) to an obese 544 kg (Henderson, 2010), but with the trend converging on larger masses over time: 30-440 kg (Greenewalt, 1975), 75 kg (Brower and Veinus, 1981), 86 kg (Langston, 1981;Wellnhofer, 1991b), 65 kg (Padian, 1984c), 64 kg (MacCready, 1985), 113 kg (Paul, 1987), 200 kg (Paul, 1991), 250 kg (Marden, 1994;Paul, 2002), 127 kg (Shipman, 1998), 63-77 kg (Atanassov and Strauss, 2002), 70 kg (Chatterjee and Templin, 2004), 50 kg (Unwin, 2006), 70-85 kg (Witton, 2007), 259 kg (Witton, 2008), 276 kg (Sato et al., 2009), 200-250 kg (Witton and Habib, 2010), 544 kg (Henderson, 2010), at least 350 kg , and 150 kg (Padian et al., 2021). ...
Full-text available
Quetzalcoatlus is the largest flying organism ever known and one of the most familiar pterosaurs to the public. Despite a half century of interest, it remains very incompletely described. This shortfall is addressed here through a full morphological description of Quetzalcoatlus and the other pterosaur material of Big Bend National Park, Texas. The first reported material was described and named Quetzalcoatlus northropi by Douglas Lawson in 1975, but in two separate publications. A ruling by the International Commission of Zoological Nomenclature was required for the name to be made available. Review of the pterosaur fauna of the Park recovers three valid species of azhdarchid pterosaurs in the latest Cretaceous Period Javelina and Black Peaks formations. The size and occurrence of these species are correlated with depositional environment. The holotype of the giant Quetzalcoatlus northropi and six other giant specimens referred to it occur in stream-channel deposits, including the youngest reported pterosaur. The vast majority of specimens (200+) are from large pterosaurs found in the abandoned channel-lake deposits at Pterodactyl Ridge; they form a diagnosable natural group erected as the new species Quetzalcoatlus lawsoni. A moderate-sized partial skull and cervical series also found in the abandoned channel-lake deposits at Pterodactyl Ridge, but lower in the section, is distinct from both species and is erected as Wellnhopterus brevirostris, gen. et sp. nov. Overbank flood-plain facies preserve another eleven specimens of extreme size variation, including small azhdarchids. The Big Bend pterosaur fauna provides the greatest known sample of azhdarchid pterosaurs and three-dimensional pterosaur morphology.
... increases (Pennycuick, 1975). This means that birds as heavy as ostriches cannot become airborne even if they had the largest of wings (Norberg, 1990;Marden, 1994). Such biomechanical constraints (i.e., high-wing loading expressed as grams body mass/cm 2 wing area) associated with flight have been invoked to explain why, for example, swans and ducks require a running takeoff to become airborne and fly (Lovvorn and Jones, 1994), the flightlessness of steamer ducks (Livezey and Humphrey, 1986), and why there are relatively few bird species that fly and eat only plants due to gut size limitations of herbivory (Dudley and Vermeij, 1992;McWilliams, 1999). ...
... For example, the accumulation of large body reserves during the prelaying period results in some female common eider unable to take off (Guillemette and Ouellet, 2005). Such thresholds for flightlessness seem best explained by biomechanical models that integrate wing morphology, muscle mass, and maximum power output required for take off (Marden, 1994). Thus, limitations associated with the power requirements of flapping flight constrain the extent of energy and nutrient storage that can be accumulated especially for larger birds. ...
Migratory birds face a host of physiological challenges during their annual peregrinations including (a) maintaining synchrony with the changing environments encountered as they migrate by relying on environmental cues in conjunction with endogenous rhythms to coordinate patterns of movement and stasis; (b) using fats as their primary fuel to satisfy the very high-metabolic costs of continual flapping flight—this requires more oxygen and lipid transporters and energy production, produces more reactive species, produces less metabolic water, and generates more heat. Overcoming these challenges requires flexible (reversble) modifications to physiology including key components of the endocrine, circulatory, respiratory, antioxidant, and thermoregulatory systems, all of which we have described here. A major theme of this chapter is that the life history of a typical migratory bird includes two migration stages—vernal and autumnal—that occur at separate times of the year under differing environmental conditions, that are regulated by unique neuroendocrine mechanisms, and that present somewhat similar yet distinct physiological challenges. Major gaps remain in our understanding of both the network of specific molecules and regulatory relationships that maintain and adjust homeostasis across the life history stages, and especially how the concentrations of key molecules and the relative strengths of certain regulatory relationships change with the context and the conditions of vernal and autumnal migration. More integrative studies (from molecules to genes to physiology to whole organisms) that are also comparative (multiple systems, multiple tissues within the same individual, migration state vs. nonmigration periods, vernal vs. autumnal migration, multiple species that differ in migration strategy) are needed in order to gain a more complete understanding of how the environment influences migration of birds, how birds overcome the multifaceted physiological challenges of migration, and how individuals will cope with the challenges of climate change.
... These characteristics are ideal for low manoeuvrability flap-gliding and rapid travel across open regions, and match expectations for comparably sized birds 67 and other large pterosaurs 51 . These predictions accord with general trends seen in other scaling regimes, such as reduced humeral RFFs at larger size ( Fig. 5 and Table 2 51 ) and the increased need for soaring at larger wingspans, on account of reduced power available for flapping 68 . (Table 2), hatchling Sinopterus and Pterodaustro would not have been as efficient as their parents at long-distance travel. ...
... Lower aspect wings perform better at elevated angles of attack 59 ; their reduced power requirements could sustain flapping over longer periods; their proportionally stronger skeletons could accommodate rapid shifts in centre of mass, and thus allow greater agility 60 ; and their reduced wing loading would allow for slower flight speeds. Moreover, launch velocity requirements (and thus energy investment) scale with body mass 68,69 , meaning that smaller pterosaurs had an energetic advantage during takeoff. Collectively, these attributes might have rendered juvenile pterosaurs more dynamic fliers than their parents, better able to switch between aerial and terrestrial locomotion, better suited to executing sudden changes in direction and velocity, and capable of nimbler flight in complex environments. ...
Full-text available
Competing views exist on the behaviour and lifestyle of pterosaurs during the earliest phases of life. A ‘flap-early’ model proposes that hatchlings were capable of independent life and flapping flight, a ‘fly-late’ model posits that juveniles were not flight capable until 50% of adult size, and a ‘glide-early’ model requires that young juveniles were flight-capable but only able to glide. We test these models by quantifying the flight abilities of very young juvenile pterosaurs via analysis of wing bone strength, wing loading, wingspan and wing aspect ratios, primarily using data from embryonic and hatchling specimens of Pterodaustro guinazui and Sinopterus dongi. We argue that a young Sinopterus specimen has been mischaracterised as a distinct taxon. The humeri of pterosaur juveniles are similar in bending strength to those of adults and able to withstand launch and flight; wing size and wing aspect ratios of young juveniles are also in keeping with powered flight. We therefore reject the ‘fly-late’ and ‘glide-early’ models. We further show that young juveniles were excellent gliders, albeit not reliant on specialist gliding. The wing forms of very young juveniles differ significantly from larger individuals, meaning that variation in speed, manoeuvrability, take-off angle and so on was present across a species as it matured. Juveniles appear to have been adapted for flight in cluttered environments, in contrast to larger, older individuals. We propose on the basis of these conclusions that pterosaur species occupied distinct niches across ontogeny.
... The weight of pollen loads carried by bees is positively correlated with body mass (Giejdasz, 1998;Ramalho et al., 1998;Goulson et al., 2002;Kerr et al., 2019) with larger females carrying heavier loads than their smaller conspecifics. The maximum load that an animal can lift during take-off flights is positively correlated with body mass (Marden, 1994). However, larger bees may be spending more of their available flight power to lift their mass and maintain hovering flight (Dillon and Dudley, 2004;Buchwald and Dudley, 2010;Seidelmann, 2014), leading to a reduction in power available for flight. ...
... Smaller individuals with lower wing loading have the capacity to carry heavier loads per gram of body mass (Marden, 1987) which may decrease cost of flight. Higher wing loading, as we observed in larger M. rotundata, indicates that more power is needed to accomplish the same lift as a smaller bee (Marden, 1994). This may be because larger bees in our study have smaller wings than expected based on their mass. ...
Body size is related to many aspects of life history, including foraging distance and pollination efficiency. In solitary bees, manipulating the amount of larval diet produces intraspecific differences in adult body size. The goal of this study was to determine how body size impacts metabolic rates, allometry, and flight-related morphometrics in the alfalfa leafcutting bee, Megachile rotundata. By restricting or providing excess food, we produced a range of body sizes, which allowed us to test the effect of body size on allometry, the power required for flight, and amount of energy produced, as measured indirectly through CO2 emission. The power required during flight was predicted using the flight biomechanical formulas for wing loading and excess power index. We found larger bees had higher absolute metabolic rates at rest and during flight, but smaller bees had higher mass-specific metabolic rates at rest. During flight, bees did not have size-related differences in mass-specific metabolic rate. As bees increase in size, their thorax and abdomens become disproportionately larger, while their wings (area, and length) become disproportionately smaller. Smaller bees had more power available during flight as demonstrated by flight biomechanical formulas. Smaller body size was advantageous because of a reduced power requirement for flight with no metabolic cost.
... Even more confusingly the actual lift capacity tracked the mass of dragonflies in an almost linear manner, so in theory there shouldn't be any limit to a dragonfly size. Marden (1994) later returned to the problem to suggest that the actual limit to size was related to burst and sustainable lift performance, although the exact mechanism wasn't clear. ...
Full-text available
Dragonflies are obviously limited in size by physical constraints during flight. However, various studies on dragonflies have shown that the exact physical mechanism limiting their size is still unclear. This paper shows that increasing dragonfly size would increase the stress levels in the wing. The increasing wing stress must exceed the maximum allowable stress in the wing tissue at some point and the wing would begin to fail if the dragonfly became any larger. It is proposed that failure of the wing is the true physical size limit for dragonflies.
... It therefore requires further investigation. However, if supported, then the larger sterna of burst fliers may be explained by their short, powerful flapping bursts that require greater power and thus greater muscle mass and a corresponding larger sternum for muscle attachment [57]. ...
Full-text available
Background: The origin of powered avian flight was a locomotor innovation that expanded the ecological potential of maniraptoran dinosaurs, leading to remarkable variation in modern birds (Neornithes). The avian sternum is the anchor for the major flight muscles and, despite varying widely in morphology, has not been extensively studied from evolutionary or functional perspectives. We quantify sternal variation across a broad phylogenetic scope of birds using 3D geometric morphometrics methods. Using this comprehensive dataset, we apply phylogenetically informed regression approaches to test hypotheses of sternum size allometry and the correlation of sternal shape with both size and locomotory capabilities, including flightlessness and the highly varying flight and swimming styles of Neornithes. Results: We find evidence for isometry of sternal size relative to body mass and document significant allometry of sternal shape alongside important correlations with locomotory capability, reflecting the effects of both body shape and musculoskeletal variation. Among these, we show that a large sternum with a deep or cranially projected sternal keel is necessary for powered flight in modern birds, that deeper sternal keels are correlated with slower but stronger flight, robust caudal sternal borders are associated with faster flapping styles, and that narrower sterna are associated with running abilities. Correlations between shape and locomotion are significant but show weak explanatory power, indicating that although sternal shape is broadly associated with locomotory ecology, other unexplored factors are also important. Conclusions: These results display the ecological importance of the avian sternum for flight and locomotion by providing a novel understanding of sternum form and function in Neornithes. Our study lays the groundwork for estimating the locomotory abilities of paravian dinosaurs, the ancestors to Neornithes, by highlighting the importance of this critical elem
Full-text available
Pterosaurs thrived in and around water for 160 + million years but their take-off from water is poorly understood. A purportedly low floating position and forward centre of gravity barred pterosaurs from a bird-like bipedal running launch. Quadrupedal water launch similar to extant water-feeding birds and bats has been proposed for the largest pterosaurs, such as Anhanguera and Quetzalcoatlus. However, quadrupedal water launch has never been demonstrated in smaller pterosaurs, including those living around the Tethys Sea in the Late Jurassic Solnhofen Lagoon. Using Laser-Stimulated Fluorescence, we singled out aurorazhdarchid specimen MB.R.3531 that alone preserved specific soft tissues among more than a dozen well-preserved Solnhofen pterosaur specimens. These soft tissues pertain to primary propulsive contact surfaces needed for quadrupedal water launch (pedal webbing and soft tissues from an articulated forelimb) that permit robust calculations of its dynamic feasibility without the need to make assumptions about contact areas. A first-principles-based dynamics model of MB.R.3531 reveals that quadrupedal water launch was theoretically feasible and that webbed feet significantly impacted launch performance. Three key factors limiting water launch performance in all pterosaurs are identified, providing a foundation for understanding water launch evolution: available propulsive contact area, forelimb extension range and forelimb extension power about the shoulder.
The vulture guild is composed of two distinct groups, Old and New World, that provide a unique insight into how morphology varies among convergent species. All vultures are considered to be large birds of prey that utilize a style of flight called thermal soaring to search and feed primarily on carrion. Even though this flight style is exhibited among all 23 species, slight variations in their skeletal morphology may relate to their differences in ecology. We hypothesized that vulture humeral morphology varies in relation to these organisms’ habitat, average body mass, courtship displays, and migratory behavior. To address this hypothesis, we used three-dimensional geometric morphometrics to measure the overall shape differences of vulture humeri. Humeral morphology was found to vary most by habitat association and migratory tendency. The humeri of vultures that inhabit forested areas exhibit features that suggest increased flapping flight compared to those in open and mountainous regions. Migratory species were found to possess more robust features near the glenohumeral joint. We found these (and other features) have some utility for predicting ecology and behavior, but we suggest that further investigation into skeletal and muscular wing elements may reveal greater understanding of the habits of extinct vulture species. This article is protected by copyright. All rights reserved.
We reconstruct the proportions and possible motions of the skeleton of the giant azhdarchid pterosaur Quetzalcoatlus. The neck had substantial dorsoventral mobility, and the head and the neck could swing left and right through an arc of ca. 180°. In flight, it is most plausible that the hind limbs were drawn up bird-like, with the knee anterior to the acetabulum. In this position, an attachment of the wing membrane to the hind limb would have been useless. A straight-legged posterior extension of the hind limb, such as rotation of the hind limb into a fully ‘bat-like’ pose, was likely prevented by soft tissues of the hip joint. Given these difficulties, the traditional ‘broad-winged’ bat-like restoration is unrealistic. On the ground, Quetzalcoatlus, like other ornithodirans, had an erect stance and a parasagittal gait. Terrestrial locomotion was powered almost entirely by the hind limbs. The pace length would have been limited to the length of the glenoacetabular distance, except that Quetzalcoatlus (like other pterodactyloids) had a unique gait in which the forelimb was elevated out of the way of the hind limb from step to step. If the humerus were retracted 80° and adducted nearly to the body wall, the elbow and wrist may have been able to extend to effect a quadrupedal launch with assistance from the hind limbs, assuming sufficient long bone strength and sufficient extensor musculature at these forelimb joints. A bipedal launch using the hind limbs alone also appears plausible: despite the animal’s great size, the hind limb to torso length ratio is the greatest for all known pterosaurs.
Avian flight is a rapid and energy-efficient form of locomotion on a per unit distance basis, enabling long daily foraging trips and impressive seasonal migrations. A mixture of flapping flight and periods of gliding and soaring are optimized to each species' aeroecology and environmental circumstances, such that birds are able to extract assistance from their environment, such as thermal and orographic air currents, tailwinds, and formation flight. Sustained flapping flight requires a well-developed respiratory and cardiovascular system which is matched to the size and fiber types of the primary locomotor muscles. The power required by the flight muscles exhibits a U-shaped curve against speed, for hummingbirds, budgerigars, and cockatiels, but, for a number of other species, the shape of the relationship is more linear (at least at their aerobically sustainable air speeds). For migrant birds to sustain flapping flight while fasting, they must transport and oxidise fatty acids in their muscles at much higher rates than mammals, and at a higher percentage of their maximum rate of oxygen consumption.
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The flight of an insect is of a very complicated and extremely energy-demanding nature. Wingbeat frequency may differ between various species but values up to 1000 Hz have been measured. Consequently metabolic activity may be very high during flight and the transition from rest to flight is accompanied by an increase of 50-100-fold in metabolic rate. Small mammals running at maximal speed and flying birds achieve metabolic rates exceeding resting levels by only 7-14-fold. The exaggerated metabolic rate during insect flight is not accompanied by an oxygen debt, which implies -apart from metabolic adaptations- ample availability of oxygen in the organs responsible for flight. Metabolic rate therefore can be estimated, apart from the depletion of fuel depots, by rates of oxygen consumption.
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Summary The flight energetics of hovering hummingbirds was examined by simultaneous collection of metabolic and kinematic data followed by a morphometric analysis of wing characteristics. These data were then used for an aerodynamic analysis of the power output required to generate sufficient lift; this, together with the metabolic power input, allowed an estimate of the flight efficiency. The use of two closely related species demonstrated common design features despite a marked difference in wing loading. Considerations of the inertial power costs strongly suggest that hummingbirds are able to store kinetic energy elastically during deceleration of the wing stroke. This analysis predicts that hummingbirds hover with a muscle power output close to 100-120W kg21 at 9-11% mechanochemical efficiency.
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Summary Flight performance seems to change systematically with body size: small animals can hover and fly over a wide range of speeds, but large birds taxi for take- off and then fly over a narrow speed range. The traditional explanation for this is that the mass-specific power required for flight varies with speed according to a U-shaped curve, and it also scales between m° and m1/6, where m is body mass. The mass-specific power available from the flight muscles is assumed to scale as m~1/3. As available power decreases with increasing body size, the range of attainable flight speeds becomes progressively reduced until the largest animals can only fly in the trough of the U-shaped curve. Above a particular size, the available power is insufficient and flapping flight is not possible. The underlying assumptions of this argument are examined in this review. Metabolic measurements are more consistent with a J-shaped curve, with little change in power from hovering to intermediate flight speeds, than with a U-shaped curve. Scaling of the mass-specific power required to fly agrees with predictions. The mass-specific power available from, the muscles, estimated from maximal loading studies, varies as m 013 . This scaling cannot be distinguished from that of the power required to fly, refuting the argument that power imposes an intrinsic scaling on flight performance. It is suggested instead that limitations on low-speed performance result from an adverse scaling of lift production with increasing body size
Current scenarios frequently interpret the Late Jurassic bird Archaeopteryx as having had an avian-type physiology and as having been capable of flapping flight, but only from "the trees downward." It putatively lacked capacity for takeoff and powered flight from the ground upward. Data from extant reptiles indicate that if Archaeopteryx were physiologically reptilian, it would have been capable of ground upward takeoff from a standstill, as well as "trees downward" powered flight. This conclusion is based largely on a previously unrecognized attribute of locomotory (skeletal) muscle in a variety of extant reptiles: During "burst-level" activity, major locomotory muscles of a number of active terrestrial taxa generate at least twice the power (watts kg-1 muscle tissue) as those of birds and mammals. Reptilian physiological status also helps resolve the apparently uneven development of various flight support structures in Archaeopteryx (e.g., well-developed flight features but relatively unspecialized pectoral girdle, supracoracoideus muscles, etc.). Endothermy and capacity for longer-distance powered flight probably evolved only in Early Cretaceous birds, which were the first birds to have a keeled sternum, strap-like coracoid, and hypocleidium-bearing furcula.
Many members of the extinct insect order Protodonata were much larger than modern Odonata, although structural similarities between the two groups are marked. Many extant dragonflies are endothermic, and in general their reliance on endothermy increases with increasing size. I hypothesize, following Heinrich and Casey (1978) and Heinrich (1981), that large Protodonata were strongly endothermic and used mechanisms similar to those of Odonata to modulate heat production and loss. Protodonata lived in tropical regions and so may often have been exposed to heat stress. Their morphology suggests that, like Odonata, they were strong-flying, aerial, diurnal predators and probably flew for extended periods; they therefore probably had high rates of heat production during much of their active periods. Their wings were similar in proportions to those of dragonflies, but their bodies were considerably smaller in proportion to the wings. Nevertheless, body mass was much greater and surface: volume ratio much lower in the largest species than in any odonate. Based on known and inferred dimensions of Protodonata, and on the assumptions that heat production and heat loss scaled with size in ways that were similar to living dragonflies, it is possible to estimate the excess of thoracic temperature over air temperature. In Meganeura monyi, one of the largest species, this excess could have been as great as 74 C if these insects were insulated as well as dragonflies. Even if they were uninsulated, the excess might have exceeded 50 C. Smaller species would have had smaller, but still quite substantial, elevation of body temperature. It seems inescapable that the larger species must have reduced heat input by crepuscular activity, gliding, or augmented heat loss, perhaps by circulation of haemolymph to the abdomen. Since thoracic temperature must nevertheless have been high during flight, they probably had to elevate their temperature by wing-shivering before flight.
Pennycuick's theory for the energetic requrements of avian flight predicts the metabolic rates of budgerigars and laughing gulls flying level at intermediate speeds in a wind tunnel with an accuracy of 10% or better. However, its predictions appear to be low for most birds with masses less than 0.1 kg and high for most birds with masses greater than 0.5 kg. Four modifications are made to Pennycuick's theory: a different computation of induced power; a different estimate of equivalent flat plate area that includes Reynolds number effects, and is based on additional measurements; a different estimate of profile power that includes Reynolds number effects; and the addition of power terms for respiration and circulation. These modifications improve the agrement between the theoretical predictions and existing measurements for flying birds and bats. The metabolic rates of birds and bats in level flight at various speeds can be estimated by the modified theory if body mass alone is measured. Improved estimates can be made if wing span is measured as well. In the latter case the theory predicts measured values with a mean absolute error of 8.3%. The results of the modified theory are presented by approximate equations that can be solved quickly for metabolic rate and flight speed with a slide rule.