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

Abstract

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.

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266:1077-1084, 1994. Am J Physiol Regulatory Integrative Comp Physiol
J. H. Marden
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From damselflies to pterosaurs: how burst and
sustainable flight performance scale with size
JAMES H. MARDEN
Department
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
exceeding
0.003-1.0
kg, depending on relative wing length and flight
muscle mass.
allometry; muscle physiology; birds; bats; insects; lift; power; locomotion
AERIAL PERFORMANCE,
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 >
1
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
(18,25,26,28,37,38).
Recent empirical studies (8, 20,
21)
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
fossils.
Short-burst vs. sustainable performance. The North
American wild turkey (Meleagris gallopavo) is one of
the largest extant flying animals (body mass reaches
10
kg; Ref.
31).
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
R1077
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EDITORIAL REVIEW
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 -
100
W/kg,
which represents
strictly aerobic power because
insect flight muscle has little or no anaerobic capacity
(1).
This est imate agrees nicely with the value obtained
from a starling’s pectoralis muscle during steady horizon-
tal flight in a wind tunnel
(104
W/kg; Ref. 3), similarly
obtained data for various modes of flight in pigeons
(51-119
W/kg; Ref. 6), and estimates based on meta-
bolic rates and aerodynamic analyses of hovering hum-
mingbirds
(120
W/kg; Ref. 40).
Josephson
(16)
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
(15).
From these data, they con-
cluded that muscle stress and strain during cyclic con-
traction vary inversely with contraction frequency. Con-
sequently
9
workloop area
(i.e.,
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 -
100
W/kg.
Thus data from a number of sources and methodologies
all suggest that the upper limit of aerobically sustain-
able mass-specific power output is -
100
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.
21,28>.
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
limits.
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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R1079
z
0
A
A
A
A
AA fi
100 15 0 200
Muscle mass-specific
power
ww
A
Sphinx moth
A
A
A A
A
A A
A
A
A
I
0
l
o* l a
Harris’ Hawk
I I I
I I I
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.
-5
-4 -2
Loibody mass (Kg)
-1
by their muscle power output capacity, which can be
further differentiated into burst and sustainable capaci-
ties.
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
x
P,,
x
L/P (1)
7
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
0
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.
animals
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EDITORIAL REVIEW
Q
AA
AA A
A
A
A
-0.6
-I+
-5 -4 -3
-2
’
0
Log Body Mass (Kg)
Log Lift/Power (NM/)
Fig. 2.
A:
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.
1.
B:
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
(8).
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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EDITORIAL REVIEW
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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
Species
Body
Mass, kg
Flight Muscle
Mass, kg
Wing Length,
cm
L/P,
N/W
Maximum
Aerobic
Performance,
N/kg body wt
Muscle Power
Output Required
for Standing
Takeoff, W/kg
Birds
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
250
60 520
0.187-0.190 4.52 217
0.2 0.014 28 0.629-0.630 4.41
222
Wandering albatross
Turkey
Kori bustard
Swan
Fossil birds and pterosaurs
Quetzalcoatlus northropi
Archaeopteryx lithographica
Insects
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
A
50
1
a
Meganeura
Albatross
Turkey
1 J&&$3
-- &J
0
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).
I
-4
on Pi constraints
Albatross
Turkey
Swan
Bustard
I/ Meganeura
Quetzalcoatlus
1
---------------------
P
cl
Megasoma
Archaeopteryx
I I
-2 0
Log Body Mass (Kg)
I
2
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EDITORIAL REVIEW
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
follows
maximum muscle metabolic rate (W/kg)
= (0.96 x 15 x 3.76M;.73g)/M,
(2)
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,
(3)
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-
-
30
z
.-
x 5
2
0
l Performance limited by
0
scaling of maximum
0 metabolic rate
0
0 Performan ce limited by
0
aerobic SC ope = 15
00
0.
0
0. 0
w
@
a
Q
0
Q
I
I I I I I
0
I
-3 -2 -1 0
1
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.
l
, 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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EDITORIAL REVIEW
R1083
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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