Two main results emerged from our analyses; (1) that flight speeds
among bird species scaled significantly differently with mass and wing
loading than predicted from basic aerodynamic principles and (2) that
phylogenetic group contributed in a highly significant way to explain
the considerable variation in bird flight speeds that remained, even
after the biometrical dimensions of the bird species had been taken
Scaling of Flight Speed
The scaling exponents fell below predicted values for both of the tested relationships, for Ue versus m as well as Ue versus Q.
Predicted scaling exponents were based on the assumptions of
geometrical and dynamical similarity. Could deviations from one or both
of these assumptions explain our results? Earlier studies have
demonstrated that bird species are not, on average, geometrically
identical, but larger species tend to have proportionately longer
wingspans and larger aspect ratios [2,5,10]. This was confirmed for the sample in the present study with aspect ratio scaling significantly positively to m as well as Q.
overall scaling exponent of 0.14 for flight speed versus body mass was
calculated for theoretical flight speeds after taking the slight
positive allometry in wing size into account for a large sample of bird
This fits well with the corresponding exponent for observed speeds in
this study, making departure from geometrical similarity a likely
explanation for this result. The negative scaling exponent of Ue in relation to m
for the swans, geese, and ducks may be an effect of a reduced flight
power margin with increasing size restricting the largest flyers like
swans to fly close to the minimum power speed rather than at the faster
speed associated with maximum effective lift-drag ratio [18,19].
Such constrained flight speeds for the largest flyers will also have
the effect of reducing the overall scaling exponents, thus providing
another contributory explanation for the observed results in this study.
similarity is reflected by Reynolds number, which will differ between
bird species in proportion to their size (length dimension) and speed .
Reynolds number shows a 15-fold range among the species in our sample
(ranging from approximately 25,000 to 375,000 based on mean wing chord,
S/b, as length measurement). Such a range of Reynolds
number may well be large enough to give rise to significant departures
from dynamical similarity. The main expected consequence would be a
reduced coefficient of frictional drag for birds with large Reynolds
number (i.e., large and fast birds) leading to an increased optimal
cruising speed among these species [14,20]. Thus, such a departure from dynamical similarity is expected to show up as an augmented scaling exponent for Ue versus m (and also for Ue versus Q), rather than a scaling exponent lower than expected as in this analysis.
In view of the opposite effects on scaling exponents of departures from geometrical and dynamical similarity, respectively , we conclude that only the departure from geometric similarity can explain why the scaling exponent for Ue versus m falls significantly below one-sixth among birds in cruising migratory flight.
Do geometrical differences provide a sufficient explanation also for the fact that the scaling exponent for Ue versus Q
fell clearly below the expected value of one-half? One way to evaluate
this is to calculate the scaling exponent for flight speed versus span
loading (m × g/b2, where b is
wingspan). Span loading is equivalent to wing loading divided by the
aspect ratio, and for birds differing in their geometric wing shapes
cruising flight speed is expected to scale most closely with the square
root of span loading (under geometrical similarity flight speed is
predicted to scale with the same exponent of one-half versus both span
loading and wing loading) .
The scaling exponent for Ue versus span loading (species level, exponent 0.36 with 95% confidence interval 0.31–0.40, n = 129 and phylogenetic contrasts, exponent 0.37 with 95% confidence interval 0.26–0.48, n = 17) exceeded that versus Q (with corresponding exponents of 0.31 and 0.32, respectively, Table 1)
although still falling significantly below the predicted value of
one-half. This suggests that the geometrical differences explain part,
but not all, of the discrepancy between observed and expected scaling
of Ue versus Q. Departure from dynamical
similarity will, in its most simple form (as reflected by differences
in Reynolds number), contribute to an augmented rather than reduced
scaling exponent in relation to that predicted and can therefore not
provide any useful additional explanation in this case (see above).
Still, dynamical differences of other kinds may exist for reasons that
are notoriously difficult to predict for flapping flight. Future
studies of vortex patterns associated with flapping flight of different
species will be important to demonstrate possible dynamical differences
between species (see below).
We suggest that the unexpectedly small scaling exponent for Ue versus Q
may be the result of general evolutionary forces acting to increase
cruising speeds for species with the lowest wing loadings and reduce
speeds for species with the highest wing loadings. The bird species in
our analysis show approximately a 10-fold difference in their range of Q (from about 15 to 150 N/m2, Figure 1). With an observed scaling exponent for flight speed of 0.31, this range of Q is associated with a 2-fold (100.31
= 2.0) difference in flight speed. However, with a predicted scaling
exponent of 0.5 we would have expected more than a 3-fold difference in
cruising speed (100.5 = 3.2). Given that birds with low Q (about 15 N/m2) fly at a speed about 10 m/s (as observed), species with high Q (about 150 N/m2)
would fly at 32 m/s according to the general aerodynamic scaling rules.
This may well be impracticably fast and difficult to reconcile with
flight performance in situations of start, landing, flock manoeuvres,
etc. Conversely, given that birds with high Q fly at a speed about 20 m/s (as observed), species with low Q
would fly at only about 6 m/s according to the general aerodynamic
scaling rules. Such very slow speeds will be disadvantageous because of
sensitivity to wind, vulnerability to predation, etc. Hence, it seems
reasonable to expect that there are evolutionary forces operating to
compress the range of cruising flight speeds among bird species  and thus reducing the scaling exponent for Ue versus Q.
This compression of the range of flight speeds is attained partly
through general geometrical differences between species (larger aspects
ratios among species with larger mass and wing loading, as discussed
above), but additional unknown mechanisms, perhaps associated with
different kinematics of flight or different muscle operation between
species, seem to be required to fully explain the restricted range of
flight speeds among bird species.
Bounding flight seems to be a mode for small birds (mainly passerines) to mitigate the costs of fast flight [1,2,10,21], while flap-gliding, used by many raptors, is associated with a reduction in cruising flight speed . Both of these styles of intermittent flight are used by species with low or intermediate Q (Figure 1),
and, having opposite effects on flight speed, they are unlikely to
provide a sufficient explanation for the low scaling exponent of Ue versus Q among bird species as a whole.
Variability of Flight Speeds
analyses have demonstrated that scaling relationships between wing
loading and total mass differ significantly between different types of
The expected consequence of this is that wing loading will be a more
reliable predictor of flight speed, explaining more of the variation in
flight speeds among bird species than body mass [1,5]. This expectation was fully confirmed in the present study, with Q accounting for almost half of the variation in Ue between species, while m explained only 12% of this variation (Figure 2). However, our findings that Q
still left a large part of the variation in flight speed unexplained
and that phylogenetic group accounted for a significant fraction of
this remaining variation were unexpected from earlier analyses based on
theoretically calculated flight speeds [5,10].
are the causes for the discrepancies in flight speed between
phylogenetic groups? Differences in flight mode and the use of bounding
flight by many passerines have been suggested as explanations for
important group-specific deviations from aerodynamic predictions of
optimal bird flight speeds .
We provisionally assigned, based on our own field experience, the
different bird species to three main modes of flapping flight; (1)
continuous flapping (e.g., shorebirds and ducks), (2) intermittent
flapping with short gliding phases (raptors, swifts, and swallows), and
(3) bounding flight (many but not all passerines use this mode of
intermittent flapping with phases of wing folding). Ue differed significantly between flyers in these three categories (p < 0.001, adjusted R2 = 0.26, and F2,135 = 25.1), and the explanatory power of a model incorporating both flight mode and Q was high (p < 0.001, adjusted R2 = 0.60, and F3,125
= 64.5). This suggests that difference in flight mode is one element
affecting the characteristic cruising flight speeds among phylogenetic
Depending on their ecological life style and foraging,
birds are adapted to different aspects of flight performance, e.g.,
speed, agility, lift generation, escape, take-off, cost of transport,
and power [2,10].
These adaptations are likely to have implications for the flight
apparatus (anatomy, physiology, and muscle operation) and the flight
behaviour that may constrain the cruising flight speed. The variations
in power-versus-speed relationships between different species  and in muscle efficiency (conversion from metabolic power input to mechanical power output) with mass and flight speed [23,24]
may be related to such differential complex flight adaptations among
birds. Constraints on flight speed may also be associated with
differences in fluid dynamics and vortex patterns, hereto investigated
only for a few species [25–27].
Variable airspeeds may still be associated with high power efficiency
if accompanied with the proper variation in wing stroke frequency and
flying at comparatively slow cruising speeds frequently use thermal
soaring (raptors and storks), are adapted for hunting and load carrying
(raptors), or for take-off and landing in dense vegetation (herons).
Associated with these flight habits they have a lower ratio of elevator
(supracoracoideus) to depressor (pectoralis) flight muscle
(particularly low among birds of prey) compared with shorebirds and
We suggest that functional differences in flight apparatus and
musculature among birds of different life and flight styles
(differences often associated with evolutionary origin) have a
significant influence on the birds' performance and speed in sustained
cruising flight. Thus, our results strongly indicate that there is a
diversity of cruising flight characteristics among different types of
birds over and above the general scaling effects of mass and wing
loading that remains to be investigated and understood, aerodynamically
, kinematically [26,31], physiologically , as well as ecologically [2,10].