Flight speed is expected to increase with mass and wing loading among …

• Abstract
• Author Summary
• Introduction
• Results
• Discussion
• Materials and Methods
• References

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 into account.

Scaling of Flight Speed

The scaling exponents fell below predicted values for both of the tested relationships, for U_e versus m as well as U_e 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.

An 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 species [9]. 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 U_e 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.

Dynamical similarity is reflected by Reynolds number, which will differ between bird species in proportion to their size (length dimension) and speed [20]. 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 U_e versus m (and also for U_e 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 [1], we conclude that only the departure from geometric similarity can explain why the scaling exponent for U_e 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 U_e 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) [5].

The scaling exponent for U_e 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 U_e 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 U_e 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 (10^0.31 = 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 (10^0.5 = 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 [5] and thus reducing the scaling exponent for U_e 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 [21]. 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 U_e versus Q among bird species as a whole.

Variability of Flight Speeds

Dimensional analyses have demonstrated that scaling relationships between wing loading and total mass differ significantly between different types of birds [5,10]. 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 U_e 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].

What 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 [15]. 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). U_e differed significantly between flyers in these three categories (p < 0.001, adjusted R² = 0.26, and F_2,135 = 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 F_3,125 = 64.5). This suggests that difference in flight mode is one element affecting the characteristic cruising flight speeds among phylogenetic groups.

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 [22] 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 amplitude [28,29].

Species 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 anatids [2]. 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 [30], kinematically [26,31], physiologically [22], as well as ecologically [2,10].