Robert L. Nudds

Flying and swimming animals cruise at a Strouhal number tuned for high-power efficiency

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U). St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2 < St < 0.4 (refs 3–8). Because natural selection is likely to tune animals for high propulsive efficiency, we expect it to constrain the range of St that animals use. This seems to be true for dolphins, sharks and bony fish, which swim at 0.2 < St < 0.4. Here we show that birds, bats and insects also converge on the same narrow range of St, but only when cruising. Tuning cruise kinematics to optimize St therefore seems to be a general principle of oscillatory lift-based propulsion.

Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanisms, controlled primarily via angle of attack.

SUMMARY Here we show, by qualitative free- and tethered-flight flow visualization, that dragonflies fly by using unsteady aerodynamic mechanisms to generate high-lift, leading-edge vortices. In normal free flight, dragonflies use counterstroking kinematics, with a leading-edge vortex (LEV) on the forewing downstroke, attached flow on the forewing upstroke, and attached flow on the hindwing throughout. Accelerating dragonflies switch to in-phase wing-beats with highly separated downstroke flows, with a single LEV attached across both the fore- and hindwings. We use smoke visualizations to distinguish between the three simplest local analytical solutions of the Navier–Stokes equations yielding flow separation resulting in a LEV. The LEV is an open U-shaped separation, continuous across the thorax, running parallel to the wing leading edge and inflecting at the tips to form wingtip vortices. Air spirals in to a free-slip critical point over the centreline as the LEV grows. Spanwise flow is not a dominant feature of the flow field – spanwise flows sometimes run from wingtip to centreline, or vice versa – depending on the degree of sideslip. LEV formation always coincides with rapid increases in angle of attack, and the smoke visualizations clearly show the formation of LEVs whenever a rapid increase in angle of attack occurs. There is no discrete starting vortex. Instead, a shear layer forms behind the trailing edge whenever the wing is at a non-zero angle of attack, and rolls up, under Kelvin–Helmholtz instability, into a series of transverse vortices with circulation of opposite sign to the circulation around the wing and LEV. The flow fields produced by dragonflies differ qualitatively from those published for mechanical models of dragonflies, fruitflies and hawkmoths, which preclude natural wing interactions. However, controlled parametric experiments show that, provided the Strouhal number is appropriate and the natural interaction between left and right wings can occur, even a simple plunging plate can reproduce the detailed features of the flow seen in dragonflies. In our models, and in dragonflies, it appears that stability of the LEV is achieved by a general mechanism whereby flapping kinematics are configured so that a LEV would be expected to form naturally over the wing and remain attached for the duration of the stroke. However, the actual formation and shedding of the LEV is controlled by wing angle of attack, which dragonflies can vary through both extremes, from zero up to a range that leads to immediate flow separation at any time during a wing stroke.

The quality of the fossil record of Mesozoic birds

The Mesozoic fossil record has proved critical for understanding the early evolution and subsequent radiation of birds. Little is known, however, about its relative completeness: just how ‘good’ is the fossil record of birds from the Mesozoic? This question has come to prominence recently in the debate over differences in estimated dates of origin of major clades of birds from molecular and palaeontological data. Using a dataset comprising all known fossil taxa, we present analyses that go some way towards answering this question. Whereas avian diversity remains poorly represented in the Mesozoic, many relatively complete bird specimens have been discovered. New taxa have been added to the phylogenetic tree of basal birds, but its overall shape remains constant, suggesting that the broad outlines of early avian evolution are consistently represented: no stage in the Mesozoic is characterized by an overabundance of scrappy fossils compared with more complete specimens. Examples of Neornithes (modern orders) are known from later stages in the Cretaceous, but their fossils are rarer and scrappier than those of basal bird groups, which we suggest is a biological, rather than a geological, signal.

Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds.

The wing kinematics of birds vary systematically with body size, but we still, after several decades of research, lack a clear mechanistic understanding of the aerodynamic selection pressures that shape them. Swimming and flying animals have recently been shown to cruise at Strouhal numbers (St) corresponding to a regime of vortex growth and shedding in which the propulsive efficiency of flapping foils peaks (St ≈ fA/U, where f is wingbeat frequency, U is cruising speed and A ≈ bsin(θ/2) is stroke amplitude, in which b is wingspan and θ is stroke angle). We show that St is a simple and accurate predictor of wingbeat frequency in birds. The Strouhal numbers of cruising birds have converged on the lower end of the range 0.2 < St < 0.4 associated with high propulsive efficiency. Stroke angle scales as θ ≈ 67b−0.24, so wingbeat frequency can be predicted as f ≈ St. U/bsin(33.5b−0.24), with St = 0.21 and St = 0.25 for direct and intermittent fliers, respectively. This simple aerodynamic model predicts wingbeat frequency better than any other relationship proposed to date, explaining 90% of the observed variance in a sample of 60 bird species. Avian wing kinematics therefore appear to have been tuned by natural selection for high aerodynamic efficiency: physical and physiological constraints upon wing kinematics must be reconsidered in this light.

Narrow Primary Feather Rachises in Confuciusornis and Archaeopteryx Suggest Poor Flight Ability

Poor Flight of the Ancients In order to fly, the feathers of birds must be strong enough to support the birds weight without breaking or bending. The main part of a feather providing structural support is its central shaft, which stiffens the feather along its length. In modern birds, this is hollow to reduce weight. Nudds and Dyke (p. 887) show that the cross-section of the shaft of the Mesozoic birds Archaeopteryx and Confuciusornis was much smaller than that of modern birds. Calculations imply that even if it was solid, it would have been too weak to support powered flight and barely strong enough to allow gliding. Thus, powered flight probably arose later in the evolution of birds and these early birds were poor fliers. The flight feathers of early Mesozoic birds Archaeopteryx and Confuciusornis were too weak to support powered flight. The fossil birds Archaeopteryx and Confuciusornis had feathered wings resembling those of living birds, but their flight capabilities remain uncertain. Analysis of the rachises of their primary feathers shows that the rachises were much thinner and weaker than those of modern birds, and thus the birds were not capable of flight. Only if the primary feather rachises were solid in cross-section (the strongest structural configuration), and not hollow as in living birds, would flight have been possible. Hence, if Archaeopteryx and Confuciusornis were flapping flyers, they must have had a feather structure that was fundamentally different from that of living birds. Alternatively, if they were only gliders, then the flapping wing stroke must have appeared after the divergence of Confuciusornis, likely within the enantiornithine or ornithurine radiations.

AN INTERSPECIFIC TEST OF ALLEN'S RULE: EVOLUTIONARY IMPLICATIONS FOR ENDOTHERMIC SPECIES

Abstract Ecogeographical rules provide potential to describe how organisms are morphologically constrained to climatic conditions. Allens rule (relatively shorter appendages in colder environments) remains largely unsupported and there remains much controversy whether reduced surface area of appendages provides energetic savings sufficient to make this morphological trend truly adaptive. By showing for the first time that Allens rule holds for closely related endothermic species, we provide persuasive support of the adaptive significance of this trend for multiple species. Our results indicate that reduction of thermoregulatory cost during the coldest part of the breeding season is the most likely mechanism driving Allens rule for these species. Because for 54% of seabird species examined, rise in seasonal maximum temperature over 100 years will exceed that for minimum temperatures, an evolutionary mismatch will arise between selection for limb length reduction and ability to accommodate heat stress.

Forelimb proportions and the evolutionary radiation of Neornithes

Analysis of a comprehensive dataset demonstrates that the brachial index (BI = humerus length/ulna length) of modern birds (Neornithes) varies significantly between clades at all taxonomic levels, yet is strongly correlated with recent phylogenetic hypotheses. Variance in BI at the infraclass level is low, but increases rapidly during the proposed major radiation of neornithines in the Palaeocene and Eocene. Although a BI of greater than 1 is primitive for Neornithes, more basal groups of Mesozoic birds (Confuciusornithidae and some members of the diverse Enantiornithidae) had BIs comparable with those of ‘higher’ modern clades. It is possible that occupation of ecological niches by these Mesozoic clades precluded the divergence of some groups of neornithines until after the Cretaceous–Tertiary boundary. We suggest that with further analysis and data collection the relationships between flight behaviour, ecology and BI can be determined. Hence, BI may provide a useful tool for characterizing the ecology of fossil birds.

Avian cerebellar floccular fossa size is not a proxy for flying ability in birds

Extinct animal behavior has often been inferred from qualitative assessments of relative brain region size in fossil endocranial casts. For instance, flight capability in pterosaurs and early birds has been inferred from the relative size of the cerebellar flocculus, which in life protrudes from the lateral surface of the cerebellum. A primary role of the flocculus is to integrate sensory information about head rotation and translation to stabilize visual gaze via the vestibulo-occular reflex (VOR). Because gaze stabilization is a critical aspect of flight, some authors have suggested that the flocculus is enlarged in flying species. Whether this can be further extended to a floccular expansion in highly maneuverable flying species or floccular reduction in flightless species is unknown. Here, we used micro computed-tomography to reconstruct “virtual” endocranial casts of 60 extant bird species, to extract the same level of anatomical information offered by fossils. Volumes of the floccular fossa and entire brain cavity were measured and these values correlated with four indices of flying behavior. Although a weak positive relationship was found between floccular fossa size and brachial index, no significant relationship was found between floccular fossa size and any other flight mode classification. These findings could be the result of the bony endocranium inaccurately reflecting the size of the neural flocculus, but might also reflect the importance of the flocculus for all modes of locomotion in birds. We therefore conclude that the relative size of the flocculus of endocranial casts is an unreliable predictor of locomotor behavior in extinct birds, and probably also pterosaurs and non-avian dinosaurs.

Evidence for energy savings from aerial running in the Svalbard rock ptarmigan (Lagopus muta hyperborea)

Svalbard rock ptarmigans were walked and run upon a treadmill and their energy expenditure measured using respirometry. The ptarmigan used three different gaits: a walking gait at slow speeds (less than or equal to 0.75 m s−1), grounded running at intermediate speeds (0.75 m s−1 < U < 1.67 m s−1) and aerial running at high speeds (greater than or equal to 1.67 m s−1). Changes of gait were associated with reductions in the gross cost of transport (COT; J kg−1 m−1), providing the first evidence for energy savings with gait change in a small crouched-postured vertebrate. In addition, for the first time (excluding humans) a decrease in absolute metabolic energy expenditure (rate of O2 consumption) in aerial running when compared with grounded running was identified. The COT versus U curve varies between species and the COT was cheaper during aerial running than grounded running, posing the question of why grounded running should be used at all. Existing explanations (e.g. stability during running over rocky terrain) amount to just so stories with no current evidence to support them. It may be that grounded running is just an artefact of treadmill studies. Research investigating the speeds used by animals in the field is sorely needed.

The shape of pterosaur evolution: evidence from the fossil record

Abstract Although pterosaurs are a well‐known lineage of Mesozoic flying reptiles, their fossil record and evolutionary dynamics have never been adequately quantified. On the basis of a comprehensive data set of fossil occurrences correlated with taxon‐specific limb measurements, we show that the geological ages of pterosaur specimens closely approximate hypothesized patterns of phylogenetic divergence. Although the fossil record has expanded greatly in recent years, collectorship still approximates a sigmoid curve over time as many more specimens (and thus taxa) still remain undiscovered, yet our data suggest that the pterosaur fossil record is unbiased by sites of exceptional preservation (lagerstätte). This is because as new species are discovered the number of known formations and sites yielding pterosaur fossils has also increased – this would not be expected if the bulk of the record came from just a few exceptional faunas. Pterosaur morphological diversification is, however, strongly age biased: rarefaction analysis shows that peaks of diversity occur in the Late Jurassic and Early Cretaceous correlated with periods of increased limb disparity. In this respect, pterosaurs appear unique amongst flying vertebrates in that their disparity seems to have peaked relatively late in clade history. Comparative analyses also show that there is little evidence that the evolutionary diversification of pterosaurs was in any way constrained by the appearance and radiation of birds.