Abstract
Birds morph their wing shape to accomplish extraordinary manoeuvres1–4, which are governed by avian-specific equations of motion. Solving these equations requires information about a bird’s aerodynamic and inertial characteristics5. Avian flight research to date has focused on resolving aerodynamic features, whereas inertial properties including centre of gravity and moment of inertia are seldom addressed. Here we use an analytical method to determine the inertial characteristics of 22 species across the full range of elbow and wrist flexion and extension. We find that wing morphing allows birds to substantially change their roll and yaw inertia but has a minimal effect on the position of the centre of gravity. With the addition of inertial characteristics, we derived a novel metric of pitch agility and estimated the static pitch stability, revealing that the agility and static margin ranges are reduced as body mass increases. These results provide quantitative evidence that evolution selects for both stable and unstable flight, in contrast to the prevailing narrative that birds are evolving away from stability6. This comprehensive analysis of avian inertial characteristics provides the key features required to establish a theoretical model of avian manoeuvrability.
Highlights
Where v is velocity vector and ω is the angular velocity vector
Studies often overlook the essential inertial properties (Fig. 1a) or use static morphology approximations for individual species13, . 17–20 Here we fill this gap by investigating the variable inertial characteristics of flying birds to provide the necessary step towards establishing a general framework of avian manoeuvrability
To determine how inertial characteristics vary during wing morphing, we developed a general analytical method to quantify any flying bird’s centre of gravity and I, and used a comparative analysis to investigate 22 species spanning the phylogeny defined by Prum et al.[21], except for Palaeognathae as this clade contains largely flightless birds
Summary
An Ornstein Uhlenbeck model was a good fit for the mean xCG such that the phenotypic optimum (θCG) was 10% of the body length behind the humeral head (ΔAICc = −8.23, αOU = 0.11, σ2 = 0.1 × 10−3; Extended Data Fig. 2a). The stability of this centre of gravity position depends on the location of the neutral point (Fig. 4c, d). It is important to highlight that further work is required to incorporate the inter- and intra-specific aerodynamic capabilities, shoulder and tail ROM, and in vivo configurations to definitively confirm the optimal phenotype(s) for static pitch stability. 23% of the species in our study were unable to shift between stable and unstable modes with the elbow and wrist alone, and there are many combinations of stability characteristics in modern birds
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