Predicting Trends in Avian Wing Motion and Energetics Across Scales

Birds exhibit monotonic trends in their flight kinematics across a broad range of scales. For example, in 10g to 10kg birds flight speed increases with scale while wingbeat frequency decreases. Existing hypotheses propose that aerodynamic and biomechanical factors may drive these trends. Predictive simulation models have used these drivers to computationally synthesize flying birds. However, only a small number of species have been simulated and so this approach has not explained the kinematic trends observed across different scales of birds. This work uses predictive models to synthesize flight across all scales and shows that profile drag of the avian aerofoil is the key physical driver of self-selected kinematics. Profile drag causes the monotonic increase in flapping speed across scales and the near-constant ratio of flapping speed to flight speed (Strouhal number). The most efficient kinematics minimize Strouhal number to minimize the cost of transport, with the minimum cost of transport being bounded by the aerofoil maximum lift-to-drag ratio. The decrease of wingbeat frequency and increase of wing elevation amplitude with scale are attributable to balancing induced drag and the lateral component of profile drag. The analytical and low-order numerical models presented provide transparency in understanding how modelling choices influence flight predictions. The work provides a platform for developing higher fidelity flight energetics models that address the scale limits of flying birds.