Abstract
A theoretical model of avian flight is developed which simulates wing motion through a class of methods known as predictive simulation. This approach uses numerical optimization to predict power-optimal kinematics of avian wings in hover, cruise, climb and descent. The wing dynamics capture both aerodynamic and inertial loads. The model is used to simulate the flight of the pigeon, Columba livia, and the results are compared with previous experimental measurements. In cruise, the model unearths a vast range of kinematic modes that are capable of generating the required forces for flight. The most efficient mode uses a near-vertical stroke-plane and a flexed-wing upstroke, similar to kinematics recorded experimentally. In hover, the model predicts that the power-optimal mode uses an extended-wing upstroke, similar to hummingbirds. In flexing their wings, pigeons are predicted to consume 20% more power than if they kept their wings full extended, implying that the typical kinematics used by pigeons in hover are suboptimal. Predictions of climbing flight suggest that the most energy-efficient way to reach a given altitude is to climb as steeply as possible, subjected to the availability of power.