ArticleProceedings of the National Academy of Sciences of the United States of America2026
A minimal wake-vortex model explains formation flight of flapping birds.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Collective patterns of motion emerge across biological taxa: insects swarm, fish school, and birds flock. In particular, many large migratory bird species form distinctly ordered V-shaped formations, which experiments and direct numerical simulations have demonstrated provide substantial energetic benefits during long-distance flight. However, the precise aerodynamic and morphological mechanisms which underlie these benefits remain unclear. In this work, we develop a reduced-order model of the wake-vortex interactions between two flapping birds flying in tandem. The model retains essential unsteady flapping dynamics while remaining computationally tractable. By optimizing over a six-dimensional state space, which comprises the follower's three-dimensional relative position as well as three independent flapping parameters, we identify the energetically optimal leader-follower configuration of northern bald ibises (
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