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- Title
A theoretical analysis of formation flight as a nonlinear self‐organizing phenomenon.
- Authors
Sugimoto, Takeshi
- Abstract
This study analyses the existence, stability and self‐organization of formation flight utilized by migrant birds. Air is approximated as an incompressible inviscid flow, while birds are modelled as elliptically loaded lifting‐lines. Application of conventional wing theory leads to newly derived, basic equations that describe the problem as a dynamical system of multiple wings interacting with each other through induced flow field. Formation flight is defined as the steady‐state solution of the basic equations, in particular the solution that all the birds fly at the same speed. In the case of a prescribed thrust, constant transverse interval between adjacent birds, and a flock of physically identical birds, analytical study of the basic equations reveals the facts that (1) formation flight is self‐organized and (2) this formation flight is stable. The new implication is that a configuration of formation emerges as a result of nonlinear dynamical interaction between many birds and that this nonlinear dynamical system does not exhibit chaotic behaviour. Numerical calculation has also been done for cormorant‐type birds with the same transverse interval between flock members. The proposed numerical scheme quickly converges to very accurate results owing to the recently derived, closed‐form expression of induced velocity distribution around an elliptically loaded lifting‐line. Transverse intervals between birds are found to be a more important factor than the number of birds. Configurations of formations are found to be inverted U rather than inverted V. In these formations every bird enjoys the same amount of drag reduction.
- Subjects
ANIMAL flight; CONFIGURATION space; NUMERICAL analysis; NUMERICAL calculations; BIRD watching
- Publication
IMA Journal of Applied Mathematics, 2003, Vol 68, Issue 5, p441
- ISSN
0272-4960
- Publication type
Article
- DOI
10.1093/imamat/68.5.441