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. 2017 Sep 5;7:10452. doi: 10.1038/s41598-017-09986-5

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Comparison between experimental results and numerical simulations. (A) 200 s long (1000 time steps) segment of flight trajectories from flock D release ff2. For better visibility, only three pigeons are exhibited. (B–D) The distances between the average circular centers and loft, average curvature radius, and distances between the average positions and loft, respectively. If the pigeon flock flies relatively straight for three continuous instants, the average curvature radius will grow larger in synchronized manner with peaks in (B) and (C). (E–H) Results corresponding to the 1000 steps of the numerical simulations.