Modeling flying formations as flow-mediated matter

Collective locomotion of flying animals is fascinating in terms of individual-level fluid mechanics and group-level structure and dynamics. Here we introduce a model of formation flight that views the collective as a material whose properties arise from the flow-mediated interactions among its members. It builds on an aerodynamic model that describes how flapping flyers produce vortex wakes and how they are influenced by others' wakes. Long in-line arrays show that the group behaves as a soft, excitable "crystal" with regularly ordered member "atoms" whose positioning is, susceptible to deformations and dynamical instabilities. Perturbing a member produces longitudinal waves that pass down the group while growing in amplitude; with these amplifications even causing collisions. The model explains the aerodynamic origin of the spacing between the flyers, the springiness of the interactions, and the tendency for disturbances to resonantly amplify. Our findings suggest analogies with material systems that could be generally useful in the analysis of animal groups.