Part of the answer about how birds fly in a coordinated and effortless way lies in precise, and previously unknown, aerodynamic interactions, mathematicians have found. The researchers found that flow-mediated interactions between neighbours are, in effect, spring-like forces that hold each member in place. However, these ‘springs’ act in only one direction — a lead bird can exert force on its follower, but not vice versa — and this non-reciprocal interaction means that later members tend to resonate or oscillate wildly.

To replicate the columnar formations of birds, in which they line up one directly behind the other, the researchers created mechanized flappers that act like birds’ wings. The wings were 3D-printed from plastic and driven by motors to flap in water, which replicated how air flows around bird wings during flight. This ‘mock flock’ propelled through water and could freely arrange itself within a line or queue. The flows affected group organisation in different ways — depending on the size of the group. For small groups of up to about four flyers, the researchers discovered an effect by which each member gets help from the aerodynamic interactions in holding its position relative to its neighbours. For larger groups, the flow interactions cause later members to be jostled around and thrown out of position, typically causing a breakdown of the flock due to collisions among members. This means that the very long groups seen in some types of birds are not at all easy to form, and the later members likely have to constantly work to hold their positions and avoid crashing into their neighbours.