A flight formation mechanism: The weight of repulsive force

Abstract Large birds always choose orderly flight formations for migration. The energy-saving hypothesis and visual communication hypothesis have provided explanations for the formation mechanisms of flight formations of large birds. However, the experimental data differ greatly from the theoretical results of the energy-saving hypothesis, and the visual communication hypothesis lacks sufficient supporting evidence. Moreover, neither of these two hypothesises can explain the differences between flight formations of large and small birds. In this article, the authors investigated the formation mechanism of bird flocks from a new perspective, i.e., the weight of repulsive force between individuals, and provided explanations for the differences between flight formations of large and small birds. The authors believe that the weight of repulsive force between large birds is greater than that between small birds, which makes them better at preventing collisions between individuals. The simulation results show that as the weight of repulsive force between individuals is gradually increased, the flight formation of the flock converts from a cluster formation (corresponding to the flight formation of small birds) to a single-row formation (corresponding to the flight formation of large birds). And the migration speed of the single-row flight formation is larger than that of the cluster formation. In addition, the authors also studied the effects of population and density of individuals on flight formations: the entire flock will lose the ability to migrate when the number or density of individuals is large enough. The findings of this article may provide theoretical guidance for the autonomous control for unmanned aerial vehicle swarms.