Statistics of individual midge velocities.
(a) Standard deviations of swarm velocity components; note that the mean velocity in all directions is nearly zero. Typical horizontal velocities, as measured by these standard deviations, exceed vertical velocities, perhaps improving flight efficiency. (b) Polarisation p is near zero for all swarms observed, distinguishing swarming behaviour from flocking and schooling. (c, d) Standardised velocity distributions along (c) the vertical direction and (d) one horizontal direction. The distributions are nearly Gaussian (a reference Gaussian curve is shown in grey), with slight deviations in the tails. (e) Standardised speed distributions, with the standardised Maxwell–Boltzmann distribution shown in grey for comparison. A heavy, nearly exponential tail develops for large swarms, which may indicate the formation of clusters.