Classification of Pedestrian Crowds by Dimensionless Numbers

Presently, classifications of pedestrian crowds primarily rely on density. This fails to encompass the diverse behaviours and risk profiles observed. We introduce two dimensionless numbers, the Intrusion number In, based on the desire to maintain one’s personal space, and the Avoidance number Av, based on the anticipation of collisions. These two numbers delineate different flow regimes, as we intuitively expect and as we empirically demonstrate using an extensive dataset. Similarly to Fluid Mechanics, where dimensionless numbers guide the choice between different approximations, the dynamics of crowds can be approached in each regime by perturbative expansions, which yield pedestrian models applicable in the corresponding regime (and only there).