On critical densities and velocities for pedestrians entering a crowd

Abstract

The problem of pedestrians trying to enter and/or advance against an incoming crowd is studied. The analysis shows that starting with a very limited set of assumptions (elliptical cross-section of pedestrians; constant ratio of forward to lateral separation) one is able to derive from purely kinematic considerations critical densities beyond which it is impossible for pedestrians to enter and/or advance into an incoming crowd. The results obtained indicate that for the common pedestrian size of $a=0.5m$, $b=0.3m$, the limit densities range from $\rho =O(5.0-6.06)[p/m^{2}]$, in good agreement with empirical observations.

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