On Critical Densities and Velocities for Pedestrians Entering a Crowd

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 = 0.5 m, b = 0.3 m, the limit densities range from ρ = O(5.0 – 6.06) [p/m2], in good agreement with empirical observations.