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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): a = 0.5 m , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): b = 0.3 m , the limit densities range from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): \rho = O(5.0 - 6.06) [p/m^2] , in good agreement with empirical observations.

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