Sonic Speed on Pedestrian Dynamics: Relation between Sonic Speed and Density

This paper discusses the sonic speed on pedestrian dynamics, in which the flow of pedestrians at bottlenecks shows some similarity to a supersonic airflow in aerodynamics at narrow passage. In order to consider the analogy between these two dynamics, we have investigated the propagation speed of starting wave of pedestrians by performing walking experiments along a line. The propagation speed of successive reaction of pedestrians is regarded as the sonic speed in pedestrian dynamics in terms of propagations of a perturbation. The experimental result shows that the sonic speed in pedestrian dynamics is inversely proportional to the power of the density of pedestrians like in aerodynamics, if the pressure in pedestrian dynamics is assumed as a constant. Moreover, we have found that the power index obtained from the numerical simulations based on the stochastic cellular automaton model is the same with the power index in experiments.