Estimating density limits for walking pedestrians keeping a safe interpersonal distancing

Abstract

With people trying to keep a safe distance from others due to the COVID-19 outbreak, the way in which pedestrians walk has completely changed since the pandemic broke out1,2. In this work, laboratory experiments demonstrate the effect of several variables—such as the pedestrian density, the walking speed and the prescribed safety distance—on the interpersonal distance established when people move within relatively dense crowds. Notably, we observe that the density should not be higher than 0.16 pedestrians per square meter (around 6 m2 per pedestrian) in order to guarantee an interpersonal distance of 1 m. Although the extrapolation of our findings to other more realistic scenarios is not straightforward, they can be used as a first approach to establish density restrictions in urban and architectonic spaces based on scientific evidence.

A novel social distance model reveals the sidewall effect at bottlenecks

“…With this parameter setting, our quasi-L-J model achieved a PDF distribution of d very similar to that from experimental data 12 , where PSD = 2 m (Fig. 1 b).…”

“…Figure 1 a shows the negative gradient of potentials between individual i and j ( ) for three different potential functions: quasi-L-J potential, Helbing and Molnar 1995 exponential potential 2 and adjusted exponential potential. The determination of the parameters for the quasi-L-J potential is based on experimental data 12 . Since we observe that the Helbing and Molnar 1995 potential 2 has repulsive force much smaller than the force from the quasi-L-J potentials at all distances, we adjust the two parameters of the exponential potential to make its negative gradient as close as possible to the one from the quasi-L-J potential and name the potential function as adjusted exponential potential.…”

“…Partially due to the coronavirus pandemic, we could not conduct experiments to obtain suitable data on the social-distanced crowds 9 , 13 , 14 . We calibrate the model based on recent experimental work by Echeverrá-Huarte et al 12 , which explores the dynamics of social-distanced walking pedestrians. We compare the resulting social distance PDFs from both our new model and the exponential models with the experimental social distance PDF to examine the performance of these models in reproducing the prescribed social distance between individuals in a social-distanced crowd.…”

“…The work by Echeverrá-Huarte et al 12 measured the PDFs of the distance of each individual to the first nearest neighbor ( d ) under different prescribed safety distances (PSD) and crowd densities ( ). Volunteers in this work were asked to walk randomly in an enclosed area, during which the movement of each individual was recorded and analyzed.…”

“…For a fair comparison between models, we keep and terms same as that in Helbing and Molnar’s classical model 2 for all models discussed here. Moreover, we keep the crowd density of our model the same as the crowd density in the experiments 12 for comparisons with experimental data. We set m 2 s −2 and m. is set to be 0.5 s .…”