Use of Dimensional Analysis in the X-, Y-, and Z-Axis to Predict Occurrence of Injury in Human Stampede

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Abstract
Background: Human stampedes (HS) may result in mass casualty incidents (MCI) that arise due to complex interactions between individuals, collective crowd, and space, which have yet to be described from a physics perspective. HS events were analyzed using basic physics principles to better understand the dynamic kinetic variables that give rise to HS. Methods: A literature review was performed of medical and nonmedical sourced databases, Library of Congress databases, and online sources for the term human stampedes resulting in 25,123 references. Filters were applied to exclude nonhuman events. Retrieved references were reviewed for a predefined list of physics terms. Data collection involved recording frequency of each phrase and physics principle to give the final proportions of each predefined principle used a single-entry method for each of the 105 event reports analyzed. Data analysis was performed using the R statistics packages "tidyverse", "psych", "lubridate", and "Hmisc" with descriptive statistics used to describe the frequency of each observed variable. Results: Of the 105 reports of HS resulting in injury or death reviewed, the following frequency of terms were found: density change in a limited capacity, 45%; XY-axis motion failure, 100%; loss of proxemics, 100%; deceleration with average velocity of zero, 90%; Z-axis displacement pathology (falls), 92%; associated structure with nozzle effect, 93%; and matched fluid dynamic of high pressure stagnation of mass gathering, 100%. Conclusions: Description or reference to principles of physics was seen in differing frequency in 105 reports. These include XY-axis motion failure of deceleration that leads to loss of human to human proxemics, and high stagnation pressure resulting in the Z-axis displacement effect (falls) causing injury and death. Real-time video-analysis monitoring of high capacity events or those with known nozzle effects for loss of proxemics and Z-axis displacement pathology offers the opportunity to prevent mortality from human stampedes.

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