Euclidean Geometry Paradigm for Electrical Safety: A Novel Approach

Abstract

This paper introduces a novel geometric paradigm for electrical safety that models hazards and worker exposure as time-dependent vectors. By drawing an analogy with the Euclidean concept of coplanar parallel lines, which never intersect, the framework posits that safety is maintained when the worker’s effective distance (the sum of their actual separation and the protective buffer provided by personal protective equipment, PPE) never crosses the hazardous zone. The model captures the dynamics of hazard expansion, such as arc flashes, alongside the worker’s movement toward the hazard, while incorporating the time-dependent decay of PPE effectiveness. Furthermore, human factors such as fatigue, which affect worker response and movement, are integrated into the model, emphasizing their role in altering safe exposure windows. The geometric framework is also aligned with the Hierarchy of Controls, where elimination of the hazard is viewed as the ideal state, and the other controls are interpreted as vector transformations that maintain safe separation. While the model simplifies the complex phenomena of arc flash events by focusing solely on geometric expansion, it provides a clear baseline for quantitative risk assessment and offers promising directions for enhancing real-world safety protocols.