Lightning rod system: mathematical analysis using the rolling sphere method

Abstract

In electrical protection, there is a method of electrical protection of buildings against atmospheric discharges called the electro-geometric method or the rolling sphere method. So far, it is possible to achieve the implementation of this method graphically, that is, representing through plans and technical drawings, the protection conditions of the analyzed structure and obtaining from these graphic representations the protection parameters with the consequent errors caused by the scales and dimensions of the work plane. In the present work, a mathematical model is obtained that allows, using specific calculations, to analyze the dynamic behavior of a protection system against atmospheric discharges without worrying about the limitations given by the scales and planes. The set of equations obtained in the model allows us to determine the different parameters that define the protection system against atmospheric discharges (lightning) without depending on the graphical representation of the system's topology.