A Note on Mathematical Modelling of Elliptical Fire Propagation

Abstract

Mathematical modelling of forest fire propagation in time plays a key role in existing fire propagation predicting systems. Such systems are capable of simulating the growth of fire front in time and space and predicting spatial and temporal fire behaviour. In our previous papers, we studied mathematical foundations of the elliptical fire propagation model implemented in several advanced simulation systems.

The model is based on Huygens' principle applied on fire propagation assuming locally elliptical fire spread. However, in the literature various other mathematical representations of local fire propagation have been reported, such as double ellipse, lemniskata, oval shape, tear shape, and others. Such types of local fire propagation have been experimentally observed in certain conditions during laboratory and field fires. In this paper, we demonstrate several simple examples of fire propagation corresponding both to the elliptical and non-elliptical local fire propagation in homogeneous conditions.