Applications of Randers metric to track the paths through which the fire surrounds the power transmission lines

Abstract

. We utilize Randers geometry to model the propagation of fire waves, deriving the equations for paths surrounding power transmission lines in a flat terrain during a wildfire outbreak with varying wind patterns. These paths, known as strategic paths, can play a critical role in managing firefighting strategies. By identifying these paths, we can allocate firefighters and resources to specific locations instead of trying to cover a large area. This approach enables us to predict the path of the fire toward the transmission lines, thus reducing the time and cost of firefighting operations. We demonstrate the effectiveness of our approach using MATLAB by simulating two hypothetical wildfire scenarios.