The Effects of Slope Upon Propagation Speed and Pattern Formation in Forest Fires

Robin Morillo


We examined forest fires both experimentally and computationally to more fully understand the effects that slope has upon fire propagation. For the experimental investigation we designed and 3D printed plastic molds in order to hold an array of matches in place as a model forest. These molds were designed to feature slopes of different angles. By recording the burning of these model forests and analyzing the resulting videos, a relationship between the slope of the forest floor, θ, and the speed at which the flames propagated across the model forest, R, was found. The best fit we found for this data, after making certain assumptions about the data collected, was that for positive values of θ the relationship is R = (38 ± 4) tan2θ + (15.04 ± 0.07) and for negative values of θ the relationship is R = (−24.9 ± 0.7) tan2θ + (14.51 ± 0.05). This supports the findings of Richard C. Rothermel, who found that R ∝ tan2θ [1]. An introduction to the mechanics of fire is also presented to give a proper understanding of the results.

For the computational analysis a cellular automata model made by Punckt et al. [2] that simulates forest fires was built upon. An adjustable slope factor was built into the code, as well a method to measure the speed of the simulated flame front. Using this simulation, theoretical flame spirals and the effect slope had upon them was studied. The effect of inhomogeneity within the simulated trees upon the formation of the fire spirals was also examined. An overview of cellular automata is also provided to help give the proper background information before discussing the specific simulation we used.