Aim: The article describes the results of creating a mathematical model aimed to determine the flame spreading velocity of ground forest fire fronts. The model involves a fire front located on a plane under the influence of slope, wind, and their joint action. The experimental results were used for validation of the model.

Project and methods: The mathematical modeling was performed using the methods of vector algebra and analytical geometry as well as the Froude number and the empirical relationships derived from the already known experimental results. Experimental studies on the fire propagation velocity were carried out on the training ground and involved an analysis of three most common types of forest fuels: coniferous litter, leaf litter, dry grass. The combustible material was chosen maintaining its humidity balance and placed on a plane arranged horizontally and at angles to the horizon. The wind action was simulated using the motor blower and the speed was controlled using anemometer.

Results: The mathematical modeling of the speed of the fire front propagation was performed taking into account the dependencies of the Froude number on the wind speed and flame height as well as the angle of the flame on the Froude number. The influence of wind on the spreading velocity of the fire front was described with the corresponding coefficient whose value was determined by the empirical dependence. Influence of slope brought about given wind speed. At such wind speed, during the spread of fire, in the case of the horizontal plane of the flame, the flames would be deviated from the normal at the same angle. In the case of ground fire wind speed coefficient should be divided by the cosine of the angle of the surface to the horizon, which is confirmed by comparing the simulation results with experimental and empirical relationships. The cumulative effect of the wind and the slope was described using vector algebra. The results of the mathematical model were compared with experimental data. Good compliance was noted in the case of combustible material – coniferous litter, a little worse – for leaf litter and satisfactory – for dry grass.

Conclusions: The dependence of the velocity of the ground fire front propagation and the combined effect of wind and slope surface was described by the mathematical model. There is a good correspondence between the data obtained with the use of the model and the experimental results, especially in the case of coniferous litter – combustible material of the most flammable coniferous forests. The application of the proposed model gives an opportunity for the creation of the forest fires spread computer system modelling that will be useful for effective commanding and control of forest fires.

Keywords: mathematical model, forest fire, fire spread, fire front, topography

Type of article: original scientific article