A mathematical model for predicting the maximum potential spotting distance from a crown fire

Abstract

A mathematical model is presented for predicting the maximum potential spot fire distance from an active crown fire. This distance can be estimated from the height of the flame above the canopy top, wind speed at canopy-top height and final firebrand size (i.e. its residual size on alighting), represented by the diameter of a cylinder of woody char. The complete model system comprises several submodels or components: a model for the height and tilt angle of the wind-blown line-fire flame front, a simplified two-dimensional model of the wind-blown buoyant plume from the fire, an assumed logarithmic wind speed variation with height, and an empirically based model for the burning rate of a wooden cylinder in cross flow, which represents the firebrand. The trajectory of the burning particle is expressed analytically from where it leaves the lower boundary of the plume until it enters the canopy top. Adding the horizontal distance of this flight to that of the point where the particle can no longer be held aloft by the plume flow gives a spotting range that depends on the final diameter of the burning particle. Comparisons of model output with existing information on crown fire spotting distances has initially proved encouraging but further evaluation is warranted.