Journal of the International Association of Wildland Fire
RESEARCH ARTICLE

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

Frank A. Albini A F , Martin E. Alexander B D E and Miguel G. Cruz C
+ Author Affiliations
- Author Affiliations

A Montana State University, Department of Mechanical and Industrial Engineering, Bozeman, MT 59717-3800, USA.

B Canadian Forest Service, Northern Forestry Centre, 5320-122 Street, Edmonton, AB, T6H 3S5, Canada.

C Present address: University of Alberta, Department of Renewable Resources and Alberta School of Forest Science and Management, Edmonton, AB, T6G 2H1, Canada.

D Bushfire Dynamics and Applications, CSIRO Ecosystem Sciences and Climate Adaptation Flagship, GPO Box 1700, Canberra, ACT 2601, Australia.

E Corresponding author. Email: mea2@telus.net

F Deceased 3 December 2005.

International Journal of Wildland Fire 21(5) 609-627 https://doi.org/10.1071/WF11020
Submitted: 3 February 2011  Accepted: 6 December 2011   Published: 18 June 2012

## 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.

Additional keywords: canopy-top height, crowning, ember, extreme fire behaviour, fire plume, firebrand, flame height, ignition, spot fire, wind speed.

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