On elliptical model for forest fire spread modeling and simulation

A new approach for the derivation of elliptical model of steady-state forest fire spread in time based on classical envelope theory is described. The derivation of this model known in the literature is based on the introduction of a special transform of co-ordinate system which allows to utilize geometrical properties of points lying on common tangent line of two circles. However, the use of this transform means the necessity to apply some specific assumptions onto the model. The proposed new procedure allows us to derive the model without the use of this transform. The new approach enables to better explain the internal coherence of studied problem, assumptions and limitations of the model, as well as to suggest its further generalizations.