Mathematical model of Rothermel

In this section we will show how FPA uses proven technology and takes advantage of equations in use for fire fighting in addition to creating an index that provides information on how exposed an area is to being stoned by a fire.

This index gives us a guideline on the danger of a fire and how likely it is that it will thrive and become an uncontrollable focus.

We go on to enunciate this equation

Ir: reaction intensity - index of energy released from the fire front.

E: Index of propagation flow (reaction intensity, which heats up adjacent fuel particles to burn).

∅w: Effect of wind.

∅s: Effect of slope.

Pb: Amount of fuel.

e: measure of proportion of the partial fuel that is heated to ignition temperatures at the time ignition begins. 

Qig: amount of heat required to burn one pound of fuel (pre-ignition).

Prediction Index

We see clearly in the previous index that parameters are used that are important at the time of the fire such as the intensity of the reaction or the amount of fuel at ignition temperatures. However, these do not exist before the start of the fire and as we said before what we are looking for is not only to know how dangerous a fire is but also how likely it is that one will start.

The question we did not ask was, what factors are influential in starting a fire? We decided to answer this question by modifying Rothermel's mathematical model, adding important factors prior to the start of the fire and removing those that do not influence or do not exist at that time. The result of all this is the following equation.

All variables used that match those of the Rothermel index are exactly the same

T= Temperature 

H= Soil moisture

It should be clarified that higher values of the above indices will mean greater speed of fire propagation or greater possibility of the start of a fire outbreak.