Primary Goal
Create a three-dimensional program with two-dimensional exactness.
Problem Definition
How can the flow of heat required to ignite a fire on all levels of a forest
environment be accurately modeled using Huygens principles and other mathematical
equations?
How to model the spread of heat using equations that model convection, conduction,
and heat radiation which all effect fire flow?
On average, nearly six and a half million acres of woodland forest burn in
the United States every year (O’Driscoll, 2005). The recent Cerro Grande
Fire of 2000 which quickly got out of hand and burned 47,650 acres of federal
forest, cost the Federal Government 10 million dollars to contain (nifc.gov,
2002) and caused more than a billion dollars in damage (Masse, 2003).
In the previous year’s project, a C++ was created to randomly model
the forest environment. Heat flow was achieved by averaging temperatures between
neighboring patches of forest. Fire spread was achieved by programming logic
into each patch so that if one were on fire, then the other patches around
it would ignite and further spread the fire.
The new program will differ in that it will include vertical fire spread from
the ground up into the tree top canopy. Huygens principle, which models fire
spread from the origin based on wind and characteristics of the burning fuel
to create an elliptical fire flow path. This will allow the program to more
accurately spread based on a dynamic environment. The new program will be
able to model fire over a larger area; will incorporate movement from tree
to tree and overall growth of the fire in that environment. This data will
be recorded and used for statistical interpretation then it will be validated
by comparing the results to the USFS data.
Problem Solution
The program will function on a two-dimensional plane using Huygens principles
(Finey, 2002) for flow in elliptical cells. The program will then proceed
to encompass equations used in the Farsite program to incorporate the fire
spread and wind specifics on the edge of a fire and accurately spread it in
a three-dimensional pattern. Crown fire is the most important factor because
the tree top crown will burn with more heat and will therefore flow more intensity.
Progress to Date
To date, a two-dimensional program has been created which allows for the forest
environment to be accurately drawn in a single plane. The two-dimensional
program can then be incorporated into a separate three-dimensional program,
which is still in development. Combined, the two programs will be used to
model three-dimensional fire spread on multiple levels of the forest. The
team has also analyzed and incorporated Newton’s Law of Cooling (wikipedia.com,
2005), and Fourier’s Law of Conduction (wikipedia.com, 2005) and are
close to including Huygen’s equation (Finey, 2002) which will allow
for more accurate elliptical flow.
Expected Results
Once the three-dimensional program is completed, the team expects this model
to accurately portray how a fire spreads in a three-dimensional environment
based on heat, oxygen, and fuel supply. The program could be used to take
the place of fire modeling programs like Farsite which neglects many of the
variables inherent in heat flow, and may someday help to predict how a fire
travels in various forest settings and conditions. It could possibly be used
to determine if it is safe to attempt a prescribed burn given certain conditions
in the forest. One day, it may even be used to predict the threat of another
large scale fire like the Cerro Grande.
References
Masse, B. & Nisengard, J. (2003). Cerro Grange Fire Assessment Project
Cultureal Resources Report No. 211.
O’Driscoll, P. (2005). Studies at odds over logging
after wildfires. USA Today Nov. 2nd
Finey, M. (2002) Australian Mathematical Society Fire growth
using minimum travel time methods