Analytical Methodology

Mathematical Bases

For predicating the behavior of a prescribed burn many analytical models and calculation techniques are used. Many of these calculation utilize formulas developed by the forest service prior to the development of a prediction fire behavior program. The following formula calculates the rate at which a fire spreads through a uniform fuel array that may contain fuel particles of mixed sizes created by Rothermel in 1972; called the Fire Spread Model.

R= Ir €(1 + Fw + Fs)/Pbe Qig

R - is the forward rate of spread of flaming front (ft/min)
Ir – reaction intensity - Energy Release Rate of fire front (Btu/ft2/min)
– propagating flux ratio; measure proportion of reaction intensity, which heats adjacent fuel particle to ignition
Fw – a dimensionless multiplier that accounts for effect of wind in increasing the flux ratio
Fs – dimensionless multiplier that accounts for the effect of slope in increasing the flux ratio
Pb – amount of fuel (lb/ft3)
e – measure of the proportion of fuel partial that is heated to ignition temperatures at time flaming combustion starts
Qig – amount of heat required to ignite one pound of fuel (Btu/lb)
Numerator: amount of heat actually received by potential fuel
Denominator: heat required to bring the fuel to ignition temperature.

Wildfires spread based on the type, quantity, and quality of fuel surrounding it. The fuel load is the amount of flammable material that surrounds a fire. It is measured by the amount of fuel per unit area (tons per acre). A small load will spread slowly and with low intensity. A lot of fuel will make the fire spread quickly and more intensely. When the fuel load is very dry it also increases the consummation rate. Some basic fuel characteristics are:
· size,
· shape,
· arrangement (such as slash, litter) , and
· moisture content of the wood and/or fuel.

“Small fuel materials also called flashy fuels such as dry grass, pine needles, dry leaves, twigs, and other dead brush, burn faster than large logs or stumps”(Bonsor 2). On a chemical level, different fuel materials take longer to ignite than others. As the fire grows it dries the fuel ahead of it, as a result, making the fuel easer to ignite and burn. Spread out fuel burns faster and the fire consumes more because there is more oxygen available and the fire will not suffocate, that is self extinguish. Fuels that are more tightly packed maintain more moisture, hence, absorbing the heat of the fire (Bonsor 2). Figure 2-3 demonstrates the average depth area for the shrubs. Average grass or shrub depth is about seventy percent of the maximum leaf or stalk height. Figure 1-4 demonstrates the difference between slash (S layer), litter (L layer), fermentation (F layer), and humus (H layer).

Weather plays a major role played in the ignition, growth, and extinguishment of the fire. Drought promotes extremely favorable conditions for a wildfire. Three of the most important factors, which determine the behavior of the wildfire, are: temperature, wind, and moisture. Temperature of the environment, fuel, and of the fire effects the ignition of the fire. The higher the temperature the faster the fuel will burn. Wind has the biggest impact on the way a fire burns. The following figures(figure 2-5 and figure 2-6) demonstrate the affect the wind has in respects to the slope.

Moisture obviously effects how much, how long, and how rapid it will blaze. The relationship between the fire and wind is known as coupled fire at mosphere dynamics. The fire can produce its own winds and weather patterns. Fire whirls are the winds which large violent fires generate. These fire whirls act like tornados, the whirls are the part of the fire which throw flaming logs and burning derbies in front of the fire creating what is known as spot fires(Bonsor 5).

The lay of the land is the last major influence in the behavior of the fire. It can either help or hurt the fire. Fires travel much faster uphill than down. If the slope is steeper than the fire travels at a greater velocity. When the fire reaches the top of the hill it will most likely burn itself out because it cannot pre-heat the fuel on the reverse slope on the other side of the mountain (Bonsor 5-6).

It's Getting Hot In Here
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