Elliptical Fire Theory
The basis of this project is the concept that under perfect conditions,
fire grows in the form of a perfect circle. Even in space, fire maintains
the shape of a sphere. This is the Elliptical Fire Theory. The theory suggests
that fire growth is circular and is only acted upon by external forces.
While not proven, the Elliptical Fire Theory is the underlying assumption
of this project. Once this basis has been determined it opens the door to
incorporating many other characteristics.
Heat
If a wildfire is burning in the winter, it will not have the same ability
to spread as a fire in the summer. This is due to heat’s effect upon
fire spread. There are three basic forms of heat flow: conduction, convection,
and radiation. Heat flow in the atmosphere occurs everyday and has highs
and lows as the day passes but is very different when a fire produces heat.
Convection
Convection is relevant to this project because of heat flow and loss to
the atmosphere and has been incorporated with Newton’s Law of Cooling
which states:
T(1) = ambient temperature + (T(0) – ambient temperature) x ekt
Whereas:
T(1) = New temperature *temperature units are interchangeable
T(0) = Old temperature
K = Negative variable constant dependent on the object’s heat retaining
rate
T = Time elapsed in minutes
Conduction
Conduction is the heat flow into and from solid objects and integrated
using Fourier’s Law of Conduction
Whereas:
Temp(2) > Temp(1)
dh/dt is the amount of heat flow from Temp(2) to Temp(1)
k is the thermal conductivity of the material of transfer
A is the area^2 of the two materials in meters
Pos(2)-Pos(1) is the difference in meters between the two Temp()
Note: Air has been treated as a solid for conduction object with k=.026
(Wikipedia.com)
Radiation
Radiation is the chief transport of heat flow from a fire. Radiation is
the flow of heat from rays through space whether matter is present or
not. Radiation has been defined with the Stephan Boltzmann Law of Radiation
E = KsAT4
Whereas
K = Stefan-Boltzmann Constant=5.67*10^(-8)
S = Emissivity
A = surface area (meters)
T = Kelvin Temperature of object
E = heat transfer in joules that is emitted
Note: This law doesn’t account for radiation emitted
from fire only from an object
Fuel
The heat fire produces is developed from rapidly oxidizing the fuel in a
chemical reaction, and fire needs fuel to produce heat. This chemical reaction
is a self-perpetuating reaction that breaks off the oxygen atoms from its
fuel. Yet, before this reaction can take place, the water contained in the
fuel must be evaporated. Once the moisture content is evaporated, fire needs
only to attain the piloted flashpoint or combustion temperature to combust
the fuel and begin to spread.
Fuel types
In a forest there are many types of fuels. For example, the Russian olive
tree and the cottonwood tree possess distinctive properties. When burned,
the Russian olive produces a higher heat value and is consumed much faster
than the cottonwood. There are thousands, if not millions, of varying
kinds of fuels ranging from low grass to, piñon, and other deciduous
hardwoods. Each fuel type governs different characteristics of fire flow
when they are aflame and radically change the flow of fire. Also, some
fuel types like oak are very thick and slow to burn. Others like redwoods
have fire-retardant bark which prevents a crown fire. Depending on the
forest, different fuel types must be defined empirically and entered into
the program.
Wet and Dry Fuels
Each of these above fuels can be further generalized into two groups:
wet fuels and dry fuels. Wet fuels are living fuels, which contain a moisture
content that must be evaporated before igniting. Dry fuels consist of
the dead underbrush that has lower flashpoints due to the minimal moisture.
Piloted Flash Point
The basic flash point, or piloted flashpoint, is the temperature the fire
must attain to ignite the fuel and, with a fire present burst into flames.
This flashpoint value is dependent upon the atomic structure of the material
being burned and varies depending on the fuel source.
Unpiloted Flashpoint
The unpiloted flashpoint of a fuel is the temperature at which the fuel
will be combusted, whether fire is present or not. Examples of such ignition
without fire radiation include using friction to start a fire, a match
on fire, rubbing two twigs together, or even focusing light under a magnifying
glass to ignite a fire. This means the temperature of the heated area
becomes hot enough to begin a fire without a fire present.
Crown Fires
The crown of a tree is the height at which its leaves or needles are located.
The fire cannot burn the crown if it cannot reach that height. Tree trunks
are generally too high for the heat of a ground fire to reach. Many forest
fires behave in a pattern as if they were two separate fires a fast-moving
crown fire and slow-moving ground fire. Crown fires constitute a major
danger to forests and inhabitants because if a crown fire ignites a tree,
it will likely determine whether the tree will survive the fire.
Oxygen
In order for the chemical reaction of rapid oxidization to take place, oxygen
must be present. If there is no oxygen, then there is no fuel and thus no
fire. As fire burns, it consumes the oxygen and produces carbon dioxide.
The rate at which fire consumes oxygen can be partially attributed to convection
movement of the oxygen-containing wind that fire produces. This is caused
by the fact that when fire burns, it produces wind from convection, which
further stimulates the fire because it brings in air rich in oxygen.
Environmental Factors
In addition to the heat, fuel, and oxygen factors, environmental factors
also affect fire. They are named environmental factors because they are
derived from the forest conditions.
Wind speed and angle
Wind speed and wind angle will ultimately determine the prevailing path
and intensity of the fire. Sometimes fire can travel much faster than
a human can run because of the result of wind. To firefighters, this is
known as a bad day.
Ambient Temperature
Temperature plays a large role in determining fire flow. A fire burning
in cold temperatures will have a lower intensity than a fire burning in
the hot temperatures of the afternoon, which is why a fire’s intensity
decreases after nightfall and increases in the afternoon. This suggests
that heat has an affect upon fire flow.
Humidity
Humidity slows fire flow by increasing the moisture content of all fuels.
The higher the moisture content, the longer and hotter a fire must burn
to remove the moisture.
Elevation
Elevation plays a big role in fire flow. Fire will spread uphill faster
than downhill to gain access to oxygen-rich air. Fire acts as a force
that will oppose gravity. Therefore it affects fire flow in the third
dimension and when elevation changes with slopes and cliffs, fire is also
affected on the two-dimensional plane.
Fire is not totally inexplicable in its nature. This is
because there are many variables acting upon fire that are yet to be defined.
Those variables which have been defined and incorporated however, allow
for a fire model to be constructed.
Fire Flow/Spread
As stated earlier, fire spread is something that, to date, can only be approximated.
A commonly used approximation is based on Huygen’s Principle. In accordance
with the Elliptical Fire Theory, fire will spread in all directions as fast
as it possibly can while still maintaining its three fundamental bases:
heat, oxygen, and fuel. However, the exact determination of fire spread
is still not as simple as that. There are so many factors bearing upon fire
that it is currently impossible to incorporate them all into some finite
formula. To determine basic fire flow one must look at the basic intrinsic
parts and develop an approximation. This is the goal of this year’s
project.