Fundamentals - Wildland Fuel Fundamentals and Applications - page 20

I ξφφ

ρε

(1 ++ )

R =

r Ws

(2.5)

( )( )( Q )

b ig

where I r is reaction intensity, ξ is the propagating flux ratio (dimensionless), φ w is a
scaling function for wind (number between zero and one), φ s is a scaling function
for slope, ρ b is the bulk density of the fuelbed (kg m −3 ), ε is the effective heating
number, and Q i is the heat of pre-ignition (kJ kg −1 ; Table 2.2 ). Reaction intensity ( I r )
can be estimated by the amount of fuel consumed ( W c ) and that fuel's heat content
( h ) using a reformulation of the Andrews and Rothermel ( 1982 ) relationship:

Wh
t

c

I = (2.6)

r

r

where t r is the residence time (min) that is computed from the Anderson ( 1969 )
empirical relationship:

= 12 595

.

(2.7)

t r

SAVR

where SAVR is the characteristic surface-area-to-volume ratio (m −1 ) of the fuelbed.
SAVR is the third important fuel property because it is in the majority of fire behavior
calculations (Table 2.2 ). The characteristic SAVR is estimated from the weighted
averages across all surface fuel components specified in the model and the SAVR
values for each fuel component is estimated as an average for each particle using the
diameter in the following equation:

SAVR= 4
d

(2.8)

where d is the average diameter of the particles in the fuel component (m). Particle
diameter is the fourth important fuel property because it is related to SAVR and it is
used to estimate loading. The next important fuel property is the parameter ρ b (bulk
density of the fuelbed, kg m −3 ). This parameter is also used to estimate the effective
heating number ( ε ) in Eq. 2.5 using the empirical Rothermel ( 1972 ) relationship:

− 138

ρ
ρ

(2.9)

b

∈= = e

SAVR

e

where ρ e is the effective fuelbed bulk density (kg m −3 ; Table 2.2 ). However, the ef-
fective heating number can also be accurately estimated from SAVR, which is used
to represent fuel particle size (Eq. 2.8). Fuelbed bulk density ( ρ b ) is often calculated
from the following equation:

W

ρ = (2.10)

b

δ

where δ is the fuelbed depth (m), the sixth important fuel property, and W is fuelbed
loading (kg m −2 ).