Agriculture Reference
In-Depth Information
Table 2.2
Equations of the basic fire spread model taken from Rothermel (
1972
) and Albini
(
1976
) (courtesy of Pat Andrews) and converted to metric units
Variable
Equation
Equation number
Rothermel (
1972
)
Rate of spread (m min
−1
)
(Eq. 52)
I
ξφφ
ρε
(1
++
)
R
=
R
WS
Q
b
ig
Reaction intensity
(kW m
−2
min
−1
)
(Eq. 27)
I
=Γ′
wh
ηη
r
n
Ms
Fire line intensity
(kW m
−1
fire line)
Added later
=
12 61
60
.
R
SAVR
I
r
b
(
)
Optimum reaction
velocity (min
−1
)
(Eqs. 38, 39)
A
(1
−
ββ
/
)]
Γ =Γ
′
′
(/
ββ
)
[
A
e
op
,
max
op
−
0 7913
.
where
ASAVR
=
133
(
)
Maximum reaction
velocity (min
−1
)
(Eq. 36)
Γ
'
max
=
(
SAVR
)
15
.
(
495 0 0494
+
.
(
SAVR
)
15 1
.
)
−
Optimum packing ratio
(fraction)
(Eq. 37)
β
=
3.348(
SAVR
)
−
0.8189
op
Packing ratio (fraction)
(Eq. 31)
ρ
β
ρ
=
b
p
Oven-dry bulk density
(kg m
−3
)
(Eq. 40)
w
ρ
=
o
b
δ
Net fuel loading
(kg m
−2
)
(Eq. 24) replaced
by Albini (
1976
)
ww S
n
=−
(
1
)
o
T
Moisture damping coef-
ficient (fraction)
(Eq. 29)
η =−
1
2.59
r
+
5.11(
r
)
2
−
3.52(
r
)
3
,
M
M
M
M
where
r MC M
M
=
/
(max. )
=
10
x
Mineral damping coef-
ficient (fraction)
(Eq. 30)
−
0.19
(max = 1.0)
η
=
0.174
S
s
e
Propagating flux ratio
(fraction)
(Eq. 42)
0.5
−
1 [(0.792
e
+
0.681(
SAVR
)
)(
β
+
0.1)]
ξ
=+
(192
0.2592(
SAVR
))
Wind factor (fraction)
(Eq. 47-50)
φ
=
CU
B
(/
ββ
−
)
E
,
w
op
055
.
(.
−
0 133
(
SAVR
)
)
where
C
=
747
.
e
;
−×
−
35910
04
.
)
.
054
[.
(
SAVR
)]
B
=0 02526
.
(
SAVR
;
E
=
0 715
.
e
Slope factor (fraction)
(Eq. 51)
φ
=
5.275
β
−
0.3
(tan
φ
)
2
Effective heating
number
(Eq. 14)
ε
=
e
( 138/
−
SAVR
)
Heat of pre-ignition
(kW kg
−1
)
(Eq. 12)
Q
ig
=+
250 1116
FMC
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