31
LP-80
τ
τ
=
=
K
K
p
ln
ln
1
2
1
2
so:
τ
τ
Θ = Θ
( )
( )
p
1
2
Calculate
p
from
:
p
=
χ
2
+
(tan
Θ
1
)
2
χ
2
+
(tan
Θ
2
)
2
⎡
⎣
⎢
⎤
⎦
⎥
1
2
If
Θ
1
= 0°,
p
=
χ
2
χ
2
+
(tan
Θ
2
)
2
⎡
⎣
⎢
⎤
⎦
⎥
1
2
If
χ
is not known, assume
χ
= 1.
EXAMPLE PROBLEM 5
From the measurements in Example Problem 4, find the canopy cover. Take
Θ
= 35°,
τ
= 0.21.
The
χ
value is 0.9.
p
=
0.9
2
0.9
2
+
(tan35)
2
⎡
⎣
⎢
⎤
⎦
⎥
1
2
τ
=
=
(0) 0.21 0.79 0.29
0
τ
−
= −
=
Cover =
(0) 1 0.29 0.71
Intercepted radiation averaged over an entire day can be estimated from:
Equation 23
τ
= −
f
1
d
where
τ
d
is the transmission coefficient averaged over all elevation angles.
τ
d
can be
calculated from:
τ
−
=
uL
ln
d
v
where
u
and
v
are functions of
χ
which can be calculated from:
χ
= −
−
u
1 0.33exp( 0.57 )
χ
= −
−
v
1 0.33exp( 0.97 )
The following table shows typical values for
u
and
v
.