Environmental Engineering Reference
In-Depth Information
2
π
δ
=
−
23
,
45
cos
(
n
+
10
)
(2.8)
365
,
25
If the receiving surface is horizontal to the solar radiation, the zenith angle
ψ
z
can be calculated according to Equation (2.9).
cos
ψ
=
sin
ϕ
sin
δ
+
cos
ϕ
cos
δ
cos
ω
(2.9)
z
h
Conversion of the direct solar radiation on a tilted, aligned surface
G
b,t,a
(i.e.
oriented towards a particular direction) can be calculated from the direct radiation
G
b
on the horizontal surface, using the angle of radiation incidence
ψ
, the inclina-
tion of the surface with respect to the horizontal level
α
, the solar azimuth angle
β
,
and the collector azimuth angle (alignment of the surface normal according to the
direction)
γ
, using Equation (2.10).
(
)
)
(
G
=
G
sin
ψ
cos
α
−
sin
α
cos
ψ
sin
β
−
γ
(2.10)
b
,
t
,
a
b
Diffuse radiation on tilted, aligned surfaces.
The conversion of the diffuse pro-
portion of the solar radiation on the tilted and aligned surface
G
d,t,a
depends on a
number of influencing factors and cannot be described entirely analytically. If it is
assumed, as a simplification, that diffuse radiation is evenly distributed within
space, the same proportion incidents from all directions on a particular point of
the surface of the earth (isotropic model). Under these simplified boundary condi-
tions, the diffuse radiation incident on tilted, aligned surfaces is calculated with
the diffuse radiation incident on the horizontal surface
G
d
and the angle of inclina-
tion of the receiving surface against the horizontal
α
according to Equation (2.11).
(
α
1
G
=
G
1
+
cos
(2.11)
2
d
,
t
,
a
d
Assuming an isotropic distribution of radiation only describes the given cir-
cumstances to a limited extent. If the atmosphere is solely filled with diffuse ra-
diation due to a heavy and homogenous cloud cover, the area around the position
of the sun is nevertheless generally brighter than the rest of the sky. This aspect is
considered in Equation (2.12), that assumes an even distribution of isotropic ra-
diation in space, superimposed by a so-called circumsolar share (see /2-9/).
⎛
G
G
⎞
1
⎛
−
⎞
⎛
cos
ψ
⎞
(
)
⎜
⎝
b
,
t
,
a
b
,
t
,
a
⎟
⎠
G
=
G
⎜
⎝
1
⎟
⎠
1
+
cos
α
+
⎜
⎝
⎟
⎠
(2.12)
d
,
t
,
a
d
2
E
E
cos(
90
°
−
α
)
SC
SC
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