Environmental Engineering Reference
In-Depth Information
Figure 2.13
Definition of the Solar Angle of Incidence on a Tilted Surface
θ
tilt
= arccos(
s
•
n
) =
= arccos(-cos
α
S
•
cos
γ
S
•
cos
α
t
•
sin
γ
t
-
sin
α
S
•
cos
γ
S
•
sin
α
t
•
sin
γ
t
+ sin
γ
S
•
cos
γ
t
)
= arccos) - cos
γ
S
•
sin
γ
t
•
cos(
α
S
-
α
t
) + sin
γ
S
•
cos
γ
t
)
(2.24)
I
RRADIANCE ON
T
ILTED
S
URFACES
The global irradiance
E
G,tilt
on a tilted surface is composed of the direct
irradiance
E
dir,tilt
, the diffuse sky irradiance
E
diff,tilt
and the ground reflection
E
refl,tilt
(a factor that does not exist for horizontal surfaces):
E
G,tilt
=
E
dir,tilt
+
E
diff,tilt
+
E
refl,tilt
(2.25)
Direct irradiance on tilted surfaces
The horizontal surface in Figure 2.14 with the area
A
hor
receives the same
radiant power
as a smaller area
A
s
which is normal (perpendicular) to the
incoming sunlight.
Φ
With
Φ
dir,hor
=
E
dir,hor
•
A
hor
=
Φ
dir,s
=
E
dir,s
•
A
s
and
A
s
=
A
hor
•
cos
θ
hor
=
A
hor
•
sin
γ
S