Environmental Engineering Reference
In-Depth Information
The parameter
L
e,iso
is the isotropic radiant intensity, that falls out of the
equation when calculating the degree of diffuse shading. When using the
anisotropic distribution, the integral also includes the angle-dependent radiant
intensity
L
e
. However, only numerical methods are able to solve this integral.
When simulating tilted planes, the angle of incidence
, according to Equation
(2.24), must be considered. Therefore, a complex analytical solution also exists
(Quaschning and Hanitsch, 1998).
The diffuse irradiance
E
diff,P
θ
through the polygon surface of an object
polygon with
n
polygon points
p
1
=(
α
1
,
γ
1
) to
p
n
=(
α
n
,
γ
n
) can be calculated
by:
(2.39)
Finally, the degree of
shading of diffuse irradiance S
diff,hor
for a horizontal
surface is the ratio of the diffuse irradiance reduction and the total diffuse
irradiance. For an isotropic radiant intensity distribution, the shading becomes:
(2.40)
The degree of diffuse irradiance for a tilted surface is calculated analogously:
(2.41)
If the object polygon is transparent, the shading degree
S
must be weighted
additionally with the transmittance
τ
.
Estimation of total shading
The global irradiance
E
G,hor
on a horizontal surface can now be calculated
using the direct irradiance
E
dir,hor
and diffuse irradiance
E
diff,hor
on the
horizontal plane and the degrees of shading
S
dir
and
S
diff,hor
:
(2.42)
The global irradiance
E
G,tilt
on a tilted surface can be calculated analogously.
A corrected albedo value
A
can be used to consider any possible reduction of
the ground reflection
E
refl,tilt
(see also Equation 2.35). Hence, the global
irradiance becomes:
(2.43)
The methods described here are implemented in the SUNDI software that can
be found on the CD-ROM of this topic.
