aleo
aleo solar Deutschland GmbH
| Osterstraße 15| 26122 Oldenburg |
Germany
installation instructions Edition 01/2012 en-GB-Intl (120508b)
Page
49
/
60
B.
Creation and Avoidance of
Shadowing
B.1
Deepest shadow and half shadow
The deepest shadow is the area behind an object
casting a shadow in which no direct sunlight
strikes. It occurs at a certain position when an
object casting a shadow is, when viewed from the
shadowed position, so large that it completely
blocks out the sun.
Note: For purposes of differentiation, this manual
uses the term 'full shadow' for the shadow of a long
edge.
The half shadow is the area behind an object
casting a shadow in which –in contrast to the
deepest shadow- direct sunlight still strikes. It
occurs at a certain position when an object casting
a shadow is, when viewed from the shadowed
position, so small that it does not completely block
out the sun.
NOTICE
With respect to shadowing, you should avoid the
deepest shadow above all as it has a greater effect
than a half shadow.
Whenever possible, also avoid half shadowing.
Shadow-casting objects should be as small as
possible. This keeps the deepest shadow short,
thereby preventing or reducing shadowing from
deepest shadows.
Shadow-casting objects should be located as far
away from the photovoltaic generator as possible.
The half shadow that is created moves more quickly
over the course of the day and therefore shadows
for a shorter time.
B.2
Shadows from cylindrical objects
The creation of deepest and half shadows by a cylindrical
object (e.g. lightning rod, ventilation pipe) can be illustrated as
follows:
Fig. 32 Shadow cast by a cylindrical object (diagram)
UM
: deepest shadow (umbra),
PE
: half shadow (penumbra),
d
S
: diameter of the sun,
a
S
: distance from the sun,
d
UM
: diameter of the shadow-casting object,
a
UM
: length of the
deepest shadow.
The length a
UM
of the deepest shadow that an object with a
diameter of d
UM
casts has the same ratio to d
UM
as the
distance from the sun d
S
to its diameter a
S
.
The ratio a
S
/d
S
and therefore a
UM
/d
UM
is approx. 107.4.
Deepest shadow (umbra)
If the distance from the solar module to the shadow-casting
object is smaller than the length of the deepest shadow, then
the deepest shadow will strike the solar module.
Fig. 33 Shadowing caused by the deepest shadow to be
avoided (diagram)
Avoiding a deepest shadow
A deepest shadow can be avoided by maintaining a sufficient
minimal distance from the shadow-casting object to the solar
module. If the shadow-casting object maintains this clearance
from the module, then the deepest shadow will no longer
strike the module.
To determine the length of the deepest shadow a
UM
behind a
cylindrical object (e.g. lightning rod, ventilation pipe) with the
diameter d
UM
, the following rule of thumb applies:
a
UM
= d
UM
·
108
Avoiding a half shadow (penumbra)
The half shadow behind a cylindrical object will be lighter the
further away the point at which the shadow strikes:
is from the end of the deepest shadow
-AND-
is from the axis of the deepest shadow.
The following table shows the degrees of shadowing along the
deepest shadow axis:
Clearance
Degree of
shadowing
In multiples of the
deepest shadow
length
In multiples of
the object’s
diameter
1
108 100%
2
215 61%
3
323 42%
4
430 31%
5
537 25%
…
… …
10
1074 13%
GID AS001a
a
UM
d
UM
a
S
d
S
UM
PE
a
<
d ⋅ 108
d
a
UM
a
GID AS002a
