aleo
aleo solar Deutschland GmbH
| Osterstraße 15| 26122 Oldenburg |
Germany
| service@aleo-solar.com
Page 50/60
installation instructions Edition 01/2012 en-GB-Intl (120508b)
Fig. 34 Degrees of shadowing at a point in relation to the
distance from the shadow-casting object (100%: deepest
shadow)
Avoid a half shadow by making sure the clearance of the
module is significantly greater than the length of the deepest
shadow. aleo solar recommends maintaining a clearance of at
least 3 times the length of the deepest shadow.
RECOMMENDATION
To determine the minimum clearance from a cylindrical
object (e.g. lightning rod, ventilation pipe) with the
diameter d
UM
, the following formula can be used to
calculate triple the length of the deepest shadow:
a = d
UM
· 323
Fig. 35 Deepest shadow avoidance (shadowing only due to
half shadow) (diagram)
For example
An aerial mast with a diameter of 10 cm must be, in the line of
sight, located at least 10.8 m away from the solar module so
that its deepest shadow no longer strikes the module and the
module is only in a half shadow.
A clearance of 32.3 m only results in limited shadowing of the
module. Due to the greater distance, the half shadow is
lighter; it also moves faster over the course of the day and
therefore usually casts a shadow for a shorter time.
B.3
Shadows from edges
The creation of full and half shadows by an extended object
(e.g. a flat roof) can be illustrated as follows:
Fig. 36 Shadow cast by a horizontal edge (diagram)
UM
: full shadow (umbra),
PE
: half shadow (penumbra),
r
S
: radius of the sun,
a
S
: distance from the sun,
a
K
: distance
from the edge,
h
PE
: height of the half shadow.
The height of the half shadow zone h
PE
to a horizontally
running edge, in the line of sight, with clearance a
K
has the
same ratio as the radius of the sun to its clearance. This ratio
is approx. 1 : 214, calculated from 1/(2·107.4).
Above this height, over the line of sight, (h
K
+ h
PE
)
no shadow strikes the solar module.
Below this height, under the line of sight, (h
K
- h
PE
) a
full shadow strikes the solar module.
A half shadow is cast on the solar module between
these two heights. This half shadow becomes
lighter the further away the point at which the
shadow strikes is from the edge of the deepest
shadow.
For vertically running edges a clearance to the side
respectively applies.
Avoiding a full shadow
Avoid the full shadow of an edge by taking into consideration
the expansion of the half shadow (referred to in the following
as displacement) against the line of sight of the edge.
If the lower edge of the lowest cell of a module is situated a
distance of less than this displacement
below
the
'sun/shadow-casting object' line of sight, then the module is
no longer struck by a full shadow, but only by a half shadow.
If temporary daily shadowing due to site conditions cannot be
avoided (e.g. in winter), be sure to take this into account for
yield planning.
To estimate the maximum height displacement h
PE
of the
lower edge of the lowest cell of the solar module below the
line of sight of the sun/edge (e.g. dormer of a roof) with a
clearance a
K
, the following formula can be used:
h
PE
= a
K
/ 214.
Degree of shadowing
0%
10%
20%
30%
40%
50%
60%
80%
1
2
3
4
5
6
7
8
9
10
70%
90%
100%
Clearance (in multiples of the
deepest shadow length)
GID AS003a-en-GB
a
>
d ⋅ 323
d
a
UM
a
GID AS004a
a
S
PE
UM
h
PE
a
K
h
K
r
S
GID AS005a
