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19
An additional angle of interest is the
profile angle,
α
p
,
of beam radiation on a
receiver plane R that has a surface azimuth angle of
γ
.
It is the angle through which a plane that is initially horizontal must be rotated
about an axis in the plane of the surface in question in order to include the sun.
The profile angle is useful in calculating shading by overhangs and can be
determined from:
ANGLE RELATIONS – Profile angle,
α
p
(13)
Three types of shading problems typically occur:
a) shading of a collector, window, or other receiver by nearby trees, buildings or
other
obstructions.
The
geometries
may
be
irregular
and
systematic
calculations of shading of the receiver in question may be difficult.
Recourse is made to diagrams of the position of the sun in the sky, for example
plots
of
solar
altitude,
α
s
,
versus
solar
azimuth
γ
s
,
on
which
shapes
of
obstructions (shading profiles) can be superimposed to determine when the
path from the sun to the point in question is blocked.
b) The second type includes shading of collectors in other than the first row of
multi-row arrays by the collectors on the adjoining row.
c)
shading of windows by overhangs and wingwalls.
When the geometries are regular, shading problems can be assessed through
analytical calculation, and the results can be presented in general form.
SHADING - 1
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20
SHADING - Solar plots
Solar plots are a
2D representation
of the sun paths over the sky dome.
These paths are plotted for different periods of the year and are the projection of
the sun orbits over the horizontal plane.
Each solar plot is draw for a specific location (that is, for a certain latitude,
φ
) and
allows to assess the sun position for every hour of the day and for every day of
the year, by means of the solar altitude angle,
α
s
, and of the solar azimuth,
γ
s
.
Solar plots may be plotted in either polar or rectangular coordinate charts.
Solar position plot of
θ
z
and
α
s
, versus
γ
s
, for latitudes of ± 45°is shown in Figure.
Lines of constant declination,
δ
, are labeled by dates of mean days of the months
(see Table 1.6.1). Lines of constant hour angles,
ω
, are labeled by hours.
(plots for latitudes from 0 to ± 70°are included in App endix H of
Duffie & Beckman).
SHADING -
Type a) – Use of Solar plots
(rectangular coordinate plot)
The angular position of buildings, wingwalls, overhangs, or other obstructions can
be entered on the same plot (the angular coordinates corresponding to altitude and
azimuth angles of points on the obstruction - the object azimuth angle,
γ
o
, and
object altitude angle,
α
o
) can be calculated from trigonometric considerations and
drawn on the plot). For obstructions such as buildings, the points selected must
include corners or limits that define the extent of obstruction. It may or may not be
necessary to select intermediate points to fully define shading.
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21
SHADING -
Type a) – Use of Solar plots

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