16 Solar Radiation CCB 2009color
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Transcript of 16 Solar Radiation CCB 2009color
Presentation title: Solar Radiation
Solar Radiation
Lecture 16.
A refresher: Solar Geometry variables
Angle of Incidence (Θ) Angle of sun to a line normal to the surface in question (time and orientation specific)
Solar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)
Profile Angle (Ω) Angle in the sun’s position in a two-dimensional section and a line normal to the surface in question (time and orientation specific)
Surface Tilt (Σ)Tilt of a surface relative to the ground plane (orientation specific)
Schema for
Equidistant
Sun Path Diagram
Solar Surface Azimuth diagramSolar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)
Angle of incidence diagramAngle of Incidence (Θ) Angle of sun to a line normal to the surface in question (time and orientation specific)
Angle of incidence diagramProfile Angle (Ω)Position of sun translated into a two-dimensional vertical plane (as in section)
Recall that a profile is
the view of a person or
an object from the side
SITE SOLAR ANALYSIS
Tools of the Trade
Using Profile Angles (Ω)
Using Profile Angles (Ω)
A
A
Using Profile Angles (Ω)
Solar
Altitude (β)
Using Profile Angles (Ω)
Solar
Surface
Azimuth (γ)
Using Profile Angles (Ω)
This is the sun’s position in three dimensions,
now let’s consider its representation in section.
Using Profile Angles (Ω)
Cut a section perpendicular to the back wall
Using Profile Angles (Ω)
B
B
Section perpendicular to back wall
Using Profile Angles (Ω)
Profile Angle (Ω) for
section perpendicular
to back wall
Using Profile Angles (Ω)
Cut a section parallel to the back wall
Using Profile Angles (Ω)
C
Section parallel to back wall
C
C
Using Profile Angles (Ω)
Profile Angle (Ω) for
section parallel to back wall
Profile Angle (Ω)
Profile Angle (Ω)
Profile Angle (Ω)
Profile Angle (Ω)
An example problem:
Let’s cast some shadows for
an declined vertical dial. A
two-foot horizontal gnomon
is placed in a southwest-
facing wall at 36º NL. Cast
the shadow for 3 pm on 21 the shadow for 3 pm on 21
May.
Southwest
Note that this vertical gnomon could easily be the corner of
an awning or other shading device.
Southwest
I confess a deep
and continuing
fondness for
renderings in
the Beaux Arts
tradition
Our familiar LOFSAC
– a Sun Path Diagram
in the equidistant
polar form
3 PM, 21 May
We will use our
LOFSAC overlay
for calculating
1. Profile Angle
2. Angle of
Incidence
3. Solar- Surface
Azimuth
Let’s look at the development of
this overlay. We begin with a wall
of random orientation.
The wall can only ‘see’ the half of the
sky vault that lies in front of it.
One can map positions in that quarter
sphere using coordinates relative to
the wallΘ = 60º
This fix set of relative positions can be translated
into several variables that are dependant on
position – e.g., angle of incidence, profile angle,
radiation
Overlay for
calculating Profile
Angle, Angle of
Incidence, and
Solar- Surface
Azimuth
Overlay for
calculating Profile
Angle
Overlay for
calculating Angle of
Incidence
Overlay for
calculating Solar-
Surface Azimuth
3 pm,
21 May
Back to our
sample
calculation
problem: our
southwest-facing
wall ‘sees’ this
half of the sky
vault21 May
Start with a wall elevation.
What do we have to work with?
The Beaux Arts
rendering wizards
used orthographic
projections – our
familiar plans,
elevations, and
sections
We can project plan and
section to provide three views
of the same object.
Since sunpath diagrams are projections of the sun’s path onto a
plan diagram let’s focus on plan for a moment.
Here is the
sunpath diagram
placed in position
relative to our
wall in plan
And the profile And the profile
angle overlay in
position relative to
our wall in plan.
Note the normal to
window line. This
will yield a profile
angle in a section
perpendicular to
the wall
Problem setup for Profile
Angle (Ω), section
perpendicular to wall
3 PM, 21 May
The two
diagrams
combined.
Now we can
derive a value
for Ω for a
southwest –
facing surface
3 pm
21 May
facing surface
at 3 PM, 21
May
21 May
Ω = 54°
Find the intersection of
the 3 pm and 21 May
lines. This is the
absolute position of
the sun in the sky.
Read a value for
profile angle
from the
contours of
the profile
3 pm
the profile
angle overlay.
This overlay is
positioned relative
to the wall.
The result is profile angle equals 54°
OK, what do
we do with our 54°profile
angle value?
Ω = 54º
Problem setup for
Profile Angle (Ω),
section parallel to
wall
3 PM, 21 May
Problem setup for
Profile Angle (Ω),
section parallel to
wall
3 PM, 21 May
Profile angle
overlay in place
for normal parallel
to wall
21 May
Read the value for
profile angle parallel
to the wall from
the contours of
the profile
angle overlay.
The result is
3 pm
The result is
profile angle equals 62°
Ω = 62°
Ω = 54º
54ºΩ = 62º
Add the new Add the new
profile angle
value to the
elevation. The
intersection of
these two lines is
the end of the
shadow.
We can now run a
check on the
shadow position
using solar-surface
azimuth.
Solar surface azimuth
protractor in place for
normal parallel to wall
Problem setup for
Solar-Surface
Azimuth (γ)
3 PM, 21 May
Determining
solar surface
azimuth
value
Find the intersection of
the 3 pm and 21 May
lines. Then draw a
straight line from
the zenith (center
of sunpath diagram)
through the
month/time
intersection to the
perimeter.
γ = 36º
Read a value for
solar-surface azimuth on
the perimeter scale of the
overlay.
The result is solar-surface azimuth equals 36°
54ºΩ = 62º
54º62º
Shadow position for
3 pm, 21 Mayγ = 36º
Problem setup for
Angle of Incidence (Φ)
3 PM, 21 May
Angle of Incidence
21 May
Find the intersection of
the 3 pm and 21 May
lines. This is the
absolute position of
the sun in the sky.
Read a value for
angle of incidence
from the
contours of
the angle of
incidence overlay.
Θ = 57º
Shadow length = gnomon height x tan Θ
= 3.1’
incidence overlay.
This overlay is
positioned relative
to the wall.
The result is angle of incidence equals 57°
54º62º
Shadow position for
3 pm, 21 Mayγ = 36º
54º62º
Θ = 57º
3.1’
Angle of incidence
yields a shadow
length of 3.1 feet
Penumbral shadows – go ponder a flagpole
Penumbral shadows – go ponder a flagpole
But wait -- it is time for the 7th inning stretch
PEC Monthly Solar Geometry Spreadsheet
PEC Annual Solar
Geometry
Spreadsheet
Annual Version
Benton’s Solar
Geometry
Spreadsheet
Annual Version
1. The Solar Constant
The earth receives a relatively
constant flux of solar radiation
at the edge of its atmosphere.
This value will vary about 7%
during the year and is taken to during the year and is taken to
average 429.2 BTU/Ft2 Hr.
Values for each month can be
found in ASHRAE Handbook of
Fundamentals.
2. Earth’s Movement
The orbit of the sun about the
earth (declination) and the
earth's rotation on its axis.
(hour) establish the seasonal
and diurnal cycles of solar and diurnal cycles of solar
radiation at the earths surface.
Declination and hour are
fundamental inputs to all
methods of calculating solar
geometry.
3. Location on Earth
The location of a site on the
earth's sphere will determine
the range and limits of seasonal
and diurnal solar variation.
Latitude will affect solar Latitude will affect solar
altitude, azimuth and day
length Longitude will establish
the relationship between solar
time and standard time.
Altitude will establish
atmospheric attention.
4. Surface Tilt & Orientation
At a given location, the
relationship of a target plane
to the earth's surface and to
south will establish the angle of
incidence between the surface incidence between the surface
and the sun at any given time.
The angle of incidence will
indicate if the surface is shade
or in the sun. If the surface is
in the sun, the impact will vary
with angle of incidence.
5. Weather / Climate Patterns
Solar radiation impact at the
earth's surface will vary
according to the weather
patterns characteristic to a
given region. This variation, given region. This variation,
primarily due to shading by
clouds, can be established
using calculation procedures
(see article by S.A. Klein in
Solar Energy Journal, Vol. 19,
pp. 325) or referring to climatic
data.
6. Microclimatic Shading
Topography and vegetation
establish site specific radiation
patterns that vary through the
year. These shading effects can
be examined using horizon be examined using horizon
shading diagrams sunpath
projections or using three-
dimensional models for scale
simulation
7. Surface Shading Devices
The three-dimensional
character of a surface will
establish the extent of self
shading that occurs with hour
and seasonal changes. This may and seasonal changes. This may
be studied graphically using
profile angle projections or sun
path shading mask. Three-
dimensional models provide an
accurate analysis method.
8. Transmission through Glazing
The transmitted component of
radiation striking a glazing
material will vary with the
physical properties of the
glazing, the assembly of glazing
components, and the angle of components, and the angle of
incidence. Consult glazing
manufacturers or Duffie and
Beckman, Solar Energy Thermal
Processes, p. 108.
9. Surface Absorption
The conversion of radiation t
heat and the transfer of heat
from the surface to storage, or
to the air, will vary with
surface absorptance, angle of surface absorptance, angle of
incidence, target mass, target
temperature, and air
temperature.
A radiation
overlay for
the sun
Diffuse radiation only
when sun is behind
the surface
the sun
path
diagram
Direct and diffuse
radiation when sun is
in front of the surface
The radiation
overlay applied to
our SW-facing
wall example
The radiation
overlay applied to
a SW-facing wall
example
Solar Geometry
Spreadsheet
Annual Version
The radiation
overlay applied to
our SW-facing
wall example
21 May
Find the intersection of
the 3 pm and 21 May
lines.
Read a value for solar
3 pm
Read a value for solar
radiation from the
contours of the solar
radiation overlay.
The result is 180 Btu/Hr
for a clear sky.