A Matlab GUI for Calculating the Solar Radiation and Shading of Surfaces on the Earth BASTIAN KELLER, ALEXANDRE M. S. COSTA Universidade Estadual de Maringa ´, Av. Colombo 5790, Bloco 104, Maringa ´, PR, CEP 87020-900, Brazil Received 18 December 2007; accepted 29 October 2008 ABSTRACT: Predicting the amount of solar radiation that strikes a surface is of the highest importance in several engineering applications. Just to name a few, solar radiation estimates is fundamental during the design of technologies such as: flat plates and concentrating collectors, solar energy storage devices, solar heaters, and photovoltaic systems. Furthermore, solar radiation estimates are important in energy studies for buildings, as during the cooling load calculation for air conditioning systems. The calculation of the solar radiation and shading involves many equations and a lot of influencing factors must be considered. Therefore, a Matlab GUI was developed that execute the equations and considers all the influencing factors. The program calculates the solar radiation and shadows caused by a rectangle as well as shadows on a rectangle surface caused by fins beside it. The user only has to set few values (like the location, time, etc.) and he can choose between the calculations either for a selectable time of the day or for a completely day. Then the results are plotted either in simple editor frames or in 2D- and 3D-graphics. The program also shows the results of some influencing angles subject to the location of the sun in the sky that can be helpful for many applications. Finally, on the educational side, the Matlab program can be useful for the engineering student performing some what if studies involving solar radiation. ß 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20301 Keywords: solar radiation; shading; sun movement; solar angles INTRODUCTION A star in the universe, the sun is a giant nuclear fusion reactor. Combining hydrogen to form helium, the sun generates a great amount of energy. This energy (called solar radiation) strikes the earth, heats the air, Correspondence to A. M. S. Costa ([email protected]). ß 2009 Wiley Periodicals Inc. 1
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A Matlab GUI for Calculating the Solar Radiation on Earth
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A Matlab GUI forCalculating the SolarRadiation and Shading ofSurfaces on the Earth
BASTIAN KELLER, ALEXANDRE M. S. COSTA
Universidade Estadual de Maringa, Av. Colombo 5790, Bloco 104, Maringa, PR, CEP 87020-900, Brazil
Received 18 December 2007; accepted 29 October 2008
ABSTRACT: Predicting the amount of solar radiation that strikes a surface is of the
highest importance in several engineering applications. Just to name a few, solar radiation
estimates is fundamental during the design of technologies such as: flat plates and
concentrating collectors, solar energy storage devices, solar heaters, and photovoltaic
systems. Furthermore, solar radiation estimates are important in energy studies for buildings,
as during the cooling load calculation for air conditioning systems. The calculation of the solar
radiation and shading involves many equations and a lot of influencing factors must be
considered. Therefore, a Matlab GUI was developed that execute the equations and considers
all the influencing factors. The program calculates the solar radiation and shadows caused by a
rectangle as well as shadows on a rectangle surface caused by fins beside it. The user only has
to set few values (like the location, time, etc.) and he can choose between the calculations
either for a selectable time of the day or for a completely day. Then the results are plotted
either in simple editor frames or in 2D- and 3D-graphics. The program also shows the results of
some influencing angles subject to the location of the sun in the sky that can be helpful for
many applications. Finally, on the educational side, the Matlab program can be useful for the
engineering student performing some what if studies involving solar radiation. � 2009 Wiley
Periodicals, Inc. Comput Appl Eng Educ; Published online in Wiley InterScience (www.interscience.wiley.com);
DOI 10.1002/cae.20301
Keywords: solar radiation; shading; sun movement; solar angles
INTRODUCTION
A star in the universe, the sun is a giant nuclear fusion
reactor. Combining hydrogen to form helium, the sun
generates a great amount of energy. This energy
(called solar radiation) strikes the earth, heats the air,Correspondence to A. M. S. Costa ([email protected]).
� 2009 Wiley Periodicals Inc.
1
water, soil, etc and supplies a lot of the energy systems
on earth.
In making energy studies and in the design of
solar passive homes and solar collectors as well as in
dimensioning air conditioning systems the total
radiation striking a surface over a specified period
of time is required.
The quantity of solar radiation that strikes a
surface (absorber) depends on different influencing
factors, for example, on the location of the sun in
the sky and the clearness of the atmosphere as well
as on the nature and the orientation of the striking
surface.
Shadows, caused by roofs, fins, buildings, trees or
other things next to the surface, reduces the solar
radiation and therefore the shadows must be consid-
ered during the calculation of the energy that strikes
the surface.
At the beginning of this work the fundamentals of
the solar radiation will be discussed. Then the
required equations will be described, and at the end
the usage of the developed GUI will be explained.
SOLAR RADIATION
Solar radiation is radiant energy emitted by the sun
from a nuclear fusion reaction that creates electro-
magnetic energy. The spectrum of solar radiation is
close to that of a black body with a temperature of
about 5,800 K. About half of the radiation is in the
visible part of the electromagnetic spectrum. The
other half is mostly in the near infrared part, with
some in the ultraviolet part of the spectrum (Fig. 1).
The radiant energy that strikes on a surface is
called the solar irradiation. Beyond the earth atmos-
phere the solar irradiation is almost constant:
Equation (1) shows the value for the solar irradiation
outside the atmosphere:
Gsc ¼ 1; 367W
m2ð1Þ
As will be discussed in the next section, on the earth
surface the solar irradiation depend on further
mechanisms.
INFLUENCING FACTORS OF THE SOLARIRRADIATION
The solar radiation striking a surface on the Earth’s
surface is affected by a number of mechanisms.
As can be seen from Figure 2, a part of the
incident energy is scattered and absorbed by air
molecules, clouds and other particles in the atmos-
phere. The radiation that is not reflected or scattered
and reaches the surface directly is called direct
irradiation GD. The scattered radiation which reaches
the ground is called diffuse irradiation Gd. Some of
the radiation is reflected from the ground onto the
receiver; this is called reflected (or albedo) irradiation
Gr. The total (or global) irradiation Gt that strikes the
absorber is the summation of these three components.
The amount of radiation is also strongly depend-
ent on the lengths of the path of the rays through the
atmosphere (air mass). The air mass the sunrays have
to pass until they strike the surface is in the morning or
evening much more and thereto the irradiation is
much less than at noontime. So the influence of the air
mass is also in coherency with location of the sun in
the sky.
Figure 1 Solar radiation spectrum [1]. Figure 2 Parts of solar radiation.
2 KELLER AND COSTA
If the absorber surface is not a horizontal surface
the absorber can produce shadows when the sun is
behind the absorber. Similarly, objects around the
absorber can cause shadows on the absorber.
Summarizing the influencing factors of total
radiation are:
1. The effects of the Atmosphere and the Earth.
2. The location of the sun in the sky.
3. The nature and the orientation of the absorber.
These influencing factors are complex and
some of them (e.g., the effect of clouds) are only
approximately to determinate.
EFFECTS OF THE ATMOSPHERE ANDTHE EARTH
The processes affecting the intensity of solar radiation
are scattering, absorption, and reflection. Reflection
occurs in the atmosphere and on the Earth’s surface.
The depletion of the sun’s rays by the earth
atmosphere depends on the composition of the
atmosphere (cloudiness, dust and pollutants present,
atmospheric pressure, and humidity).
The scattering of solar radiation is mainly by
molecules of air and water vapor, by water droplets,
and by dust particles. This process returns about 6% of
the incident radiation to space, and about 20% of the
incident radiation reaches the Earth’s surface as
diffuse solar radiation.
The absorption of solar radiation is mainly by
molecules of ozone and water vapor. Absorption by
ozone takes place in the upper atmosphere at
heights above 40 km. It occurs mainly in the ultra-
violet region of the spectrum, where it is so intense
that very little solar radiation of wavelength less
than 0.3 mm reaches the Earth’s surface. About 3%
of the solar radiation is absorbed in this way. At
low levels in the atmosphere about 14% of the solar
radiation is absorbed by water vapor, mainly in the
near infra-red region of the spectrum. Clouds
absorb very little solar radiation, which explains
why they do not evaporate in sunlight. The effect
of clouds on solar radiation is mainly scattering and
reflection.
The reflection of solar radiation depends on the
nature of the reflecting surface. The fraction of the
solar irradiation that is reflected from the surface of
the Earth is called the albedo of the surface. The total
albedo, which includes all wavelengths, is closely
related to the visible albedo, which includes only light
in the visible region of the spectrum.
If there is cloud between the sun and the point of
observation, then the direct solar irradiation is
weakened or eliminated. Diffuse solar radiation, on
the other hand, may be greater or less in the presence of
cloud than under a clear sky, depending on the type and
amount of the cloud. Thin layers of clouds and
scattered clouds reflecting sunlight, increase the diffuse
solar irradiation. Thick layers of cloud reduce diffuse
solar irradiation. Total solar irradiation is usually
reduced by cloud, but if the sun is shining in a clear
part of the sky and there are brightly illuminated clouds
nearby, then global solar irradiancemay be greater than
it would be under a completely clear sky [2].
The consideration of all these effects is complex,
because there are often many different reflectors
around the absorber and the effects of clouds and other
particles on the solar radiation received at the Earth’s
surface. But there are many recommendations and
publications that are concerned with that Refs. [3�5].
A common method that deals with the prediction of
these effects is the ASHRAE Clear sky model (see
ASHRAE Clear Sky Model Section).
LOCATION OF THE SUN IN THE SKY
The earth revolves around the sun every 365.25 days
in an elliptical orbit and rotates about its own polar
axis, inclined to the ecliptic plane by 23.458, in
approximately 24-h cycles. The direction in which the
polar axis points is fixed in space and is aligned with
the North Star (Polaris) to within about 45 min of arc
(13 mrad).
As can be seen from Figure 3 the tilt of the earth
axis relative to the ecliptic plane produces our seasons
as the earth revolves about the sun.
The location of the sun in the sky above a surface
depends on the day of the year (date) and the time of
the day as well as the location of the surface on the
earth (longitude and latitude). The used angles that
describe the location of the sun are shown in Figure 4.
Figure 3 Circulation of the earth around the sun.
SOLAR RADIATION AND SHADING OF SURFACES 3
The declination angle d is the angle between a
line connecting the center of the sun and earth and the
projection of that line on the equatorial plane. This
angle varies from þ23.458 till �23.458 throughout
a year. The following equation (developed from work