Chapter 1 Solar RadiationSecure Site ...THE SOLAR CONSTANT • The distance between the sun and the earth varies by 1.7% due to the eccentricity of the earth’sorbit • Nearly fixed

Chapter 1 Solar Radiation

THE SUN

• The sun is a sphere of intensely hot gaseous matterwith a diameter of 1.39 × 109 m

• It is, on the average, 1.5 × 1011 m away from the earth.

• The sun rotates on its axis about once every 4 weeks,

• It does not rotate as a solid body

• The sun has an effective blackbody temperature of5777 K♣

• The temperature in the central interior regions isvariously estimated at 8 × 106 to 40 × 106 K

♣1The effective blackbody temperature of 5777 K is the temperature of a blackbody radiating the same amount

of energy as does the sun.

THE SUN

• Sun’s density is about 100 times that of water.

• Several fusion reactions have been suggested tosupply the energy radiated by the sun.

• The one considered the most important is a processin which hydrogen combines to form helium

• The energy produced in the interior of the solarsphere is

• first transferred out to the surface

• and then radiated into space

THE SOLAR CONSTANT

• The distance between the sun and the earth varies by1.7% due to the eccentricity of the earth’s orbit

• Nearly fixed intensity of solar radiation reaches to theoutside of the earth’s atmosphere.

• The solar constant Gsc=1367 W/m2

• is the energy from the sun per unit time received on a unit areaof surface perpendicular to the direction of propagation of theradiation at mean earth-sun distance outside the atmosphere.

SOME DEFINITIONS

• Air Mass m: The ratio of the mass of atmospherethrough which beam radiation passes to the mass itwould pass through if the sun were at the zenith (i.e.,directly overhead)

• Beam Radiation: Solar radiation received from the sunwithout having been scattered by the atmosphere.(Often referred to as direct solar radiation)

• Diffuse Radiation: Solar radiation received from thesun after its direction has been changed by scattering bythe atmosphere. (Referred to in some meteorologicalliterature as sky radiation or solar sky radiation)

SOME DEFINITIONS

• Total Solar Radiation: The sum of the beam and thediffuse solar radiation on a surface. (The most commonmeasurements of solar radiation are total radiation on ahorizontal surface, often referred to as global radiationon the surface.)

• Irradiance, W/m2: The rate at which radiant energy isincident on a surface per unit area of surface. Thesymbol G is used for solar irradiance, with appropriatesubscripts for beam, diffuse, or spectral radiation.

• Irradiation or Radiant Exposure, J/m2: The incidentenergy per unit area on a surface, found by integrationof irradiance over a specified time, usually an hour or aday.

SOME DEFINITIONS

• Insolation: is a term applying specifically to solarenergy irradiation.• H is used for insolation for a day.

• I is used for insolation for an hour (or other period if specified).

• H and I can represent beam, diffuse, or total and can be onsurfaces of any orientation.

• Subscripts on G, H, and I are as follows:• “o” refers to radiation above the earth’s atmosphere, referred to

as extraterrestrial radiation;

• “b” and “d” refer to beam and diffuse radiation;

• “T” and “n” refer to radiation on a tilted plane and on a planenormal to the direction of propagation.

• If neither “T” nor “n” appears, the radiation is on a horizontalplane.

SOME DEFINITIONS

• Radiosity or Radiant Exitance, W/m2: The rate atwhich radiant energy leaves a surface per unit area bycombined emission, reflection, and transmission.

• Emissive Power or Radiant Self-Exitance, W/m2: Therate at which radiant energy leaves a surface per unitarea by emission only.

• Any of these radiation terms, except insolation, canapply to any specified wave-length range (such as thesolar energy spectrum) or to monochromatic radiation.

• Insolation refers only to irradiation in the solar energyspectrum.

SOME DEFINITIONS

• Any of these radiation terms, except insolation, canapply to any specified wave-length range (such as thesolar energy spectrum) or to monochromatic radiation.

• Insolation refers only to irradiation in the solar energyspectrum.

SOME DEFINITIONS

• Solar Time: Time based on the apparent angular motionof the sun across the sky

• Solar noon: The time the sun crosses the meridian ofthe observer.

• Solar time is the time used in all of the sun-anglerelationships; it does not coincide with local clock time.

meridian or longitude

SOME DEFINITIONS• It is necessary to convert standard time to solar time

by applying two corrections• 1st there is a constant correction for the difference in longitude

between the observer’s meridian and the meridian on which thelocal standard time is based♠.

• The sun takes 4 min to transverse 1◦ of longitude.

• 2nd correction is from the equation of time, which takes intoaccount the perturbations in the earth’s rate of rotation whichaffect the time the sun crosses the observer’s meridian.

♠ To find the local standard meridian, multiply the time difference between local standard clock time and

Greenwich Mean Time by 15.

SOME DEFINITIONS

DIRECTION OF BEAM RADIATION

• The geometric relationships between a plane of anyparticular orientation relative to the earth at any time andthe position of the sun relative to that plane, can bedescribed in terms of several angles

• Φ or L: Latitude,

• δ: Declination,

• β: Slope,

• γ: Surface azimuth angle

• ω or h: Hour angle,

• θ: Angle of incidence,

• θz:Zenith angle,

• αs:Solar altitude angle,

• γs:Solar azimuth angle

ANGLES FOR TRACKING SURFACES

• Some solar collectors ‘‘track’’ the sun by moving inprescribed ways to minimize the angle of incidence ofbeam radiation on their surfaces and thus maximize theincident beam radiation.

• The angles of incidence (θ) and the surface azimuthangles (γ) are needed for these collectors.

• Tracking systems are classified by their motions:• Rotation can be about a single axis (which could have any

orientation) but which in practice is usually• horizontal east-west,

• horizontal north-south,

• vertical,

• or parallel to the earth’s axis

• or rotation can be about two axes


• Figure shows extraterrestrial radiation on a fixedsurface with slope equal to the latitude and also onsurfaces that track the sun about a horizontal north-south or east-west axis at a latitude of 45◦ at thesummer and winter solstices

• Summer solstices:δ=23.5o

• Winter solstices:δ=-23.5o


• It is clear that tracking can significantly change the timedistribution of incident beam radiation.

• Tracking does not always result in increased beamradiation;• compare the winter solstice radiation on the north-south

tracking surface with the radiation on the fixed surface.


• For a plane rotated about a horizontal east-west axiswith a single daily adjustment so that the beamradiation is normal to the surface at noon each day,

• The slope of this surface will be fixed for each day andwill be

• The surface azimuth angle for a day will be 0◦ or 180◦depending on the latitude and declination:


• For a plane rotated about a horizontal east-west axiswith continuous adjustment to minimize the angle ofincidence,

• The slope of this surface is given by

• The surface azimuth angle for this mode of orientationwill change between 0◦ and 180◦ if the solar azimuthangle passes through ±90◦. For either hemisphere,


• For a plane rotated about a horizontal north-south axiswith continuous adjustment to minimize the angle ofincidence,

• The slope is given by

• The surface azimuth angle γ will be 90◦ or −90◦depending on the sign of the solar azimuth angle:


• For a plane with a fixed slope rotated about a verticalaxis, the angle of incidence (θ) is minimized when thesurface azimuth and solar azimuth angles are equal.From Equation 1.6.3, the angle of incidence is

• The slope is fixed, so

• The surface azimuth angle is


• For a plane rotated about a north-south axis parallel tothe earth’s axis with continuous adjustment to minimize θ,

• The slope varies continuously and is

• The surface azimuth angle is

• Where


• For a plane that is continuously tracking about two axesto minimize the angle of incidence,

RATIO OF BEAM RADIATION ON TILTED SURFACE TO THAT

ON HORIZONTAL SURFACE

• For solar process design, it is necessary to calculate thehourly radiation on a tilted surface of a collector frommeasurements or estimates of solar radiation on ahorizontal surface.

• The most commonly available data are total radiationfor hours or days on the horizontal surface, whereasthe need is for beam and diffuse radiation on the planeof a collector.

measures all

beamdiffuse



• The geometric factor Rb, the ratio of beam radiation onthe tilted surface to that on a horizontal surface at anytime, can be calculated exactly by appropriate use ofEquation 1.6.2.

• Figure indicates the angle of incidence of beamradiation on the horizontal and tilted surfaces.

• The ratio Gb,T /Gb is given by♥

♥ The symbol “G” is used in this book to denote rates, while “I” is used for energy quantities integrated

over an hour.

• and cos θ and cos θz are both determined from Equation1.6.2 (or from equations derived from Equation 1.6.2).



• The optimum azimuth angle for flat-plate collectors isusually 0◦ in the northern hemisphere (or 180◦ in thesouthern hemisphere).

• Thus it is a common situation that γ = 0◦ (or 180◦).

• In this case, Equations 1.6.5 and 1.6.7 can be used todetermine cos θz and cos θ, respectively, leading in thenorthern hemisphere, for γ = 0◦, to

• In the southern hemisphere, γ = 180◦ and the equationis



• A special case of interest is Rb,noon, the ratio for south-facing surfaces at solar noon.

• From Equations 1.6.8a and 1.6.9a, for the northernhemisphere,

• For the southern hemisphere, from Equations 1.6.8b and1.6.9b,

SHADING

• Three types of shading problems occur so frequentlythat methods are needed to cope with them.

• The first is shading of a collector, window, or otherreceiver by nearby trees, buildings, or otherobstructions.

• The second type includes shading of collectors in otherthan the first row of multirow arrays by the collectors onthe adjoining row.

• The third includes shading of windows by overhangsand wingwalls.

SHADING

• At any point in time and at a particular latitude, φ, δ, andω are fixed.

• From the equations given above, the zenith angle θz orsolar altitude angle αs and the solar azimuth angle γscan be calculated.

SHADING• A solar position plot of θz and αs versus γs for latitudes of

±45◦ is shown in Figure.

• Lines of constant declination are labeled by dates of meandays of the months from Table 1.6.1.

• Lines of constant hour angles labeled by hours are shown.

SHADING• The angular position of buildings, wingwalls, overhangs,

or other obstructions can be entered on the same plot.

• For example• if a building or other obstruction of known dimensions and

orientation is located a known distance from the point of interest(i.e., the receiver, collector, or window),

• the angular coordinates corresponding to altitude and azimuthangles of points on the obstruction (the object azimuth angle γoand object altitude angle αo) can be calculated fromtrigonometric considerations

• Alternatively, measurements of object altitude and azimuthangles may be made at the site of a proposed receiver and theangles plotted on the solar position plot.

SHADING

• The solar position at a point in time can be representedfor a point location.

• Collectors and receivers have finite size, and what onepoint on a large receiving surface ‘‘sees’’ may not be thesame as what another point sees.

• The problem is often to determine the amount of beamradiation on a receiver.

• If shading obstructions are far from the receiver relativeto its size, so that shadows tend to move over thereceiver rapidly and the receiver is either shaded or notshaded, the receiver can be thought of as a point.

SHADING

• If a receiver is partially shaded, it can be considered toconsist of a number of smaller areas, each of which isshaded or not shaded.

• Or integration over the receiver area may be performedto determine shading effects.

• These integrations have been done for special cases ofoverhangs and wingwalls.

SHADING

• Overhangs and wingwalls are architectural features thatare applied to buildings to shade windows from beamradiation.

• The solar position charts can be used to determine whenpoints on the receiver are shaded.

• The projection P is the horizontal distance from theplane of the window to the outer edge of the overhang.

• The gap G is the vertical distance from the top of thewindow to the horizontal plane that includes the outeredge of the overhang.

• The height H is the vertical dimension of the window.

SHADING

• The angle of incidence of beam radiation on a shadingplane can be calculated from its surface azimuth angle γand its slope β = 90 + ψ by Equation 1.6.2 or equivalent.

• The angle ψ of shading plane 1 is

• And that for shading plane 2 is

• Note that if the profile angle αp is less than 90 − ψ, theouter surface of the shading plane will ‘‘see’’ the sun andbeam radiation will reach the receiver

SHADING

• Shading calculations are needed when flat-platecollectors are arranged in rows.

• Normally, the first row is unobstructed, but the secondrow may be partially shaded by the first, the third by thesecond, and so on.

• As long as the profile angle is greater than the angleCAB, no point on row N will be shaded by row M.

• If the profile angle at a point in time is CA’B’ and is lessthan CAB, the portion of row N below point A’ will beshaded from beam radiation.

Documents

Chapter 1 Solar RadiationSecure Site ...THE SOLAR CONSTANT • The distance between the sun and the earth varies by 1.7% due to the eccentricity of the earth’sorbit • Nearly fixed