EE6623 Chap.3 Solar Geometry and Irradiance
Solar Geometry and Irradiance
Geometry comes before output
Solar irradiance on a collector depends on where the sun is and how the surface is oriented. Latitude fixes the site, declination moves seasonally, and hour angle follows the sun around solar noon. Together they produce altitude above the horizon and azimuth around it.
Collector tilt and surface azimuth then determine the incidence angle between the incoming beam and the surface normal.
Solar noon is a useful special case
At solar noon the hour angle is zero, so noon altitude can be found from latitude and declination with a short angular separation. Clock noon need not equal solar noon, because civil time follows a time-zone reference rather than the local meridian.
Write the time basis used by the question before applying the shortcut.
Sun-path diagrams carry two kinds of information
Following one dated path across hourly marks reveals a single day. Comparing several dated paths at the same hour reveals seasonal movement. The diagram can therefore support orientation, shading and daylight judgments without replacing the calculation.
Mark the horizon, altitude, azimuth and collector normal so complementary angles are not confused.
Build tilted-plane irradiance in three pieces
Direct beam radiation is projected according to sun-surface geometry. Diffuse sky radiation is multiplied by a view factor under the stated sky model. Ground-reflected radiation uses total horizontal irradiance, ground reflectance and a ground view factor.
Add the three contributions only after their bases are clear. A horizontal measurement is not automatically a collector-plane input.
Check the limiting orientations
At zero tilt, the isotropic sky view factor becomes one and the ground factor becomes zero. At a vertical tilt, both become one half. When the sun approaches the zenith, beam projection onto a horizontal surface approaches its direct-normal value.
Near the horizon, the horizontal projection approaches zero. These limits are quick tests for an angle or sign error.
What this chapter covers
- 01
Solar spectrum and radiation basis
- 02
Latitude, declination and hour angle
- 03
Altitude, azimuth and zenith
- 04
Sun-path diagrams
- 05
Collector tilt and incidence
- 06
Beam projection
- 07
Diffuse and reflected irradiance
Worked example · free
Find solar-noon altitude
- 2Find the latitude-declination separation.
- 2Subtract the separation from ninety degrees.
- 2Interpret the collector geometry.
Key terms
- Declination
- The seasonal angular position of the sun north or south of the equatorial plane.
- Hour Angle
- Angular displacement of the sun from solar noon caused by earth's rotation.
- Solar Altitude
- Angular height of the sun above the local horizon.
- Azimuth
- Horizontal direction of the sun or collector under a stated directional convention.
- Insolation
- Solar energy received per unit area over a stated period and surface orientation.
Solar Geometry and Irradiance FAQ
Why can clock noon differ from solar noon?
Solar noon is the moment the sun crosses the local meridian and hour angle is zero. Clock time also reflects the time-zone reference longitude and other corrections. Use the time basis supplied by the problem rather than assuming twelve o'clock is exact solar noon.
What does a sun-path diagram show?
It maps solar altitude and azimuth across hours and dates. Follow one dated curve to trace a day, or compare curves at the same hour to see seasonal movement. It is especially useful for collector orientation and shading analysis.
How are diffuse and reflected irradiance added?
Use the sky and ground view factors associated with collector tilt, then add those contributions to the projected beam term. State the diffuse model and ground reflectance. The beam ratio is geometric and should not be confused with either view factor.
Exam move
Begin each session with an unlabelled sketch and add horizon, zenith, sun vector, altitude, azimuth, collector plane and surface normal without notes. If two angles appear complementary, state which is measured from the horizon and which from a normal. Practise solar-noon altitude for northern and southern declinations before adding hour angle, and write the hemisphere signs rather than relying on a memorised subtraction.
Use a sun-path diagram twice: trace one date through the day, then compare several dates at one hour. For collector irradiance, create three rows headed beam, sky diffuse and ground reflected. Write the geometry or view factor and the irradiance basis on each row before summing. Test the sky and ground factors at zero tilt and vertical tilt. Test the beam term at overhead sun and near the horizon.
When an instrument reading is supplied, identify its plane before using it. Close every answer with a short direction statement explaining how turning the collector toward the sun changes beam projection and how greater tilt trades sky view for ground view.
Keep an error list for clock noon mistaken as solar noon, a surface angle used instead of a normal angle, and horizontal irradiance inserted directly as collector irradiance.
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