# Solar Position

Figure 1 The position of the sun in the sky can be determined by knowing the solar altitude (q) and azimuth (f) angles.

The geometric position of the sun as seen from a particular place on the surface of the earth varies from day to day and hour to hour. At any given instance, the sun’s position can be fixed by two angles, altitude and azimuth (Figure 1).

Altitude is the angle between the sun and the horizon. When the sun is on the horizon (at sunrise and sunset), this angle is zero. Solar altitude is at the maximum at solar noon. The complement of solar altitude angle, or the angle of the sun from a vertical line directly overhead, is called the zenith angle.

Azimuth is the angle between a north-south line on the earth’s surface and the horizontal projection of the sun’s rays; it is measured from true south. By convention, solar azimuth is negative before noon and positive after noon.

To calculate the sun’s angle we need to know not only the relative position of the sun, but also the geographical location of the observer on earth. Two angles define the position of any point on the surface of the earth.

Latitude is the angular distance measured along a meridian north or south of the equator. All points on the equator have a latitude of zero; the north and south poles have latitudes of +90o (90o N) and –90º (90o S). Los Angeles is located at a latitude of 33.9º N.

Longitude is the angular distance measured east or west from the Prime (International) Meridian -- an imaginary circle passing through Greenwich, England. Since the period of rotation of earth about its own axis is 24 hours, each hour covers 360/24 = 15º longitude. Los Angeles has a longitude of 118° W. Calculating the relative position of the sun in the sky from earth at different locations and times is outside the scope of this book, but readers are encouraged to refer to more advanced texts (1).

## References

(1) See for example, Duffie, J, and Beckman, William A., “Solar Engineering of Thermal Processes,” 2nd. Ed., John Wiley and Sons, 1991.

(2) Toossi Reza, "Energy and the Environment:Sources, technologies, and impacts", Verve Publishers, 2005

Markvart, T., and Castanar, L., Solar Cells: Materials, Manufacture and Operation, Elsevier Publishing Company, 2005.

Galloway, T., Solar House, Elsevier Publishing Company, 2004.

Stine, W. B., and Harrington, R. W., Solar Energy Systems Design, John Wiley and Sons, Inc., 1985.

Solar Energy, Direct Science Elsevier Publishing Company, the official journal of the International Solar Energy Society, covers solar, wind and biomass energies.

National Renewable Energy Laboratory: Solar Research (http:// www.nrel.gov/solar).

Energy Efficiency and Renewable Energy: Solar Energy, US Department of Energy (http://www.eere.energy.gov).

American Solar Energy Society (http://www.ases.org).

Solar Electric Power Association (http://www.solarelectricpower.org).

California Solar Center (http://www.californiasolarcenter.org).