Derivation of the solar geometric relationships using vector analysis

Abstract

The standard mathematical approach used in deriving equations to describe the apparent motion and position of the Sun is spherical trigonometry. Additionally, the derivation of the equations for the intensity of the direct beam radiation, incident on the surface of a solar collector or architectural surface, also generally relies on the same approach. An alternative approach utilizing vector analysis is used to derive all of these equations. The technique greatly simplifies the derivation of equations for quantities such as the declination, altitude and azimuth of the Sun, and the intensity of the direct beam radiation on a tilted panel with an arbitrary orientation. Additionally, it allows a simple derivation of the equations needed to accurately describe the Equation of Time and the right ascension.