UC Santa Barbara

Equations for the solar radiation input and the duration of the daily insolation on surfaces of arbitrary slope and aspect are presented in this work. It is shown that the sunrise- and sunset-hour angles and the duration of daily insolation depend on the roots of the equation Acos + B sin + C = 0, in which is the hour angle and A, B, and C are coefficients that involve the slope of the surface, the aspect of the sloping surface, the solar declination, and the latitude of a point of interest on the sloping surface. The equation developed to calculate the duration of daily insolation can be applied to any sequence or combinations of days to obtain the total number of daylight hours over arbitrary periods. It is applicable to clear-sky conditions and, therefore, it produces the theoretical upper limit of the duration of daily insolation. Equations are also developed in this paper to calculate the input of solar radiation on a slope for arbitrary atmospheric transmissivity, and coupled with other radiatiative fluxes to quantify the energy budget on the surface of the earth. The effect of changing climate and variable atmospheric conditions on solar insolation are cited in this work. The paper identifies areas of application for the methods herein presented. © 2011 ASCE.