Atmospheric transmittance models and an analytical method to predict the optimum slope of an absorber plate, variously oriented at any latitude

Abstract

Two new atmospheric transmittance models are proposed to calculate the diurnal profile of solar radiation intensity. These two, together with six other models proposed by earlier researchers, are used to obtain analytical formulae for the optimum tilt angle for a plane absorber plate at any latitude in either hemisphere. In all cases two sky models, namely the isotropic model and the anisotropic model proposed by Hay and Davies, are used. This gives a total of 16 different analytical formulae for the optimum tilt angle. The optimum slopes calculated from these formulae for Kabul, Afghanistan ( φ = 34.5°) for certain days of the year, when γ = 0 and γ = ±45°, are compared with the experimentally measured optimum slopes for those days. A simple empirical formula which is a function of latitude φ and the day of a year n is also proposed to calculate the optimum slope when γ = 0. For any given day of the year, the empirical formula reduces to a linear correlation between the optimum tilt and the latitude. The linear correlations for the monthly optimum slopes (corresponding to the Julian days) and latitude are given. The analysis is further extended to predict the optimum tilt angle, and optimum surface azimuth angle when W p is not equal to zero, and it is concluded that when W p ≠ 0, the optimum surface azimuth angle is also not equal to zero. The mean year optimum slope and the mean heating season slope for Gaborone, Botswana ( φ = −24.5°) are calculated. A formula to calculate sunset and sunrise hour angles when β ≠ 0 and γ ≠ 0 is obtained. The various symbols used are given in the Nomenclature.