The proper interpretation of analytical sky view factors for isotropic diffuse solar irradiance on tilted planes

Abstract

The consistency of well-known analytical models used for determining the sky view factor (SVF) in comparison with the theoretical definition of SVF is quantified in this paper. A general formula for SVF is derived, which can be configured to use various methods of computing solar irradiance approaching from all directions in a hemispherical vault around an arbitrarily tilted plane. The true model is then derived by choosing the receiving plane as the reference plane in a general formula. The true model most accurately follows the radiation theory. Different settings are then proposed for adapting the general formula to depict the response of each of the analytical models over the range of tilt angles. These settings realistically represent the analytical model, as there is satisfactory agreement between the results from an appropriately configured general formula and those from the corresponding analytical model. Simulations of the true model are performed to compare with the analytical models. The results show that all the analytical models are consistent with the true model when the plane is horizontal or vertical. At other tilt angles, these models mostly produce overestimated or underestimated results. Consequently, settings for analytical models that do not align with the corresponding settings in the true model are the causes of inconsistency. Based on this assessment, two analytical models are recommended for use in further research.