A new trigonometric model for solar radiation and shading factor: Varying profiles of building façades and urban eccentricities

Abstract

Solar energy utilizations in buildings are contingent on efficient shading models. This paper presents a new trigonometric model that was simple in application and robust in handling diverse site environments. The developed model was experimentally validated and compared to existing shading techniques such as pixel counting and polygon clipping. Additional analyses were performed to examine building façades ranging from flat to free-form surfaces in both linear and non-linear urban forms. This study integrated two submodels into the shading model to estimate the reduction in cooling demand and the energy production from solar applications. On annual basis, elliptical urban grids provided less normal beam radiation by a mean of 4.7 % or 22.8 W/m2 than the linear grids tangent to the curvilinear ones. South-facing façades gained more radiation by a factor ranging from 1.26 to 1.55 due to wider street grid conditions. Shade-less protrusions of the free-form façades allowed the incidence factor to reach up to 0.91 compared to 0.35 in flat façades. Although the developed model had an average error of 5.2 %, the computational time was reduced by more than 40 %.