Generalization of the Direct Sky Component Calculation to Openings of Arbitrary Tilt Angle

Abstract

Among the three components of daylight affecting a surface's illumination inside a room, the direct component, due to light flux reaching the surface element directly from the sky, (also called sky factor) is the most significant one. Its estimation must therefore be as accurate as possible when assessing the daylighting performances of a building.To estimate its value for a given surface, analytical methods can be employed, based on the luminance distribution of the sky and the window's geometric properties: dimensions and position in regard to the surface element. However, such methods have always been restricted to vertical and horizontal windows, requiring heavy approximations to be applied whenever a tilted rectangular opening was considered.A generalized method for assessing the sky component is proposed here, extending it to rectangular windows of any tilt angle. As a purely analytical result could not be derived, it is based on an optimized combination of vertical and horizontal windows situations.To validate the methodology, scale model measurements were performed with a sky simulator for two rectangular openings of varying tilt angle (every 15° from vertical to horizontal): the experimental results proved to be in very good agreement with the calculation-based approach.