Mathematical model of building envelope element insolation

Abstract

In this paper, the problem of estimation of building envelope oriented element insolation by direct sunlight is solved using mathematical model of Earth's rotation. Quaternions are used as mathematical tool for description of rotation. The model allows to obtain automatically estimation of building element insolation by direct sunlight for given latitude and given time interval (month, week, day, etc.). The model takes into account schedule of change of day and night, change of direct sunlight angle on a given element of the surface caused by sun motion over horizon (changes of its height and azimuth during time of day). Distinctive feature of the model is simplicity of program-algorithmic implementation due to using description of rotation by means of quaternions. © Published under licence by IOP Publishing Ltd.