A New Method for Predicting the Solar Heat Gain of Complex Fenestration Systems I. Overview and Derivation of the Matrix Layer Calculation

A new method of predicting the solar heat gain through complex fenestration systems involving nonspecular layers such as shades or blinds has been examined in a project jointly sponsored by ASHRAE and DOE. In this method, a scanning radiometer is used to measure the bidirectional radiative transmittance and reflectance of each layer of a fenestration system. The properties of systems containing these layers are then built up computationally from the measured layer properties using a transmission/multiple-reflection calculation. The calculation produces the total directional-hemispherical transmittance of the fenestration system and the layer-by-layer absorptances. These properties are in turn combined with layer-specific measurements of the inward-flowing fractions of absorbed solar energy to produce the overall solar heat gain coefficient. In this first in a series of related papers describing the project, the assumptions and limitations of the calculation method are described and the derivation of the matrix calculation technique from the initial integral equations is presented.In this first in a series of related papers describing the project, the assumptions and limitations of the calculation method are described and the derivation of the matrix calculation technique from the initial integral equations is presented.