Mathematical model for designing a light redirecting prismatic panel

Abstract

Adequate daylighting inside built spaces helps reaching satisfactory levels of energy consumption by reducing the usage of artificial lighting. Moreover, it is a major source in adjusting the occupants’ visual comfort which boosts productivity and concentration. Nevertheless, inefficient design would result in increasing the solar hear gain and increasing the indoor temperatures, as well as uneven light distribution would result in the “cave effect” phenomena. A Sustainable complex fenestration system is proposed in this paper that diffuses and redirects daylight through a prismatic panel. The panel will redirect the excessive direct light upwards and reduce the light from going downwards in hot climate desert areas with high solar altitudes in the summer. A suitable design was obtained through a self-developed optical mathematical model using evolutionary algorithm. Afterwards, the mathematical model was validated using an optical ray tracing software called TracePro. Further analysis and interpretation on the light behaviour was viable using the ray tracing software which included the power transmission of the light. The final design resulted in the redirection of light upwards for all solar altitudes, increasing as the solar altitude is higher. And the mathematical model was validated against the computer ray tracing model with a standard error of the mean (SEM) of ±1.03 for the upward angles and ±2.47 for the downward angles. The design workflow including the mathematical model and the optimization tool proved to be a cheap and reliable solution for an initial design of light redirecting panels.