The popularity of the atria after its revival since the 1970's has caught the attention of designers and opened ways for new strategies of energy conservation for large buildings. Early atria were visual statements rather than integrated energy systems. But a growing recognition of the contribution of daylight for energy conservation in atria requires study in greater depth to exploit the potential of the atrium in the use of daylight for energy conservation. Present methods for calculating daylight distribution in conventionally designed buildings are not presently configured to deal with atria. This study takes advantage of scale model simulation process to develop a mathematical model which will predict daylight distribution in a square atrium under an overcast sky. Data generated from twelve model studies representing thirty six cases were analyzed using statistical methods as a measure to develop the mathematical model. The mathematical model developed has the ability to predict illumination level on the vertical surface at different floor locations in a square type atrium within the specified limitations. This model is reliable, as the predicted illumination levels have been found to have strong correlation with the values obtained from scale model studies. The mathematical model can be effectively used to assist designers in estimating illumination levels in an atrium and to provide opportunity to test design alternatives while the design is in the preliminary design stage. / Master of Science

There is a growing recognition in design professions that lighting is a significant factor in energy consideration. This has generated an interest in daylighting; the bringing of direct and diffuse daylight into buildings to reduce the use of artificial lighting. Many methods exist for quantifying diffuse daylight distribution for use in the design of buildings, but the methods vary widely both in technique and capability. Moreover, no present method deals with direct daylight (sunshine) distribution. Additionally, none have taken advantage of improvements in computer technology that make feasible more complex mathematical computational models for dealing with direct and diffuse daylight together. This dissertation describes the theoretical development and computer implementation of a new mathematical approach to analyzing the distribution of direct and diffuse daylight. This approach examines light transfer from extraterrestrial space to the inside of a room based on the principles of astrometry, solid geometry, and radiation transfer. This study discusses and analyzes certain aspects critical to develop a mathematical model for evaluating daylight performance and compares the results of the proposed model with 48 scale model studies to determine the validity of using this mathematical model to predict the daylight distribution of a room. Subsequent analysis revealed no significant variation between scale model studies and this computer simulation. Consequently, this mathematical model with the attendant computer program, has demonstrated the ability to predict direct and diffuse daylight distribution. Thus, this approach does indeed have the potential for allowing designers to predict the effect of daylight performance in the schematic design stage. A microcomputer program has been developed to calculate the diffuse daylight distribution. The computation procedures of the program use the proposed mathematical model method. The program was developed with a menu-driven format, where the input data can be easily chosen, stored, and changed to determine the effects of different parameters. Results can be obtained through two formats. One data format provides complete material for analyzing the aperture size and location, glass transmission, reflectance factors, and room orientation. The other provides the graphic displays which represent the illuminance in plan, section, and 3-dimensional contour. The program not only offers a design tool for determining the effects of various daylighting options quickly and accurately in the early design stage, but also presents the daylight distribution with less explanation and with more rapid communication with the clients. The program is written in BASICA language and can be used with the IBM microcomputer system. / Ph. D.