A legibility equation for determining ideal viewing areas in lecture halls

Text presented in modern lecture halls often simultaneously appears on multiple visual media (e.g., blackboard, projection screens, TV) that have different locations, geometries, orientations, and lighting conditions. An ideal viewing area inside which all text is legible to the entire audience could be calculated using equations that predict the spatial legibility of text viewed from any directions across the lecture hall. However, among the 95 legibility equations ever published in the literature, none can serve this purpose. After using ten assumptions to narrow down the research scope, this study applies a constant-solid-angle hypothesis to develop the demanded equation from the existing Howett's equation (1983). This derived equation examines seven critical factors but the surrounding luminance of the ambient environment, which may reduce its accuracy.; The hypothesis is first verified consistent with how retinal images of text activate cones in the centre fovea of an observer's eyes, then tested in the lighting laboratory at the University of Michigan Transportation Research Institute using legibility data collected from 3 subjects in a pilot experiment and 20 subjects in a follow-up main experiment. Both experimental setups abide by the typical viewing conditions surveyed in 38 lecture halls at the University of Michigan. The outcomes show that the hypothesis holds when incident angle 0° ≤ xi ≤ 65.7°, but it does not hold when 65.7° < xi ≤ 82.8° (the largest angle examined). The derived equation is thus accordingly improved. Moreover, this study uses 20 human subjects with a modified setup at four different ambient light levels in the same laboratory to verify the negligible effect of ambient light on legibility.; The validated equation is then improved and used as the underlying algorithm for developing a computation-program-aided design method in MatLab. This method allows architects to find an overlapped two-dimensional ideal viewing area of text viewed in modern lecture halls along any viewing plane, such as that parallel to the sloped floor at eye height level. This program-aided method is verified using a field experiment carried out in the lecture hall in the Art & Architecture building at the University of Michigan.