Accurate tool for express optical efficiency analysis of cylindrical light-tubes with arbitrary aspect ratios

Abstract

The vertical straight pipes are a desirable technology for delivery daylight into interior spaces because this concept benefits from luminance distribution of the whole upper hemisphere, including sunlight that is most important source of light under clear sky conditions. Vertical pipes can transport sunbeams to deep interiors independent of solar azimuth and/or room orientation. Currently, the tools for modelling different pipes are widely available, but their accuracy decreases as the aspect ratio of a light-pipe increases. In sunny environments with high solar altitudes and favorable clear skies the tubular light-guides allow to deliver daylight into deep offices, halls, or even underground spaces in building cores. The optical efficiency of such systems strongly depends on number of reflections the beams undergo on their path from the top to the bottom of a light pipe. In general, dense-grid and high CPU requirements meet when accurate numerical predictions are required. Such computations are non-attractive if intended for routine (mass) modelling.In this paper we introduce an analytical solution to the optical efficiency of straight pipes that is applicable to all aspect ratios and provides accurate predictions with very low demands on processor time. The new analytical model is validated and benchmarked against accurate HOLIGILM calculations, while showing the percent deviations are kept below 10% for most cases studied.