Analytical Estimation of Optical Efficiency of Cylindrical Light-Tubes Under Various CIE Sky Types

The light pipes represent a common device for enhancement of daylight amount in buildings with complex architecture and insufficient lighting by vertical windows or in underground spaces. The advantage of straight vertical light pipes is that they transport light into interior spaces from the whole sky vault independently on solar azimuth. So mainly at higher solar altitudes and under clear sky conditions they can significantly contribute to better daylight availability in buildings. The optical efficiency of a light pipe strongly depends on number of reflections of the light beams between the particular interfaces. There are available some numerical tools based on ray-tracing algorithms that enable to calculate the efficiency with high precision under given conditions. However, such calculations are adequately time-consuming and so non-attractive for routine (mass) modelling. This contribution presents an analytical method for prediction of the optical efficiency of straight light-pipes which is applicable on 15 types of sky luminance defined by CIE. Due to the analytical approach, the calculation is very fast. The method is validated by accurate numerical simulations for all the sky types and at various pipe aspect ratios. Mainly in the extreme cases of clear and overcast sky, the results are in good agreement.