Mathematical model for the performance of light pipes

Abstract

Owing to increasing demand for improvement in working and living conditions and for energy saving, a great deal of attention has been paid to the development of natural daylight exploitation products. One invention is the light pipe (or sun pipe) system that not only brings natural light indoors where sunlight cannot reach but also improves the internal environment without generating excessive heat. A mathematical model of the light pipe system is desirable for assessment of its performance in terms of efficiency and economy. A modified form of daylight factor, widely used in building design, has been introduced to build a sophisticated model that enables prediction of the illuminance admitted by the light pipe system under investigation. Furthermore, the present model identifies those parameters that have a significant influence on the illuminance transmitted by light pipes. One 330 mm straight-run light pipe was installed within a Scottish dwelling house, and measurements have been carried out to monitor its performance under all weather conditions. The maximum and average values of internal illuminance were noted as 512 lx and 138 lx, respectively, and an average daylight penetration factor of 0.25% was obtained. Sophisticated models were developed and validated against measurements. Analysis shows that the light pipe daylight penetration factor is a function of sky clearness index, solar altitude and geometric factors. Two models, one simple and the other more involved, are reported. Statistical analysis results show that the two proposed models have comparable performances. In the case of the more involved model, the root mean square error (RMSE) of calculated internal illuminance was found to be 27 lx, the mean bias error (MBE) - 2 lx and the percentage average deviation (PAD) 21%. The corresponding figures for the simplified model are 28 1x, - 21x and 21%, respectively.