Mathematical Expression of Mean Sky in Japan

Daylighting Calculation Method with Mean Sky (Part 1)

Abstract

An excellent method based upon Mean Sky was developed by H. Nakamura et al. for predicting daylight illuminance in interiors. Numerical tables are given for the application for Japan. However, calculations using the numerical tables are not easy in practice.
The goal of this research work is to develop a practical method of computer-aided daylighting calculation. For that purpose, the numerical tables are modified into mathematical equations. This paper presents the detailed procedure for converting the table on Mean Sky in Japan as the first step of this research work.
The conversion was done by performing regression analyses repeatedly. The final equation is proposed as a function of the azimuth and altitude of the sky element. The average difference between the values in the original table and those calculated by the equation was 0.970% and with a standard deviation of 0.748%.