The Sun’s apparent position and the optimal tilt angle of a solar collector in the northern hemisphere

In this paper, the Julian dating system is adopted to calculate the Sun’s apparent position. Both the sunshine duration and the optimal installation angle of a fixed solar collector are obtained for different time periods and latitudes in the northern hemisphere. To simulate different operating environments, both kinds of radiation flux are considered, i.e. extraterrestrial radiation and the global radiation calculated using an empirical model. The results show that Julian dating system is precise enough to predict the Sun’s locus according to analyses of the solar declination and the azimuth and elevation angles. The orientation that a solar collector must be installed at can be roughly estimated by determining the sunshine duration. The majority of the Sun’s path lies in the southern sky over a year, and hence the sunshine duration in the southern sky is longer, except for locations with latitudes below 1.5°. The yearly optimal angles are positive (approximately 0.91 and 0.76 multiplied by the latitude for extraterrestrial and global radiation, respectively), for latitudes below 65o. Above this, the curves are flatter, and the differences between the two types of radiation flux become greater. The ratio of the yearly irradiation captured by a collector installed at its yearly optimal angle to that captured by the ground surface increases with latitude, and reaches a maximum of 1.71 and 1.35 near latitudes of 65° for extraterrestrial and global radiation, respectively. The efficiency of a solar collector decreases when operating in a cloudy environment. The amount of global radiation incident on the ground surface is about 0.51–0.66 times that of extraterrestrial radiation throughout the hemisphere.