General Calculation Methods for Solar Trajectories

A diagram of solar trajectories is useful for the calculation of a shadow projected by an obstacle such as a building, tree or other obstruction which intercepts solar radiation on a collector, window, or other receiver. This diagram can be of the polar or Cartesian type [1 3], in which the instantaneous position of the sun is shown, defined by the solar altitude and solar azimuth angles in the various hours of the day for specific days of the month typifying the said month (in which the solar declination is equal to the monthly average). To plot these diagrams it is therefore necessary to calculate, for every instant, the altitude and solar azimuth of the place under consideration. An examination of the major works published on this argument leads to the conclusion that the calculation methods reported in the literature do not have a general validity : the Walraven method [4], in fact, is only valid for the northern hemisphere, while that of Braun and Mitchell [5], also presented by Duffle and Beckman [2], does not appear applicable ( for all the declination and latitude values) in the tropics, although there is no specific mention of these limitations in the said papers. In this paper two calculation methods are outlined which have a general validity and are applicable to all latitudes. Finally, some polar and Cartesian solar trajectory diagrams for various latitudes of both the northern and southern hemispheres are presented.