The solar angle of incidence 0hor on a horizontal surface is a direct function of the sun height yS. This angle is also called the zenith angle dZ:
The calculation of the angle of incidence 0tilt on a tilted surface is more complicated. The surface azimuth angle at describes the deviation from the south. If the surface faces to the west, at is positive. The inclination angle yt describes the surface tilt or slope of the surface. If the surface is horizontal, yt is zero. Figure 2.13 visualizes these angles.
The angle of incidence is the angle between the vector s in the direction of the sun and the normal vector n perpendicular to the surface. The position of the sun has been defined in spherical coordinates and thus must be transformed into Cartesian coordinates with the base vectors north, west and zenith for further calculations. The vectors s and n become:
s = (cosas • cosYS, - sinas • cosYS, sinYS)T n = (-cosat • sinYt, sinat • sinYt, cosYt)T
Both vectors are normalized, and thus the solar angle of incidence on a tilted surface is obtained by calculating the scalar multiplication of these two vectors:
= arccos(-cosaS • cosyS • cosat • sinyt -sinaS • cosyS • sinat • sinyt + sinyS • cosyt) = arccos) - cosyS • sinyt • cos(aS-at) + sinyS • cosyt)
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