Angle of incidence & other angles

The altitude and azimuth bearings of the sun enable some further important sets of angles to be computed.

  1. The first is the angle of incidence, i. This is important information as the intensity of direct irradiance is a function of the angle of incidence being a maximum at 0° (the angle of incidence is always measured from the normal to the surface), and dropping off as the cosine of the angle of incidence, until it reaches zero at 90° incidence.
  2. The second are the shadow angle, that is the angle the sun makes on section (the vertical shadow angle e) and on plan (the vertical shadow angle d). These angles enable the shadows cast and the patches of sunlight on surfaces inside and outside buildings to be predicted and plotted on sections and plans.
  3. The third is the wall solar azimuth, g, of a vertical or tilted surface, which describes the angle between its orientation and the sun"s bearing (solar azimuth, f).

The relationship between these angles is illustrated in Fig. To calculate the angle of incidence I on any plane, including the horizontal, the following equation may be used.

cos i = cos b cos g sin s + sin b cos s
slope angle of surface from horizontal.
angle of incidence
horizontal shadow angle
vertical shadow angle
azimuth of wall

For a vertical surface, when s=90°:

cos i= cos b cos g

For a horizontal surface, when s=0°:

cos i = sin b.