Incidence ANGLE

The solar incidence angle, 9, is the angle between the sun's rays and the normal on a surface. For a horizontal plane, the incidence angle, 9, and the zenith angle, are the same. The angles shown in Figure 2.9 are related to the basic angles, shown in Figure 2.5, with the following general expression for the angle of incidence (Kreith and Kreider, 1978; Duffie and Beckman, 1991):

cos(9) = sin(L) sin(6) cos(|3) - cos(L) sin(6) sin(|3) cos(Zs)

+ cos(L) cos(6) cos(h) cos(|3) + sin(L) cos(6) cos(h) sin(|3) cos(Zs) + cos(6) sin(h) sin(|3) sin(Zs) (2.18)

Solar Angle Incidence

where

ß = surface tilt angle from the horizontal

Zs = surface azimuth angle, the angle between the normal to the surface from true south, westward is designated as positive

For certain cases Eq. (2.18) reduces to much simpler forms:

■ For horizontal surfaces, ß = 0° and 9 = and Eq. (2.18) reduces to Eq. (2.12).

■ For vertical surfaces, ß = 90° and Eq. (2.18) becomes cos(9) = - cos(L)sin(6)cos(Zs) + sin(L)cos(6)cos(h)cos(Zs)

■ For a south-facing, tilted surface in the Northern Hemisphere, Zs = 0° and Eq. (2.18) reduces to cos(9) = sin(L) sin(6) cos(ß) - cos(L) sin(6) sin(ß) + cos(L) cos(6) cos(h) cos(ß) + sin(L) cos(6) cos(h) sin(ß)

which can be further reduced to cos(9) = sin(L - ß) sin(8) + cos(L - ß) cos(6) cos(h) (2.20)

■ For a north-facing, tilted surface in the Southern Hemisphere, Zs = 180° and Eq. (2.18) reduces to cos(9) = sin(L + ß) sin(6) + cos(L + ß) cos(6) cos(h) (2.21)

Equation (2.18) is a general relationship for the angle of incidence on a surface of any orientation. As shown in Eqs. (2.19)-(2.21), it can be reduced to much simpler forms for specific cases.

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Responses

  • Fredrik Lassila
    Is solar angle of incidence tilted surface?
    8 years ago
  • celeste
    What is Solar Zenith Angle on Tilted Surface?
    8 years ago
  • michela
    How to calculate solar incidence angle on tilted surface?
    8 years ago
  • Falco
    How ro calculate incident angle in solar water heater?
    3 years ago

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