Solar Azimuth Angle - Formulas

Formulas

It can be calculated to a good approximation with the following formula, however angles should be interpreted with care due to the inverse sine, i.e. x = sin−1(y) has two solutions (unless y is -1 or +1), only one of which will be correct.

\, \sin \phi_\mathrm{s} = \frac{-\sin h \cos \delta}{\cos \theta_\mathrm{s}}


The following formulas can also be used to approximate the solar azimuth angle, but these formulas use cosine, so the azimuth angle will always be positive, and should be interpreted as the angle less than 180 degrees when the hour angle, h, is negative (morning) and the angle greater than 180 degrees when the hour angle, h, is positive (afternoon). (These two formulas are equivalent if you assume the "solar elevation angle" approximation formula).

\, \cos \phi_\mathrm{s} = \frac{\sin \delta \cos \Phi - \cos h \cos \delta \sin \Phi} {\cos \theta_\mathrm{s}}
\, \cos \phi_\mathrm{s} = \frac{\sin \delta - \sin \theta_\mathrm{s}\sin \Phi} {\cos \theta_\mathrm{s}\cos \Phi}


The formulas use the following terminology:

  • is the solar azimuth angle
  • is the solar elevation angle
  • is the hour angle of the present time
  • is the current sun declination
  • is the local latitude

Read more about this topic:  Solar Azimuth Angle

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