Solar Power » Radiation

The sun's observed position

The angle under which the sun is observed from a point on the earth’s surface is affected by the earth’s daily rotation, the annual rotation of the tilted earth and the latitude of the surface in question.

Daily Rotation

The solar hour angle Ω expresses the daily rotation of the earth. As the earth rotates 360° within 24 hours, every hour adds another 15° to the sholar hour angle. When the sun is in its highest point in the sky, the solar hour angle is zero. Angles before noon count negative, after noon positive.

As the earth rotates, the angle between the sun and due south, the solar azimuth angle, α, varies from -90° at sunrise (east) to +90° at sunset (west)..

Longitudinal Movement


The declination angle, δ, is the angular position of the sun at solar noon with respect to the plane of the equator. It varies from -23.45° at winter solstice to +23.45° at summer solstice according to:
Declination Angle
As before, n denotes the day in the year with n = 1..365.



For locations other than the equator, the latitude, φ, changes the zenith angle further.


Zenith Angle

The orientation of an area with respect to the sun is best described by the zenith angle, θ, which is related to latitude, day and time via:

cosine zenith

To get the intensity, the peak intensity should be multiplied with the cosine of the zenith angle。

The above equation is only true while the sun can be observed, which allows us to determine the hours of daylight on a horizontal surface as

Daylight Hours

Obviously, averaged over the year, every location on earth has the same amount of hours of daylight. However, the annual distribution varies by latitude. While cities with higher latitude enjoy more hours of daylight in summer, the peak intensity remains lower due to the larger zenith angle.


Graphing Intensity and Energy

Using the above formulae, we have put together a few graphs to demonstrate the impact of latitude, time of day and day of year on the intensity and energy observed on horizontal surfaces. All graphs have been normalised to 1kW / m2.

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