## Calculation of the Solar Angle of Incidence

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: Figure 2.13 Definition of the Solar Angle of Incidence on a Tilted Surface

= arccos(-cosaS • cosyS • cosat • sinyt -sinaS • cosyS • sinat • sinyt + sinyS • cosyt) = arccos) - cosyS • sinyt • cos(aS-at) + sinyS • cosyt)

+1 0 ## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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### Responses

• jessamine
Is solar angle of incidence tilted surface?
8 years ago
• benjamin vogt
How to calculate the incidnece angle in solar panel?
7 months ago
• johan
How calculate the incidence angle from sun on water using pyrhon?
5 months ago
• jamila
How to calculate incident energy from a planet W/m^2?
4 months ago
• carol
How to calculate angle of incidents?
5 days ago