The elevation edge (used interchangeably through altitude angle) is the angular height of the sun in the skies measured indigenous the horizontal. Confusingly, both altitude and also elevation are also used to explain the height in meters above sea level. The elevation is 0° at sunrise and also 90° when the sunlight is directly overhead (which occurs for instance at the equator ~ above the spring and also fall equinoxes).

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The elevation angle varies throughout the day. It also depends on the latitude that a specific location and the work of the year.

An necessary parameter in the style of photovoltaic equipment is the maximum elevation angle, that is, the maximum height of the sun in the sky at a specific time of year. This best elevation edge occurs in ~ solar noon and also depends ~ above the latitude and declination edge as shown in the number below.

The preferably elevation edge at solar noon (α) is a role of latitude and the declination edge (δ).

From the ahead figure, a formula for the elevation angle at solar noon deserve to be figured out according come the formula:


When the equation above gives a number greater than 90° then subtract the result from 180°. It way the sun at solar noon is coming from the southern as is common the northern hemisphere.

where:φ is the latitude that the location of interest (+ve for the north hemisphere and -ve because that the southerly hemisphere).δ is the declination angle, which relies on the job of the year.

At the Tropic that Cancer on the summer solstice, the sun is straight overhead and also the elevation edge is 90°. In summer at latitudes in between the equator and the Tropic that Cancer, the elevation edge at solar noon is higher than 90°, implying the the sunlight is comes from the north fairly than indigenous the south as in most of the north hemisphere. Similarly, in ~ latitudes in between the equator and the Tropic that Capricorn, during some periods of the year, sunshine is incident from the south, quite than native the north.

While the preferably elevation edge is used also in very basic PV system design, much more accurate PV device simulation needs the expertise of just how the elevation edge varies transparent the day. This equations are offered in the complying with page.

The elevation, \(\alpha\), can be discovered using the adhering to formula:

key Angle

α= sin −1

where HRA is the hour angle

Zenith Angle

The zenith angle is the angle in between the sun and the vertical. The zenith edge is similar to the key angle but it is measured from the vertical rather than from the horizontal, hence making the zenith angle = 90° - elevation.

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zenith Angle

ζ= 90 0 −α


Sunrise and also Sunset

To calculate the sunrise and also sunset time the key is set to zero and also the key equation above is rearranged to give:

Sunrise Time

Sunrise=12− 1 15 0 cos −1 ( −sinφsinδ cosφcosδ )− TC 60

and sunset:

Sunset Time

Sunset=12+ 1 15 0 cos −1 ( −sinφsinδ cosφcosδ )− TC 60

these equations deserve to be streamlined as:

Sunrise Time (Simplified)

Sunrise=12− 1 15 0 cos −1 ( −tanφtanδ )− TC 60

Sunset Time (simplified)

Sunset=12+ 1 15 0 cos −1 ( −tanφtanδ )− TC 60

where TC is the moment correction.

Christiana Honsbergand Stuart Bowden
1. Introduction2. Properties of Sunlight3. Semiconductors & Junctions4. Solar cell Operation5. Style of Silicon Cells6. Manufacturing Si Cells7. Modules and also Arrays8. Characterization9. Material Properties10. Batteries11. Appendices
Declination AngleAzimuth angle