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Calculation of Solar Insolation

What is Solar Insolation?

Solar insolation is the quantity of solar radiation, or electromagnetic energy, received at a certain point on the surface of the earth. Variables such as solar declination angle, zenith angle, hour angle and Cloud coverage, are necessary to consider when calculating solar insolation. Solar insolation units are normally  kWh /m2 / day — which represents the daily amount of solar energy in kilowatt hour striking a square meter area on the earth’s surface.

 

Solar Insolation calculations

Hour angle (H) is calculated using:

H = 15 deg x (time – 12).

Time equals hour of day from midnight

Zenith angle (Z)  is calculated using :

Z = cos-1 (sinXsinY + cosXcosYcosH).

Zenith angle is the angle from the point directly overhead to the point of the sun’s position in the sky.

Where

X: latitude

Y: solar declination angle

H:  the hour angle

Solar declination angle is the angle between the perpendicular plane to incoming solar radiation and the earth’s rotational axis. The solar declination angle varies from + 23.5 deg on summer solstice to -23.5 deg on winter solstice, and  0 deg on the vernal equinox and autumnal equinox.

Solar insolation (I)  can be calculated using the following formula:

I = S cosZ.

Where is the S: solar constant — around 1000 W/m2

Z: zenith angle from the equation above

The maximum amount of solar insolation on a surface at a specific tilt angle can be calculated with the knowledge of latitude and the day of the year, based on the equation of the sun’s position in the sky throughout the year. These calculations are also critical for using experimental data from sunshine hour recorders.

 

Using Sun hours

The daily insolation is equal in numerically to the number of sun hours in a day. The module is assumed to face the equator so that it is directed South in northern hemisphere, while directed North in southern hemisphere. When the latitude is changed through zero going across the equator, the module is facing the opposite direction.

Number of hours the sun is shining each day,is the number of hours between sunrise and sunset in that day. For parts of the year,in the latitudes above 67 deg the sun shines for 24. Astonishingly, when averaged over the course of the year, the sun shines by  an average of 12 hours daily everywhere in the world. In the latitudes to the north the average intensity is lower than at the latitudes to the south.

The number of sun hours is merely the time between both

Sunrise which is calculated as:

Sunrise = 12− (1150cos−1(−sinφ sinδ /cosφ cosδ)

and sunset which is calculated as:

Sunset = 12+( 1/150 cos − 1(−sinφ sinδ /cosφ cosδ)

Air mass is used to determine the direct component of the solar radiation:

 

Air Mass formula is used to determine the air mass:

AM=1/cosθ

 

 

 

References:

https://sciencing.com/calculate-solar-insolation-8435082.html

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