# Calculation of Solar Insolation

Based on the equation of the sun's position in the sky throughout the year, the maximum amount of solar insolation on a surface at a particular tilt angle can be calculated as a function of latitude and day of the year. These calculations are also essential in using experimental data from sunshine hour recorders. The following animations calculate the daily solar irradiance, the solar insolation and the number of hours during the day which the sun is shining. They do not include local weather effects and so these theoretical graphs are not used in system sizing or prediction of operation. A description of each graph is given in the caption underneath.

Latitude:

-9090

Day:

1365

The graph shows the intensity of direct radiation in W/m² throughout the day. It is the amount of power that would be received by a tracking concentrator in the absence of cloud. The time is the local solar time. Set the latitude to your location and then adjust the day slider to see how much radiation there is for each day of the year.

latitude2 =

-9090

arrayTilt =

080

The average daily solar insolation as a function of latitude. The three curves are the incident solar insolation, the horizontal solar insolation and the solar insolation on a titled surface as defined in the page Module Tilt. The daily insolation is numerically equal to the number of sunhours in a day. The module is assumed to face the equator so that it faces South in the northern hemisphere in North in the southern hemisphere. As the latitude is adjusted through zero going across the equator, the module faces in the opposite direction. the graph changes suddenly at the equator since the module is now facing in the opposite direction.

latitude3 =

-9090

The number of hours the sun is shining each day, that is the number of hours between sunrise and sunset each day. In latitudes above 67° the sun shines for 24 hours during part of the year. Surprisingly, when averaged over the year, the sun shines an average of 12 hours per day everywhere in the world. In the northern latitudes the average intensity is lower than at the southern latitudes.

The equations to generate the above plots are given below. These equations are calculated in solar time, and not in local time. The correction between local solar time and local time is given in the page The Sun's Position.

The number of sun hours is simply the time between sunrise:

$Sunrise=12-\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(\frac{-\mathrm{sin}\phi \mathrm{sin}\delta }{\mathrm{cos}\phi \mathrm{cos}\delta }\right)$

and sunset:

$Sunset=12+\frac{1}{{15}^{0}}{\mathrm{cos}}^{-1}\left(\frac{-\mathrm{sin}\phi \mathrm{sin}\delta }{\mathrm{cos}\phi \mathrm{cos}\delta }\right)$

The direct component of the solar radiation is determined from the air mass:

${I}_{D}=1.353×{0.7}^{\left(A{M}^{0.678}\right)}$

The airmass can be determined from the Air Mass formula:

$AM=\frac{1}{\mathrm{cos}\theta }$