# Solar Radiation on a Tilted Surface

The amount of solar radiation incident on a tilted module surface is the component of the incident solar radiation which is perpendicular to the module surface. The following figure shows how to calculate the radiation incident on a tilted surface (Smodule) given either the solar radiation measured on horizontal surface (Shoriz) or the solar radiation measured perpendicular to the sun (Sincident).

Tilting the module to the incoming light reduces the module output.

The animation shows the calculation of the various insolations. In each case the length of the vector gives the relative intensity of the radiation.

The equations relating Smodule, Shoriz and Sincident are:

where
α is the elevation angle; and

The elevation angle has been previously given as:

where φ is the latitude; and
δ is the declination angle previously given as:

From these equations a relationship between Smodule and Shoriz can be determined as:

The following active equations show the calculation of the incident and horizontal solar radiation and that on the module. Enter only one of Smodule, Shoriz and Sincident and the program will calculate the others.

Components of Radiation on Tilted Surface Calculator

The tilt angle has a major impact on the solar radiation incident on a surface. For a fixed tilt angle, the maximum power over the course of a year is obtained when the tilt angle is equal to the latitude of the location. However, steeper tilt angles are optimized for large winter loads, while lower title angles use a greater fraction of light in the summer. The simulation below calculates the maximum number of solar insolation as a function of latitude and module angle.

X

-9090

X

090

The effect of latitude and module tilt on the solar radiation received throughout the year in W.h.m-2.day-1 without cloud. On the x-axis, day is the number of days since January 1. The Module Power is the solar radiation striking a tilted module. The module tilt angle is measured from the horizontal. The Incident Power is the solar radiation perpendicular to the sun's rays and is what would be received by a module that perfectly tracks the sun. Power on Horizontal is the solar radiation striking the ground and is what would be received for a module lying flat on the ground. These values should be regarded as maximum possible values at the particular location as they do not include the effects of cloud cover. The module is assumed to be facing south in the northern hemisphere and north in the southern hemisphere. For some angles, the light is incident from the rear of the module and in these cases the module power drops to 0.