## Incident Angle of Sunlight

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When the Sun's rays are perpendicular to an absorbing surface, the irradiance incident on that surface has the highest possible power density. As the angle between the sun and the absorbing surface changes, the intensity of light on the surface is reduced. When the surface is parallel to the sun's rays (making the angle from perpendicular to the surface 90°) the intensity of light falls to zero because the light does not strike the surface. For intermediate angles, the relative power density is cos(θ) where θ is the angle between the Sun's rays and direct normal (or perpendicular) to the surface.

The irradiance absorbed by the surface can be found by multiplying the total irradiance by cos(θ).

Ii = It cos(θ)

Where
Ii:  Irradiance absorbed by the surface
It : Total irradiance
θ:  Incident angle

Therefore under peak sun conditions (1,000 Watts/meter2) if the angle of the sun's rays strike a surface 15° off from perpendicular, the irradiance absorbed the surface would be:

Ii= 1,000 W/m2 x cos(15°) = (1,000)(~.966) ≈ 966 W/m2

Ultimately, this makes sense because the incident angle is 0° if the sunlight is directly normal to the absorbing surface and cos(0°) = 1, meaning that 100% of the available irradiance is absorbed by the surface. Similarly, when the surface is parallel to the Sun's rays, the incident angle is 90°, and because cos(90°) = 0, the surface absorbs no irradiance. In the above example, cos(15°) = .966, and so the surface is absorbing 96.6% of the available solar power.

In designing photovoltaic (PV) systems, this question of how much available irradiance is absorbed by the photovoltaic modules is very important, since the amount of energy the system is able to produce is directly proportional to the amount of energy it absorbs from the Sun. Some systems are therefore designed with trackers on them, which cause the photovoltaic modules to follow the Sun's movement across the sky, maximizing the amount of time that the PV modules are directly normal to the sunlight. For fixed tilt systems, however, this is not possible, and so the system must be designed using the tilt angle and orientation that will best fits the needs of the system's owner. Most often, this means installing the system at the angle that will absorb the most irradiance over the course of the year, but in some cases there may be times when there is a critical need for energy and so the system can be designed to produce more electricity when it's most needed.