Calculating the incidence angle of the Sun

In summary, the conversation discusses two different formulas for calculating the incidence angle for incoming solar radiation on a sloping surface. The first formula uses the cosine function and takes into account the surface slope, altitude angle, and surface aspect. The second formula involves the azimuth angle and the tangent function and calculates the angle between the Sun's projection on the horizontal plane and the plane of the gridcell's slope. The two formulas seem to be calculating different angles and may have different applications.
  • #1
jones123
10
0
Hi all,

I have some difficulties understanding a formula for calculating the incidence angle for incoming solar radiation on a sloping surface. I found that:

angle of incidence calculated as cos(j) = sin((pi/2)-surface slope)*sin(altitude angle) + cos((pi/2)-surface slope)*cos(altitude angle)*(cos(surface aspect - azimuth angle))

However, in my textbook it says "The angle between the sun’s projection on the horizontal plane and the plane of the gridcell’s slope is calculated as: azimuth angle * tan(surface slope + cos(azimuth angle - surface aspect))"

Can anyone explain me what the difference between these two formulas is and how they are related?

Thanks in advance!
 
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  • #2
Without looking very deeply into those formulae, it looks to me that they are calculating different things. The angle of incidence relates to the normal and the incident ray but the second formula gives the angle between the Sun's projection on the ground and a "plane". The only unique angle relative to a plane has to be relative to the normal. Your textbook may have a diagram that it's referring to.
 
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What is the incidence angle of the Sun?

The incidence angle of the Sun refers to the angle at which sunlight hits a particular point on the Earth's surface. It is the angle between the incoming sunlight and a line perpendicular to the Earth's surface at that point.

How is the incidence angle of the Sun calculated?

The incidence angle of the Sun can be calculated using trigonometric functions, specifically the cosine function. The formula is:
incidence angle = arccos(sin(latitude) * sin(solar declination) + cos(latitude) * cos(solar declination) * cos(hour angle))
where latitude is the geographic location of the point, solar declination is the angle of the Sun relative to the Earth's equator, and hour angle is the difference between the local solar time and solar noon.

What factors affect the incidence angle of the Sun?

The incidence angle of the Sun is affected by the geographic location of the point, the time of day, and the time of year. The tilt of the Earth's axis, the Earth's rotation, and the Earth's orbit around the Sun all contribute to changes in the incidence angle throughout the year.

Why is it important to calculate the incidence angle of the Sun?

The incidence angle of the Sun is important for a variety of purposes, including solar energy production, agriculture, and climate research. It helps determine the amount of solar radiation that reaches a specific location, which can impact plant growth, temperature, and other environmental factors.

Can the incidence angle of the Sun be negative?

Yes, the incidence angle of the Sun can be negative if the sunlight is hitting the Earth's surface at an angle below the horizon. This occurs during sunrise and sunset when the Sun is below the horizon but still illuminating the sky.

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