The angle of incidence of solar radiation, which is the angle at which solar rays strike a surface, is influenced by several factors including the sun's position in the sky and the orientation of the surface. The angle of incidence can be calculated using the following general formula:
\[ \cos(\theta) = \sin(\delta) \cdot \sin(\phi) + \cos(\delta) \cdot \cos(\phi) \cdot \cos(H) \]
Where:
- \(\theta\) = angle of incidence
- \(\delta\) = solar declination (the angle between the rays of the sun and the plane of the Earth's equator, which varies throughout the year)
- \(\phi\) = latitude of the location
- \(H\) = hour angle (the measure of time since solar noon, expressed in angular measurement (degrees), where 15° corresponds to one hour)
Steps to calculate the angle of incidence:
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Calculate Solar Declination \((\delta)\): The solar declination can be approximated using the formula: \[ \delta = 23.45° \cdot \sin\left(\frac{360}{365} \cdot (N - 81)\right) \] where \(N\) is the day of the year (1 for January 1, 365 for December 31).
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Calculate Hour Angle \((H)\): \[ H = 15° \cdot (T - 12) \] where \(T\) is the local solar time.
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Calculate Angle of Incidence \((\theta)\): You can now substitute \(\delta\), \(\phi\), and \(H\) into the angle of incidence formula.
The angle of incidence can also be derived for a flat surface tilted at an angle \(\beta\) (the tilt angle of the surface), but the basic relationships with solar declination, latitude, and hour angle remain fundamental to the calculation.
For specific types of surfaces or applications (like solar panels), the formulas may differ slightly, so it's essential to consider the context in which you're measuring the angle of incidence.
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