Horizontal Shadow Angle Calculator

Formula

To calculate the Horizontal Shadow Angle (HSA):

\[ HSA = \arctan\left(\frac{\tan(SAA)}{\cos(SAL)}\right) \]

Where:

\(HSA\) is the horizontal shadow angle in degrees
\(SAA\) is the solar azimuth angle in degrees
\(SAL\) is the solar altitude angle in degrees

What is a Horizontal Shadow Angle?

The horizontal shadow angle (HSA) is the angle between the horizontal plane and the shadow cast by an object due to the position of the sun. It is an important parameter in solar energy applications, architectural design, and shading analysis. The HSA helps in understanding how shadows will fall on surfaces, which is crucial for optimizing the placement of solar panels, designing shading devices, and ensuring adequate natural lighting within buildings.

Example Calculation

Let's assume the following values:

Solar Azimuth Angle (SAA) = 45 degrees
Solar Altitude Angle (SAL) = 30 degrees

Using the formula:

\[ HSA = \arctan\left(\frac{\tan(45)}{\cos(30)}\right) \approx 49.11 \]

The Horizontal Shadow Angle is approximately 49.11 degrees.