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Shadow Formula:
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The shadow length formula calculates the length of a shadow cast by an object based on its height and the sun's altitude angle. This trigonometric calculation is based on the principles of similar triangles and the tangent function.
The calculator uses the shadow formula:
Where:
Explanation: The formula uses the cotangent of the sun's altitude angle to determine how many times longer the shadow is compared to the object's height.
Details: Calculating shadow length is important in architecture, photography, solar panel placement, and various outdoor activities. It helps determine optimal positioning for sunlight exposure and shadow avoidance.
Tips: Enter the object height in meters and the sun's altitude angle in degrees (must be between 0 and 90 degrees). The calculator will compute the shadow length in meters.
Q1: What is sun altitude angle?
A: Sun altitude is the angle between the horizon and the center of the sun's disc, measured in degrees. At sunrise and sunset, it's 0°, and at solar noon it reaches its maximum value.
Q2: Why does the shadow length approach infinity as the sun approaches the horizon?
A: As the sun altitude approaches 0°, the cotangent function approaches infinity, meaning shadows become extremely long near sunrise and sunset.
Q3: How accurate is this calculation?
A: The calculation is mathematically precise for a point light source. For the sun, it's an excellent approximation, though atmospheric refraction can cause slight variations.
Q4: Can I use this for artificial light sources?
A: Yes, the same formula applies to any distant light source where the light rays are effectively parallel.
Q5: What if the sun is directly overhead?
A: When the sun is at 90° altitude (directly overhead), the cotangent is 0, resulting in no shadow (or a minimal shadow directly beneath the object).