1. What is the Shadow Length Formula?

The shadow length formula calculates the length of a shadow cast by an object based on its height and the angle of the sun. This trigonometric calculation is essential in architecture, photography, and solar energy applications.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \( Length \) — Shadow length in meters
• \( Height \) — Object height in meters
• \( \theta \) — Sun angle in degrees from horizontal

Explanation: The formula uses the tangent trigonometric function to relate the object's height and the sun's angle to determine the shadow length.

3. Importance of Shadow Length Calculation

Details: Accurate shadow length calculation is crucial for architectural planning, solar panel placement, photography composition, and understanding solar positioning throughout the day and seasons.

4. Using the Calculator

Tips: Enter the object height in meters and the sun angle in degrees (0-90°). The angle should be measured from the horizontal plane to the sun's position.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum valid angle for calculation?
A: The angle must be between 0° and 90° (exclusive). At 90°, the sun is directly overhead and casts no shadow.

Q2: How does time of day affect shadow length?
A: Shadows are longest at sunrise and sunset (low sun angles) and shortest at solar noon (highest sun angle).

Q3: Does this work for any object shape?
A: The formula calculates the shadow length for the object's height. For complex shapes, additional calculations may be needed.

Q4: How does season affect shadow calculations?
A: The sun's maximum altitude changes with seasons, affecting shadow lengths throughout the year.

Q5: Can this be used for solar panel placement?
A: Yes, understanding shadow patterns helps optimize solar panel placement to avoid shading and maximize energy production.