1. What is the Shadow Length Formula?

The shadow length formula calculates the length of a shadow based on an object's height and the sun's altitude angle. This trigonometric calculation is essential in various fields including architecture, photography, and solar energy planning.

2. How Does the Calculator Work?

The calculator uses the shadow length formula:

Where:

• \( Height \) — Object height in meters
• \( Altitude \) — Sun's altitude angle in degrees from GPS
• \( \tan \) — Trigonometric tangent function

Explanation: The formula uses basic trigonometry where the shadow length equals the object height divided by the tangent of the sun's altitude angle.

3. Importance of Shadow Length Calculation

Details: Accurate shadow length calculation is crucial for architectural planning, solar panel placement, photography composition, and understanding sun position effects on structures and landscapes.

4. Using the Calculator

Tips: Enter object height in meters and sun's altitude angle in degrees (0-90°). All values must be valid (height > 0, altitude between 1-90 degrees).

5. Frequently Asked Questions (FAQ)

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/sunset it's 0°, at solar noon it's highest.

Q2: How accurate is GPS for sun position?
A: Modern GPS systems can provide reasonably accurate sun position data based on location, date, and time, typically within 0.1-0.5 degrees accuracy.

Q3: Does this work for any object shape?
A: The formula calculates the shadow length for vertical objects. For irregular shapes, additional calculations would be needed.

Q4: What time of day gives the longest shadows?
A: Shadows are longest when the sun is lowest in the sky - at sunrise and sunset when the altitude angle is smallest.

Q5: Can I use this for solar panel planning?
A: Yes, this calculation helps determine potential shading issues for solar installations throughout the year.