1. What is the Hour Angle at Sunrise and Sunset?

The hour angle at sunrise and sunset represents the angular displacement of the sun from the meridian at these specific times. It is a crucial parameter in solar energy calculations and astronomical observations, helping determine the duration of daylight and the sun's position throughout the day.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \omega \) — Hour angle (radians)
• \( \Phi \) — Latitude angle (radians)
• \( \beta \) — Tilt angle (radians)
• \( \delta \) — Declination angle (radians)

Explanation: The formula calculates the hour angle based on the difference between latitude and tilt angles, and the sun's declination angle. The arccosine function returns the angle whose cosine equals the computed product.

3. Importance of Hour Angle Calculation

Details: Accurate hour angle calculation is essential for solar energy system design, agricultural planning, architectural design, and various astronomical applications. It helps determine optimal sun exposure times and daylight duration.

4. Using the Calculator

Tips: Enter all angles in radians. Ensure inputs are valid numerical values. The calculator automatically handles domain restrictions for trigonometric functions.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid values for the hour angle?
A: The hour angle typically ranges from 0 to π radians (0 to 180 degrees), representing the angular displacement from solar noon.

Q2: How do I convert degrees to radians for input?
A: Multiply degrees by π/180 (approximately 0.0174533) to convert to radians.

Q3: What happens if the calculated value is outside the domain of arccosine?
A: The calculator automatically clamps the value to the valid range [-1, 1] before applying the arccosine function.

Q4: Can this calculator be used for both sunrise and sunset calculations?
A: Yes, the formula gives the absolute hour angle value, which applies to both sunrise (negative value) and sunset (positive value) when measured from solar noon.

Q5: What are typical values for declination angle?
A: The sun's declination angle varies between approximately -0.409 radians (-23.45°) and 0.409 radians (23.45°) throughout the year.