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How to Calculate Solar Hour Angle?

Published in Solar Calculations 3 mins read

The solar hour angle is calculated as the angular displacement of the sun east or west of the local meridian due to the Earth's rotation. It is expressed in degrees, with negative values indicating time before solar noon and positive values indicating time after solar noon.

Here's how to calculate it:

Understanding the Basics

  • Solar Noon: This is the time when the sun reaches its highest point in the sky. At solar noon, the hour angle is 0°.
  • Earth's Rotation: The Earth rotates 360° in 24 hours, which means it rotates 15° per hour.

Formula for Calculating Solar Hour Angle (HRA)

The basic formula is:

HRA = 15° * (Time past solar noon in hours)

Steps for Calculation

  1. Determine Local Apparent Time (LAT): This is the actual time based on the sun's position. It may differ from your standard clock time due to factors like longitude and the Equation of Time. For simplicity, we'll assume LAT is known or can be calculated elsewhere.

  2. Find Solar Noon Time: Determine the time of solar noon for your location on the specific day. Many online calculators or astronomical resources can provide this information.

  3. Calculate Time Difference: Subtract the solar noon time from the local apparent time. This gives you the time difference from solar noon.

    Time Difference = LAT - Solar Noon Time

  4. Apply the Formula: Multiply the time difference (in hours) by 15° to get the solar hour angle.

    HRA = 15° * (Time Difference in hours)

Sign Convention:

  • If the Time Difference is negative (i.e., LAT is before solar noon), the HRA is negative.
  • If the Time Difference is positive (i.e., LAT is after solar noon), the HRA is positive.

Example:

Let's say the local apparent time (LAT) is 10:30 AM and solar noon is at 12:00 PM.

  1. Time Difference = 10:30 AM - 12:00 PM = -1.5 hours
  2. HRA = 15° * (-1.5 hours) = -22.5°

Therefore, the solar hour angle at 10:30 AM is -22.5°.

Summary:

The solar hour angle is a simple calculation once you know the local apparent time and solar noon. It provides a measure of the sun's position relative to the local meridian, crucial in many solar energy and astronomical applications. Remember to pay attention to the sign convention to indicate whether the time is before or after solar noon.

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