Question

In order to calculate the SAA, it is help to start by calculating the zenith angle which is the angle between the Sun and the point directly overhead at solar noon. To determine the zenith angle, subtract the solar declination from the location latitude. If either the declination or location is in the Southern Hemisphere, assign it a negative value. Always report the absolute value of the calculated zenith angle (no negative zenith angles).

Zenith angle = (Location latitude) – (Solar declination)

Lastly, in order to calculate the SAA, simple subtract the zenith angle from 90°. Remember that the SAA is an angle, so do not label the SAA with North or South.

Example:

Las Vegas, Nevada (36°N) on December 21 (23.5°S solar declination)

Zenith angle = 36° - (-23.5°)

Zenith angle = 36° + 23.5°

Zenith angle = 59.5°

SAA = 90° - 59.5°

SAA = 30.5°

Q13. Calculate the zenith angles and solar altitude angles for the following locations at the specified dates. Recall the dates of the solstices and equinoxes in order to determine the solar declination for each of the dates listed. Replace the question marks with the related answers.

Answer 1

a) Honolulu, Hawaii (21.3°N) on June 21st (23.5°N solar declination)

Zenith angle = 21.3° - 23.5° = -2.2° (absolute value is 2.2°)

Solar altitude angle = 90° - 2.2° = 87.8°

b) Rio de Janeiro, Brazil (22.9°S) on December 21st (23.5°S solar declination)

Zenith angle = -22.9° - (-23.5°) = 0.6°

Solar altitude angle = 90° - 0.6° = 89.4°

c) Cairo, Egypt (30.0°N) on March 21st (0° solar declination)

Zenith angle = 30.0° - 0° = 30.0°

Solar altitude angle = 90° - 30.0° = 60.0°

d) Sydney, Australia (33.9°S) on September 23rd (0° solar declination)

Zenith angle = -33.9° - 0° = 33.9°

Solar altitude angle = 90° - 33.9° = 56.1°