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Wndsn Sun Calculator

Companion to Wndsn Quadrant Telemeters: Low tech, high utility graphical distance computers from the Wndsn applied science lab.

By way of using a Wndsn Quadrant to measure local latitude and calculate declination for a given date, a number of values can be derived through further Quadrant computations.

Earth, declination, and the celestial sphere.

Knowing the noon altitude of the Sun, we can calculate the solar declination δ and vice versa.

The declination of the Sun is the angle between the Sun's rays and the equatorial plane of the Earth. The declination angle is the same for anywhere on Earth on a given day.


Enter latitude φ and solar declination δ to compute a variety of Sun data.


[Load sample values (JSON) (XML) (CSV).]

Sun altitude at noon H from latitude:
H = (90° − φ) + δ
Azimuth αsr of rising/setting sun:
cos αsr = sin δ / cos φ
Hour angle tsr of rising/setting sun (from noon):
cos tsr = -tan φ * tan δ
Hour angle t from instantaneous Sun altitude h:
sin t = (sin h - sin δ * sin φ) / (cos δ * cos φ)
Sun azimuth αs for a given hour:
tan αs = (sin t / (sin φ * cos t)) - cos φ * tan δ

where H = Sun altitude at noon, h = instantaneous Sun altitude, t = hour angle, φ = latitude, and δ = declination.


1        rad =  57.3    deg
6.2832   rad = 360      deg = 6283.2   mil = 21,600     minutes (moa)
0.017453 rad =   1      deg =   17.453 mil =     60     minutes (moa)
                 0.0573 deg =    1     mil =      3.438 minutes (moa)

See also