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.
The celestial sphere with all relevant variables showing the relationship between the equatorial and azimuthal coordinate system.
Input
Results
The equations are proof-of-concept formulas based on ancient formulas of spherical trigonometry and ignore specifics like nutation, precession, etc. The calculated results are FOR EDUCATIONAL PURPOSES ONLY; some are exact, some are approximate, and some are simplified. Actual Sun data may vary significantly.
Input
- Latitude φ:
52.5° - Longitude λ:
13.3° - Time zone:
(GMT +1:00) Berlin, Copenhagen, Paris, Zagreb - Declination δ:
19.54° - Date:
2024-05-17 - Daylight Saving Time (DST):
In effect
General calculations for latitude
- Maximum solar altitude H for latitude given
- on equinoxes:
37.5° - on June solstice:
60.94° - on December solstice:
14.06°
- on equinoxes:
- Sunrise αsr and sunset αss azimuth
- on equinoxes:
90°and270° - on June solstice:
49.2°and310.8° - on December solstice:
130.8°and229.2°
- on equinoxes:
Diurnal calculations for latitude and declination
- Day #:
138 - Declination δ:
19.54° - Sunrise azimuth αsr:
56.67° - Sunset azimuth αss:
303.33° - Hour angle at sunrise τsr:
119.22° - Noon altitude H:
57.04° - Solar midnight depression:
-17.96° - Sun hours:
15:53 - Length of unequal Sun hour:
01:19:28 - Equation of time:
+03:20
Diurnal calculations for longitude
03:21: Start of nautical dawn04:23: Start of civil dawn05:06: Sunrise13:03: Solar noon21:00: Sunset21:43: End of civil dusk22:45: End of nautical dusk
The display precision set is .2. To change that, edit the variable &digits=x in the URL where 0 <= x <= 9.
Formulas
[Load sample values (JSON) (XML) (CSV).]
- H(φ,δ)
- Sun altitude at noon H from latitude:
H = (90° − φ) + δ - αsr(φ,δ)
- Azimuth αsr of rising/setting Sun:
cos αsr = sin δ / cos φ - τsr(φ,δ)
- Hour angle τsr of rising/setting Sun (from noon):
cos τsr = -tan φ · tan δ[To offset refraction, for true sunrise/set, a constant of 1.66667° is added to the result.] - τ(h,φ,δ)
- Hour angle τ from instantaneous Sun altitude h:
cos τ = (sin h - sin δ · sin φ) / (cos δ · cos φ) - αs(τ,φ,δ)
- Sun azimuth αs for a given hour:
tan αs = sin τ / (sin φ · cos τ - cos φ · tan δ)
where H = Sun altitude at noon, h = instantaneous Sun altitude, τ = hour angle, φ = latitude, and δ = declination.
Notes
- For certain locations, such as Sevilla in Spain, which is located at 6°W but belongs to the "wrong" timezone CET (UTC+1), the results returned may be partially wrong, since Tycho calculates from true longitude only.