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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. The celestial sphere and the navigational triangle with all relevant variables.

## Input

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

## Results

The equations are proof-of-concept formulas and ignore specifics like atmospheric refraction, 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°`
• Date: `2019-01-06`
• Instantaneous Sun altitude h: `10°`

### General calculations for latitude

• Maximum solar altitude H on equinoxes for latitude given: `37.5°`
• Maximum solar altitude H on summer solstice for latitude given: `60.94°`
• Maximum solar altitude H on winter solstice for latitude given: `14.06°`
• Summer solstice sunrise αsr and sunset αss azimuth: `49.2°` and `310.8°`
• Winter solstice sunrise αsr and sunset αss azimuth: `130.8°` and `229.2°`

### Diurnal calculations for latitude and declination or date

• Day #: `6`
• Declination δ: `-22.49°`
• Sunrise azimuth αsr: `128.93°`
• Sunset azimuth αss: `231.07°`
• Hour angle at sunrise tsr: `57.35°`
• Sun hours: `07:36`
• Length of unequal Sun hour: `38 min`
• Noon altitude H: `15.01°`
• Equation of time: `-05:12`

### Instantaneous calculations for Sun altitude

• Hour angle t: `31.98°`
• Time to or from noon: `02:04`
• Sun azimuth αs: `136.1°`
• Shadow length (of a stick with a height of 1 unit): `5.67`

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`
tsr(φ,δ)
Hour angle tsr of rising/setting sun (from noon):
`cos tsr = -tan φ * tan δ`
t(h,φ,δ)
Hour angle t from instantaneous Sun altitude h:
`cos t = (sin h - sin δ * sin φ) / (cos δ * cos φ)`
αs(t,φ,δ)
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.