Ex Mensura, Scientia

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 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.

- Latitude φ:
`52.5°`

- Declination δ:
`-21.5°`

- Daylight Saving Time (DST):
`No`

- Maximum solar altitude H for latitude given
- on equinoxes:
`37.5°`

- on June solstice:
`60.9°`

- on December solstice:
`14.1°`

- on equinoxes:
- Sunrise α
_{sr}and sunset α_{ss}azimuth- on equinoxes:
and`90°`

`270°`

- on June solstice:
and`49.2°`

`310.8°`

- on December solstice:
and`130.8°`

`229.2°`

- on equinoxes:

- Sunrise azimuth α
_{sr}:`127°`

- Sunset azimuth α
_{ss}:`233°`

- Hour angle at sunrise τ
_{sr}:`60.8°`

- Noon altitude H:
`16°`

- Solar midnight depression:
`-59°`

- Sun hours:
`08:06`

- Length of unequal Sun hour:
`00:40:31`

The *display* precision set is `.1`

. To change that, edit the variable `&digits=x`

in the URL where `0 <= x <= 9`

.

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

- H(φ,δ)
- Sun altitude at noon H from latitude:

`H = (90° âˆ’ φ) + δ`

- α
_{sr}(φ,δ) - Azimuth α
_{sr}of rising/setting Sun:

`cos α`

_{sr}= sin δ / cos φ - τ
_{sr}(φ,δ) - Hour angle τ
_{sr}of rising/setting Sun (from noon):

`cos τ`

[To offset refraction, for true sunrise/set, a constant of 1.66667° is added to the result.]_{sr}= -tan φ · tan δ - τ(h,φ,δ)
- Hour angle τ from instantaneous Sun altitude h:

`cos τ = (sin h - sin δ · sin φ) / (cos δ · cos φ)`

- α
_{s}(τ,φ,δ) - Sun azimuth α
_{s}for a given hour:

`tan α`

_{s}= 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.

- 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.