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 celestial sphere with all relevant variables showing the relationship between the equatorial and azimuthal coordinate system, source: GQT5

[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.