Looking for the Wndsn store? This way, please.

## 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, source: GQT5

## Input

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

## 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.