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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
H = (90° − φ) + δ
cos αsr = sin δ / cos φ
cos τsr = -tan φ · tan δ[To offset refraction, for true sunrise/set, a constant of 1.66667° is added to the result.]
cos τ = (sin h - sin δ · sin φ) / (cos δ · cos φ)
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.