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Azimuthal
Orthographic Sundial Applet

Enter latitude in decimal degrees and press return key, 
Select "Solar
Time" or "Standard Time" from the menu. Chosing "Standard Time" the circle of the hour points will by rotated by an angle determined by the longitude and the current equation of time. 


You may use the keys "y", "m", "d", "h",
"n" to increase
the year, month, date, hour, or minute, Click
the applet first !

The fixed
gnomon of this sundial is perpendicular to the
horizontal dial plane. Orthographic projection of the Sun (declination δ, hour angle H, latitude φ): x
= R*sin(H)*cos(δ)
y
= R*[sin(φ)*cos(δ)*cos(H)
 cos(φ)*sin(δ)]
The declination lines are ellipses, the semimajor axis a=R*cos(δ) being parallel to the eastwest direction, and the small semiaxis b=R*sin(φ)*cos(δ) parallel to the northsouth direction. The displacement of the declination ellipse from the center is y=R*sin(δ)*cos(φ): The
declination
ellipse δ=0° (blue) and the hour
ellipse for 6h/18h are touching at the points
east and west:
At
local
noon the altitude of the Sun (declination δ) at latitude φ is:
α
= 90°  φ + δ
Latitude φ=50°:The
projection
to the horizon plane:
y = R*cos(α)=R*sin(φ + δ)
summer
solstice:
δ=23.5°,
α=63.5°
y/R=0.96
equinox: δ=0°, α=40° y/R=0.77 winter solstice: δ=23.5°, α=16.5° y/R=0.45 L
= R*cos(φ23.5°)
The time is indicated by the intersection of the gnomon shadow with the black declination line. 
Books 
Denis Savoie: La
Gnomonique, Les Belles Lettres, Paris 2007; p
201203. 

Orthographic
projection (Wikipedia) C. Macrez:
Cadrans Solaires d'Azimut  Projection
Orthographique et Stéreographique 
Updated:
2023, Oct 06
©
20102023 J. Giesen