Applet Collection


Azimuthal Orthographic Sundial Applet





Enter latitude in decimal degrees and press return key,

enter longitude in decimal degrees
and press return key.

solar time
                  standard time
Select "Solar Time" or "Standard Time" from the menu.
"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,
Shift key and "y", "m", "d", "h", "n" to decreaseyear, month, date, hour, or minute !

Click the applet first !

My Sundial Applet Collection

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 semi-major axis a=R*cos(δ) being parallel to the east-west direction, and the small semi-axis b=R*sin(φ)*cos(δ) parallel to the north-south direction. The displacement of the declination ellipse from the center is y=R*sin(δ)*cos(φ):

declination ellipse

The hour lines are also ellipses (red for -23.5°< δ <+23.5). The ellipse for 14:00 solar time:

hour ellipse

The declination ellipse δ=0° (blue) and the hour ellipse for 6h/18h are touching at the points east and west:


Sun altitude
At local noon the altitude of the Sun (declination δ) at latitude φ is:
α = 90° - φ + δ

The projection to the horizon plane:
y = R*cos(α)=R*sin(φ + δ)

Latitude φ=50°:
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

The minimum length of the gnomon is:

gnomon style

L = R*cos(φ-23.5°)

The time is indicated by the intersection of the gnomon shadow with the black declination line.

Select "Transit Table" from the "Details" menu:


Select "EoT Table" from the "Details" menu:

The sundial in action: Aug 7 at 10:00 solar time (11:31 CEST):

azimuth sundial

Denis Savoie: La Gnomonique, Les Belles Lettres, Paris 2007; p 201-203.

Web Links

Orthographic projection (Wikipedia)

C. Macrez: Cadrans Solaires d'Azimut - Projection Orthographique et Stéreographique

Enhanced Software for Displaying Orthographic, Stereographic, Gnomonic and Cylindrical Projextions of the Sunpath Diagram and Shading Mask Protractor.

Updated: 2013, Jul 28

© 2010-2013 J. Giesen

jgiesen (at)