Orthographic Sundial Applet
Enter latitude in decimal degrees and press return key,
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,
Click the applet first !
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):
The hour lines are also ellipses (red for -23.5°< δ <+23.5). The ellipse for 14:00 solar time:
The declination ellipse δ=0° (blue) and the hour ellipse for 6h/18h are touching at the points east and west:
The minimum length of the gnomon is:
At local noon the altitude of the Sun (declination δ) at latitude φ is:
α = 90° - φ + δLatitude 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(φ-23.5°)
The time is indicated by the intersection of the gnomon shadow with the black declination line.
|Denis Savoie: La
Gnomonique, Les Belles Lettres, Paris 2007; p
2013, Jul 28
2010-2013 J. Giesen
jgiesen (at) t-online.de