Definitions
phi |
latitude of the place of the dial. -90° <= phi <= 90°, northern latitude positive, southern latitude negative. |
g |
length of (pin) gnomon perpendicular to the dial's plane. The tip of the gnomon is the shadow casting point. 1 < g < 100. |
i |
inclination of the plane: the zenith distance of the endpoint
of the (pin) gnomon. 0° <= i < 180°. |
d |
declination of the plane: azimuth of the gnomon: south = 0°,
positive to west, negative to east. -180° <= d <= 180°. |
SM |
standard meridian of time zone. Greenwich = 0°,
positive to west, negative to east. -180° <= SM <= 180°. |
LM |
local meridian. Greenwich = 0°,
positive to west, negative to east. -180° <= LM <= 180°. |
LC |
longitude correction LC = SM - LM. |
E |
equation of time in degrees. In november E is positive. Conversion minutes of time into degrees: 1 minute = 0.25 degrees. |
v |
height of a style, parallel to the earth axis. -90° <= v <= 90°. |
b |
angle of substyle, measured from y-axis. pos. is anti clockwise neg. is clockwise. -180° <= b <= 180°. |
ts |
hourangle of substyle. -180° <= ts <= 180°. |
decl |
declination of the sun, positive if sun in northern hemisphere, negative if sun in southern hemisphere. -23.°5 <= decl <= 23.°5 |
t |
hourangle of the sun: noon = 0°, positive to west, negative to east. -180° <= t <= 180°. |
x, y |
coordinates of shadow point.
Footpoint gnomon = 0,0. x to right, y upwards. For horizontal dial x east, y north. |
dn |
daynumber. January first at 00:00:00 is daynumber 1.0 , at 12:00:00 is daynumber 1.5. |
threads |
parallel to the plane and perpendicular above 0,0
at distance height. If rotation = 0 thread-x parallel to x-axis, thread_y parallel to y-axis. |
rotation |
angle of rotation of the threads for bifilar dial.
-180 <= rotation <= 180. rotation positive is anti clockwise, rotation negative is clockwise |
height_x height_y |
perpendicular distance from pount 0,0 to threads. 1 < height < 100. |
refraction index |
for water the refraction index is about 1.333 |