definitionscomputation of flat sundials. fer j. de vries
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 dials plane. The tip of the gnomon is the shadow casting point. g > 0. |
| i | inclination of the plane: the zenith distance of the endpoint of the (pin) gnomon. 0° <= i < 180°. (horizontal i = 0 vertical i = 90) |
| 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. ( longitude of the place of the sundial. ) 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 relative to the dial's plane, parallel to the earth axis. -90° <= v <= 90°. |
| b | angle of substyle, measured from y-axis. pos. anti clockwise. -180° <= b <= 180°. |
| ts | hourangle of substyle. -180° <= ts <= 180°. |
| decl | declination of the sun, pos. if sun in northern hemisphere, neg. 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. |
| ... | diverse other variables are used in the procedures as x0,y0,z0, x1, y1, z1, day, mth and so on. See the procedures. |
While these definitions are, of course, arbitrary, many of them are common
in gnomonics and the others are constrained by the requirement that the method
should be universal all over the world.
If you want to change the
definitions , you may also have to change some of the formulae, or introduce a
conversion sub-routine.
English-speaking people nowadays use the word gnomon to refer to the whole of the line casting the shadow, but in this paper gnomon is used in its older and more traditional sense. Here the gnomon is a pin, perpendicular to the plane.
