(2a) The Sundial
(Attributed to an essay by a student
in elementary school.)
As the Sun rises, passes the highest point in its path (at noon and to the south, in the northern hemisphere) and sets, the shadow rotates around the stick in a clockwise direction, and its position can be used to mark time. Indeed, it has been claimed that the "clockwise" direction in which the hands on a clock rotate was chosen for this reason.
A sundial with a vertical pointer ("gnomon") will indicate noon correctly when its shadow points north. However, the direction of the shadow at some other time of the day may depend on the season--its value in summer, when the Sun's path is high, may differ from what it is in winter, with Sun low above the horizon.
Such a sundial will however work equally well at all times if the pointer is slanted, to point towards the pole of the celestial sphere (click here for an explanation--but be warned, it is a bit complicated!). The angle between it and the base then equals the geographic latitude of the user.
A Paper SundialOrnamental sundials are often found in parks and gardens, with the pointer widened into a triangular fin, which must point northwards. A sundial of this type can be constructed from folded cardboard or stiff paper: click here to see the basic design, which can be printed and then photo-copied onto suitable sheets of stiff paper or cardboard [You may want to use the "option" menu to reduce size to 90% before printing--but make sure to return the setting to 100% afterwards!]. It is meant to be used at a latitude of 38 degrees and should work adequately in most of the continental US.
If you want to make a sundial of more durable materials, draw the pre-noon hour lines at the angles to the fin (given in degrees) given below. These lines are meant for a latitude of 38 degrees; if your latitude is markedly different, see note at the end.
AccuracyThe sundial will obviously be one hour off during daylight saving time in the summer, when clocks are reset.
In addition, "clock time" (or "standard time") will differ from sundial time, because it is usually kept uniform across "time zones"; each time zone differs from its neighbors by one full hour (more in China and Alaska). In each such zone, sundial time matches clock time at only one geographical longitude: elsewhere a correction must be added, proportional to the difference in longitude from the locations where sundial time is exact.
Note on LatitudeThe angles listed above are intended for a latitude of 38 degrees. If your latitude is L, SQRT denotes "square root of" and K (=cotg2L) is
then the angle between the fin and the line corresponding to the hour N+6 (N going from 0 to 6) satisfies
Here 15N (=15 times N) is an angle in degrees, ranging from 0 to 90, and of course, the afternoon angles are mirror reflections of the morning ones. If your calculator has a button (sin-1), if you enter (sin A) and press it, you will get the angle A. For an explanation of sines and cosines, look up the math refresher. And don't forget to adjust the angle of your fin to L, too!
Next Stop: #3 Seasons of the Year
Author and curator: David P. Stern, firstname.lastname@example.org
Last updated 24 August 1998