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sundials. technical explanation.

M. S. Davis on thu 16 may 96

There is a large variety of sundials that can be constructed
in a large variety of ways, the most commonly seen garden
variety being called a horizontal sundial. As was pointed out
by the first correspondent on this thread, the gnomon, or piece
that casts the shadow, must be cut at an angle equal to the
latitude of the site.

For the sake of convenience, think of the gnomon as a right
triangle with the angle at the bottom equal to the latitude.
The triangle must then be lined up to point to geographic
north. This being so, the hypotenuse, which in this case is
called the style, will point to the North Celestial Pole,
a point in the sky around which the entire sky seems to turn.
This point in the sky is closely approximated by the position
of the North Star.

At noon as seen on a sundial (astronomers call it local apparent
solar noon), the sun will be due south and the shadow will be due
north (geographic north) and the 12:00 shadow line, or hour line,
will be on the observer's local meridian. (Before that time it is
A.M., ante meridiem and after that P.M., post meridiem.)

Suppose the hour lines are drawn from the base of the triangle
where the style touches the base of the sundial, call it O.
The hour lines for other times may be calculated according to the formula:

tan A = tan H sin L

where A is the angle you wish to calculate for the hour lines
for different hours of the day (measured from O), H is successively
given the values 0 (for noon, already known to be 0), 15, 30, 45,
60, 75, 90 etc. (all degrees), corresponding to 1:00, 2:00, 3:00, 4:00,
5:00, 6:00, etc., and L is the latitude of the site. A hand calculator
with trigonometric functions is all you need to make these calculations,
perhaps with the help of someone who knows the math.

The time given by the sundial is local apparent solar time, which
is not the time we carry on our watches. Eastern, Central, Mountain,
and Pacific Time (in continental US) is the mean solar time of a
standard meridian. Eastern is based on 75 deg. W. longitude, Central
is based on 90 deg. W. longitude etc. And, of course, when Daylight
time is used, one hour is added to the standard time.

Time given by a sundial is not uniform from day to day as measured
by a uniform timekeeper, our watches, for example, for some complicated
reasons. To convert sundial time to standard time requires a sundial
correction which astronomers call the Equation of Time (listed in
many almanacs as the sundial correction or Equation of Time) as well
as a correction for the observer's site not being on one of the
standard meridians listed above. If anyone is interested, I could
go into more detail.

One book I would recommend for those who would like to build sundials
(and there are many very interesting, non garden variety sundials) is:

"Sundials. Their Theory and Construction." Author is Albert E. Waugh
and this is printed by Dover, so should be available.

Morris Davis
msd@unc.edu
Chapel Hill, NC 27514