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I wrote earlier:
"Anyone have a quicker method? Something you can do in fifteen seconds
instead of fifteen minutes? I've been working on a few..."

So here's one. As I've mentioned the principal problem with the 'watch
as compass' trick is that it confuses azimuth with hour angle. We can
partially fix that by tilting the face of the watch, but I think it
would be better to go a slightly different route and build a "pocket
hour angle model" since many watches are no longer analog. The concept
of using local time to get compass direction is fine. It's basically a
sundial in reverse. A sundial when aligned properly for compass
direction and latitude yields local apparent time. Therefore if we
have local apparent time already and align ourselves properly for
latitude, we can get compass direction.

I assume I have a timepiece of some sort and it is set to local zone
time. The first step is to convert to local apparent time --time by
the Sun. You can get as accurate as you want here, but the key step is
to subtract an hour for Daylight Saving Time if it's in effect (and
more days than not, it is in effect, by current laws). Equally
important, if you are at the western end of a time zone, you may need
to subtract another hour or a good fraction thereof. For example, if
you're wandering around in the U.P. of Michigan, most of it is on
Eastern Time even though it's fairly close to 90 degrees West
longitude, the middle longitude of the Central Time Zone (for those
not familiar with it, the "U.P." of Michigan is the "Upper Peninsula",
a detached, mostly rural section of the state of Michigan north of
Wisconsin).

With your estimate of local apparent time, you calculate the Sun's
local hour angle by counting the number of hours from Noon and
multiplying by 15. As an example, if it's 7:20pm CDT in Chicago, the
local apparent time is close to 6:20pm so the Sun's local hour angle
is close to 95 degrees. It's important to remember at this point that
the Sun is always east of the meridian in AM hours, always west in PM
hours, everywhere on Earth. Now it's time to build a model...

To model the geometry of the Sun's local hour angle, we need a piece
of stiff cardstock or maybe a strip of bendable metal. A matchbook
cover will work nicely. Let's imagine using an ordinary index card.
Fold the card cleanly in half. You now have two planes and an
"axis" (the axis is the fold in the card). Bend the card along the
fold until the angle between the two sides is roughly equal to the
Sun's hour angle (15 degrees times the number of hours since noon).
Hold the bent card in front of you and tilt it so that the axis (the
fold) makes an angle with the horizontal equal to your latitude. Also
turn the card so that one side is vertical. Now turn slowly around
without changing the tilt of the card until the Sun is exactly aligned
in the plane of the other side of the index card. This is an easy
condition to meet by looking at the shadow of the tilted side cast on
the vertical side. When the shadow just disappears, the Sun is lined
up in that plane. And you're done: the vertical side of the card is
now aligned north-south (you're facing south in the northern
hemisphere, north in the southern). This method works because the
planes of the card are aligned with the abstract geometric planes that
we require. The vertical side of the card corresponds to the plane of
the observer's meridian. The tilted side of the card corresponds to
the plane containing the observer, the elevated pole, and the Sun.
Note that you can re-construct the rules easily if you understand the
basic geometry of local hour angle and the altitude of the elevated
pole.

This method for determining north with known watch time will work
anywhere on Earth, and it will give compass direction within ten
degrees if you're careful aboud setting the angles. It can be done
with a card as small as a matchbook cover, or if required, by making a
larger model of the geometry and by being more careful with the
estimated angles and the number of hours since Noon, the accuracy can
be increased. After a few trials, it takes only a few seconds to set
up the angles and do the observation repeatedly during the day. It's
as good as a magnetic compass and naturally requires no correction for
magnetic variation/declination, but of course it does depend on having
a functioning timepiece.

-FER


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