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Jim, you wrote:
"You don't even need the local time - just a stick and a piece of
level ground. Poke a stick in the ground and mark where the end of its
shadow falls.  Wait.  The shadow will move directly east. "

Yes. For a good portion of the day in most latitudes, the shadow moves
nearly due east, just as you say. But bear in mind that the path of
the shadow is not normally a straight line. Most of the time, in most
latitudes, if you trace the shadow path all through the day, it's a
hyperbola. The shadow starts out at dawn running towards the azimuth
where the Sun is rising (that's one asymptote of the hyperbola). Then
it curves about and, right at noon, the shadow is heading due east
exactly. During the afternoon, the shadow turns slowly until, in the
late afternoon, it is running rapidly away from the azimuth where the
Sun is setting (the other asymptote of the hyperbola). The shadow's
path along the ground is curved. But I should emphasize here that the
deviation of the shadow path from straight "due east" is not large
except close to sunrise and sunset and close to the solstices in
higher latitudes.

Under the assumption that the Earth is flat (definitely close enough
for this issue) and under the assumption that the Sun's declination
doesn't change (also definitely close enough), the path drawn on the
ground tracing out the end of the shadow of any fixed object during
the day is a conic section, usually a hyperbola. When the Sun's
declination is reasonably close to zero (even 10 degrees away is not
bad), that hyperbola will be close to a straight line running east-
west. If it's an equinox, then it's exactly a straight line. So, most
of the time, this rule works just fine. But there are important
exceptions... If the observer is in a latitude where the Sun does not
set, the path of the shadow tip is still a conic section. Instead of
being a hyperbola, it is an ellipse. In short, do not use this trick
in high latitudes. One interesting special case: if you're in the
Arctic (northern latitudes, that is) and the Sun just barely sets on
the northern horizon, then the path traced out on the ground by the
shadow is a parabola. This is an exceptional case. For most latitudes
and times of the year, the path of the shadow is a gently curved
hyperbola, and for most hours of the day, the path is nearly straight
due east.

I would add that you can use a "spot" of sunlight just as well as a
shadow to determine compass direction. If you're sitting under a tree
and you see a nice circular spot of sunlight on the ground beneath the
canopy of foliage (actually a projected image of the Sun), then it
will work just as well as a shadow. As long as the air is calm, so the
spot isn't bouncing around with the wind, it functions just the same
as the shadow cast by some fixed object. Its path, just like the
shadow, will be a hyperbola, and during most of the day in most
latitudes, it will move very nearly due EAST. The error will rarely
exceed 20 degrees.

And you wrote:
"Of course, checking your directions this way very often will slow
your
progress."

Yep. That's the principal disadvantage of this method and its cousins.
You have to sit down and observe for at least fifteen minutes. Anyone
have a quicker method? Something you can do in fifteen seconds instead
of fifteen minutes? I've been working on a few...

-FER


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