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    Re: watch as compass
    From: Frank Reed CT
    Date: 2007 Jul 30, 17:40 -0700

    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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