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    Re: watch as compass
    From: Gary LaPook
    Date: 2007 Jul 30, 22:19 -0700

    Gary writes:
    Looks like you have just reinvernted the diptych.
    Diptych sundial
    Portable diptych sundial
    Portable diptych sundial
    One popular portable sundial design was called a diptych. It consisted
    of two small flat faces, joined by a hinge. Diptychs usually folded
    into little flat boxes suitable for a pocket. The gnomon was a string
    between the two faces. When the string was tight, the two faces formed
    both a vertical and horizontal sundial. The best material was white
    ivory, inlaid with black lacquer markings. The best gnomons were black
    braided silk, linen or hemp.
    With a knot or bead on the string as a nodus, and the correct
    markings, a diptych can keep a calendar well-enough to plant crops.
    By making the two sundials have different angles to the string (and
    thus different projections), a diptych can be self-aligning. When both
    faces show the same time, and the hinge is level, the diptych shows
    the local apparent solar time. Additionally, the hinge will point
    north (in the northern hemisphere), and the diptych will be angled so
    the gnomon is parallel to the Earth's axis of rotation. At solar noon,
    sunrise and sunset, the latitude adjustment of the diptych can't
    affect the time of either sundial, but at 9am and 3pm, each degree of
    latitude error (from holding the sundial at the wrong angle) creates
    four minutes of difference between the two faces.
    This means that a diptych can also act as a compass and even measure
    latitude. Some diptychs included a small scale and a plumb-bob to read
    the latitude. Some others included a compass rose to measure angles to
    geographic features. Large (meter-sized) diptychs may have been used
    for navigation in ancient times.
    On Jul 30, 5:40 pm, Frank Reed  wrote:
    > 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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