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    FW: Latitude and Longitude by "Noon Sun"
    From: Peter Fogg
    Date: 2005 Jun 5, 13:06 +1000

    At first glance this looks like an excellent post here by Frank:
    seems simple, practical and eminently doable.
    As he has added in a follow up posting:
    " lat/lon by noon sun is something that can be learned and re-learned in an
    afternoon. It's not quite as accurate (does that matter? depends on what
    you're trying to achieve) as full-blown celestial navigation, but fewer and
    fewer students are interested in toiling over the details of the Nautical
    Almanac's interpolation tables and the tedious study of H.O. 229 or other
    sight reduction tables. They wanna play with their sextants and figure out
    where they are in the fewest possible steps (just in case something bad
    happens to GPS)."
    From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]
    On Behalf Of Frank Reed
    Sent: Sunday, 5 June 2005 9:54 AM
    Subject: Latitude and Longitude by "Noon Sun"
    First things first: I've put the phrase "Noon Sun" in quotes here because
    the set of sights required for this system goes a little beyond the standard
    procedure for shooting the Noon Sun for latitude only.
    This short method of celestial navigation will get you latitude and
    longitude to about +/-2 miles and +/-5 miles respectively --more than
    adequate for any conceivable modern practical purpose. You can cross oceans
    safely and reliably for years on end using this technique if it suits you to
    do so. Its enormous advantage is simplicity. It's easy to teach, easy to
    demonstrate, easy to learn, and also easy to re-learn if necessary. I
    mention this because most people who are learning celestial navigation today
    will quickly forget it. What's the point of learning something if you can't
    reconstruct your knowledge of it quickly when and if the need actually
    arises to use it? It's tough to resurrect an understanding of the tools of
    standard celestial navigation on short notice, but easy with this lat/lon at
    noon method. Additionally, this method does not require learning all the
    details of using a Nautical Almanac (you don't need one at all --only a
    short table of declination and equation of time, possibly graphed as an
    "analemma") and it needs no cumbersome sight reduction tables.
    Here's how it's done:
    Start 20 or 30 minutes before estimated local noon. Shoot the Sun's altitude
    with your sextant every five or ten minutes (or more often if you're so
    inclined) and record the altitudes and times by your watch (true GMT).
    Continue shooting until 20 or 30 minutes after local noon. [note the
    difference from a noon latitude sight --we're recording sights leading up to
    and following noon-- usually these are thrown away]
    Next you need to correct for your speed towards or away from the Sun. For
    example, if we're sailing south and the Sun is to the south of us, then each
    altitude that we have measured will be a little higher as we get closer to
    the latitude where the Sun is straight up. We need to 'back out' this effect
    so that the data can be used to get a fix at a specific point and time. This
    isn't hard. First, we need the fraction of our speed that is in the
    north-south direction. If I'm sailing SW at 10 knots, then the portion
    southbound (in the Sun's direction) is about 7.1 knots. You can get this
    fraction by simple plotting or an easy calculation. Next we need the Sun's
    speed. The position where the Sun is straight overhead is moving north in
    spring, stops around June 21, then heads south in fall, bottoming out around
    December 21 (season names are northern hemisphere biased here). It is
    sufficient for the purposes of this method to say that the Sun's speed is 1
    knot northbound in late winter through mid spring, 1 knot southbound from
    late summer through mid autumn, and 0 for a month or two around both
    solstices (it's easy to prepare a monthly table if you want a little more
    accuracy). Add these speeds up to find out how much you're moving towards or
    away from the Sun. If you're moving towards the Sun, then for every six
    minutes away from noon, add 0.1 minutes of arc for every knot of speed to
    the altitudes before noon and subtract 0.1 minutes of arc for every knot of
    speed to the altitudes after noon. Reverse the rules if you're moving away
    from the Sun. Spelled out verbally like this, this speed correction can
    sound tedious but the concept is really very simple and it's very easy to
    do. [Incidentally, George Huxtable deserves credit for emphasizing the
    importance of dealing with this issue (although I don't think he ever
    spelled out how to do it)]
    Now graph the altitudes (use proper graph paper here if at all possible):
    Sun's altitude on the y-axis versus GMT on the x-axis. The size of the graph
    should be roughly square, maybe 6 inches by 6 inches so that you can clearly
    see the rise and fall of altitude. For longitude, you will need to determine
    the axis of symmetry of the parabolic arch of points that you've plotted.
    There is a simple way to do this: make an eyeball estimate of the center and
    lightly fold the graph paper in half along this vertical (don't "hard
    crease" the fold yet). Now hold it up to the light. You can see the data
    points preceding noon superimposed over the data points following noon which
    are visible through the paper. Slide the paper back and forth until all of
    the points, before and after, make the best possible smooth arch (half a
    parabola). Now crease the paper. Unfold and the crease line will mark the
    center of symmetry of the measured points with considerable accuracy.
    Reading down along this crease to the x-axis, you can now read off the GMT
    of Local Apparent Noon. Reading back up the crease to the data, you can pick
    off the Sun's maximum noon altitude (which is probably already recorded but
    if you missed the exact moment of LAN you can get it this way).
    Next we need two pieces of almanac data: the Sun's declination for this
    approximate GMT on this date and the Equation of Time for the same date and
    time. You do NOT need a current Nautical Almanac for this. The exact value
    of declination and Equation of Time varies in a four-year cycle depending on
    whether this year is a leap year or the first, second, or third year after.
    So we don't need an almanac for this. A simple table will do (where to get
    one? Today, they're very easy to generate on-the-fly... or you could use an
    old Nautical Almanac... or you could also use an analemma drawn on a
    sufficiently large scale).
    Apply the Equation of Time to the GMT of Local Apparent Noon that you found
    above. You now have the Local Mean Time at LAN, and you already know the
    Greenwich Mean Time. The difference between those two times is your
    longitude. Convert this to degrees at the rate of 1 degree of longitude for
    every four minutes of time difference. Done. We've got our longitude.
    Now for latitude. Notice that we didn't correct any of our altitudes for
    index correction or dip or refraction or the Sun's semi-diameter. These
    corrections are totally unnecessary for the longitude determination. But we
    need them for latitude. Take the Sun's altitude at the time of LAN (read off
    the "crease" or actually observed by watching the Sun "hang" at the moment
    of LAN). Correct it for index correction, dip, refraction and semi-diameter
    as usual. This gives you the Sun's corrected observed altitude. Subtract
    from 90 degrees. This "noon zenith distance" tells us how many degrees and
    minutes we are away from the latitude where the Sun is straight up. The
    latitude where the Sun is straight is, by definition, the "declination" that
    we have looked up previously from our tables. So if the Sun is north of us
    at noon, then we are south of the Sun's declination (latitude) by exactly
    the number of degrees and minutes in the noon zenith distance. If the Sun is
    south of us at noon, then we are north of the Sun's declination by the same
    amount. A simple addition or subtraction yields the required latitude. Done.
    We've spent about ten minutes making and recording observations of the Sun's
    altitude over the course of 45 minutes to an hour, and reduced those
    observations to get our latitude and longitude at noon with about five
    minutes of paperwork. Not bad!
    Again, the overwhelming advantage of this "short celestial" is that it can
    be taught easily, learned quickly, and RE-learned quickly on the spot if
    necessary. An additional advantage is that it requires an absolute minimum
    of materials. You need a sextant (metal if at all possible, but plastic will
    do), a decent, cheap watch or small clock, tables of refraction and dip (one
    sheet of paper), a four-year revolving almanac of the Sun's declination and
    equation of time (another sheet or two of paper), and some graph paper and a
    pencil. You could even print out these (or equivalent) instructions and
    throw everything in the case with your sextant.
    As for disadvantages, they really depend on the student and his or her
    expectations. What is it that we want to do with celestial navigation? Why
    study any method? And for a thousand students, you will get a thousand
    answers. The days are gone when celestial navigation was essential and fixed
    curricula could be dictated for students to either take in their entirety or
    leave. This field has moved on to the stage of "a la carte" learning. It can
    be a pain in the neck for instructors accustomed to doing things the same
    way year after year but it's a real liberation for students and possibly
    also for more creative teachers and "information publishers".
    42.0N 87.7W, or 41.4N 72.1W.

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