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    Fix by equal altitude sights around local apparent noon
    From: Mal Misuraca
    Date: 1997 Nov 13, 11:02 AM

      The objections to the use of equal altitudes of the sun around local
    apparent noon are simple mischief, and they miss the most essential point
    about celestial navigation in the age of GPS.  Most yacht sailors now resist
    learning celestial at any level, because they consider that a GPS and backup
    is more than they will ever need---and the backup can be purchased cheaply and
    at less cost that a sextant and related materials and equipment.
      The point is, therefore, that for all those who are fully invested in their
    own mastery of sights not on the meridian, and who therefore deplore the local
    apparent noon methods, and who use all sorts of claims and disclaimers to
    discourage others from doing so, a terrible disservice is being done to the
    effort to teach enough celestial to make yacht sailors safe even if their GPS
    and backups fail.
      The difference between teaching equal altitudes around local noon and the
    use of sight reduction tables is a very significant difference.  In my class,
    over four years now, I have taught both and found that the resistence to
    learning how to reduce sights not on the meridian is increasing.  No one will
    buy sight reduction tables anymore, and my friend at Armchair Sailor says it
    is all he can do to persuade people about to sail into the Pacific to buy an
      For those who claim that if the equal altitudes method were valid there
    would be references to it in respected elements of the literature, I would
    simply say that you have not looked into the literature before giving out an
    opinion.  Hewitt Schlereth in his book on navigation by the noon sight
    explains the equal altitude method and corrections for movement of the vessel
    for those who want to reduce the small error induced by the difference in
    position of the boat between sights before and after noon.  And Volume 3,
    pages 157-160 of The Admiralty Manual of Navigation (1954) explains the equal
    altitudes method and gives a correction table to account for change in
    position of the ship between pre- and post-LAN sights.
      The principle of the equal altitudes method could not be simpler.  By
    definition, the sun increases in altitude before local apparent noon at the
    same rate as it declines in altitude after noon.  Local Apparent Noon is by
    definition the moment when the sun reaches its highest altitude at your
    position and is therefore on the meridian (either due south or north of your
    position).  Everyone knows that the noon sight was used to determine latitude,
    but the use of sights before and after noon is even more useful.
      If you take a sight at exactly 50 degrees sextant altitude before noon and
    later, as soon as you know that noon has been reached by the fact that the
    altitude of the sun does not increase, reset your sextant to 50 degrees, you
    then wait for the sun to descend in the sextant until it is tangent to the
    horizon and note the time.  Exactly mid-way between the 50 degree sight before
    noon and the 50 degree sight after noon, as determined by the time of each
    sight, is local apparent noon.  A brief look in the almanac for the Greenwich
    Hour Angle of the sun at that moment yields longitude, and the time of local
    noon is a good check on your latitude sight as well.
      By taking several such pairs of sights, a series of estimates of local noon
    is made and the average of them yields an even more comforting check on the
    time of local noon.  If, as someone said in a recent comment, the sun is being
    obscured by clouds during the run-up to noon, start earlier and take as many
    sights as possible.  (The same clouds that are conjured up by the nay-sayers
    to get in the way of doing this are ostensibly clouding their sights for lines
    of position, and once again they are doing a disservice to this simple and
    precise procedure.)  This increases the odds of one or more pairs of sights,
    even if the sun is being obscured after local noon, as before.  This procedure
    can be used for sights taken relatively early in the  morning, well before
    noon, if necessary, so long as they are matched by equal altitude sights after
      No one claims this method had advantages over the use of sight reduction
    tables, because the methods are complimentary, not competitive.  What makes
    the objections to the LAN method tedious and sometimes misleading is the
    uninformed claim that the equal altitudes method does not appear in the
    literature and must therefore be voodoo.  It is the objections that are in
    deep voodoo, not this method that has saved, and will do so again, the
    relatively inexperienced and untutored navigator who has dropped a GPS
    overboard and is trying to cope with anxiety and forgotten instruction to find
    a way home.
      For those, finally, who say this method has been tried and does not work,
    remember that a large part of the success of any endeavor is attitude.  If you
    don't want to use equal altitudes, because your private view of the world
    might be threatened, by all means navigate as you please.  But stop trying to
    discourage those whose hold on the theory, math, or practice of sight
    reduction methods may be tenuous from saving themselves or making their
    passage more comfortable by knowing this simple and effective way to sail to
    any point on any ocean.
      I repeat my offer to xerox the Admiralty Manual pages on this method, or
    Schlereth, for that matter, for anyone who will send me an email with that
    request.  Surprisingly, or maybe not so surprisingly, those who on these pages
    have written that there is no scientific or academic support for the equal
    altitude method don't seem to want the pages from the Admiralty Manual to
    contend with.  For shame.
                                           Mal Misuraca
                                           "Celestial in a Day"
                                           San Francisco
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