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    Re: Principles and Being Practical
    From: Vic Fraenckel
    Date: 2003 Sep 7, 06:29 -0400

    I didn't realize how many azimuth ambiguities could dance on the head of a
    pin!
    
    Enough already, this horse has long since been flogged to death.
    (and flayed into hambuger)
    
    Vic
    ________________________________________________________
    
    Victor Fraenckel - The Windman                 vfraenc1{at}nycap.rr.com
    KC2GUI                                                      www.windsway.com
    
          Home of the WindReader Electronic Theodolite
                                   Read the WIND
    
    "Victory at all costs, victory in spite of all terror, victory however long
    and hard the road may be; for without victory there is no survival."
    - Winston [Leonard Spencer] Churchill (1874 - 1965)
    
    Dost thou not know, my son, with how little wisdom the world is governed?
    -Count Oxenstierna (ca 1620) to the young King Gustavus Adolphus
    
    ----- Original Message -----
    From: "Peter Fogg" 
    To: 
    Sent: Sunday, September 07, 2003 5:32 AM
    Subject: Re: Principles and Being Practical
    
    
    | ----- Original Message -----
    | From: "George Huxtable"
    |
    | > >However, I ask Peter if he has checked out the two examples that I
    | > >provided, and compared the azimuth result from Bennett's table with
    that
    | > >given by his nav. calculator, and if not, to do so, please. And I ask
    him
    | > >to REPORT HIS RESULTS BACK TO US. If he finds a discrepancy between the
    | > >Bennett azimuth and his own calculator (which he will), I hope he will
    | then
    | > >tell us where he thinks the fault lies.
    | > >
    | > >Example 1. dec = 55deg 29', LHA = 54deg 31', alt = 61deg 31'.
    | > >
    | > >Example 2. dec = 55deg 31', LHA = 54deg 29', alt = 61deg 29' .
    | > >
    | > >I chose those examples to show up where the faults in the method are
    near
    | > >their worst, but have no reason to think that they are in any way
    unique.
    |
    | Well of course they are unique, they have been carefully chosen to show
    the
    | same worst case scenario. Look at how the 2 examples are almost identical,
    | and in each case the minutes are the hardest to round up or down to the
    | nearest whole degree. They fall, no surprise, in the very circumstance of
    | body near the prime vertical (the east/west line of the observer) that
    leads
    | to an ambiguity in the result.
    |
    |  In the book ("The Complete On-Board Celestial Navigator" by George G
    | Bennett, 2003-2007 edition, if anyone has just tuned in)
    | the user is shown how to resolve this rarely occuring ambiguity, and there
    | are 2 methods shown. For both the latitude of the observer is required.
    |
    | So what is the latitude of this (essentially the same) Huxtable example?
    | Without it the ambiguity cannot be resolved. The first method is simpler
    | (notice a pattern here?), the resulting azimuth to adopt then becomes
    | obvious. In even more remote circumstances 'the declination has the same
    | name as the latitude but is numerically smaller' there is another process
    to
    | be followed. I can't take this example along these routes without the
    | latitude. Now I have to wonder whether George Huxtable ever got this far?
    |
    | 'and compared the azimuth result from Bennett's table with that
    | > >given by his nav. calculator'
    |
    | Same problem of incomplete data. The nav. calculator, silly machine, is
    | designed to be used in the real world. I would need the DR, time and date,
    | sextant altitude, body, etc for it to do its magic.
    |
    | But how often will a navigator run into this particular set of dec, LHA
    and
    | alt? And when he does the Weir diagrams are available, as is his compass,
    as
    | is his common sense, hopefully.
    |
    | There has been no effort made to cover up this potential problem in the
    | book; indeed it is discussed and, once again, the methods to resolve it
    are
    | explained - with examples! Adding an additional warning note to the latest
    | edition is like MacDonalds adding a warning to their cups of coffee
    advising
    | you might burn your lips on the hot coffee.
    |
    | There is, perhaps, nothing new under the sun. These azimuth tables are a
    | clever adaptation of an old navigator's tool, known as the Rust Diagram,
    | which used a visual or graphic method for a similar result. Those old-time
    | navigators liked the simplicity of the method and were prepared to trade
    off
    | the simplicity against greater accuracy against the ambiguity occuring
    | around the prime vertical.
    |
    | Those of you with access to Bowditch (potentially all as it is available
    | online) can research it there, and also possibly elsewhere.
    
    
    

       
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