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    Re: Why are NA sight reduction tables not popular?
    From: Gary LaPook
    Date: 2012 Apr 8, 15:50 -0700
    Now that I have looked at those pages in my N.A. I am again left scratching my head as to how somebody can come up with unnecessarily complicated ways to express simple things.

    The N.A.  implementation of he law of cosines formula is:
    S= sin Dec
    C = cos Dec cos LHA
    Hc = arc sin (S sin Lat + C cos Lat)

    What's wrong with the way we all learned it:

    sin Hc = (sin Lat sin Dec + cos Lat cos Dec cos LHA)

    And the N.A. azimuth formula implementation:

    X = (S cos Lat - C sin Lat)/cos Hc
    If  X > +1 set X = +1
    If X < -1  set X = -1
    A = arc cos X

    Which is the equivalent of :

    cos A = (sin Dec cos Lat - cos Lat cos LHA)/cos Hc

    instead the standard:

    sin A = sec Hc cos Dec sin LHA

    Where do they find those people at the N.A. office?


    --- On Sun, 4/8/12, slk1000@aol.com <slk1000@aol.com> wrote:

    From: slk1000@aol.com <slk1000@aol.com>
    Subject: [NavList] Re: Why are NA sight reduction tables not popular?
    To: NavList@fer3.com
    Cc: SLK1000@aol.com
    Date: Sunday, April 8, 2012, 7:35 AM

    I personally like the Nautical Almanac Concise method, but I have heard it is unpopular because it requires "three page openings". I don't find the pages all that heavy :-).  I guess what is really being said is that it is more subject to error because of the number of page openings.  I don't see it myself.

    The Law of Cosines is being taught in the Power Squadron Junior Navigation course, with the Nautical Almanac Concise method being added in the Navigation course

    You really can't compare the Law of Cosines "calculator" method, regardless of which formulae are used, with a tabular method like the Nautical Almanac Concise method.  Let's face it, if you don't have a calculator or a computer, the Nautical Almanac Concise method has the advantage over other tabular methods in that everything you need, no matter where you are located, is already included in the book you must have anyway, the Nautical Almanac.  Sure, it only gives 1 nm resolution, but I think its advantages outweigh its disadvantages.

    As to why the Power Squadrons does not use the NA version of the Law of Cosines formulae, that I do not know.


    -----Original Message-----
    From: Geoffrey Kolbe <geoffreykolbe@compuserve.com>
    To: NavList <NavList@fer3.com>
    Sent: Sun, Apr 8, 2012 3:44 am
    Subject: [NavList] Why are NA sight reduction tables not popular?

    Frank said that he didn't know anyone who liked them (or words to that effect).
    Given that the NA tables  system is taught in Power Squadron 
    navigation classes, I would have thought that the biggest hurdle of 
    any system - becoming familiar with the method - would have been 
    overcome and made this method popular.
    The NA sight reduction system has the advantage of being angles all 
    the way, so you are not changing in and out of logs, and once you get 
    the hang of it, this method seems to be as quick as any.
    Any thoughts on why it is not popular?
    Lu Abel says that the "Law of Cosines" is what is being taught to the 
    Power Squadron these days as the principal method of sight reduction. 
    I went and had a look at the Power Squadron website and sure enough, 
    in the 'Nautical Tools' section, there is a handy little online sight 
    reduction program, showing the formulae used - and presumably taught 
    in Power Squadron classes.
    Now, there may be good reasons why the NA sight reduction tables are 
    not popular, but as was pointed out some years ago by Herbert Prinz, 
    the formulae given in the NA for sight reduction using a calculator 
    are the best formulae available for a number of reasons and I am 
    surprised that the Power Squadron do not teach those instead. The 
    formulae for Hc is the same, but the Power Squadron formula for Zn 
    blows up in polar regions, whereas the NA version does not.
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