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    Re: Hav-Doniol Lat/Dec subtractions
    From: Stan K
    Date: 2016 Oct 18, 09:57 -0400
    Michael,

    Agreed, this could be confusing for someone not familiar with haversines.  Perhaps the best way to handle this is to add a line in the instructions to ignore the sign when entering the table if Lat-Dec comes out negative.  Another way might be to use absolute value bars in the formulas, |Lat-Dec|, or Abs(Lat-Dec), but either of these would assume that the user knows what an absolute value is and what the bars or the Abs means.  Using the tilde, Lat~Dec, would also require a verbal explanation.  

    I never did discuss hav-Doniol in class.  Too much time was already devoted to the two methods USPS currently requires to be taught - the Law of Cosines using a basic scientific calculator, and the Nautical Almanac Concise method.  Sadly, much of the teaching of the Law of Cosines involves teaching the students how to use their calculators.

    As I said in a subsequent message, there were not enough responses to my original request about whether L and d should be treated as signed or unsigned to make a statistically sound decision.  Maybe it depends on whether you are trying to do it as it might have been done before calculators, in which case the unsigned values, with the "rules", might be best; or, if using a calculator, where negative values can be entered, the signed values might be best.  Or maybe not... 

    Stan


    -----Original Message-----
    From: Michael Bradley <NoReply_Bradley@fer3.com>
    To: slk1000 <slk1000---.com>
    Sent: Mon, Oct 17, 2016 7:10 pm
    Subject: [NavList] Re: Hav-Doniol Lat/Dec subtractions

    Hi Stan K
    Re your 2015 postings discussing the subtractions of Dec and Lat. 
    I came upon another possible minor tweak to the Hav Doniol formulas tonight, reducing a sight of gamma Cassiopiea ( Declination roughly 61 North ) from the local beach (at Latitude roughly 55 North). Lat-Dec comes out negative. 
    IMHO the subtractions would be better expressed as differences, e.g. Dec ~ Lat or Lat ~ Dec. All those worked examples of sun sights undertaken from north of the sun in the northern hemisphere in summer are obviously not a complete set of possible position finding problems. A first time user coming across a negative answer to one of the 'normal' subtractions would not know what to do, unless he or she knew that hav(A-B) = hav(B-A), or expressed as in the Doniol formulas Hav(-n) = Hav(n) and Hav(-p) = Hav(p). The difference form of the formulas might give an additional clue about what to do.... or might not. 
    How did the use of Doniol in class go? I don't recall any reports, but I do go off message for great lumps of time.
    Michael Bradley
     
       
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