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    GreatCircle Calculations - precision
    From: Rino
    Date: 2002 Sep 30, 20:57 -0400

    This is my first post on this list.  I happened upon it when I did a search
    for 'haversines' (an alien concept to me).  I thought some of the posts were
    very insightful and entertaining, and I hope I can get an answer to some of
    my questions:
    
    Last weekend I decided to convert an old navigation spreadsheet application
    I had built in my seafaring days to a VB.NET solution.
    It basically became a full rewrite; first because the spreadsheet used old
    Excel macro's and not VBA, and second because I hadn't given a thought to
    spherical triangles, Mr. Neper's rules and various other laws, in over ten
    years.
    
    In rewriting the whole thing in .NET, I used 'double' (64-bit floating
    point) precision data type for all variables (Latitude, Longitude, course,
    etc).  I did this because I use the value PI, which is an .NET constant of
    type 'Double', and I wanted to preserve that precision in my calculations.
    
    When testing my code, I found that my results varied slightly from the
    answers given in one of my old textbooks, from results returned by my old
    casio programmable calculator, and also from my spreadsheet.  I am 99%
    certain that my code is accurate, I checked all intermediate results, and
    they all checked out.
    
    So, my question to those of you with a better grasp of math (and programming
    perhaps), is:  why do I see these differences? Is the textbook correct, or
    my code?  The differences are negligible in outcomes for course and
    distance, but they have a more significant impact on the Vertex (probably
    because the slight difference in course propagated through the formulas for
    the vertex).
    
    I will include an example here:
    
    Lat1: 34 40.0N  Lon1:139 55.0E
    Lat2: 37 45.0N  Lon2:122 50.0W
    
    GreatCircle distance:
    TextBook:       4473.8
    VB.NET: 4473.8
    
    GreatCircle course:
    TextBook:       54.5
    VB.NET  54.3
    
    Vertex:
    TextBook:       47 59.4N        168 36.8W
    VB.NEt: 48 06.0N        168 26.2W
    
    I would appreciate any insights from the 'brains' on this list.
    
    Thanks.
    
    Rino
    
    
    

       
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