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    Re: Tables vs. Calculators
    From: Dan Allen
    Date: 2002 Sep 20, 14:51 -0700

    On Friday, September 20, 2002, at 11:32 AM, Chuck Taylor wrote:
    > I could even reproduce the sines and cosines if I wanted to trouble
    > myself with going through a Taylor series expansion.
    You're lucky: you've got a series expansion named after yourself,
    but the rest of us (except for Maclaurins) are just out of luck... ;-)
    Seriously, I totally agree with Chuck.  I can and do have the basic
    formula for great circle nav and sight reduction memorized because it
    is so simple:
       cos(a)*cos(b) + sin(a)*sin(b)*cos(ab) = cos(c)
    Many of our nav problems boil down to using this simple formula.
    For example, for great circle problems with arguments in degrees
       IF a = 90 - lat1
        & b = 90 - Lat2
        & ab = Lon2 - Lon1
          c = GC Distance in degrees, or multiply it by 60 for nautical miles
    or for sight reduction with arguments in degrees
       IF a = 90 - estimated latitude
        & b = 90 - declination
        & ab = LHA = GHA - estimated longitude
          90 - c = altitude
    This formula is easy to program into calculators, or easy to write
    down on a piece of paper and do by hand with a basic scientific
    calculator.  This is the essence of self-reliant navigation.

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