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    Re: Lindy Line
    From: George Huxtable
    Date: 2002 Dec 6, 21:53 +0000

    Walter Guinon said-
    
    >George H has the right idea, Bowditch gives his approach as an approximation to
    >the shortest distance. Howerver the shortest path, subject to a maximum
    >Latitude, is given by a GC thru the departure point that is tangent to the
    >limiting parallel, then along the parallel to another GC thru the destination
    >point and which is also tangent to the limiting parallel.
    >
    >When this approach is studied on a gnomic chart the extension to arbitraty
    >curves which exclude certain areas (e.g. land) seems clear.
    >
    
    Response from George Huxtable.
    
    Yes, Walter is quite right. I have done a bit more pondering and now accept
    that my approach, even when using a globe-and-string, was still
    over-simplistic.
    
    In my first contribution on this topic I posed this question- "Similarly,
    when reaching X why not then turn through an angle onto a new great circle
    between X and Yokohama?"
    
    With hindsight, that could never provide a solution to the shortest-path
    problem. It can never involve a sudden turn through an angle on to a new
    course, because if one's path involves such a change of course, one can
    always shorten it a bit further by cutting across, or smoothly rounding,
    the angle. So it's intuitively obvious that the shortest ship's-path must
    be a smooth curve with no corners, a condition that's met by choosing an
    initial great circle (and a final one) that merges smoothly at a tangent
    into the constant-latitude leg of the course. Just as Walter (and Bill
    Noyce too) have suggested.
    
    In my second mailing, I said-
    
    "I had indeed missed something, by ignoring the possibility that under some
    (but by no means all) circumstances the great-circle path between X and the
    end-points could take the vessel nearer the pole than X is. Thanks to the
    others for pointing it out."
    
    I suspect that statement too may be inaccurate. Perhaps instead of "under
    some (but by no means all) circumstances", I should have said "in all
    circumstances". I'm still pondering about that.
    
    The problem is certainly a bit knottier than I first thought. My thanks to
    the other contributors who have understood it better.
    
    We all seem to agree (including Dan) that the procedure quoted by Dan Allen
    from a website is certainly NOT the best way to do the job.
    
    In my 1981 edition of Bowditch vol2, the relevant formulae are listed in
    art. 1016, "Great-circle sailing by computation, on page 604.
    
    George Huxtable.
    
    
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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