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    The pedant's rhumb-line.
    From: George Huxtable
    Date: 2002 Oct 10, 20:31 +0100

    Every now and again, rhumb-lines appear as a topic on this list.
    
    Most list-members are aware that wherever you start from on the Earth, with
    whatever course, if you keep following a rhumb line (constant course), you
    will end up spiralling into one or other of the poles. You will have made a
    number (perhaps an infinite number?) of turns, in longitude, to get there,
    but will have travelled (in general) a finite distance.
    
    Navigators frequently ask for the rhumb-line course from A to B. Here I
    wish to display my pedantry by insisting that there is not just one
    rhumb-line course between A and B, but many (perhaps an infinite number?).
    The one required by the navigator is the SHORTEST rhumb-line course.
    
    This can be illustrated by a simple example. Take a navigator on the
    equator at position A, long = 0 degrees. What is his rhumb-line course and
    distance to a destination B, lat 10 deg North, long 0 deg.? The obvious
    answer is a course of zero degrees, which happens to be identical with the
    great-circle in this case. But what if he sets off from A with a course of
    about 88.4 degrees, that is, slightly North of due East, and holds that
    course? Well, that's a rhumb line, also, which will also take him to B (or
    it would if no continents got in the way), but he has to go Eastwards,
    right round the world, to get there. Similarly, a course of about 271.6
    degrees will also take him round the world to B, but Westwards.
    
    He could set off with a course even closer to due East, roughly 89.2
    degrees, and if he sticks to that while making two whole circuits of the
    Earth it will take him to B. Again, there's another corresponding rhum line
    Westwards. Other courses, progessively closer still to due East or West,
    would take him to B after 3, 4, or more circuits of the Earth, right up to
    infinity.
    
    What's the practical importance of this? None whatsoever. I am just
    pointing out that these alternative, but quite impractical ways of getting
    from A to B are all genuine rhumb lines between A and B, and each fully
    meets the definition of a rhumb line. There is no unique rhumb line. The
    only rhumb line that's of any practical significance, however, is the
    shortest rhumb line.
    
    Just something to ponder over on a quiet watch.
    
    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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