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Well. Crap. Although this piece was entertaining, educational, and thought
provoking, it will have everyone on this listed specifying "shortest"
rhumb-line where just rhumb-line used to do :-}

On Thu, 10 Oct 2002 20:31:54 +0100 George Huxtable 
wrote:

> 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@huxtable.u-net.com
> George Huxtable, 1 Sandy Lane, Southmoor,
> Abingdon, Oxon OX13 5HX, UK.
> Tel. 01865 820222 or (int.) +44 1865 820222.
> ------------------------------
>



Dave Weilacher
.US Coast Guard licensed captain
.    #889968
.ASA certified sailing and celestial
.    navigation instructor #990800
.IBM AS400 RPG contract programmer

   

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