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Subject: Precise great-circle calculation
From: George Huxtable (george@XXX.XXX)
Date: Mon Nov 19 2001 - 02:41:39 EST
I have renamed this thread from "Haversine formulae for Great Circles" to
"Precise great-circle calculation", to avoid the dreaded word Haversine. I
hope nobody objects.
Chuck Taylor asks-
>> Even with this high
>> accuracy, distances of 0.1 nautical miles have started to go a bit
>> inaccurate, and distances which should be .01 miles are calculated as zero.
>> With a computer using single-precision, things would be a lot worse. So the
>> problem Lu has raised is a real one, in these special circumstances of
>> close approach.
>
>
>Why would one be interested in great circle routes for such short distances?
>Mercator Sailing or Mid-Latitude Sailing would seem much more applicable for
>distances under, say, 60 nautical miles.
>
>Chuck Taylor
>Everett, WA, USA
=========================
My reply-
Over such short distances. it becomes a plane-sailing problem, where you
can ignore any shortening of the length of a degree of longitude along the
short path between the point of departure and the destination..
If you were devising software for the internal workings of a GPS receiver
(the example that Lu suggested) then you would want to use an expression
for distance that worked in all cases. It would be inconvenient if you had
to make a test first to decide which formula was going to be applicable.
Much better is a one-size-fits-all expression that provides a seamless
answer, wherever it is used. And it's not clear to me how such a test could
me simply made, to cope with every possible circumstance.
As an example, imagine yourself as a polar explorer, approaching one of the
poles. Doubtless, you would nowadays use GPS rather than a theodolite, to
establish whether you had got there. You would not be pleased if the
internal software of your receiver was insufficiently robust to cope with
that special situation (something that the maker of the equipment might
find it hard to test in advance).
It's simpler for everyone if a formula can be devised and accepted that can
be used in all circumstances, everywhere. In these days of computers and
calculators, it matters little that the formula is more complex. The
computer can cope. For those that have to (or choose to) do their
calculations longhand, the priorities are entirely different.
George.
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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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