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Precise great-circle calculation
From: George Huxtable
Date: 2001 Nov 19, 12:42 AM
From: George Huxtable
Date: 2001 Nov 19, 12:42 AM
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. ------------------------------ george@huxtable.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------