NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: How good is St. Hilaire?
From: George Huxtable
Date: 2010 Feb 28, 20:22 -0000
From: George Huxtable
Date: 2010 Feb 28, 20:22 -0000
Richard Reed wrote, about my test-to-destruction of the least-squares algorithm in the almanac, by starting it off from, not the DR position, but from its antipode- "Thanks George and Peter for the education. My little plane geometry demonstration didn't use real sights or spherical triangles, and I didn't suspect a navigation triangle that stretched halfway around the world would still work! I had a look at a sun sight from a book and soon saw that George's trial, as I understand it, couldn't be done in Pub. 249 tables using that sight because large negative calculated altitudes are not listed, so I guess this would be done using a calculator, which I'll work on out of curiosity. If this comes out as I expect, the first intercept will place the LOP nearly as far back as DR was displaced, 180 degrees." Well, it's not really a practical task for doing by calculator, in my view. First few iterations would, at a guess, produce immense cocked-hats, from which you would have to estimate, each time, a best new starting-position for the next iteration. And Richard is right, the first few iterations would involve large negative altitudes, which tables are not designed to cope with. Though you can get round these things, often, by working out the altitude of an antipode of the point you really wanted, and subtracting it from 180º. Or something like that. Such tricks exist. But it would be an awful lot of slog. What I've wondered is this: say you offered the least-squares algorithm a collection of six assorted position lines, three clustered round a cocked-hat in one part of the World, the inconsistent contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.others around another cocked-hat in an entirely different area. Would it home in on one or the other, or would it choose to produce a solution that was somewhere in no-man's land, between the cocked hats, with an immense error-ellipse? My guess is, the latter. By the way, included with the AstroNavPC booklet, from the UK Nautical Almanac Office, but not within the back pages of the Almanac itself, is the algorithm for calculating the error-ellipse which that software displays. I think it has a minor error in its text, but more important, in my view the whole concept of deducing an error-ellipse from a single cocked-hat is fundamentally flawed. Anyone like to take up that question? George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.