NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Graphs of Lunar Distances.
From: George Huxtable
Date: 2010 Oct 2, 00:09 +0100
From: George Huxtable
Date: 2010 Oct 2, 00:09 +0100
Time for another look at recent mailings about lunar distances. Frank wrote- "With those objects as the "other body" in lunars, I routinely get results with a standard deviation of about a quarter of a minute of arc in individual observations and about twice as good when sets of four are averaged." and in his next mail- "As I have noted, I can routinely get lunar distances accurate to nearly a tenth of a minute of arc (standard deviation) when sets of four are averaged. A tenth of a minute of arc error in the angle is generally equivalent to twelve seconds error in the resulting Greenwich Time." That's not the first time we have seen such a claim from Frank. I have no wish to dispute his prowess, but it does raise a few questions, to which I've tried to get answers before. It's true that when observations are affected by statistical random scatter, then averaging a set of four will halve that scatter. But that averaging won't affect any non-random, "systematic" error. The analysis that Frank has provided can apply, only if the inherent systematic error is precisely zero. So I ask him to estimate an upper-limit value on what such non-random components of error might possibly be. That estimate could include the following- Imprecision in index-error checking; scale calibration error of sextant, collimation error, shade prismatic error; personal error in estimating position of Moon limb. There may be other possible sources, that Frank may think of that I've missed. Let's have an informed estimate of what each of these might possibly be contributing. If zero, state zero. When this question was asked before, an answer was evaded. If Frank considers it to be an unfair question, he can say so (and why). Frank added, in a claim which we've also seen before- "I have conducted a number of workshops in lunars since 2004, and when observers without previous experience in lunars shoot them with a properly adjusted sextant fitted with a decent telescope, I find that they, too, can get observations with a standard deviation of about a quarter of a minute of arc. There's no law to this, and there are plenty of ways to screw it up, but I can assure you that it's not just me." And yet, when I've appealed, on Navlist, for anyone who claims to get comparable precision, repeatably, not a single hand has gone up. I ask again; can anyone else reproduce the results that Frank claims anyone can get? =========================== Now we come to the matter of the Elephant in the Room, that nobody has yet mentioned. Conclusions are being drawn about lunars taken at sea, on the basis of observations made under completely different conditions, on land. We know that Douglas has taken his lunar distances from a firm footing, on-land. We might presume that all the observations that Frank has described were also made on land, though he hasn't said so. Perhaps he will correct that presumption, if it's wrong. Yet on the basis of that experience, he presumes to tell us what precision a navigator in the era of lunars could expect to achieve. And how real navigators should go about making such observations, as in the following-. "... you mentioned putting the sextant on a tripod. For some purposes that may be a good idea. Another trick you can use is to sit down on the ground with a knee up and your elbow resting on that knee. This adds stability, reduces fatigue, and we know that navigators actually did things like this in the 19th century. It's a trick that would work nearly as well on the deck of a ship at sea back then as in our backyards today." It may be a trick that might work in today's vessels of many tens of thousands of tons, such as Jeremy reports his lunars from. But in the "lunar era", typical vessels were around 100 to 300 tons, small vessels which, in ocean conditions would be expected to jump around; motion which a sextant user had to counteract, and which would call for complete freedom of movement of the instrument to do so. Flinders and Bass used lunars at sea in exploring van Diemen's land, in a 25-tonner. Cook's seven Atlantic crossings (made just before he learned about lunars) were made in a 70-ton brig. Backyard techniques were not appropriate on such ships, except in millpond weather. In the past Frank has claimed, unconvincingly, that there's little difference in precision between measurements made at sea and on land. I don't believe it. In recent years, we've had no reports, that I can recall, of Navlist members taking lunars from on board small craft at sea; not since Steven Wepster's Atlantic observations of ten years or so ago. Why not? It isn't an easy task; that's why not. We now learn, for the first time, that when Frank made his claims for extraordinary precision, a x9 telescope was in use. That is not a tool for use at sea. Even a 3x telescope can present real problems, in keeping the two bodies in view, when the vessel is bucking around. Every sextant is always provided with a 3x (or thereabouts) telescope for regular use at sea, and sometimes with an additional 6x (or so) for special conditions when it was possible to use it. Cook frequently observed lunars without a telescope, writing that it was impossible for him to say "whether those made with the telescope are the nearest the truth, circumstances seem to be in favour of both- we certainly can observe with greater accuracy with the telescope when the ship is sufficiently steady which seldom happens so that most observations at sea are made without". This was on Resolution, 336 tons. So it's clear how completely inappropriate Frank's 9x telescope would be, in such conditions. 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.