NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The Noon Fix
From: George Huxtable
Date: 2009 Apr 8, 17:32 +0100
From: George Huxtable
Date: 2009 Apr 8, 17:32 +0100
Jim Wilson wrote about his new book in an attachment that came with [7875]. I have no objection at all to Jim Wilson plugging his book on this list. But his posting raises a few questions in my mind. One problem is that, presumably, he reserves the details of his arguments to his book, perhaps in order to encourage us to buy it, but that inhibits informed on-list discussion of his points. Here and there, he mentions (reference 1), which is presumably that book, but I think most of us can see what he's getting at, in that posting, without it. As has been discussed at some length on this list in the past, there are two major snags about trying to derive longitude from an observation of Sun altitude made at noon, and Jim's posting deals with one of those snags, and the most tractable one at that. This is the difficulty that the moment of maximum altitude differs from the moment of the meridian passage of the Sun (or other body) if the observer is moving Northward or Southward, or if the declination is changing. The simple method of determining the time of maximum altitude of the Sun, ignoring that difficulty, is to time the moment before noon when the altitude is at a particular value, near maximum, leave the sextant at the same setting, and time the moment after noon when it has the same altitude once again. Then split the difference between those times. Jim proposes to allow for changes in the observer's latitude, or the body's declination, by adjusting the altitude of the second observation, by an amount that is proportional to the two speeds, and the time interval. And I see a practical and logical difficulty here. What the second observation is trying to measure is the time of the moment when the body is at the adjusted sextant altitude. But you don't know the amount of the adjustment to make to the sextant, until you know the time-interval after the first observation, which is exactly what you are trying to discover. Each depends on the other. Which do you work out first? By the time you've pondered on that, the moment may have passed. Am I misunderstanding something, here? It's not insoluble, of course. Simply plotting the altitude curve allows you to adjust the altitude in retrospect. And adjusting each point on that curve according to the Northing that's been logged would even allow for a change of tack, around noon, to be allowed for. Jim wrote- "Relying on single observations is not recommended, but it does illustrate the basic approach." I don't see how a single observation is feasible, in this context, and presume that a single pair of observations, one before and one after noon, was what he meant. =================== All that leaves aside the biggest problem about determining the longitude at noon. Whis is this: it can't be done. It's impossible. What is hidden, under that catchy title of "The noon fix", or "longitude at noon", is that it's actually longitude AROUND noon, comparing observations over a time span that extends well before and well after noon. The shorter that time span is, the less accurate is the result. Unless that time-span is a well-extended one (Bowditch recommended 30 minutes each side of noon), then "longitude around noon" becomes impractical, a fact that its proponents often gloss over. I hope Jim has come out straight and made reasonable assessments of the scatter in the deduced longitude that will result from some plausible time-span and a reasonable level of observational scatter in his altitudes-at-sea. I suggest we might assume an arc-minute (standard deviation), which wouldn't be bad going even in a large vessel, depending on sea-conditions. We can allow that one of the more serious error-contributors, variation in horizon-dip, doesn't affect us in this instance. It would be good to see assessments of how the resulting accuracy is affected by higher latitudes and lower declinations; and is not confined to climes with a high Sun, when the method becomes more practicable. I'm aware that Jim's previous postings show a high level of awareness of these problems, so I live in hopes that all this will be addressed. . 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. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---