# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT**

**From:**George Huxtable

**Date:**2009 Apr 23, 15:33 +0100

Brad wrote Gentlemen, -I originally proposed this "Prove It" method, so that I could discover the truth and cut through the hyperbole. We proposed a test, in which George would give several altitudes around noon, and each contributor would then calculate the noon fix (lat lon) from the given altitudes. At this juncture, we seem to be waiting for a data set to be present to Jim Wilson. George, I urge you to complete that task so that we can see how a manually graphed method compares to the mathematically rigorous Excel least squares fit. We can see that the least squares fit certainly provides a fix much like Frank said it would. That is, Frank indicated longitude to within 5 miles, and Dave got 5.68 miles. Let us hope that there is no quibbling over 0.68 miles. I think for a least squares fit, we can convince ourselves as to the validity of the experiment. What remains then is the manual graphing or paper folding methods. While we can expect some degradation in performance, I do not believe we are discussing wholesale failure. Rather, there will be some variance from a rigorous curve fit to a mark-1 eyeball fit. This can be debated endlessly, as to the performance of one individual or another. However, it is my estimation that the fix will be within the ballpark, and the method "proven". I still want to see how Jim's method performs.... ===================== I concur with the thrust of Brad's message. When tested using the full might of Excel's least-squares fitting, Frank's procedure performed significantly better than my expectation, and conformed reasoably well with the claims he had made for it. It's a pity that nobody has chosen, as yet, to apply his own hand and eye to a graphing technique suitable for use onboard, which I expect would be somewhat degraded compared with the least-squares fit, though not a lot. Hewitt Schlereth has generated a set of random numbers which we haven't seen, and derived from them, using his own producedure, a result which he claims to be within 1' of the initial longitude. That is certainly possible, but a single result tells little about the scatter. Simple luck can cause your first shot at a dartboard to hit the bull's-eye. I ask Hewitt to deduce a few more sets of numbers, taken from the data set that I put out attached to [7940] as noon1a.rtf, or (the same data), attached to [7959], as noon1a.doc . I don't ask for all 20, but just a few, to get an idea of scatter. As for the principle of Hewitt's approach, it may indeed be the best, to work out the centre of symmetry before correcting for North-South speed, then allow for the effect of that speed afterwards. I expected it to be a simple matter to provide a set of tinkered data to meet Jim's needs, but is has proved a surprisingly awkward task. Dave Walden has kindly offered some help, so between us we may have some numbers to offer Jim very shortly. He is being very patient. Here's what I've tried to generate, for Jim, and he can say if it would meet his needs. I wanted to allow simulated data to be collected in a procedure that a real observer might follow, not allowing any foresight about what's coming next. What I proposed was to provide predictions at fixed times of 12:10, 12:11, 12:12, 12:13; 12:14. then a gap until 12:35, 12:40, 12:45. Then keep predicting and noting (but not recording) altitudes over the next half-hour, at 1-minute intervals, looking out for the first moment that the predicted altitude falls below or equal to that made for 12:14. We can call that moment time T. Predictions made between 12:45 and time T are immediately discarded. Record time T and its altitude, and then record a further 4 altitudes. So the last batch of 5 is at - T, T+1, T+2, T+3, T+4. Then I would present Jim with a table with a table with 13 columns showing those 13 altitudes, similar to what went before, together with an additional column showing time T (the time that the observation in column 9 was taken), and another with an identifier code. Further columns showing assumed lat, long, and speed, including their scatter, will be retained, not disclosed until later, as we did before. My aim would be to put out no more than a page-full of stuff, say 20 data-sets as before, enough to give a rough idea of scatter. I might expect that no more than a few of those 20 would be actually tackled by a graphical procedure. I strongly suspect that Jim's procedure, because it concentrates on the outer fringes of the timing, in which altitudes are more sensitive to hour-angle, could actually provide a marginal statistical improvement in determining longitude (not latitude) over the simpler equally-timed case. But it would be hard to detect marginal differences without lots of statistics. George. contact George Huxtable, at george{at}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 unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---