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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: Hewitt Schlereth
    Date: 2009 Apr 23, 11:03 -0400

    George, it looks like I may have misunderstood the document I got the
    (nearly) equal AM/PM altitudes from. I thought it was your spreadsheet
    and cited it's designation - LONG AROUND NOON.XLS (SS) - in the
    worksheet I attached to my e-mail. The numbers I used were from that
    document - which I took to be yours. They looked mighty like sextant
    altitudes; so, certainly not random numbers generated by me.
    
    Maybe my worksheet didn't come through to the List?  Here it is again.
    
    Hewitt
    
    
    On 4/23/09, George Huxtable  wrote:
    >
    >  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.
    >
    >
    >
    >
    >
    > >
    >
    
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    File: 108023.lon-by-eq-alts.doc
       
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