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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@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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