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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: George Huxtable
    Date: 2009 Apr 16, 13:55 +0100

    Jim Wilson wrote
    
    
    | George:
    |
    | Thanks, and I'm sorry to be a bother, but if I plan to use my method, I
    | need simulated data in the same form that I took it for my example.
    | Specifically, I need at least five altitudes at about one minute
    | intervals starting 30 minutes before LAN. Then I need a few around
    | maximum altitude. I could live with what you offered for that. Finally, I
    | need another five altitudes at about one minute intervals starting at the
    | last altitude of the first run. Anything else is wasted on me. Figure 2
    | shows what I took, and I don't really need that much, but the format is
    | natural. I'll attach it.
    |
    | I hope that this is not too much to ask.
    
    And added later, off-list-
    
    I think there may be a method that doesn't inundate everyone with
    superfluous data. You could use your program to generate the tons of data
    on one minute intervals, and then throw away what isn't needed. Is it
    that easy?
    
    ========================
    Response from George-
    
    I'm keen to meet Jim's requirements.
    
    It's no problem to create a lot more columns in the spreadsheet, and thus
    simulate 61 altitudes at 1-minute intervals. From those I could select three
    groups of six, each spanning five minutes. The most useful observations for
    determining longitude are near the limits of the period, as far from Local
    Apparent Noon as possible, and Jim wishes, quite properly, to take advantage
    of that. The important observations for latitude, however, are those close
    to LAN.
    
    Frank Reed stated his requirements to be observations spanning 40 to 60
    minutes at 5 or 10 minute intervals, therefore 5 to 13 in all, and I've bent
    over backwards, in this demanding test, by choosing that maximum number of
    13. Jim's extended series would be 18 observations rather than 13, but if
    that will do the trick, we should try it. Can a skilled observer take timed
    altitude readings as close as 1 minute intervals, though? Can he do so
    without an assistant for noting times and recording results? If not, we
    should be told, because it becomes a disadvantage in the procedure.
    
    I have no problem in providing data for the first part of Jim's procedure,
    covering the first five minutes, from the start of the chosen hour. Not so
    easy to choose "a few around maximum altitude", because each scan is
    unpredictably different, in the time of maximum altitude, and the height,
    and the scatter of its points around it.. I am reluctant to allow hindsight,
    in examining the data-set after it's been captured, to determine when the
    peak was, for the purpose of deciding which observations should have been
    used, as a real observer couldn't do that. So I would prefer Jim to
    preselect a fixed time-bracket, if he can, which will meet his requirements
    around the peak.Those observations around the peak don't need to be spaced
    so closely in time as 1 minute, and we don't have to take equal intervals
    all through. If Jim can find a way to restrict his total number of
    observations to 13, that would allow a fairer comparison with Frank's
    procedure, though I certainly wouldn't insist on it.
    
    My problems comes with the final set, of falling altitudes, taken toward the
    end of the measurement-hour. Jim wants these to start "at the last altitude
    of the first run". That's all very well with hindsight, but how does a real
    observer do that, unless he has been observing at regular intervals, or
    coninuously, to discover when that moment has arrived, to start noting
    results?
    
    And then, there's another problem. I can see that Jim would wish to make his
    set of falling amplitudes symmetrical with his set of rising ones. But what
    happens it the peak hapens to be delayed after LAN? Then the falling part of
    the altitude curve can't be accommodated within the allotted hour for
    observation. Indeed, that will normally be the case, because the effect of
    Northerly vessel-speed alone will normally act to delay the moment of the
    peak. [That effect has been somewhat tempered by my failure to allow for
    equation of time, in choosing the appropriate time-span around LAN, which
    should really have run from 12:08:16 to 13:08:16, rather than from 12:10 to
    13:10 (though all the numbers have, I hope, been properly calculated
    according to the GMT times that were given)]. This is a problem that will
    also face an observer in real-life, and to ensure that he will be able to
    complete a symmetrical observation within the specified hour, perhaps he
    should delay, somewhat, the start of his data-collecting, to be a bit
    after12:10. Or else, accept that a longer interval than an hour will have to
    be accpted, on many, perhaps most, occasions. The longer the duration of the
    observation-scan, the more precise the answer will be, and the more it will
    depart from an "observation around noon".
    
    If Jim can provide a simple recipe for choosing fixed timing of his three
    blocks of altitudes, I'll try to meet his needs. If he can suggest an
    algorithm, which doesn't presume knowledge of any data before it's actually
    arrived, I will try to implement it.
    
    What we're discovering, here, are real difficulties in interpreting the
    procedure that would be faced by a real observer, and are not just artefacts
    of the simulation process, so we can learn from them
    
    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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