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    Re: The Noon Fix
    From: George Huxtable
    Date: 2009 Apr 11, 21:49 +0100

    I hope Jim, and Navlist readers, will bear with me a bit longer, because it
    appears that not all questions about Jim's example procedure are yet fully
    resolved.
    
    As a reminder, this is what he first wrote-
    
    "From reference 1, (Sn - d) is the rate of movement between the observer and
    the body, where Sn is the northerly component of speed, and d is the rate of
    change of declination, here positive if the change is northerly. Multiplying
    this by the time between observations gives the resultant change in
    altitude.
    At meridian transit the navigational triangle has become a line. At this
    time, the change in sextant altitude (Δhs) is (Sn - d)ΔWT, where ΔWT is the
    difference in watch times between observations. It can be simply added to or
    subtracted from the initially measured altitude hs. Averaging the times of
    the initial hs and the adjusted second hs gives the time of meridian
    transit. That’s it!
    
    Relying on single observations is not recommended, but it does illustrate
    the basic approach...."
    
    (taking particular note of that last sentence, which Jim has since
    emphasised)
    
    As I've pointed out more than once, the method can't be applied in such 
    circumstances, except if enough observations are taken to make some sort of 
    plot against time, because to calculate Δhs the time  ΔWT needs to be known, 
    before it has been measured.
    
    ==============================.
    
    Jim has acknowledged shortcomings in trying to do the job by a single 
    observation before noon, and another after noon, and now adds-.
    
    "To be exact, Dh should be calculated at LAN, whose exact time is unknown as 
    yet. I calculated Dh at the time of highest altitude for simplicity. For my 
    example the change in Dh  is quite slow. DWT is almost an hour, and the 
    resultant difference in time is 95 seconds. That gives a change in Dhof 
    0.2', less than the expected sextant reading scatter."
    
    But it seems to me the point is still being missed, here. The uncertainty in 
    ΔWT is not the 95 sec difference between Local Apparent Noon and time of 
    maximum altitude. It's that the observer has little notion of when the Sun 
    is going to return to the starting altitude again. Unless he knew how long 
    it took for the Sun to reach the top, after the first observation, he has no 
    idea how long it will take to come back down again.
    
    Jim followed with-
    
    "Should anyone really try to just set the sextant to the adjusted altitude, 
    Dh can be calculated based on the best approximation of the time of highest 
    altitude, thus theoretically achieving the same accuracy as my example."
    
    I ask, how well can that be done? If it was easy to determine the moment of 
    maximum altitude, we would simply do so, and this method of discerning a 
    mid-point in time would be unnecessary. I ask Jim to take a look at that 
    part of his data-set that embraces the peak, in the smaller plot in his 
    fig.2 , attached to [7894]. Then erase (in his mind) the theoretical 
    parabola, which was presumably fitted to the complete data set. And then 
    tell us, from those plotted points alone, how precisely he can time the 
    moment of the maximum. The uncertainty in deducing ΔWT will be twice that 
    uncertainty in timing the peak from that "best approximation".
    
    Remember, that's an assessment based on the basis of recording and plotting 
    a set of 12 altitudes, a minute or so in time apart. If, instead, it was to 
    be done on the basis of shouting "noon" when the first fall was seen, that 
    would happen at 11-54-30.
    
    It may be that the errors caused by such an approximate procedure do not 
    give rise to a significant error in overall timing, as they are no more than 
    an error in a correction. I'm open to be convinced about that, but it isn't 
    obviously the case, the matter needs to be argued first.
    
    But as I see it at present, the procedure Jim used as an illustration, 
    described by him as "not recommended", seems completely impracticable.
    
    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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