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    Re: Noon Fix
    From: George Huxtable
    Date: 2009 Apr 12, 10:37 +0100

    John Karl wrote-
    
    "I've read with interest this discussion of the noon fix.  So I though I 
    would run off some exact results that simulate Jim's example -- as far as I 
    understand it.  I thought such a simulation would give us some insight to 
    the problem.
    
    So attached is a plot of altitude versus time observations around LAN with 
    our boat sailing with four different components of northerly speed, the 
    maximum being 10 knots.  The top red curve is for no speed, the bottom curve 
    for the 10 knts.  The Dec = N11 degrees, the initial latitude at t = 0 min 
    is N69 degrees. The zero-speed LAN is at 30 min with Ho of 32 degrees, 
    virtually Jim's Ho, but I don't know his Dec or Lat.
    
    As expected, you can see the northerly velocity component shifts the maximum 
    Ho progressively earlier as the speed increases to the 10 knts, and 
    depresses Ho since the boat is moving progressively away from the sun.  The 
    apparent LAN for the 10-knt boat is shifted 6 min early, resulting in a 
    apparent Lon shift of 1.5 degrees -- a huge amount.  The apparent Ho is 
    depressed 4.3', small in comparison to the Lon shift."
    
    =====================
    
    I suggest that John Karl has muddied the waters by presenting a misleading 
    diagram, attached to [7918]. What he has done is plot these altitude curves 
    on a common time-scale, the zero-time of which has been set, quite 
    arbitrarily, to be the moment when the increasing altitude passes through a 
    chosen value, which appears to be something like 31�48'. For each of those 
    various speeds, however, the Local Apparent Noon will fall at a different 
    point, along that time-scale, so John is not measuring the shifts that he 
    thinks he is. The shifts in the plotted times of  those peaks are not the 
    shifts with respect to local apparent noon.
    
    So I suggest that John should replot his diagram, fixing LAN in each case at 
    a common spot on the time axis, and let the plotted curves of changing Sun 
    altitude fall where they will. His results will become significantly 
    different.
    
    He added-
    
    "As we all know the geometry of the spherical nav triangle, at times, can be 
    counter intuitive.  So I would hesitate to adopt Jim's simple linear 
    correction as gospel without further study. "
    
    That's a weak line of argument. If John thinks the correction is non-linear 
    he should provide some evidence in that direction. In fact, Jim's linear 
    correction does the right thing. The reason for any non-linearity that John 
    has suspected is because he has been plotting the altitudes against the 
    wrong time-scale (see above).
    
    John ended-
    
    "One last academic thought:  The "noon fix" is exactly just that.  We're 
    trying to measure both the sun's altitude and its azimuth ( zero or 180) 
    which does indeed give a true fix.  And as commonly appreciated, we can't 
    measure the azimuth very accurately -- even when we're dead in the water."
    
    and I agree. The only way to get a true "noon fix" from the Sun is to 
    determine its altitude and the time at the moment when its azimuth is due 
    South (or North). Though you can do that from land, with a properly-set-up 
    theodolite, it's impossible at sea with sextant and compass.
    
    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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