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    Noon Fix
    From: John Karl
    Date: 2009 Apr 11, 19:28 -0700

    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.
    
    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.  From the little bit of 
    experimentation I've done, it seems like the example discussed here is 
    somewhat on the extreme side.  Other Lats & Decs have produced smaller 
    effects for the 10 knt case.  Depending on Lats & Lons, some only had 2-min 
    time shift, but the 4' depression was typical.
    
    I haven't had the time, maybe not even the inclination, to develop an 
    approximate sight-reduction method along Jim's idea to confirm his method.  
    In fact, like George, not sure I understand exactly what his method is.  So 
    far, I view this whole discussion as rather academic considering how easy the 
    intercept method is, and how satisfactory the standard noon shot is, even 
    with its horrible Lon accuracy, for standby or emergency situations.
    
    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.
    --JK
    
    
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