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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: Gary LaPook
    Date: 2009 May 12, 23:07 +0200

    You get us back to the drum that I am constantly beating, "just how 
    accurate do you need your fix to be at the moment"?
    
    First, there is never going to be a perfect celestial fix, accurate to a 
    nanometer. Now that we have GPS we can compare our celestial fixes to a 
    highly accurate benchmark, we couldn't do that in the past. Many on this 
    list try to squeeze almost perfection out of their celestial fixes but I 
    think it is useful to ask how much accuracy is actually needed and see 
    if the technique yields that level of accuracy.
    
    The traditional noon fix was achieved by crossing an advanced morning 
    sun line with the noon latitude sight. How accurate could we expect this 
    type of fix to be? Pick your own value for the probable accuracy of each 
    sextant shot by let's use one half minute for this discussion. So the  
    morning sun line has an error band one NM wide. Lets say we advance this 
    for one hour at six knots westbound and add one tenth of the distance 
    covered as the degradation of the position due to to possible errors in 
    the DR. (This is a commonly used estimate in flight navigation but a 
    smaller number may be appropriate on a boat.) This adds another 
    six-tenths of a NM to the error band making it 2.2 NM wide. (Since the 
    morning sun line will not have an azimuth of straight east or west not 
    all of the error will be in the longitude but we have bounded it worst 
    case, plus and minus 1.1 NM in longitude.) Assuming the same level of 
    accuracy with the noon sight, you have determined your position plus or 
    minus one-half NM in latitude and 2.2 NM in longitude. Let's call this 
    the accuracy level of a traditional noon fix.
    
    We have been taught that you cannot determine longitude from the noon 
    observation due to the difficulty in determining the exact instant of 
    LAN. What this actually means is that you cannot determine your 
    longitude to the "accuracy level of a traditional noon fix." But if you 
    can determine the time of LAN within one minute then the uncertainty in 
    longitude is only plus and minus 15 minutes of longitude, plus or minus 
    15 NM at the most. Although this is not to the "accuracy level of a 
    traditional noon fix" it is probably accurate enough for the purpose of 
    a backup navigation system. There are techniques to use in an attempt to 
    identify LAN more accurately (equal altitude sights) and the technique 
    discussed on this thread, producing about five minutes of longitude 
    uncertainty and also accurate enough for backup navigation. (I am 
    impressed by the level of accuracy achieved by this method.)
    
    Soooo, why go to the extra complication of the method discussed here, 
    just mark down the time of LAN, place an error band +/- 15 NM on the 
    longitude, and plan your landfall based on the most critical longitude 
    determined? One of the arguments made for this method is that it is easy 
    to relearn, but it is not nearly as easy to relearn as just taking the 
    time of LAN.
    
    gl
    
    
    
    Brad Morris wrote:
    > Report of the Secretary of the Navy
    >
    > "We recognize in navigation two classes of astronomical problems; one 
    possessing perfect accuracy of computation; the other uncertain, and 
    approximate only in its results.  The first class is, of course, always 
    employed when the weather and other circumstances are favorable.  The second 
    class of problems, that which gives only approximate deductions, is never 
    resorted to except from necessity.  The latter, however, serves a useful 
    purpose by enabling the navigator to know his position more nearly than he 
    could otherwise do, and by often affording perfect security by informing him 
    of the limit of safety, beyond which he should not venture."
    >
    > --------------------------
    >
    >
    > I would like to assign the latitude and longitude by the noon sun fix to the 
    second class of problems.  It can provide us with a useful figure of merit, 
    albeit without perfect accuracy. Certainly, with a least squares curve fit, 
    the method affords us a very reasonable fix.
    >
    > So if Frank wants to "trot out his hobby horse" one more time, I for one will applaud it.
    >
    > Proven??  A resounding YES!
    >
    > Best Regards
    > Brad
    >
    >
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    >
    >   
    
    
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