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    Re: That darned old cocked hat
    From: George Huxtable
    Date: 2010 Dec 9, 13:28 -0000

    Reading John Karl's attached document "That darned old cocked hat", I am 
    surprised by his second result, that "the probability that the ship is 
    outside the cocked hat is 84%"
    That differs from the conclusion previously aired, at some length, on this 
    list and elsewhere, that if there were no systematic error so that the 
    remaining random error made an intercept towards or away equally likely, 
    the chance of a vessel being outside the cocked-hat would be exactly 75%. 
    The logic leading to that conclusion appears to be unshakeable. If asked, I 
    will go over it once again.
    In addition, I've convinced myself of its truth by a computer simulation, 
    for what that's worth.
    So John's figure of 84% throws his other conclusions into some doubt, in my 
    eyes. Is he prepared to argue why it should differ from 75%?.
    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.
    ----- Original Message ----- 
    From: "John Karl" 
    Sent: Wednesday, December 08, 2010 10:22 PM
    Subject: [NavList] That darned old cocked hat
    That darned old cocked hat seem to keep popping up.  I’ve given this some 
    thought lately and have computed some examples to investigate questions --  
    such as where the point of maximum probability is.  I’ve thought for a long 
    time, and still do, that this is all perhaps rather interesting 
    academically, but of no practical importance for a navigator who is only 
    interested in the safety of the ship.  In that case you’re never sure where 
    you are better than the known random-error distances from each LOP.  (Ocean 
    racing or armed combat might have different objectives.)
    The linked PDF file gives my results and observations.  I’d be glad to run 
    off other examples if anyone is interested.
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