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    Re: Still on LOP's
    From: Bill Murdoch
    Date: 2002 May 8, 12:56 EDT
    I am standing on a small island whose position is accurately charted.  I take a round of three sights all equally spaced around the horizon.  When I reduce them with respect to my known position, they can give me two kinds of LOPs; those are toward (T) and those that are away (A).  There are eight possible combinations all equally probable.  In only two of those eight combinations, A-A-A and T-T-T, will the cocked hat that I draw on the chart enclose my small island.  I will find that I am within the cocked hat only 25% of the time.

    If I get a 'toward' twice as frequently as an 'away' because of a measuring bias on my part, I will have three different kinds of LOPs; those that are toward because of the bias (TT), those that are toward (T), and those that are away (A).  The two kinds of towards (TT and T) are together twice as likely to occur as the one kind of away (A).  There are now 27 combinations of the three kinds of LOPs.  There are nine of these that will include my island; TT-TT-TT, TT-TT-T, TT-T-TT, TT-T-T, T-TT-TT, T-TT-T, T-T-TT, T-T-T, and A-A-A.  With the bias, I will be within the cocked hat 33% of time.

    Thus, a skillful navigator will actually be within his cocked hat less often than an unskilled navigator.  I may be on the verge of finding the root cause of my all too frequent success.

    Bill Murdoch
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