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Maybe when you say "a round of three start" perhaps you mean
implicitly that they are chosen so the azimuths cover greater than 180
degrees as of course is best. (And I wonder if there is a CN term for
such a well chosen round?). My point is that if you have ONLY index
error then the true position is at the incentre, the centre of the
inscribing circle of the cocked hat.  The point being that the index
error would be a fixed distance from the lines of position on the
chart. The inscribed circle is tangent to each line of position and so
its centre, the incentre, is the same distance, the radius of the
incircle and your index error expressed in nautical miles,  from each
line.   However if the situation is not so ideal so that one of the
index errors puts you outside the cocked hat then you will be at the
centres of one of the excircles, tangent to all three lines of
position but outside the cocked hat.

I have a feeling that this discussion has arisen on NavList possibly
several times before already and I should provide a link. Not actually
seen it in book though (and I fully expect one of our community to
provide a link to a very old French book in which it first appears, as
was the case for the symmedian point and identically distributed
random errors).  In any case I would appreciate if there is a name for
these "good and bad rounds of three stars".


On Mon, 14 Oct 2019 at 18:48, Ed Popko  wrote:
>
> And on a slight tangent should you try stars: Greg pointed out, many posts 
back, that if your sextant has a slight index error in it (either on or off 
the arc) and you do a round of stars for a three body fix, the only effect 
the IE will have is to make the cocked hat bigger or smaller than what it 
might be if you had no IE at all. In other words, the center of the cocked 
hat, however you want to analyze the triangle's center (and there are more 
than one way), is unaffected. The center remains the same
>

   

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