# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Cocked hats, again.**

**From:**George Huxtable

**Date:**2007 Mar 13, 21:30 -0000

I hardly ever find anything to disagree with in Gary LaPook's contributions. They are usually full of sense. That applies, too to most of his 6th March posting, Navlist 2236, labelled "resolution of systematic error". Though actually, what he discusses there is the situation of entirely random error, where all systematic error has been corrected out. But Gary concludes with this- "Again, no one is suggesting that the position of the observer is at the center of the triangle but this represents the center of possible positions of the observer. In fact, the position of the observer will be outside of the triangle often but I don't agree with the three out of four allegation. Counter intuitively, the smaller the triangle the more likely that the position of the observer is outside the triangle! If you think about it, this should be obvious. Using reducio ad absurdum, think about a triangle only one inch in size, it would be impossible for the observer to be within the triangle. At the other extreme, a very large triangle with all of the displacements of the LOPs from the center of the triangle equal to 3.3 NM (3.3 sigma's, linear sigma's are slightly different than circular sigma's, see Bowditch), the only place that the position of the observer could be is at the fix in the center of the triangle!" Here, Gary is wrong. The statement, that "with entirely random errors, three times out of four the triangle will not embrace the position of the observer", is precisely correct, and based on irrefutable statistical arguments. If Gary doesn't accept this, unlikely though it may seem to him at first sight, he should scan through previous discussion of cocked hats on this list, as Geoffrey Kolbe suggested. If he remains unconvinced, we can go through the arguments once again, until one way or another, either he accepts it, or else he convinces us otherwise. The best way to consider the matter is not to take a particular triangle, and then consider "where can the true position be?", but to take a true, known position of an observer, and three celestial bodies. Now plot in his vicinity a set of three position lines that have been displaced by Gaussian amounts, toward or away from the GPs of the bodies in question. (Indeed, the argument doesn't rely on a Gaussian distribution, just equal numbers toward and away). And then, with the same observer position, and the same three bodies, plot another triangle, with different displacements, and another, until you are tired of it. The resulting triangles will be different each time; some will be large, some will be tiny, some long and thin, others nearly equilateral. And in the end, if you check enough triangles, you find that 25% of those triangles will embrace the true position that you started with. It doesn't matter how skilled or unskilled the observer is; it remains true. For a skilled navigator, of course, the triangles will indeed be smaller on average, which is where his skill shows itself, but still, only 25% of those smaller triangles will include the true position. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---