# NavList:

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

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Re: Cocked hats, again.
From: Gary LaPook
Date: 2007 Mar 21, 10:54 -0700

```GAry LaPook wrote:

Well, this thought experiment did help. It is hard to dispute the 1 in
4 arguement so I will accept that point.

to all of us who were taught that our position must be inside the
cocked hat that it ain't necessarily so and a simple statement like
"only 1 in 4" is a good way to drive that point home.

Gl

On Mar 15, 11:44 pm, Paul Hirose  wrote:
> My cocked hat "thought experiment" confirms Huxtable's Theorem.
>
> Imagine three perfect observations, so the LOPs all meet at a point.
> That's the true position of the vessel.
>
> In the real world all observations have error. None of the LOPs will
> pass precisely through that point. To simulate observational error, move
> each LOP some random distance toward or away from its body.
>
> Moving the first LOP generates a triangle with the true position at one
> vertex. For the remaining two LOPs (which meet at the vertex) there are
> four possible permutations of toward and away. Only one yields a
> triangle containing the true position: 1) move one LOP in the direction
> that enlarges the triangle, 2) move the other LOP in the direction that
> enlarges the triangle.
>
> If you move the LOP in step 1 the other way, the true position is
> outside the triangle, and on the LOP that hasn't moved yet. Then no
> matter which direction you move that LOP, it's impossible to form a
> triangle containing the point.
>
> None of this depends on how the sights are distributed in azimuth. As
> long as all three are equally likely to err toward or away, there's a
> 25% probability that the true position lies within the triangle.
>
> Skewing the toward/away probability will change that. For example, if
> the azimuths are about equally spaced and you forget to apply the dip
> correction, it becomes *more* likely that the cocked hat contains the
> true position!
>
> --
> I block messages that contain attachments or HTML.

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