# 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 16, 12:57 -0700

```Gary laPook wrote:

On Mar 15, 6:04 pm, "P F"  wrote:
> Gary wrote:
> > his true position may be significantly outside the cocked
> > hat
>
> Oh come on, Gary. How would the "true position" get to be "significantly
> outside"?

Easy. If by chance plotting the LOPs resulted in a small triangle this
doesn't mean that sigma is necessarily small. So in that case the true
position will lie in the circles of probability that are larger than
the triangle. So, for example, picking a number for sigma out of the
air of one nautical mile, the position of the observer will be
somewhere within the one mile circle (one sigma) centered on the
plotted fix only 39.3% of the time and within a circle of  1.177 sigma
(1.177 NM)  50% of the time. This circle is also known as CEP or
circular probable error. Continuing drawing circles, 66% within 1.48
NM, 75% within 1.67 NM,  90% within 2.15 NM, 99%  within 3 nm and
99.9% of the time within 3.72 NM. Put another way, one third of the
time  the position will be more than 1.48 NM away, 10% of the time the
position will be more than 2.15 NM from the plotted fix and 1 % more
than 3 NMs away.
At the other end of the distribution there is only a 10% chance that
the position of the observer will be within .48 NM of the fix. ( See
table Q6c of Appendix Q on page 1221 of vol. 1 of Bowditch, 1977
ed.)So, what does this tell us. There is about a 30% chance that the
position of the observer will be more than .48 NM but less than 1.0 NM
and about a 61% chance that the position of the observer will be more
than 1.0 NM from the plotted fix.

If the triangle plots with LOPs only one half mile from the center
then there is approximately a 1 in three chance that your position
could be up to 1 NM outside the triangle, a 10 % chance that it is
1.65 NM outside and a 1% chance that it is 2.5 NM outside.

Even if you don't know what the sigma numerically is it doesn't mean
that it doesn't exist and that you can ignore it.

By "significantly" I mean rocks in the bilge.

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```
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