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I can see why Byron might be puzzled by the current arguments about cocked
hats.

To start with, they concern cocked hats from astronomical position lines;
whereas he appears to be more accustomed to cocked hats arising from
coastal bearings to landmarks. But those two situations, and the cocked
hats they produce, have so much in common, that the differences between
them present few problems. Let's choose to deal with the coastal-bearing
situation.

Byron is usually trying to discover, and then correct for, any systematic
error (which I expect he will label "gyro error"), which affects every
bearing that he takes in exactly the same way. And if he takes the same
bearing, of the same landmark, from the same position, again and again, he
will get the same answer. There's no problem of "scatter", in that the
reading of a gimballed gyro repeater holds steady. This is what I think of
as the "big ship" situation, in which there's no "random" component to the
bearing error, only a "systematic" error, which needs to be discovered.

On the small vessel that's more familiar to many Navlist members, things
are very different, especially in rough weather. I expect that Byron has
been involved in such ship's-boat work in his time. Instead of a stable
gyro repeater, the observer has to sight across some sort of hand-held
compass, which must be held as horizontal as possible, and then read the
bearing from a swinging card, as well as he can, while hanging on.

Then he has to correct for compass error, as well as possible, which on a
non-steel boat is usually mostly  variation. And in the situation we're
discussing, we are assuming, rightly or wrongly, that any such "systematic"
compass error has been properly corrected for. And if it has, the only
remaining error is the "random" component, as the card swings about. If the
systematic correction has been properly made, we assume, then, that the
resulting random error is equally likely to be one way or the other; the
azimuth either too-big or too-small. Then if we take three such bearings,
simple logic decrees that only one in four such cocked hats will actually
embrace the true position.

Of course, neither of these scenarios actually represents real life. I have
no experience of a big-ship's navigationa gear, but presume that there's a
bit of motion when reading the gyro repeater, particularly in tempest
conditions. And we never know the compass corrections, on a small boat,
well enough to be sure that no systematic errors remain. But those are the
assumptions we make.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Byron Franklin" 
To: 
Sent: Monday, December 13, 2010 6:25 PM
Subject: [NavList] Re: That darned old cocked hat


The augument of the math of the cocked hat is over my head. I would offer
my experence with the problem, but no soild solution. Part of my piloting
technique is how to treat the hat from the compass error. If by facing each
bearing NAVAID that are with in 180 degree of each other the error LOP of 3
or more NAVAIDS with the compass error will pass you to the right (EAST
ERROR)or the left (if WEST ERROR) for sure You will not be in the triangle
unless the error is mostly random. You will also be closer to the LOP'S of
the closer NAVAID. The same idea
with the CELSTRAL cocked hat.bodies being with-in 180 degrees, if you
measure high or low they will go over head or short, you will not be in the
triangle.
With an underway fix as I have seen. I would pick what I felt to be good,
with a lean towards the LOP'S closer to 90 degrees spred. HOW could I be
wrong?
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