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Based on our discussion placing the position at the center of the
cocked hat put you at good probability of not really being there...
and the smaller the cocked hat the less likely you are to be there.  I
find this most entertaining.  But despite the well reasoned arguments
I can find no better way to place the "dot" than to put it someplace
in the center-ish of the cocked hat by what ever method you find most
stimulating.  Voltaire said of my profession "The Art of Medicine
Consists of Amusing the Patient While Nature Cures the Disease".  I
suspect methods for placing the "dot" are "Entertaining the Navigator
While Waiting to Run Aground" ; )

Thomas A. Sult, MD
3rd Opinion
1415 First First St. South #5
Willmar, MN 56201
320 235 2101 Office
www.3rdOpinion.us
tsult@mac.com




On Dec 10, 2010, at 4:22 PM, Gary LaPook wrote:

> So we now have four geometric constructions (plus visual estimation
> making a total of 5 ways) to plot the fix inside the cocked hat.
> John Karl's probability diagram shows the probability of each of
> these points to be essentially equal although the Symmedian point my
> be ever so slightly more probable. So, what method should you use? I
> think the decision should be based on ease of construction.
> Obviously the easiest way is by eyeball and is the method I
> recommend. The next easiest construction is my method of determining
> the centroid by the "median" method. You only have to use dividers
> to halve one of the LOPs, lay a straight edge from the opposite
> corner to this point, and then use the dividers to mark the 2/3rds
> point along the straight edge. The standard way to determine the
> centroid is the text easiest, halve two of the LOPs and draw the two
> lines from the opposite angles to those points. More difficult is
> measuring the angles of two of the three corners, then dividing them
> in half, and then finally plotting those lines. ( You can also find
> the bisectors of the azimuths and plot them, you get the same point,
> if the spread of azimuths exceed 180 degrees.) The most difficult
> point to plot is the Symmedian point which requires that you first
> plot both the medians and bisectors, measure the angle between each
> of the lines in each set, and then draw in the additional lines
> shifted by the angle between the lines in each set to the opposite
> side of the bisector. Plotting the Symmedian point takes a lot more
> work with no significant in probability that it represents the
> actual position of the vessel.
>
> ( See my diagrams on the "three body fix" thread.)
>
> gl
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