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    Re: That darned old cocked hat
    From: Gary LaPook
    Date: 2010 Dec 10, 14:22 -0800

    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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