# NavList:

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

**Re: That darned old cocked hat**

**From:**Hewitt Schlereth

**Date:**2010 Dec 10, 20:06 -0400

My method in practice was to imagine where the cocked hat would balance on a pin and take that point as my fix. This I think is essentially Gary' first and easiest way. What I was more curious about was George's explication to the effect that the fix had a 25% chance of being inside the hat versus a 75% chance of being outside it - i.e., being three times more likely to be outside the hat than in it. Where would that outside point be? How would you figure that out? Hewitt On 12/10/10, Herbert Prinz <666@poorherbert.org> wrote: > This post reminds me of what happened long after the Board of Longitude > had paid out their price: There was no end to the submission of "better" > solutions. > > Herbert Prinz > > On 2010-12-10 22:22, 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 >> ---------------------------------------------------------------- >> NavList message boards and member settings: www.fer3.com/NavList >> Members may optionally receive posts by email. >> To cancel email delivery, send a message to NoMail[at]fer3.com >> ---------------------------------------------------------------- >> > > > > >