# NavList:

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

**Re: The Darn Old Cocked Hat - the sequel 1**

**From:**Hanno Ix

**Date:**2013 Mar 13, 09:54 -0700

Hewitt:

It cannot be strictly a "bell" since that a bell is valid also for negative *absolute distances*

that dont exist.

Looking forward to your photograph!

h

**From:**Hewitt Schlereth <hhew36---.com>

**To:**hannoix---.net

**Sent:**Wednesday, March 13, 2013 7:59 AM

**Subject:**[NavList] Re: The Darn Old Cocked Hat - the sequel 1

I'd say a bell curve. Most in the range of, say, 3 to 6 miles off. One spot-on. One off the chart. Hewitt Sent from my iPad On Mar 12, 2013, at 11:49 PM, "Hanno Ix" wrote: > Gary: > > Thanks for those copies! > > With them you have answered the first question, and personally I agree. > > Now to the second question. FER has stipulated that only *absolut* distances (errors) of the fixes from > the announced position are going to be considered for the competition, the azimuths will be ignored. > > So he will rank all entries as to their fix error in sm from the location announced by T. Cruise. > He might put them in ascending order and, of course, the one on top is the winner. > (He will receive a sparkling and working MHR1 donated by the Navy of the Federal Republic of Germany! ) > > Since FER is a passionate navigator, he wants to know more: frequency of errors over size of errors. > He will establish a row of buckets: 1. bucket for, say, 1 sm error, the next for 2 sm and so on to maybe > to the 20th for the ones with a 20 sm error. > > Next he will put the entries into the appropriate buckets, i.e. each entry into the bucket that is labeled > with the error made by that entry. Of course, the whole thing is a histogram. > > My 2. question asks: what curve will the contents of the buckets follow when the buckets are lined up? > Actually: What might the curve "error *frequency* vs error *size* " look like? > > Note: that curve is just a 2D diagram, frequency (Y) vs size (X), not a 3D world with a surface of > frequency (Z) vs. lat (X), Long (Y). As you can see, the latter is the one we already considered in the prior question. > > One thing is clear from the beginning: the curve we are looking for will only have a positive X axis and a positive Y axis > simply because frequency and absolute size are both positive. > > Again: What curve, do you think, will the contents of the buckets follow? No math, just a rough sketch! > > Thank you for participating in this puzzle. > > h > > > > From: Gary LaPook > To: hannoix---net > Sent: Tuesday, March 12, 2013 9:06 PM > Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1 > > > > ________________________________ > Assuming no error in the true position announced by Tom Cruise (presumably from a GPS) the distribution should look like those in appendix Q of Bowditch. > > http://fer3.com/arc/imgx/HO-9-1977-Appendix-Q.pdf > > http://fer3.com/arc/imgx/Figure-Q6d_0001.pdf > > http://fer3.com/arc/img/114399.extended%20table%20q7d.pdf > > http://fer3.com/arc/m2.aspx/Accuracy-sextant-observations-sea-LaPook-nov-2010-g14399 > > If it is a two body fix with the LOPs crossing at 90° it should be a circle and if they cross at a different angle then it should be an > ellipse. > > The size of the ellipse (or circle) will be based on the average standard deviation of the observers. > > gl > > > --- On Tue, 3/12/13, Hanno Ix wrote: > > >> From: Hanno Ix >> Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1 >> To: garylapook---net >> Date: Tuesday, March 12, 2013, 1:52 AM >> >> >> >> ________________________________ >> John and Gary: >> >> >> May I ask you to embark with me on a mental cruise? >> >> >> Say FER has organized a navlist convention here in San Diego. The agenda includes one evening >> at sea on the carrier "Barak Obama" thanks to the Navy. The attendees have been asked to get their >> CelNav gear along. Together with 3000 other navigators we are going to find a fix somewhere 20 sm out. >> There will be a competition and prizes.The night is warm and clear. >> >> >> Shortly before dinner FER asks that everybody takes a fix of the "Barak Obama" at 7 pm local time. >> Before returning, he will present the results. >> >> >> My questions are now: >> >> >> 1.What kind of distribution of the fixes is found around the true location as announced by the First Officer, Tom Cruise? >> 2 .For the purpose of competition azimuth errors will disregarded, only the distance of the fixes to the true location will >> be considered. What will the distribution of these distances be? >> Of course, I have my own opinion but may I ask for yours? Even crude drawings would be appreciated. >> Regards >> h >> >> >> >> >> >> >> From: Gary LaPook h >> To: hannoix---net >> Sent: Tuesday, March 12, 2013 12:32 AM >> Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1 >> >> >> >> ________________________________ >> I posted the following in 2010: >> >> >> "We have been having a very interesting conversation about cocked hats > this month, which I have really appreciated. What I take from both John > Karl's and George Huxtable's postings is that a high percentage of the > time the actual position of the vessel will be outside the cocked hat > but, even so, any point within the triangle is a more probable location > for your vessel any point outside the triangle. (John Karl's diagrams > also show, that for some shapes, that a point slightly outside the > triangle may be slightly better than some of the points inside the > triangle.) But we have to remember that although a point within the > triangle may be the "most probable position" (and I think we have been > convinced that it is the Symmedian point) it is still not very probable. Although all the points within the triangle may have an > aggregate probability of 25% (or something slightly different) any > particular "point" you choose inside the triangle will have a very low > probability of being the actual position of the vessel. As an analogy, > for example, your ship is 100 feet long with a beam of 20 feet and the > triangle is a right equilateral triangle with legs one NM long. The area within the triangle is approximately 18,000,000 square feet and the > area occupied by your ship is only 2,000 square feet. This means that > there could be 9,000 ships of your size inside the triangle so (if all > points were equally probable) the odds are 8,999 to 1 that you have > chosen the wrong point for the fix. Even using the Symmedian point and > assuming that that point is twice as probable as any other point within > the triangle (which is a gross exaggeration as shown by John Karl's > curves) then the odds are still 4,499 to one that the vessel is actually at that point. John's curves show very slight variation in probability > for points within the triangle. >> >> So, as I said before, pick any point within the triangle you like, by > eyeball or by any construction you like, and use it for planning the > next leg of your voyage since there is very little likelihood that any > other point is any better than the point you have chosen, to represent > the actual position of your ship." >> >> http://fer3.com/arc/m2.aspx/old-cocked-hat-synthesis-LaPook-dec-2010-g14919 >> >> >> gl >> >> >> >> >> --- On Mon, 3/11/13, Hewitt Schlereth wrote: >> >> >>> From: Hewitt Schlereth >>> Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1 >>> To: garylapook---net >>> Date: Monday, March 11, 2013, 8:07 PM >>> >>> >>> >>> ________________________________ >>> >>> To me "'celestial is "the high art of the useful approximation." I think it's an art because of the big part played by judgement. Hewitt Sent from my iPad On Mar 11, 2013, at 7:12 PM, "Tom Sult" wrote: > Thanks. I will be interested in all of you math geeks duking it out. >> >> What it all mean to me is that CelNav is not a close quarters nav set. For that you need pilotage or in the modern era GPS. >> >> Tom Sult >> Sent from my iPhone >> >> On Mar 11, 2013, at 20:36, John Karl wrote: >> >>> >>> First, to Hanno Ix, I apologize for miss typing your name. I'm surprised that happened. >>> Second I'd like to get my attachment on the NavList, but 'am having trouble for some unknown reason. >>> I'm trying again on this post -- hopefully it will be found below. >>> >>> JK >>> ---------------------------------------------------------------- >>> 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 >>> ---------------------------------------------------------------- >>> >>> Attached File: >>> f1-Cocked-Hat-V2.pdf (no preview available) >>> >>> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122790 >> >> >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122792 >> >> >>> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122793 >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122803 >> >> >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122804 > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122823 > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122826 > >

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