# 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:**Hewitt Schlereth

**Date:**2013 Mar 13, 10:36 -0700

Ah. More like the positive side of a tangent curve, then? Hewitt Sent from my iPad On Mar 13, 2013, at 10:14 AM, "Brad Morris"wrote: > correct Hanno, but then you *must* consider azimuth. > On Mar 13, 2013 12:56 PM, "Hanno Ix" wrote: > >> ------------------------------ >> 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 >> *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 >>> >>> >> >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122837 >> >> >> View and reply to this message: http://fer3.com/arc/m2.aspx?i=122839 >> > > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122840 > >