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    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
    > 
    > 
    
    View and reply to this message: http://fer3.com/arc/m2.aspx?i=122837


       
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