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    Re: The Darn Old Cocked Hat - the sequel 1
    From: Hanno Ix
    Date: 2013 Mar 12, 23:44 -0700

    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.


    From: Gary LaPook <garylapook---.net>
    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.





    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.


    --- On Tue, 3/12/13, Hanno Ix <hannoix---net> wrote:

    From: Hanno Ix <hannoix---net>
    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.

    From: Gary LaPook <garylapook---net>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."



    --- On Mon, 3/11/13, Hewitt Schlereth <hhew36---com> wrote:

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

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