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    Re: The Darn Old Cocked Hat - the sequel 1
    From: Hanno Ix
    Date: 2013 Mar 13, 14:13 -0700
    If you have some time please read the 1 page of my memo -  1 page only!

    h


    From: Hewitt Schlereth <hhew36---.com>
    To: hannoix---.net
    Sent: Wednesday, March 13, 2013 9:45 AM
    Subject: [NavList] Re: The Darn Old Cocked Hat - the sequel 1


    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
    > 
    > 
    
    View and reply to this message: http://fer3.com/arc/m2.aspx?i=122843


       
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