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    Re: Multi-Moon line exercise in 2 parts
    From: Jeremy C
    Date: 2009 Aug 8, 09:56 EDT
    Hi Peter,
     
    I don't think there is a normal way of doing these, as they are not normally done.  Before computers and other rapid calculating devices, this process would take several hours, especially with this many LOP's to be reduced by tabular means.  Of course a slide rule would quicken the pace of reduction (I hope someone rises to that challenge) but after shooting for over half an hour, you have a lot of reduction to do.
     
    My methods were from the realm of sailors, meaning that I plugged 25 (the maximum number of LOP's my program accepts) into my navigation software and it then calculated all of the data and a subsequent fix.  I know next to nothing about statistics so they don't figure into my navigation techniques.  I will hold off a bit longer, but my fixes are different than the solutions thus presented, although the difference isn't substantial.
     
    I think that you caught a typo from my transcription of the data.  The second observation is way off base, and certainly outside of any error I would normally make while shooting.  I suspect that the Hs is actually 52-53.4 not 43.4.  That gives a MUCH closer intercept to the GPS position (0.3 Away) and should fit more into the data set.  I didn't catch it earlier since i didn't use that LOP for my fix determination.
     
    The real question, and debate, is whether these fixes that we are determining are within the acceptable margin of error for navigation; and to a lesser degree, is it worth the time and effort to do these sights.
     
    Jeremy
     
    In a message dated 8/8/2009 9:51:43 A.M. Central Asia Standard Time, pmh099@yahoo.com writes:
    Jeremy,

    I processed your away-from-transit data in the following manner:

    1) Using your 1800 DR position as the AP, I calculated the intercepts and azimuths for all 30 moonlines (see the attached file rapid_in.txt).

    2) I advanced or retarded all moonlines to UT = 09:00:00 = 1800L.

    3) I calculated running fixes using all possible pairs of LOP's.  From them I extracted average values of latitude and longitude and their standard deviations (see the attached program rapid.f90).

    The term "rapid-fire fix" I borrowed from Frank Reed, although I do not know whether this is the way it's normally done.

    This way I get for the 1800L fix:
    Latitude:     N   22 degrees 02.2'  ;  standard deviation =  13.3'
    Longitude:  E 130 degrees 14.6'  ;  standard deviation =  46.1'

    An important detail is that I obtained this result by disregarding the second measurement (at 8:54:46) because its intercept does not seem to "belong" among all the others (it is AWAY, while all others are TOWARD).  If I do include this outlier, the results get worse:

    Latitude:      N   21 degrees 58.0'  ;  standard deviation =  39.7'
    Longitude:  E 130 degrees 01.7'  ;  standard deviation = 110.5' (almost 2 degrees...)


    Peter Hakel



    From: "Anabasis75@aol.com" <Anabasis75@aol.com>
    To: NavList@fer3.com
    Sent: Tuesday, August 4, 2009 8:33:54 PM
    Subject: [NavList 9359] Multi-Moon line exercise in 2 parts

    I figured that I need to give some LOP data to reduce with all of these people building and using their Bygrave's slide rules, and to stir the pot a bit on the list.  So in order to kill two birds with one stone, I offer the attached Excel spreadsheet.  Lying therein are a plethora of upper limb moon LOP's which should allow eager navigators to fix the position of my ship.  There are a few features of particular note that should appeal to certain members of the list.
     
    1)  The given DR is a real DR tracked from the AM star fix some 14 hours earlier
    2) The moon is fairly close to the celestial equator (please note the LARGE hourly change in declination)
    3) The ship's track is at a fair clip and nearly Southerly.
     
    These should be considered fairly extreme conditions to work out the Latitude and Longitude of the ship; the first position from many LOP's away from upper transit, and then again around the time of transit.
     
    I will be most appreciative if people who solve the transit portion graphically can post an image or file of their curve and to see what the  1900L fixes is. (ZD -9)
     
    I offer the following challenges:
    1) what would you calculate the local zone time of transit to be?
    2) what was the 1800L fix?
    3) what was the 1900L fix?
    4) what was the actual local zone time of transit by observation?
    5) most critically, how much faith would you put in these fixes?
     
    I will post the actual GPS fixes and my celestial solutions for both times at a later time.
     
    Have fun!
     
    Jeremy



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