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    Re: errors in plotting and a possible/partial fix thereof, as menti...
    From: Gary LaPook
    Date: 2010 Dec 29, 12:36 -0800
    Jeremy,

    If you want the most precision in advancing the LOPs mathematically then you can compute the Motion Of the Observer (MOO) correction on your calculator. First you calculate the relative bearing to the star by subtracting course (or "track" in flight practice) from the azimuth of the body. The table I posted:

    http://fer3.com/arc/img/114591.moo-rev.pdf

    limits the relative bearing to the range of 0 to 180, from straight ahead to straight behind on either side of the vessel but, when using a calculator, you can use any relative bearing from +360 to - 360 since the calculator will come up with the correct sign for the cosine so the result will have the correct sign for applying the correction to the Ho. So to calculate relative bearing just subtract course from azimuth:   RB=Zn - C.

    Then you take the cosine of the RB and multiply by the speed in knots (which would give you the correction for a one hour time period,) divide by 60 to find the correction per minute and then multiply by the time you are advancing the LOP, the number of minutes and fractions of a minute. (If you want to work with seconds of time, divide the speed by 3600 and then multiply by the number of seconds to advance the LOP.)

    So the complete formula to find the correction in minutes of arc is:

     MOO = cos (Zn - C) * speed /60 * time.

    gl


    --- On Wed, 12/29/10, Gary LaPook <glapook---.net> wrote:

    From: Gary LaPook <glapook---.net>
    Subject: [NavList] Re: errors in plotting and a possible/partial fix thereof, as menti...
    To: NavList@fer3.com
    Date: Wednesday, December 29, 2010, 11:40 AM

    If you are looking at my explanation of the use of the MOO table that I posted here

    http://fer3.com/arc/m2.aspx?y=200807&i=105937

    remember that I my explanation the sign of the correction, a minus for bodies ahead and a plus for bodies behind, are for corrections to be applied to the Hc not to the Ho. In aviation you precompute the Hc and then adjust it for MOO and motion of the body and you also apply refraction to the Hc with the sign reversed to arrive at Hp, precomputed altitude. Since you use the marine practice of making adjustments to the Ho you should use the signs in the MOO table in H.O. 249, plus for bodies ahead and minus for bodies behind, These are also the signs I used in the tables that I computed and posted.

    gl



    --- On Wed, 12/29/10, Gary LaPook <glapook---.net> wrote:

    From: Gary LaPook <glapook---.net>
    Subject: [NavList] Re: errors in plotting and a possible/partial fix thereof, as menti...
    To: NavList@fer3.com
    Date: Wednesday, December 29, 2010, 11:14 AM

    Jeremy wrote:


    "If I am using the GPS fix as the AP, I first have to advance and retard each of the stars along the track line. The trouble then becomes that I have such small intercepts it is difficult to mark them accurately (my normal dividers leave a 2mm gap between points). My other dividers have much larger points which are also not as accurate. Then I have to spin the triangles from the azimuth to the LOP angles and i always get a bit of error trying to get the exact distance from the AP. Do this over 5 stars and so, and the error just starts to compound."

    --------------------------------------------------------------------


    Jeremy, look at my prior posts on mathematically advancing LOPs. In addition to the tables I posted you can also use the Motion Of the Observer table in HO 249, just divide the speeds by one hundred and the corrections by one hundred. For eighteen knots just double the 9 (900) knot correction. The table I posted goes up to 15 knots but you can calculate the values for higher speeds and make you own table.
    ------------------------------------------------------------------------------------------------------


    http://www.fer3.com/arc/m2.aspx?i=114591&y=201012


    15 knot table

    http://fer3.com/arc/img/114591.moo-rev.pdf

    -----------------------------------------------------------------------------


    http://www.fer3.com/arc/m2.aspx?i=114523&y=201011
    http://www.fer3.com/arc/m2.aspx?i=114867
    ------------------------------------------------------------------

    Five minute table for eighteen knots:

    http://fer3.com/arc/img/114867.moo%2018-5.pdf
    -----------------------------------------------------------------------------
    http://fer3.com/arc/m2.aspx?y=200807&i=105937

    http://fer3.com/arc/m2.aspx?i=111994

    http://fer3.com/arc/img/111994.moo.pdf

    http://www.fer3.com/arc/m2.aspx?i=114568&y=201011

    gl
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