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    Re: Silicon Sea: Leg 79
    From: Bill Noyce
    Date: 2001 Sep 28, 8:31 AM

    I finally got some time to work on Silicon Sea.
    Here are my answers to Leg 79.
    
    > Our last FIX position was (03d 00.00'N  082d 00.0'W) {at} 10:51:11UT {at}
    > 26/06/2001. We are sailing toward MOP1(03d 00.0'N  110d 00.0'W) where
    > we will turn and head for Hawaii.
    >
    > At a Log distance traveled of 710.5 Nmi from the FIX position. TC
    270.0d,
    > Speed 10.0 Kts, we determine that we have entered the Equatorial
    Counter
    > Current.
    >
    > 1)  What is the DR position on entering the Equatorial Counter
    Current?
    > --
    -------------------------------------------------------------------
    
    A sliderule should provide enough accuracy to do these
    time/distance/course problems.  My sliderule says cos(3d)
    is essentially equal to 1.0, so with the course due west,
    this one is simple enough to do in one's head.
    
    departure = 710.5 mi W
    dLon = 710.5' W = 11d 50.5' W
    DR Lon = 93d 50.5' W   DR Lat = 3d 0.0' N
    
    Using a log-cosine table, 710.5/cos(3d) = 711,
    which would make our DR Lon = 93d 51' W -- certainly
    not a significant difference over such a distance.
    
    You didn't ask, but the info given suggests the time should
    be 71.05 hours (71h03m) giving 29 June 2001 09:48:11 UT.
    
    > On the morning of 30/06/2001 we manage the following sights:
    >
    >         Body            UT/GMT          Hs
    >
    >         Fomalhaut       11:53:00        54d 01.8'
    >         Deneb           11:55:10        30d 03.8'
    >         Altair          11:57:20        27d 35.1'
    >         Saturn          11:59:05        23d 17.4'
    >         Venus           12:04:11        38d 50.8'
    >
    > 2)  What is the DR position at the time of the Fomalhaut sight?
    > --  -----------------------------------------------------------
    
         30d 11h 53m 00s
       - 26d 10h 51m 11s
       -----------------
          4d  1h  1m 49s  = 97.03 hours, or 970.3 miles
    
    Taking cos(3d)=1.0, this gives
    dLon = departure = 970.3' W = 16d 10.3' W
    DR Lon = 98d 10.3' W   DR Lat = 3d 0.0' N
    
    More careful calculation puts us 0.6' further west - negligible.
    
    > 3)  What is the position FIX?
    > --  -------------------------
    
    Using aLat = 3d 0' N, aLon = 98d 10' W
    
    Body  Fomalhaut      Deneb       Altair       Saturn       Venus
    GHA  112d 26.1'   147d  2.4'   160d 14.4'    30d 56.3'   46d 54.5'
    decl  29d 36.8'S   45d 12.0'N    8d 52.2'N   20d  7.0'N  16d 11.4'N
    Hc    54d 38.2'    30d  0.1'    28d  6.5'    22d 22.9'   37d 55.9'
    Int       42.6'A        3.5'A       38.7'A       46.9'T      48.1'T
    Az       201.7d       322.3d       278.2d       069.2d      071.7d
    
    This plots out to a sloppy intersection near
    FIX = 3d 28' N  97d 18' W
    
    When I do these, I ignore any distance the boat has moved between
    the fixes.  Here it's about 2 miles due west.  Looking at my plot,
    it doesn't seem it would be improved by moving the earlier LOP's
    westward.  The two planet lines that are a mile apart now on the
    same azimuth would move further apart.  If I had made the sights,
    I'd be happy to have two disagree by only about a minute, but I
    wonder if Dan's initial data was better than that -- perhaps I've
    made a calculation error.  (I certainly found and fixed quite a
    few in getting this far!)
    
    
    > TC 270.0d, Speed 10.0 Kts, Current Drift 1.0 Kts, Set 280.0d. Var
    2.0dE,
    > Dev 1.5dE.
    >
    > 4)  What is the Compass Course(CC)/Course-to-Steer to MOP1(03d 00.0'N
    >     110d 00.0'W) from the FIX position?
    > --  -----------------------------------------------------------------
    
    From    3d 28' N         97d 18' W
    To      3d  0' N        110d 00' W
           ----------------------------
        dLat = 28' S  dLon = 12d 42' W = 762' W
    
    Taking departure = dLon, and using a rule of thumb that
    sin(x degrees) = tan(x degrees) = x/60 for small angles,
    our true course is 60*28/762 = 2.2 degrees south of due west.
    The current sets us 1.0*sin(7.8d)=.13nm to the left each hour,
    during which we travel 11 miles, so we need to adjust course
    to the right 60*.13/11 = 0.7 degrees.  Adding it all up,
    CCTS = TC + current + var + dev
    CCTS = 270 - 2.2 + 0.7 - 2.0 - 1.5 = 265d
    
    More careful calculation with log tables gives CCTS = 265.2d
    
    > 5)  What is the distance to MOP1(03d 00.0'N  110d 00.0'W)?
    > --  ------------------------------------------------------
    
    With such a small deviation, and our low latitude, distance
    is essentially equal to dLon: 762 miles.  More careful
    calculation gives 761.5 mi.
    
    > With all times rounded to the nearest whole minute.
    >
    > 6)  What is the UT day and date of our ETA at MOP1?
    >     What is the Zone Time(ZT) and date of our ETA at MOP1?
    > --  ------------------------------------------------------
    
    Dist = 761.5 mi, Speed over Ground = 11.0 kts, time = 69.32 hrs
    
    FIX time 30 June 11:53:00 UT
    Add       2 days 21:19
             -------------------
              3 July 09:12 UT
                3 July 02:12 ZT
    
    OK, looking at the answers, it appears my fix is about 12 miles
    to far east.  Can you see what I did wrong?  The errors in
    distance and ETA probably follow directly from the bad fix, but
    I can't explain the difference in CCTS that way.
    

       
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