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    Re: Silicon Sea : Leg 69
    From: Michael Wescott
    Date: 2001 Apr 09, 11:43 EDT

    I tried sending this once before but it seems to have gotten lost ...
    Well this one has me stumped. I'm either missing something, or I'm
    so rusty that I'm a danger to myself and others should I get on my
    boat anytime soon.
    >
    > Dead-Reckoning problem     Leg 69  040401   Test your knowledge!
    > ----------------------     ------  ------   --------------------
    >
    > The last DR position was(10d 27.9'N 52d 26.4'W) on 18/05/2000
    > {at}XXX.XXX Dev
    > 1.5dE. Current Set 285d Drift 0.5Kts.
    Figure roughly 10hrs {at}XXX.XXX Using traverse tables
    for 289 d we get
    D.Lat =  34.8
    Dep   = 101.2
    D.Lo ~= 101.2 / cos 11 = 103.1
            10  27.9N       52  26.4W
                34.8           103.1
            =========       =========
            11  02.7N       54  09.5W
    Using A.P. of 11 00.0 N  and  54 00.0 W.
    > On that evening we take the following sights:
    >
    >         Body            UT                  Hs
    >
    >         Sirius          22:15:30            28d 16.3'
    >         Spica           22:17:02            42d 20.6'
    >         Avior           22:19:00            15d 55.3'
    >         Bellatrix       22:19:45            13d 26.5
    >         Dubhe           22:20:12            37d 56.1'
    > 1)  What is our FIX position?
    > --  -------------------------
    Using AP 11N 54W:
                 Sirius       Spica     Avior     Bellatrix   Dubhe
    UT          22:15:30    22:17:02   22:19:00    22:19:45  22:20:12
    Hs           28 16.3     42 20.6    15 55.3     13 26.5   37 56.1
    IC              -2.5        -2.5       -2.5        -2.5      -2.5
    Dip (9')        -2.9        -2.9       -2.9        -2.9      -2.9
    ========    ========    ========   ========    ========  ========
    Ha           28 10.9     42 15.2    15 49.9     13 21.1   37 50.7
    R               -1.8        -1.1      -3.4         -4.0      -1.2
    =======     ========    ========   ========    ========  ========
    Ho           28 09.1     42 14.1    15 46.5     13 17.1   37 50.7
    GHA-A(:00)  206 53.2    206 53.2   206 53.2    206 53.2  206 53.2
    GHA-A(inc)    3 53.1      4 16.2     4 45.8      4 57.1    5 03.8
    SHA         258 43.0    158 41.8   234 22.5    278 43.3  194 04.0
    Long        -54 00.0    -54 00.0   -54 00.0    -54 00.0  -54 00.0
    ==========  ========    ========   ========    ========  ========
    GHA-star    415 29.3    315 51.2   392 01.5    436 33.6  352 01.0
    Lat          11 00.0     11 00.0    11 00.0     11 00.0   11 00.0
    Dec         -16 43.2    -11 09.8   -59 30.9      6 20.8   61 45.3
    Hc           28 32.3     40 51.1    14 56.3     14 21.0   38 54.8
    Z              243.9       115.4      196.2       173.8     004.8
    Delta(dir)    23.2 A      83.0 T     50.2 T      64.0 A    65.3 A
    Plotting these gives a fix near 10 00.0 N and 53 00.0W. Reducing sights
    again with A.P. of 10 N and 53 W:
    GHA-star    416 29.3    316 51.2   393 01.5    437 33.6  353 01.0
    Lat          10 00.0     10 00.0    10 00.0     10 00.0   10 00.0
    Dec         -16 43.2    -11 09.8   -59 30.9      6 20.8   61 45.3
    Hc           28 05.1     42 10.1    15 37.1     13 18.0   37 59.6
    Z              244.8       115.1      196.7       274.2     004.2
    Delta          4.0 T       4.0 T      9.4 T       0.9 A    10.1 A
    Plotting these gives a good fix at about 9d 50.5'N  53d 00.0' W
    This is a bit far off course. What did I get wrong?
    Every thing gets further askew from here on...
    > 2)  What is the TC and distance to Barbados(13d 10.0'N  59d 20.0'W)?
    > --  ----------------------------------------------------------------
    Hmmm ... isn't that a few miles east of Barbados?
    Barbados  13 10.0            59 20.0
    Fix      - 9 50.5          - 53 00.0
             ========           ========
     D.Lat =   3 19.5     D.Lo =  6 20.0
           =    199.5'         =   380.0'
    dmp = mp(13d 10.0') - mp(9d 50.5')
        = 202.3
    TC = 270 + arctan(202.3/380.0)
       = 270 + 28
       = 298d
    Dist = 199.5/sin 28
         = 424.5
    > We continue sailing maintaining the same speed and True Course with an
    > overcast sky. Then, with the navigator on deck waiting for an opening
    > for a Sun shot, we see a spot of land on the horizon ahead. It is
    > 20/05/2000 {at}XXX.XXX
    > 3)  What is the DR position?
    > --  ------------------------
    S = 10.7 C = 288.9 T,
      20/05/2000 12:13:00 ZT = 20/05/2000 16:13:00 UT
                              -18/05/2000 22:20:00 UT
                             ========================
                                1 day     17:53:00
    or 41.88 hrs
    Dist = 41.88 * 10.7 = 448.1 nmi
    D.Lat = 448.1 * cos 288.7 = 145.2 = 2d 25.2'
    DR Lat = 9d 50.5' + 2d 25.2' = 12d 15.7'
     dmp = mp(12d 15.7') - mp(9d 50.5')
         = 147.0
    D.Lo = 147.0 * tan(288.9)
         = -429.4
         = -7d 09.4
    DR Lo = -53d  00.0 - 7d 09.4'
          = -60d 09.4
    DR  12d 15.7'N    60d 09.4'W
    Actually this is too far off to make any sense.
    We seem to be well past Barbados.
    > 4)  What day of the week is this?
    > --  -----------------------------
    >From the almanac -- Saturday.
    This I'm (almost) sure I have right :-)
    <PRE>
    --
            Mike Wescott
            wescott{at}XXX.XXX
    </PRE>
    

       
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