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    Re: Silicon Sea : Leg 69
    From: Yves Arrouye
    Date: 2001 Apr 09, 18:55 EDT

    Hi,
    Here's my navigation. I have to thank Ed Falk for his sample leg
    (http://www.best.com/~falconer/Navigation/) which was a great help (the
    plotting sheets were nice, especially since my local West Marine didn't
    carry the real ones). I used as much of the online government calculators I
    could find, and included links to them. They're really nice. I'll do other
    legs using paper after I get the books :)
    > Chart(s): Plotting Sheet
    >
    > 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}
    > 12:30:01UT.
    > Our Speed has been 10.7 Kts, TC 288.9d Var 19dW. Dev 1.5dE.
    > Current Set
    > 285d
    > Drift 0.5Kts.
    Using a transverse table (http://pollux.nss.nima.mil/calc/traverse.html), we
    use:
    Course angle: 288d 54'
    Distance: 107 (10.7 * 10 hours, which includes an approximation for the
    current)
    and we find:
    Difference of latitude: 0d 34.66'
    Departure:                 101.23
    which gives us:
    Difference of longitude: 1d 43.1' (102.23 * cos 11)
    Our DR position is:
         1  11               1
        10d 27.9'N          52d 26.4'W
      +     34.7'         +  1d 43.1'
        ----------          ----------
        11d 02.6'N          54d 09.5'W
    We'll use an AP of 11d 00.0'N and 54d 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?
    > --  -------------------------
    Instead of a paper Almanac, I used the celestial navigation data from the
    U.S. Naval Observatory at http://aa.usno.navy.mil/ (then click on Data
    Service and then click on Celestial Navigation Data). This page gave me Hc
    and Zn directly, which I feel is cheating. Is there a page there that would
    give me just the almanac data?
    Star:        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
    +/- ie: -       2.5    -       2.5    -       2.5    -       2.5    -
    2.5
    -dip:   -       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
    +/- ro: -       1.8    -       1.1    -       3.6    -       3.5    -
    1.2
              ---------      ---------      ---------      ---------
    ---------
    Ho:         28 09.1        42 14.1        15 46.3        13 17.6        37
    49.5
    GHA:         109 29.3         9 51.2        86 01.4       130 33.5        46
    01.0
    Decl:   -   16 43.2    -   11  9.8    -   59 30.9         6 20.8        61
    45.3
              ---------      ---------      ---------      ---------
    ---------
    Hc:         28 32.3        40 51.1        14 56.3        14 21.1        38
    54.8
    Zn:           243.9          115.4          196.2          273.8
    4.8
    Int:         23.2 A
    Big intercepts! Wow. If I plot these, I end up near 10d 53'. Using this as a
    new AP, I get:
    Star:        Sirius          Spica          Avior      Bellatrix
    Dubhe
              ---------      ---------      ---------      ---------
    ---------
    Hc:         28 05.1        42 10.1        15 37.1        13 18.0        37
    59.6
    Zn:           244.8          115.1          196.7          274.2
    4.2
    Int:          4.0 T          4.0 T          9.2 T          0.6 A
    10.1 A
    Much better intercepts. The fix reads 9d 50'N 53d 00'W.
    > |2)  What is the TC and distance to Barbados(13d 10.0'N  59d 20.0'W)?
    > --  ----------------------------------------------------------------
    From 4mulas.txt (an attachment to
    http://www.i-DEADLINK-com/lists/navigation/9805/0001.html), part 1, mid-latitude
    sailing:
    Fix L1:           9 50.0'N          53 00.0'W
    Destination L2:  13 10.0'N            59 20.0'W
                     --------           ---------
    Diff.:            3 20.0'N           6 20.0'W
                   l = 200.0'N      DLo = 380.0'W
    1/2 l:    1 40.0'
    + L1:     9 50.0'
            ---------
    Lm:      11 30.0'
    1) p = DLo * cos Lm
         = 380 * cos 11 30.0'
         = 372.37 nm
    3) tan C = p / l
       tan C = 372.37 / 200 = 1.86
       C = 61.75 = 61 45.5'
    Thus the course is (360 - 61 45.5') = 298 degrees.
    2) DLo = p / cos Lm
           = 372.37 / cos 11 30.0'
           = 379 nm
    > |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}
    > 12:13:00ZT.
    >
    > 3)  What is the DR position?
    > --  ------------------------
    What is a good resource to convert from ZT to UT given one's lat/lon?
    > 4)  What day of the week is this?
    > --  -----------------------------
    According to my calendar, it's a Saturday..
    

       
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