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    Re: Silicon Sea: Leg 71
    From: Michael Wescott
    Date: 2001 May 12, 14:24 EDT

    > Sight Reduction and
    > Dead-Reckoning problem     Leg 71  050801   Test your knowledge!
    > ----------------------     ------  ------   --------------------
    > At 18:27:00ZT {at}XXX.XXX6'N
    > 61d 30.1'W) as we passed between the Lessor Antilles islands of St, Lucia and
    > St. Vincent. We are bound for, Mid Ocean Point(MOP1)(12d 30.0'N  70d 00.0'W),
    > in water of more than 1000 mtrs North of Aruba. This is to avoid unfavorable
    > currents along the coast.
    > Dev 1.5dE, Var 12dW. Speed is 8.7 Kts, Current Drift 0.7Kts, Set 270.0d.
    > TC 263.7d.
    > 1)  At the log reading of 89.6Nmi, what is the DR position?
    > --  -------------------------------------------------------
    Using mid-Latitude computation (since Lat is low and course is almost
    due west, error due to choice of middle latitude is low as well).
    dLat = 89.6 * cos 263.7 = -9.8
    dLo = (89.6 * sin 263.7)/cos 13d 20.0 = -91.5
    Lat = 13d 25.6'N - 09.8 =    13d 15.8N
    Lon = -61d 30.1' - 91.5 =    63d 01.6W
    > 2)  At the DR position what is the celestial phenomena that is starting
    >     at this DR Zone Time(ZT)?
    > --  -------------------------------------------------------------------
    Time enroute = 89.6/8.7 = 10h 18m
    ZT = 18:27:00 + 10:18:00 = 04:45:00 30/05/2001
    Nautical Twilight.
    > NOTE: Sextant Index correction is on the arc 1.5d.
    > We then take the following sights:
    >     Body        UT          Hs
    >     Fomalhaut   08:50:10    40d 54.7'
    >     Polaris     08:50:55    13d 17.3'
    >     Deneb       08:51:05    56d 56.3'
    >     Mars        08:52:03    25d 35.0'
    >     Venus       08:53:22    28d 13.8'
    >     Vega        08:53:45    45d 55.6'
    > 3)  What is the FIX position?
    > --  -------------------------
    Polaris is almost due north, and Venus due east. From the Polaris table in
    the back of the almanac we find a Lat of 13d 01.5'N given an AP of 13d 15.8N
    and 63d 01.6'W. For Venus we get:
    UTC      08:53:22
    Hs        28 13.8
    Ic           -1.5
    Dip          -2.9
            =========
    Ha        28 09.4
    R            -1.8
    Add Cor       0.2
            =========
    Ho        28 07.8
    GHA-hr   345 25.3
    GHA-ms    13 20.5
    v             0.3
    AP-Lon   -63 01.6
            =========
    LHA      295 44.5
    Dec-hr     7 16.5
    d             0.5
             ========
    Dec        7 17.0
    AP-Lat    13 15.8
    Hc        26 38.5
    Delta        89.3 T
    Z            88.4
    Inspection shows that a closer AP would be about 90 nmi to the east:
            13d 00.0N    61d 30.0'W
    Working the sights based on new AP:
            Fomalhaut    Polaris     Deneb      Mars      Venus      Vega
    UTC      08:50:10   08:50:55   08:51:05   08:52:03   08:53:22   08:53:45
    Hs        40 54.7    13 17.3    56 56.3    25 35.0    28 13.8    45 55.6
    Ic           -1.5       -1.5       -1.5       -1.5       -1.5       -1.5
    Dip          -2.9       -2.9       -2.9       -2.9       -2.9       -2.9
            =========   ========   ========   ========   ========   ========
    Ha        40 50.3    13 12.9    56 51.9    25 30.6    28 09.4    45 51.2
    R            -1.1       -4.1       -0.6       -2.0       -1.8       -0.9
    Add Cor                                        0.3        0.2
            =========   ========   ========   ========   ========   ========
    Ho        40 49.2    13 08.8    56 51.3    25 28.9    28 07.8    45 50.3
    GHA-hr     7 54.0     7 54.0     7 54.0   101 22.5   345 25.3     7 54.0
    GHA-ms    12 34.6    12 45.8    12 48.3    13 00.8    13 20.5    13 28.5
    v                                              2.7        0.3
    SHA       15 34.4               49 37.7                          80 45.0
    AP-Lon   -61 30.0   -61 30.0   -61 30.0   -61 30.0   -61 30.0   -61 30.0
            =========   ========   ========   ========   ========   ========
    LHA      334 33.0   319 09.8     8 50.0    52 56.0   297 16.1    40 37.5
    Dec-hr   -29 36.9               45 16.8   -25 47.4     7 16.5    38 47.0
    d                                            - 0.1        0.5
            =========   ========   ========   ========   ========   ========
    Dec      -29 36.9               45 16.8   -25 47.5     7 17.0    38 47.0
    AP-Lat    13 00.0               13 00.0    13 00.0    13 00.0    13 00.0
    Hc        40 49.6    13 00.3*   56 51.5    25 31.5    28 07.2    45 50.3
    Delta          .4 A                  .2 A      2.6 A       .6 T      0.0
    Z           150.4                 348.6      232.8       88.6      313.2
    *Lat from polaris table
    Plotting this out gives a fix  13d 00.3 N  61d 29.4 W  09:00:00 30/05/2001
    > The navigator has been examining nautical chart INT 400. It shows an area
    > labeled the Aruba Gap (13d 50.0'N  70d 00.0'W) with a favorable current of
    > 1.15 Kts. He decides to make for this waypoint. Var 12dW, Dev 1dE.
    > Current Set 275d Drift 0.8 Kts. Speed 9.3 Kts.
    > 4)   What is the TC and Dist from our FIX to the Aruba Gap
    >      (13d 50.0'N  70d 00.0'W)
    > --  ------------------------------------------------------
    dLo = -70d 00.0 - -61d 29.4 = -510.6'
    dLat = 13d 50.0 - 13d 00.3 = 49.7'
    dep = 510.6 * cos 13d 25' = 496.7
    TC = atan2(-496.7, 49.7) = 275.7
    Dist = sqrt(49.7^2 + 496.7^2) = 499.2 nmi
    TC = 275.7   D = 499.2
    with current directly behind us there's no need to adjust for drift
    > 5)  What is the Compass Course(CC)/Course-to-Steer for Aruba Gap?
    > --  -------------------------------------------------------------
    CC = 275.7 + 12 - 1 = 286.7
    > 6)  What is the time enroute to Aruba Gap?
    > --  --------------------------------------
    T = D/S = 499.2/(9.3 + 0.8) = 499.2/10.1 = 49.5 hr
    > 7)  What is the anticipated Speed Made Good(SMG) to Aruba Gap?
    > --  ----------------------------------------------------------
    Speed is 9.3 with drift 0.8 in the same direction so SMG = 9.3 + 0.8
    or 10.1 knots
    

       
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