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    Re: Silicon Sea: Leg 72 -NEW
    From: Michael Wescott
    Date: 2001 May 26, 13:43 EDT

    > Sight Reduction and                Revised
    > Dead-Reckoning problem     Leg 72  052301   Test your knowledge!
    > ----------------------     ------  ------   --------------------
    >
    > Our Last position FIX was (13d 00.0'N  61d 30.1'W) at 08:50:10UT on
    > 30/05/2001. We are bound for a point on chart INT 401 marked as Aruba Gap
    > (13d 50.0'N 70d 00.0'W). Aruba Gap provides a favorable westerly current of
    > 1.5 Knts.
    >
    > We have had overcast skys and have missed some possible sights. The winds
    > have been fluky and we have had to tack several times since our last FIX
    > position.
    >
    >     Tack 1: CC 333.0d - 04Hrs {at}XXX.XXX5 Kts - Var 12dW Dev 1dE
    >     Tack 2: CC 242.0d - 11Hrs {at}XXX.XXX5dE
    >     Tack 3: CC 262.0d - 08Hrs {at}XXX.XXX5dE
    >     Tack 4: CC 307.0d - 10Hrs {at}XXX.XXX0dE
    >
    > 1)  What is the DR position at the end of the Tack 4?
    > --  -------------------------------------------------
              TC     Dist   D.Lat  dep
    Tack 1: 319.0    30.0   22.6  -19.7
    Tack 2: 231.5    93.5  -58.2  -73.2
    Tack 3: 252.5    40.0  -12.0  -38.1
    Tack 4: 297.0    90.0   40.9  -80.2
                          =============
                            -6.7 -211.2
    D.Lo = -211.2/cos 13.4 = -216.8 = 3d 36.8'
    DR Position =  12d 53.3'N   65d 06.9W
    > 2)  What is the DR position local Zone Time(ZT) and Date?
    >     What is the DR position GMT/UT time and Date?
    > --  -----------------------------------------------------
    4 + 11 + 8 + 10 = 30hrs = 1d 6h
    DR UT = 17:50:10 31/05/2001
    DR ZT = 13:50:10 31/05/2001
    > 3)  From the DR position, what is the TC to Aruba Gap
    >     (13d 50.0'N  70d 00.0'W)?
    > --  -------------------------------------------------
    D.Lat =  13d 50.0 -  12d 53.3 = 56.7
    D.Lo  = -70d 00.0 - -65d 06.9 =  4d 53.1 = 293.1'
    dep   = 293.1 * cos 13d 20 = 285.2
    TC = 270 + atan(56.7/285.2) = 281.2d
    > Our speed is 8.5 Kts, Var 10dW Dev 1.0dE. Current Drift 0.7 Kts Set 265.0d
    >
    > 4)  What is the Compass Course(CC)/Course-to-Steer for Aruba Gap
    >     from the DR position?
    > --  ------------------------------------------------------------
    CC = 281.2d + 10 - 1.0 = 290.2d
    correction for current (by simple plot) adds a fraction more than
    one degree: CC = 291.5 and gives a speed over ground of about 9.0
    > The following morning the navigator see stars through breaks in the
    > clouds. He takes the following sights. Same data as for Q3 & Q4.
    >
    >     Body        ZT              Hs
    >
    >     UNKNOWN     05:39:00        13d 53.6' (Bearing 349.7 M)
    >     Mars        05:39:11        18d 14.5'
    >     UNKNOWN     05:40:03        54d 58.9' (Bearing 327.3 M)
    >     Vega        05:41:06        40d 10.3'
    >     Venus       05:43:33        35d 25.8'
    >
    > 5)  What is the FIX position?
    > --  -------------------------
    9 knots {at} 281 for 16 hrs gives AP of about 13d 20'N  67d 30W
    Plotting the sights gives us a crossings all in the vicinty of 67d 00'W
    and 13d 30'N. A correction of 1.0' T gives a very small set of crossings
    at
     13d 30.5'N  66d 59.5'W
    Was the IC really -1.5' rather than the -2.5' given?
    > 6)  What are the names of the two unknown bodies?
    > --  ---------------------------------------------
    Unknown #1:
    349.7 + 10 - 1 = 358.7d
    almost due north and altitude is about same as our latitude:
    got to be Polaris
    Unknown #2:
    327.3 + 10 - 1 = 336.3
    This is visually in the angle between Polaris to the north and Vega
    to the northwest.  GHA Aries is about 34d and Long is 67W so zenith
    has SHA of about 33d. Looking at the starchart in the almanac, there
    is only one navigational star between Vega and Polaris: Deneb
    > 7)  What is the TC and Distance to the Aruba Gap (13d 50.0'N  70d 00.0'W)
    >     waypoint from our FIX?
    > --  ---------------------------------------------------------------------
    dLat = 13d50.0' - 13d30.5' = 19.5'
    dLo  = 70d00.0 - 66d59.5' = 180.5'
    dep = 180.5*cos 13d40' = 175.4
    TC = 270 + atan(19.5/175.4) = 276.3
    Dist = sqrt(19.5^2 + 175.4^2) = 176.5
    <PRE>
    --
            Mike Wescott
            Wescott_Mike{at}XXX.XXX
    </PRE>
    

       
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