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    Re: Silicon Sea: Leg 73
    From: Michael Wescott
    Date: 2001 Jun 07, 11:05 PM

    > We are bound for a waypoint North of Aruba called Aruba Gap(13d 50.0'N
    > 70d 00.0'W).Our last position FIX was (13d 30.0'N 67d 00.0'W) 01/06/2001
    > {at} 09:39:00UT. Speed 9.5 Kts Var 10dW Dev 1dE. Current Drift 0.7 Kts,
    > Set 275.0d.
    >
    > 1)  What is the Compass Course/Course-to-Steer for Aruba Gap(13d 50.0'N
    >     70d 00.0'W)?
    > --  -------------------------------------------------------------------
    
    dLat = 13d 50.0'' - 13d 30.0' = 20.0
    dLo = 70d 00.0' - 67d 00.0 = 180.0'
    
    Since we're in low latitudes and going almost due west, error in choice
    of mid-latitude gives rise to very small error in calculations.
    
    dep = 180.0 * cos 13d 40.0' = 174.9
    TC = 270 + atan 20.0/174.9 = 276.5
    CC = TC + 10 - 1 = 285.5
    
    With the current going almost exactly our way, there's no point in
    correcting CC for current.
    
    > At 14:30:22UT the same day. We take an Sight of the SUN LL. Hs 60d 54.0'.
    > Speed 9.5 Kts, TC 276.5d.
    >
    > 2)  What is the DR position at the time of the 14:30:22UT sight?
    > --  ------------------------------------------------------------
    dT = 14:30 - 09:39 = 04:51
    Dist = 9.5 * 4.85 = 46.1
    dLat = 46.1 * sin 6.5 = 5.2
    Dep = 46.1 * cos 6.5 = 45.8
    dLo = 45.8 / cos 13.5 = 47.1
    
    DR = 13d 25.2'N  67d 47.1'W
    
    > We continue sailing and prepare for a Noon sight which according to the
    > Nautical Almanac occurs at 11:58:00LMT.
    >
    > 3) What is the estimated Zone Time(ZT) of our Local Meridian Passage?
    >    Only required to the nearest whole minute.
    > -- -------------------------------------------------------------------
    We are near the Eastern edge of the zone GMT-5, therefore LAN is going
    to be about 11:30 ZT or 16:30 UT or 2 more hours of sailing. At 9.5
    knots this will put us just to the west of 68W or 7d E of the center
    of the zone. LAN should be 7/15 * 60 = 28 minutes sooner.
    
    11:30 GMT-5
    
    > Ten minutes before LAN we are on deck and prepare for a Noon Sight.
    > SUN LL Hs 81d 16.3'.
    >
    > 4)  What is the Noon latitude?
    > --  --------------------------
    Hs = 81d 16.3'
    Ic =     -2.5
    Dip =    -2.9
    =================
    Ha = 81d 10.9'
    Main =  +15.8'
    ================
    Ho = 81d 26.7
    
    Since the Sun's Declination is > Lat, Lat = Dec - 90 + Ho.
    Lat = 13d 34.2N
    
    > Using the morning Sun sight at 09:30:22ZT and the Noon LAN work a
    > RunningFIX(RFIX) to the Noon sight.
    >
    > 5) What is the Running FIX(RFIX) position?
    > -- ---------------------------------------
    
    Plotting a 2 hour run {at} 9.5 + 0.7 = 10.2 knots gives RFIX of:
    
    13d 34.2N    67d35.0W
    
    > Speed 9.5Kts, Var 9dW, Dev 1.0dE. Current Set 270.0d Drift 1.0Kts.
    >
    > 6) What is the Estimated Zone Time of Arrival(ETA) at Aruba Gap
    >    (13d 50.0'N  70d 00.0'W):
    >    ZT time and date?
    >    UT time and date?
    > -- ------------------------------------------------------------
    
    >From plotting sheet, estimated distance is about 140 nmi.
    SOG is 9.5 + 1.0 = 10.5 knots
    Time elapsed is 13h20m
    
    UTC = 16:30 + 13:20 = 29:50
        = 0550 2/6/2001
    
    ZT  = 0050 2/6/2001 (GMT-5)
    
    > We will change our heading when the elapsed time and distance on the
    > Knotmeter log indicate that we are at the Aruba Gap(13d 50.0'N 70d 00.0'W)
    > waypoint.
    >
    > 7)  What is the TC, Compass Course(CC)/Course-to-Steer, and distance from
    >     the RFIX to Aruba Gap?
    > --  ----------------------------------------------------------------------
    
    Again estimating from plotting sheet
    
    TC = 276.5
    Dist = 140nmi
    CC = 276.5 + 9 - 1 = 284.5d
    
    --
            Mike Wescott
            Wescott_Mike{at}EMC.COM
    

       
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