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    Re: Silicon Sea: Leg 77 Rev 08/13/2001
    From: Michael Wescott
    Date: 2001 Aug 19, 2:02 PM

    Does no one else wish to publish their results?
    > Promptly at Sunrise on 24/06/2001 we raise anchor at Isl Flamenco
    > (08d 55.2'N  79d 31.6'W) and head for our departure point at Isla
    > San Jose Light(08d 10.5'N  79d 15.0'W) motoring.
    > Speed = SQRT LWL x 1.34
    > 1)  What is the Zone Time (ZT) of our Estimated Time of Arrival(ETA)
    >     at the Isla San Jose Light?
    >     What is the UT/GMT ETA?
    > --  ----------------------------------------------------------------
    ETA = 1141 GMT-5 = 1641 GMT
    We need starting time, and time en route. For time en route we need the
    distance and speed. Speed is given as 1.34*sqrt(LWL) a.k.a. "hull speed".
    This is easy with a calculator and S=8.4.
    The distance I'd get directly from the chart with dividers. Without the
    chart, any of the sailings will do. Simple traverse with Mid Latitude
    of 8d 30' gives us D=47.6 (so does a Great Circle calculation, Meridional
    Parts is just enough more so as to round up to 47.7).
    Time en route is T=D/S=5.67hrs=5h 40m.
    Sunrise is calculated by taking the almanac entry (0559), interpolating
    for latitude (-16m) and interpolating for longitude differnce from central
    meridian of the zone (+18m). Dawn is at 0601 (give or take a little).
    > On our ETA at Isla San Jose we take a departure FIX off of the light that
    > is (08d 10.5'N  079d 18.0'W). We set our course for the Mid-Ocean Point
    > (MOP) at (03d 00.0'N  110d 00.0'W).
    > Variation 2.0dW, Dev 0.5dE. Drift 0.6 Kts Set 285.0d. Speed 10.1 Kts.
    > 2)  What is the TC and Distance from the Isla San Jose Light departure
    >     point (08d 10.5'N  079d 18.0'W) to the MOP(03d 00.0'N  110d 00.0'W)?
    > --  --------------------------------------------------------------------
    C = 260.4T D = 1858.0
    I used plane sailing with mid lat of 6d (easy with a calculator). Mercator
    Sailing calculation (Meridional Parts) gives same course and a slightly
    longer distance (1871.0), but still only a difference of 0.7%.
    > We plot our track on INT Chart 811 and see that we can not head direct for
    > the MOP(03d 00.0'N  110d 00.0'W) without crossing land above Punta Mala in
    > Panama. So we alter course to MOP2 at (05d 00.0'N  80d 00.0'W).
    > Variation 2.0dW, Dev 0.5dE. Drift 0.6 Kts Set 285.0d. Speed 10.1 Kts.
    > 3)  What is the True Course and distance to MOP2 from our Departure point?
    >     What is the Compass Course(CC)/Course-to-Steer?
    > --  ----------------------------------------------------------------------
            C = 192.3T
            D = 195.0 nmi
            CC/CTC = 188.9T = 190.9M = 190.4C
    I used plane sailing calculation (mid lat = 7) for Course and Distance.
    Comparison with Mercator calculations show a difference of .1d and .1nmi.
    For me, it is easier to use a plotting sheet to adjust for current than
    to use the law of sines, since I have to draw it out either way. The
    difference should be less than a half a degree, and in this case I
    lucked out and got it within 0.1d
    > The weather has high Cirrus clouds building, wind from the Southwest.
    Hmm. A tropical Low to the west, perhaps?
    > At 14:45:30UT the next morning we take a SUN LL sight. Other Data as above.
    > |    Hs 47d 27.2'
    > 4)  What is the DR position?
    > --  ------------------------
            DR = 4d 32.6N  80d 05.8W
    Time difference is 22h05m, speed is 10.1, D = 223.0.
    Plane sailing calculation with Mid lat = 6.5d. C = 192.3T
    dLat = 3d 37.9' dep = 47.5, dLo = 47.8'.
    > At 22:45:23UT we take another sight of the SUN LL
    >     Hs 10d 07.2'
    > 5)  What is the DR position?
    > --  ------------------------
            DR = 3d 13.8N   80d 22.9'W
    Using last fix as starting point we have T = 30h 04m. S = 10.1, so
    D = 303.7. dLat = 296.7' = 4d 56.7', dep = 64.9, dLo = 64.9' = 1d 04.9'
    (with mid lat of 6d).
    > 6)  What is the Running FIX(RFIX) position at the 22:45:23UT sight?
    > --  ---------------------------------------------------------------
            RFIX = 3d 14.7'N  80d 23.5'W
    For a running fix, there is a distinct advantage to using a sight
    reduction method that uses AP = DR. It means that we can translate
    the derived LOP to the next DR directly.
    The first sight reduces to Ho = 47d 36,9' Hc = 47d 36.9'  Z = 59.8
    The second one reduces to  Ho = 10d 12.5' Hc = 10d 11.7'  Z = 293.2
    The first is spot on. The second is .8T. Plotting gives the RFIX.
    > Checking our Running FIX against the position of MOP2(05d 00.0'N
    > 080d 00.0'W) it seems we have passed MOP2. So we alter course to our
    > original Mid-Ocean Point which we re-name MOP1(03d 00.0'N  110d 00.0'W).
    > Speed 10.5 Kts. Current Set 285, Drift 0.6 Kts. Var 1dW Dev 2dE.
    > 7)  What is the TC and Dist to the MOP1(03d 00.0'N  110d 00.0'W)?
    >     What is the Compass Course(CC)/Course-to-Steer?
    > --  -------------------------------------------------------------
            C = 269.5T
            D = 1777.4
            CC/CTC = 267.8
    Plane sailing calculation used, but in a non-trafitional way. In
    this part of the globe, a degree of Latitude is smaller (by 0.5%)
    than 60 nmi. and a degree of Longitude is actually slightly more
    (by 0.05%) than 60 nmi. For that reason Mercator sailing will tend
    to overstate the distance by 0.5%. By calculating the departure
    directly from the length of a degree of Longitude and likewise
    the N/S distance travelled we get D = 1777.4. Courses calculated
    by either method should be about the same within 0.1d.
    The CTC was obtained by plot. Calculation by law of sines puts
    the course 0.2d more southerly.
            Mike Wescott

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