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    Adrian V's Leg 21 Solutions
    From: Adrian P. Vrouwenvelder
    Date: 1997 Feb 28, 09:31 EST

    Here are my solutions for leg 21, albeit somewhat late.
    I'm comfortable with my results up until #4.
    1. Using Mercator Sailings and
        c'=arctan(DLo/m) and D=DLat/(cos c')
       and where c' must be converted to C North by East
        C=180-sCe (sCe means C South by East, which is what c' is)
        Dlat = 63.3
        Dlo = 261.0
        m1 = 2055.6, m2=1981.2   m = 74.4
        sCe = arctan(261/74.4) = 74.0894
        D = 63.3 / (cos 74.0894) = 230.9 nm
        C (north by east) = 180 - 74 = 105.9T, or just 106T
        Time in route: 230.91/9.5 = 24h, 18m
    2. Using CC=TRK-arcsin(DFT/SPD * sin(SET-TRK))
       CC = 104.7T
       104.7 - 4 (var E) = 100.7, or just 101M
    Got into some trouble here, until I realized that 19:08:38 was Zone Time.
    3. Civil twilight ends:  19:26 at 30N, 1941 at 35N.  Via interpolation,
       CT = 1932.  Add 0005 for the longitude adjustment to get 1937.
       That should give us plenty of time, especially since Naut Twilight is
       about an hour later.
    4. First, our new DR position.  By plot on mercator sheet, and given our
       distance travelled is 4.4 nm, I get 32d 12.0'N, 28d 49.4'E,
       which differs significantly from the solution.  No matter how I plot it,
       I can't see how I could be 3 miles off the computed solution with my
       plot -- I _am_ using a mercator plotting sheet, and am also using the
       longitude scale appropriate for our latitude.
    5. Using HO 22, and retarding each
       LOP to 17:40UT, I get a small cocked-hat, the center of which is
       approx at 32d 13'N, 28d 48'E.  A bit off, but I checked all the
       work, and that's my answer.
       The results of the SR were (June 5, 1996)
              Vega       Spica       Regulus
       main    -2.8'      -1.0'       -0.9'
       APlat  32dN        32dN       32dN
       APlo   28d 49.9'E  28d 1.6'E  29d 35.1'E
       gha   240d 11.1'  319d 58.4'  11d 24.9'
       lha   269d        348d        41d
       AA    18d 51.6'   45d 24.3'   47d 55.9'
       Ho    18d 48.8'   45d 23.3'   47d 55.0'
             18d 20.2'   45d 29.6'   46d 50.1'
         d     (+20.8)     (-58.1')    (+34.5')
        Corr    +21.0        -8.3'      +34.0'
        Hc   18d 41.2'   45d 21.3'   47d 24.1'
       azim       7.6nm       2.0nm      30.9nm (APlo was 29d 35.1E)
        Dir     --- All were Towards ---
         Z   55.4d      163.1d      109.7d
         Zn  55.4d      163.1d      360-109.7= 250.3d
    6. Due to the fact that my fix was a bit off, these are
       also a bit off.
       Using the EP given in problem 1, and destination of 32d 13'N, 28d 48'E,
       and mercator sailings as before,
        m1=2031.5, m2=2055.4, m=23.9  Dlo=79.0, Dlat=20.4
        C (south by east) = 73.2,  C (north by east) = 106.8T
        CC = 106.8 - 4 (var E) = 102.8M, or just 103M
        Using time/distance computations, I get a SMG of 9.4kts.
        (70.4 / (17:40 - 10:08:38) = 70.4/7.5228 = 9.358)
    7. See 6.
    8. No, my helmsman doesn't steer that accurately, and we're not using any
       "no greater than" or "no less than" bearings, and my compass card is
       only marked to 5d intervals.
    My wife, incidentally, is down below, surreptitiously checking Silicon Sea's
    GPS unit against my results.  She thinks I don't notice.
    Maybe I'll simulate a lightning strike  :-)
    I realize it's a lot of work, but if any of you happen to see where I might
    have gone off, you have my gratitude.
    Thus far, and enjoyable cruise.  Looking forward to Leg 22.
    Adrian P. Vrouwenvelder
    Catalina 22 #12435 "Pookums"
       These are my personal opinions; no one else's.  No one should be
         held liable for these comments or what they might engender.
    If I thought I or anyone else was going to be held liable, I wouldn't
                          even have posted this.

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