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    Re: Silicon Sea: Leg 82 results
    From: Paul Hirose
    Date: 2001 Dec 16, 12:08 AM

    Silicon Sea Leg 82 answers. Solution by 10-inch slide rule and
    mid-latitude sailing. For the Sun lines I used the U.S. Naval
    Observatory Web page, not having a current almanac. However, I
    interpolated the coordinates between exact hours to simulate the
    almanac as closely as possible.
    
    Compute course to landfall at Hawaii:
    
    19 30 N  destination lat.
    11 30 N  fix 2001 July 11 0340
    -----
     8 00    DLat (lat. diff.) = 480 min
    
    154 45 W  dest. lon.
    132 30 W  fix 2001 Jul 11 0340
    ------
     22 15  DLo = 1335 min
    
    15.5  Lm (mid lat) = mean of dest. & fix lats
    
    1289  p (departure) = DLo cos Lm
    
     290  C (course) = 360 - arctan(p / DLat)
     -11  correction for variation & deviation
    ----
     279  CC (compass course)
    
    1368 nm  Distance = p / (sin C)
    
    ==========
    1. Compass course from last fix to Hawaiian landfall = 279.
    
    2. Current is practically on our stern, so speed made good = speed
    thru water + drift = 10.4 kt.
    ==========
    
    1170  D (distance)
    
    11 30 N  Fix lat 2001 Jul 11 03:40 Z
     6 40    DLat = 400 min = D cos C
    -----
    18 10 N  DR lat 2001 Jul 15 20:11 Z
    
    14.8   Lm = fix lat + 1/2 DLat
    1100   p = 1170 sin C
    
     17 40 W  DLo = 1138' = p / cos Lm
    132 30    fix lon 2001 Jul 11 03:40 Z
    ------
    151 28 W  DR lon 2001 Jul 15 20:11 Z
    
    
    ==========
    3. DR at 2001 Ju1 15 2011 Z = 18 10 N 151 28 W
    ==========
    
    
    Reduce sun line at this position.
    
    61 20.6  Hs Sun LL Jul 15 20:10:35 Z
       -2.9  dip
       -2.5  IC
       15.4  R + SD
    -------
    61 30.6  Ho
    
    118 30.3  N21 24.9  20h Sun GHA & dec
    133 30.2  N21 24.5  21h
    --------   -------
     14 59.9
         -.1       -.4  Sun v & d
    
     118 30.3  GHA 20 h
       2 38.8  increment 10 m 35 s
          0.0  v corr.
     --------
     121 09.1  GHA at sight time
     360 00.0
    -151 28.0  assumed lon.
    ---------
     329 41.1  LHA at sight time
      30 18.9  t
    
    N21 24.9  dec 20 h
         -.1  d corr.
    --------
    N21 24.8  dec at sight time
    
    Use Bayless version of HO 211 for sight reduction.
    
    t    30 19   A  29690
    dec N21 25  +B   3107   A  43753
                 A  32797  -B   5420   B   5420   A  32797
    K   N24 26              A  38333
    L   N18 10
    K-L   6 16                        +B    260
    Hc   61 20                         A   5680  -B  31902
    Ho   61 31
    int     11 toward       Z  N 78 E             A    895
    
    
    Correct the DR by "sailing" 11 miles toward the body.
    
    11  D (distance)
    78  C (course)
    
    18 10 N  DR lat
     0 02    DLat = 2 min = D cos C
    -----
    18 12 N  EP lat 2001 Jul 15 20:11 Z
    -----
    
    14.2   Lm (mid lat)
    11     p = D sin C
    
    151 28 W  DR lon
    - 0 11    DLo = 11' = p / cos Lm
    ------
    151 17 W  EP lon 2001 Jul 15 20:11 Z
    
    
    
    Update EP to the 2001 Jul 16 0144 Z sun sight.
    
    16 01:44
    15 20:11
    --------
        5:33  elapsed time since last EP
    
     57  D (distance) = 10.2 kt * 5 h 33 m
    290  C (course) (use 70 for trig functions)
    
    18 12 N  EP lat 2001 Jul 15 20:11 Z
       19    DLat = D cos C
    -----
    18 31 N  EP lat 2001 Jul 16 0144 Z
    
    18.4   Lm (mid lat)
    53     p = D sin C
    
    151 17 W  EP lon 2001 Jul 15 20:11 Z
        56 W  DLo = 56' = p / cos Lm
    ------
    152 13 W  EP lon 2001 Jul 16 01:44 Z
    
    
    Reduce the 0144 Z sight.
    
    40 44.1  Hs Sun LL Jul 16 01:44:36 Z
       -2.9  dip
       -2.5  IC
       14.9  R + SD
    -------
    40 53.6  Ho
    
    
    193 30.0  N21 22.8  01 h Sun GHA & dec
    208 29.9  N21 22.4  02 h
    --------   -------
     14 59.9
         -.1       -.4  Sun v & d
    
     193 30.0  GHA 01 h
      11 09.0  increment 44 m 36 s
          -.1  v corr.
     --------
     204 38.9  GHA at sight time
    -152 13.0  assumed lon.
    ---------
      52 25.9  LHA and t at sight time
    
    
    N21 22.8  dec 01 h
         -.3  d corr. 44 m 36 s
    --------
    N21 22.5  dec at sight time
    
    
    
    t    52 26   A  10092
    dec N21 22  +B   3093   A  43850
                 A  13185  -B  17101   B  17101   A  13185
    K   N32 42              A  26749
    L   N18 31
    K-L  14 11                        +B   1344
    Hc   40 50                         A  18445  -B  12113
    Ho   40 54
    int      4 toward       Z  N 77 W             A   1072
    
    
    Update the EP by moving 4 miles toward the body.
    
    18 31 N  AP lat
     0 01    DLat = 1 min = D cos C
    -----
    18 32 N  corrected EP lat 2001 Jul 16 01:44 Z
    
    18.5   Lm (mid lat)
     4     p = D sin C
    
    152 13 W  AP lon
         4    DLo = 4' = p / cos Lm
    ------
    152 17 W  corrected EP lon 2001 Jul 16 01:44 Z
    
    
    ==========
    5. Azimuth of Sun = 360 - 77 = 283
    6. Fix position Jul 16 01:44 Z = 18 32 N 152 17 W
    7. Not practical to compute distance since I didn't carry the DR
    forward. I should have done so, and then simply summed the lat and lon
    corrections at the time of the second sight.
    ==========
    
    
    True course & distance to Hawaiian landfall (mid-lat method):
    
    19 30 N  destination lat.
    18 32 N  running fix 2001 July 16 0145
    -----
     0 58  DLat (lat. diff.)
    
    154 45 W  dest. lon.
    152 17 W  running fix 2001 Jul 16 0145
    ------
      2 28  DLo = 148 min
    
    19.0  Lm (mid lat)
    140   p (departure) = DLo cos Lm
    
    292  C (course) = 360 - arctan(p / DLat)
    152 nm  Distance = p / (sin C)
    
    
    True course & distance to Hawaiian landfall (great circle, HO 211)
    
    t     2 28   A 136615
    dec N19 30  +B   2565   A  47650
                 A 139180  -B     36   B     35.5 A 139180
    K   N19 31              A  47614
    L   N18 32
    K-L     59                        +B      6.4
    Hc   87 29                         A     41.9-B 135744
                            Z  N 68 W             A   3436
    
    
    ==========
    8. course 292 distance 152 by mid-latitude, 292 / 151 by great circle
    ==========
    
    
    The longitude difference to Sydney is small, so I'll use mid latitude
    sailing to figure the course and distance.
    
    33 50 S  destination lat.
    18 32 N  lat 2001 July 16 0145 Z
    -----
    52 22    DLat (lat. diff.) = 3142 min
    
    151 20 W  dest. lon.
    152 17 W  lon 2001 Jul 16 0145 Z
    ------
        57    DLo
    
    13.1  Lm (mid lat) = DLat/4
    
    56  p (departure) = DLo cos Lm
    
    
    ===========
    8a.
     179  course to Sydney = 180 - arctan (p / DLat)
    3142  Distance = DLat / (cos C)
    ===========
    
    
    No correct answer was provided for the last question, but my other
    results were close enough. I do wish the running fix had been better,
    but then I didn't work it the "correct" way.
    
    --
    
    
    paulhirose---.net (Paul Hirose)
    

       
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