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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@earthlink.net (Paul Hirose)

   

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