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Subject: Re: Silicon Sea: Leg 82 results
From: Paul Hirose (paulhirose@XXX.XXX)
Date: Sun Dec 16 2001 - 02:07:53 EST
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@XXX.XXX (Paul Hirose)
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