NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2009 Oct 5, 12:32 +0200
Last friday early in the morning I went to sail.
Maximum VOG = 8 kt, and average of 3, 4 kt. This is the real world on a sloop.
Now back in business again, a lot of mails about the
subject in navlist. A good test bench.
With the data provided by Gary LaPook in Navlist 10041, using general SR methods, the fix
at 17:00:00 is:
Fix(24.161666623101908, -79.441666294194576) (
24º 9.7' -79º 26.5') LopLSSR
Fix(24.161666624470591, -79.441666332809163) (
24º 9.7' -79º 26.5') KaplanSR_Bm = 0
Solving for course and speed:
Fix(24.161665279196630, -79.441682214842487) (
24º 9.7' -79º 26.5' 180.0 300.0) KaplanSR_Bm_BLRV = 0
If anybody wants to use the standard intercept
method:
|
t |
B2 |
L2 |
gha |
dec |
HC |
Z |
HO |
LHA |
LHA |
p |
|
17 |
24.1616667 |
-79.4416667 |
75.3093102 |
-23.4350226 |
42.2346691 |
174.876739 |
42.2347 |
-4.13235651 |
355.8676 |
0 |
|
17.0833333 |
23.745 |
-79.4416667 |
76.5588778 |
-23.4349961 |
42.7370395 |
176.39795 |
42.737 |
-2.88278887 |
357.1172 |
0 |
|
17.1666667 |
23.3283333 |
-79.4416667 |
77.8084456 |
-23.4349696 |
43.2097856 |
177.943863 |
43.2098 |
-1.63322105 |
358.3668 |
0 |
|
17.25 |
22.9116667 |
-79.4416667 |
79.0580133 |
-23.4349429 |
43.6518901 |
179.513496 |
43.6519 |
-0.3836534 |
359.6163 |
0 |
|
17.3333333 |
22.495 |
-79.4416667 |
80.3075809 |
-23.4349161 |
44.0623645 |
181.105656 |
44.0624 |
0.86591425 |
0.8659 |
0 |
|
17.4166667 |
22.0783333 |
-79.4416667 |
81.5571487 |
-23.4348893 |
44.4402573 |
182.718937 |
44.4403 |
2.11548207 |
2.1155 |
0 |
|
17.5 |
21.6616667 |
-79.4416667 |
82.8067164 |
-23.4348623 |
44.7846626 |
184.351715 |
44.7847 |
3.36504972 |
3.365 |
0 |
|
17.5833333 |
21.245 |
-79.4416667 |
84.0562842 |
-23.4348352 |
45.0947284 |
186.002154 |
45.0947 |
4.61461754 |
4.6146 |
0 |
|
17.6666667 |
20.8283333 |
-79.4416667 |
85.3058519 |
-23.4348081 |
45.369665 |
187.668209 |
45.3697 |
5.86418519 |
5.8642 |
0 |
|
17.75 |
20.4116667 |
-79.4416667 |
86.5554197 |
-23.4347809 |
45.6087536 |
189.347636 |
45.6088 |
7.11375301 |
7.1138 |
0 |
|
17.8333333 |
19.995 |
-79.4416667 |
87.8049873 |
-23.4347535 |
45.811354 |
191.038003 |
45.8114 |
8.36332067 |
8.3633 |
0 |
|
17.9166667 |
19.5783333 |
-79.4416667 |
89.0545552 |
-23.4347261 |
45.9769119 |
192.736715 |
45.9769 |
9.61288849 |
9.6129 |
0 |
|
18 |
19.1616667 |
-79.4416667 |
90.3041228 |
-23.4346986 |
46.1049657 |
194.441025 |
46.105 |
10.8624562 |
10.8625 |
0 |
|
18.0833333 |
18.745 |
-79.4416667 |
91.5536905 |
-23.434671 |
46.1951522 |
196.148068 |
46.1952 |
12.1120238 |
12.112 |
0 |
|
18.1666667 |
18.3283333 |
-79.4416667 |
92.8032583 |
-23.4346432 |
46.2472108 |
197.854883 |
46.2472 |
13.3615916 |
13.3616 |
0 |
|
18.25 |
17.9116667 |
-79.4416667 |
94.052826 |
-23.4346154 |
46.2609872 |
199.558445 |
46.261 |
14.6111593 |
14.6112 |
0 |
|
18.3333333 |
17.495 |
-79.4416667 |
95.3023938 |
-23.4345875 |
46.236435 |
201.255697 |
46.2364 |
15.8607271 |
15.8607 |
0 |
|
18.4166667 |
17.0783333 |
-79.4416667 |
96.5519615 |
-23.4345595 |
46.173617 |
202.943584 |
46.1736 |
17.1102948 |
17.1103 |
0 |
|
18.5 |
16.6616667 |
-79.4416667 |
97.8015293 |
-23.4345314 |
46.0727033 |
204.619083 |
46.0727 |
18.3598626 |
18.3599 |
0 |
|
18.5833333 |
16.245 |
-79.4416667 |
99.0510969 |
-23.4345033 |
45.9339704 |
206.279233 |
45.934 |
19.6094303 |
19.6094 |
0 |
|
18.6666667 |
15.8283333 |
-79.4416667 |
100.300665 |
-23.434475 |
45.7577962 |
207.921172 |
45.7578 |
20.8589981 |
20.859 |
0 |
|
18.75 |
15.4116667 |
-79.4416667 |
101.550232 |
-23.4344466 |
45.5446567 |
209.542153 |
45.5447 |
22.1085658 |
22.1086 |
0 |
|
18.8333333 |
14.995 |
-79.4416667 |
102.7998 |
-23.4344181 |
45.2951193 |
211.139581 |
45.2951 |
23.3581334 |
23.3581 |
0 |
|
18.9166667 |
14.5783333 |
-79.4416667 |
104.049368 |
-23.4343896 |
45.0098361 |
212.711022 |
45.0098 |
24.6077013 |
24.6077 |
0 |
|
19 |
14.1616667 |
-79.4416667 |
105.298936 |
-23.4343609 |
44.6895371 |
214.254228 |
44.6895 |
25.8572689 |
25.8573 |
0 |
Simulating with the data provided by
|
|
t |
B2 |
L2 |
gha |
dec |
HC |
Z |
LHA |
|
LAN |
17.27583333 |
22.7825 |
-79.44166667 |
79.44537934 |
-23.43493459 |
43.78256526 |
180.0047182 |
0.003712671 |
|
H max |
18.23833333 |
17.97 |
-79.44166667 |
93.87788659 |
-23.43461934 |
46.26136592 |
199.3202558 |
14.43621992 |
LAN: 17:16:33
Time of Hmax: 18:14:18
Conclusion:
- The generality and
power of the least squares SR method based in the Marcq Saint Hilaire, and
the one by Mr. Kaplan is checked for cases of high speed.
- For obtain the Hmax,
the Least squares fitting H = a0+a1*t+a2*t2 is OK. The maximum gives: t
max = -a1/(2a2) and Hmax = a0-a2t2. It retains the asymmetrical nature of
the curve.
- For shoots made
aboard a vessel the equation for time of meridian transit proposed by Jim
Wilson in his paper “Position from observation of a single
body” work fine.
- For high speed, in
aircrafts, the equation doesn’t work, and iteration doesn’t
improve the result. I think the problem is in the assumption made in the
appendix I: the error in time is little, and differentiating is possible.
Is Jim Wilson agree with
these last points? Or I am doing some thing wrong?
Regards,
Andrés Ruiz
Navigational Algorithms
http://sites.google.com/site/navigationalalgorithms/
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