NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2007 Oct 29, 16:21 +0100
Considere this figure: Earth’s normal section to the plane of the CoP. 

Tan(90H) = R(CoP)/R(Earth)
A spherical Earth hás R(Earth) = 60*360/2PI = 21600/2PI
Then R(CoP) = R(Earth)/ Tan(H)
We can discern between the radius of the CoP in his plane, and the angular distance that is the radius of the CoP on the surface of a sphere: R = 90H
Gary, In this table you can see that for high altitude CoP are near the same
H 
zd = 90H 
360/(2*PI)/TAN(H) 
10 
80 
324.94 
20 
70 
157.42 
30 
60 
99.24 
40 
50 
68.28 
50 
40 
48.08 
60 
30 
33.08 
70 
20 
20.85 
71 
19 
19.73 
72 
18 
18.62 
73 
17 
17.52 
74 
16 
16.43 
75 
15 
15.35 
76 
14 
14.29 
77 
13 
13.23 
78 
12 
12.18 
79 
11 
11.14 
80 
10 
10.10 
81 
9 
9.07 
82 
8 
8.05 
83 
7 
7.04 
84 
6 
6.02 
85 
5 
5.01 
86 
4 
4.01 
87 
3 
3.00 
88 
2 
2.00 
89 
1 
1.00 
90 
0 
0.00 
Andrés Ruiz
Navigational Algorithms
http://www.geocities.com/andresruizgonzalez
Mensaje original
De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de glapook{at}PACBELL.NET
Enviado el: lunes, 29 de octubre de 2007 10:01
Para: NavList
Asunto: [NavList 3691] Computaion of table of offsets.
In the discusssion of the St. Hilaire method the subject of the table
of offsets used to approximate the curved LOP came up. This is table 4
in Bowditch (1975 ed), table 19 in the online Bowditch and is also
printed in each volume of H.O. 229. Bowditch gives the formulas for
this calculation and one of the formulas gives the radius of the
circle of postion. The formula for this is: R = 3438' cot altitude.
Ruiz gives a similar formula: R = (60*180/pi) cot altitude which
reduces to the other formula given in Bowditch.
My question is why do you use this formula? Why isn't the radius of
the circle of position simply 60 times the zenith distance? This is
the formula we have always used for plotting high altitude circles of
positions around the GP. Should we use the Bowditch formula for this
purpose also.
gl
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