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    Re: Computaion of table of offsets.
    From: Andrés Ruiz
    Date: 2007 Oct 29, 16:21 +0100

     

     

    Considere this figure: Earth’s normal section to the plane of the CoP.

     

     

    Tan(90-H) = 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 = 90-H

     

     

    Gary, In this table you can see that for high altitude CoP are near the same

     

    H

    zd = 90-H

    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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