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    Re: Marq St. Hilaire - Altitude intercept method:
    From: Andr�s Ruiz
    Date: 2007 Oct 29, 08:49 +0100

    [NavList 3635] Re: Marq St. Hilaire - Altitude intercept method:
    An accurate position is determined by meridian transit
    Latitude and subsequent Longitude by Time Sight,
    utilizing the accurate Latitude. In your opinion, will
    or will not an intercept determined by the Marc St.
    Hillarie method, utilizing the so determined accurate
    position, be equal to zero, If not, why?
    Henry, if you know your exact position; Yes
    The intercept is the great circle distance between the CoP based on calculated 
    altitude, Hc, and the one based on the observed altitude, Ho. The calculate 
    altitude is a function of the position. But Ho always has a little error, and 
    the true CoP and the observed one may be different. 
    If you use the St-Hilarie in an iterative way, the estimated position is not 
    important, because you can improve it. Only the accuracy of the star 
    shootings with the sextant is. And of course the knowledge of the conditions: 
    temperature, pressure, height of the eye,
    The accuracy deepens only on the bodies and the measurements, not in the 
    method. You can obtain a fix by iterative St-hilaire, by sight reduction with 
    matrices, by T. Metcalf LS method or by Kaplan STELLA method, and the final 
    solution in the case of two sights is the same. Also by Summer in an 
    iterative way.
    If tree or more sights are involved, the solution can be different because the 
    technique to obtain the most probable position is different.
    Using St-Hilaire in the old traditional graphic way to obtain the MMP, from a 
    cooked hat, is the use of bisectors of the azimuth angle.
    Meridian sight has tree main problems:
    1. the maximum altitude
    2. the time of the LAN
    3. The speed of the vessel. (aboard a sailboat 4,8 kn are insignificance)
    But taking a series of sight before and after the local noon, and adjusting 
    them by a least squares method I usually get good results.
    About accuracy, in coastal navigation is more important that in blue water, because the shallow.
    One friend of mine says: "Navigating, is not important to know where you are, 
    the important thing is to know where you are not" (Is well expressed)
    An example: some different AP and the effect of the improvement by iteration
    GHA = 338.391817 � = 338� 23.5'
    Dec = 9.896533 � =   9� 53.8'
    Ho = 50.77
    GHA = 294.303014 � = 294� 18.2'
    Dec = 56.560600 � =  56� 33.6'
    Ho = 46.44
    Result by exact 2 CoP solution, NA and Kaplan algorithm:
    B = 43.32162 =  43� 19.3' N
    L = -2.00219 = 002�  0.1' W
    For AP:
    Be = 43.3166�
    Le = -2.0000�
    BI = 43.3216 
    LI = -2.0021
    HC   Z   p 
    50.7749 141.4002    -0.0049
    46.4378 47.7147 0.0022
    For AP:
    Be = 41.5�
    Le = -3.5�
    BI = 43.3614
    LI = -2.0890
    HC   Z   p 
    51.4421 137.8834    -0.6721
    44.3881 46.1244 2.0519
    For AP:
    Be = 30.0000 
    Le = -10.0000
    BI = 45.0388 
    LI = -5.5543
    HC   Z   p 
    54.3421 117.6633    -3.5721
    32.353  39.2049 14.087
    After five iterations:
    HC   Z   p 
    50.7700 141.4011    -0.0000
    46.4400 47.7183 -0.0000
    43.321611 N
    2.002105  W
    Best regards,
    Andr�s Ruiz
    Navigational Algorithms
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