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    Re: Marq St. Hilaire - Altitude intercept method
    From: Henry Halboth
    Date: 2007 Oct 26, 20:47 -0700

    Andres,
    
    I have long enjoyed your posts and have frequently
    visited your website. Thank you for your insightful
    contributions. This is my first opportunity to
    communicate with you directly.
    
    In responding to Gary�s post, it was my primary intent
    only to emphasize that the Time Sight could and was/is
    customarily employed in LOP navigation and that it had
    evolved from the two (2) position plotting
    metho-dology, initially postulated by Sumner, to the
    single position plus azimuth methodology. The Time
    Sight, when so employed, is not an intercept method
    and I had no intent of inferring that it was or, for
    that matter, to make any statememt with respect to
    comparative accuracy.
    
        We all know, or certainly should, that the straight
    LOP, no matter how determined, is an approximation to
    the truth, acceptable to the needs of practical ocean
    navigation. It is also obvious that comparative
    accuracy between methods, or even within methods may
    well be somewhat affected by the trigonometric
    functions employed; there being some slight difference
    in solutions by 4 or 5-figure functions as opposed to
    those employing 6 or even 8-figure functions, as well
    as in those employing different functions in certain
    angular ranges � unfortunately all is simply not
    perfect, yet again these differences are generally not
    relevant to practical ocean navigation. It is also
    accepted that grossly inaccurate assumed positions
    also can affect the resultant accuracies, as well as
    any comparison between methods. In some instances, it
    may well be considered adviseable to recalculate
    positions established on the latter basis.
    
    Aside from the foregoing, I understand it to be stated
    that there is a difference in the LOP solution as
    between the Marc St. Hillarie and Time Sight methods
    of solution, regardless of how small that difference
    may be. In complete naivet�, I am academically
    interested in this proposition, and to clear the
    matter in my own mind, I would ask as follows ,,,,,
    
    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?
    
    Regards,
    
    Henry
    
    --- Andres Ruiz  wrote:
    
    > 
    > Gary, my question for you is: are you saying I and
    > writing silly things????
    > No mere controversy please. You can retract your
    > question!
    > 
    > Language is for providing communication to people.
    > Not is the same:
    > "St. Hilaire's method created the exact same LOP as
    > Sumner's method" or
    > "Sumner and St. Hilaire methods produce the same
    > LOP" or -In the practice of old celestial navigation
    > the result of using Sumner or St-Hilaire LoPs is the
    > near the same assumed usual circumstances.-
    > 
    > 2+2= 4
    > 1.99+2.001 approx 4
    > 
    > Anybody with good background knowledge in navigation
    > can filter the information and read between the
    > lines, but write without rigor can confuse to the
    > beginners in CN.
    > 
    > Of course navigation is an art, but also a science
    > and the advances in sciences arise by understanding
    > previous knowledge and acquiring new one. 
    > Are you agree?
    > 
    > To test the discrepancy between the to lines,
    > imagine you are in the middle of the North Atlantic
    > Ocean and a two days storm apart from your course
    > several miles away. Now your DR position is far away
    > from the true one. The differences of the results
    > using the two methods depends on the assumed
    > position, and increase, as the distance between the
    > true and assumed position do.
    > 
    > ________________________________________
    > De: NavList@fer3.com
    > [mailto:NavList@fer3.com] En nombre de Gary
    > J. LaPook
    > Enviado el: viernes, 26 de octubre de 2007 9:48
    > Para: NavList@fer3.com
    > Asunto: [NavList 3620] Re: Marq St. Hilaire -
    > Altitude intercept method
    > 
    > Gary LaPook writes:
    > 
    > My question for you is "how many angels� to you want
    > to get dancing on the head of your pin?"
    > 
    > You are right, one line is a chord and one is a
    > tangent but to the available level of accuracy of
    > measuring the altitude and of plotting it on a chart
    > they are the same for all practical purposes. For
    > example, if you plotted two positions determined by
    > the Sumner method 30 NM apart and drew the line
    > between them making one LOP. Then you calculate the
    > same LOP using St. Hilaire for a spot in the center
    > of the two Sumner positions you are right, you would
    > end up with two different LOPs that parallel each
    > other. However, for any altitude up to 77� they
    > would be less than .1 NM apart, that's right, one
    > tenth of one nautical mile! How thick is the line
    > your pencil makes on the chart? How accurate are all
    > of your sextant sights? Do you always achieve one
    > tenth of a minute accuracy? People on this list talk
    > about getting .5 minute of accuracy as a very good
    > result on a boat and with that level of accuracy the
    > difference between a Sumner line and a St. Hilaire
    > line only becomes an issue for sights above 86�. How
    > many times have you taken sights above 86�?
    > Navigation is the art and science of directing a
    > vessel or aircraft safely from one place to another,
    > it is not a mathematical exercise that you do at
    > home on a computer to an accuracy of 42 significant
    > figures. And I don't use "the analytic equation of
    > each LoP on a Mercator chart" I draw a pencil line
    > that has thickness and some level of inaccuracy in
    > azimuth. Everything plotted on a chart is an
    > approximation to some extent and for navigation
    > purposes (not theoretical discussion purposes) the
    > Sumner and St. Hilaire methods produce the same LOP.
    > 
    > gl
    > 
    > 
    > Andres Ruiz wrote: 
    > In messages: [NavList 3572], [NavList 3588],
    > [NavList 3596] There is an error of concept.
    > 
    > Gary is not absolutely correct.
    >   
    > St. Hilaire's method created the exact same LOP as
    > Sumner's method but 
    > only required doing the computation one time, saving
    > work and reducing 
    > the chance for an error.
    >     
    > 
    > The Sumner and the St-Hilaire LoPs are not the same.
    > One is secant to the circle of equal altitude and
    > other is tangent. This means that the points in
    > common between the CoP and the each LoP are
    > different. If You get the analytic equation of each
    > LoP on a Mercator chart You can see that the two
    > lines are not the same.
    > 
    > For more details see the attached PDF.
    > 
    > Please, I want to hear more opinions.
    > 
    > Andr�s Ruiz
    > Navigational Algorithms
    > http://www.geocities.com/andresruizgonzalez
    > 
    > 
    >   
    > 
    > 
    > 
    >
    > 
    > 
    
    
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