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    Re: Marq St. Hilaire - Altitude intercept method
    From: Gary LaPook
    Date: 2007 Oct 29, 01:03 -0700

    Gary LaPook responds:
    
    
    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!"
    
    
    I'm sorry if  it came across that I was saying that what you have 
    written was silly, I was merely making reference to the medieval  
    theologians who got into very  heated debates about  minutiae of 
    religious doctrine:
    
     "Fact is, Aquinas did debate whether an angel moving from A to B passes 
    through the points in between, and whether one could distinguish 
    "morning" and "evening" knowledge in angels. (He was referring to an 
    abstruse concept having to do with the dawn and twilight of creation.) 
    Finally, he inquired whether several angels could be in the same place 
    at once, which of course is the dancing-on-a-pin question less comically 
    stated."
    
    Although such careful dissection of religious principles might be 
    important to theologians (and not silly)  it held little relevance to 
    the normal parishioner.
    
    Likewise, the fact that a Sumner line and a St. Hilaire line are in fact 
    different, that difference is only relevant to mathematicians and not at 
    all relevant to the practitioners of CN at sea or in the air. To 
    practical navigators, those actually on a vessel or aircraft proceeding 
    between two points,  the two lines are the same for all practical purposes.
    
    You asked the question:
    
    "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."
    
    
    My response to this question is "it doesn't matter." In the middle of the 
    Atlantic there is no need to know your position to a high level of precision. 
    For example, on a voyage of 2,000 NM if you are 100 miles off course in the 
    middle you will end up sailing 2,010 miles instead of 2,000 an increase of 
    only .5%, and extra 5 minutes in a slow airplane or and extra half hour on a 
    ship.
    
    gl
    
    
    
    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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