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Re: Marq St. Hilaire - Altitude intercept method
From: Gary LaPook
Date: 2007 Oct 29, 01:03 -0700
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 > > > > > > >> > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---