NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Marq St. Hilaire - Altitude intercept method
From: Gary LaPook
Date: 2007 Oct 26, 00:48 -0700
From: Gary LaPook
Date: 2007 Oct 26, 00:48 -0700
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 77º 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 86º. How many times have you taken sights above 86º? 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:
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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 77º 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 86º. How many times have you taken sights above 86º? 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. Andrés Ruiz Navigational Algorithms http://www.geocities.com/andresruizgonzalez
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