NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: AP terminology
From: Peter Hakel
Date: 2009 Nov 15, 10:23 -0800
From: Geoffrey Kolbe <geoffreykolbe---.com>
To: navlist@fer3.com
Sent: Sun, November 15, 2009 12:07:18 AM
Subject: [NavList 10688] Re: AP terminology
Frank, Peter H and Peter F.
The confusion comes from a loose (I hesitate to say incorrect) use of
terminology. Peter Fogg is right, I think, that because the tables
generally used for sight reduction require an Assumed Position, this
term has degenerated into a generic term for the starting position
when using the St Hilaire method - but that does not make it the
"correct" term.
Frank has a point, that we bring the baggage of our backgrounds with
us when getting to grips with new concepts and problems and this can
cause confusion. Peter Hakel tells us that his background is as a
"theoretical and computational physicist (in the area of radiative
properties of plasmas)". As I did my Ph.D. in the radiative
properties of (atoms in) plasmas, there is no excuse there ;-).
My problem was the term 'LOP'. To me, an LOP (or position line as we
call it over here) is a straight line. We must remember that the St.
Hilaire method is essentially a graphical method where a fix is
generated by drawing lines on a chart. The LOP's drawn on the chart
are lines which are tangential to a circle of position, centered on
the Geographical Position of the celestial object of
interest. Looking at Bowditch, there is some fuzziness in the
definition of a line of position. "Circular lines of position" are
synonymous with "circles of position" and lines of position, it
seems, can be circles. But when discussing the St Hilaire method,
Bowditch (article 1703 in my 1984 edition) describes the LOP as a
straight line drawn to be tangential to the circle of position.
In his post [NavList 10683], Peter Hakel finally tells us that...
"The LOP's are circles", so now we know where he is coming from and
his single parameter to describe a circle of position makes more
sense. But since we are talking about LOPs in the context of the St
Hilaire method, where LOPs are straight lines, I could not see what
John Karl was getting at when he talked about "calculating the LOP
directly" and I suspect he, too, was talking about the circle of
position, not the LOP as (usually) drawn on a chart.
Geoffrey
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From: Peter Hakel
Date: 2009 Nov 15, 10:23 -0800
I agree that misunderstandings often occur simply because of different interpretations of key words, not necessarily because anyone has a factually wrong idea.
The universal plotting charts that I have show five parallels of latitude and a compass rose in the middle. By putting numbers on those parallels and drawing the corresponding meridians, we are automatically "assuming" that this is where the ship is, somewhere in that region. Then, within this "assumed region" (AR) we choose an "assumed position," draw a straight-line LOP, etc.
Since the question was about how to compute the LOP "directly" without any AP, we have to consider the LOP in its entirety. That is a circle and not just the relevant section approximable by a straight line. The only "natural" reference point, independent of navigator's choice, is the GP which will be at the root of the parametrization of the entire LOP.
I believe that computing an LOP "directly without an AP" and yet "within the context of the St Hilaire method" is an oxymoron and thus this question cannot be answered. Indeed, John Karl calls this section of his book "Position without St. Hilaire" in which he writes (p. 79): "Note that this is a sight reduction in its own right, completely avoiding the St. Hilaire intercept method."
BTW, Problem 5.9 in his book (p. 192) does find the fix using the St. Hilaire method, but with equations of planar analytical geometry instead of actual plotting. There the (straight-line!) LOP's are necessarily parametrized. John chose relative azimuth angles as parameters and used the common AP as a reference location.
Peter Hakel
PS. I used the term "compass rose" above. Is that the correct term, or is it properly called "azimuth rose" or something different altogether? Well, "a rose by any other name…" right? :-)
The universal plotting charts that I have show five parallels of latitude and a compass rose in the middle. By putting numbers on those parallels and drawing the corresponding meridians, we are automatically "assuming" that this is where the ship is, somewhere in that region. Then, within this "assumed region" (AR) we choose an "assumed position," draw a straight-line LOP, etc.
Since the question was about how to compute the LOP "directly" without any AP, we have to consider the LOP in its entirety. That is a circle and not just the relevant section approximable by a straight line. The only "natural" reference point, independent of navigator's choice, is the GP which will be at the root of the parametrization of the entire LOP.
I believe that computing an LOP "directly without an AP" and yet "within the context of the St Hilaire method" is an oxymoron and thus this question cannot be answered. Indeed, John Karl calls this section of his book "Position without St. Hilaire" in which he writes (p. 79): "Note that this is a sight reduction in its own right, completely avoiding the St. Hilaire intercept method."
BTW, Problem 5.9 in his book (p. 192) does find the fix using the St. Hilaire method, but with equations of planar analytical geometry instead of actual plotting. There the (straight-line!) LOP's are necessarily parametrized. John chose relative azimuth angles as parameters and used the common AP as a reference location.
Peter Hakel
PS. I used the term "compass rose" above. Is that the correct term, or is it properly called "azimuth rose" or something different altogether? Well, "a rose by any other name…" right? :-)
From: Geoffrey Kolbe <geoffreykolbe---.com>
To: navlist@fer3.com
Sent: Sun, November 15, 2009 12:07:18 AM
Subject: [NavList 10688] Re: AP terminology
Frank, Peter H and Peter F.
The confusion comes from a loose (I hesitate to say incorrect) use of
terminology. Peter Fogg is right, I think, that because the tables
generally used for sight reduction require an Assumed Position, this
term has degenerated into a generic term for the starting position
when using the St Hilaire method - but that does not make it the
"correct" term.
Frank has a point, that we bring the baggage of our backgrounds with
us when getting to grips with new concepts and problems and this can
cause confusion. Peter Hakel tells us that his background is as a
"theoretical and computational physicist (in the area of radiative
properties of plasmas)". As I did my Ph.D. in the radiative
properties of (atoms in) plasmas, there is no excuse there ;-).
My problem was the term 'LOP'. To me, an LOP (or position line as we
call it over here) is a straight line. We must remember that the St.
Hilaire method is essentially a graphical method where a fix is
generated by drawing lines on a chart. The LOP's drawn on the chart
are lines which are tangential to a circle of position, centered on
the Geographical Position of the celestial object of
interest. Looking at Bowditch, there is some fuzziness in the
definition of a line of position. "Circular lines of position" are
synonymous with "circles of position" and lines of position, it
seems, can be circles. But when discussing the St Hilaire method,
Bowditch (article 1703 in my 1984 edition) describes the LOP as a
straight line drawn to be tangential to the circle of position.
In his post [NavList 10683], Peter Hakel finally tells us that...
"The LOP's are circles", so now we know where he is coming from and
his single parameter to describe a circle of position makes more
sense. But since we are talking about LOPs in the context of the St
Hilaire method, where LOPs are straight lines, I could not see what
John Karl was getting at when he talked about "calculating the LOP
directly" and I suspect he, too, was talking about the circle of
position, not the LOP as (usually) drawn on a chart.
Geoffrey
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