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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Fw: Advancing COPs Revisited
From: Peter Hakel
Date: 2010 May 4, 22:20 -0700
From: Peter Hakel
Date: 2010 May 4, 22:20 -0700
If I had to do a rigorous (assuming spherical Earth but otherwise exact) advancement of a celestial LOP, this is what comes to my mind:
1) Calculate the original circular LOP, which is a 1-parameter set of points.
2) At each LOP point construct a rhumb line using the appropriate course (track). Each rhumb line is yet another 1-D parametric curve. Distance along the curve from the point of origin (on our LOP) would be the most suitable choice of parameter for our purposes.
3) Use the distance traveled to construct the advanced LOP using the rhumb lines of step 2). Its one parameter (enumerating all its points) would be the same one used in step 1) for the original LOP.
This is really a straightforward, brute-force approach without much finesse. However, if one wants to be really very rigorous about running fixes, then it should be possible to encode this procedure into a computer and run it with whatever accuracy is desired.
Running fixes are typically only extended over a few hours, during which the vessel covers a distance that is tiny compared Earth's circumference, and remains far away from either Pole. In that case the standard running fix with (usually) straight LOP sections near an AP should be adequate.
Just my $0.02.
Peter Hakel
1) Calculate the original circular LOP, which is a 1-parameter set of points.
2) At each LOP point construct a rhumb line using the appropriate course (track). Each rhumb line is yet another 1-D parametric curve. Distance along the curve from the point of origin (on our LOP) would be the most suitable choice of parameter for our purposes.
3) Use the distance traveled to construct the advanced LOP using the rhumb lines of step 2). Its one parameter (enumerating all its points) would be the same one used in step 1) for the original LOP.
This is really a straightforward, brute-force approach without much finesse. However, if one wants to be really very rigorous about running fixes, then it should be possible to encode this procedure into a computer and run it with whatever accuracy is desired.
Running fixes are typically only extended over a few hours, during which the vessel covers a distance that is tiny compared Earth's circumference, and remains far away from either Pole. In that case the standard running fix with (usually) straight LOP sections near an AP should be adequate.
Just my $0.02.
Peter Hakel
