Intermediate points-You are right, of course.
Sigh, nothing like showing your ignorance in front of a thousand people. At least most have lost interest in this thread (fewer than a hundred viewed have your last post so far).
I said
>Isn't it true that a great circle becomes a straight line in SPC because they use "conformal" projections? Is that only an approximation?
The references you gave show that it is only an approximation. One that was good enough that the old books I learned SPC from seem to have ignored it (e.g. McEntyre). I find that Wolf and Ghilani do cover the topic, now that I know what to look for, but I've never systematically studied their book but only sections as topics catch my interest.
In your spreadsheet after finding the azimuth, what method do you use to project forward each meter?
Thanks for your patience in teaching me.
MathTeacher, post: 320708, member: 7674 wrote: Page Baseline--Bill's intermediate points
That's an interesting question that you raised about geodetic (great circle) lines becoming straight grid lines. It's a bit of a fuzzy area for me, so feel free to correct me, but please be kind. I'm old, you know.
James Stem addresses this issue in two places in his NGS Manual 5, once on pages 18 and 19 and then again on pages 52 and 53. In reading these sections, we need to make a distinction between "projected geodetic lines" and "reduced geodetic lines."
Projected geodetic lines come about when we calculate State Plane Coordinates directly from the coordinates on a geodetic line, with no regard to length or the azimuth that the grid line should have. Reduced geodetic lines come about when we create a grid line by multiplying the geodetic length by a scale factor and adjusting the geodetic azimuth to a grid azimuth.
I think that comparing my coordinates to yours directly is closely akin to projecting a geodetic line onto the State Plane grid rather than reducing the geodetic line to the grid.
On page 53, Stem gives a diagram that shows how the projected geodetic line looks when compared to the grid line. Note that, when the lines are north of the central parallel on a Lambert projection, the projected geodetic line lies to the north of the grid line.
The Page Base Line is north of the Nebraska SPC central meridian and all of my intermediate coordinates are north of yours. Additionally, the differences in latitude grow and then shrink as we proceed down the line. Our separate results fit Stem's diagram.
To reduce the geodetic line to the State Plane grid, we would multiply its length by the average scale factor, adjust the geodetic azimuth to a grid azimuth, and then calculate the State Plane coordinates of the terminal point using grid length and grid azimuth. Those coordinates should agree with the State Plane coordinates of the projected geodetic line.
Note that in Stem's diagram on p. 19, the grid coordinates of the initial and terminal points of the grid line are the same as the grid coordinates of the projected geodetic line. However, the grid coordinates of the intermediate points of the two lines are different.
I think that our separate results look just as they should look.
However, we did make some different assumptions and there is another source of difference. If you enter the State Plane coordinates of the SW Base into either Corpscon or the NGS software, the resulting geodetic coordinates will not agree with the data sheet. Going from State Plane to geodetic has always been problematic and there can be a small amount of error introduced in that process.
Additionally, we don't know how precisely "straight" the measured line is. If any of the points are a bit off-line, then the measured distances will not be those of a straight line and our coordinates will be off. I don't think it's possible to reconcile the differences down to zero.
This has been a very interesting exercise and I'm happy with the small differences in our coordinates. I share your pessimism about actually finding all of the points, but if they're not found, it won't be because of faulty search coordinates.
Bill93, post: 320975, member: 87 wrote: Intermediate points-You are right, of course.
Sigh, nothing like showing your ignorance in front of a thousand people. At least most have lost interest in this thread (fewer than a hundred viewed have your last post so far).
I said
>Isn't it true that a great circle becomes a straight line in SPC because they use "conformal" projections? Is that only an approximation?The references you gave show that it is only an approximation. One that was good enough that the old books I learned SPC from seem to have ignored it (e.g. McEntyre). I find that Wolf and Ghilani do cover the topic, now that I know what to look for, but I've never systematically studied their book but only sections as topics catch my interest.
In your spreadsheet after finding the azimuth, what method do you use to project forward each meter?
Thanks for your patience in teaching me.
MathTeacher, post: 320708, member: 7674 wrote: Page Baseline--Bill's intermediate points
That's an interesting question that you raised about geodetic (great circle) lines becoming straight grid lines. It's a bit of a fuzzy area for me, so feel free to correct me, but please be kind. I'm old, you know.
James Stem addresses this issue in two places in his NGS Manual 5, once on pages 18 and 19 and then again on pages 52 and 53. In reading these sections, we need to make a distinction between "projected geodetic lines" and "reduced geodetic lines."
Projected geodetic lines come about when we calculate State Plane Coordinates directly from the coordinates on a geodetic line, with no regard to length or the azimuth that the grid line should have. Reduced geodetic lines come about when we create a grid line by multiplying the geodetic length by a scale factor and adjusting the geodetic azimuth to a grid azimuth.
I think that comparing my coordinates to yours directly is closely akin to projecting a geodetic line onto the State Plane grid rather than reducing the geodetic line to the grid.
On page 53, Stem gives a diagram that shows how the projected geodetic line looks when compared to the grid line. Note that, when the lines are north of the central parallel on a Lambert projection, the projected geodetic line lies to the north of the grid line.
The Page Base Line is north of the Nebraska SPC central meridian and all of my intermediate coordinates are north of yours. Additionally, the differences in latitude grow and then shrink as we proceed down the line. Our separate results fit Stem's diagram.
To reduce the geodetic line to the State Plane grid, we would multiply its length by the average scale factor, adjust the geodetic azimuth to a grid azimuth, and then calculate the State Plane coordinates of the terminal point using grid length and grid azimuth. Those coordinates should agree with the State Plane coordinates of the projected geodetic line.
Note that in Stem's diagram on p. 19, the grid coordinates of the initial and terminal points of the grid line are the same as the grid coordinates of the projected geodetic line. However, the grid coordinates of the intermediate points of the two lines are different.
I think that our separate results look just as they should look.
However, we did make some different assumptions and there is another source of difference. If you enter the State Plane coordinates of the SW Base into either Corpscon or the NGS software, the resulting geodetic coordinates will not agree with the data sheet. Going from State Plane to geodetic has always been problematic and there can be a small amount of error introduced in that process.
Additionally, we don't know how precisely "straight" the measured line is. If any of the points are a bit off-line, then the measured distances will not be those of a straight line and our coordinates will be off. I don't think it's possible to reconcile the differences down to zero.
This has been a very interesting exercise and I'm happy with the small differences in our coordinates. I share your pessimism about actually finding all of the points, but if they're not found, it won't be because of faulty search coordinates.
Bill93, post: 320975, member: 87 wrote: Intermediate points-You are right, of course.
Sigh, nothing like showing your ignorance in front of a thousand people. At least most have lost interest in this thread (fewer than a hundred viewed have your last post so far).
I said
>Isn't it true that a great circle becomes a straight line in SPC because they use "conformal" projections? Is that only an approximation?The references you gave show that it is only an approximation. One that was good enough that the old books I learned SPC from seem to have ignored it (e.g. McEntyre). I find that Wolf and Ghilani do cover the topic, now that I know what to look for, but I've never systematically studied their book but only sections as topics catch my interest.
In your spreadsheet after finding the azimuth, what method do you use to project forward each meter?
Thanks for your patience in teaching me.
