Today's reading of the most high Manual comes from the Book of Large Scale Cadastral Surveys, Chapter 2, Verse 11:
[INDENT=1]By statute, in PLSSia. a straight line is a line of constant bearing, as it crosses every meridian at the same angle. (BECAUSE of the curvature of the earth, a line of constant bearing is an arc). A straight line is not to be confused with a "line of site" Most lines in PLSSia are intended to be surveyed as lines of constant bearing. This is a direct result of the requirement that the lines be run "according to the true meridian," thereby crossing each meridian at the same angle. Other terms for such lines are rhumb lines, small circles or loxodromes.[/INDENT]
[INDENT=1] [/INDENT]
[INDENT=1]Some boundaries of the PLSS are defined by a "line of sight." Many conventional survey instruments make measurements long the line of sight. THIS LINE OF SIGHT IS A LINE OF CONSTANTLY CHANGING BEARING. The only exceptions are meridional lines and the equator. Such a line is traditionally called a great circle.[/INDENT]
[INDENT=1] [/INDENT]
[INDENT=1]Because of convergence of meridians and the requirement to use the true meridian as the basis for direction of lines, lines not along a meridian are run on a CONSTANT BEARING in order to intersect meridians at the same angle. A line of site line passes each meridian at a different angle and hence is a line of constantly changing bearing; in other words, it is not a straight line.[/INDENT]
[INDENT=1] [/INDENT]
So sayeth the Chief Cadastral Surveyor.
John Hamilton, post: 327411, member: 640 wrote: What projection? I am talking about latitude/longitude. The only line you can go on a constant bearing is a north-south line which is a line of constant longitude. You cannot go on a constant bearing and stay on a latitudinal line.
Yes, you can.
Kevin Samuel, post: 327418, member: 96 wrote: This is the key phrase to keep in mind.
I agree with John.
Staying on a constant latitude is one thing, but the development of your distance (read as: elevation factor) is also a big consideration.
How detailed are the instructions (from the court) you are referencing Andy?
Sent from my iPhone using Tapatalk
East along the arc xxx varas. (see sketch above)
John Hamilton, post: 327331, member: 640 wrote: Absolutely the convergence of the meridians enters into this. If you were going due north or due south then and only then would there be no meridian convergence.
That is completely wrong. If you follow the meridians (lines of longitude) on a globe from the equator to either pole, they start out far apart and they all intersect at the pole. They CONVERGE at the pole.
If you are going east or west, you are on a line of latitude, also known as a parallel. My instructor in college used the mnemonic device of remembering a ladder->latitude and the rings on the ladder are parallel like the lines of laddertude. Parallel lines do not converge. As I said previously, convergence has NOTHING to do with calculating points on latitude.
Andy, you've got this thing mostly right. I'm a little shocked at all the bad advice you're getting. Especially this gem: "The only line you can go on a constant bearing is a north-south line which is a line of constant longitude. You cannot go on a constant bearing and stay on a latitudinal line." I guess that depends on what the definition of "go" is. Certainly you cannot just use line of sight to lay out a latitudinal line (you would need to use offsets from a secant or tangent line), but you can (and in fact MUST!) be on a line of constant bearing to stay on a latitudinal ine.
I'll disagree with you on this comment though: "As I said previously, convergence has NOTHING to do with calculating points on latitude."
Convergence does matter, because angle of convergence changes with latitude, so if you were to use a secant or tangent method, this angle (or rate) of convergence would matter.
On a broader note, this conversation illuminates a massive problem with our order of surveying education, where we start with Plane Surveying (fake) and work our way up to Geodetic Surveying (real). We've got it in the wrong order. Why not start with reality?
Loyal, post: 327320, member: 228 wrote: How about...
Forward azimuth FAZ = 89 58 22.5267 From North
Back azimuth BAZ = 270 1 37.4733 From North
Ellipsoidal distance S = 9656.0827 m
First Station : Center
----------------
LAT = 32 0 0.57550 North
LON = 103 49 53.96752 WestSecond Station : East
----------------
LAT = 32 0 0.57550 North
LON = 103 43 46.08939 WestForward azimuth FAZ = 89 58 22.5267 From North
Back azimuth BAZ = 270 1 37.4733 From North
Ellipsoidal distance S = 9656.0830 mkind of a quick and dirty solution, assumes [zero] ellipsoid height, and needs a little tweaking.
Loyal
That looks like the right numbers, Loyal but how did you arrive at that? Is that a particular program or good old fashioned calculator work?
Andy: Hardly wrong at all, maybe a matter of how I phrased it, maybe I should have left out the word "meridian". Yes, the meridians do converge (get closer together). Convergence as I used it is a numerical value that is computed by taking into account the delta longitude and the latitude. When I say convergence, it would be ZERO if going north south, meaning there is no correction to the azimuth, you would stay on a line of 0å¡ or 180å¡, and always be on the same longitude.
However, if I go due west from a point and go 5 km, when I look back to where I started from the bearing is 89 57 44.5". So obviously I was not on a line of constant bearing. And, i am not at the same latitude anymore either. Tell me what azimuth (or bearing) will keep me on a line of constant latitude.
Yes, a due east-west line (90 from north) is tangent to the latitudinal line, but will soon deviate from it.
FrozenNorth, post: 327454, member: 10219 wrote: Andy, you've got this thing mostly right. I'm a little shocked at all the bad advice you're getting. Especially this gem: "The only line you can go on a constant bearing is a north-south line which is a line of constant longitude. You cannot go on a constant bearing and stay on a latitudinal line." I guess that depends on what the definition of "go" is. Certainly you cannot just use line of sight to lay out a latitudinal line (you would need to use offsets from a secant or tangent line), but you can (and in fact MUST!) be on a line of constant bearing to stay on a latitudinal ine.
I'll disagree with you on this comment though: "As I said previously, convergence has NOTHING to do with calculating points on latitude."
Convergence does matter, because angle of convergence changes with latitude, so if you were to use a secant or tangent method, this angle (or rate) of convergence would matter.On a broader note, this conversation illuminates a massive problem with our order of surveying education, where we start with Plane Surveying (fake) and work our way up to Geodetic Surveying (real). We've got it in the wrong order. Why not start with reality?
I was considering my words after I posted them and I agree that there are changes to the lines of latitude as they get closer to The North Aboyne Irregular, but I didn't consider it to be a factor of convergence, more of a change in the radius of the latitudinal arc.
I am trying not to be a DB in my replies because 1) I have been asking for help and 2) I'm coming from the same place, my experience with geodetic surveying has limited. I went to a really good, classical plane surveying program and it has served me well but I wouldn't say it was a complete education.
I've been doing a ton of reading on the subject and talking to others off of the forum and I think the light at the end of the tunnel is not a train this time. And I do appreciate everyone's input.
FrozenNorth, post: 327454, member: 10219 wrote: Andy, you've got this thing mostly right. I'm a little shocked at all the bad advice you're getting. Especially this gem: "The only line you can go on a constant bearing is a north-south line which is a line of constant longitude. You cannot go on a constant bearing and stay on a latitudinal line." I guess that depends on what the definition of "go" is. Certainly you cannot just use line of sight to lay out a latitudinal line (you would need to use offsets from a secant or tangent line), but you can (and in fact MUST!) be on a line of constant bearing to stay on a latitudinal ine.
I'll disagree with you on this comment though: "As I said previously, convergence has NOTHING to do with calculating points on latitude."
Convergence does matter, because angle of convergence changes with latitude, so if you were to use a secant or tangent method, this angle (or rate) of convergence would matter.On a broader note, this conversation illuminates a massive problem with our order of surveying education, where we start with Plane Surveying (fake) and work our way up to Geodetic Surveying (real). We've got it in the wrong order. Why not start with reality?
I agree that at each individual point (like integrating), you are on the latitudinal line at a bearing of 90å¡. But, if you have a line of sight of say 1 mile, the end of that line of sight is not at the same latitude. And if I go the actual azimuth needed to be at the same latitude at the end of that mile, then before or after the 1 mile point it is no longer on the same latitude.
John Hamilton, post: 327456, member: 640 wrote: Andy: Hardly wrong at all, maybe a matter of how I phrased it, maybe I should have left out the word "meridian". Yes, the meridians do converge (get closer together). Convergence as I used it is a numerical value that is computed by taking into account the delta longitude and the latitude. When I say convergence, it would be ZERO if going north south, meaning there is no correction to the azimuth, you would stay on a line of 0å¡ or 180å¡, and always be on the same longitude.
However, if I go due west from a point and go 5 km, when I look back to where I started from the bearing is 89 57 44.5". So obviously I was not on a line of constant bearing. And, i am not at the same latitude anymore either. Tell me what azimuth (or bearing) will keep me on a line of constant latitude.
Yes, a due east-west line (90 from north) is tangent to the latitudinal line, but will soon deviate from it.
In the context of PLSSia, I'll have to disagree on that one, John. My quotation earlier was from the 2009 Manual of Survey Instructions, page 29. Your statement is in direct conflict with the published definitions and the nice little sketches.
Maybe this example will help. Calculates azimuth of secant at one mile intervals.
Andy Nold, post: 327459, member: 7 wrote: In the context of PLSSia, I'll have to disagree on that one, John. My quotation earlier was from the 2009 Manual of Survey Instructions, page 29. Your statement is in direct conflict with the published definitions and the nice little sketches.
Yes, the parallel of latitude crosses each meridian at an azimuth of 90å¡. But what I am trying to describe (apparently not very well) is that if I start at A, backsight a point due north and turn 90å¡, I will not cross the other meridians that i come to at 90å¡ azimuth nor will I be on the same latitude. If I was able to extend that line by going as far as I could see, then turning 180å¡, etc, I would be going at a skew angle to each meridian. If I was to maintain a constant 90å¡ bearing, that would not be a straight line but rather a curved arc.
I found out why FORWARD was not working for me. I had calculated the azimuth incorrectly. And, I have to correct my comment to FrozenNorth about convergence not being a factor as it DOES affect the calculation of the azimuths between the points on the line of latitude. That's why the program wasn't working for me.
Great exercise and I learned a lot this week.
Thanks for the PDF, Duane. That is very helpful.
Andy,
Inasmuch as I deal with PLSS "curved lines" quite often, I wrote a DOS-BASIC program many years ago that "solves" the "latitudinal arc" problem for me. It basically uses a series of å? chain "vectors" and a "custom" Transverse Mercator projection to generate a "true bearing" (in the BLM/PLSS sense) between a pair of Lat/Lon positions. In this case, I simply "generated" a point 6 miles EAST, and another 6 miles WEST of your initial point (assuming a zero ellipsoid height).
The program actually generates a Lat/Lon every 33 feet along (in this case) a parallel of Latitude, AND creates a .DXF file with a 2d polyline connecting the dots (every 33 feet) in whatever projection that I need (UTM/SPC/LDP).
I use the program from time to time, but most often to solve between two "known" points. It also allows input of Ellipsoid Heights at each end, and adjusts the 33 ft. vectors to the mean height of the line (+/- <1ppm).
The arc to chord variance [length] is trivial on a short line (like these). The OFFSETS between the ARC and a geodesic at various points along the line between the two points, is NOT (as a general rule), even on a SHORT (1 mile) "line."
Loyal
Andy Nold, post: 327469, member: 7 wrote: ..Great exercise and I learned a lot this week....
Thanks for the PDF, Duane. That is very helpful.
Andy, We all need to give you a big thanks, also. Through all the repetitive surveying exercises I perform to make a living, sometimes stirring up the pot reminds me of things I don't often do...and have almost forgotten. I'm sure I'm not the only one, either!
I will fess up that it was Kent who turned the light bulb on about my azimuth problem after discussing it on Facebook.
Andy Nold, post: 327474, member: 7 wrote: I will fess up that it was Kent who turned the light bulb on about my azimuth problem after discussing it on Facebook.
Ol' K-Mac in the clinch! That's a hoot.
Andy Nold, post: 327469, member: 7 wrote: I found out why FORWARD was not working for me. I had calculated the azimuth incorrectly. And, I have to correct my comment to FrozenNorth about convergence not being a factor as it DOES affect the calculation of the azimuths between the points on the line of latitude. That's why the program wasn't working for me.
Great exercise and I learned a lot this week.
Thanks for the PDF, Duane. That is very helpful.
Andy, what program are you using?
If it's trimble there is a very simple routine that does exactly what you want, take you maybe five minutes.
The odd thing to me is that there is an unmonumented state line, isn't there surveys that staked it already?
Andy,
Did you per chance run the numbers using the formula I posted? I've checked offsets in real world notes with it and found some were likely computed that way. Those notes pre-date the publication (and author) cited for its discovery. I often wonder how widely the 'tricks' we learn were used in times past. Many of the folks that called themselves Surveyors 150 years ago were pretty smart...
TTYL, Tom
John Hamilton, post: 327435, member: 640 wrote: Convergence of the meridians has nothing to do with any grid system. The convergence angle is what you describe as between grid north and geodetic north at a point.
I did read your initial post incorrectly. The formula you posted is the formula used to compute the convergence angle in a Transverse Mercator projection. While many of the same factors impact azimuth computations on the sphere, they aren't similar enough problems to interchange formulas.
