MightyMoe, post: 327483, member: 700 wrote: 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?
I am using NGS program FORWARD and INVERSE as a check as recommended on page 1(?) of this thread.
I am not recreating the state line. I am trying to recreate the sections along the state line.
The 32å¡N line of the State Boundary was marked by John Clark in 1859. The land east of the Pecos River from the state line to a line 16 miles south was reserved from entry and appropriation by settlers and set aside for the Texas and Pacific Railway to subsidize the construction of the southern transcontinental rail line. Surveyors Peck and Champlin surveyed that reservation in 1876 beginning at a point "36 miles west of the S.E. Cor of the Territory of New Mexico". They were in a big hurry because they had a lot of land to survey before the deadlines in the T&P Charter expired. They were only surveying exterior block lines and no interior lines. They skipped 36 miles west of the corner of New Mexico to get through a stretch of sand dunes which was believed to have no farm or commercial use.
My goal is to recreate Peck's field notes based on recoverable evidence. For Blocks 54, 55 and 56, Township 1, Peck gives the call for 36 miles from the southeast corner of New Mexico but there is no evidence he actually ran the line so the state corner is not considered a controlling monument. Following Peck's field notes, the first currently existing original monument on the ground that you come to is John Clark's Monument No. 26. West of that, the next existing original monument is Jacob Kuechler's Monument No. K-0, which was supposedly established first by Peck for the northwest corner of Block 57. Kuechler was hired to locate the T&P lands in the 80 mile reservation west of the Pecos River beginning in October 1878. Kuechler's establishment of K-0 is considered reliable because Peck was on Kuechler's crew and he helped "the old dutch man" find it at the beginning of their survey.
There is some disagreement among surveyors, landowners and the GLO as to whether Clark's monument No. 27, which is east of 26, still exists or can be recovered. No. 27 would normally be the east controlling monument for my survey since it was called for in Peck's notes, but I am not trying to resolve the question of the missing monument 27. (If 27 did exist, it would push everything east and substantially change numerous surveys in an area with rapid development of petroleum production. Holding Clark 27 would move the section lines about a quarter of a mile east. For what it's worth, Stan Piper evaluated the existing monument purported to be 27 and believes that W.D. Twichell did in fact find and remonument Clark 27 in 1902 when Twichell was surveying the sand dunes for the Public School Land Surveys.)
So, assuming 26 is our first controlling monument and ignoring 27, we are working backwards to the east following the field notes in reverse. Since he calls to be on the state line, which is a line of latitude, I am calculating along the line (arc) of constant bearing and going the called distances to re-establish the block corners. Luchinni, Armstrong, Schumann and various other surveyors who surveyed this area in the late 1950s early 60s have held the block corners on the arc and just did a line of sight line between the block corners on which the section corners were set. I believe it was Luchinni who did the survey for the District Court Case in question. That may not be the best way to do it, but I am trying to retrace their work and not perform an original resurvey of the block at this time.
thebionicman, post: 327486, member: 8136 wrote: 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.
I mentioned that it was approximate, valid on the sphere, but close enough for short lines. The actual formula for convergence on the ellipsoid is
ëÓëÈ is in seconds of arc, and the resulting C is in seconds of arc. This is the difference between the forward and back azimuth of a line. For an east-west line ëÓë? is near zero
Andy Nold, post: 327491, member: 7 wrote: I am using NGS program FORWARD and INVERSE as a check as recommended on page 1(?) of this thread.
I am not recreating the state line. I am trying to recreate the sections along the state line.
The 32å¡N line of the State Boundary was marked by John Clark in 1859. The land east of the Pecos River from the state line to a line 16 miles south was reserved from entry and appropriation by settlers and set aside for the Texas and Pacific Railway to subsidize the construction of the southern transcontinental rail line. Surveyors Peck and Champlin surveyed that reservation in 1876 beginning at a point "36 miles west of the S.E. Cor of the Territory of New Mexico". They were in a big hurry because they had a lot of land to survey before the deadlines in the T&P Charter expired. They were only surveying exterior block lines and no interior lines. They skipped 36 miles west of the corner of New Mexico to get through a stretch of sand dunes which was believed to have no farm or commercial use.
My goal is to recreate Peck's field notes based on recoverable evidence. For Blocks 54, 55 and 56, Township 1, Peck gives the call for 36 miles from the southeast corner of New Mexico but there is no evidence he actually ran the line so the state corner is not considered a controlling monument. Following Peck's field notes, the first currently existing original monument on the ground that you come to is John Clark's Monument No. 26. West of that, the next existing original monument is Jacob Kuechler's Monument No. K-0, which was supposedly established first by Peck for the northwest corner of Block 57. Kuechler was hired to locate the T&P lands in the 80 mile reservation west of the Pecos River beginning in October 1878. Kuechler's establishment of K-0 is considered reliable because Peck was on Kuechler's crew and he helped "the old dutch man" find it at the beginning of their survey.
There is some disagreement among surveyors, landowners and the GLO as to whether Clark's monument No. 27, which is east of 26, still exists or can be recovered. No. 27 would normally be the east controlling monument for my survey since it was called for in Peck's notes, but I am not trying to resolve the question of the missing monument 27. (If 27 did exist, it would push everything east and substantially change numerous surveys in an area with rapid development of petroleum production. Holding Clark 27 would move the section lines about a quarter of a mile east. For what it's worth, Stan Piper evaluated the existing monument purported to be 27 and believes that W.D. Twichell did in fact find and remonument Clark 27 in 1902 when Twichell was surveying the sand dunes for the Public School Land Surveys.)
So, assuming 26 is our first controlling monument and ignoring 27, we are working backwards to the east following the field notes in reverse. Since he calls to be on the state line, which is a line of latitude, I am calculating along the line (arc) of constant bearing and going the called distances to re-establish the block corners. Luchinni, Armstrong, Schumann and various other surveyors who surveyed this area in the late 1950s early 60s have held the block corners on the arc and just did a line of sight line between the block corners on which the section corners were set. I believe it was Luchinni who did the survey for the District Court Case in question. That may not be the best way to do it, but I am trying to retrace their work and not perform an original resurvey of the block at this time.
Ok!!!
Looks like you have surely done your research.
And to get the points you just need to tweak the numbers.
I haven't used that program, but I suspect you tried to do a due east forward calculation, that should get you 6 miles away but slightly off the latitude you need, if you run the inverse you will see that the az is different forward and backward.
That is expected since you are not inversing along the curve, only at the equator would it work that the two would be east and west, but if the inverses are equally deflected from east-west then you are on the curve.
Rather than learn all the math, simply create a point with your needed lat and the long you already calculated at six miles (it probably will be very close to six miles if you swing it slightly). then inverse between them using the NGS program and you should see the same deflection from east-west, if forward is 89-58-00 then back should be 270-02-00.
That will get you on the curve. From there simply prorate the longitudes, its easier to do that if they are in ddd.dddddd format, simple prorates to get each mile along the six miles, using of course the latitude which will be the same number for the seven points. Then you should be able to import them into your database as LAT, LONG and let it convert it to your coordinate system.
You need to pay attention to elevations, most programs will do this calc on the ellipsoid so you may be a bit off the ground distance you need.
MightyMoe, post: 327501, member: 700 wrote: ...you should see the same deflection from east-west, if forward is 89-58-00 then back should be 270-02-00.
Since the NGS software is computing a geodetic azimuth the sum of the forward and back azimuth will not equal 360d.
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Kevin Samuel, post: 327513, member: 96 wrote: Since the NGS software is computing a geodetic azimuth the sum of the forward and back azimuth will not equal 360d.
Even on the same lattitude??
Kevin Samuel, post: 327513, member: 96 wrote: Since the NGS software is computing a geodetic azimuth the sum of the forward and back azimuth will not equal 360d.
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that may be here is an example, but it's trimble
NS Fwd Az 89-59-35.42
NS Back Az 270-00-24.59
Not exactly the same deflection, but really close, this is between two points one mile apart at lat 43-25-22
Andy Nold, post: 327455, member: 7 wrote: 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?
I recommended that method on this thread back on March 5.
Use CorpsCon to get SPCS coordinates from LatLon.
Never got any LatLon info from you.
I'm not sure I'm understanding your thoughts correctly.
Are you saying that you can:
*use NGS Direct
*enter LatLon - Distance - Due East or West Direction
*expect to be on the same Lat at six miles???
The Direction is only valid at the given Lon.
As one poster mentioned, when you do an NGS Inverse you get a Forward and Back Direction for the line.
Due to Convergence of Meridians
If so you must be pulling our collective legs.
BobKrohn, post: 327519, member: 6827 wrote: I recommended that method on this thread back on March 5.
Use CorpsCon to get SPCS coordinates from LatLon.
Never got any LatLon info from you.I'm not sure I'm understanding your thoughts correctly.
Are you saying that you can:
*use NGS Direct
*enter LatLon - Distance - Due East or West Direction
*expect to be on the same Lat at six miles???The Direction is only valid at the given Lon.
As one poster mentioned, when you do an NGS Inverse you get a Forward and Back Direction for the line.
Due to Convergence of MeridiansIf so you must be pulling our collective legs.
There is not an ounce of humor intended in this thread.
I don't know what NGS Direct is.
If you are talking about NGS Program Forward, one does not enter a due east or west direction, it is an azimuth from north and I was calculating the azimuth between points incorrectly.
I don't understand what you mean when you say direction. That term is too general. I have already addressed my confusion over the function of convergence. I was aware of its existence but attributed it to the change in radius of the lesser circle.
The question has been answered to my satisfaction.
The point that is 2,710.185 meters from the POB is, I think, very, very close to 32 00 00.5755 N, 103 48 10.7312 W. When you check
with Inverse, use 2,709.751 as the distance. I looked at some (there weren't many) NGS points nearby (4-5 miles was closest) and the ellipsoid height seemed to be about 1,020 meters. That gives an elevation factor of 0.99983987 and 2709.751 as the ellipsoidal distance.
This was done from basic geometry and trigonometry principles. It's very close to Andy's first estimate using 90 degrees as the azimuth. So, strong or weak or whatever in geodesy, he's been close from the beginning.
And I thought I had some difficulty being a colonial surveyor. I'll take a bounded by survey any day.
R.J. Schneider, post: 327517, member: 409 wrote: Even on the same lattitude??
On the same latitude, the sum is 360d.
I even entered it in reverse fashion to check.
My previous statement is not a rule for every situation. It does apply to a scenario with points of differing latitude.
Yes they are. This turns out to be an easy problem to solve. All you need is good ol' s = r theta and a way to find r, the radius of a parallel. You have s, the distance and you solve for theta, the difference in the longitudes of the two points.
The radius is the length of the normal to the ellipsoid at the first point multiplied by the cosine of the latitude. The normal is designated N in most sources and there's a fairly easy (and easy to find) formula for it.
Andy's going East, so, when you get theta, subtract it from the known longitude and, voila, you have the longitude that you need.
So there's no need for plane ccodinates or long formulas. It's just basic circle geometry, a little trig, and a smidgen of geodesy.
MathTeacher, post: 327608, member: 7674 wrote: Yes they are. This turns out to be an easy problem to solve. All you need is good ol' s = r theta and a way to find r, the radius of a parallel. You have s, the distance and you solve for theta, the difference in the longitudes of the two points.
The radius is the length of the normal to the ellipsoid at the first point multiplied by the cosine of the latitude. The normal is designated N in most sources and there's a fairly easy (and easy to find) formula for it.
Andy's going East, so, when you get theta, subtract it from the known longitude and, voila, you have the longitude that you need.
So there's no need for plane ccodinates or long formulas. It's just basic circle geometry, a little trig, and a smidgen of geodesy.
s = r theta
Don't forget to use radians for angular units.
Yields an ellipsoid distance, but you mention the elevation factor in your post above.
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.
You're welcome! Here's a follow up I put together that might be more clear. My only personal involvement in a project like this was very brief in MN back in the 80's, but had to teach PLSS so developed these. CFEDS is teaching a more precise method, but I believe these are the methods you would be retracing, and I think was what we used even in the 80's in MN.
Our model is an ellipsoid, which, in this case, seems to be more than 1,000 meters below the surface that we want to establish a point on. The normal, when it reaches the ellipsoid, has another thousand or so meters to go before it reaches the surface of the earth. The ellipsoid model and the surface of the earth are sort of, very loosely speaking, like two concentric ellipsoids.
So, any line we establish on the ellipsoid is going to be shorter than the one it's modeling on the earth's surface. Since Andy gave us a distance on the earth, we have to shorten it when we model it on the ellipsoid. The elevation factor does this.
Now, there's always a wrinkle, and the one in calculating elevation factors is that they use the average radius of the ellipsoid at the point where the elevation factor is being computed. A very user-unfriendly spreadsheet that I used for calculating the elevation factor for the POB is attached. You'll be able to see how you can use it for any point anywhere.
Also, a second file shows the r theta connection. You just have to change your perspective from a ground view to a polar view.
That 360-degree total was a great piece of insight. Where did you learn that?
Kevin Samuel, post: 327513, member: 96 wrote: Since the NGS software is computing a geodetic azimuth the sum of the forward and back azimuth will not equal 360d.
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I wasn't thinking about it adding to 360d, but once I thought about it, it has to. Of course if you inverse a due north line the forward and back will add to 180d, then each angle between will add to something else.
What I was thinking about was the deflection from due east and west.
This is an unusual question, generally (for me always) the calcs to get on a curve are between known points, just shoving one out there is not something I've ever had to do, and state lines are really touchy, many will say a private guy can't survey along them like this and can only recover them if found. I've only seen one 6 mile stretch where the MM's were lost and the BLM resurveyed it in 1974.
I agree Moe. Unless you are running original PLSS townships in Alaska with the BLM, this is not something that pops every day!
Andy,
It is not every day one needs to traverse a parallel of latitude - but it can be done with the right tools. And, it appears you are working in my part of the world - SE New Mexico. I'm in Las Cruces, NM. I'll be happy to help.
The first suggestion is to compute the change in longitude for each east-west line (component). The latitude will not change if you stay on the parallel but latitude does change if you are computing on the geodetic line (great circle if the earth were a sphere).
Another option would be to use the global spatial data model (GSDM) to do the computations - it offers several options that address your issues. You can do your computations on the ellipsoid if you like or the GSDM can be used to perform ground level computations.
If you wish to follow-up send me an email at [email protected]
Kevin Samuel, post: 327654, member: 96 wrote: I agree Moe. Unless you are running original PLSS townships in Alaska with the BLM, this is not something that pops every day!
Honestly, I've never heard of such a thing, what kinda lands are to the north, and why aren't they controlling?
Sounds like a court case. I did have one similar, a line of longitude to stake. It was blank also, much easier...........
Ran 4 miles of fence along it, took an afternoon.
MathTeacher, post: 327621, member: 7674 wrote: That 360-degree total was a great piece of insight. Where did you learn that?
If this was directed towards me, I was just visualizing a spherical triangle and I am cognizant of the difference between a spherical triangle and planar triangle.
Also credit is due to Jack Walker at OIT his tutelage in Geodesy in the Geomatics program.
We used the following text by Elithorp and Findorf. From a brief Google search it appears to be the text of choice for most surveying/geomatics programs.