As for azimuth, my celestial observations corrected for grid convergence. I used UTM Zone 18, which renders a 1.66929652 convergence factor. That matches NCAT, which I just looked up. Also did LaPlace correction and Xi and Eta corrections, but don't ask me to explain them now. i forgot a lot of stuff I once knew!
What I don't understand is that in NCAT, they show an entirely different convergence (-00 03 25.12) for SPC than for UTM, so I may have made that mistake. But in any case, my astro azimuth delta is off by 20", not minutes or degrees, so I don't think convergence explains the difference.
UTM (Universal Transverse Mercator) and State Plane Coordinates for your state are two completely different projections from ellipsoid to plane surface. The convergence angle will always be different between the two systems at any any one Lat, Long position
Make only one point in your data to have the same point number as the other survey so they are tied at that point.
Would it make sense to use the point to tie, the point from which I did all my my celestial, and which the surveyor used for his base station? My understanding is that a base station that sits there for several hours renders more accuracy as to location.
After that I would translate and rotate your traverse to that 2042 foot line (that might have a new bearing now) and see how the points compare.
I can't figure out how to translate and rotate survey data with my software. Might someone be so kind as to take a look at this file and move my five points (500, 3000, 7, 2 and 3102 such that my surveyor's base (100) and my base (500) are co-located, and then rotate my four points to the 2042 line around the base point?
I will if someone doesn't beat me to it, but I can't do it today.
@bill93 NADCON
@bill93 NADCON
I'm not trying to go from one datum to another.
I'm trying to move my survey 9.55' S17 42'12"E and then rotate it 27" counter clockwise around point 500.
Have you converted to the feet that you want to use? The units need to be the same in both systems.
Your Northings are substantially greater than the surveyor's while the Eastings are fairly close. That indicates a significant southerly translation and a slight rotation.
How close the resulting fit will be is anybody's guess. There is some degree of error in both systems and they're tied to an ellipsoid using different methods. The software will move your points south, rotate to align the Eastings, adjust the southerly move to bring Northings closer and so on. How it does this is also anybody's guess, but we have to have faith.
I'm still investigating that aspect. I thought my surveyor's survey is using US Survey feet and mine International feet, but I'm not absolutely sure of that. The two longest legs are very close in matching length (.04' delta for the 2042' line and .00 for the 1689' line). I'm confirming with my surveyor what he used.
The software will move your points south, rotate to align the Eastings, adjust the southerly move to bring Northings closer and so on. How it does this is also anybody's guess, but we have to have faith.
I know this is probably dead simple using Carlson (or even just Autocad), but is it possible to do this using just mathematics? My dim memory of college math courses (linear equations, vector transformations?) makes me think that this could be done using matrices. Am I hallucinating?
If I got every point in my survey into an excel spreadsheet with cells denoting Point, Northing, Easting, Elevation, then said:
"Point 500, at 28158.252,1618337.901,1032.70 should be moved (along with all other points) by -9.0978 in Northing, 2.9043 in easting and raised 10.8' in elevation".
Then, after doing that with all the points, create a new coordinate file, renumbering all my points with "New" added to the end, like 500New, 2New, 7New etc., and brought them back into my survey, would this be a legitimate strategy? Of course I've no clue how to use Excel to rotate the whole mess, but one step at a time I guess.
The older I get the more important twisting my brain to solve such problems becomes.
Thanks for your continued helpful insight.
It is easy math for the translate. And you have it right.
i have a little DOS program from back in the day that takes common coordinates on different systems and computes a least square rotation and translation. I hve used ot to rotate and shift a plat to what is found in the field.
You can let if compute a scale factor or force it to 1.00.
Out put is a set of coordinates in both systems for a basis to translate and rotate about ( it calls them center of gravity point) NOT RELATED TO GEODESY !
It will then give you the difference in N and E after the shift and rotation. attached is an output file.
I run it in a VDOS window and works like a charm.
If you want I can email you a zip file of the set up and some rudimetary directions.
G
Here is your data translated and rotated like you asked. There is a problem with using point #100 as a benchmark. It makes all your other traverse points an average of 2.65' 3.1' higher than the matching GPS points.
I have used PCSurvey for 25 years. It is low cost and works perfectly for all my survey needs.
EDIT: Calc'd a better average but something is very wrong with elevations.
Here are the coords for the translated and rotated points. I translated your points by moving all of them so that 500 moved to 100. I then rotated around 500(now the same as 100) so that your azimuth matched the azimuth of the surveyor on the line which he has a length of 2042.66 and you have a length of 2042.62. These are the resulting coordinates for your points. All of his coordinates remain unchanged.
Note all of the elevations were raised 10.80' so that 500 matched 100 in elevation also.
I keyed in the northing on Point 2 incorrectly. Landbutcher's coords are correct.
@gary_g has the right take. I do this in Excel. It goes like this.
Northing transform: surveyor's Northing = a + b*RFC Northing + c*RFC Easting
Including both Northing and Easting accounts for rotation. The a will turn out to be something close to the average RFC Northing, b will be close to 1, and c will be close to 0.
I use Excel Solver to do this. First, assume values for a, b, and c. One of your Northings will do for a, 0.98 for b, and 0.01 for c. Put these in 3 different cells.
Your spreadsheet will have 5 columns: RFC Northing, RFC Easting, Adjusted RFC Northing, Surveyor Northing, and Squared Difference Column.
Enter RFC and Surveyor Northing.
Suppose that you entered a, b, and c in A1, B1 and C1. Then your Adjusted RFC Northings will be A1 + B1 * RFC Northing + C1 * RFC Easting.
The Squared Dicference column will be (Adjusred RFC Northings - Surveyor Northings)^2.
Sum the squared differences in a cell, at the bottom of that column.
Solver is in the data tab, if you have it. If you don't, it's an add-in free from Microsoft.
In the solver screen, you minimize the sum of squared differences cell subject to changing $A$1, $B$1, $C$1. Then let 'er rip.
Do the analogous workflow for Eastings. Here, b will be near 0 and c will be near 1 while a is near the average of Suyveyor's Easting.
If I haven't left out something, you should get an excellent transform, maybe not professional, but likely pretty much indistinguishable.
RFC also note the distances Landbutcher shows on his map are grid distances or State Plane distances. The distances you show and that your surveyor showed are ground distances and that is why they look different but are actually the same. Those distances are just being expressed in different datums.
@mathteacher Can you make excel do a rotation?
RFC also note the distances Landbutcher shows on his map are grid distances or State Plane distances. The distances you show and that your surveyor showed are ground distances and that is why they look different but are actually the same. Those distances are just being expressed in different datums.
Ya I did not know where this was nor the CSF so I just left the surveyor's GPS data alone. Also the 1689.16' distance is the same for GPS and TRAVERSE so maybe the surveyor had his GPS set for ground measurements.
Wow. Thank you gentlemen. I've got my work cut out for me now. Regarding elevation: I now have the .rw5 from the surveyor's data collector. In the .rw5 it shows the antenna height as both 0.620 and 6.562. Which is it lol? I might have to add the height of my steel pier upon which he mounted the unit.
Also, is it worth submitting the file to OPUS? Still not sure about the "antenna type" in OPUS
When doing an RTK survey you need 2 antennas if you use your own base. Likely the base antenna height was .62' and the antenna he had on his rod was at 2 meters which is the 6.562' height.
I'm guessing he measured from the top of your steel pier to the bottom of his antenna or he may have measured to a specific measuring mark on the side of his antenna