A quick projection calculation
We are tasked with "redoing" a site survey from about ten years ago. Changes have been made to the site so they want an updated topo for design and new construction. The company that originally did the survey isn't in business any more. All we were given was PDF of the original site survey that shows 4 control points #3-4-5 #6. The survey shows XYZ coordinates (Modified SP) and elevations with the bench mark that was used indicated. It also shows a scale factor to correct to surface of 1.0002227145. Lots of numbers there. Clearly state plane coordinates were not multiplied by the scale factor to produce site control as DOT always does, they were scaled up by that factor around a local point. The one missing meta-data piece was where is the point the control values were scaled up from.
We occupied control point #3, did the topo survey, located control points 4 & 5, however, point #6 was removed during construction.
I processed the base point using the local CORS point. I put that lat long into a SP file along with the given XY of #3. I actually hit the elevation of point #3 flat from my CORS processing which made me think I did something wrong so I did it in a second file and it hit flat again..
The SP from lat, longs of the CORS point was W-NW 0.55' from the given value for point #3. So I now know the expansion point is W-NW.
Now I had a bearing and distance to the Expansion point. I calculated the bearing using the two points, figured out that 2475' would work well so I calculated the expansion point using the bearing and 2475' from the CORS location..
I entered the local site parameters into Trimble using the expansion point and 1.000223 for a scale factor, recalculated the DC file moving the base to the XYZ that was given for #3, Checked into points 4 & 5 less than .02'. We are good to go, now we have a definable projection closely related to the original and usable for this site.
Of course, my expansion point isn't the same as the original, that is unknown. However, for the purposes of the 20 acre topo it's as close to perfect as we can do without trying to dig out files from a defunct company. Also, it avoids calibration which would really screw with the data.
I suspect that the original expansion point was near the ROW of a State highway which is about a hundred feet south of my new one. But if you consider the error induced by that it will be 100*1.000223-100 or maximum of .02' north or south of that point, and we aren't surveying in those directions.
When you have those kind of coordinates they just have to be treated the same as any other local 5000/5000 system. The only difference is that the orientation might be on an SP basis. My procedure in these situation goes along these lines:
1. Determine fresh grid coordinates for the control.
2. Establish a reasonable combined scale factor for the project area and apply it to the record drawings and data.
3. Translate the de-scaled record data onto the newly determined control coordinates, best fit. Assuming that the differences will be negligible.
In my case I like to work in a statutory low distortion projection so step 2 can usually be skipped, and step 3 becomes a translation and rotation.
Finally, IMO, a pdf is only a little more useful than a paper print in terms of re-survey data. Even the vectortized versions. I get pdfs thrown at me routinely and always ask for the .dwgs, which usually cannot be acquired.
A new LDP or any change in the coordinate system isn't applicable to this job. The original coordinate system which was given has to be held. 10 minutes of calculations created a definable projection usable in TBC and ACAD, the added plus was that the elevation control with Geoid 18 was extremely tight. I'll assume the construction guys will do a calibration, but at least my numbers will be "clean" for future surveys which will probably come up.
We often assigned the scale about to CP #1 in these situations when we did things that way. Of course we quit doing things that way at least 10 years ago. Realize you weren't given #1. Good job. I'd say you were rather fortunate on the height check. When we adjust to an arbitrary coordinate system rather than translate to the geodetic system we translate to arbitrary on top of the underlying geodetic. Using the offset value from the project state plane coordinate to the local and rotating and scaling as needed for best fit. Same thing a calibration does essentially but gives the surveyor more control over what is used to define the transformation. Also provides a record of the parameters used if your favorite flavor of field software doesn't do it.
I'm still scratching my head over the elevation check. I was expecting something around 1/2 tenth of a foot, I didn't expect it would be flat. The scale factor pointed to a local DOT project and I could have contacted DOT to get local projects along that section, but it would take much more time than my quick calculation.
I agree that it's similar to a calibration, the big difference is it's "clean". Trimble adjusts the Geodetic numbers when it calibrates. I don't like that at all and I disagree that they should ever do that to fit an XYZ set of coordinates. Taking a set of local Coordinates and warping Geodetic numbers to fit them seems so backwards to me. I can continue on with this projection for as many miles as you like in any direction and still be able to relate them easily to any other projection, a calibration will fall apart rather quickly.
It's also possible to sweep an LDP through the same coordinates, a bit more of a calculation process, but it works. The times I've done it, I have to do some trial and error adjustments before I Get there.
