Chapter 11 of the Eighth edition of Surveying by Moffit and Bouchard (1987) bring into focus purpose and use of plane surveying. It is entitled SPC and UTM Systems. This is before everyday use of satellite survey.
> Methods of plane surveying are based on the assumption that all distances and directions are projected onto a horizontal plane tangent to the earths surface at one point within the area of the survey.
> When discrepancies of angles and distances measured on the ground as projected onto the horizontal plane become intolerable, the limits of the plane have been reached.
> SPC systems have been devised to allow simple methods of plane surveying to used over great distances while at the same time precision is mainained APPROACHING that of geodetic surveying.
> SPC maps become useful to engineers who desire data for reducing their surveys to state grid. (customers demand a usable, simple system)
> As originally designed, the size of the zones were kept small enough to keep maximum distortion at any point to 1:10000 ( 100 ppm). Sidenote: The book list Montana as having 3 Lambert zones covering the state.
> The lengths of measured lines must be reduced to sea level or spheroidal lengths. The sea level lengths must be further reduced to grid lengths.
> Most large engineering projects will create construction plans containing drawings of grid lines and state coordinates. The difference between grid length and ground length can be taken into account by one of two methods. The first WHICH IS QUITE PRACTICAL, is to ignore the difference. This method assumes that the errors in layout measurements are larger than the errors introduced by neglecting the difference between grid and ground. Suppose the difference in grid to ground length is ONLY 0.22 ft/ 1000 ft. This SMALL discrepancy can be ignored on most construction projects. The second method is to compute a combination sea level grid factor, and then to divide all grid distances indicated on or derived from the plans in order to obtain the correct ground or project lengths. In order to accomplish this WITHOUT MISUNDERSTANDING between the surveyor, engineer and contractor a note should accompany each construction drawing giving explicit instructions to the user. The note could possibly read, " All distances shown on the set of plans or derived from state plane coordinates shown on the plans are grid distances on the _____ Coordinate System, Zone ______. To obtain ground distances for laying out lines, divide grid distances by 0.9998940."
Takeaways: Tolerable differences have changed due to technology; thus, smaller zones are required and SPCS2022 is the result. Even before CADD surveyors were expected to deliver a simple cartesian coordinate system to customers that approximates the ground on a horizontal plane. That expectation has not changed. Methods that devise accurate mark to mark distances between project points and reference meridians that are not parallel while possible are not useful or efficient. The demand and applications for plane surveying that is geo referenced goes far beyond the maps that surveyors produce for boundary surveys. There is a benefit to have boundary surveys geo referenced. Because standard survey practices seem to drive survey law most states have not yet codified that boundary surveys must be geo referenced. GIS requirements will probably be the driving force behind that since surveyors aren't.
I would rewrite part of your takeaways. Neither TM nor Lambert state plane SPCS have parallel meridians.
A Mercator projection has parallel meridians, but a Transverse Mercator projection does not. Lambert projections have meridians that all intersect at a common point, usually a significant distance above a pole. Parallels are curved, so it's possible for these straight-line meridians to be perpendicular to the curved parallels, and they are.
What those 18th century mathematicians did is both remarkable and crazy.
There is a benefit to have boundary surveys geo referenced. Because standard survey practices seem to drive survey law most states have not yet codified that boundary surveys must be geo referenced. GIS requirements will probably be the driving force behind that since surveyors aren't.
And mark my words, as the benefit of this because more and more clear, if we prove to be a hindrance to the public by dragging our feet and screeching about "original footsteps" or "monuments rule" or "Get It Surveyed", there will be serious attempts to cut surveyors out of the equation altogether.
They likely won't succeed (as should happen), but it will be yet another area where we yield ground to other geospatial practitioners due to our pride and stubbornness, rather than take control and be the expert authority on something that absolutely be in our wheelhouse as licensees.
And then we'll close the loop by bitching on SurveyorConnect about how we're not respected and our work is being taken away by "those damn GISPs" and "it's only a matter of time before they get burned and come running to us for help"...
When we take our ball and go home, someone else will step up with another ball and the game will go on, while we sit at home stewing.
GIS requirements will probably be the driving force behind that since surveyors aren't.
Who wants to guess why this is likely the case?
What those 18th century mathematicians did is both remarkable and crazy.
But apparently those folks could do it.
You can take heart in the fact that most GISers have less understanding of map projections than the average surveyor and need to be experts in the discipline. They're the epitome of button-pushers.
"Well, I put this WKT into Proj.whatever and it didn't error out and it put points on the map and so it must be right and the lines between them must be right, too. Thank God I don't have to deal with spreadsheets anymore. I never could get those parentheses right."
Parden me, please. This stuff ain't easy to learn, but, by golly, people who need to be experts should have to learn it.
Rant over.
Again, you're mixing up calculations that aren't applicable.
NAD27 is monument based. If you really need to get on NAD27 for some reason (can't imagine what it might be) you need to survey between monuments.
It's basically the same as sectional surveying, the monument is king.
The monuments control, and with NAD27 the values on the data sheets are fixed.
So, you survey between monuments, there is no world wide (ellipsoid) calculation, there is no NCAT.
The radius of the earth used for elevation scale is 20,906,000'. That radius can be drastically changed and the new elevation scale factor will essentially be the same (all scale factors in NAD 27 stop at the 6th place or 1PPM). Try 20,904,000' and use an elevation at 4000' and you will see the numbers don't fluctuate enough to change the SP distance.
NAD27 is a hands on experience, there were no satellites, it was boots on the ground and compared to today's process there were huge errors in it.
NAD27 needs to disappear, unfortunately it can't in some circumstances. There are permitting issues that force 27 to continue. Also, geology maps are often based on it, crudely based, so rough estimates (CORPSCON OR NCAT) are normally "good enough" for that purpose.
They're the epitome of button-pushers.
That doesn't seem to be hindering their progress?!
There are permitting issues that force 27 to continue.
I'm from the government, and I'm here to help...
Now, Moe, you're arguing against yourself. Above, you said, "Z is there, you had to have Z." Now I'm not sure what you're arguing, but I think you're either saying there is a Z coordinate or there is not.
Did you know that the monument in your 1925 data sheet has a current data sheet? Did you know that the superseded coordinates on that data sheet are identical to the 1925 data sheet?
Those plane coordinates were rigorously calculated from the lat/lon position using the Clarke 1866 ellipsoid.
Monuments may rule, but the NGS ones don't have made-up coordinates nor a Z coordinate.
No, and the licensing requirement in NC and other states doesn't seem to be guaranteeing their competence either.
Indeed. In the 17th and 18th centuries, the most valuable asset for a sea captain was an accurate map. Mercator developed one in 1659. No WKT files, Proj.whatever, or even an HP calculator.
What he did have was a deep understanding of curved surfaces and plane surfaces and how one could be converted into the other.
His map, though, enabled mariners to plot a constant-bearing course, a rhumb line, not a geodesic. Mariners didn't care, the map helped them to not get lost.
We still have a problem today understanding the difference between a straight line on a map and a geodesic on the earth.
Yes, my bad, I meant z is there. Z will not be there, and yes I know there are new datasheets. And that the superceded control will be the record.
However, locate point Badger with GPS and place a NAD83 coordinate on it. It will not match the data sheet, therefore a recalculation of the NAD27 number will not match the superceded control value which they took from the old datasheet.
It's possible that we did locate Badger, I would have to dig for it, it's not an easy task to get there. Normally I drive past all the old monuments and don't bother with them, that one was a helicopter trip at one time. I occupied it circ 1981 with a T2 and topcon distance meter. It's in the big country.
You said: "The radius of the earth used for elevation scale is 20,906,000'."
There is no "elevation scale" in NAD27. There is a scale factor, but there is no elevation factor, so "elevation scale" is a puzzling term.
For each individual calculation of (x, y), (Easting, Northing) coordinates from lat/lon, the radius of the ellipsoid at that lat/lon is used. I'm not familiar with an overall average radius, but there is one for each SPC zone.
To imply that the computation of NAD27 plane coordinates was haphazard is misleading. By today's standards, the measurements were not exact, but the mathematical conversions were sound and rigorous.
When you calculate in NAD27 you calculate the grid scale and the elevation scale for each line, in TM it's the mean of the easting giving you the Grid scale you interpolate from the charts, the elevation scale is 20,906,000/20,906,000+the mean of the two points elevation. You multiply the grid scale and the elevation scale to get the combined scale factor which is multiplied to the measured ground horizontal distance to get the State Plane Grid distance.
Right. I stand corrected on the 20,906,000 number. The 1945 instructions dictate that number.
Consider now these distance calculations for QW0575 and QW0554, two points in Yellowstone County. The first is with NAD 27 coordinates and factors and the second is with NAD 83 coordinates and factors.
I believe that the difference in the two distances is about a decimeter:
The old NAD 27 was a rigorous plane coordinate system, but the computations were heavy for the equipment of the day. Those who used it successfully were a talented bunch.
Yes, again however, there wasn't anyway to step outside the monumented control points, and they aren't all that accurate, especially many of the easy to access monuments which might be 3rd order. Many of the first order points are difficult to get to.
I can understand that. I've seen a lot of data sheets for monuments both here, in Montana and other states that show 5 decimal places in seconds in the superseded NAD 27 fields.
Bad data will overcome rigorous math every time.
@rover83 That is exactly correct. For what it’s worth. A very good mapping agency almost closed the door completely on geodetic surveyors within the agency. An independent study was done. The cartographers understood completely why they needed geodetic control and checks. The photogrammetry folks understood as well. The new young GIS software gurus. We’re showing how they could do everything without and pushing for the closing down of the geodetic surveying. Well finally after all the research was done and the facts presented they found they didn’t have enough geodetic surveyors. I knew personally one of the gis folks that was pushing the end. He is actually a good friend. Much older than I. But one day as we were getting ready to brief and he had his part and I had my part. I had my ppt slides reviewing and he did as well. The one famous slide that is in text books internet pages even esri of the different layers. One thing is missing at the bottom which is Geodesy and geodetic control. Then at each level between the layers and especially at the top again is geodetic control checks. Of course i was doing GPS wgs84 and how the monitoring stations gave the realizations to the surface of the earth and creates a foundation for the datum which in turn provides all other branches of geomatics including the gis folks a foundation to work from and check to. That is how he and I became friends. I had experience in gis and he knew it but he never thought of it that way. All satellite imagery and all is directly related to gps and wgs84 . Surveyors have both geodetic and land surveying a tremendous responsibility In national and local security and the protection of the public for many things. We should be leading. Again a motto was brain washed with in the USMC. Lead Follow or get the Hell outa the way. I think surveyors should be the same way but nicer than a old jar head.
Mathteacher. Take a look on NGS website in Virginia south right on the line between North Carolina and VA. Due southwest of south boston east of danville. Pull the ngs data sheets on some classical control in that area and see what’s missing on some of the old nad83 classical control. Also do some grid to ground conversions in that area not a lot of control. But notice something a little different about the grid vs ground lenths.
An interesting area. Looking along ol' Highway 58, also known as suicide alley in older days, for the few complete control points, the combined factor is very nearly equal to one. So grid and ground are equal.
In another life, I chased a crook all over the Tidewater Region during the summer of 1987, travelling 58 twice a week and meeting many good people who had been cheated. I won't go into detail, but it ended favorably for me and my company.