Didn't you know??ÿ We live on one of these!
What is that thing? Is it "THE" powerball they keep pulling out of their hat several times a week? ?????ÿ
Vincenty used the distance at the mean height of the two endpoints as the distance to reduce to an ellipsoid distance. How that translates to this discussion I don't know, but it defines "the plane" as well as the measured distance.
What is a "ground" measurement?
I'm not sure how to define a ground measurement, per se, but I think a good example would be the relationship along the edges of the triangles and between the vertices of those points within a TIN/DTM.
Still problematic because we're going from 3d (real life, data collection), to 2d (mapping plane/computer), to (pseudo) 3d computer (displayed in 2d on monitor).
Odd how humans can only conceptualize and operate (in real time) in 1 or more dimensions lower than what we actually need to, to represent reality.
4d reality represented in 3d position + 1d time.
3d positions represented in 2d plane + 1d height + 1d time.
2d plane of 3d points is only accurate at 1 point.
1d point (technically undefined?), but can be located with 3d position + 1d time.
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Looks like we need to define reality in 5 or 6 dimensions, so we can get to meaningful 3d/4d representations that accurately archive a given situation?
3 points on the Earth's surface and at least two of those 3 points referenced or projected to the horizontal plane are not the same points. The law says distances must refer to the horizontal plane - whatever that is. In the interest of consistency it would be best to define the plane as the appropriate low distortion plane coordinate system established by the NGS. No calibration to some other horizontal plane that is just another approximation allowed.?ÿ
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Vincenty used the distance at the mean height of the two endpoints as the distance to reduce to an ellipsoid distance. How that translates to this discussion I don't know, but it defines "the plane" as well as the measured distance.
The classic way to calculate points on the projected surface was to measure the distance, reduce it to horizontal, then apply the combined factor using the mean of the eastings (Transverse) and the mean of elevations placing the scale calculation at the mid-point on the line between the two observed points. The measured horizontal distance was then multiplied by the combined factor and the calculation was done for the SPC at the forward point.
As Vicenty observes the actual radius of the earth isn't all that important since the elevation/height scale calculation is a ratio. 20,906,000ft was the number always used for NAD27.
However, each and every traverse point creates a plane. As you move forward you are surveying on a different surface, depending on your elevation. The larger the elevation difference between the two observed points the larger the difference between the two observed horizontal distances.?ÿ
I believe it was about 1981 when a sometime poster on this forum developed a program for our HP calculator that would calculate the geodetic number from classical terrestrial observations then calculate the state plane number. Saved so much time from doing that by hand.
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If ever there were an 'it depends' question...
There are more ways to attain approximate ground values than I am capable of learning. The key is to select the method that introduces no more than an acceptable level of distortion for the task at hand. Of course the business side requires the selection of an efficient method.
As applied to boundary we add two goals. First, get me to the called for monument (that thing we should accept over advisory measurements). Second, express a measurenent so it has value as evidence if the monument is disturbed.
The bottom line is simple. If we tossed out every method that was not technically correct we'd still live in caves.
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And report which method you used to get those "horizontal" ground measurements if there is any possible misinterpretation.
I'm sure I know of a set of several surveys that report SPC distances with no note explaining that. Fortunately they are on flat land at a location where it only makes a difference of a couple tenths of a ft per mile. They don't say what points were held for basis of bearings, either.
And report which method you used to get those "horizontal" ground measurements if there is any possible misinterpretation.
I'm sure I know of a set of several surveys that report SPC distances with no note explaining that. Fortunately they are on flat land at a location where it only makes a difference of a couple tenths of a ft per mile. They don't say what points were held for basis of bearings, either.
That would be a first for me, SPC distances but a different bearing basis.
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no idea what you're talking about with the theoretical definition stuff.
I believe this was Norm's point in the post that started the thread. We all believe there is a mark-to-mark distance between two precisely marked points on a round earth and at different elevations, and it can be measured pretty accurately with GNSS, with distance computed from the XYZ coordinates.
But what is the horizontal ground distance between them? This is undefined a because the horizontal plane at one point misses the other point,.
It isn't just an academic or philosophical matter, as shown by Moe's practical example involving modest distances and significant elevation differences..
I see.?ÿ I would just say this is simply the price you pay for using simple math.?ÿ We could be using calculus and there most certainly is an equation for the curve between any 2 stations on the surface of the earth that would answer that question precisely, but surveyors chose not to go down that road so...
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we'd still live in caves
Some portion of the world's population still lives in caves.
And they routinely demonstrate how ineffective the world's most advanced technology can be.
There are more ways to attain approximate ground values than I am capable of learning.
So why not accept the work that's been done to design an approximate ground plane that works for everyone? Surveyor's. Engineers. GISr's, even dare I say architects and construction contractors. Everyone on the same sheet of music. I've seen it work on projects statewide with way more positive than negative comments.?ÿ
@norm The long and short is, nothing will always work for everyone all the time.
Where a record LDP exists I nearly always use it. That covers about 15% of the places I work. Even the new datum and projections (if they arrive before I retire) won't suffice for most of what I do. That's not taking anything away from that work. It just means it doesn't fit the needs of my client.
doesn't fit the needs of my client
Interesting?ÿ
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That would be a first for me, SPC distances but a different bearing basis.
Oh, I think they are SPC bearings, but I don't know which line he held when he did the fitting to get perfect closure on each of the several abutting and/or nearby plats, and there is enough span that they can't all be pure SPC bearings and still close.
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Even the new datum and projections (if they arrive before I retire) won't suffice for most of what I do. That's not taking anything away from that work. It just means it doesn't fit the needs of my client.
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I would agree. Quite a few states appear to have bagged it on the "third layer" LDPs that could have minimized distortion way beyond the state zones, and dialed in their zone boundaries around administrative/political boundaries.
The state zones are an improvement over NAD83, to be sure, but I think an extra opportunity was squandered. Especially considering that we have another 2.5 years before the new datums drop. Plenty of time to fix it, but unlikely anything will be done.
Custom LDPs are awesome and will always have their place, but it would have been great to blanket the nation with standardized definitions.
