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What is a “ground” measurement?
Posted by Norm on December 19, 2022 at 2:58 pmHere’s something to ponder this week.
I was taught to measure on a projection perpendicular to gravity pull at both ends of the measurement in 1974. I always got chewed out for not using a plumb bob. I was told by use of a plumb line and a level bubble I was measuring along the horizontal plane. When I asked what THE horizontal plane was, they told me to shut up and cut brush. Later on, I figured out I was measuring between two projected string lines that get closer together the lower I go and further apart the higher I go (as a rule). I also figured out that THE horizontal plane that is held in such high esteem and is called the GROUND by many is truly only accessible at one threedimensional point on the earth. Everything else we report on and certify to as being on THE horizontal plane relative to that one point is a lie to one extent or another. My state law even tells me I must survey on THE horizontal plane ( i.e. lie ). We have a lot of interesting discussions about how to lie the best in an effort to certify the world is flat. The least it seems we could do is to codify the plane we should be using in the location we are so the lie we are perpetrating is consistent.
mathteacher replied 1 year, 6 months ago 17 Members · 50 Replies 
50 Replies

how to lie the best
I hope everyone has a great day; I know I will! 
Here’s something to ponder this week.
I was taught to measure on a projection perpendicular to gravity pull at both ends of the measurement in 1974. I always got chewed out for not using a plumb bob. I was told by use of a plumb line and a level bubble I was measuring along the horizontal plane. When I asked what THE horizontal plane was, they told me to shut up and cut brush. Later on, I figured out I was measuring between two projected string lines that get closer together the lower I go and further apart the higher I go (as a rule). I also figured out that THE horizontal plane that is held in such high esteem and is called the GROUND by many is truly only accessible at one threedimensional point on the earth. Everything else we report on and certify to as being on THE horizontal plane relative to that one point is a lie to one extent or another. My state law even tells me I must survey on THE horizontal plane ( i.e. lie ). We have a lot of interesting discussions about how to lie the best in an effort to certify the world is flat. The least it seems we could do is to codify the plane we should be using in the location we are so the lie we are perpetrating is consistent.
I’m surveying across some mountain ranges in central Nevada, 1979 or so. One measurement in particular stood out. Measured from a high point down into the valley, about a 3 mile distance. Then, measured back up to the high point. Try as I might the two horizontal distances wouldn’t mesh. There was about .4′ difference. All because of the difference in elevation from the point the measurement was taken from. The higher HD was .4′ longer. It’s always helpful to see it with real numbers, both were correct.

Don’t forget that in many cases we are explicitly told, if not mandated, to both use “the plane” as well as “ground distances”. Technically an impossible task from a mathematical standpoint.
“…people will come to love their oppression, to adore the technologies that undo their capacities to think.” Neil Postman 
@mightymoe This is the exact scenario I have found useful in explaining successfully to attorneys and others why I cannot certify to “true, accurate and complete” or some such nonsense regarding measurements.

All we really we need is some sort of laser beam (Dr Evil) that doesn’t bend or disperse, and shoots through rocks so we can measure the actual straight line distance between points. Then we can do away with this gravity and elevation hogwash. I mean really, how hard can this be? It’s like we’re working with caveman tools out there.

The problem isn’t the measurement. It’s that there is no single theoretical definition for your measurement to try to match.
In most cases there is a practical value that is good enough, but it would be nice if you knew what you were trying to achieve the best approximation to.
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it’s all relative…. How much error do you think you were introducing by pulling on a steel tape and holding a plumb bob steady? It’s >0, for sure.
I try not to sweat the small stuff.

My state law even tells me I must survey on THE horizontal plane ( i.e. lie ). We have a lot of interesting discussions about how to lie the best in an effort to certify the world is flat
“I do hereby certify that the world is flat, and that all the round earth people are not in compliance with the law…”
Ho boy! I can see a cartoon series somewhere here!
N

Didn’t you know? We live on one of these!

Well. Whether you’re on the earth’s surface or taking a geometry exam, it takes three points to determine a plane.
If you don’t believe that, try to make your tripod wobble, level or not.

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 marktomark 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..
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Didn’t you know? 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? ????

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.
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.

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.
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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 midpoint 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.
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.

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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