You posted:
"The point is that the ellipsoid and the ground are quite close to one another, which means the grid isn't that far off. (In Michigan,the geoid height is about -33 meters)"
You're kidding us, right?
You DO KNOW what a projection (grid) scale factor at a given point is, right?
Inquiring minds want to know,
Yes, when you're teaching yourself with NGS publications and Google books from the beginning of the last century, PACs, SACs, runway ends, CBLs, DOT control points and the like are good friends. They've destroyed many a misconception and myth that I've conjured up.
I've never visited one, but they're my friends nonetheless.
@mightymoe has an excellent grasp of the relationships and we can confirm his reasoning by referring to the Computed Constants for te Montana SPCS.
That last little number, r0, is the distance from either the semi-minor axis or the semi-major axis, I forget which, but it doesn't matter for this computation.
Dividing that number by the scale factor at the origin yields the distance from whichever point to the mapping plane, the State Plane. Subtracting r0 from that result yields the distance from the ellipsoid to the plane.
So, 6,375,730/.999392636277 - 6375730 = 3874.74 meters, or 12,593 feet. Adding an ellipsoid height of 5,000 feet yields Moe's 17,000 foot number.
Again, it doesn't matter because after you divide the grid distance by the combined factor, the distortion is near zero.
Here's a diagram that shows the relationship:
They need digging, but I traded my shovel for a computer a decade ago. But here's a list of airport monuments at RUT or KRUT as FAA wants.
It looks as though there's some Iroquois land nearby. I hope the airport didn't encroach.
Again, it doesn't matter because after you divide the grid distance by the combined factor, the distortion is near zero.
I'd say it does matter in the context of this discussion, because the fact that state plane often has to be altered to match ground distances within acceptable tolerances is indeed a problem with state plane.
There are a multitude of ways to approach that alteration, with the result that surveyors might (I certainly have) run across half a dozen surveys within the same township that all claim to be "state plane", each with a different set of hoops to jump through to get to a project system which is clearly not state plane.
Once we scale those coordinates and distances, they're no longer state plane, and to me that is an indication that a better system/projection could have been chosen from the start.
I don't know of a commercial geospatial software package that doesn't handle Transverse Mercator, Lambert Conformal Conic, and Oblique Mercator projections. But a lot of them have trouble handling random math applications to rigorously defined coordinate systems, and they all seem to handle it in very different ways.
While one could argue that all these software packages should be made to "deal with it", I would maintain that they are already equipped to deal with the proper solution - let them work with projections as intended. All we need to to is pick the right projection if already defined - or create the right one if it hasn't been defined.
But I am likely in the minority...
Apparently a few of the comments in this thread have been censored, because they are missing.
They appear to all be here. Even some that are a bit rough.
I hear you, but the question is, Why does state plane have to be modified to ground? The answer is, it doesn't. In fact, it is adjusted to ground using an algorithm that removes all distortion in most cases.
Using a single combined factor certainly works within limits but, in this era of unlimited computing power, why not use the system as it was designed to be used?
Consider the three points below. Two are from Helena Airport control and the third is south of them and off airport property.
Then consider the following calculations:
Now all three distances are close in both calculations, but the single-combined factor distances still contain distortion, while the individual combined factor distances do not.
So when you say acceptably close to ground distances, you also mean acceptably close to more rigorously calculated from grid distances.
But each of the lines has a different combined factor in the rigorous calculation and that may or may not be a problem for CAD. I have no clue about its needs.
Using the same parameters the LDP can serve many "ground" uses in the Helena valley area.
RX1056 about 12 miles east of the airport has a 15 ppm error and RX0088 8.5 miles north has a 2 ppm error.
Out of the valley will not perform as well however a Helena valley high LDP could be developed that would work fine for most purposes at around 6 to 8000 ft.
You can't legitimately charge a client to calculate each line the way you propose. Sure, we can figure out the ground distance using CSF for the mean of each line. But no one wants to sit down and do that for the thousands of lines in a subdivision. Instead project adjustment factors are used for "small" geographic areas and applied uniformly to each line. CAD automatically labels each line. Imagine changing each label by exploding it, calculating each line then manually editing it simply because you want to only use SPC.
Plus many customers (engineers) want cartesian ground modeled coordinates, not distances between points.
Our engineering clients decide what coordinate systems to use. And like you say, they want what works well using their existing computer programs for design. We of course what to give our clients as close to correct areas and dimensions as possible when land is being sold, especially when it's sold by the sq ft.
I agree. The software should do that, In goes xyz from GPS, out comes lat/lon, Northing, Easting, scale factor, convergence angle, and elevation factor for each point.
Then you have state plane coordinates and distances and distortion-free ground distances. If you need "ground coordinates," the software can compute an average combined factor and apply it to each point.
CAD, regardless of how expensive it is, how complicated it is, and regardless of how much Autodesk brags about it, should not drive surveying procedures. Combining management arrogance with the high opinion that computer science people have of themselves, making CAD follow NGS algorithms should be a piece of cake.
The dimensions of the project wouldn't matter; we could use NC SPCS to build a road to Montana and MT SPCS to build one back to NC.
I will leave it up to you to create that software, you still have giant rotations to deal with.
