When I hear complaints about the inaccuracy of State Plane calculations, I usually formulate an outrageous example to answer them.

Today's outrageous example is this: Use the North Carolina State Plane Coordinate system to calculate the length of Runway 05 at Helena, MT, Regional Airport.

The numbers are in the picture below. Runway lengths are slope distances while state plane calculated distances are horizontal distances at an average ellipsoidal height.

The runway end elevations are orthometric heights and I don't know if they're NAVD 88 or NGVD 27, but the two systems are very close, so I adjusted then to the ellipsoid with the Geoid 18 height of the airport's PAC.

Anyway, the given slope distance is 4644 feet and the slope distance calculated from North Carolina State Plane Coordinates is 4643.989 feet.

You were saying about State Plane inaccuracies...?

Edit: The airport data are here: Airport Data and Information Portal (faa.gov)

Cool

So how's that SP bearing along the runway? Anywhere near close to true north?

Now do the Montana SP distance. 😉

The convergence angle at Runway 05 is -19 02 42.516. The grid azimuth is 85.28132189 degrees, so the geodetic azimuth is 66.23617856 degrees.

The published true bearing of the runway is 66 degrees, so that looks pretty good.

Going a step further, NGS Inverse puts the geodetic azimuth at 66 14 05.6571 and the adjusted grid azimuth above converts to 66 14 10.243.

The two azimuths are 4.586 seconds different. Is that a lot or a little? I don't know how to judge that.

As to the Montana SPC, I'll leave it to you to compute the grid and slope distances and the grid and geodetic azimuths. But I'll bet you a quarter that your slope distance and geodetic azimuth won't differ significantly from mine.

The point is, a state plane system is extremely accurate and can be used successfully far beyond its intended zone for both distances and angles. However, if you want ground distances and geodetic azimuths, you have to do the adjustments designed to accomplish that.

This works because the SPCS is rigorously attached to the ellipsoid, period. It can be modified as long as you don't destroy that attachment.

In MSP the Grid distance is 3.6' short, the AZ is almost 2d rotated, so there's some big distortions just using Montana. I'm not sure why you think a 19d rotation from true north isn't a big distortion. Plus I don't believe NC SP grid distance in Montana gives a distance within .02' of a surface distance. But I'm not going to do the calculations. I've seen engineers shove zones beyond where they should go and it was a disaster.

Here's the inverse:

3.6' in 4644' is a huge number.

This is why using SP is a problem.

Apples and oranges. There isn't much to be gained in discussing differences between points on a grid system of any kind and points on a system that uses a different combined scale factor between any two points on a project. Most everyone knows SPC works when a different scale is applied to each inverse. Imagine a project with 10,000 points and going through these calculations between each point. Not practical and that's where an accurate enough model is used. I suppose you could calc 10,000 vectors in a project. But you would never have plane closure or the same coordinates without an LSA. Of course doing a LSA would give an average of truth which is what LDP does.

Well, the grid distance using NCSPCS is 4,739.896 feet, so there is a huge distortion. But when I divide that by the average combined factor, 1.020651751, the answer is 4,643.989.

See, what the combined factor does is eliminate the distortion between distances on the grid and distances on the ground.

If you demand that the plane coordinate calculations match your on-the-ground physical measurements, then State Plane distances are sure to disappoint. If you use the system as it was intended to be used, you'll have no distortion problems.

As to the accuracy of the line using NCSPCS, all you need to do is check the coordinates and the scale and elevation factors. You can do this in NCAT. Were I you, I would do that before I questioned the veracity of someone else's numbers.

Thank you! I failed to apply the t - T correction and that is the difference between my adjusted grid azimuth and the geodetic azimuth.

With Montana being so far away from the central meridian in the NC system, t -T correction has to be applied.

If you

use the system as it was intended to be used, you'll have no distortion problems.

And therein lies the problem.

If people: read the manual, had some training, used their tools (hardware/software) the right way, we wouldn't have all this Frankenstein garbage.

Most people half-ass it all their professional career because of this concept.

Every adjusted point in LSA introduces a ppm error into each computed non distorted vector. I would venture a guess the ppm error is similar to the LDP ppm.

If we all just accepted the fact the earth is not flat we all would not be having these conditions lol. No state plane system and no assuming the earth was flat and just did everything geodetic no issues would arise. But then we could not use simple math to perform traverse closures and such. But that will not change until we no longer make flat maps.

Running geodetic north will close azimuths but ya can’t use the same exact math we use to check angular closures around as corrections need to be applied.

We surveyors rule the roost as flat earth kings. Flat on grid flat on surface Because our distances along the surface are distorted as well as the grid systems because it’s not flat. The distortions on a spc system is from ellipsoid to plane when we set our instruments up on the surface and reduce our slope differences to horizontal and hopefully correcting our ZA prior to. We are assuming everything is flat but thats flat between those two measured points at an average difference in height period. And we assume gravity is the exact same where ever we plumb our rods and instruments as well. Curvature / refraction etc. we also know that gravity changes and anomalies happen. But i will keep doing what i need to do in order to meet job requirements and state standards per the limits of what we do.

I think that SPC with combined factor adjustment will slightly outperform an LDP with no adjustment.

Typically, an LDP scale factor is derived from some elevation factor, either one at an identified point or an average elevation factor for the project.

But at any LDP point, a combined factor can be computed that can actually tighten up a distance calculation.

If I were designing an LDP for this runway, I would create a tangent (single parallel) Lambert Conformal Projection, put the grid origin at the endpoint of Runway 05, and set the scale factor at 1/0.99981685, the reciprocal of the elevation factor at that point.

The projection plane would be tangent to the topographical surface at that point. There would be little distortion from scale and a bit from elevation, but the grid and ground would be close enough over a mile or two so that no corrections would be needed.

At least, that would be the hope.

Yep, this is what everyone working in state plane did and every day. We calculated each and every measured distance, it was part of the job.

You are backing in the process.

Surveying the Helena area 15,000' below ground is what MSP is doing.

It's always been hard for me to fathom that surveying equipment didn't automate those same calculations. Conversions from lat/lon to any plane coordinate system are embedded in GIS software and surveying software, too, I would guess.

Data collectors collect everything that's needed to calculate scale factors and elevation factors.

Why on earth did they not implement the procedures for a SPCS survey?