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?
Mathteacher surveying equipment has automated it. If I survey a state plane job, all my equipment projects it with the GPS, the Robot, everything. It doesn't fix the issue of SPC rotations or distance distortions. If I worked in a small low state east of the Rocky Mountains, state plane would probably be good enough. I prefer to not work in state plane, little of our work is, the last few property boundaries I did in state plane were done for two clients that insisted they be on state plane. Both had major issues with area calculations.
@mathteacher they do???
what am I missing?
In the 1930s they had transit and tape, they used SPC to be able to use triangulation stations and do their calculations using their familiar plane methods and I’m sure there were published tables to help them derive scale factors and convergence angles. Everything was done manually, no computers.
If people: read the manual,
Most manuals are VERY vague as to what the software is actually doing
@mathteacher our first date collectors were really dumb boxes. They kinda started out just recording data so one had all the hz angles slope distance za a point number and a code ama description like GS for ground shot etc. I believe we owe it to those before us that we’re writing there own cogo software and implementing it with some of those first data collection tools. C&G smi hp. I mean it took Trimble years years to develop a roading package that was close to what a person could do in a dos based C&G or hp and SMI package. One of the first data collectors i used daily that i could apply a scale factor to was sdr33. But it would not apply it to nothing but a topo type shot. It didn’t have the processing power to apply the correction on staking a point. I found that out the hard way. Now all the state plane systems nad 27 nad 83 we did the computations by reducing the ground distance to ellipsoid and then to grid. Now it’s backwards with gps we want to go from grid to ground well some do. And this has caused issues as cad operators and technicians see a scale factor they honestly assume its a combine factor i have seen it applied incorrectly so many times its not funny. I have seen the scale factor used as if it were a combined factor. Same with just elevation factor or ellipsoid factor. I use those terms because we still have the elevation factor terms used instead of ellipsoid factor. I read dot survey manuals across the usa as I guessed it might help with my preparation in FS exam. And PS exam. Because they being national exams I wanted to make sure when i saw a term i could quickly identify terminology they might be discussing as input is from across the usa not just local terminology. But i have seen some DOT manuals state something like this “combined and elevation factors “. But only one number for an area. I as well ask which is it. I can only speculate. Anyway times have changed and I assume all field software now days can compute everything but i have only seen carlson and Trimble access recently. I would assume one did not have to type in a factor as it should have everything in the data collector to do it on its own if one selected the datum and projection system needed and had a couple starting values. I think as we move our datums closer to wgs84 or shall i say itrf with gnss becoming the predominant tool for a lot of work we could see states and or counties asking for lat Long ellipsoid heights instead of plane coordinates. I say this because then they can project them to whatever system makes since for that purpose. I see a lot of plats showing northing and easting on a few property corners. Some our grid some or coordinate from a grid scaled to ground but left looking like spc. I guess if i were mandated to attach a coordinate to a couple coordinates i would place lat Long ellipsoid height and which datum and realization epoch. Then no confusion if i were grid or ground and any new datum a 100 years from now could have a transformation done without losing accuracy by reversing it from grid or sudo grid values. I think a lot of spc on plats have been pushed by the GIS community. Unfortunately there are good GIS folks and some who are software operators that have not studied geodesy or cartography science. So they lack an understanding of what they are doing. The lat and long and ellipsoid height would be tough on some surveyors that do not use gnss at all as well because some simply do not need that on lot surveys i use to set a couple pairs for a company that never used gnss but per county requirements needed a known datum coordinates on a couple corners i did this under a ls fyi i was not practicing without a license They would simply show us the job and we would pop them in and my boss would sign off on it. Etc I personally see that boundary surveys do not have to be on a datum but i also see the value in it as well. We have come a long ways since 1900’s in all of this for sure
That may be true for many vendors and their products, but I think Trimble does (used to do?) a decent job with their manuals.
More importantly, I was referring to these manuals:
https://geodesy.noaa.gov/library/
The NOAA Manuals are fantastic.
(Click the name and it takes you down to them.)