@mathteacher yeah i have a spot that ground is less than grid in that area. I have not ran the numbers by hand yet but i was handed some control that is supposed to be grid and putting a quick field package together for crews that needed to leave yesterday but we were given control today lol any way i was inversing in TBC before i lost internet and i was caught by the ground distances being shorter. Cf close by ngs data sheets were like 1.00004 or 3 I will have to investigate a little further. But i have been in point clouds all day so i am brain dead.
@mathteacher chasing crooks. I love it. We had a few incidents in the rural area outside of Memphis in north Mississippi were i grew up. City folks running from the law dawgs. High speed pursuits. I was about 14 and just got back from town picking up the mail and milk and bread. One of those iroc z comes flying by and later cops from memphis germantown and collierville tn all in hot pursuit. About 30 minutes later the helicopter come over and phone rang. My dad said drive down to wildcat bottom and tell the sheriff what he needs to know. I drive down and meet our sheriff and he said yalls land right. I said yes sir my uncles. He said how do we get in. The fellow done ran into the dead end road and was on foot. Thick bottom land for a while. I said best thing is to drive around to hwy and come in and drive around and a couple old log cabins stop and wait. They sent some that way and i lead some through the bottoms . I can still remember i was wearing sebagos and once they caught the fellow one of the officers asked how i was not soaked he had stepped in a blue hole and was wet to the waist . I laughed and said i told you to follow me . I had hunted those woods and bottoms so much i could maneuver the soggy land easily. Poor fellow was torn up from briars and devil canes and I imagine when he came down off of whatever it was he was on he was feeling the pain .
OK, I see. When you criticize NAD27, NAD83, or any state plane system, you're speaking of the totality, the data, the coordinates, the concept, all of it. And that's in terms of its applicability today.
My view is much narrower, focusing heavily on the developmental mathematics and much less on the other questions.
Indeed, it is difficult to incorporate state plane into today's surveying workflow. One has to be warped and warping state plane is the easiest and most productive thing to warp.
Thanks for the insight and the great conversation.
I did a quick search to help explain.
When 83 took over for 27 it became clear why 27 couldn't continue as the basis for satellite control. You might believe there a math connection between them, but I will disagree. There is in theory but not in practice. The NGS has done some work to make a computer file to do the conversions but I doubt it's pure math as much as it is lots of adjustments between observations.
I called up two data sheets, one in NC and one in AZ at about the same latitude.
the NC sheet Castalia has an 83 lat of 36-03-06.493, long of 78-01-56.513 it's 27 lat is 36-06-05.950, long of 78-01-57.570, a rough in your head conversion (using 100'/second for lat, 80'/second for long) will place the 83 number about 50'North and 80' East
Go to the AZ point Kletha, 83 lat of 36-33-19.302, long 110-32-38.920, 27 lat 36-33-19.311, long 110-32-36.4053, lat a foot, long is +200' West!!!
Even if we start from different beginning locations (Meades Ranch, Greenwich), the Long should hold a steady shift, the lat should be very close since that's "easy" to measure. Yet that's not what happens.
Why?
Imagine the process of laying out NAD27. A short baseline is measured somewhere relatively flat using chaining tables, umbrellas, ect. From there a network is laid out using triangulation, do you think that's going to get you "on" the worldwide system? It was never intended to.
Point being is that NAD27 isn't really on the Clarke Ellipsoid and it's based on the measured monuments only, so it was time to redo the control.
Agreed, there is no mathematical connection between 83 and 27.
What I study is the connection between GRS80 and state plane grids and the connection between Clarke 1866 and state plane grids.
The mathematics in both cases is sound and both grid and ground distances from either will be accurate within the limits of accuracy of the input data.
I disagree that NAD27 is not on the Clarke ellipsoid. When you compare the 27 and 83 positions of Castalia, the difference is the difference between the two ellipsoids. Both point to the same position on the earth's surface. Ditto for point Kletha.
Moving from Castalia to Kletha, the separation of the ellipsoids changes, so the coordinate differences change as well.
If you look at the distance calculation between the two Yellowstone County points (shown below) you'll see a big difference between the 27 and 83 grid distances, but a very small difference in the ground distances.
Just as there is no connection between NAD27 and NAD83, there is no connection between GRS80 and Clarke 1866. Both are accurate relative to the figure of the earth, but points cannot be exchanged between the two without great mathematical angst.
You're so close, almost there.
I'm not implying that NAD27 doesn't calculate using the Clarke Ellipsoid, what I'm saying is that NAD27 isn't ON the Clarke Ellipsoid. The difference is that 83 is on the Ellipsoid.
This may help. NAD27 is indeed on the Clarke 1866 ellipsoid, but the center of the ellipsoid is not near, let alone at, the center of the earth. Satellitess orbiting around the center of the earth obviously detected positional differences.
But GRS80 is also not centered at the earth's center. It's close, but that's why WGS84 positions have drifted away from GRS80 positions. WGS84's position is relatively frequently updated.
NAD2022 will change that. I don't know if that might change surveying, but it might.
https://www.e-education.psu.edu/geog862/node/1797
Math teacher, I just showed you 50' and 300' differences. That's not the difference between the two earth centers, that's the big errors imbedded in NAD27 state plane execution, not the Clarke Ellipsoid, you can cling to the idea that NAD 27 was somehow surveyed precisely across the continent on the Ellipsoid, but it's a fantasy. NAD83 is precisely surveyed lat, long.
The math is Clarke the physical location of the monuments are not that accurate, except for z, that's really good.
So you believe that a position on the Clarke 1866 ellipsoid should have the same coordinates on the GRS80 ellipsoid?
The ellipsoids have different shapes. A point can't possibly have the same coordinates on each, regardless of the location of the centers. But having different centers pushes them further apart.
C'mon, Moe.
No, this isn't about belief, it's about measuring. You are under the misconception that NAD27 was precisely laid out in a global context akin to satellite based measurements across North America on the Clarke Ellipsoid in the early 1900's using chaining tables and triangulation.
You seriously believe this?
Despite me showing you shifts in opposite directions, those are peppered all throughout NAD27. If it was precisely laid out as you seem to believe, then why even bother going to NAD83. Just use the ellipsoid from 1866.
Moe, when you define the lat/lon of a point on an ellipsoid, Meades Ranch, and an azimuth to another point on that ellipsoid, Waldo, then you have fixed the ellipsoid relative to the earth and you have a datum.
Now when you define another ellipsoid with a different shape and center, then Meades Ranch and Waldo are going to have a different lat/lon on this other ellipsoid.
Points on the first ellipsoid are apples and points on the second one are oranges. Your distance comparisons have no basis. It's like subtracting the elevation of Helena from its population and claiming that the answer is meaningful.
There were several reasons why NAD27 was replaced. The ellipsoid height was not zero throughout and others, but the satellites also couldn't match its coordinates because they were orbiting around the earth's center and the Clarke 1866 ellipsoid was not earth centered.
Don't insult me, Moe. I know what I'm talking about and the distance calculation posted above is strong evidence that you're wrong.
Math teacher QW0554 isn't a measured point. QW0575 is a measured point. The distance comparison isn't meaningful cause it's calculated.
Two close together measured points are rare in this part of the world, I can't really think of two you might use for your calculation.
I understand you know this math, I respect that. And I have the utmost respect for the surveyors that laid out the geodetic control with boots on the ground. But they had technical limitations. They did an amazing job and were incredibly accurate. No one will care about a 100' error across the continent or what ever it might be in the context of the two ellipsoids. But there is error in NAD27, measurable error and surveyors that used it extensively realized it when more advanced equipment became available.
Indeed, there was error, a lot of it related to the assumption that the ellipsoid height was everywhere zero. When NGS did long precise levelling runs, it was apparent As a datum, NAD27 was flawed and as instruments and measurements improved, the errors became easier to find and harder to deal with.
Again, I think that when you say NAD27, you're talking about a datum in totality, including how well it conforms to the shape of the earth.
I am concerned mainly with how ground distances can be converted to grid distances and back again.
You have to take a much broader view because you deal with broader issues with real-world implications. I just like the math and hope that I can contribute meaningful conversation.
NAD83 has problems, too. It's not really ECEF and updating positions, as was done for Meades Ranch and Waldo in going from USSD to NAD27, is getting tedious and burdensome.
Change is inevitable.
It may be easier to find in NC, it's rare here that the NGS placed measured numbers on existing NAD27 triangulation stations. It's important to understand the datasheets often contain calculated positions instead of measured ones.
I have a point a few miles north of town that some of my engineering partners used. They couldn't understand why they were .8' from my value for the point since they took the datasheet number. I explained that my number was from CORS and they insisted that the "official" number from the datasheet was the one to use. The NAD83 number was calculated from the old 27 number.
Anyway, I know you like to play with numbers so I have three actual datasheets for you that are both NAD83 and NAD27 real numbers. If you want to work with them they are PW0138 a CBN, QV0300 a FBN and PW0217 a CBN. They are relatively close to each other and ready for some serious calculations. I would suggest transforming back and forth holding the datasheet values and inversing between them NAD83 and 27. I did that some years ago because we were using them and I tried to "get on" NAD27 as well as 83, I got frustrated with 27 and scrapped the Idea of a local projection, couldn't make it work.
I'll do that and thanks. You earlier gave me a point in AZ. It's a relative newcomer, set if I remember correctly in the 1970s. I went to this old publication:
to do a little more. The advantage here is that I can get both Clarke 1866 lat/lon and NAD27 plane coordinates that are pure, like the old data sheet you posted earlier.
Distances are given between many points and reading a bit of the text is interesting and informative:
Anyway, the two points I've selected are DV2104 DESIGNATION - MARICOPA NORTHWEST BASE and DA1442 DESIGNATION - TABLE. The NAD27 lat/lons on their data sheets duplicate the ones in Publication 224 described above. Elevations have to be taken from the data sheets or else hunted for in other C&GS publications. They're not close, so simple averages of combined factors may not work too well, but I'll cross that bridge when I get to it.
So the coordinates are verified and we need scale factors. NCAT is the source and the way I do that is to enter lat/lon, set the From and To both to NAD27 and get the results.
If the NCAT state plane coordinates match the Publication 224 coordinates, then I think I'm good to go with the scale factors.
Then I compute ground distances using NAD27 and whatever the data sheet has for its state plane coordinates.
If they're very, very close, then I think that the NAD27 numbers are reliable from a mathematical perspective.
Now whether the marks on the ground are where the lat/lon says they are is another issue. That has to be verified in the field.
Thanks again for the data and the great discussion and have a great weekend.
Those points will be inappropriate for your task. They are converted points not measured points. What you need to find are points measured in NAD27 which they both are. Then you need to find points that have 27 measurements that were later measured in NAD83. They are out there, one that you first used was a point like that, neither of these are.
The three I sent to you are duel measured monuments, look for CBN, FBN and HARN points. Many HARN points will be old Bench Marks but sometimes they used tri monuments. DV2104 is a really interesting monument, read about in the comments. It was set in 1899 and I'd imagine it's one of the two baseline points for the region, very important point. However, I don't believe it survived to today which is sad, but there won't be any NAD83 data for it. Basically doing math using it will produce a conformation bias calculation. Same with Table, although it's still there, but it only has converted NAD83 positions. Not what you need.
Here are two AZ points that you might try out, FQ0759 and GP0641, I'm not sure what type of NAD27 they were I don't see the order for them but they both and 27 and measured 83 numbers.
So this statement on a data sheet
DV2104.The horizontal coordinates were established by classical geodetic methods
DV2104.and adjusted by the National Geodetic Survey in August 1993.
means that the classical geodetic methods were used to get the NAD27 coordinates and the NAD 83 coordinates were derived from those earlier coordinates. Whatever measurement error is in the 27 coordinates is brought forward to the 83 coordinates. The correlation between the two is near perfect. and the original measurement error is not detectable.
Measured 83 positions are assumed to be very accurate and will expose the 27 errors.
Thank you for explaining. it's a good lesson: The accuracy of derived points depends on the accuracy of the source point. Any errors in the source point will also be in the derived point.
LOL! I have work to do.
Well, when I calculate the distance between PW0138 and PW0217, the 27 and 83 distances are within 3 decimeters for both the grid distance and the ground distance.