Epping Base
maybe you would have gotten a rise from Mr."NOLTON" if you called it the "Effing baseline" instead of the Epping Base.;-)
For anyone interested in studying the minutae, the NGS data sheets are
Southwest Base
http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=NN0174
Northeast Base
http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=NN0646
There were some apples, oranges, and pomegranates in the calculations presented earlier in the thread before EFB. In particular, NAD83 coordinates on the Clarke ellipsoid make no sense.
Using Inverse, I find geodetic distances
USSD coordinates, Clarke ellipsoid, 8251.0093 meters (rounded lat/lon)
NAD27 coordinates, Clarke ellipsoid, 8251.0058 meters (rounded lat/lon)
NAD83 coordinates, GRS80 ellipsoid, 8251.0138 meters
The old USSD latitude and longitude appear to have been rounded to 0.001 second, which could cause a worst case shift of about +/-9 mm, usually less.
The ellipsoid made a significant difference, so you must use the ellipsoid that matches the coordinates.
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I like John's comment that the weighted adjustments would only move the distance slightly. This lets us make a rough comparison while avoiding work with the old horizontal and vertical datums.
I used NGS program INVERSE3D with the NAD83(95) coordinates, GRS80 ellipsoid heights computed from the data sheets, and used points at those lat/lon both at the mean height. This is a lot less work than EFB went through.
I get
8251.7619 Inverse3D chord length at mean height
8251.7569 old measurement
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0000.0050 or 5 mm longer than old measurement.
So this difference could include
a) the small adjustment when this value was weighted into the NAD83 network
b) differences in treatment of height between datums
c) original measurement error
Compare EFB's number 8251.7602, 3.3 mm longer than the old measurement. This shows that we are working down in the range where any approximation can move the result around by as much as the difference we are finding from the old measurement.
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The "right" way to make the comparison would be to work with the original horizontal and vertical datums, do the conversion on the Clarke ellipsoid, figure out how to convert elevation to ellipsoidal height using the old (dependent only on latitude) geoid model, and raise the distance to the surface. That's more work, and we're limited by the USSD rounding of lat/lon and original height uncertainty so the result wouldn't be any more reliable.
Page Base Link USC&G Annual Report 1901
Hope this works.
Some interesting insight into the measurement and just what that length actually represents.
See page 269-270.
Page Base Link USC&G Annual Report 1901
Great find. So the line was reduced to "sea level" in 8 segments.
They give an overall probable error in the length of +/-5.6 mm or 1/ 1,473,000
Page Base Link USC&G Annual Report 1901
Ground distance: 8251.7569m
Sea Level distance: 8250.9880m
Perhaps next spring I will search for the intermediate points. The local crowd was really interested in this, so it might result in having the entire town out to watch.
I promised earlier to post a follow-up. This is it.
I apologize for taking so long, but my distractions this week included several grandkids and a paying client. You know how that goes!
I was very gratified in pursuing the minutiae to find that the "simple" method of using ECEF coordinates (the GSDM) provided answers that agreed superbly well with the ellipsoid distance and with the mean horizontal distance by other.
There is a ton of detail posted at http://www.globalcogo.com/NebBaseLineMay2015.pdf
I'll be happy to respond as appropriate.
I also note that others have continued to pursue the origin of the 1900 measurement. I read that after I wrote my piece.
Thanks again for the kind help.
Page Base Link USC&G Annual Report 1901
On further reading, I see that 8251.7569m was the sum of 8 surface distances, each with a different height. They measured the treads of a staircase.
Therefore a different reduction to their (or any) ellipsoid is used for each segment. The individual reductions differ by several millimeters. So the sum of measured segments is not the best target for comparing a calculation back from NAD83/NAVD88.
We need to use their data to find the equivalent distance at some known GRS80 height if we are going to finish the comparison. I'm confused by their statement "sea level," which I would take to mean the simple model (latitude-only dependent) geoid. Their height 626.6 isn't far from NGVD29 at 626.026 or NAVD88 626.231. But for triangulation work, wouldn't they have wanted to reduce to the Clarke ellipsoid, which is surely a smaller number than that? (I need to find the data) Educate me, please.
The whole exercise makes you appreciate how many things you have to consider to get REALLY precise numbers that mean anything.
I also note that the crew spent parts (most?) of 7 days on the distance measurement. The end points and intermediate monuments had to be carefully set before that. $$$
Page Base Link USC&G Annual Report 1901
Page Base Link USC&G Annual Report 1901
The base line report says the SW Base elevation was 626.6 meters and gives the average for each of the 8 segments. I computed the change in length from those average elevations up to the SW Base elevation as totaling 42.2 mm, giving a "measured" length at that elevation = 8251.7991 meters.
Using the current data sheet values and Inverse3D with both ends at the height of SW Base, I get 8251.7920 or 7.1 mm less.
Changing SW Base elevation to 626.7212 as given in the leveling report changes the difference in length to 7.2 mm and using the NGVD 626.026 gives 6.3 mm.
So I guess I've run out of ways to make the comparison.
Intermediate points?
What are the chances any intermediate points remain?
The description says "marked with copper rivets in the top of 4 by 6 inch posts set at least 3 feet in the ground" and two points "limestone blocks 54 inches long dressed to 6 by 6 inches at the top, carrying copper bolts"
This sounds like they were left protruding above ground, with no underground mark.
A very crude Google Earth file (points very approximately placed by ruler function)
https://dl.dropboxusercontent.com/u/25124076/PageBase.kml
shows that these tend to fall in crop/hay fields where the farmers would likely have removed anything near or above the surface, except possibly 141 which is nearer a fence.
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This brings up the question of how to best compute search coordinates (to, say, RTK accuracy). I can imagine converting to SPC and trying to scale the distances well enough. This would make a great circle into a straight line (I think). Then convert back to lat/lon. Or perhaps Star*Net would let you operate entirely in the geodetic world? I haven't done that.
What do people do for this calculation?
Intermediate points?
I would say there is a good chance of finding some of them, but probably none undisturbed. The first one southwest of Page NE Base looks like it might be in the fence line. A few of years ago I found a copper nail that was set in a wood post in 1900 for a magnetic station. It usually comes down to a matter of how hard you want to find something.
How do you find the intermediate points?
I still want to know how others would work the problem of finding the intermediate points.
I converted the end stations to SPC using CORPSCON, used a spreadsheet to interpolate the SPC between the end stations according to the measured segment lengths as scaled to a common height, updated the average scale factor for each segment to iterate the SPC, and converted back to lat/lon. There must be an easier way.
I hope these are decent search coordinates.
SW Base 42 25 25.39941 N 98 26 00.79833 W
Page20 42 25 50.61853 N 98 25 33.33917 W
Page40 42 26 15.84066 N 98 25 05.86869 W
Page61 42 26 42.31591 N 98 24 37.02466 W
Page81 42 27 07.54064 N 98 24 09.53483 W
Page101 42 27 32.76710 N 98 23 42.03503 W
Page121 42 27 57.98584 N 98 23 14.53558 W
Page141 42 28 23.20001 N 98 22 47.03302 W
NE base 42 28 53.47527 N 98 22 13.99939 W
I also updated the kml file linked above. I have to say, the array of half-mile diameter circles in quarter-sections are quite a sight.
How do you find the intermediate points?
> I still want to know how others would work the problem of finding the intermediate points.
I'd convert to the endpoints to SPC, bring those into CAD, scale to an average ground factor, set the intermediate points at record distances, and export the points for field stakeout. Close enough for search, especially using RTK.
That's the procedure i used on the Yolo Base Line, except I ignored the ground scaling since we're so close to sea level. The first one i looked for i hit within 5 cm or so.
How do you find the intermediate points?
Next thread link
To cross reference in case someone reads this in the future, here is the [msg=319870]next thread[/msg]
Page Baseline--Bill's intermediate points
A couple of years ago, I wrote a spreadsheet that computes intermediate points on a geodetic line. It's kind of tortuous as it progresses down the line in 1-meter increments, calculating coordinates and a new azimuth at each 1-meter interval using Clairaut's constant. It sounds bad, but Excel can generate 10,000 rows so fast that you never see it blink. Sometimes it's fun to brute-force math problems.
Anyway, here are the coordinates that the spreadsheet produced for the Page Baseline intermediate points:
Note the small discrepancy in the Northeast Base coordinates. It happened because the line is too long for 1-meter increments to produce an exact ending result. Since we're just looking for coordinates to use to locate the intermediate points on the ground, I didn't see a need to rerun it with, say, a 0.75 meter increment.
Bill, there's not enough difference between yours and mine to cause a miss in the field. I've checked the spreadsheet using enough CBL datasheets and airport runway intermediate coordinates to be confident in its results. So, too much work or not, you calculated good coordinates.
Please help me with another facet of this baseline. Most of what I've seen here used Apppendix 3 of the 1901 C&GS report, but Appendix 6 of that report contains more data, specifically the elevation of the Northeast Base. Using that and the Appendix 3 average elevations for each section, I tried to calculate the elevations of the intermediate points. Here's the result:
Note that the calculated value for the Northeast Base is 3.5 meters different from the published value. Have I done something wrong? Please help me learn.
Page Baseline--Bill's intermediate points
I'm disappointed that our coordinates differ by up to 15 mm.
I also got 583.6 as the NE base elevation. Note that this number derives from the 1900 measurements, and the 580.1 is NADV88. But the difference at the SW Base is much smaller, 626.6 vs 626.231 = 0.369 m. This implies a tilt that I can't explain or a misreading of what they did.
I still have another issue unresolved. They seem to have scaled their lengths to "sea level", which would seem to be their (simple) geoid model. Why not to the Clarke ellipsoid? I'm not sure what the numerical difference is between the old geoid model and current values, nor the numerical difference between ellipsoids at this location.
Page Baseline--Bill's intermediate points
I guess we have a different level of expectations. I was excited that our coordinates agreed so closely. Because we used two entirely different methods, I think that each set tends to confirm the other with, of course, some undetermined uncertainty.
Your coordinates, I think, assumed a constant azimuth along the whole line. Mine approximated a continuously changing azimuth. On the other hand, you adjusted for scale at every intermediate point whereas I used the ratio of the ellipsoidal distance to the measured distance as an overall elevation factor.
Given that a straight line on the earth's surface is neither a straight line on a State Plane nor a geodetic line, I think we're in remarkably good agreement. And, I think that Jerry can use either version to find the points on the ground. Perhaps he'll share their actual coordinates when he finds them.
The elevation published for the Page NE Base on page 422 of the 1901 C&GS annual report is 580.98 meters, not the 580.1 meters that I showed earlier. That correction reduces the height misclosure by about a meter. The text above the table advises that we should consult the precise leveling tables to get good values, but I don't know where those tables can be found.
I didn't know that C&GS had a geoid model for the Clarke 1866 ellipsoid. I always thought that they assumed negligible difference between the geoid and the ellipsoid. That's why I wasn't surprised when Scott Zelenak's ellipsoidal distance agreed so closely with the reduced distance in the 1901 report. Please share some more information about the geoid model.
Page Baseline--Bill's intermediate points
Our agreement seems to show lack of blunders, but if they are modeling the same thing, shouldn't they get the same result to computational precision?
>Your coordinates, I think, assumed a constant azimuth along the whole line.
A constant azimuth in SPC.
>Mine approximated a continuously changing azimuth.
As it does when you remain in geodetic coordinates.
>On the other hand, you adjusted for scale at every intermediate point whereas I used the ratio of the ellipsoidal distance to the measured distance as an overall elevation factor.
I think that wasn't the main difference. The differences between our coordinates were sideways to the line and not along the line.
>Given that a straight line on the earth's surface is neither a straight line on a State Plane nor a geodetic line
Isn't it true that a great circle becomes a straight line in SPC because they use "conformal" projections? Is that only an approximation?
>Perhaps he'll share their actual coordinates when he finds them.
I think there is a very slim chance for one and almost none for the others.
>I didn't know that C&GS had a geoid model for the Clarke 1866 ellipsoid. I always thought that they assumed negligible difference between the geoid and the ellipsoid.
Maybe you are right. I recalled reading that the gravity model depended only on latitude, and I guess that is consistent with saying the geoid is the ellipsoid.
Page Baseline--Bill's intermediate points
That's an interesting question that you raised about geodetic (great circle) lines becoming straight grid lines. It's a bit of a fuzzy area for me, so feel free to correct me, but please be kind. I'm old, you know.
James Stem addresses this issue in two places in his NGS Manual 5, once on pages 18 and 19 and then again on pages 52 and 53. In reading these sections, we need to make a distinction between "projected geodetic lines" and "reduced geodetic lines."
Projected geodetic lines come about when we calculate State Plane Coordinates directly from the coordinates on a geodetic line, with no regard to length or the azimuth that the grid line should have. Reduced geodetic lines come about when we create a grid line by multiplying the geodetic length by a scale factor and adjusting the geodetic azimuth to a grid azimuth.
I think that comparing my coordinates to yours directly is closely akin to projecting a geodetic line onto the State Plane grid rather than reducing the geodetic line to the grid.
On page 53, Stem gives a diagram that shows how the projected geodetic line looks when compared to the grid line. Note that, when the lines are north of the central parallel on a Lambert projection, the projected geodetic line lies to the north of the grid line.
The Page Base Line is north of the Nebraska SPC central meridian and all of my intermediate coordinates are north of yours. Additionally, the differences in latitude grow and then shrink as we proceed down the line. Our separate results fit Stem's diagram.
To reduce the geodetic line to the State Plane grid, we would multiply its length by the average scale factor, adjust the geodetic azimuth to a grid azimuth, and then calculate the State Plane coordinates of the terminal point using grid length and grid azimuth. Those coordinates should agree with the State Plane coordinates of the projected geodetic line.
Note that in Stem's diagram on p. 19, the grid coordinates of the initial and terminal points of the grid line are the same as the grid coordinates of the projected geodetic line. However, the grid coordinates of the intermediate points of the two lines are different.
I think that our separate results look just as they should look.
However, we did make some different assumptions and there is another source of difference. If you enter the State Plane coordinates of the SW Base into either Corpscon or the NGS software, the resulting geodetic coordinates will not agree with the data sheet. Going from State Plane to geodetic has always been problematic and there can be a small amount of error introduced in that process.
Additionally, we don't know how precisely "straight" the measured line is. If any of the points are a bit off-line, then the measured distances will not be those of a straight line and our coordinates will be off. I don't think it's possible to reconcile the differences down to zero.
This has been a very interesting exercise and I'm happy with the small differences in our coordinates. I share your pessimism about actually finding all of the points, but if they're not found, it won't be because of faulty search coordinates.
