Very Old Datum Conversion to WGS84 Datum

[+Klemmer]

I suspect this is not an easy (or short) question, but here goes:

 

1) Background: Several years ago, 2oldfarts, fossillady & myself (Klemmer) recovered some very neat old survey marks ("benchmarks") out in the desert west of Laughlin, NV. They are drill holes from the survey of the CA-NV Oblique Boundary Line, most from 1899. We're heading out there again in April (although we may do other areas). But – I may have extra time there. I starting doing some research on those old marks, "got hooked" and I dug out the original survey report from the US C&GS Annual Report of 1900 (Appendix 3). It's 282 pages with full scanned in maps, and details of the whole survey from lake Tahoe to the Colorado River. Nice job putting them all on-line, NGS!

(BTW: if you get into it, some maps ended up in later appendices – tricky!)

 

2) There are tables in the report of Lat/Longs of all sorts of neat marks out there, including all their own new marks, and even lots of marks ("mileposts") from earlier surveys, including the original von Schmidt survey of 1873. Some are on USGS topos & some are even still in the NGS database, but many are not. Of course, the Lat/Long are of a much earlier Datum, in this case from the Yolo Base Datum (details on report page 346, bottom note), which was before the US Standard Datum (of 1901). I want to look for some of the marks not presently in the NGS database (or in there improperly). Decent (hand-held consumer grade GPS) coordinates would be very helpful.

 

3) Here's the problem / question: I know neither NGS nor USGS have datum conversions that old. No luck on-line anywhere else either. I'm looking into doing my own (local) datum conversion for that area. There are several instances where the 1899 original marks are still in the NGS database, and are (of course) also in the survey field report I have. Using the Vincenty formula / spreadsheet (thanks, Aussies!) so I can work off-line and have records, I have done the INVERSE calculations for two points that are available in both datums*, specifically T 134 (FS1155) and T138 (FS1149). Vincenty assumed WGS84 ellipsoid in this case (invalid for the 1899 coordinates!). The question is, before I setup more of them, how valid is that? In other words, if the position difference between the two datums is, for example, 5 meters at true azimuth 090°, is that correction valid for other points nearby (say 25 miles)?

 

4) Preliminary result: Using T 134 and T 138, I calculated the distance and azimuth for each mark, between the two datums (a correction vector of roughly 14° true azimuth and 219 meters), and compared the two results. Not too bad, but not as good as I had hoped. The difference between the two correction vectors is 0.857 meters and 0° 14' 36.691" azimuth. Makes me wonder. I haven't run more comparisons yet (it's just spreadsheet data entry time). Is my methodology valid? I suppose less than 1m is decent for HH2 GPS search, but is it real?? Maybe it is really 20m? It's a big desert.

 

Any surveyors / historians / mathematicians / casual readers out there with an opinion?

 

*I know, plural of datum is data, but it gets too confusing in this context.

Edited February 26, 2010 by Klemmer & TeddyBearMama

[southpawaz]

I found this definition of the Yolo Base datum, which may be useful to you:

 

Standard (California) Astronomical Datum 1885 :

The horizontal-control datum which is defined by the following coordinates of the origin and by the azimuth (clockwise from South) of triangulation station Mt Diablo, on the Clarke spheroid of 1866; the origin is at triangulation station Mt Helena:

longitude of origin --- 122o 38' 01 410" W

latitude of origin --- 38o 40' 04 260" N

azimuth from origin to Mt Diablo 324o 01' 31 04"

The name is taken from the so called old registers of the Division of Geodesy It is identical with the Yolo base datum used in the report on the California-Nevada boundary line

 

source: Ole Miss Glossary of the Mapping Sciences

 

I may have some thoughts later, but right now my head hurts...

[+Klemmer]

southpawaz:

 

Yes, that might be helpful. Thanks. I suspected that the Clark spheroid (ellipsoid) of 1866 was used, and I have that data.... Wops! I have the Clark speroid of 1858 as an option in the Vincenty formulas. Ahhh....

Now my head hurts too.

 

My main post above corrected to use WGS84 ellipsoid instead of the previously stated GRS80. Difference insignificant.

 

One problem is using two different ellipsoids in the same INVERSE (Vincenty formula) calculation. I'm reviewing it, but it might not be possible (at least by me)......

Edited February 26, 2010 by Klemmer & TeddyBearMama

[+Klemmer]

Here is what the 1900 Survey Report has to say about the Datum used for their coordinates:

[AZcachemeister]

I passed out from lack of oxygen...twice!

 

Since at least one (you logged it!) mark seems to have accurate numbers, perhaps if you could somehow get the pre-correction numbers and make a comparison, you would have a hip-shot idea of how far off the old numbers might be.

[Papa-Bear-NYC]

I've had good results doing something like you propose and found marks that were otherwise lost. This was my method:

 

1) Find the "lost" station and a nearby station which is still in the NGS database in the old publication. They will generally give coordinated on the old datum to 2 or 3 decimal places in the seconds.

 

2) using these old coordinates, run the Inverse program (on the Clarke Spheroid) to find the distance and azimuth from the good station to the lost station.

 

3) Using these numbers (i.e. distance and azimuth from good to lost), run the Forward program and calculate the position of the lost station from the good station using the adjusted coordinates of the good station on modern datum.

 

Stick these coordinates into you GPS, and go find it. It works.

 

It works, because although the datum change may cause significant changes in the absolute locations, the relative locations (represented by the distance and azimuth between the two stations) changes very little.

Edited February 26, 2010 by Papa-Bear-NYC

[foxtrot_xray]

Stick these coordinates into you GPS, and go find it. It works.

Assuming you can still get to the mark. I've done this method once, did a whole bunch of planning (days), got permission from my railroad to go out and hike down to the mark, finally, after a week of various plotting and knowledge of where rock outcroppings were along my line, I get there only to discover that the month before there was a mudslide in that area and the station was supposedly 10 feet under the slick.

 

Klemmer - if you do go hunting for some of these, be sure to document them and share pictures. I'd be really curious to see these and see if they can be 'rediscovered'.

[Papa-Bear-NYC]

Stick these coordinates into you GPS, and go find it. It works.

Assuming you can still get to the mark. I've done this method once, did a whole bunch of planning (days), got permission from my railroad to go out and hike down to the mark, finally, after a week of various plotting and knowledge of where rock outcroppings were along my line, I get there only to discover that the month before there was a mudslide in that area and the station was supposedly 10 feet under the slick.

 

Klemmer - if you do go hunting for some of these, be sure to document them and share pictures. I'd be really curious to see these and see if they can be 'rediscovered'.

Spoilsport!

 

Come to New England where we don't have mud slides - but maybe a little snow.

[foxtrot_xray]

Spoilsport!

 

Come to New England where we don't have mud slides - but maybe a little snow.

I'm in New England now!

 

DC's part of New England, right? Heck, with all this snow, it FEELS like it did when I lived in Vermont back in the mid-80's!!

[+Klemmer]

Papa-Bear:

 

Thanks! I like your method. Appreciate the feedback. I believe it also takes out the variable of different ellipsoids, which was bothering me. I'll give it a shot, and see how it compares to my method. Should be interesting. Will report back.

 

Since the original post, I've looked at 4 other "dual datum" stations inteh area, and the average of the correction vector is still under a meter, so that gives me a bit more

 

Thanks goodness for "computers". I can't imagine doing the transformations we're doing by hand. In the 1900 report, they sometimes refer to "computers" also, but were referring to a person!

 

AZcachemeister:

Exactly. A hip-shot is the idea.

Breathe slowly.....

 

FX:

You bet pictures will be forthcoming (with some luck)...

Edited February 27, 2010 by Klemmer & TeddyBearMama

[southpawaz]

If you think the vector method may get close enough given Papa Bear's confirmation that he's used successfully, you can also get couple more data points to average by using Round Top and Mount Lola. JS3905 is ROUND TOP RESET and KS1453 is MOUNT LOLA RESET (now destroyed).

[+Klemmer]

southpawas:

Right, thought about that. Ran the numbers, but the result of the old pre-1900 ROUND TOP to the current ROUND TOP RESET were quite different than I got using (so far) four old/new conversions in the area of interest. I don't think ROUND TOP RESET is in the same position as the original ROUND TOP. Or, something else is wrong. I would need to try to find the older datasheets, if they exist.

 

In any case, there are plenty of dual datum stations available along the whole border.

 

Thanks, though.

[+jwahl]

My intuition is that datums and orientations are minor issues. You can probably achieve a reasonable degree of accuracy simply by doing an arithmetic transformaion. That is differences in lat longs between common stations in the general region. It is going to be within feet or better.

Edited February 27, 2010 by jwahl

[+Klemmer]

Comparison of two methods:

1) Klemmer's method:

• Determine an average correction vector based on "Dual Datum" marks in area of interest (using Vincenty formula). Four results averaged for this trial.
  
• Apply the correction to old mark coords to get current datum (WGS84) coords
  
• Result for No 135:
  

N35° 09' 40.7957", W114° 49' 52.6149"

 

2) Papa-Bear-NYC's method:

• Determine Dist/Az vector from known "Dual Datum" mark to target mark in Old Datum/Ellipsoid
  
• Apply same vector from the "Dual Datum" mark to target mark in current Datum/Ellipsoid
  
• Result for No 135:
  

N35° 09' 40.7702", W114° 49' 52.6141"

 

My conclusion:

The difference between the two methods (in one trial) is insignificant in terms of the precision available from HH2 (consumer handheld) GPS receivers. For one or two marks, Papa-Bear's method might be easier to setup (only one "Dual Datum" mark required). For more marks, Klemmer's method might be easier to setup (at least several "Dual Datum" marks are needed to get reliable average).

 

As the results of the two independent methods are so close, it sure gives me confidence in the results.

Now -- to go find No 135 (mid-April or so near Laughlin NV) !

 

Interesting stuff (for me it was). Thanks for the help, folks!

[holograph]

Just for the heck of it, I used a complicated method using least squares to estimate the location of a station, using surrounding control points whose positions are known in both the old datum and NAD83. The working principle is that the station was located using triangulation, so by transforming the assumed geometry of the network in the old datum to the current geometry in NAD83, we can estimate the station position in NAD83.

 

It's kind of Klemmer's and Papa Bear's methods on steroids.

 

The result is mixed: you can get lucky with the simpler methods, and get a good estimate, but you can also get unlucky and get a bad estimate. The least squares method tends to even things out. Here is a sample using 3 control points and a test point, with coordinates in the old US Standard Datum of 1901, as well as NAD83:

 

Control points:

MY2568 US 1901 - N42.641119 W71.106908, NAD83 - N42.641056 W71.106410

MY4858 US 1901 - N42.611644 W70.730322, NAD83 - N42.611579 W70.729815

MY3374 US 1901 - N42.342606 W71.133944, NAD83 - N42.342380 W71.133682

 

Test point:

MY5139 US 1901 - N42.502850 W70.965125, NAD83 - 42 30 10.04107(N) 070 57 52.65249(W)

 

The least squares method estimated MY5139's position to be 42 30 9.89 (N) 70 57 52.79 (W) NAD83

Using a single vector from MY2568, MY5139's position was 42 30 10.03 (N) 70 57 52.66 (W)

Using a single vector from MY4858, MY5139's position was 42 30 10.26 (N) 70 57 54.45 (W)

Using a single vector from MY3374, MY5139's position was 42 30 10.26 (N) 70 57 54.45 (W)

 

Those estimates have errors of 18 feet, 1 foot, 136 feet, 136 feet, respectively.

 

So if you chose to use the vector method from MY2568, you would be lucky and get within 1 foot, but if you chose MY4858 or MY3374 (or averaged all three), you could be off by a hundred feet.

 

The least squares method is far too complicated for me to describe here, but I may try to encode it in a spreadsheet at some time. Most of it is already in a spreadsheet that I developed to test it, but it would take considerable work to put it in an easily-used form. I only did it because I've been curious about ways to convert old datums, and have wanted to try some kind of geometry-based least squares for a long time.

[Bill93]

The exercise by Holograph is a good idea, but there is something wrong with the coordinates for MY3374.

 

If you Inverse between each pair of the 4 points in one datum and compare to the distances in the other datum, you find reasonable agreement between all the pairs that do not involve MY3374 (0.066 m, 0.161 m, and 0.037 m), and orders of magnitude larger difference on the ones involving it (19.8 m, 26.6 m, 26.4 m).

 

Looking at it another way, if you ignore the fact that they are different ellipsoids, and Inverse between the US1901 and NAD83 values for each point, 3 of them shift about 41 or 42 meters at 99 degree azimuth, but that point shifts 33 meters at 139 degrees.

 

Did I copy something wrong, or does anybody else find that discrepancy?

Edited March 1, 2010 by Bill93

[holograph]

If you Inverse between each pair of the 4 points in one datum and compare to the distances in the other datum, you find reasonable agreement between all the pairs that do not involve MY3374 (0.066 m, 0.161 m, and 0.037 m), and orders of magnitude larger difference on the ones involving it (19.8 m, 26.6 m, 26.4 m).

 

Looking at it another way, if you ignore the fact that they are different ellipsoids, and Inverse between the US1901 and NAD83 values for each point, 3 of them shift about 41 or 42 meters at 99 degree azimuth, but that point shifts 33 meters at 139 degrees.

 

You may be right that MY3374 is suspect, but it is also true that it is not unique in that aspect. I have a small dataset of 430 stations in the same neighborhood with both US 1901 coordinates and NAD83 coordinates. The shift in latitude averages about 7.1 meters southward, with a standard deviation of 4.4 meters, and a shift in longitude of 43 meters eastward, with a standard deviation of 7.4 meters. The result is that the azimuth of the change vector varies considerably across the dataset. The least squares method tends to smooth out that variation.

 

I didn't single out MY3374, other than filtering out obvious outliers (probably due to misprints in the source document for the US 1901 coordinates). The way I chose the control was by selecting a few first- and second-order stations surrounding the test point. I didn't pay attention to whether the control points had a uniform change, because past experience indicated to me that the changes are not consistent, and that was the motivation for using least squares.

 

edit: corrected eastward/westward average

Edited March 1, 2010 by holograph

[+Klemmer]

Wow, Holograph, you sure got into it! So, if you ignore the problematic MY3374, then your least squares method is consistent and reasonably accurate (for our purposes). Right? Great. However, if we ignore MY3374, and there is not really a problem with it, them we're kidding ourselves.

 

Hmmm....

 

Well, as I said above, my test was Klemmer's method vs Papa-Bear's method. The results were nearly identical to each other (31 inches Latitude and less than one inch Longitude). My thinking is that two different methods yielding essentially the same result pretty much proves both methods. I'll test it again in the process of doing the actual conversions for my trip, and advise. I suppose I might have just gotten lucky on one test.

[holograph]

Well, as I said above, my test was Klemmer's method vs Papa-Bear's method. The results were nearly identical to each other (31 inches Latitude and less than one inch Longitude). My thinking is that two different methods yielding essentially the same result pretty much proves both methods. I'll test it again in the process of doing the actual conversions for my trip, and advise. I suppose I might have just gotten lucky on one test.

 

Klemmer's and Papa-Bear's methods were essentially the same method, just differing in the detail of when the average was taken. They are both assuming a simple linear shift in datum -- no stretching, warping, or rotation. The least squares method makes no such assumption -- its assumption is that the measured angles between stations should change as little as possible, and it is able to adjust for rotation, stretching, and warping.

 

In the case of the CA-NV boundary, since all the stations were part of the same survey project and adjustment, the method that Klemmer and Papa-Bear are using should work as well or better than anything else. The CA-NV boundary has the advantage of a dense neighborhood of stations that have coordinates in both datums and were part of the same network, so it is easy to find nearby control points to use and it is not likely that the network was stretched or warped significantly.

 

It is possible/likely that the orientation of the datums varied slightly, which would introduce a systematic error in azimuth, but it would be easy to check that by comparing the azimuths between control stations. In other words, a difference in datum orientation would mean a difference in the assumed direction of true north, and should be accounted for when using the Forward routine to compute the location of the missing station.

 

That could be another slight advantage of the least squares method -- it only uses differences in azimuth rather than absolute azimuths -- so it won't be affected by differences in datum orientation.

Edited March 2, 2010 by holograph

[holograph]

The exercise by Holograph is a good idea, but there is something wrong with the coordinates for MY3374.

 

If you Inverse between each pair of the 4 points in one datum and compare to the distances in the other datum, you find reasonable agreement between all the pairs that do not involve MY3374 (0.066 m, 0.161 m, and 0.037 m), and orders of magnitude larger difference on the ones involving it (19.8 m, 26.6 m, 26.4 m).

 

Looking at it another way, if you ignore the fact that they are different ellipsoids, and Inverse between the US1901 and NAD83 values for each point, 3 of them shift about 41 or 42 meters at 99 degree azimuth, but that point shifts 33 meters at 139 degrees.

 

I modified the least squares calculation to use MY0001 instead of MY3374, and now the result is within about 2 feet of the NAD83 location.

 

So the "bad" control point MY3374 did affect the calculation to the tune of 16 feet of error, as you would expect, but not as much as if it were the unlucky choice of the other methods, which may have resulted in 136 feet of error.

[Papa-Bear-NYC]

The exercise by Holograph is a good idea, but there is something wrong with the coordinates for MY3374.

 

If you Inverse between each pair of the 4 points in one datum and compare to the distances in the other datum, you find reasonable agreement between all the pairs that do not involve MY3374 (0.066 m, 0.161 m, and 0.037 m), and orders of magnitude larger difference on the ones involving it (19.8 m, 26.6 m, 26.4 m).

 

Looking at it another way, if you ignore the fact that they are different ellipsoids, and Inverse between the US1901 and NAD83 values for each point, 3 of them shift about 41 or 42 meters at 99 degree azimuth, but that point shifts 33 meters at 139 degrees.

 

I modified the least squares calculation to use MY0001 instead of MY3374, and now the result is within about 2 feet of the NAD83 location.

 

So the "bad" control point MY3374 did affect the calculation to the tune of 16 feet of error, as you would expect, but not as much as if it were the unlucky choice of the other methods, which may have resulted in 136 feet of error.

 

When ever I have done this, I always used first order points and tried to make sure the old datum points were in the same survey. For New England, these tended to be in the major CGS surveys done in the 19th century.

 

Ironically, for one point, Watatatick Borden (1834) which an early survey had explicitly said was about 7 feet in a certain direction from Watatick (a "newer" CGS point.), the old points from the early publication using the old datum gave almost exactly the numbers that were found on the ground. OTOH the new adjusted points and the new datum was off in the wrong direction by 3 feet.

 

Lesson: 1) stick to the same survey if possible (obviously not possible here since no modern survey used the Borden point) and 2) using the method for very short distances is generally useless due to the poor "leverage" in the triangulation (actually an "excess" of leverage). But both methods gave a position within 6-10 feet, so I can't complain.

[+billwallace]

.....

The least squares method is far too complicated for me to describe here, but I may try to encode it in a spreadsheet at some time. Most of it is already in a spreadsheet that I developed to test it, but it would take considerable work to put it in an easily-used form. I only did it because I've been curious about ways to convert old datums, and have wanted to try some kind of geometry-based least squares for a long time.

I'd like to understand what you did. You determined corrected/adjusted vectors for the 1901 data using all four points (least-squares adjustment of a quadrilateral?) ? Then you applied these corrected/adjusted vectors to the NAD83 data of the control points to determine the NAD83 coordinates of the reference station?

 

A few months back I tried to test my understanding of all this stuff - I tried to go around a triangle using the vectors listed in an old CGS publication starting at the NAD83 coordinates of one of the points/stations. I didn't think that the the stretching and translation of the datum should have affected those observed vectors. When I got back to the first station the coordinates were off by enough that I figured I was doing something wrong. Any thoughts? That should have worked right?

 

I've been eyeing some of the stations at the other end of that Ca/Nev line/border for a possible trip this spring to try and put some color in Alpine county on your map.

 

thnx

[Bill93]

Did you try to go around a plane triangle or around a triangle on the ellipsoid of choice? For distances of more than a very few miles the curved surface makes a big difference.

 

To work with angles on an ellipsoid, we use some version of the Vincenty equations, my preference being the NGS Toolkit programs FORWARD and INVERSE. If you take two points in Lat-Lon and use INVERSE to find the length and azimuth of the line connecting them, it will show you that the reverse azimuth differs from the forward azimuth because of the curvature (except for a North-South line).

 

The other thing that is different about geodetic computations is the distances are usually reduced to distances on the ellipsoid. If anyone measures on the surface, they get a different answer depending on the elevation above the ellipsoid.

[+billwallace]

Did you try to go around a plane triangle or around a triangle on the ellipsoid of choice? For distances of more than a very few miles the curved surface makes a big difference.

 

To work with angles on an ellipsoid, we use some version of the Vincenty equations, my preference being the NGS Toolkit programs FORWARD and INVERSE. If you take two points in Lat-Lon and use INVERSE to find the length and azimuth of the line connecting them, it will show you that the reverse azimuth differs from the forward azimuth because of the curvature (except for a North-South line).

 

The other thing that is different about geodetic computations is the distances are usually reduced to distances on the ellipsoid. If anyone measures on the surface, they get a different answer depending on the elevation above the ellipsoid.

Hmm I definitely didn't put it together that the distances are measured on the ellipsoid - duh.

And I thought the reverse azimuth difference was because the meridians are not parallel.

 

I was using FORWARD or maybe FizzyCalc with the distances and azimuths from the old publication and starting with the NAD83 coordinates of one of the stations - I definitely was lost - I thought those azimuths were empirical and the distances were calc'd from a measured baseline and that they shouldn't change with the datum.

 

thnx,

bill

[holograph]

Bill93 and Billwallace, I posted a description of the process at this page.

 

As I said, it is too complex to do routinely without having some software to do it automatically. I was just trying a proof-of-concept, and may or may not try to make it easy to do with an Excel spreadsheet or comparable program.

[MarkDuster]

The BLM-GLO has surveyed a lot of that line. The current boundary and the Von Schmidt line.

You might find some useful info there. The survey plats are available online like this one 33 S 65 E but unfortunately not the field notes you might be able to get these at the Las Vegas field office or for sure in Reno. From that search page you can choose Rectangular Survey Plats or Geographic Coordinate Database The GCDB data might give you some good search areas and Nevada has this at NV GCDB the .geo file has the lat long (NAD 27) coordinates but the boundary monuments might have some odd numberings like (711-799 - Boundaries with Mileposts)

Look here for more info on GCDB GCDB Users Guide

Good luck.

 

Here's one boundary mon I found way north of where your looking. JR1151

 

I did find some field notes online for T 32S R 64E not sure exactly where you are looking but there are some State Boundary surveys here

Edited March 3, 2010 by MarkDuster

[+Klemmer]

Mark Duster:

Thanks for the idea on BLM-GLO. I should have thought of them! Will dig into it over there.

I have the field notes from the 1899 survey (link in my original post above). They went to great lengths in 1898 or so to find field notes from von Schmidt's survey in 1873, but never did find them.

Klemmer

[+Klemmer]

Several days ago, I found a good email contact point for the datum experts at the National Geospatial-Intelligence Agency (NGA) [previously NIMA, previously DMA], and asked if they had any data on the older datums in question here (Yolo Base and US Standard 1901). Earlier this evening I got the answer: No data there. It was worth a shot. I also gave them the link here, so.....

 

Here is their page with reports on datums, WGS84, and related geodesy information (TR8350.2 and TM8358.1). There you will find pretty much anything you ever wanted to know about datums, and the conversions from every datum worldwide known to man (except the really old ones we are working with in this thread).

Klemmer

Edited March 4, 2010 by Klemmer & TeddyBearMama

[Bill93]

I can't access TR8350.2 from that link because it wants me to log in.

 

But isn't that the report that says NAD83 and WGS84 are the same thing? Last I knew, the NGA had never updated their list since the original plan to make them the same within the precision available at that time, later found to be a meter or so different.

[+Klemmer]

Bill:

Yes, I suppose it does say that. I didn't read the whole thing.

The reason I mentioned it was more for the Appendices (A, B and C) which have all the datum transformations. Those guys know their datums (except the one I was hoping for).

 

Here is a better link. Sorry, I didn't realize the next page from my original link was a sign-in deal. I had a different link yesterday with all their geodetic reports, that didn't require a sign-in, but I'm not able to find it again at the moment.

 

Take a look at item 5 (GEOTRANS). It does all sorts of transforms, including one datum to another (as well as the usual geodetic to UTM, etc). Looks handy.

 

P.S. I was able to go back and fix the link in my above post (in case you were wondering what Bill was talking about...)

Edited March 4, 2010 by Klemmer & TeddyBearMama

[Bill93]

To explore some of the geodetic aspects, I did a few simple comparisons between ellipsoids using INVERSE to find the distance, forward azimuth, and backward azimuth of point pairs. I arbitrarily picked a latitude and longitude, and then the points 1 degree greater north, west, and northwest.

 

N30 W90 to N31 W90 (looking 68.9 miles North)

Clarke 110,857.0290 meters FAZ 0 BAZ 180

NAD83 110,860.9256 meters FAZ 0 BAZ 180

 

N30 W90 to N30 W91 (looking 60 miles West)

Clarke 96,487.9213 m. FAZ 270 15 0.02 BAZ 89 44 59.98

NAD93 96,485.9741 m. FAZ 270 15 0.02 BAZ 89 44 59.98

 

N30 W90 to N31 W91 (looking91 miles NW)

Clarke 146,645.5398 m. FAZ 319 21 37.90 BAZ 138 51 10.66

NAD83 146,647.1994 m. FAZ 319 21 43.58 BAZ 138 51 16.34

 

So over a fairly long line, the distances differed by 3.9, 2.0, and 1.7 meters. The near cardinal azimuths were essentially the same, and the diagonal azimuth was different by less than 6 seconds.

 

If you have a smaller triangle the effects are much less. The difference between datums is nearly accounted for by a local shift, and only for very accurate results do you need to worry about the difference of the ellipsoid shapes.

 

It appears from what Holograph tells us that the accuracy of some of the old points isn't as good as the difference due to ellipsoid shape.

 

---

The forward and back azimuths are not 180 degrees apart when there is an east-west component. On this large a figure, the difference is up to a half degree.

 

On the other hand, a triangle is mostly "twisted" and only slightly fattened so, even though the azimuths aren't reciprocal, the sum of angles in a triangle is still very close to 180 degrees, differing only by a small "spherical excess". For the triangle formed by the 1st, 3rd, and 4th point the excess is 27.2 seconds, and always near 1 second per 75 square miles of area in the spherical or ellipsoidal triangle.

 

This "twist" in azimuths is indeed due to the earth curvature in the same way that the meridians converge.

Edited March 4, 2010 by Bill93

[holograph]

It appears from what Holograph tells us that the accuracy of some of the old points isn't as good as the difference due to ellipsoid shape.

 

Also, many of the published coordinates for the older datums only list to the nearest tenth of a second, which amounts to roughly +/-5 feet. It isn't reasonable to expect any greater accuracy in that case, unless you average a large number of points.

Edited March 4, 2010 by holograph

[+Klemmer]

Status (of the original problem):

Doing Yolo Base Datum conversions (Klemmer's method, as easier for multiple points).

Plotted the first two 1899 missing marks (No. 135 and No. 139) on map program (TOPO USA 8)

1) Both fell on the CA-NV border line (on USGS 1:24K Topo), well within reasonable error range

2) Both are located at spots on topographic features (hills) that compare favorably with the hand sketched topographic features from the 1900 field report. Remarkable!

I'm happy!

I think I may have a shot at recovering some of these 1899 marks that are not presently in the NGS database. Of course, I also plan to recover a number of 1899 marks that are in the NGS database.

 

Company welcome. I plan to look for these 1899 marks (and others) west of Laughlin NV, in the time frame of several days (4/19-21) after our benchmark hunting gathering in Laughlin 4/17-18.

 

Thanks for all the help!

[MarkDuster]

A dependant resurvey of the US Coast and Geodetic Survey boundary line between California and Nevada

from monument 129 to the Colorado River, as executed by U.S Transitman Roger F. Wilson under Group No. 204 was made between Feb. 24, 1933 and May 11, 1933.

 

The field notes can be found in Book No. 0018 Dated 05/01/1935, Search for Rectangular Survey Field Notes for Tp. 31 S. R. 64 E.

 

From page 24:

 

70.085 Monument 135 on California-Nevada State line, which is a redwood post 4 ins. sq., 1 ft. exposed, set

in a mound of stone, 4 1/2 ft. base, 2 ft. high, marked 135 on NW., N on NE. and C on SW. sides; on top of hill bears NE. and SW.

 

Land rolling.

Soil, gravelly, 3rd rate; and rocky, 4th rate.

Timber, none.

Undergrowth, scattered creosote brush, catus and sage.

 

It looks like they set iron posts every 1/2 mile so if you find one of these you should be able to follow the line to where you want.

 

The same search of that Township will bring up Volume B0005 "Field Notes of the Eastern Boundary of the State of California as surveyed by Allexey W. Von Schmidt " 1873 if you want to go look for those.

 

Your trip sounds like fun I wish I could join you.

 

Mark

 

Found a little more GCDB has coordinates for 711135 I think is monument 135

Lat/Lon: 35° 09' 40.4390" N, 114° 49' 48.8435" W (NAD 27)

Lat/Lon: 35° 09' 40.4286" N, 114° 49' 51.7452" W (NAD 83)

Edited March 5, 2010 by MarkDuster

[+Klemmer]

Thanks, Markduster.

So - the 1899 survey folks couldn't find Von Schmidt's Field Notes, but now we have them on line (sort of - a bit difficult to retrieve). Huh.

Will look into your info more this weekend.

[+billwallace]

Bill93 and Billwallace, I posted a description of the process at this page.

 

As I said, it is too complex to do routinely without having some software to do it automatically. I was just trying a proof-of-concept, and may or may not try to make it easy to do with an Excel spreadsheet or comparable program.

thankyouverymuch