Beginning on page 53 of NGS Manual 05 is a traverse example using state plane coordinates, apparently a famous one that dates back to NAD27. It seemed to me that this example should be updated to more modern methods, so I developed a single parallel Lambert Conformal LDP for the traverse.
Then it occurred to me that if someone would redo the example using ground coordinates computed from State Plane combined factors, the world could have one traverse adjusted with three different models: State Plane, LDP, and Ground Coordinates. Is someone up for that?
Here are the original data, which you should check against the source. Especially look at the geodetic azimuth from Station 1 to its azimuth mark, considering the church spire. The adjustment shouldn't be difficult.
And here are the parameters for the LDP that I used:
]
I put the central meridian at the longitude of Point 1 to make convergence zero at the beginning point, so that's why it looks messier than they usually do.
For Point 1, I got LDP coordinates: N 51,851.820 meters, E 100,000.000 meters, h = 227.64 meters, Scale Factor = 1.00003704, Elevation Factor = 0.99996430, total distortion = 1.341 ppm.
For Point 6, the numbers are: N 49,313.806 meters, E 113,653.419 meters, h = 243.82 meters, Scale Factor = 1.00003701, Elevation Factor = 0.99996176, total distortion = -1.233 ppm.
Certainly, anybody's LDP is welcome, as are anybody's ground coordinates. The interesting thing will be the linear closure of these methods compared to each other and the original example.
Hope everybody's New Year has begun well. Mine starts Monday.
looks like an interesting example. i will look into it, as i expect several others will also
> Beginning on page 53 of NGS Manual 05 is a traverse example using state plane coordinates, apparently a famous one that dates back to NAD27. It seemed to me that this example should be updated to more modern methods, so I developed a single parallel Lambert Conformal LDP for the traverse.
Actually, to really update that traverse example to modern methods, the missing pieces of information are the elevations of the intermediate stations 2 through 5. It's a fudge to apply an average project CSF to the reduction of distances when it is entirely too simple to let the least squares adjustment software compute the correct CSF for each line and to use that factor to reduce the measured distances to grid.
What would be interesting would be to plot the traverse on a quad sheet to get better elevations for those stations instead of having to assume some average project elevation.
> Actually, to really update that traverse example to modern methods, the missing pieces of information are the elevations of the intermediate stations 2 through 5. It's a fudge to apply an average project CSF to the reduction of distances when it is entirely too simple to let the least squares adjustment software compute the correct CSF for each line and to use that factor to reduce the measured distances to grid.
>
> What would be interesting would be to plot the traverse on a quad sheet to get better elevations for those stations instead of having to assume some average project elevation.
But after doing some computations on the traverse in the NGS example, it definitely appears that the quality of the work isn't good enough to worry about polishing it up. The raw closure is only about 1:30,000 and even with an s.e. of +/-10" on the angles, they look as if they contain blunders, particularly angle 2-3-4, which has a residual larger than 20".
Unless I've made some transcription error (always a possiblity) and if the angles and distances are in fact properly transcribed, the uncertainties of the intermediate control points computed from the traverse example aren't even better than 100ppm (95% confidence) in relation to the fixed control.
I think that NGS example is too long in the tooth to be useful as a demonstration of much of anything.
In case anyone wants to work with the NGS traverse, here it is in Star*Net input format:
[pre]
P 1 42-33-00.01150 89-15-56.24590 ! !
P 6 42-31-37.32888 89-05-58.04271 ! !
P AzMk 42-31-21.65360 89-06-03.59289 0.1 0.1
M 6-1-Spire 260-19-01.5 3701 & !
B 1-Spire 0-20-31.2
B 6-AzMk 194-03-28.59
M Spire-1-2 90-44-18.3 4805.468
M 1-2-3 265-15-55.2 3963.694
M 2-3-4 82-48-26.9 4966.083
M 3-4-5 105-03-08.6 3501.223
M 4-5-6 304-33-46.2 4466.935
A 5-6-AzMk 245-17-39.5
[/pre]
here are the other adjustment settings, not including standard errors of angles, distances, etc. :
[pre]
Type of Adjustment : 2D
Project Units : Meters; DMS
Coordinate System : Lambert NAD83; WI South 4803
Default Project Elevation : 263.6500 Meters
Geoid Height : -30.5000 (Default, Meters)
Longitude Sign Convention : Positive West
Input/Output Coordinate Order : North-East
Angle Data Station Order : From-At-To
[/pre]
The data does seem a bit sloppy. I first looked at this example in detail last July. I had trouble deciphering the notes and finally calculated the azimuth from Point 1 to the Church Spire to get started.
Your listing is very helpful and I suspected that you would do the work with least squares. As a rough first approximation, could you use the average of the combined factors for Points 1 and 6 for the traverse average combined factor?
Considering that the example was first used in NAD27 seminars and then updated in 1980, perhaps we shouldn't expect perfect data.
My expectation is that the precision of the traverse will be about the same on the LDP basis as it is on an average combined factor basis. What do you think?
> My expectation is that the precision of the traverse will be about the same on the LDP basis as it is on an average combined factor basis. What do you think?
The fundamental problem with this example is that it is presented as a traverse between two stations established by classical triangulation. Typically, those could easily have had errors of as much as 1:30,000 between their published values to begin with.
That being the case, the connecting traverse between stations 1 and 6 with coordinates fixed by triangulation was more of an exercise in distributing the relative errors in the control, to minimize the relative errors of any of the new points in relation to the control from which they were established.
As for whether the use of an average CSF is as good as an LDP or not, that depends upon whether the lines in the LDP are rigorously corrected by the different height scale factors and (small) changes in Projection Scale Factor across the survey or not. If the LDP is just used as if it were a plane coordinate system with SF=1.000000, then the results from both should be similar, particularly in this example where the survey is computed in a Lambert projection and extends more East-West than North-South.
> My expectation is that the precision of the traverse will be about the same on the LDP basis as it is on an average combined factor basis. What do you think?
You know, probably the cleanest way to deal with this problem would be to create a traverse between geodetic positions that were exact to the submillimeter. Just pick latitudes and longitudes, assign ellipsoid heights to those positions, and compute the inverses between them. After correcting the geodetic azimuths to derive the observed angles at successive stations, and calculating the mark-to-mark distances. You'd have the theoretically error-free traverse measurements.
The test would be to see how closely different approaches computed the exact geodetic positions of points on the traverse from the angles and distances of the traverse. Adjustment wouldn't figure into the problem.
I hear you. If the earth's surface would only comply, calculations and measurements would always agree perfectly. That not being the case, we have to model and then judge the usefulness of our models. Sometimes they work and sometimes they don't and sometimes they're inconsistent, working here but not there.
The lesson that I'm after here is that the precision of the traverse is determined by the raw data, not by the model used for computation. As long as the model is close to the truth, it will produce results consistent with those of other models. We have the NGS solution from 1980 and we have at least two other ways to generate alternative answers. I think, but I do not know, that the results of all three computations will be similar.
Straight lines have been used successfully to model (approximate) curved lines at least since the time of Archimedes. To the extent that the lines are not "too long", the approximation works well. Here, we're looking at three different techniques to judge their appropriateness in a not-so-perfect application.
> I hear you. If the earth's surface would only comply, calculations and measurements would always agree perfectly. That not being the case, we have to model and then judge the usefulness of our models. Sometimes they work and sometimes they don't and sometimes they're inconsistent, working here but not there.
The real demonstration, though, is in showing the superiority of using a method of computation that make rigorous corrections for projection and height scale to distances and the t-T corrections to angles as opposed to just about any alternate method that skips those steps.
Can't disagree with that. In Dr, Ghilan's September 2013 article, achieved 1:9,400 precision using raw measurements and 1:36,000 using fully-adjusted State Plane computations. My LDP on the same data achieved 1:28,800 using raw measurements and 1:35,800 with full adjustment. As you've pointed out before, getting full results from LDP computations requires essentially the same steps as required by State Plane and neither plane is inherently superior to the other.
Apparently though, there is an advantage, perceived or real, to working exclusively with ground coordinates. To me, a layman in the field, the real question is how to achieve that, and I think that an LDP has a clear advantage over adjusted ground coordinates. That advantage lies in the fact that the LDP is tied directly to the ellipsoid exactly in the same way as State Plane is. It is the best straight-line approximation to a curved line that we can make.
That said, it's also obviously true that adjusted ground coordinates have been and continue to be used successfully on many a survey. I have an old NCDOT paper espousing the method and giving an example of its use on a project in the NC foothills. I don't think it's used by our DOT now, but it seems to have been the standard.
Anyway, I'd still be interested in the 3 results for the old Wisconsin traverse. They might prove informative.
One clear advantage of the LDP is that your ground coordinates will not be confused with grid. Another advantage is the ability to use distances at ground in the field without applying a scale factor.
Correct me if I'm mistaken, but isn't the discrepancy between what surveyors in the field see and the scaled distances that they collect the primary reason for the desire to establish a ground coordinate system? Mathematically, moving from one coordinate system to another is not problematic, but when what you see doesn't agree with what you record, there's room for doubt.
Having a set of coordinates that each differ from State Plane by a fraction of a foot seems to be asking for confusion as the data move through different hands. Yes it is, no it isn't, we can't ask him because he's on vacation, etc.
OOne solution to confusion over scaling grid coordinates to ground is to subtract off a bunch of most significant digits that won't change over the reach of the project. It's a trivial mod that makes them obviously different but hardly any more difficult to compute. Put the formula in the metadata and go.
Other people say no, their DOT has always scaled and kept all the numbers, so they have to keep doing it that way. I don't work there to know, but to an outsider this seems like perpetuating the confusion for no good reason.
Same here, but it must work. They sure keep building roads!
Most DOT's scale up the state plane coordinates around 0,0 by multiplying the coordinate by the combined scale factor, then use those coordinates as a "working plane coordinate".
There are lots of legal documents I place coordinates on, but they are almost universally expressed as a lat, long (almost every agency wants them in decimal degree format) Very few are actual xy coordinates and if they are requested I also add the lat, long to avoid any confusion.
I can't think of any plats I file except for DOT ROW plats that have actual xy coordinates and those also show all control points and how the coordinates are developed, what the combined factor is and how to use it.
A LDP projection also needs to have a "scale factor" applied or you are surveying on the ellipsoid just like a state plane projection and each 20 foot of elevation change creates a 1 ppm of distance "error".
Most LDP's that I've used are tranverse Mercator projections, most computer programs can handle them, the lambert projections are not as easily put into a program as a tranverse Mercator projection, so I avoid them when I create a LDP.
I think that they divide the State Plane coordinate by the combined factor, but your point is well-made. The process must work, else there would be lots of poorly placed roads and highways. Do you calculate the lat/lon from the coordinates or is that a different process?
Transverse Mercator seems to be the go-to projection for most cases. Mathematically and geometrically, it's much more complicated than the Lambert Conformal Projection. The first clue that this is so is in James Stem's manual. For the Lambert, the closed form equations are given, but for the Transverse Mercator, everything is given in terms of truncated infinite series solutions to the equations. The series solutions are easy to program and the programmer does not have to understand the ins and outs of the projection, so it's a natural choice for mass-produced computer-driven applications.
I'm just an experimenter, but Michael Dennis is a pro. For more insight into LDPs, his handbook for the new Iowa Regional Coordinate System is an excellent resource. Here's the link:
http://www.iowadot.gov/rtn/pdfs/IaRCS_Handbook.pdf
Somebody in Iowa thinks that a lot of LDPs are better than one State Plane. I would imagine that not everyone agrees. It will be interesting to follow the implementation of this system.
>> http://www.iowadot.gov/rtn/pdfs/IaRCS_Handbook.pdf
>
> Somebody in Iowa thinks that a lot of LDPs are better than one State Plane. I would imagine that not everyone agrees. It will be interesting to follow the implementation of this system.
Keep in mind that the DOT engineers are fixated on highway corridors and don't take any larger picture into account as land surveyors typically need to do. Where the entire purpose of a coordinate system is to locate things within a few hundred feet of the centerline of a highway and the main object is just to help some contractor's folks build the highway and related structures approximately where the engineers wanted them to be, that's a rather different situation than a land survey that is made for the benefit of someone ten, fifty, or a hundred years from now.
Actually where I generally work the combined factor is always quite a bit larger than one, so the spc coordinate is multiplied by the factor giving the working coordinate a larger number which will reflect the desired distance correction when coordinates are inversed.
Back in the NAD27 days they used one correction for most work in this area of 1.0003.
I suspect that you're multiplying by the reciprocal of the combined factor, not the combined factor itself. Sometimes this is called the inverse of the combined factor.
Ground distance multiplied by combined factor gives grid distance. Grid distance divided by combined factor gives ground distance. The relationship is purely mathematical; whether the combined factor is larger or smaller than one does not alter the matheatics.
In pre-computer days, multiplying 8-decimal place numbers was much easier than dividing by them. Thus calculating the reciprocal once and then using it forever more as a multiplier was very efficient. It appears that the concept survives today.
Actually, what I'm talking about isn't really the combined factor, but an adjustment factor sometimes referred to as a Datum Adjustment Factor (DAF).
Back in the day control was set and run for these projects between NAD27 monuments. Then to be usable and avoid dealing with reducing distances every time you made a measurement in the field a DAF was developed for the project. Prior to modern equipment the DAF was usually crude, in my area it was 1.0003 which covered a large area. Since the fixed NAD27 control wasn't all that accurate itself getting the DAF "close" was good enough.
The state plane coordinates are multiplied by the DAF to obtain "working Plane coordinates" or "surface coordinates". This allows inversed distances to be close to ground distances. Most DAF's are restricted to the ten mile project runs. The next project gets a new DAF. To push these numbers beyond 6 decimal places is not really useful but many of these will be shown as a number like 1.0002968872 which is actually silly, but you need to know the entire number when you multiply a coordinate of over a million feet.
It's important to know that "surface coordinates" are divided by the DAF to obtain state plane coordinates.
Also, most computer programs that I know of, actually every one I use treats the scale factor this same way. For example the local site adjustment in Trimble needs the "scale factor" to be imputed as a value larger than 1, at least anywhere I would work or you will not like the results.
The distances in state plane projections are really trivial to deal with, it's more the angular "distortions" that are the driver of LDP's (remember to project a LDP based on NAD83 a "scale factor" or k value will need to be applied or you will generate distances the same as state plane). The vexing issue, particularly with the larger Lambert projections is the distortion from grid to true north. Since most legacy surveys were based on true north and state plane bearings will often times be quite shifted from that. Also, because much of the old true north surveys were not all that precise, being "close" to true north, even though you aren't exactly "on", is still simulating true north much like the older surveys. Where I am north swings a bit less than a minute each mile of east west shift, so 6 miles makes about 4 minutes giving you a 12 mile wide LDP area that is all within 4 minutes of true north.
This is the reason for LDP's not the distances which are easily dealt with in state plane and are "adjusted" up with an LDP anyway. The meridian for the LDP is placed near the center of your working area and then true north and grid north are "close". Of course as you move east and west they diverge just like state plane does and you have to restrict the size of the LDP or you have the same issues the larger state plane zones create.
