Here's something for you guys to chew on.
This is a [TYPICAL] excerpt from a legal description written in 1976 by a LARGE Railroad company. The Main Line (and ROW) described dates to 1902. The parcel being conveyed adjoined the Railroad, and had been in Railroad ownership for about 70 years (part of an aliquot 40 BTW). I have been plotting all of these (about 10 miles worth so far) into CAD....great fun!
thence northerly along said curve and parallel with said centerline of the main track, through a central angle of 27 degrees 56 minutes 21 seconds, an arc distance of 2,046.72 feet;
thence tangent to said curve and continuing parallel with said centerline of the main track North 27 degrees 31 minutes East, a distance of 1,077.0 feet to a point opposite the beginning of an increasing O.W. taper spiral curve to the right in said centerline of the main track;
thence northeasterly along a line concentric with and 100.0 feet easterly measured radially from said centerline of main track (which centerline has 7-30 foot chords, a spiral length of 210.0 feet and a spiral angle of 4 degrees 12 minutes), a spiral length of 203.0 feet more or less, the long chord of which bears North 23 degrees 59 minutes 41 seconds East, a distance of 202.61 feet to a point opposite the end of said spiral curve in said centerline of main track, said point being the beginning of a tangent curve concave southeasterly, having a radius of 1332.69 feet;
thence northeasterly along said curve and concentric with said centerline of the main track, through a central angle of 27 degrees 26 minutes, and arc distance of 638.09 feet to a point opposite the beginning of a decreasing O.W. taper spiral curve to the right in said centerline of the main track;
And so forth and so on through several additional spiral and simple curve combinations.
Piece of cake!
Loyal
I hope that you aren't plotting that in plane coordinates, Loyal. :>
County LDP...
But all of the "shots" in the area are NAD83 geocentric XYZ transformed to said LDP.
🙂
Loyal
> County LDP...
>
> But all of the "shots" in the area are NAD83 geocentric XYZ transformed to said LDP.
So, you're cheating and plotting it all up in plane coordinates? I'm very disappointed. :>
I don't understand the comment about "cheating." If/when using the global spatial data model (GSDM) based upon geocentric X/Y/Z values, it is possible to obtain the local tangent plane directions and distances with little (or no) distortion.
I don't know exactly how the computations were performed but, although there are others, I list FYI one reference and one example as:
Reference: http://www.globalcogo.com/psgsdm.pdf
Example: http://www.globalcogo.com/3DGPS.pdf
When using the GSDM it is the users perogative to display the data in any stated system without cheating on the integrity of the underlying values in the data base.
But, the conscientious surveyor will state specifically how the values shown were obtained - regardless of the system or data base being used.
Other points can also be made.
Earl F. Burkholder, PS, PE
Global COGO, Inc.
Las Cruces,NM 88003
www.globalcogo.com
It may be that Kent is saying that the railroads were laid out true north and should be calculated that way and not on a grid.
No doubt Loyal is also well aware of this and has taken it into account. It is a little odd that the deeds reference spirals which were usually intended for track layout only. However, I do know of one railroad in this area with spirals in the ROW (1970's era deeds). I always assumed that it was more of a mistake that the spirals were written into those deeds.
> It may be that Kent is saying that the railroads were laid out true north and should be calculated that way and not on a grid.
Actually, I was merely remarking on how we've read so much on this message board about how useless plane coordinates are but when it comes time to actually work land survey problems, what is the first tool in the box to be put to use? Right.
Loyal has dealt with the elevation issue by a strategy identical with applying a project average Combined Scale Factor in a state plane projection. That is, his CSF is approximately built into his county's standard projection.
Loyal has dealt with the elevation issue by a strategy identical with applying a project average Combined Scale Factor in a state plane projection.
So we are back to the LDP and the Combined Scale Factor. Yes, it does introduce slight errors compared to precise surface distances. To adjust each distance to true surface numbers would be more precise. Of course, with a large legal and enough elevation changes the figure wouldn't quite close. That would cause all kinds of distress in some mapchechers.
With those railroad deeds I'd be more concerned that the 1902 deeds were true north and simple curves, and the 1970 were written parallel and spiral curves. They do say that they are parallel to the centerline of the main track and not the centerline of the ROW so..... it should work. Seems like a lot of extra work-including spirals in those 76 deeds.
LDP's are a plane projection same as a SPC. They are just set up so as to make north closer to real north and the grid distances closer to ground distances. So once the LDP is being used no need to rotate and scale back and forth.
Since a smart user is keeping all the raw data in native GPS 3D ECEF coordinates (whether they realize it or not) switching into any other coordinate system (including SPC's) is simple and easy.
Why not look at your data in a system as close as what the deed was written in as possible? If I have a deed that says it was developed in SPC's (both bearing and distance) then of course I'd use the SPC. I've seen deeds that used SPC bearings and ground distances (popular in Happy Valley Utah), kind of a hybrid trying to match ground distance but ignoring the bearing from the GLO survey everything derived from.
I suppose if you want everything to be in the same system, that it's important that two parcels hundreds of miles apart really need to be mapped in the same system (as if the owners really care) then UTM of SPC's are the way to go. The way to map the whole earth in the same system is using ECEF or lat, long and elipsoid height. From that you can look at it any way that simplifies your problem.
As far as spiral curve offsets go there is no continuous easy math formula but you could measure out the distance on the radial as the description says and connect the dots with a smoothing polyline.
I have found “spiral ROWs” to be quite uncommon, and in many cases the Railroads have made a conscious effort to describe their ROW limits with simple curves. Like everything else though, there are exceptions. IF the Legal Description clearly recites a “Spiral Boundary,” then it's a Spiral Boundary. The beauty of the Searles Spiral, is that it is simply a compounding series of circular curves, and is therefore easy to compute, and the ROW can be truly CONCENTRIC with the [design] Centerline.
Loyal
Actually the 1902 deeds and documents used the EXACT same Searles Spirals and other curvalinear data.
🙂
Loyal
“Loyal has dealt with the elevation issue by a strategy identical with applying a project average Combined Scale Factor in a state plane projection”
Well, NO...NOT EXACTLY.
The net effect is very similar (aside from the convergency issue with State Plane Coordinates), BUT in reality there is a subtle difference.
When one applies a “Combined Average Factor” (CAF) to a State Plane Coordinate scenario, one is often dealing with significantly sub-parallel surfaces. This can be seen by computing the “Scale Factor Progression” in your area of interest. Although this is usually a rather trivial component on SMALL projects, it can add up on Larger projects, ESPECIALLY when one is situate near the design limits of said State Plane Projection (Scale Factors >1).
Well designed and reasonably small LDPs don't have this problem simply because the scale variation within a given “zone” is MUCH smaller (+/-1 ppm or so) than a State Plane Zone (+/- 100ppm or so). Therefore scale progression and sub-parallel surfaces are NEVER a problem.
As a practical matter, this rarely makes enough difference to worry about, BUT it is different in the theoretical sense (basic geometry).
Loyal
That is unusual; at least from what I've seen. Usually the old maps show a simple curve that define the ROW and the tax maps that the railroad would hand out show the spiral that the track was constructed with. Sounds like you have it well in hand.
Mighty
The 1868/69 Transcontinental Railroad Railroad (UP through Wyoming & Utah) was/is like that! Simple Curves (NO spirals) in ALL of the Original Documents, the spirals didn't show up until later. In my OPINION, the spirals don't mean swat when it comes to the Original ROW limits, UNLESS there were formal ROW acquisitions AFTER the fact (which sometimes there were).
As always...IT DEPENDS
Loyal
I've seen a situation where the original ROW is all simple curves. Then a surveyor got the track centerline data from the railroad maps (which of course included spiral curves) and set markers based upon offsets from the track centerline. Sort of made a mess.
Leon
I hear ya buddy...
I have seen it go BOTH ways too.
It ALWAYS comes down to doing PROPER RESEARCH. If you don't have ALL of the relivant documents, then you ain't gunna to get it right except by blind luck. I don't think that is what folks pay us for...
Loyal
If you do not mind I am gonna steal that
"It ALWAYS comes down to doing PROPER RESEARCH"
> The net effect is very similar (aside from the convergency issue with State Plane Coordinates), BUT in reality there is a subtle difference.
Yes, sure, if you're worried about a projection scale factor that changes by a couple of ppm per mile, you can use a small-scale projection, but you'll still have to contend with the height scale factor unless you're surveying Bonneville Salt Flat. So, either way, the COMBINED scale factor won't be constant, although for the special case of surveying railroads, the height changes ought to generally be smaller than for anything else of similar extent, aside from rivers.
The point I was making is that the process of reconstructing surveys using your county-scale projection should be essentially identical to using the relevant zone of the SPCS. Grid North in your county scale projection won't most likely be Geodetic North and you'll still have to deal with a combined scale factor. Those differences are a bit underwhelming.
I was watching my young grandkids at dinner Sunday night and I noticed at their age they were rapidly switching back and forth between the spoon and fork their grandmother provided for them and couldn't seem to decide which utensil was best for the task at hand. Finally their mother had enough and gave them a spork which seemed to make everyone happier. I guess LDP's are a little like those sporks.
Your analogy is like asking whether would you rather face the firing squad or the guillotine. Neither is appropriate.
The fact remains that LDP and state plane coordinates are both 2-dimensional models and we surveyors work with 3-dimensional data. The global spatial data model (GSDM) is a 3-dimensional model that preserves the integrity of survey data and, once one gets into the details, is easier to use and the equations are more straight-forward than map projections. No more grid scale factors, no elevation factors, no grid convergence (depending on user choice), and no zone constants. Distances and directions are plane surveying latitudes/departures in the local tangent plane with respect to the origin selected by the user. What more can you ask? The equations are all public domain and the same set of equations work equally well world-wide.
See http://www.globalcogo.com/psgsdm.pdf and other references.
Earl F. Burkholder, PS, PE, F.ASCE
