Gound Projection and Curvature of the Earth

Anyone who thinks that it is a good idea to introduce the confusion created by scale factor, etc. on a project this small should really be doing something else for a living.

My $0.02

A 1 part per million (ppm) Transverse Mercator Projection will span about 16 miles East-West. At that scale reduction (0.999999), your developed surface (grid) and the ellipsoidal surface (ground), will remain within ~21 feet (vertically) of each other. This means a distortion of no more than 1ppm (+/-0.005 feet per mile), anywhere within the projection LIMITS.

In an LDP sense, you simply “move” the developed surface “UP” to the desired “elevation” by using a Scale Reduction Factor greater than 1. There's somewhat more to it than that, but that's the general idea. You still get 16 miles to play with (East-West), and almost unlimited North-South possibilities.

The REAL LIMITING Factor in MOST cases, is the relative vertical RELIEF within a given project or area. Each ~21 feet of relief, imparts another 1ppm of potential “grid-ground” distortion. Sometimes it mitigates (to some degree) your initial 1ppm, sometimes it makes things worse.

Of course there is the GEOID undulations to account for too, but that rarely imparts a non-trivial variation into the proposition (at least on small projects).

When “modifying” SPC (or UTM) projections to “fit the ground,” you are usually playing with sub-parallel surfaces. This gets WORSE the farther you are from the Central Meridian (Transverse Mercator), or Central Parallel (Lambert). This sub-parallel condition is usually a trivial consideration, BUT the relative RELIEF ISSUE is pretty much the same can of worms no matter which route you go.

Hope that makes sense.

Loyal

That would be a combined scale factor of 1.000066 which is pretty small-they really might consider just staying on state plane.

If you project to the “ground” then you are really “raising” the state plane grid from sea level to your elevation and also adjusting whatever grid scale factor that the state plane system has at your location. Depending on the contour of the area you are trying to control you might be able to get your distances within .05’ in 10,000’, which would be a nice result. The curvature of the earth plays a part in all plane projections but at 10,000’ across it is not as big an issue to the grid to ground distances as elevation changes.

Be sure you include enough metadata to explain the conversion, so that anyone else knowledgeable about such matters can see exactly what was done. And don't forget to subtract off a few million false northing and easting so that the ground numbers don't look like SPC to confuse everybody. Give true SPC for one point to tie the systems together.

I suspect that the worse issue is it sounds like the city is requiring them to use a CSF to "scale up" their grid coordinates to so-called "modified coordinates", as opposed to using an LDP. This is a solution I don't recommend, because of all the problems it creates. But it's one lots of people have used, historically. (And I've seen many of them get bitten BIG TIME, because it's not a good solution.)

sinc

I agree 110%

Since the advent of the PC some 30 years ago, "modifying" State Plane Plane Coordintes to [sorta] "fit the ground" has been a solution in search of a problem. As you indicate above, as often as not, it creates NEW problems that only serve to muddy the water even more.

Loyal

0.7'/ mile adds up.

-JD-

About 15 years ago we surveyed and designed a road for a local county. They provided control (didn't work but that's another story) and wanted ALL coordinated shown on construction and right-of-way plans in SPC. No Problem, I can do that. NOW, we want the road STAKED using SPC. HUH? Every 100 foot station had to be staked (most were PK's in existing asphalt) using 100.015 feet. I asked if we were building a road or developing their GIS. The boss says just stake it like they want. Now when property corners are set they won't match (contractor is responsible for corners) but the numbers (SPCs) do.

Andy

The second biggest mistake is not specifying the factor or method to use. If every project, contractor, etc. uses different values then none of them will relate to each other. If they are going to use a bastardized system they should at least standardize it.

- jlw

Ground Coordinates

Using one average CGF seems to work well enough in relatively flat areas, but one of our projects is 20 sq. miles at about 10,000 feet. With around 2000 feet of elev difference, this approach is not perfect but "good enough". Carlson's SurvNet can output a coordinate file on ground coordinates using the mean CGF. With a couple hundred points in the network, it's the only efficient way to do it. I wish SurvNet could output a file using the real CGF's for each leg. Maybe there's software that can...:-/

> ....There is some disagreements on whether the job is to large in size to project to ground due to horizontal errors from the curvature of the earth. To me 2 miles doesn't seem large enough to worry about curvature of the earth. Any thoughts from someone with more of a geodetic background than me of when curvature of the earth begins to significantly affect horizontal distances?

Hmmm....I don't think your error's are really significant due to "curvature of the earth". Applying a grid scale factor gets the distance to a curved ellipsoid, and applying an elevation scale factor projects a distance to 'ground'. The greatest effect of grid to curvature is the bearings over a long east-west project (in my opinion).

However, I think I am arguing your terminology and not your real point. You are talking about, I think, applying an overall scale factor to the whole project, and not adjust it for each distance. The real problem starts to rear its ugly head, if there is a lot of differences in elevation, and you are just applying one elevation scale factor for distances at different elevations.

Anyway, I say it depends on your project and what you are doing. Applying an overall combined scale factor, will probably make all the distances correct close enough between any two "adjacent" points; which might suit your needs perfectly well. Who cares if the distance between two points two miles apart from each other are that far off (except, as I say, depending on the job) (oh, yeah, and the 0.66' in two miles, if that is what it is, is a difference in state-plane grid and your adjusted distance....what would the distance difference be in your incorrectly-modified distance, and if you applyed the scale factor for the distance between those two individual points at a mean of their elevations?

Of course, I am not expert like, I believe, 'sinc' and Loyal are.

Here's a good wee example of curvature for those who are interested

I've been playing with some 3d modelling in sketchup and google earth

I've been working with a NZ wide planar coordinate system where the origin is about 350 miles from the model location

Bringing the sketchup model, which has elevations around zero, into google earth results in the structure "floating" a thousand feet or more above the ground.

It shows very clearly the differences between the curvature of the earth compared to the planar coord system.

Sounds like you have a better understanding than most.

And that kind of touches at the crux of the problem... Since I understand this stuff (and have been teaching my understanding to others in various venues, most-importantly my colleagues at Edward-James Surveying), we can figure out what is going on, even when others make gross errors. Once you understand the basic theory, and also understand the typical mistakes, you can generally make anything work, and even fix lots of problems created by others who don't understand it.

But a "fix" often involves actual field measurements, so you can really identify which error somebody else made. That means field-crew time, to fix an error that never should have been made in the first place. And in most cases, these errors go back to a so-called "Modified State Plane" coordinate system (a term I hate, not to mention a thing that I hate), as well as a lack of communication between different companies or a failure to really explain the "metadata" of how things were done. This can create HUGE swaths of problems, that can have big ramifications for years, on some projects.

And that doesn't even include the errors such a system can create in smaller construction sites, especially these days, when so many parts are pre-fabricated to very high degrees of accuracy. When your 500' building is made of pre-fab metal pieces, and they don't match up by a few inches, you can find yourself liable for creating all-new pieces, having them shipped... It can run MANY thousands of dollars.

Ground Coordinates

The usual way to deal with this is to use a grid system with a floating scale factor. That means you NEVER use so-called "ground coordinates". THAT'S the bastardization of the system that causes all the problems.

In a true grid system, EVERY point on a ray from the center of the Earth to outer-space has the same coordinates. Your distance between points may vary, depending on your elevation, but your coordinates don't change.

Ground Projection and Curvature of the Earth

I can see a time, maybe in the near future, as computing and modelling continue to develop that projections will become redundant and we'll be surveying, modelling, designing and staking out on a virtual earth, where all distances are 'ground'.

Ground Projection and Curvature of the Earth

> I can see a time, maybe in the near future, as computing and modelling continue to develop that projections will become redundant and we'll be surveying, modelling, designing and staking out on a virtual earth, where all distances are 'ground'.

Actually, I believe that we've been doing that since the dawn of time. The problem we have is overcoming our "flat earth" mentality.

Ground Coordinates

> In a true grid system, EVERY point on a ray from the center of the Earth to outer-space has the same coordinates. Your distance between points may vary, depending on your elevation, but your coordinates don't change.

What sinc is trying to say, here, is that we really need to learn how to "transform" points to the true grid instead of "scaling" our points by some bastardized "factor."

Right on, sinc.

JBS

Ground Coordinates

> > In a true grid system, EVERY point on a ray from the center of the Earth to outer-space has the same coordinates. Your distance between points may vary, depending on your elevation, but your coordinates don't change.
>
> What sinc is trying to say, here, is that we really need to learn how to "transform" points to the true grid instead of "scaling" our points by some bastardized "factor."
>
> Right on, sinc.
>
> JBS

Agreed. But when DOT requires a control sheet to list both state plane and project coordinates (modified state plane, local etc) that agree with ground distances, and the method of converting a point from one system to the other (CGF, rotation, shift), we're kinda stuck using the one factor method. Plus, Carlson and TDS Survey Pro both work that way too. It usually works pretty well. We recently did control for a long route survey in state plane, but wrote easements using ground distances (as they should be done). The engineers designed the route in state plane. The dirt contractor's surveyor had a hernia when he learned that he needed to stake the job in state plane.

Ground Coordinates

> Agreed. But when DOT requires a control sheet to list both state plane and project coordinates (modified state plane, local etc) that agree with ground distances, and the method of converting a point from one system to the other (CGF, rotation, shift), we're kinda stuck using the one factor method. Plus, Carlson and TDS Survey Pro both work that way too. It usually works pretty well. We recently did control for a long route survey in state plane, but wrote easements using ground distances (as they should be done). The engineers designed the route in state plane. The dirt contractor's surveyor had a hernia when he learned that he needed to stake the job in state plane.

Like my momma always used to say, Stupid is as Stupid does...

I work in LDP (local) day in and day out. Have for years. I can spit out SPC, LatLong, and local coordinate tables any time (and, they're transformed coordinates). Why on earth would a contractor, working at 5000 ft in Colorado, want to know how much dirt he moved on the shores of Texas?

Just because they want to know SPC coordinates is no reason to design, stake or work in them. I gotta side with the contractor on this one.

JBS