We have a large 7 mile project that has close to 2000' of vertical relief. We have never worked on a project with this much relief so all of our projects have been completed using one grid scale factor. We will be setting up the project control for Lidar flights. The work after that will consist of on the ground conventional topo and monument ties. I've been thinking about how to set all this up. We use TBC - for reference. Would we create 2-3 projects each with their own SF? If so, then I would think the LIDAR flights would need to be divided up into each project as opposed to one overall set of lidar data. Looking for anyone with experience in this area.
The project is for state agency so we can't get super fancy or go outside the box much, if you know what i mean.
At the upper and lower elevations it will create 50 ppm of "error", or 0.50' in 10,000'. If that's too much you can do two zones which will1/2 that error. I'd prefer one zone it simply gets too unwieldy otherwise, and .05' in 1000' is manageable.
Some surveyors working in the Montana Lambert will change each time they cross a township line. That zone's grid scales change quickly moving north-south. If you have a township or range line that could work as a switch line that's one way to do it.
Would a snake grid work in your situation? Is this a linear project? One thing to keep in mind is you don’t have to start at one end and run a traverse to the other end. If you can use GNSS static across the board for primary then use RTK and Conventional in between. It would not take to long to figure out based on project requirements what that spacing would need to be in order to mitigate the scale errors. Also a LDP that was tilted depending where and how the elevation difference is at along the route. Just thinking out loud here.
0.5 in 10000' might be a bit much. If split into 2 with separate scale factors would it essentially be treated as two different adjacent projects? That's how i envision it and that has it's own inherent issues for the client.
It is not linear, it's a windy steep gravel road generally east-west orientation. No traversing is planned and a tilted LDP would definitely not work for the client.
I had a project once that had an assumed coordinate system. It was a large site which had a lot of vertical change. Everyone was trying to perform a site calibration and it was just not working. So what I suggested and what ultimately was done is that two site calibration were performed. Both overlapping. So some points control had two different coordinates on them. One side of the site was laid out from 1 file up to a certain point. In which everyone agreed upon. Think match line on sheets of plans. Then that same area was tied and checked from the other side site calibration. You could do two scale factors figure out the sweet spot vertically and choose a horizontal position on both they don’t have to be the same. You could actually sometimes get away with holding the scale position horizontal on both but doing a different elevation for each side of the site. I mean if you took the average elevation of the entire site and held 1 combined factor you are splitting that 2000 ft in 1/2 anyway. So just creat the 2 but keep separate and make sure that everyone knows exactly where that line of equation is drawn. Almost like stationing 0+00 = 50+00. Sorry I am not good with explaining without pictures. So trying to help you visualize that. You can actually have all coordinates points in both systems you create . For traceability. A one point scale factor has been accepted but like you see sometimes just picking 1 point in the middle doesn’t work. I always check when I am forced to do this all points across a site for that very reason. Most of the time a decent AVg height from the site and a good central location horizontally is good enough.
It is possible to design a TM that will have grid scales that kinda follow a slope east-west up the mountain if it's a more or less even slope one way. Big problem with that is the rotation from true north will be large.
I've done a lot of custom projections for some pretty large projects, but as you mentioned elevation change is the brick wall that LDPs smash themselves apart on.
1000 feet of elevation change is ~50 ppm, which is about the upper limit for a true LDP, so I'd recommend breaking the project into two projections.
With a little bit of work, it's possible to create two different projections that result in project coordinates that sync up. As in, when you get to the outer edge of one project, you can switch from one LDP to the other and your northings and eastings will be consistent. Helpful for design (keeping everything in a single CAD project) even if it requires awareness of where the dividing line is on the construction/build side.
Usually that would involve the central meridian being the same for both projections, and located approximately where that dividing line is. Then it's just a matter of creating two different grid factors for what would otherwise be the same projection. (The false northings and eastings will need to be adjusted a bit too.)
The only other factor that might be an issue is earth curvature. But over seven miles, the curvature of the earth/grid scale factor won't ever come into play...that's a small project when it comes to projections.
I'd be happy to help out with this one, as it's something I've wanted to try out for a while now on more than just a theoretical project.
...sorry, I have to keep editing because it's Friday and my brain is fried. If doing custom projections is a no-go, you could set up two different local sites on state plane in TBC, with slightly different northing/easting offset to achieve the same goal. While it's technically better to use an LDP centered on the project, a grid-to-ground solution would probably work too.
Is the 7 miles like the odometer distance along the road or the straight line distance from beginning to end?
I agree with MightMoe's general recommendation. An Oblique Mercator would allow for North to still be North, but the cylinder would be oriented roughly perpendicular to the direction of the slope. The central meridian would be roughly parallel to a contour line along the slope. As he said, you would then slide the central meridian perpendicularly away from the project such the grid surface and topographic surface are roughly parallel in the project area. This will make the combined factor practically consistent throughout the project. Then adjust the scale factor of the projection to make the combined factor practically 1.000...
I've not actually had to do this in practice, I'm just speaking theoretically, but I have heard of it being used.
I'm a huge fan of Oregon's Low Distortion Projections. I do all my projects on that projection. The elevation change you describe would foul the CSF's, no question. Nevertheless, I'd just stick with it and accept the distortions. If I had only SP to work with I'd do the same. Accept the distortions.
Before rolling out the Low Distortion Projections the typical procedure around here was to scale the SP coordinate to ground, calling the resultant coordinates "Local Datum Plane", or LDP - and a lot of people continue that practice. It drives me nuts. Doing so makes it much more complicated to use GPS going forward. Complicated enough to disqualify it as an option for most users. And for what? To eliminate a tenth of error in a thousand foot backsight? We aren't building fine pianos here. Just accept the distortions and keep things easy.
It's the blunders that kill you. Not little scale errors.
Shawn, I'm afraid that option is not available once Math Teacher's excellent question was answered.
2.4 miles is too short a distance to make it worthwhile, the rotations from north would be excessive.
This must be a switch back road up a mountain.
I'm with Norman on this one; one projection and live with the long distances on low portion and short distances on the high end of the road.
It will be .05' per 1000', not all that bad for gravel road construction. Two surfaces will be messy with a switch back road.
One like this, using LIDAR and problematic relief, just cries out for using XYZ coordinates. All distances calculated from these coordinates would be slope distances but the difference from ground-measured slope distances would be nil.
I have no idea how to accomplish such in the field, but there ought to be a way.
For such a small area, a Local Tangent Plane should work just fine unless there's a sharp slope in the geoid across the site.
I still haven't seen a major manufacturer implement LTP coordinate systems in their software...would be nice just to play around with real-world data rather than theoretical work.
I've been away for a while. I'm familiar with a Local Tangent Plane in terms of a plane coordinate system designed so that the projection plane is tangent to the earth's surface; ie, touches the surface at a single point. The ones that I've designed have been Lambert projections with the scale factor at the origin equal to the reciprocal of the elevation factor at the origin, which is also the point of tangency.
In this case, finding the appropriate point of tangency is the problem.
Perhaps you have a different concept in mind; I haven't been involved in this math in a couple of years, so I'm both rusty and behind the curve.
