Tag Archives: Grid to Ground

Lambert Conformal Conic projections at ground

In keeping with the recent arcane subject series of this blog, I just finished figuring out the details of converting a SPC grid projection (like Utah South NAD83) into a ground system.

This method has the advantage of working in all software packages with a minimum number of system coefficients:

                Origin Lat, Origin Lon, False Northing, False Easting and a single Scale factor

With this method you can exactly duplicate the results you would get from traditional Modified State Plane Projection schemes that involve adding a Combined Scale Factor to a grid system with a single calibration point. While there is nothing wrong with the traditional way, the steps to implement it are different in every field software tool.

With the method that I describe, you just enter a new projection with the five coefficients and you are done.

The short explanation is:

  • Convert the 2-parallel LCC to a single parallel LCC by calculating an equivalent center latitude and the correct scale factor K0
  • Apply the correct ellipsoidial reduction factor with the correct point scale factor for the new projection base point.
  • Compute the correct false northing and easting

While some of the required coefficients are are in the NOS NGS5 SPC manual, I wanted to better understand how they are computed, so I did all the math.

I was surprised by how little information on this subject that I could find on the web, so I wrote a pretty detailed description with a worked example with all of the code that I used. Plus I used the X-PAD field software to validate the results.

If you are interested in this, continue reading this 10-page PDF:

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Filed under Carlson, COORDINATE STUFF, X-PAD

Low Distortion Projections: Mania, Hype or a Great Thing? JDtM!

Prerequisite Reading: If you don’t get LDP, read [ THIS ] first.

Shawn Billing’s excellent article in American Surveyor on ‘Low Distortion Projections.’ See [ Ground versus Grid: Low Distortion Projections—Part 1 ] is out.

I count Loyal Olsen to be a good friend (and drinking buddy.) Loyal is the king of LDP’s. I promise you, he is the king.

I have made a couple of Scale Factor Specific YouTube videos on [ Scale Factor ] to help customers figure out why they can’t match a total station shot to a GPS inverse.

Yesterday I met Michael Dennis in person! (You remember he knocked it out of the park on [ Nightmare on GIS Street ], right?) He showed me a crazy great [ web app ] that produces LDP’s using visual methods. Way cool. (Actually more than way cool. Awesome? Yes!)

Most everywhere I go, I hear about LDP’s. They are the new rage.

In most circumstances you can design a LDP (or better yet use the web app above) that is good to 10-ppm over a township sized survey. But not always. Sometimes they still blow up. Sometimes the job is big (think pipeline, transmission line.) Sometimes there is a couple thousand feet of relief in a mile. But, in most circumstances LDP’s are just fine.

But I am a contrarian. I don’t like LDP’s. Here is why:

1. State Plane was first pass at simplifying the round world into flat space coordinates. Our ability to survey accurately over long distances was not much better than the distortion and we accepted grid coordinates for the simplicity of being able to use an X,Y,Z(Height) coordinate system that could be easily inversed in the field.

2. At higher elevations (like where I live/work) we need to introduce a scale factor so that inversed distances from coordinates exactly match measurements at ground. For small jobs, we can pick a single scale factor, accept the small resulting errors and get our work done.

3. It was not a big deal when we were pulling tape (chain) and turning angles with transits, but golly it does not add up so well in these days of 1-second total stations and GNSS driven GPS receivers. On big jobs, state plane grids with a single scale factor to ground rarely work out well anymore.

4. LDP’s are the next step in working a bit better (I did not say smarter.) The convergence angle is smaller over a job (but it is not zero everywhere and can not be ignored.) Its better, but it still…sucks. Just in smaller breaths.

I can’t wait until we have 4,000,000 overlapping LDP’s in a variety of projection types, all with different datum and reference elevations. ESRI will be able to distribute 4,000,000 PRJ files with ArcAnything! That will certainly make the world a better place. Surveyors can use custom projections for jobs and not release the projection information. Thereby insuring a decent retirement.

6. Soon LDP’s won’t be good enough and we will design 100 micro-LDP’s (call them uLDP) for a single job. They will be piecewise linear and we can spline-fit the intersections. (I tell you this is really going to be great and simple!)

The world is NOT flat. We need to stop trying to make the world flat. We should accept it for what it is: a complicated oblate-ellipsoid like blob (think squashed basketball.)

So what is the solution? Use double-precision numbers, survey with any underlying projection (pick geographic or XYZ Cartesian for all I care) and ‘Just Do the Math.’

More on this JDtM stuff later…

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