In my previous blog/FAQ entry I noted that there will be a variety of ESF (Elevation Scale Factors) to be encountered for a given latitude and ellipsoid height.
In this arcane blog entry, I present the NGS Ellipsoid Reduction Method and a deep drive into the resulting differences for various flattening ratio values, compare results obtained with GRS80 vs. WGS84 ellipsoids, look at the scale of errors introduced by using the orthometric height instead of the ellipsoid height and provide links to additional resources.
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: