Ellipsoid Height

Share:

# Ellipsoid Height

Page 2 / 3 Posts: 4197
Member
(@norman-oklahoma)
2,500+ posts
Joined: 4 years ago
Posted by: MightyMoe

An easy way to get a combined scale factor is using the free software corpscon. I don't have Survey Pro so I don't have any idea how it works.

I have Survey Pro but  I would not attempt to use it to determine a point's CSF. I don't even know if it can be done in SP. Certainly you set up jobs in it to be on whatever grid system you want to work in and the software does it's magic on collected data. So it has the capacity at some level to determine scaling factors. But as far as reporting it to the user in real time - not so much. My go-to for such things is StarNet, with Corpscon being a back up system. Posts: 5872
Member
(@mightymoe)
5,000+ posts
Joined: 8 years ago

"My go-to for such things is StarNet, with Corpscon being a back up system."

There tends to be very slight differences in SF between programs that I've used, so I usually have corpscon as a back up to check. However, there is little chance that anything I've done with a combined SF will have an effect to the end result. Usually a SF is used to push up a grid to a surface "close" to ground. I'm assuming the OP needs it for that. Posts: 910
Member
(@geeoddmike)
500+ posts
Joined: 8 years ago

At risk of being labeled a pedant, let me clarify that the scale factor (SF) does not require an elevation. It is a function of the location of the point within a grid zone. The application of a grid factor to a length yields a distance on the ellipsoid surface.

To allow reduction of distances to account for the height of the line other than at the ellipsoid we compute an elevation factor (EF). An elevation factor does require a height; it requires an ellipsoid height.

The distance at the height of the line is computed using the combined factor (CF) the product of the GF and EF.

There is a nice graphic showing how grid and scale factors yield different lengths as a function of of the surface on which the measurements are desired here:

https://www.e-education.psu.edu/geog862/node/1815

As for the issue of where one obtains the required ellipsoid height, I would be wary of assuming that something displayed as “height” is either an orthometric or ellipsoid height. Perhaps the device is set to display an orthometric height using a stored geoid model? It would seem fundamental to know what your device is displaying.

I like the graphic showing the relationship of height systems here:

https://www.researchgate.net/figure/The-relationship-of-ellipsoid-height-h-orthometric-height-H-and-geoid-height-N-at_fig3_268516558 Posts: 910
Member
(@geeoddmike)
500+ posts
Joined: 8 years ago

For those unaware, the equation for the computation of the elevation factor (EF) is: R/ (R + h) where h is the ellipsoid height. In the US one uses NAD83 ellipsoid heights.

I once explored numerically the impact of different R and h values on computed EF values. An HTML generated from a Matlab script see: http://geodesyattamucc.pbworks.com/w/file/fetch/110168668/compRfromEF.html Posts: 2498
Member
(@john-hamilton)
1,000+ posts
Joined: 9 years ago

Important to note that older versions of Corpscon incorrectly used the orthometric height. Makes a difference of roughly 5 ppm if I recall correctly. Be sure to use the latest version to get the correct results.

There should be no reason for a difference between software. The state plane formulas compute an exact value, as does the formula shown above by GeeOddMike. Unless one uses a different value for the radius. I use R=Sqrt(M x N) where M is the radius of curvature in the N-S direction and N is the radius of curvature in the E-W direction.

Here is a plot I made of the mean radius by latitude for a presentation I gave at Trimble Dimensions in 2012. I also included a value commonly used as a "mean value" as the bold line. Member
(@mightymoe)
Joined: 8 years ago

5,000+ posts
Posts: 5872
Posted by: John Hamilton

Important to note that older versions of Corpscon incorrectly used the orthometric height. Makes a difference of roughly 5 ppm if I recall correctly. Be sure to use the latest version to get the correct results.

There should be no reason for a difference between software. The state plane formulas compute an exact value, as does the formula shown above by GeeOddMike. Unless one uses a different value for the radius. I use R=Sqrt(M x N) where M is the radius of curvature in the N-S direction and N is the radius of curvature in the E-W direction.

The differences I've noted in the past were very small, not meaningful to anything I was doing. It may have been how corpscon used to calculate using the ortho height. Where I am that would be <2ppm. I've been using Trimble for that calculation for a long time, before that it was a program created by a guy who posts here once in a while.

Page 2 / 3