Thats a great map showing the separation but the formula (at least in NC) to calculate the elevation factor uses Orthometric Height. The formula is 1 - [ (Orthometric Height + Geoid Height)/R)]. This gives the elevation factor. This formula is straight out of the manual (Application and Development of the State Plane Coordinate System). Using Orthometric Height matches the data sheets for elevation factor. I guess the formula could be modified in other states, but at least here, thats the correct way to do it.
You are absolutely correct. I apologize about getting off on a tangent for insignificant differences. The biggest errors I have run across is the use of the software and not understanding exactly what results are being generated. I might be too anal about it, but I get a big job in and I check the data with a calculator (and other tools) to see if I get to the same final answer. If someone processessed 100 points, I don't check 100 points, but I check a couple of key points and make sure everything works without any major discrepencies. I have found major errors in the past.
Understanding how to use the software, and having a good checking system is imperative. Higher technology makes it easier to make a mistake and harder to find the errors when you do. It is usually applied across the board. Even if you don't break out a calculator, you should find a way to measure between a few of the points, and see if your raw distances match to your gps coordinates with the appropriate scale factors applied.
That formula was correct for the NAD27 system, as back then the separation was not known, and was typically assumed to be zero. However, using that formula for NAD83 will introduce a bias of about 6 ppm (in the NE US) into the system.
Just because a formula is in a manual does not make it correct. However, since I could not find the document referenced, I assume it was meant to address the use of NAD27, and therefore was not incorrect per se, but rather was based on the assumptions in use at the time. However, it is a FACT that the distances should be reduced using ellipsoid heights rather than orthometric heights in NAD83.
Here is an excellent manual on the subject of state plane coordinates in NAD83. Although it is a bit old, it is still very useful:
maybe I'm missing something but isn't orthometric height+geoid height the ellipsoid height?
> However, it is a FACT that the distances should be reduced using ellipsoid heights rather than orthometric heights in NAD83.
Agreed. It is insignificant for many distances we measure with an edm, and 6ppm isn't all that much. For me, thinking about what I am trying to do is the key. The fact that I might measure a distance along the ground, and I want to reduce that distance to the mathematical "ellipsoid", I need to reduce using the "ellipsoid height". I also, generally use the estimated mean radius of the earth without worrying about the radius at the point on the ellipsoid. (20,906,000feet or 6,372,162M). I use this if I am doing a hand-calculation check. I think our software uses a more precise radius for whatever latitude I am at.
in NAD27 the geoid height was considered to be at the same place as the NGVD sea level (or close enough) so that your formula works when adding "0" as the "geoid height.
(but I'm thinking that maybe wasn't your question.)
the formula is (Orthometric Height + Geoid Height)
the elevation plus the geoid is the ellipsoid height.
At my office which is at an elevation (orthometric height) of 3792' + the geoid height which is -43 puts the ellipsoid height at 3749 and that is the number you would use in the formula, so the formula is using the ellipsoid height even though it starts with the orthometric height.
Because the earth's radius is roughly 20,000,000 feet, each 20 foot in elevation makes a 1ppm difference, so 47 feet would make 2ppm. Not much; .01' per mile.
Got it. You're pointing out how insignificant it is. (the real significance in applying an elevation factor is how many thousands of feet above sea level you are; and +/-50 feet is pretty meaningless).
I guess my only point is that if you are applying an elevation factor, why not use the correct value? I mean they are both kicked out by the black box, and both are written to the nearest hundredth of a foot, so you aren't really typing in less numbers or saving anything by typing in one over the other. If all you have is an orthometric height, maybe it's not worth the extra effort to calculate the other.
Tom: You can probably relate to this story. about 20 years ago I was working on a project in a county in Colorado. We set pairs of monuments across the county. After we were done, and we gave the client all of the data, I got a worried call from the county surveyor there. They shot between two of our monuments (about a mile apart) and got about 1.5 feet or so difference from the inverse. All that money they spent and we didn't even come close! I asked about the grid factor, if he applied it correctly. Silence. Hello? Anyone there?
I agree, a few ppm is not terribly significant in a lot of surveys. However, we do deformation surveys where we are trying to get 0.003 m (0.01') accuracy over the whole network. Our EDM has a stated accuracy of 0.001 m ± 1 ppm. So, I don't need any extra error to push me over the limit.
My point is that it is very easy to account for (i.e. to use the correct height in the computation), so why not just always do it? As I mentioned, I do comps in ECEF, so I do not deal directly with the scale factor. But, if I need to reduce a distance to compare against a grid inverse, I will usually use the factor computed at both ends:
CF=(CF1+CF2)/2
if it were a long line, maybe even use the midpoint:
CF=(CF1+4*CFM+CF2)/6, where CFM is the combined factor at the midpoint.
By the way, the choice of earth radius has very little impact on the results, except for high elevations. Here is some data I computed for a workshop I gave on EDM reductions at Trimble Dimensions in 2012:
thats exactly my point on why you use the Orthometric Height. The formula accounts for the geoid separation.If you use the ellipsoid height and then add the geoid height to it per the published formula..your correction will be wrong. The formula is what is published in NC for NAD 83.
