Many surveyors, myself included, prefer to annotate maps with approximate surface distances computed from essentially exact grid distances by applying an average Project Combined Scale Factor to them.
As an example of how to choose a good value for that average Project CSF, consider this project that I'm working on at the moment. It's a small area with all of the monumented boundary markers falling within an area about 0.6 mile by 0.6 mile in extent.
The max ellipsoid height is about 1250 ft. and the minimum about 980 ft., so the project isn't the Rocky Mountains, but it's hardly flat, either. The sketch below is annotated with the various values of CSF computed at the survey points indicated.
So, what would be a good choice for an average CSF for this project given the various values for the CSF at the specific points indicated?
Bring them in Leica Geo-Office, select them all, right click, select compute average combined scale factor, that's one way to go about it.
If you said: "What is 0.999861, Alex?", you have in fact chosen the project Average CSF that I'll be using on that one. That value will be mentioned on the map and in the written description. Project Surface Distance = Grid Distance / 0.999861.
For crying out loud!
I'm right now thinking about heading over to share a bottle of wine with Keith Williams.
You know what I'm saying?
Dayum!
Don
This looks like a quarter sectiin. I would pick the four main corners and use the average of those.
Selecting all and taking the average would create a problem, whereby the CSF would be weighted (more or less) to where the majority of the points are, rather than an average of the entire site.
> Selecting all and taking the average would create a problem, whereby the CSF would be weighted (more or less) to where the majority of the points are, rather than an average of the entire site.
Yes, that's the reason not to just average all the values of CSF, but to find a midrange value.
> I'm right now thinking about heading over to share a bottle of wine with Keith Williams.
> You know what I'm saying?
Uh, you and Keith both like wine? I'm thinking Port, right?
> The max ellipsoid height is about 1250 ft. and the minimum about 980 ft., so the project isn't the Rocky Mountains, but it's hardly flat, either. The sketch below is annotated with the various values of CSF computed at the survey points indicated.
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> So, what would be a good choice for an average CSF for this project given the various values for the CSF at the specific points indicated?
Note that the Combined Scale Factor is the product of two components, the Map Projection Scale Factor and the Height Factor. Across this project (in the South Central Zone of the Texas Coordinate System of 1983), the Map Projection scale factor varies about 0.5ppm from a midrange value, That's 0.5mm/km which virtually no surveyors will worry about. I know I wouldn't for a project this size (only about 1km x 1km in extent).
The variation in Combined Scale Factor is nearly entirely due to the changes in Height Scale Factor as the ground elevation changes within the project. So, what that means is that even if one were to design a custom projection just for this site and nowhere else, the results would have similar distortions from the height changes as appear in the changes of values of CSF noted in the sketch.
Just trying to learn here. The mean of the 13 factors is 0.99986290 and the median is 0.99986230, which, if my rheumy old eyes don't deceive me, is point 45.
Although it doesn't make a whit of difference, why not choose the median, a reproducible mid-value?
I would probably have picked a scale a bit larger than Kent did, it looks like there is a high point in the SE corner of the project, and .999861 is a bit "high" if you want to look at it like that.
However, the 6th place beyond the decimal is only 1 part per million and at that point .999861 or .999863 is just picking a nit.
The important issue is to state what you are using and get it into the record so the survey can be retraced.
For a project scale factor I never state it beyond the sixth place, at that point it is .01' in 10,000' and each 20 foot of elevation change is changing the factor that much, no real point in extending it further.
Just let the RTK controller figure it out.
What do I win?
Picking a little low on the CSF allows you to extend the range useful range of the factor (or projection if you are designing an LDP) as curvature will always fall away from the projection surface. That little tip is courtesy of Loyal.
By the way, I only recently understood the value of 6 decimal place scale factors for all the reasons you mention.
> Just trying to learn here. The mean of the 13 factors is 0.99986290 and the median is 0.99986230, which, if my rheumy old eyes don't deceive me, is point 45.
I would choose the midrange value, i.e. a value that roughly splits the maximum and minimum values.
> Although it doesn't make a whit of difference, why not choose the median, a reproducible mid-value?
The choice of an average project CSF will be exactly reproducible in that the value used will be explicitly stated, both on map and in written descriptions. Knowing the exact value used to compute the surface distances shown on a map or recited in a metes and bounds description means that the grid distances from which they were computed can be exactly reconstituted.
The thing to keep in mind is that scale errors of 1ppm amount to 1mm over 1km, which is the approximate extent of this project.
> If you said: "What is 0.999861, Alex?", you have in fact chosen the project Average CSF that I'll be using on that one.
That scale factor amounts to about 1 part in 7,000 feet. I don't know whether you are obliged to report coordinates in some state mandated zone, but I would think that a fellow like you would find that sort of distortion hard to stomach. Why not create a custom zone that produced scale factors much closer to unity? Have you figured out the parameters for the Texas Coordinate Reference System- Austin Zone (TCRS-Austin) yet?
In other words, when is Texas going to catch up with Oregon?;-)
Congratulations!
You are getting the idea of significant values. As noted here (and Kent just below) the magnitude of difference is small and I'd be willing to bet that 99% of the surveyors (or their crew) can't or don't measure to those tolerances. Until you get to the fringes of a zone or a lot higher heights and larger differences in heights worrying about a CSF is wasted energy. And worrying about grid to ground is also wasted energy.
You need long project distances, high heights, extreme height differences, or fringe zone locations to worry about things that are being discussed here.
> > If you said: "What is 0.999861, Alex?", you have in fact chosen the project Average CSF that I'll be using on that one.
> That scale factor amounts to about 1 part in 7,000 feet. I don't know whether you are obliged to report coordinates in some state mandated zone, but I would think that a fellow like you would find that sort of distortion hard to stomach.
Actually, the surface distances computed using a project CSF will be much better approximations of what a person would actually measure at ground scale than any county-wide projection could possibly accomplish. This approach is the superior one.
The Oregon projections mostly are designed for highway corridors, as I understand it. In Central Texas, very little land is actually right along some level highway, as this project illustrates.
So, the positions of boundary markers get reported as SPCS values and the distances between them get reported as surface distances that can be easily converted to grid distances. It's the best of both worlds: NAD83 coordinates in a widely used, standard system, and distances that are essentially what one would measure on the ground with a total station.
>Why not create a custom zone that produced scale factors much closer to unity?
Well the map projection scale factors only vary by about 0.5ppm from the project mean. That is the same as zero distortion for all practical surveying purposes over a project 1km in extent. The variation in values of CSF is otherwise entirely from ellipsoid height changes across the project.
>Have you figured out the parameters for the Texas Coordinate Reference System- Austin Zone (TCRS-Austin) yet?
The trick would be figuring out how to make Central Texas flat. I won't hold my breath on that one. :>
Congratulations!
You need long project distances, high heights, extreme height differences, or fringe zone locations to worry about things that are being discussed here.
I would love to work where you don't need to worry about it, but alas that isn't where I'm located; yet spending time in NC this fall, all those trees, ivy, pretty to look at but give me these open spaces to survey in;-)
The NAD83 Montana zone gets messy in the middle, works well at the edges for scale.
By low I believe he is talking about a bit lower in elevation so the .999863 CSF would be a bit "lower" than the .999861 CSF. But really these are just number games at that point, if I was in a valley surrounded by hills I would skew towards the "higher" number, by the same token if I was surveying along a ridge I would go with the "lower" or larger number.
> The Oregon projections mostly are designed for highway corridors, as I understand it. In Central Texas, very little land is actually right along some level highway, as this project illustrates.
The Oregon projections are set to fit the valleys best because that is where the roads and people are. It is not a fundamental feature of the projection. Since Texas doesn't have as much relief a projection that fit the highway well would also fit the remote places between the highway well. In short, they make more sense for a place like Texas, not less.
> Since Texas doesn't have as much relief a projection that fit the highway well would also fit the remote places between the highway well. In short, they make more sense for a place like Texas, not less.
I'm not seeing it. The county where that project is situated varies in elevation from about 600 ft. to about 1500 ft. There is simply no way to design a county-wide projection that will return grid distances closer to ground scale than my approach accomplishes.
What you end up having to do is to create either a unique projection for every project if you want the CSF to approach 1.000000 as closely as possible or a whole bunch of projections for the county, each for a different range of elevations. Good solution? I don't think so.