I was going to ask this in Nate's thread but didn't want to muddy up a really cool discussion, so decided to start another here. My situation is somewhat different anyway (no GPS).
The control network I'm developing will ultimately stretch a little less than 2000' east to west. Other than an early-in-my-learning (and quite ill fated) attempt to move the whole thing to SPC, all my observations have been on the ground, with the entire network oriented to a single azimuth at one end of the survey.
Now I'm introducing multiple Astro azimuths at various stations throughout the network. So, given Nate's point about the fallacy of using "True" azimuths everywhere, if I am to enter these bearings into Star*net, do I convert them to grid bearings first, or just put them in as I observe them (as geodetic). Put another way, if one is doing a TS only control network and adjusting it, which will produce better nonfiction: Grid or Ground?
Footnote:
I understand that the total "error" introduced from one end to the other at my Latitude (43) is about 7" per 1000'. I have a 5" instrument (no GPS here), that can do 3.8" in directions. Further, I've read that when one gets good at solar, one could expect std errors at or somewhat less than 5", so that's in the same range as my instrument can do. I raise this in the event some might say: "Don't worry about grid or ground...17" from one end to the other doesn't matter". My objective is exclusively to learn the proper way to achieve the absolute highest accuracy in the adjustment.
rfc, post: 365016, member: 8882 wrote:
... if I am to enter these bearings into Star*net, do I convert them to grid bearings first, or just put them in as I observe them (as geodetic)?...
rfc, post: 365256, member: 8882 wrote:
Starnet has some inline codes, ".bearing grid" or ".bearing measured", along with ".distance grid" or ".distance measured" -- RTM and you can probably make it work either way.
In Starnet you enter grid azimuths.
And several azimuths is always better. If each one is 5-10" in error, hopefully, that would random error and Starnet sorts that out, if they're all similar integrity.
In Starnet you enter ground distances and be sure to enter geoid height and average project elevation in the project setup for 2D.
And how are getting SPC control to your project area?
I think the theory says you will get better agreement (assuming the difference is even significant) by using grid azimuths.
If you shoot an astro azimuth, that is parallel in space to one you get by an astro from a position some distance west (since the astro object is effectively at infinity).
But the earth curvature means that a rectangle, for instance, with two parallel sides pointing north-south n space will have its north and south sides measure different lengths on earth. Going to a projection grid takes this into account. I think, but haven't checked, that the sensitivity to the grid mapping angle is greater than the sensitivity to changes in the grid distance scale factor for the kind of project you are doing.
Yes, if you use an Astro azimuth (instead of grid) at annintial location, for subsequent azimuths, elsewhere, you would have to calculate and apply convergence. Just Astro azimuths have to be reckoned for convergence relative to the starting Astro azimuth.
Converting to grid is to apply a convergence angle specific to the point in question.
I personally would go with Polaris over solar azimuths. Especially since you are not worrying about paying night differentials.
I am confused by some comments wrt corrections to astronomical azimuths. To go from Astro to grid one applies the Laplace correction to get to geodetic them the convergence angle to get to grid.
The Laplace correction can get large in mountainous areas. It is part of the output of the DEFLEC12A program in the NGS toolkit found here: http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/deflec12A_prompt.prl
Astro to geodetic is simplified Laplace.
Geodetic to grid is convergence.
So if you have a geodetic azimuths, from Astro observations, at both ends of project, to figure an angle closure you have to also include the convergence of meridians due to change in Lar/long. Additional error is due deflections in the prime vertical, and to control for that: Laplace corrections.
GeeOddMike, post: 365467, member: 677 wrote: I personally would go with Polaris over solar azimuths. Especially since you are not worrying about paying night differentials.
I am confused by some comments wrt corrections to astronomical azimuths. To go from Astro to grid one applies the Laplace correction to get to geodetic them the convergence angle to get to grid.
The Laplace correction can get large in mountainous areas. It is part of the output of the DEFLEC12A program in the NGS toolkit found here: http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/deflec12A_prompt.prl
Is it true that:
Star*net is adjusting the observations based on error factors intrinsic to the observations (centering errors, stopwatch errors, instrument errors etc.)
Corrections for LaPlace and convergence are formulaic--they have no error (of meaningful size)?
Therefore, whether you make the adjustment before or after these formulaic corrections, it shouldn't affect the adjustment one way or another.
Convergence is math.
Laplace is not. Laplace is an error much like centering, leveling. NGS deflection database is a modeled estimate. So, you apply a Laplace correction to astronomic azimuth as part of the observation.
An adjustment distributes error. A Laplace correction is not uniform (not geometric). And generally varies a little in small area projects. But, over state wide, mountainous terrain, it can be significant.
Mason/Dixon line suffered from deflection because it's hard to determine, and in 18th century, hypothetical. Not until the mid 20th century could it be properly observed over large areas.
In Starnet the default data entry is grid azimuth. You may enter geodetic azimuths and to do that the inline option .measured is used to switch from measured (geodetic) to grid. Then Starnet applies convergence.
Starnet does not apply Laplace. So, you observe Astro, and apply Laplace as your observation. Absent Laplace correction, your network will be biased by that amount, and change in Laplace across the project will be treated as error. Again, small projects, small changes. But, the average Laplace correction (3, 10, 20") will not be adjusted out.
for instance. Take two, intervisible GPS determined control points. The inverse returns a geodetic azimuth. And that can be expressed in multiple grid systems, returning any number of grid azimuths. But only one geodetic value. Now make an Astronomic azimuth observation. It may be (will be) significantly different. Retrieve and apply Laplace correction to your astronomic observation and your observation should be closer to the geodetic inverse, the remaining error is both: error in observation and error in the Laplace estimate.
Starnet can calculate convergence. Not Laplace.
For instance:
Station 1 on mountain
Station 2 in a valley
Distance between the two: 11.6 miles
Geodetic Inverse calculation returns a 'forward' and 'back' azimuth. The difference is convergence. Calculated, well understood difference based on the ellipsoid a change in Lat/long.
Az from 1 to 2 and 2 to 1 are different, but the difference is not error. It's trigonometric.
However, the Laplace correction at each is different. Therefore the astronomic azimuth from 1 to 2 is different than the geodetic inverse by an amount described as Laplace correction. Caused by deflection of the prime vertical.
The astronomic azimuth from 2 to 1 is different than geodetic by a different Laplace correction value. Due to a different deflection of the prime, not trigonometric.
(And Laplace corrections may be smaller than instrument/observation error.)
Example
In Hagerstown MD (39 42 43 N, 77 43 48 W)
UTM convergence -1å¡ 36' 20"
Laplace correction +8.80"
Near Waynesboro, PA (39 41 47N, 77 30 46W)
UTM convergence-1å¡ 44' 42"
Laplace correction +2.65"
18.7 Km apart and intervisible. (I've shot that azimuth many times.)
The change in convergence: math
The change in Laplace orthometric, modeled.
Now I can't easily measure an azimuth to 2" accuracy without several nights of star observations, but I'm getting close. But I can do better than 8". Starnet can't determine Laplace. Absent Laplace corrections at each station, Starnet would adjust the 6" difference in Laplace values as error. And the project orientation based on only astronomic would be rotated 5" relative to geodetic. (At 18.7 Km that would be about 0.5 meter.)
There's no formula to calculate Laplace. It's observed by very complicated gravity surveys.
So its importance is a matter of scale and precision.
In a 1925 textbook "local attraction" was known to exist in astronomic Lat/long determination. And cited as an assumed 2" uncertainty, with no solution to know which direction.
Larry Scott, post: 365535, member: 8766 wrote: In a 1925 textbook "local attraction" was known to exist in astronomic Lat/long determination. And cited as an assumed 2" uncertainty, with no solution to know which direction.
Oh my gosh! Now I understand what "local attraction" is! I had it completely wrong until now. 
