I've looked for previous threads on this (including one I started some time ago on "horizontal control"), but can't find what I'm looking for.
I've reduced my Polaris data, and seem to be off by 00-02-58.8. This appears to be close to what is shown on a recent survey (Convergence = -0°03').
The questions are:
1. If I've turned RIGHT from star to backlight, and my number is smaller than it should be, would it make sense that the negative notation of the convergence puts GN WEST of TN (astronomic north), and should ADD it to my azimuth?
2. Not wanting to rely just on another survey, I checked the Data Sheet for AE6516, which is less than a minute different than my location in Longitude. On the second page of that document it says:
"The following values were computed from the NAD 83(2011) position:
SPC VT North 420974.24, East 1,623,008.78 sFT Scale Factor=.99996463, Convergence = -0-02-43.5"
Convergence doesn't change over time, does it? Can I assume that what the previous surveyor called 03' (no decimals after the 3), is, just a rounding of the number above?
Finally, as many times as I've read it, and looked for it again without success:
Do I ADD the Minus 4.04" La Place correction shown on the same data sheet, in effect subtracting another 4.04" ?
The sign of the convergence angle depends on your location relative to the central meridian of your projection. If you are west of the meridian grid azimuth will be larger.
There are some missing pieces of your puzzle to compute why there is a difference in the published convergence angles. We would need your geographic location and what you are projecting to.
Convergence is a result of the map projection, going from geodetic coordinates to something like State Plane Coordinates.
LaPlace is the correction for the fact that gravity doesn't necessarily point to the rotational axis of the earth. Thus when you bring the north azimuth down from the star to earth you may be on a slight slant and you aren't pointing exactly at the geodetic north.
I'm not going to attempt to advise you on sign of the corrections.
> The sign of the convergence angle depends on your location relative to the central meridian of your projection. If you are west of the meridian grid azimuth will be larger.
> There are some missing pieces of your puzzle to compute why there is a difference in the published convergence angles. We would need your geographic location and what you are projecting to.
The projection is the Vermont Grid Coordinate system. I believe I'm East of the central meridian. I'm not sure that I understand that there IS a difference in "published" convergence angles. Of the two numbers I'm comparing, one has been published on an NGS data sheet. The other is from a survey of an adjacent property dated last year.
Here's the latitude an longitude:
N43 40 31.9
W72 34 59.7
Convergence varies significantly with only fractions of a mile toward or away from the central meridian of the map projection.
Play with the NGS tool:
http://www.ngs.noaa.gov/TOOLS/spc.shtml
La Place Azimuth Correction
Here is what NGS has to say about the sign of the Laplace correction derived by DEFLEC90:
[pre]
------------------------> THE SENSE OF THE SIGNS <--------------------------
A positive meridian component of deflection of the vertical (Xi) indicates
that the astronomic latitude will fall to the north of the corresponding
geodetic latitude of the point.
A positive prime-vertical component of deflection of the vertical (Eta)
indicates that the astronomic longitude will fall to the east of the
corresponding geodetic longitude of the point.
The computed Laplace correction (Hor.Laplace) should be ADDED to a
clockwise astronomic azimuth, to obtain a "near-geodetic" Laplace azimuth.
Note: the deflection correction is usually negligible, yielding a
geodetic azimuth.
Note: in many textbooks, the Laplace correction is shown with the
opposite sign and is subtracted from astronomic azimuth.
[/pre]
La Place Azimuth Correction
An equation would have made it so much clearer.
Final results
> The computed Laplace correction (Hor.Laplace) should be ADDED to a
> clockwise astronomic azimuth, to obtain a "near-geodetic" Laplace azimuth.
>
> Note: in many textbooks, the Laplace correction is shown with the
> opposite sign and is subtracted from astronomic azimuth.
Boy, that makes it clear, lol!
Since I started the thread, I've learned:
The origin of NAD83 SPC zone (4400) is 72-30-00W.
My Longitude (72-34-59.7W) is slightly west of the central meridian.
The sense of both the convergence factor and the La Place correction are the same in this case and are ADDED to a clockwise astronomical azimuth (The note in Kent's reference above regarding "many textbooks" must refer to subtracting a negative, which is the same as adding the positive).
My final calculated azimuth to my backlight is about 7.26" shy of what is shown on the previous survey (done with GPS and OPUS).
I'm still reducing and meaning via the various methods suggested, but given that I was able to complete only three sets, and tossed one, I'm considering this a successful first whack at Polaris. I'm thinking that with more sets (and slightly more organized preparation), I can probably do better. I should even be able to put the multiple sets into Starnet, no?
The only question left is: Why wasn't I doing this last August, when it was 72 degrees at 9 pm?+o(
La Place Azimuth Correction
> An equation would have made it so much clearer.
Yes.
Final results
>I should even be able to put the multiple sets into Starnet, no?
The better approach is just to compute the standard error of the mean with a pocket calculator and enter that mean aziumuth with its standard error into the Star*Net adjustment as a "B" data type.
Repeating the azimuth determination on a couple of nights would be a good way to test the apparent standard errors of the means from each night.
NGS datasheet box score section
If you are having trouble with the algebra involved in the conversion between grid and geodetic azimiths, it may be useful to examine the "box score" section of an NGS data sheet. This is only available for "classically positioned" sites. It shows the geodetic azimuthal to reference marks whose grid azimiths are also shown. There is a "|" symbol in the first column after the PID marking this section. See this sample datasheet for an example: http://www.rwsurvey.biz/images/beachpics/StationSteel-FW0765.pdf
The lengthy explanation of deflections deals with not only the horizontal Laplace but also the Xi and Eta corrections allowing conversions of astronomic latitude and longitude to geodetic equivalents.
I believe the text explanation rather than a formula was intended to highlight the comment that some sources apply the corrections differently. If a formula were provided, I expect many would not read the explanation.
Astronomic azimuths do not account for gravity's effect on the plumb line at the point where observations were made.
HTH,
DMM
Final results
Another way to test your errors is to recalculate one observation changing one element at a time by your estimate of the component error- ie change the latitude a tenth of a second and observe the effect, change your time by a tenth of a second and see what change you observe. I say a tenth, use your own estimates. Once you've done this for each of your components (not ephemeris data) take each difference from your initial calculation and calculate the standard deviation from that.
By the way seven seconds is really good. Nice work. How long is the baseline you were sighting? It would have to be pretty long for seven seconds to mean much.
Final results
> By the way seven seconds is really good. Nice work. How long is the baseline you were sighting? It would have to be pretty long for seven seconds to mean much.
It was very short...My original plan of using a 600' back sight was abandoned after our unexpected foot of snow. Used a pin less than 150' away. 🙁
Ya want an equation? Here's an equation.
> An equation would have made it so much clearer.
Indeed it would, so here's my whack at it:
Using this, the signs take care of themselves, as follows:
If east of the central meridian, Convergence is positive, so subtracting it will, well, subtract it.
If west of the central meridian, Convergence is negative, so subtracting it will in effect be adding it (a minus minus is a plus).
La Place can be positive or negative. If positive, the astronomic longitude will fall to the east of the
corresponding geodetic longitude of the point. If negative, the opposite is true. Either is true regardless of whether you're east or west of the Central Meridian.
But you don't need to worry about it if you just add it (positive or negative) to the Astronomic Azimuth.
This all sound right?
Standard error for a star
> >I should even be able to put the multiple sets into Starnet, no?
>
> The better approach is just to compute the standard error of the mean with a pocket calculator and enter that mean aziumuth with its standard error into the Star*Net adjustment as a "B" data type.
>
> Repeating the azimuth determination on a couple of nights would be a good way to test the apparent standard errors of the means from each night.
Would the standard pointing error to a star typically be the same as for any terrestrial target? Less?
