rfc, post: 367865, member: 8882 wrote:
Shawn:
OK then, but what does the last sentence (before the bold section) mean? Is the "vertical indexing adjustment" they're talking about the "Adjustment of Compensation Systematic Error of Instrument"? The "VCo, HCo, and HAx" thing? I asked about this eons ago and if I'm not mistaken it was you that helped me figure out how to do it. I did go through this procedure on Friday, only hours prior to the latest round of solars.I have noted that when the compensators are near zero, the bubble isn't perfectly centered. Is that what they're talking about when they refer to the "true level condition of the instrument"? So is what you're saying "Don't worry about precise leveling; the compensators do that....BUT make sure the compensators are adjusted properly"? Is that it?
I'd really like to fully understand these matters, and be able to perform adjustments available to the user, but if I'm screwing it up, I might just have to bite the bullet and send it off to a pro. My recollection is that a year or so ago when I did that, they didn't even touch these adjustments.
The "index" is the set of correction parameters stored on board the instrument so that the precise vial and the compensator match readings and/or apply the correct compensation. Pretty much getting dialed in to a point where it needs to be on a bench in an adjustment shop to be done correctly.
If this compensatory setting is off the instrument will try to compensate as if the instrument is tilted, even when it is perfectly leveled. I think there is a mercury bubble internal, or an electronic accelerometer that also checks, though, and usually this doesn't happen unless the instrument is dropped, etc.
Nate The Surveyor, post: 367718, member: 291 wrote: We used to only do solar obs. After 2 in the afternoon, and before 10 in the morning. Usually around 8 am, and around 4 or 4:30 in the afternoon.
This reduced the effect of deflection of the vertical.
Several other red neck tricks, were to intentionally run the observation 1" wrong, to see how much angle, one second of time made. We also were pretty careful to calibrate our time measurement devices. Based on this, we concluded that sunshots we're only good to about 5" of arc. Most of the time. When the angle is high, there seemed to be more error potential. Even due to standing and looking through the inst, at an odd angle. We'd remove the observation, that was 1" of time off, before averaging them. We used the C&G sunshot routine, that have us grid, and true.
A spreadsheet calculator is handy for putting in the wrong time to see the differences. I've done the same thing.
Polaris has the advantage of being time insensitive. I think a minute or so is close enough.
Minor point: I think the Laplace correction given on the NGS data sheet is for Polaris (vertical angle matches latitude) and will be different for solars at various times of day as the sun's vertical angle changes. See Wolf and Ghilani for formula. It might make a second or two difference.
Bill93, post: 367887, member: 87 wrote: Minor point: I think the Laplace correction given on the NGS data sheet is for Polaris (vertical angle matches latitude) and will be different for solars at various times of day as the sun's vertical angle changes. See Wolf and Ghilani for formula. It might make a second or two difference.
I checked the Datasheet: It says it should be -2.83 seconds. I'm using -3.92 seconds, but I don't think it's due to what you're referring to, but more likely due to the fact that -3.92 seconds seems to be the Laplace correction for the Lat/Long of my "home base", a little further to the west (w72-35-00 vs. 72-31-30). If that's the case, It' put my number even closer to the Inverse3d published AZ of 175-25-56.76.:-)
I should check my math though. Not sure why I'm using 3.92 if it should be 2.83.
Simplified horizontal Laplace is astronomic to geodetic correction for any star, any time, any zenith distance.
At station Gulf Stream, per the NGS data sheet PID AA8188: -3.8" from the latest model 12B.
(I don't see +2.83" on the sheet.)
Larry Scott, post: 367908, member: 8766 wrote: Simplified horizontal Laplace is astronomic to geodetic correction for any star, any time, any zenith distance.
At station Gulf Stream, per the NGS data sheet PID AA8188: -3.8" from the latest model 12B.
(I don't see +2.83" on the sheet.)
I was set up on AA8189...Pomfret School...Shooting South TO AA8188!
There you go. Pays to check.
And updating Laplace and DUT in the spreadsheet is s common mistake.
And it's not a Polaris or vertical angle thing. Any star, azimuth.
Google: NGS Sense of the Signs
I've looked briefly at Wolf & Ghilani _Elementary Surveying_ and realize I don't understand Laplace correction yet. What I said above is at least partly wrong.
But their section 19.14.3 (in 11th edition) "Reduction of Directions and Angles" gives a formula 19.28 that includes terms depending on the zenith angle and azimuth that are not included in the "Horizontal Laplace" value on the NGS data sheets. It uses Xi and Eta values which can be obtained from NGS program DEFLEC12B. From that formula and their example, it seems astro sights would need a more complicated computation than simply offsetting by the data sheet value if one is interested in corrections of a few seconds.
Bill93, post: 368090, member: 87 wrote: I've looked briefly at Wolf & Ghilani _Elementary Surveying_ and realize I don't understand Laplace correction yet. What I said above is at least partly wrong.
But their section 19.14.3 (in 11th edition) "Reduction of Directions and Angles" gives a formula 19.28 that includes terms depending on the zenith angle and azimuth that are not included in the "Horizontal Laplace" value on the NGS data sheets. It uses Xi and Eta values which can be obtained from NGS program DEFLEC12B. From that formula and their example, it seems astro sights would need a more complicated computation than simply offsetting by the data sheet value if one is interested in corrections of a few seconds.
Bill93:
I read that too (but don't completely understand it). I thought Laplace was "deflection of the vertical". If so, then at any given point on the earth, it could be deflected in any direction (not sure what reference system it uses, but for the sake of discussion, let's say geodetic): North, East, South or West.
Could it be that because most people use it along with convergence to determine geodetic from astronomic north, all you need is the East/West component of it? I'm trying to wrap my head around it, but it is intuitive that if you were looking at polaris, an east/west component of Laplace would make a difference, but that if you looked at a star due east or west, it wouldn't make any difference at all.
But...if there were a north south component of it, it would deflect gravity to the north or south, and that would make a difference. Is it just too small to worry about? If its vector were in between (say North-East), the result would be some cosine function of the value, making it even less.
It doesn't make sense that the deflection of the gravity vector would only be measured in an east west dimension (I think), unless it's just about correcting for "North" in the process of converting from astro to geodetic (and subsequently to grid). Now that no one even does astro anymore (except us few whackosB-)), it's probably even less relevant. Thanks for the early am wake up call.
Formulae;
And the Prime Vertical is the 'great circle' passing E/W thru the point, not a circle of latitude. Deflec program does the spherical trig combining Xi and Eta - Laplace equation.
I've always seen it referred to as simplified Laplace. And it's now commonly labeled hor Laplace, in the data sheets Laplace.
A good short paper:
http://www.terrasurv.com/azimuths.pdf
Deflections and Laplace Corrections
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: in many textbooks, the Laplace correction is shown with the opposite sign and is subtracted from astronomic azimuth.
Here's my current understanding: Astronomical north is defined by the celestial pole (which Polaris is within a degree of). If you sight the pole and drop down to horizontal, that east-west tilt will mean you are not pointing at the earth's north pole. The amount of difference is the Horizontal Laplace given on the data sheet.
In the long formula if you set the zenith angle to the complement of your latitude, and if your azimuth is zero, then you are pointing at the celestial pole and the formula says the angle offset is zero. Change your zenith angle to 90 degrees to look horizontally and the formula reduces to the simplified horizontal Laplace value. If you sight something at a different zenith angle then the correction is different.
When you sight something at a different azimuth and not horizontal (zenith angle not 90) then the north-south tilt is important and the complicated formula says you can get much different corrections. Depending on the N-S and E-W tilt at your location, it may be more or less than the horizontal values, and it will probably be larger when looking south. At neck-breaking zenith angles, it can get considerably larger than the horizontal value.
Example
Polaris declination 89.333634å¡
Latitude 0.0å¡, East elongation: azimuth of Polaris (zenith 90) is 0.666634å¡, compliment of declination. The horizontal angle from Polaris to north, astronomic
At latitude 70å¡, eastern elongation, azimuth of Polaris 1.9850å¡, the hor angle to north astronomic.
At latitude 89.999å¡, eastern elongation, azimuth of Polaris 90å¡
The increase in azimuth is 1/cos(VA). Not Laplace or deflection.
Simplified horizontal Laplace is applied to the horizontal Astro azimuth, (that value based on tilt Xi Eta and the Laplace equations via DEFLEC program). And is specific to the gravity anomaly at the point in question, to which the instrument was leveled. Hor Laplace is not part of the PZS triangle calculation.
I can't believe the NGS would not specify the zenith distance and azimuth of the celestial body observed to apply "Hor Laplace", and make a blanket statement "add to Astro to get near geodetic azimuth", unless it's applied to a hor az after resolving the PZS triangle, from any celestial body.
Same thing with solar semi diameter. At 0å¡ VA the semi diameter is 0.2672å¡, the hor angle from the edge to center. At VA 50å¡ the horizontal angle from edge to center is 0.41569å¡, increased by 1/cos(VA). Not Laplace or tilt. And the resulting azimuth is astronomic because the instrument is normal to the geoid. Hor Laplace is applied to hor azimuth last, not mid computation.
An Astro azimuth from Polaris, Arcturus, or sun are equivalent, except for observational issues; rate of change in hor angle, increased timing requirements, etc. High declination (circumpolar) stars have advantages, but the algorithms are the same. Equatorial stars are just harder to capture.
And that's what the workshop teaches. The NGS calculates the Hor Laplace (the hard part) to be added to horizontal azimuth post calculation from a celestial observation.
Now, determining Astro Lat/long from field observations, not something I've had to do.
Larry, what does the long equation (using both Xi and Eta with latitude, azimuth, and zenith angle) apply to, if not to solar, Arcturus, etc.?
If you make astro observations and can somehow relate those back to the azimuth at the celestial pole, then the horizontal Laplace is indeed the final correction. But there are a lot of computations to do that. Isn't the long formula just taking care of all that is needed to get there, but going directly from the observation to geodetic azimuth without explicitly referring it to the celestial pole first?
A = ë± öÕ ëá tan ë? öÕ (ë? sin ë± öÕ ëá cos ë±) cot z
A= Astro az
ë±= Geo az
ëá= Xi
ë? = Eta
ë?= latitude
z= zenith distance to reference piont (back sight)
I don't see Az and Zenith D of celestial body in the Eq. This is the Eq I've found in several places. And it may be the simplified Eq which may be approx (at the 1" level). And Xi Eta are not exactly known.
For station Pom School, Eta 2.97", assuming zenith distance to back sight near 90å¡, that calcs to +2.83", additive constant. And in standard trig (+) angles are CCW, but we adhere to CW angles as (+). (DEFLEC12B has -2.83")
(NGS Note: in many textbooks, the Laplace correction is shown with the opposite sign and is subtracted from astronomic azimuth.)
There is an observing procedure called Black's Azimuth which will directly yield a geodetic azimuth with no laplace correction. This was an advantage in the past when, in order to compute the laplace correction, you needed to accurately know the astronomic latitude and longitude as well as the geodetic latitude and longitude. At higher latitudes this was not so easy (astro latitude). Somewhere in all my stuff I have Black's paper, but it is discussed in Bomford and also here:
The Determination of Azimuth at Laplace Points
The deflection of the vertical is simply the slope of the geoid at a particular point. Since we are fortunate to have an accurate geoid model in the US, this all becomes moot. Simply query the geoid model, and you get the two components of the deflection of the vertical, and hence the laplace correction.
These deflection values can also be used to convert geodetic latitude/longitude (NAD83 (2011)) to astronomic values, which is what should be used in the computations to get an azimuth. These are usually pretty small, but they can be up to 1' of arc.
John Hamilton, post: 368584, member: 640 wrote: There is an observing procedure called Black's Azimuth which will directly yield a geodetic azimuth with no laplace correction. This was an advantage in the past when, in order to compute the laplace correction, you needed to accurately know the astronomic latitude and longitude as well as the geodetic latitude and longitude. At higher latitudes this was not so easy (astro latitude). Somewhere in all my stuff I have Black's paper, but it is discussed in Bomford and also here:
The Determination of Azimuth at Laplace PointsThe deflection of the vertical is simply the slope of the geoid at a particular point. Since we are fortunate to have an accurate geoid model in the US, this all becomes moot. Simply query the geoid model, and you get the two components of the deflection of the vertical, and hence the laplace correction.
These deflection values can also be used to convert geodetic latitude/longitude (NAD83 (2011)) to astronomic values, which is what should be used in the computations to get an azimuth. These are usually pretty small, but they can be up to 1' of arc.
John:
Trying my best to hang in here. But I did a search for Black's Azimuth and found this document, written by none other than...you:
http://www.terrasurv.com/azimuths.pdf
Really interesting. Thanks!
