LaPlace Corrections

You got much of the concept there.

I don't like that figure for this purpose, though. I'd move the star (really the North Celestial Pole, since Polaris isn't exactly north) up to the tip of the red line.

A pretty good explanation of why it's needed:

Almost all terrestrial survey measurements, with the exception of spatial distances, are made with respect to the Earth’s gravity vector, because a spirit bubble is usually used to align survey instruments. Accordingly, these measurements are nominally oriented with respect to the level (equipotential) surfaces and plumblines of the Earth’s gravity field, which undulate and are not parallel in a purely geometrical sense. This renders them impractical for survey computations and the representation of positions. Therefore, account must be made for the orientation of the survey instruments in the Earth’s gravity field, so that the measurements are of practical use.

http://www.metzgerwillard.us/deflecge/Featherstone.pdf

And now we have "DEFLEC12A" which is in NAD83 2011.0 reference Frame. See NGS web site.

JOHN NOLTON
Tombstone, AZ

James,

Good read. I like W. E. Featherstone. Thanks for the link.

"Almost all terrestrial survey measurements, with the exception of spatial distances,
are made with respect to the Earth’s gravity vector, because a spirit bubble is usually
used to align survey instruments..."

I can imagine a time when our total stations will be so sophisticated that they level themselves, like some laser levels do now, only with Geoidal "corrections". How cool will that be!

"...accounting for the curvature of the plumbline (described later), which is
notoriously problematic."

What kinda rabbit hole did I stumble into here? Problematic curvature of the plumbline? Someone once told me there was nothing straighter than a string line. Ha!

Dave

Thanks, guys. This has been a good read and an interesting topic. I knew the LaPlace correction existed, but since it was small, not too much was emphasis was placed on it. Since surveying instruments are getting more and more sensitive, these little factors come into play. I now have a better understanding of what this correction factor is and how it is applied.

> You got much of the concept there.
>
> I don't like that figure for this purpose, though. I'd move the star (really the North Celestial Pole, since Polaris isn't exactly north) up to the tip of the red line.

But wouldn't the "north star" be exactly on the tip of the red line only twice a day? At all other times, it's orbiting around the center of the red line? In other words, in the view shown, it would be oscillating back and forth?

Or is it nit-picking to point out that the "North Celestial Pole", aka "Astronomic North" is not the same as the direction to Polaris (except for twice a day)?

Dave and other posters; I would like to point out that this drawing that Dave posted is terrible. For a better understanding of what deflection of the vertical is it might be better to read "Geodesy for the Layman" to start with. There are some very good illustrations in that manual(I think you can get it from NGS web page).

After you read "Geodesy for the Layman" you can move on to other great works such as "Physical Geodesy" by Heiskanen and Moritz. On page 84 gives a nice 3 dimensional
depiction of deflection of the vertical.

There are many books on Geodesy that will explain and give way better diagrams that the one Dave has posted.

Dave maybe you can look for a better explanation with a better diagram and post it??

I just wonder if they (NGS) are trying to explain about "polar motion" and the "celestial intermediate pole" ? I see no reason to talk about "Polaris" (the North Star).

JOHN NOLTON
Tombstone, AZ

PS 1. I do not know how to post a picture or a diagram from something.

2. Is there a spell check here at this site?

John,

Yes, it's probably not the best drawing out there, but it was easy to grab. And I know it only shows the east-west deflection, and there is also a north-south aspect. I'm not much of an illustrator or I'd make my own drawing from Sketch-Up or AutoCAD.

As for posting a picture, I can show you how to do that.

1. When you have a page up that you'd like to share, hit the "prt sc" (Print Screen) key. On my laptop it's above the Backspace Key. When you hit Print Screen it sends your screen to your clipboard.

2. Open your Paint Program. In all Windows Operating Systems it's in "Accessories".

3. Hit ctrl(Control) + V. That will paste your screen image into the Paint Program.

4. In the top menu of Paint you can Crop, Underline, Draw Arrows & Stars, Draw Rectangles, etc.

5. Hit Save. You can save it as a JPG, BMP, GIF, or PNG. Most Websites prefer PNG.

6. Here on Wendell's site, hit the Upload Button. Follow the prompts and you're Golden:

Dave