> But why think of it as parallel and perpendicular?
Well only the centering error component perpendicular to the line of sight introduces an error into the angle measurement and only the centering component parallel with the line of sight introduces an error into distance measurement. So, since one would need to derive those components and they are easy to measure directly, why not do it?
So would this process used with a prism on your typical 2m GPS rod give a good estimate for centering the GPS rod?
I think that Kent's method of breaking the error into parallel and perpendicular components makes sense for his method.
I think the resection method lends itself to thinking in terms of radius and height components.
I use three different LSA programs, all three ask for a single estimated value for centering error for targets and instrument.
I will use the resection approach to come up with a tested value in the near future.
The thing I don't like, though, as that no software (that i know of) allows for a true mixture of on-point setups and resections, as well as mini prisms and tripods.
I can position much more accurately with a mini prism than with a prism on a tripod. I can also eliminate practically all centering error except for tripod flex when free-stationing (the proper term) over no point.
I can only enter one value, though, for all instrument points, and one value for all targeted points.
> I use three different LSA programs, all three ask for a single estimated value for centering error for targets and instrument.
Star*Net uses separate centering errors for instrument and for targets. The value that is used is the standard error of the orthogonal components for horizontal centering.
Testing Centering Accuracy (Example from Today)
Late this afternoon, after working cutting more brush along an 1860-vintage rock fence, I thought I'd test the centering error of one of my older prism poles in a prism pole tripod using the method that David Karoly suggested. This equipment is probably about 15 years old or more.
To test just the pole itself, I screwed a prism pole tip onto the top of the pole, about 5 ft. above the ground. The point made a sharp target that was a very good representation of the center of the pole (The pole could be rotated and the point observed to verify it was concentric).
So, I set a spike in the ground, punched the top of the spike to give a definite repeatable mark for the bottom tip of the prism pole to rest in, and set up a total station a comfortable distance away from the spike. That distance turned out to be 2.572m (= 8.44 ft.).
The Karoly centering test consisted of setting up the prism pole in the prism pole tripod and checking its plumbness with the bubble on the pole, rotating the pole 180° to verify that the bubble was indicating plumb in both positions. Then the angle from the bottom tip of the prism pole was measured to the top of the pole (the point of the prism pole tip screwed onto the top of the pole). That angle was taken as the mean of Face Lt and Face Rt to cancel any small tilting axis errors present (they amounted to an error of about 0-00-09 in the angle as measured only Face Lt).
The following eleven angles represent those measurements and from them the offsets from the line of sight (the centering error components perpendicular to the line of sight to the spike) were computed:
[pre]
A Sin(A) x 2.572m
Bottom
to Top (mm)
+0-00-04 +0.05mm
-0-00-06 -0.07
-0-00-01 -0.01
+0-00-07 +0.09
-0-00-22 -0.27
+0-00-43 +0.54
+0-00-40 +0.50
+0-01-05 +0.81
-0-00-08 -0.10
-0-00-11 -0.14
-0-00-10 -0.12
-------
+0.12mm = mean
+/-0.34mm = standard error
[/pre]
So, the component of the standard error of centering with that prism pole would be estimated from the above data as about 0.4mm or less perpendicular to the line of sight. There is no particular reason to think that the same standard error would not also apply to the component parallel with the line of sight.
The next part of the test would just be to verify that the target plate on the prism/target either was concentric with the top of the prism pole when mounted on it, or to measure any systematic offset between them. Naturally, any systematic offset can be made zero by adjusting the target plate if needed.
Testing Centering Accuracy (Example from Today)
So did you shake set up of the pole 11 times or just turn 11 sets to the stationary pole?
Testing Centering Accuracy (Example from Today)
> So did you shake set up of the pole 11 times or just turn 11 sets to the stationary pole?
Those were eleven different setups. I realize now that I should have made that clear in the post.
> Star*Net uses separate centering errors for instrument and for targets. The value that is used is the standard error of the orthogonal components for horizontal centering.
I didn't mean to imply that I couldn't enter separate values for targets and instruments, but that both values are a single value - not orthometric components. I actually went on to lament the fact that I can't attribute targets as rod, tripod, and mini prism and set different values for each. Ditto when using multiple TSs (with different specs) on a project.
http://www.engineeringsurveyor.com/software/starnet-v6-manual.pdf&cd=1&ved=0CB8QFjAA&usg=AFQjCNFOhOdZu4hT1gR3RQRqqKjg-Iqpjg&sig2=_hUb0hNF6zYCk7AQAujkJ Q">Star-Net V6 Manual
I see nothing in the above PDF that would encourage m to consider the separate orthometric components, either.
It is an intriguing way of addressing the subject, but I think (in terms of devising a test to ascribe a value to the error) breaking a single error value into orthometric components is unnecessarily cumbersome. In real life it is a polar value: deviation from true.
> Do you record the exact values of the nominal 2 meter distance to the prism to account for the out and in-ness of the OP out-of-plumbness during each reset-up of the tribrach or prism pole?
No, the distance isn't a critical part of the calculation. Even an error as large as 1cm over 2.572m only introduces an error of 0.4% in the calculated offset.
Testing Centering Accuracy (Example from Today)
Interesting, but if I am worried about centering accuracy I'm not using a rod...but I don't live in Texas, either (read: dealing with smaller sites).
I guess it would be a good value to have if I did a large project using mostly a rod, though.
> http://www.engineeringsurveyor.com/software/starnet-v6-manual.pdf&cd=1&ved=0CB8QFjAA&usg=AFQjCNFOhOdZu4hT1gR3RQRqqKjg-Iqpjg&sig2=_hUb0hNF6zYCk7AQAujkJ Q">Star-Net V6 Manual
>
> I see nothing in the above PDF that would encourage m to consider the separate orthometric components, either.
Actually, it's quite simple to verify that the standard errors of target and instrument centering that Star*Net uses as input are those of the orthogonal components, not a radial error. If you have even a demo version, you ought to be able to answer that question in less than five minutes.
There should even be a footnote in the manual that provides a reference to the source text for the algorithms used in error propagation a standard, well known modern surveying text. At least it was in the manual the last time I looked. However, you really don't even need to dig up that text to figure out that the standard errors of target and instrument centering are the standard errors of the orthogonal components.
Testing Centering Accuracy (Example from Today)
> I guess it would be a good value to have if I did a large project using mostly a rod, though.
Prism poles in prism pole tripods are an excellent centering tool even for urban work since they make it possible to raise the line of sight to the target. They are relatively light, relatively inexpensive, and work extremely well when handled properly.
You're both right.
Assuming a bivariate gaussian error distribution with equal orthogonal rms components, that SAME value is the radial rms value in any direction.
If the in-line and sideways components are independent, one will tend to be small when the other is large, etc. so they don't add in the way you might expect.
Imagine one instrument looking north at the target and another looking northeast at the target. If the error is random in any radial direction, the in-line and sideways component values each one measures will be the same.
> Assuming a bivariate gaussian error distribution with equal orthogonal rms components, that SAME value is the radial rms value in any direction.
Just so I understand you, Bill, you're saying that if X and Y both have a gaussian distribution with standard error of "s", that the standard error of SQRT(X^2 + Y^2) will also be "s"?
Imagine two cases where the target is centered at the maximum centering error. 68% of the time the distance from the mag nail to the target will be less than the centering error. But it seems to me that in reality for one measurement component such as the angle it must be less than that more than 68% of the time. I'm just a redneck mathematician, though.
>I'm just a redneck mathematician, though.
Well, the first problem is that if X and Y, taken as the orthogonal components of centering error of some surveying instrument or target, have Gaussian distributions, that means that they have a mound-shaped distribution about some mean. If the mean is zero, then half the values are likely to be negative and half positive.
However, the radial distance from 0,0 is SQRT(X^2 + Y^2), which I don't think has a Gaussian distribution. It should have a Chi Square distribution. Negative values of radial distance are meaningless.
> So would this process used with a prism on your typical 2m GPS rod give a good estimate for centering the GPS rod?
Yes, absolutely, but you'd probably get an even better answer just sticking a new prism pole tip on the top of the 2m GPS rod to use as a target (after you've measured the distance from the instrument to the point upon which the pole is set up).
You guys are nuts.
But I sure appreciate the education I get from reading your posts.
If I didn't know better I would think you were just messing with our heads.
Doesn't the centering error have 2 components, one that is proportional to the target height and one that is not? Could these be measured separately?
Testing Centering Accuracy (Example from Today)
I've never used a rod quite like the one you have shown in your picture. Mostly what I've used are Crain or Seco twist lock or quick clamp. You may very well get better results with that rod, and I am sure that you take good care of it.
I have never had a rod that I would trust for anything sub hundredth, and most rods I've used if I got down to a hundredth I still didn't quite believe it.