Aside from knowing the standard errors of a direction and an angle measured with a particular instrument, the uncertainties in the measurement also include:
a) centering errors of instrument over station mark,
b) centering errors of targets over backsight and foresight stations, and
c) whether survey was made on a Monday or a Friday.
I've already described an easy method for estimating the standard error of instrument centering (the value that about 68% of all setups will be expected not to exceed, typically expressed as deviations at right angles to the line from the instrument to the target and parallel with that line). For an instrument with a rotatable optical plummet, a standard error of centering in the range of 0.2mm to 0.3mm is not unreasonable for careful work.
The Monday or Friday effect will be erratic and unpredictable. More study is needed to model this error which can be huge in size, even placing the survey in entirely the wrong county.
However, evaluating the standard errors of target centering hasn't been addressed, as I recall. It seems as if there should be an easy test that would take only ten minutes. Any ideas on how to go about this?
It would be easy using multiple total stations and trilateration. Obviously one distance would need to be carefully measured.
A Wild ZNL would help make this even quicker. Center with it, measure to prisms, swap out, re-observe multiple times.
> It would be easy using multiple total stations and trilateration.
Surely there's a simpler test that a surveyor could make with just one instrument and the equipment that supports the prism/target over the ground mark, something that would just take about ten or fifteen minutes to give a very good answer.
Keep in mind that by "target centering error" what is ordinarily meant is the error either at right angles or parallel to the line of sight from the instrument to the target. In most centering methods, such as handheld prism pole, prism pole in tripod, or tribrach on tripod, the standard errors of centering components perpendicular and parallel to the line of sight should be identical.
Well... centering the target over a feature that is readily visible through the instrument seems like a good place to start...
> Well... centering the target over a feature that is readily visible through the instrument seems like a good place to start...
Hey, you may have hit on something there, Kevin. How would one go about measuring the offset of the prism/target from the line of sight to the ground mark?
When you get into testing scenarios the quality of the equipment means a lot. There is a marked difference in quality of positioning with a mini prism vs. a pole.
Cheap mini prisms will perform within a range of expectations. Top dollar Leica equipment will perform better.
I'm sure there is a simple test that could be ran, I merely proffered the first thing that came to mind.
I used to tape paper targets around the office and trilaterate to them, then (after multiple observations, and deriving error ellipses that made sense) I would run the different S6s and GPT 3000s that we had through the test.
It was really eye-opening as to the range of performances, and/or to ascertain the level of with which things like collimation adjustment were applied.
We had four S6s and a VX, the electronic fine plumb varied on each and every instrument by a surprising amount. It didn't seem to effect the quality of measurements, though. Always wondered what was going on there...
> I'm sure there is a simple test that could be ran, I merely proffered the first thing that came to mind.
Oh, I think you were on the right track. As long as the test isn't performed on a Monday or a Friday, it should be quite easy to set up a prism/target over a ground mark about ten or twenty times and measure the offsets right and left of line for each.
From that series of offsets, a person could calculate the standard error that about 68% of the setups would not be expected to exceed.
I suppose one could begin by setting zero on the feature (for convenience) then measuring the target in F1 & F2 twenty-five to thirty times. Weeding out any outliers would give a good sample set from which to calculate a standard deviation.
My concerns (perhaps invalid) might be distance from the feature to the target. Meaning I would think that making this measurement on a target set-up that is typical in practice seems best.
However I would think that finding a feature that is plainly visible at such a distance may be difficult. What feature would you suggest? A protruding 1/4 rebar or similar against a high contrast background?
I would think that avoiding "steep" sightings might help as well.
> I suppose one could begin by setting zero on the feature (for convenience) then measuring the target in F1 & F2 twenty-five to thirty times. Weeding out any outliers would give a good sample set from which to calculate a standard deviation.
>
> My concerns (perhaps invalid) might be distance from the feature to the target. Meaning I would think that making this measurement on a target set-up that is typical in practice seems best.
>
> However I would think that finding a feature that is plainly visible at such a distance may be difficult. What feature would you suggest? A protruding 1/4 rebar or similar against a high contrast background?
Okay, If I'm understanding you, you would set up the same prism/target combination that you use in regular daily work on some mark that you can see directly from the instrument setup and then measure the angle (and distance) from the instrument to the prism/target in relation to the ground mark?
Then, after doing that, you'd break the setup of the prism/target and set it up again over the same mark to repeat the angle measurement from ground mark to prism/target?
Would I be right in thinking that you might be setting up the instrument just five or six feet away from the ground mark to measure the angle from it to the prism/target?
I would set a mag nail or dimpled spike then set up a tripod, tribrach and prism target over it. Then set up the instrument 15 or 20' away, backsight the dimple and raise the telescope and foresight the target. Do it in both faces several times. Calculate the offset from the distance to the prism.
Of course, the tribrach needs to be rotated 90 degrees and re centered at least once and the test run again.
Or you could use a quarter, set up the tribrach over Geo Washington's nose.
> Okay, If I'm understanding you, you would set up the same prism/target combination that you use in regular daily work on some mark that you can see directly from the instrument setup and then measure the angle (and distance) from the instrument to the prism/target in relation to the ground mark?
>
Yes.
> Then, after doing that, you'd break the setup of the prism/target and set it up again over the same mark to repeat the angle measurement from ground mark to prism/target?
>
Yes.
> Would I be right in thinking that you might be setting up the instrument just five or six feet away from the ground mark to measure the angle from it to the prism/target?
This is the part I am unsure about.
> > Would I be right in thinking that you might be setting up the instrument just five or six feet away from the ground mark to measure the angle from it to the prism/target?
>
> This is the part I am unsure about.
Well, most modern instruments have a minimum focus distance of about five feet or less, so setting up six feet way should be pretty safe as far as being able to focus on both ground mark and on prism/target goes.
> I would set a mag nail or dimpled spike then set up a tripod, tribrach and prism target over it. Then set up the instrument 15 or 20' away, backsight the dimple and raise the telescope and foresight the target.
Why would a person need to set up more than six or seven feet away from the ground mark? At close range, wouldn't it be easier to point at the actual ground mark itself?
That was a bit off the cuff.
2 meters works well because 1 millimeter is almost 2 arc minutes.
I guess the assumption the vertical circle is in good adjustment is a given in this scenario.
I would think that a set up at 6 feet has a good chance of accentuating any bias from the eccentricity of the vertical circle, vertical circle indexing error, etc. Might one limit the potential for bias from the vertical circle by choosing a more distant target set up?
Maybe I am splitting hairs on this... didn't this get addressed on your instrument centering error thread as well.
I think my mind is running away with me here.
On a another note... If one were using an identical tripod and tribrach combination for the instrument and targets couldn't the same error estimate be used for instrument and target centering.
> On a another note... If one were using an identical tripod and tribrach combination for the instrument and targets couldn't the same error estimate be used for instrument and target centering.
I'm thinking of the more general case where some other method is used to center the prism/target over a ground mark than is used to center the instrument if the instrument has a rotatable optical plummet.
If the same method is used, this could be an alternate way to estimate the standard errors of centering of both, i.e. to just set up the instrument at close range, measure the distance to the ground mark and horizontal angle from ground mark to prism/target, and calculate the offset at right angles to the line of sight from the instrument.
> 2 meters works well because 1 millimeter is almost 2 arc minutes.
So, what you're saying is that if you were to set up the instrument about five feet away from the ground mark, you could easily measure submillimeter centering errors by just measuring the horizontal angle from the ground mark to the prism/target?
I don't think eccentricity will be a significant issue if you leave the instrument set up undisturbed, and point within a few minutes of the same direction every time you re-set up the target.
You could possibly break the target error into two components - YOUR average setup deviation with the tribrach in the same orientation but slid around and repositioned, versus the average error when you use random orientations of the tribrach, thus bringing ITS adjustment into the picture.
I believe that would be true for the horizontal circle, but I was thinking specifically about the vertical circle.
