> 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.
It would be simple enough just to measure the angles on both faces from the ground mark that the prism/target is nominally set up over, to the prism/target itself. A meticulous person could do that, possibly determine by comparison that a single angle on one face gave a result that was identical for all practical purposes with an angle on two faces, and continue with just angles on one face of the instrument.
if i remember correctly, your method for setup testing is very similar to the method i devised for adjusting/checking our tribrach plummets: i set up 3 or 4 retro reflective tape targets at 90 deg to one another from the instrument station which is set up over using the instruments rotatable laser plummet. i measure out to, and record the target stations. i then swap over to another tribrach and center over the mark with the tribrach plummet. i perform a resection using the recorded control and adjust the plummet to the resulting resection coordinates. i move the tribrach to 0,0 and repeat the resection to check. repeat for all company tribrachs. i've not seen more than 1mm on the second go so i'm concluding we are around the 1mm level for just about any careful target setup with an adjusted tribrach over an accurately resolvable ground point.
is this the kind of thing you were after?
>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.
For the one or two man owner/operator shop I would agree. I can speak from experience, though, that in may days from a multiple crew firm the error is usually ten times that.
I always protected my equipment like Robocop, and this is one reason why.
Then again, my typical week was 75% architectural stakeout, 25% monitoring. The tasks I would do that usually required the LEAST amount of accuracy were curb and gutter stakeout and ALTA traverses. Exactly opposite from a lot of people.
I get tickled every time I read "you can't get that accurate with a total station". I agree. THEY can't, and never will be able to if someone doesn't teach them. You have to have the right equipment, treat it the right way, and use it the right way, but it's definitely doable.
Here is how I would do it:
Set a bunch of the cheap little adhesive targets from Sokkia in the following fashion: four on the ground in quadrants around point A, four in quadrants on the cieling around point A, and four somewhat near horizon around point A, maybe rotated halfway off the quadrants. Measure distance to the targets that are easily accessible with a 0 offset 0 height mini prism (the point on the back) and sight line directly to the target.
The set up over point A ~20 times to derive a coordinate value for it. Derive better coordinate values for all of the sticky targets by resection over no point (0 setup error) multiple times in a distributed pattern around.
Now you can derive a coordinate for point A that is better than your ability to set up on it one time because you have allowed for so much redundancy.
You could then resection over a point B (no real point on the ground, though) and set up the prism over point A. Observe it multiple times in network with the reflective targets. You could then use the better coordinates derived for your targets to derive a coordinate for each setup of the prism.
> is this the kind of thing you were after?
That's an interesting method for adjusting tribrachs, but wouldn't it be nice to have an easy way to quantify the standard errors of target centering?
I use prism poles in prism pole tripods to hold prisms/targets over ground marks, for example, and do virtually no forced-centered traverse. Where forced centering is used for traversing, i.e. setting up a tribrach on a tripod and in succession mounting FS, instrument, and then BS in that same tribrach as the traverse advances, the centering errors should be essentially the machining tolerances of the tribrach and targets, less than 0.1mm.
There should be a way to quantify the standard errors of centering a prism/target by just about any method, including a handheld prism pole, a prism pole in a tripod, or a tribrach in tripod.
One feature of the centering error given by methods like tribrachs or prism pole in tripod is that the standard error should be the same in both components, both perpendicular to and parallel with the line of sight from the instrument to the target.
When that is the case, it would be sufficient just to measure the component of the standard error of centering perpendicular to the line of sight. It seems to me that the test might get very quick and simple then.
If you're worried about the deviation from the horizontal as you ascend/descend the vertical scale, you might try backing off the arbitrary 6' distance, to say, double that, around twelve feet. The geometry improves some and your optics will support that.
There are some instrument manufacturer's publications that graph the expected deviation from the horizontal, as a hyperbolic function of your vertical angle.
> If you're worried about the deviation from the horizontal as you ascend/descend the vertical scale, you might try backing off the arbitrary 6' distance, to say, double that, around twelve feet.
I think that Kevin meant the errors from the tilting or trunnion axis of the instrument being non-perpendicular to the spindle. As long as the instrument is sufficiently leveled, just measuring an angle as the mean of both faces cancels those errors.
"I think that Kevin meant the errors from the tilting or trunnion axis of the instrument being non-perpendicular to the spindle. As long as the instrument is sufficiently leveled, just measuring an angle as the mean of both faces cancels those errors."
Absolutely, sighting in two faces will provide a mean.
I think in terms of how accurately a prism or total station can be positioned over a point in 3D space.
Breaking it down into perpendicular/parallel seems unnecessary to me. Or at least I have difficulty thinking of it in those terms.
> Breaking it down into perpendicular/parallel seems unnecessary to me. Or at least I have difficulty thinking of it in those terms.
Those components are essential, though, when the effects of random errors of centering on angle and distance measurements are taken into account in a least squares adjustment. That's the real reason for wanting to have realistic estimates of the standard error of a direction, of instrument centering and of target centering. When realistic weights are assigned to survey measurements in an adjustment, the adjustment is better and the estimates of the uncertainties in survey results are also realistic.
Wouldn't your offsets be less than reality since it is likely the off plumbness of your OP sight is not oriented perpendicular to your line of sight?
> Wouldn't your offsets be less than reality since it is likely the off plumbness of your OP sight is not oriented perpendicular to your line of sight?
It's quite likely that the total deviation from plumbness would be larger than the component perpendicular to the line of sight, but that random perpendicular component is what would effect the uncertainty in the angle. Similarly, just the component of the centering error parallel with the line of sight would effect the uncertainty in the distance measurement.
The assumption is that the centering method used is likely to have standard errors of the same magnitude in each component, i.e. that the process is unbiased in some direction. That wouldn't probably hold for a handheld prism pole, but would be expected to for a prism pole that can be rotated in a tripod during setup.
I was thinking of both factors actually, just a general concern.
It seems that Dave Karoly's suggestion of a 20' distance may be most reasonable... 12'-20' for the most favorable sighting and geometry?
It seems we have a consensus on a good method to measure the centering error.
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?
But why think of it as parallel and perpendicular? I always think of setup error as a radius of a circle (2D) and error in height measurement (1D).
In this thread there are some comments about both faces. Is this referring to plunging the optical and turning 180 degrees to average out the index errors?
Edit:
Thinking about this some more and remembered something.
A better way to derive the coordinates for point A would be to observe it angles only as you resection around multiple times in the distributed pattern.
Yes, face1 and face2 to cancel the out of level error.
The process Kent describes involves a steep downwards sight and a nearly level sight so meaning both faces is critical.
Yes.
Although if you only care about measuring repeatability of the target placement, and will separately check its calibration as to how well it is over the ground point, then both face measurements aren't needed.