Error in Original Data Set...YES
Obviously.
Meaning 5" Readings Never Gets You Better Than 5"
5" is the inherent rounding error in the instrument, before you even take a measurement. Any one of those reported observations can be +/- 2.5" or more (due to truncation) and the instrument does not even blink.
Repeating multiple observations merely allows one to approach that 5" error from the outside.
There are old fashioned techniques designed for repeating instruments that do not translate to modern equipment.
Paul in PA
TS Direction Accuracy - Two Questions
> One thing that I should have asked about is how the direction measurements were made. For example, the Face Left and Face Right directions to Target No. 1 are identical for all four sets. That suggests that the instrument was rezeroed and set to a particular value to begin the Face Right series.
Yes, that's exactly how I did it in the case of the first set (00-00-00). For the others, I noted the initial angle, turned until I had that angle (33-30-20 for example), pressed "HOLD", then turned to the first mark...the functional equivalent of "zeroing" the instrument.
>
> In my opinion, best practice would have been not to do that, but to just change face and *read* the direction to Target No. 1 and the others. The directions will differ by nominally 180 degrees, but that should not present any problem. I would expect that there are errors introduced in the rezeroing and resetting between faces and it is easy enough to test whether the accuracy is improved by omitting that bit.
I thought the point was to plunge the instrument and turn it, so that you're reading with the scope using the other half of the disk. Doesn't simply pressing the "HL" or "HR" button on a TS simply do math internally? Isn't it still looking at the same part of the disk?
>
> The other question is how the circle was advanced between sets as would appear from the observations. Was the circle actually rotated by the increments implied by the changes in the Face Left directions to Target No.1 from set to set? Was the centering of the instrument over the ground mark altered in any wasy in the process?
At each set, I turned the instrument to the left an arbitrary amount to the left (increasing the amount each time), then zeroed it, then turned back to Target 1 and noted the angle.
Meaning 5" Readings Never Gets You Better Than 5"
If you have a two-plate instrument (two horizontal motion screws), then it is easy to use randomly different positions and improve the results by averaging.
If you only have one horizontal motion, i.e. a direction theodolite, you get some benefit from averaging between D&R faces, and maybe also averaging of sighting errors if that happens to make it cross a rounding boundary.
To get the full benefit of rounding on a direction instrument, you need to rotate the whole instrument between sets for so the alignment with the rounding is different. Of course, for the assessment being done in this thread, that makes centering excruciatingly critical or requires long target distances. Centering error may be causing a lot of the differences between sets if the targets were at 50 ft. On the other hand, just the right amount of random centering error both contributes error and randomizes the rounding so it partially averages out.
The ideal situation would be to have the target distance at about 100,000 times the expected centering error (i.e. several hundred to a thousand feet) and turn the instrument between sets.
TS Direction Accuracy - Two Questions
> > In my opinion, best practice would have been not to do that, but to just change face and *read* the direction to Target No. 1 and the others. The directions will differ by nominally 180 degrees, but that should not present any problem. I would expect that there are errors introduced in the rezeroing and resetting between faces and it is easy enough to test whether the accuracy is improved by omitting that bit.
>
> I thought the point was to plunge the instrument and turn it, so that you're reading with the scope using the other half of the disk. Doesn't simply pressing the "HL" or "HR" button on a TS simply do math internally? Isn't it still looking at the same part of the disk?
Without knowing how the circle is read on your total station, I'd say there is a chance that you are losing accuracy by that method. The method that eliminates that chance is not trying to rezero or reset the instrument when you change face. It's easy to test whether there is an advantage to one or the other.
> > The other question is how the circle was advanced between sets as would appear from the observations. Was the circle actually rotated by the increments implied by the changes in the Face Left directions to Target No.1 from set to set? Was the centering of the instrument over the ground mark altered in any wasy in the process?
>
> At each set, I turned the instrument to the left an arbitrary amount to the left (increasing the amount each time), then zeroed it, then turned back to Target 1 and noted the angle.
Does this mean that you rotated the tribrach of the instrument and recentered it over the ground mark afterwards, or is the instrument a repeating instrument with a lower motion? If it is a repeating instrument, there will be two clamps on the horizontal motion, one on the circle and one that allows the instrument to rotate with the circle clamped.
If you rotated the tribrach and recentered the instrument, then the test would be contaminated by the effect of centering errors.
Meaning 5" Readings Never Gets You Better Than 5"
> 5" is the inherent rounding error in the instrument, before you even take a measurement. Any one of those reported observations can be +/- 2.5" or more (due to truncation) and the instrument does not even blink.
Might want to check your math on that. If the rounding error is +/-2.5" then 68% of the rounding errors will be within +/-1.7".
Meaning 5" Readings Never Gets You Better Than 5"
> The ideal situation would be to have the target distance at about 100,000 times the expected centering error (i.e. several hundred to a thousand feet) and turn the instrument between sets.
You want the targets to be close enough that the intervening atmosphere doesn't adversely effect seeing. No shimmer and no blurring. 150 ft. should be good enough for the instrument under examination if the standard error of instrument centering is +/-0.4mm or less.
Error in Original Data Set...YES
> Obviously.
But apparently not *too obviously* if you're recommending that the poster convert his directions in degrees-minutes-seconds to integral seconds.
TS Direction Accuracy - Two Questions
>
> Without knowing how the circle is read on your total station, I'd say there is a chance that you are losing accuracy by that method. The method that eliminates that chance is not trying to rezero or reset the instrument when you change face. It's easy to test whether there is an advantage to one or the other.
>
Good idea. I'll add that to my "to do" list.
> Does this mean that you rotated the tribrach of the instrument and recentered it over the ground mark afterwards, or is the instrument a repeating instrument with a lower motion?
Neither. Left it perfectly centered and leveled. Never touched that.
It's not a repeating instrument. One horizontal tangent screw and lock.
To put what I did another way...
Without touching any thing but the horizontal direction, I simply started with a different number (33..., 98..., 168...) held it electronically with the "HOLD" button, then released the hold after turning to and sighting Target 1.
I assumed that it would be "using" a different part of the disk. But now that I'm thinking of it, what would be the difference between that and just keep going around the circle four times without touching a thing...starting at 00-00-00 each time. Like you say, "there's nothing magic about 00-00-00...it's just another number".
Meaning 5" Readings Never Gets You Better Than 5"
> > The ideal situation would be to have the target distance at about 100,000 times the expected centering error (i.e. several hundred to a thousand feet) and turn the instrument between sets.
>
> You want the targets to be close enough that the intervening atmosphere doesn't adversely effect seeing. No shimmer and no blurring. 150 ft. should be good enough for the instrument under examination if the standard error of instrument centering is +/-0.4mm or less.
Hey! This ain't Texas! This is Vermont. I can't walk 150' in any direction without running into a tree. Guess I'll have to get down to the local High School football field for the next round.
It's all clicking now.
Your follow up explanation on calculating and treating the means of each TARGET SET, really helped. That was the stumbling block.
This is all starting to make a lot of sense now.:-)
Error in Original Data Set...YES
> > Obviously.
>
> But apparently not *too obviously* if you're recommending that the poster convert his directions in degrees-minutes-seconds to integral seconds.
I sure wish I could change the units to grads. Unfortunately, it doesn't have that feature (that I've found so far). It'd sure make the math easier.
TS Direction Accuracy - Two Questions
> Without touching any thing but the horizontal direction, I simply started with a different number (33..., 98..., 168...) held it electronically with the "HOLD" button, then released the hold after turning to and sighting Target 1.
>
> I assumed that it would be "using" a different part of the disk. But now that I'm thinking of it, what would be the difference between that and just keep going around the circle four times without touching a thing...starting at 00-00-00 each time. Like you say, "there's nothing magic about 00-00-00...it's just another number".
Okay, all four sets would have been observed on the same parts of the circle. You need to actually rotate the circle by about 45 degrees between each of the four sets. This means physically rotating the tribrach and releveling and recentering the instrument if your instrument doesn't have a lower motion or a Zeiss spigot.
There are two different ways to deal with the errors of recentering the instrument. The easiest is to use well-defined targets that are more than 150 ft. distant. I would make some targets to affix to permanent, stable objects in convenient locations.
The second method requires setting some close-range marks from which you can calculate the instrument coordinates for successive sets relative to the those of the first set and use the actual measured centering errors to reduce the observed directions. That is most easily done via Star*Net, but can be done manually, as well.
Meaning 5" Readings Never Gets You Better Than 5"
> This is Vermont. I can't walk 150' in any direction without running into a tree. Guess I'll have to get down to the local High School football field for the next round.
My suggestion is to make up some very good targets in advance. The ideal target is not the red and white quadrant style, but is a "V" shape, with the triangle a high-contrast, high-visibility color like yellow or (better yet) yellow green. The human eye is most sensitive to that part of the visible spectrum. Outside the "V" should be flat black. If you can get some yellow corrugated plastic sign board, all you need to do is to either lay black plastic applique film onto it to form the "V" or (lower tech) use electrician's tape. Take care to make the centerline of the "V" square and parallel with the edges of the target so that when you install the target plumb, the "V" will be as well. You want the target to be well lighted, not hiding in shadow. If in doubt install six or seven targets and use the best five.
Error in Original Data Set...YES
Since his final output will be the standard deviation expressed in seconds, it seemed obvious that the fields could be populated with seconds to begin with.
The columns in the spreadsheet could be broken down as (A)degrees, (B) minutes and (C)seconds. The fourth column (D) could then be calculated as =A1*3600 + B1*60 + C1. He could directly enter the angles from the book, careful to tab between entry of degrees, minutes and seconds, and let excel do the work.
But grads or whatever is clearly the smarter choice.
Error in Original Data Set...YES
> Since his final output will be the standard deviation expressed in seconds, it seemed obvious that the fields could be populated with seconds to begin with.
The problem with that would be that the intermediate results, such as the means of Face Left and Face Right and the reduced means, would be in seconds with no immediately intelligible relationship to anything.
Meaning 5" Readings Never Gets You Better Than 5"
>if the standard error of instrument centering is +/-0.4mm or less.
That's a test that needs to be done first if the distances must stay short.
Meaning 5" Readings Never Gets You Better Than 5"
> >if the standard error of instrument centering is +/-0.4mm or less.
>
> That's a test that needs to be done first if the distances must stay short.
There is a workaround for it, though. If you add four, very sharp marks at minimum distances from the instrument (in other words, the targets of the test range consist of four targets about 8 ft. away at nominally 0, 90, 180, and 270 from the instrument and five more distant ones as previously described) and
- take directions to them in the round of directions in each set, and
- measure approximate distances to all points (+/-0.5 ft. is perfect),
you can enter the directions in Star*Net to solve the standard error of a direction to the more distant targets allowing for the small differences in centering. In this procedure, if you are actually computing the centering errors for each setup, the more distant targets could be as close as 20 ft. as long as they were perfectly stable between sets. While one is at that, it would be easy enough to add extra setups with directions to the close targets to actually determine the standard error of instrument centering at the same time. Ten setups with directions to the close targets should be plenty.
The solution via Star*Net is the value of the standard error of a direction that gives a standard error of unit weight in the residuals and can be easily arrived at by trial and error.
Next test underway
>
> Okay, all four sets would have been observed on the same parts of the circle. You need to actually rotate the circle by about 45 degrees between each of the four sets. This means physically rotating the tribrach and releveling and recentering the instrument if your instrument doesn't have a lower motion or a Zeiss spigot.
>
To make sure I understand:
I have 5 excellent targets, to be set up at or about 100-150' (not sure how big the field is yet). They'll be set at about 72 degrees apart, around the instrument.
I have 4 more excellent targets, to be set 8' or 10' away at 0, 90, 180 and 270 (this does not need to be precise).
1. I will shoot All 9 targets in each set.
2. Turn tribrach 45 degrees; re-level and center.
3. Repeat.
Question:
With this setup, is shooting with both faces necessary, and if so, how to do it? Flip the scope and turn to the first target? Just push "HL" or "HR"? Still unclear on this.
Next test underway
> Question:
> With this setup, is shooting with both faces necessary, and if so, how to do it? Flip the scope and turn to the first target? Just push "HL" or "HR"? Still unclear on this.
Yes, measuring directions on both faces of the instrument is *absolutely* necessary. When you change face, all you do is transit (flip) the telescope and turn to the targets that you want to measure directions to in that opposite face.
Log what the instrument actually displays. Do NOT rezero or otherwise reset the readining of the instrument during the sets.
When you reduce the directions, you will just subtract 180-00-00 from the second face readings and take the mean of Face Left and Face Right. If you are entering the whole works into Star*Net, you will do it as DM and D data types. There is no particular reason to reduce the means of F Lt and F Rt before data entry.