Kris Morgan, post: 374009, member: 29 wrote: However, wrapping multiple angles with an old GTS 2B (20" gun) can and will produce the same results as a 1" VX robotic station, but you're gonna have to work at it, a lot.
No one said it'd be easy. Just not impossible. I think a GTS 2B a hundred years ago would've been a mighty fine gun.
http://jerrymahun.com/library/tsi/e.htm
Excellent discussion with illustrations and examples by Jerry.
Larry Scott, post: 374033, member: 8766 wrote: No one said it'd be easy. Just not impossible. I think a GTS 2B a hundred years ago would've been a mighty fine gun.
A GTS 2B 30 years ago was a mighty fine gun over a 20" Leitz Theodolite and a K&E 100' Highway Chain. That I can promise you! 🙂
MathTeacher, post: 374010, member: 7674 wrote: Correct, everyone, but let me ask you this. If an instrument is rated at 20" but consistently produces 12" results, is it a 20" instrument or is it a 12" instrument?
The answer, of course, lies in how the angular accuracy of a theodolite or total station is specified. The usual standard is to specify the standard error of a direction angle taken as the mean of F1 and F2 pointings as evaluated by a standard test procedure such as DIN ___ or ISO ___ .
Other factors such as focus colimation, the machining of the centers, and some intentional dithering of results by the reading system (as Leica uses) may figure into the stochastic model.
Kent McMillan, post: 374051, member: 3 wrote: The usual standard is to specify the standard error of a direction angle taken as the mean of F1 and F2 pointings as evaluated by a standard test procedure such as DIN ___ or ISO
And from that specification, by procedure, one can improve the final measurement.
Real example. Last summer I collected many T2 angles by 20-40 sets.
T2 angle (30 sets):
03-38-30.91
T16 angle, 23 wraps:
03-38-31.43
T16 is a 20" gun. And 23 wraps was a lot easier than two dozen sets.
Larry Scott, post: 374059, member: 8766 wrote: And from that specification, by procedure, one can improve the final measurement.
Real example. Last summer I collected many T2 angles by 20-40 sets.
T2 angle (30 sets):
03-38-30.91T16 angle, 23 wraps:
03-38-31.43T16 is a 20" gun. And 23 wraps was a lot easier than two dozen sets.
Assuming that the seeing wasn't the limiting factor on that one, I'd expect the standard error of a direction taken as the mean of F1 and F2 with a T2 to be about 1". So, the standard error of an angle obtained from two directions would be about 1.4". Twenty different measurements of an angle, advancing the circle between rounds should give an angle with a standard error of 1.4/SQRT(20) = 0.3".
In practice, I'd expect that the targets and the observer's pointing bias would make trimming the uncertainty below that point quite difficult.
As for the repetition accuracy of a theodolite like a T16, I'd expect a standard error of about 1" to be the limit there. So, 23 reps with T16 = two sets with T2.
rfc, post: 373880, member: 8882 wrote: Is it true that some higher quantity of observations done with a so called "X" instrument" can achieve the same confidence level (say a 95% confidence interval), as a fewer number of observations done under identical circumstances with a so called "<X" instrument"? Say 5 vs. 3 or 3 vs. 1.
I've thought of mocking up the two scenarios in Star*net, but you can't very well "create" the data; you could make the outcome anything you want. I've thought of playing with the instrument variables, but that doesn't do it either as the number of redundant observations doesn't vary.
Thoughts?
nope you cannot make gold out of lead.... A one second instrument is more precise than a five second instrument and no matter how many sets you turn the five second instrument it will never be more precise than the one second instrument.
Wow. Generally, one of the things I enjoy about Beerleg is that you can always find a depth and breadth of knowledge in the answers to questions one asks. In this case, though, the question could be answered as simply as "yes" or "no", and for bonus points, maybe a "here's why".
By my count, so far, we're about a 50-50 here. Maybe I should ask: If I ask a question and the answers seem to come down about in the middle, how many more times would I have to ask the same question before the resolution one way or another emerges? Like would I take the square root of 1 divided by the "no's" squared plus 1 divided by the "yes's" squared? Am I on the right track here?:-S
DANEMINCE@YAHOO.COM, post: 374072, member: 296 wrote: nope you cannot make gold out of lead.... A one second instrument is more precise than a five second instrument and no matter how many sets you turn the five second instrument it will never be more precise than the one second instrument.
I've not seen that in any textbook, ever. Quite the contrary.
And, not by my experience.
RFC,
I'll try tipping it a little one way.
Increasing the number of observations will result in a number more closely related to true and it will provide support to express it as more precise. That is basic math that can be supported by graphing the appropriate formula.
Kent McMillan, post: 374063, member: 3 wrote: Assuming that the seeing wasn't the limiting factor on that one, I'd expect the standard error of a direction taken as the mean of F1 and F2 with a T2 to be about 1". So, the standard error of an angle obtained from two directions would be about 1.4". Twenty different measurements of an angle, advancing the circle between rounds should give an angle with a standard error of 1.4/SQRT(20) = 0.3".
In practice, I'd expect that the targets and the observer's pointing bias would make trimming the uncertainty below that point quite difficult.
As for the repetition accuracy of a theodolite like a T16, I'd expect a standard error of about 1" to be the limit there. So, 23 reps with T16 = two sets with T2.
The 1" std error of one F/R angle, T2 micrometer reading, doesn't occur in practice. That may in fact be the error contribution of the gun, but, in this case the wedge targets were less than 150 ft away. Assuming 0.25 mm pointing error, that contributes 1.6" on each sight. It's is an old style T2, so micrometer reading is subjective for a couple of seconds, no digital readout here. So, 2 sets will not present 1" std err in real world measurement. (And a reliable standard error requires a larger population.)
In this case, the task was to determine angles to a certainty of 1/4". With 30 sets, std dev of 1", the actual calculated standard error from the population of sets was 0.12" RMSE. So, the integrity of the T2 (1" micrometer gun) angle at 95% very close to 0.245"; the resolution sought after.
Just for fun: The T16 (20" gun) angle was repeated 23 times. However, I did note that there was no appreciable change in the returned angle after 10 repetitions. (Which agrees with most texts). So, the reliability of the T2 angle below one second was undeniable in this case by the high number of repetitions (even if unnecessarily so), and over determined since it's hard to tell when you cross the 1/4" threshold of standard error in the field. And, the 0.5" comparison T2 to T16, in this case, is not a one-off. I've done that enough to know it's not a coincidence.
The 1 second T2 returned an angle with a calculated 95% error of 1/4". The product of repetition and the inverse square law of errors. and a lot of Excel review.
And as to Bob's question: yes. A properly working, adjusted instrument can produce results better than its least count. Which is cited in the text books that I've encountered.
Maybe Mr Ince can call that lip-stick on pig, but the statistics, and repeat performance indicate that a 1" gun can return better than 1", and 20" gun can easily produce far better than its least count.
If not, then there are a lot of textbooks that blowing smoke, and field measurement supports the books.
rfc, post: 373880, member: 8882 wrote: Is it true that some higher quantity of observations done with a so called "X" instrument" can achieve the same confidence level (say a 95% confidence interval), as a fewer number of observations done under identical circumstances with a so called "<X" instrument"? Say 5 vs. 3 or 3 vs. 1.
I've thought of mocking up the two scenarios in Star*net, but you can't very well "create" the data; you could make the outcome anything you want. I've thought of playing with the instrument variables, but that doesn't do it either as the number of redundant observations doesn't vary.
Thoughts?
The published accuracy numbers, with modern total stations, are not very meaningful.
We (back in the '90's) bought a Topcon GTS 3C. It cost 9250.00 + -. The one we WANTED was a Topcon GTS 3B. The 3B costed some 13,500.
As we looked into it, we found out that the BLM had 3B's. And, you could (as I recall) get a 3B, in 2", 3" and 5" flavor, at differing costs.
Well, what was actually going on...
Was Lietz Sokkia had come up with a cheap gun, for some 8750. (We did not want that one) it was some Set 3 or Set 4)
And, So.
Topcon, took some of their 3B units, and RE LABELED them. The 3c did not have 2 speed tangents, and some other amenity....
But, they were essentially selling a 3 to 5 second gun, as a 10" gun, to compete with Sokkia.
We took advantage of the situation....
So, a 10" gun, is not always a 10" gun... but it might be a 5" or 3" gun.
Our 3C is probably close to a 3" gun.
N
PS, It might have been a 2b that we were wanting. Totally identical, but a little different label.
Following the line Kris Morgan initiated, if you superimposed the two error eclipses, one of a 5" gun; the other of a 3" gun, like so:
If you take a greater number of observations with the 5" gun, wouldn't a percentage of them be within the error ellipse of the 3" gun? And if you took enough of them, wouldn't there then be a greater number from the 5" gun within the 3" ellipse than there would be from the 3" gun?
If so, wouldn't this support the "ayes" as opposed to the "nays"?
Larry Scott, post: 374089, member: 8766 wrote: The 1" std error of one F/R angle, T2 micrometer reading, doesn't occur in practice.
That is certainly contrary to my experience with a Zeiss Th2. The most significant limiting factor on the uncertainties of directions taken with that one-second instrument was just the seeing, i.e. the target resolution. The standard error of a direction taken as the mean of F1 and F2 tested as +/-0.9" and that was a realistic basis for estimating the standard errors of angles calculated from such directions, i.e. 1.4 x 0.9" . This was in actual field conditions, not in the laboratory.
Where I think most surveyors fail is in neglecting to minimize non-instrumental effects, such as that of turbulence in the daytime atmosphere on lines of sight near the ground and target design.
As for the limits of double-center instruments such as the Wild T16 or the Zeiss Th43, that is simply a limit imposed by mechanical tolerances and the problems that arise from the double-center design that aren't typically present in a direction instrument like the Wild T2 or Zeiss Th2
rfc, post: 374096, member: 8882 wrote: Following the line Kris Morgan initiated, if you superimposed the two error eclipses, one of a 5" gun; the other of a 3" gun, like so:
If you take a greater number of observations with the 5" gun, wouldn't a percentage of them be within the error ellipse of the 3" gun? And if you took enough of them, wouldn't there then be a greater number from the 5" gun within the 3" ellipse than there would be from the 3" gun?
If so, wouldn't this support the "ayes" as opposed to the "nays"?
If you have enough data, and you plot the data, and if it fits Gaussian error distribution, the standard bell curve, will support ayes. And, you'll need more data from the 5" gun, than from the 3" gun. But, it is statistics. And, inspection for outliers. If there are more than 20% rejected observations, then, the noise level is too high. Which would be a flakey gun, or scintillation, or unstable ground, or plenty of other things. But, a T16 isn't stuck with 20" results, and a T2 isn't locked into 1" results. Which is the original question.
Aye.
rfc, post: 373880, member: 8882 wrote: Is it true that some higher quantity of observations done with a so called "X" instrument" can achieve the same confidence level (say a 95% confidence interval), as a fewer number of observations done under identical circumstances with a so called "<X" instrument"? Say 5 vs. 3 or 3 vs. 1.
I've thought of mocking up the two scenarios in Star*net, but you can't very well "create" the data; you could make the outcome anything you want. I've thought of playing with the instrument variables, but that doesn't do it either as the number of redundant observations doesn't vary.
Thoughts?
rfc, I trust you were watching during my postings on testing leica 1200+ and TS15 instruments.
speaking about those two instruments, statistical assumptions based on gaussian distributions do not apply as the 'errors' do not represent a gaussian curve. the errors do not occur randomly and when you bin the errors you end up with a U-shaped curve that ends abruptly at a maximum number, after which you will get NO bigger errors. it's not really a statistics problem. it's a problem of finding the exact errors and eliminating them.
the ISO rating of our Leicas will tell you very little about the actual results you can expect from them with repeated measurement. and if you know where the errors are then our 5" instruments are a 1" angle instrument, 1st reading for 1 face half-arc.
if i remember correctly, most instruments i've used were quite precise, which means the errors are probably systematic and not random. and that is why the sqrt(n) rule probably doesn't apply to simple repeated measurements. so my answer is: probably no. you need to employ techniques that are aimed at cancelling, as much as possible, the 'errors' your instrument is giving you.
Conrad, post: 374165, member: 6642 wrote: if i remember correctly, most instruments i've used were quite precise, which means the errors are probably systematic and not random.
Hmm. That would be interesting to test. The Leica system for dithering total station accuracy seemed sophisticated enough that it was unlikely to have been used in some of the down-market equipment like Topkia, but I suppose it's possible.
Kent McMillan, post: 374185, member: 3 wrote: The Leica system for dithering total station accuracy seemed sophisticated enough that it was unlikely to have been used in some of the down-market equipment like Topkia, but I suppose it's possible.
Actually, a quick look at the specs on the Topcon/Sokkia ES/CX series of total stations suggests that they may have identical circles, the same circle in the nominal 7" as in the nominal 1" instruments, and that those circles are absolute circles.
Kent McMillan, post: 374185, member: 3 wrote: Hmm. That would be interesting to test. The Leica system for dithering total station accuracy seemed sophisticated enough that it was unlikely to have been used in some of the down-market equipment like Topkia, but I suppose it's possible.
hello Kent,
I properly pulled apart a 1100 series leica lately and compared the part numbers of the Hz and V circle. I think they are the same parts as used in the 1200 as the standards are the same shape and dimensions. My testing didn't detect any dithering of the V angles which seemed only affected by the liquid compensator. As the Hz and V circle are the same parts (according to part number) my latest conclusion is that the angle 'errors' aren't printed on the circle, but purely software generated. I came to this conclusion also after getting my hands on a service report for a 1" instrument which also showed no values in the circle correction values or arrays, just like the 5" instruments. If I had to guess I'd think these compensation values may have been used for earlier instruments.
My avatar is a 1000x magnification of some of the graduations on the printed circle (leica part 707309). they look perfect even at that magnification. Any bumps you see are an artifact of downsizing the image. Considering the size of the reading array, the number of graduations sampled in a single reading, and the precision of the printing, it makes no sense to me when I hear people repeat the anecdote of circles/instruments being graded after being manufactured by some whacky, loose tolerance machine that spits out different grades at random. They can surely print those things to 1" accuracy every time.
Conrad, post: 374191, member: 6642 wrote: hello Kent,
I properly pulled apart a 1100 series leica lately and compared the part numbers of the Hz and V circle. I think they are the same parts as used in the 1200 as the standards are the same shape and dimensions.
[...]
Considering the size of the reading array, the number of graduations sampled in a single reading, and the precision of the printing, it makes no sense to me when I hear people repeat the anecdote of circles/instruments being graded after being manufactured by some whacky, loose tolerance machine that spits out different grades at random. They can surely print those things to 1" accuracy every time.
Yes, I agree. It makes more sense that the dithering of results would be via software, that the basic hardware of circle and circle reading system are quite similar between different models in the same line. I have a Sokkia CX-105 that might be interesting to test for the presence of a bounded periodic error similar to what you found in the Leica line.
