Hello Gents,
I believe I've just completed the 'world's smallest traverse' with a total station! It covered about 1.8mm in 8 legs and acheived a calculated linear misclose of 0.014mm and a misclose ratio of 1:133.
Seriously though, I did it to try and confirm the accuracy of my earlier tribrach clamping test, and the robustness (or not) of the 0-90-180 angle only resection solution. The establishment of the perimeter targets was the same as the first tribrach clamping accuracy test. The instrument was rotated by hand which, with a friction braked leica, will exert a not insignificant torque on the legs and tribrach, further testing the stability of the entire setup.
The stations were 'traversed' to by displacing the telescope by way of tilting with the tribrach footscrew to 2' away from the footscrew. This should correspond to about 0.14 mm of movement by my calculations which should be able to be repeated fairly precisely by way of the instrument's electronic bubble.
If the observations, or resection solution are not of sufficient quality to resolve below the expected displacement then the result may well be noisy, and may not show an exactly equilateral triangle shape when graphed. I completed the 'loop' twice to give 3 readings at the centre to test the possible drift/stability/whatever of the setup/targets. Here it is graphically (axes are eastings and northings in mm):
The absolute scale of the solution relies on the EDM distances to reflective tape targets and agrees fairly well with the values I calculated for telescope displacement by way of tilt. It would appear that the shape of the traverse is geometrically correct and the points all repeated within 0.034 mm. On the face of it, it would appear that sub 0.1 mm accuracies are being achieved which would validate the tribrach clamping accuracy test.
I'm more than ready to accept that what's being calculated is not what's happening in reality as I'm not a leading authority on precision measurement. Why could this result not be what it seems? If it's wrong I want it taken apart without mercy.
Cheers.
>
> I'm more than ready to accept that what's being calculated is not what's happening in reality as I'm not a leading authority on precision measurement. Why could this result not be what it seems? If it's wrong I want it taken apart without mercy.
I have to say that wins the internet this month for ingenuity. Very nice test. The idea of tilting the tribrach by a carefully measured amount to shift the center of the instrument is exceptionally clever.
I do think, though, that possibly better presentation would be to plot the best fit triangle and its centroid for comparision to the values you've derived.
Explain your tilting procedure and how you determined 2 minute tilt.
What is the distance from your plate to your eyepiece center?
Do you know how your compensation compensates?
Is it double access compensated?
Paul in PA
Careful there, guys. You sound like engineers
How's that for an insult to all but Paul in PA.
Careful there, guys. You sound like engineers
> How's that for an insult to all but Paul in PA.
Actually, this is an excellent example relevant to surveying, but at a much smaller scale than land surveyors customarily think. The point of the exercise is to test a measurement process by comparing the results it gives to a model of what the results ought to be as predicted by other means.
Just Would Like To Confirm His Calculations
Are you implying only a surveyor can be an expert measurer?
When I worked at Bethlehem Steel as a layout engineer, I could not do as well as any millwright.
What I see above are some assumed precise coordinates. What I do not see are instrument capabilities or multiple sets of D&R observations.
For all I know those points could be a random scattering of the exact same point.
Paul in PA
> Way cool Conrad, you have stepped into the world of metrology
I guess it's easy to lose sight of Conrad's objective, which is to see how well testing the standard errors of horizontal angles measured with a total station can be done indoors with very little specialized equipment and to determine how those standard errors provide a means of deriving the a priori weights to be assigned to directions and angles when land survey measurements are adjusted by least squares. So far, the only special thing that Conrad has mentioned using has been a strip of targets at nominal 1cm intervals, designed to fit the split wires on the reticle, run off with a laser printer.
The investigation so far began with trying to figure out how to measure directions to targets distributed over about a 6-degree arc of targets, and to different parts of the instrument. That raised centering issues as the instrument had to be physically rotated to make measurements over different sectors of the circle.
What this latest bit demonstrates is how well the relative coordinates of successive recenterings can be determined just by resection from three close range targets. That opens the door to using a much wider arc of targets to take directions to and just solving the coordinates of successive setups after rotation of the instrument to use different circle sectors for successive sets to reduce the observed directions to a common center.
Careful there, guys. You sound like engineers
Wow!
Wasn't that a typical engineer's reply
Please note the 2 lb. hammer in the first photo, used to make small adjustments.:-)
Just Would Like To Confirm His Calculations
> Are you implying only a surveyor can be an expert measurer?
>
> When I worked at Bethlehem Steel as a layout engineer, I could not do as well as any millwright.
>
> What I see above are some assumed precise coordinates. What I do not see are instrument capabilities or multiple sets of D&R observations.
>
> For all I know those points could be a random scattering of the exact same point.
Yes, if those are your concerns after having the method explained as Conrad has, I'd say that surveyors make much better measurement experts. What he did is remarkably simple to understand. The instrument center was shifted by very small nominally equal amounts by changing one tribrach screw a carefully measured amount. That measurement was made by using the tilt reading of the compensator along the axis defined by the instrument center and the adjusted tribrach screw.
Then the instrument was releveled and the same thing was done using another tribrach screw. In theory, that would produce three different positions for the instrument center, each shifted by nominally the same amount from the center of the instrument when level and toward each of the three tribrach footscrews, making a triangle. He measured the relative coordinates of the centers of the leveled instrument and after the successive shifts using the tribrach footscrews and found that, lo and behold, they show a pattern that matches expectation as a level well below 0.1mm and that the results are repeatible.
When your targets are 2.4m distant and you're measuring directions with standard errors of better than 1.5 seconds, you'd expect to see results like his.
Just Would Like To Confirm His Calculations
>For all I know those points could be a random scattering of the exact same point.
If I understand the process, they are. They would be separate observations of the same point in a perfect instrument observed from a slightly different elevation (HI).
Just Would Like To Confirm His Calculations
> >For all I know those points could be a random scattering of the exact same point.
>
> If I understand the process, they are. They would be separate observations of the same point in a perfect instrument observed from a slightly different elevation (HI).
No, that's not what was done, if I understood Conrad's description. The apexes of the triangular figures are the coordinates of the instrument center after being shifted in one of three different directions by carefully measured amounts using each of the three footscrews of the tribrach in succession. The tilt sensor reading on the total station was used to tilt it toward a particular tribrach screw by 2'00". That shifted the center of the instrument toward that screw.
The coordinates of the instrument were determined by resection (the instrument has dual-axis compensation) and the same screw was adjusted again to relevel the instrument. Then the next footscrew was adjusted to tilt the instrument 2'00" toward that screw and the coordinates of that position were determined by resection. And so on.
The three shifted positions should form a triangle that is proportional to the triangle of the tribrach footscrews, and they did both times.
Just Would Like To Confirm His Calculations
So are you saying the observation resections were taken with the instrument 00-02-00 out of level three different directions? I was under the impression the instrument was re-leveled for observations.
Just Would Like To Confirm His Calculations
> So are you saying the observation resections were taken with the instrument 00-02-00 out of level three different directions? I was under the impression the instrument was re-leveled for observations.
No, the instrument has dual-axis compensation and the misleveling of the tribrach was within the working ranges of the compensators. The resections are from the shifted positions with the tribrach 2'00" out of level in each of the three directions toward tribrach footscrews.
Conrad's description of the resulting figure as a traverse has a nice journalistic flair, but isn't really descriptive of what was done, which was to shift the instrument by the same amount in three known directions and to compare the arrangement of the coordinates of the successive positions to verify that they showed displacements of the same magnitude in directions 120 degrees apart, with the position of the instrument when level being nominally the mean of the three shifted positions.
Leica test range?
> Explain your tilting procedure and how you determined 2 minute tilt.
>
Paul, The tilt was read straight off the electronic bubble display while the telescope tilting axis was perpendicular (as I could get it) to a line from the centre of the tribrach to the footscrew I was turning. The instrument used is a 5" Leica TCA1105.
>
> What is the distance from your plate to your eyepiece center?
Leica TPS instruments are 195 mm above the plate. This instrument measured no different. The footscrews are 104 mm (from memory) from each other, making 60mm from the centre of a footscrew to the centre of the tribrach, and 30 mm from the centre of the tribrach to the axis on which the instrument will be tilted, which is about a line between the opposite footscrews. The tribrach upper surface is about 35 mm above the ball bearings on which I guessed the instrument will rotate when tilted by the opposite footscrew.
>
> Do you know how your compensation compensates?
>
> Is it double access compensated?
>
Yes, but it was turned off for this test, which should not have mattered as the targets are roughly on the horizon. The effect of this amount of dislevelment on readings to horizontal targets should be minimal.
The stations occupied are C-1-2-3-C-1-2-3-C. The distances are in scaled up to 'fool' the LS package into giving me an output in 100th's of a mm. Here are the readings:
h distance 99 1 286400.0
h distance 99 2 283500.0
h distance 99 3 279800.0
direction 99 1 1 359 59 58.0
direction 99 2 1 90 16 24.0
direction 99 3 1 181 56 40.0
direction 61 1 1 0 43 01.0
direction 61 2 1 90 59 37.0
direction 61 3 1 182 40 05.0
direction 62 1 1 178 03 06.0
direction 62 2 1 268 19 12.0
direction 62 3 1 359 59 35.0
direction 63 1 1 178 03 09.0
direction 63 2 1 268 19 39.0
direction 63 3 1 359 59 37.0
direction 64 1 1 122 14 30.0
direction 64 2 1 212 30 52.5
direction 64 3 1 304 11 09.0
direction 65 1 1 178 03 15.0
direction 65 2 1 268 19 50.0
direction 65 3 1 000 00 19.0
direction 66 1 1 239 10 52.0
direction 66 2 1 329 27 01.0
direction 66 3 1 61 07 22.0
direction 67 1 1 122 40 40.0
direction 67 2 1 212 57 09.0
direction 67 3 1 304 37 09.0
direction 68 1 1 151 22 48.0
direction 68 2 1 241 39 13.0
direction 68 3 1 333 19 28.0
Phweww! Just found out this thread has possibly a theoretically finite end.
Just Would Like To Confirm His Calculations
Hello Vern,
I don't need to add to Kent's description of the procedure. He has understood it exactly. I just didn't mention before that the compensator was off. To targets around the horizon this should make no difference to the corrected Hz angle at that range.
I'm slow sometimes
I assumed you leveled the instrument, I would have never contemplated turning angles with an instrument purposely out of level.:'(
World's Smallest Traverse? Plotted Error Ellipses
Okay, I ran your measurements through Star*Net with a standard error of 0.7" on directions. Here's what the 95% confidence error ellipses looked like plotted at the same scale as the network:
At first impression, I'd say that there is no statistically significant difference within the various pairs of coordinate positions. The repeatibility of the process is excellent.
Relative coordinates from adjustment:
[pre]
mm x 10^-2
Pt. N E
99 20.00 20.00
61 18.75 35.08
62 1.70 10.76
63 34.80 10.64
64 17.28 17.89
65 17.40 35.05
66 5.08 11.51
67 32.78 11.30
[/pre]