Determining Total Station Distance Standard Errors, Part 3

> I set up a prism at 100' and put the 5m mark on the tape at 100', then corrected each station backwards towards the TS (5 meters, 4.5 meters, 4 meters, etc.
>
> Then subtracted the reading from what it should have been.
> Here's the data:
>
> [pre]
> Slope Distance (m) Correction
> 2 30.480366 30.4800 0.0004
> 3 30.480366 30.4800 0.0004
> 4 30.480366 30.4800 0.0004
> 5 29.972873 29.9800 -0.0071
> 6 29.973178 29.9800 -0.0068
> 7 29.472695 29.4800 -0.0073
> 8 29.47239 29.4800 -0.0076
> 9 28.970384 28.9800 -0.0096
> 10 28.970384 28.9800 -0.0096
> 11 28.473254 28.4800 -0.0067
> 12 28.472949 28.4800 -0.0071
> 13 27.972162 27.9800 -0.0078
> 14 27.972466 27.9800 -0.0075
> 15 27.471679 27.4800 -0.0083
> 16 27.471069 27.4800 -0.0089
> 17 26.975464 26.9800 -0.0045
> 18 26.976073 26.9800 -0.0039
> 19 26.474981 26.4800 -0.0050
> 20 26.474981 26.4800 -0.0050
> 21 25.969012 25.9800 -0.0110
> 22 25.969317 25.9800 -0.0107
> 23 25.469749 25.4800 -0.0103
> 24 25.469139 25.4800 -0.0109
> 25 25.469444 25.4800 -0.0106
> [/pre]

It isn't clear from your description what the relationship between the EDM slope ranges and the tape distances was. In Rueger's test situation, the tape was stretched out at the same level as the EDM being tested, so the slope distances and horizontal distances were the same.

In your case, you would want to reduce the slope ranges to horizontal (assuming that the tape was horizontal), compute the errors and then convert the errors to their slope components if necessary (unlikely, but possible, I suppose).

You also need to pay attention to the tension and temperature corrections of the tape.

> It isn't clear from your description what the relationship between the EDM slope ranges and the tape distances was. In Rueger's test situation, the tape was stretched out at the same level as the EDM being tested, so the slope distances and horizontal distances were the same.
>
> In your case, you would want to reduce the slope ranges to horizontal (assuming that the tape was horizontal), compute the errors and then convert the errors to their slope components if necessary (unlikely, but possible, I suppose).
>
The prism height and instrument height were identical (at least within .01'. The slope distances and horizontal distances were identical to six digits.

The 100' thing is probably a red herring. I just started the test and worked backwards 5 meters, in half meter increments (as per Reuger), and just converted 100' to metric (30.480).

The tape was at 68 degrees F, so I didn't think it necessary to complicate this test with any corrections.

> The tape was at 68 degrees F, so I didn't think it necessary to complicate this test with any corrections.

So what are the details about the tape and its method of tension? The apparent error of 1cm suggests that something went haywire and the tape would be my first suspect.

What was the model of total station tested? Why didn't you just log ranges in meters instead of logging them in feet and converting them in a way that gives the illusion of great precision?

Hello rfc,

Even if you had made all of your measurements (tape and EDM) correctly you still would have a funny graph. The graph in the Rueger test shows residuals against distance. Yours shows residual against measurement number. If you had reduced your observations to an average for each distance interval it would have looked like this:

I suspect something is wrong with your procedure or EDM. I can think of a rock solid test procedure that would be very hard to balls-up if you want to try it.

Busted!

OK. I give up. I keep thinking I have the ability to perform these highly precise laboratory experiments and produce graphs (like Conrad's), that Math Teacher would be proud of, and you wouldn't be able to poke holes in...

It's useless though.

Here's my setup:

My steel Lufkin is in Ft, and I didn't have a Metric version, so used a common Stanley metric steel tape, placed the 5 meter mark on the 100' mark and worked backwards, because if I went forward I'd be outside the building. I laid the tape on the floor, not streched, held down with masking tape at intervals as shown.

Then, adjusted the height of the prism to exactly match the instrument, and started by aligning (using the prism's optical plummet tribrach) on the first mark (5 meter mark on the tape, at 100'.

But something went south, because 1cm is way too big...remember I just shot multiple observations to a fixed prism with much smaller residuals. I thought a variable might be aiming the prism, as when I rolled the tripod towards the instrument, I had to re-aim the prism...Reuger talks about this, but the differences in distance due to prism alignment seemed way below the numbers we're looking at here.

While I'm very interested in learning all the components of error in the instrument, I'm feeling like I'm trying to drive a tack with a sledge hammer. I'm very open to hearing about Conrad's test, so long as he knows that if anything could be "balls-ed up", I'd be the candidate to do it.:-D

Busted!

> But something went south, because 1cm is way too big...remember I just shot multiple observations to a fixed prism with much smaller residuals. I thought a variable might be aiming the prism, as when I rolled the tripod towards the instrument, I had to re-aim the prism...Reuger talks about this, but the differences in distance due to prism alignment seemed way below the numbers we're looking at here.

First, the apparent precision of repeat range measurements to a fixed prism is not a good estimator of the actual errors in a range measurement.

Secondly, in the case of your test setup, as you rolled your prism stand, any deviations from level in the floor would have made the optical plummet in the tribrach adapter go off plumb. My first suspicion would be that the plumbing of the prism over tape graduation added lots of noise (up to the 1cm) to your results.

In Rueger's early version of that test, the tribrach was in contact with the tape and its edge was aligned with the tape graduation. So that significantly improved the accuracy of the incremental changes in distance.

Non-tilting prism?

> Here's my setup:
>

What sort of prism and target is that on the tribrach? It appears to be a non-tilting prism. If so, put it back in the box and buy a good tilting prism and target before spinning your wheels any more.

>I can think of a rock solid test procedure that would be very hard to balls-up if you want to try it.

Hmmm. Are you thinking of a test whereby a tape or string is stretched out for alignment on fairly level ground and two prisms are set up at points (A + 0.5)L distant (where A is an integer and L is the basic measuring length of the EDM) and the instrument is successively set up approximately midway and advanced at more or less regular increments over an interval covering the basic measuring length with distances to both prisms being measured at each set up? That *should* be simple enough.

Non-tilting prism?

> What sort of prism and target is that on the tribrach? It appears to be a non-tilting prism. If so, put it back in the box and buy a good tilting prism and target before spinning your wheels any more.

It's non tilting, but I never use it (except for this test, because I knew the prism was at exactly the same height as the instrument. I bought it for the three identical Topcon Prisms that came with it, not for field work at all.

Non-tilting prism?

I think that is a triple holder with a centered threaded hole in the center for use as a single. It looks like rfc screwed the prism to the single hole with a target plate from another target holder?

If you are plotting graphs in Excel, be sure to select XY scatter plot. The other types assume equal spacing on the X axis.

It looks to me like you are measuring the positioning (1-dimensional centering) error as much as anything else. That's why, as discussed in an old thread that I recently linked to one of your discussions, I tried to use two prisms and let the instrument make all the measurements, knowing that the total of the measurements in each direction had not changed. I didn't do enough combinations to finish the job, but I think that's how I'd do it if I tried again.

Hello rfc and Kent,

I'm going rudimentary on this one. This is just for cyclic error.

Go and buy one of the cheap 'Leica style' 17.5mm offset prisms with the screw-in lengths and sharp tip. Get a smooth length of wood around the unit length of your EDM, or screw some lengths together to make a long track on the floor. Use a nail or small drill bit to make 2mm or so holes on the wood along the length you want to measure at 0.5m intervals (or whatever). Set up the instrument on the (concrete?) ground and have your significant other to aim at the prism at each spot, trigger and record the measurement. Make about 5 per hole. Once done, measure the intervals between holes with your steel tape from the front of the track and the back of the track to help reduce errors due to graduation printing in the tape. Measure as many times as you like on as many different sections of your tape to try and eliminate graduation printing errors. I'll just add: don't measure hole to hole. Lay the tape out along the whole track length and read the distance at each each hole. If you go hole to hole your errors will turn your experiment to poop in no time.

With this method centering errors disappear and are replaced by just the wobble of the prism. With a couple of rod lengths screwed in to your prism your wobble will be < 0.5mm. You should be able to determine the intervals on your wooden track to < 0.5mm with a magnifying glass. Horizontal distances will be accurate enough. Post the measurements and interval distances. I may even try it on our own 1mm+1.5ppm instrument one day and post the results.

> Go and buy one of the cheap 'Leica style' 17.5mm offset prisms with the screw-in lengths and sharp tip. Get a smooth length of wood around the unit length of your EDM, or screw some lengths together to make a long track on the floor. Use a nail or small drill bit to make 2mm or so holes on the wood along the length you want to measure at 0.5m intervals (or whatever). Set up the instrument on the (concrete?) ground and have your significant other to aim at the prism at each spot, trigger and record the measurement. Make about 5 per hole. Once done, measure the intervals between holes with your steel tape from the front of the track and the back of the track to help reduce errors due to graduation printing in the tape

This sounds like, and looks like a variation on what Reuger suggests. I'm still digesting Kent's "(A+.5)L" setup, though. If the task is to minimize prism centering errors, why can't I just build a very short right angle bracket that holds my zero-offset prism to a beam of appropriate design?

My instrument has a 5 meter unit length, and I have a pristine straight 2" x 6" rectangular aluminum tube I can drill and tap to hold the bracket. Using a center drill to start the holes, I'd have to believe I can get them within .020" (if not .010") of the proper place. I could build a drill jig with a locator pin .5m from a drill bushing (as measured by the digital readout on a mill), but it'd be a good idea to double check the distances between the holes.

Am I correct that the "absolute" distance between the instrument and the first hole is irrelevant?

> ...why can't I just build a very short right angle bracket that holds my zero-offset prism to a beam of appropriate design?

You can do that.

> My instrument has a 5 meter unit length, and I have a pristine straight 2" x 6" rectangular aluminum tube I can drill and tap to hold the bracket. Using a center drill to start the holes, I'd have to believe I can get them within .020" (if not .010") of the proper place. I could build a drill jig with a locator pin .5m from a drill bushing (as measured by the digital readout on a mill), but it'd be a good idea to double check the distances between the holes.

That all sounds good. But there is no 'proper place' for any of the holes. Just make the holes at regular intervals and determine the distances to the greatest relative accuracy you can after drilling. Actually determining the distances of the holes along the track to the highest accuracy you can is the most important part in the whole test. This is a case where it would be easier to drill first and measure later.

> Am I correct that the "absolute" distance between the instrument and the first hole is irrelevant?

Yep, distance to the first hole is not relevant for a cyclic error test. It's good enough to adopt the reported distance from the EDM corrected for offset to your measured pin locations.

Here's another way to evaluate cyclic errors of the EDM with very little fuss. To do it, you need to know the basic measuring length of your total station. That is half the carrier wavelength at fine modulation frequency. The example below is for an instrument with a 10m basic measuring length.

This method is neat because it does not require exceptionally careful alignments or centering and does not require knowing any distance with great accuracy. The range consists of eight stations that can be something as crude as chalk marks made on a sidewalk at the following distances +/- a couple of centimeters. Chalk marks made the same distance in from the straight edge of a sidewalk are an easy way to lay this test range out. We don't particularly care what the actual distances between rough chalk marks is. They only serve to get the spacing of stations and prisms approximately correct with the actual spacing to be worked out from EDM ranges.

Sta Dist (m)
A1 0.00
B1 2.50

C 16.25
D 18.75
E 21.25
F 23.75

B2 35.00
A2 37.50

On a fairly level lawn, just pulling a tape for alignment and setting nails at the distances +/- a couple of centimeters should work fine.

The test consists of setting up two prisms in tripods at the stations B1 and B2 and then successively occupying stations C, D, E, and F, all of which are on line with B1-B2 within a few centimeters.

At each setup in F Lt and F Rt, log slope ranges in meters to B1 and B2, zenith angles to B1 and B2 for each slope range, and the angle B1-Station-B2.

Occupy C, D, E, and F getting what in effect would be sufficient data to solve the instrument position at those stations by resection if the coordinates of the prisms at B1 and B2 were known.

Then shift the prisms and tripods to A1 and A2 and occupy C, D, E, and F again, logging the same measurements as before at each.

The following ranges +/- a cm or two will have been measured:

Prisms @ B1 & B2 (32.50m total length)

13.75
18.75
16.25
16.25
13.75
18.75
11.25
21.25

Prisms @ A1 & A2 (37.50m total length)

16.25
21.25
18.75
18.75
21.25
16.25
23.75
13.75

From these measurements, the cyclic errors of EDM ranges at increments of 2.5m representing four points in the cyclical error pattern that repeats every 10m can be worked out from these ranges:

11.25m
13.75
16.25
18.75
21.25

The distances A1-A2 and B1-B2 corrected for cyclic error are taken as the arithmetic means of the sums of the distances measured A1-Station-A2 and B1-Station-B2, respectively. The actual ranges may contain some error in the instrument or prism constants. That doesn't matter for the purpose of this exercise, which is to describe the pattern of cyclic error.

Knowing the mean distances A1-A2 and B1-B2, the apparent errors at the stations where ranges 16.25 and 18.75 were measured to both prisms at the same station can be worked out as the correction that would have to be applied to each of the pairs of 16.25m or 18.75m ranges that would give the mean distance between the prisms.

The first assumption is that the cyclic errors in 11.25m and 21.25m are essentially the same for an instrument with a 10m basic measuring length. Likewise, the cyclic errors in 13.75m and 23.75m,

That gives the cyclic corrections for ranges _1.25m, _3.75m, _6.25m, and _8.75m.

To verify that these same corrections apply at longer ranges, the stations A1, B1, A2, & B2 can be moved away from C,D,E,& F by some integral multiple of the basic measuring length and the test repeated.

> Here's another way to evaluate cyclic errors of the EDM with very little fuss. To do it, you need to know the basic measuring length of your total station. That is half the carrier wavelength at fine modulation frequency. The example below is for an instrument with a 10m basic measuring length.

> Sta Dist (m)
> A1 0.00
> B1 2.50
>
> C 16.25
> D 18.75
> E 21.25
> F 23.75
>
> B2 35.00
> A2 37.50

And here's an example for an EDM with a 5m basic measuring length:

Sta Dist (m)
A1 0.00
B1 1.25

C 12.50
D 13.75
E 15.00
F 16.25

B2 26.25
A2 27.50

Or another somewhat longer 5m range design that illustrates how the stations A1,B1,A2 and B2 may be located more distant (at even 5m multiples) from the central cluster of C, D, E, and F while maintaining the basic result.

Sta Dist (m)
A1 0.00
B1 1.25

C 17.50
D 18.75
E 20.00
F 21.25

B2 36.25
A2 37.50

Or to test cyclic errors over yet longer ranges:

Sta Dist (m)
A1 0.00
B1 1.25

C 117.50
D 118.75
E 120.00
F 121.25

B2 236.25
A2 237.50

hey Kent, can I email you some testing results? you got an email to send to?

> hey Kent, can I email you some testing results? you got an email to send to?

Sure, I'm kentmcmATswbellDOTnet.