Determining Total Station Distance Standard Errors, Part 4

> So I changed the setup to this:
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> It's a rectangular aluminum tube, scribed every .5 meters, using an X-acto knife and a steel square.

Couldn't you possibly have found a material with a higher coefficient of thermal expansion than aluminum?

> The marks on the tape measure about .007" or less than .2mm wide, so I'm pretty sure, I've done away with centering errors by placing the prism, mounted on a bracket up against the marks (with the X-acto knife in the mark, used as a "stop".

Between the aluminum tube rail and the method of marking stations on it, that's certainly a less than ideal test setup. You should at least mount that prism on a longer base so that it is consistently squared to the rail. That small foot on the mount looks as if it would introduce significant noise in the measurement, so I'd recommend thinking about using a piece of clear acrylic with a "cross hair" scribed on its bottom to align with your scribes on the rail and a guide on one edge to ride parallel with the edge of the rail.

Then there's the method of calibration of the rail. Measure the distances from one end of the tube to the scribes and from the other end to the same scribes. read the tape to the nearest 0.25 or 0.50mm. As a check on your layout, you'd want to do the same for both sides of the scribes.

Compute the taped distances from the first scribe to the others, making such arithmetical correction as is necessary to correct the reversed measurements.

Compare the taped distances to the scribes for each side of the scribes to check for parallelism.

> I observed the distance, in meters. The instrument/DC brought them in to 4 decimal places, rounded to 3 in Topcon Link.

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> It still doesn't look like a sine wave (unless you squint real hard);

That's because you rounded the ranges to the nearest 1mm and the amplitude of the cyclic error appears to be about 1.5mm. You'd get the same effect by taking a smooth sine-curve, sampling it and rounding off the values to the nearest half-amplitude or so.

Just as a footnote: the coefficient of thermal expansion of aluminum is

12.3 x 10^-6 in/in°F

and that is roughly twice that of A36 steel, which is:

6.7 x 10^-6 in/in°F

and nearly seven times that of wood in a direction with the grain

1.7 x 10^-6 in/in°F

> Couldn't you possibly have found a material with a higher coefficient of thermal expansion than aluminum?
>

Hey! What do you think I'm running here...The National Bureau of Standards?:-D

Yes, the coeficient of thermal expansion of aluminum is high, but consider that both the steel tape and aluminum tube were both acclimatized at 68 degrees for more than 12 hours. Aluminum doesn't grow and shrink if the temperature doesn't change. And since this isn't a "standard" that I'm going to use again and again, I'm confident that my measurements are extremely close. I measured each .500m against each other with a steel machinist's rule and also with another tape from both ends.

The errors associated with the tape and scribe marks are close to an order of magnitude lower than what I'm trying to measure.

The aluminum channel seems to be in a basement, which probably has a stable temperature. So expansion and contraction between marking from the steel tape and measurement with the total station is probably negligible. The coefficient of the steel tape is probably more significant.

> The aluminum channel seems to be in a basement, which probably has a stable temperature. So expansion and contraction between marking from the steel tape and measurement with the total station is probably negligible. The coefficient of the steel tape is probably more significant.

The value of a test rail is that it can be used to evaluate cyclic error over a variety of ranges up to and beyond 100m. That means taking the thing out of doors where materials like aluminum with large coefficients of thermal expansion are more problematic than wood is.

> I measured each .500m against each other with a steel machinist's rule and also with another tape from both ends.

I think my point was that scribes squared off the edge of an extruded aluminum tube would seem unlikely to be parallel within less than 0.50mm. So, taping to both ends of the scribes would either demonstrate that they are parallel or give a basis for correction.

Step One would be to post the taped distances (tape readings) to the scribes as measured from each end of the rail.

> The value of a test rail is that it can be used to evaluate cyclic error over a variety of ranges up to and beyond 100m. That means taking the thing out of doors where materials like aluminum with large coefficients of thermal expansion are more problematic than wood is.

Just for the record, One of the main reasons I began this endeavor was because it was too damn cold to do anything outdoors. Believe me, when the temp gets back above the freezing mark for any significant length of time, I sure ain't going to be lugging a 24' aluminum tube around the yard. I'll put cyclic error far behind me, and get on to a list of things I need to learn/practice that's a mile long.

I'm getting a feel, though, for the magnitudes of various errors, and so far, I believe that centering the instrument and targets is the big elephant in the room.

> Just for the record, One of the main reasons I began this endeavor was because it was too damn cold to do anything outdoors. Believe me, when the temp gets back above the freezing mark for any significant length of time, I sure ain't going to be lugging a 24' aluminum tube around the yard.

Yes, that's why the best design is out of seasoned wood (or some other low-expansion material) that is demountable/disassemblable.

However, now that you've got the tube/rail down in the basement in position to measure ranges to it, the first item of business is calibrating the intervals on the rail by taping. The second is actually extracting the ranges measured to the prisms from the SDR files that apparently contain them.

> However, now that you've got the tube/rail down in the basement in position to measure ranges to it, the first item of business is calibrating the intervals on the rail by taping.

Actually it's NOT in a basement at all. It's in my shop (where my day job is). As usual you have me thinking. I don't have to move the rail much at all to carry on at longer distances. I can move it in front of our overhead door, which is visible for at least 200m across a vast lawn (when the snow's gone). When it gets warmer (like 68 degrees F), I can just set up at 50m, 100m, even 200m and run the tests again for comparison.

> Actually it's NOT in a basement at all. It's in my shop (where my day job is). As usual you have me thinking. I don't have to move the rail much at all to carry on at longer distances.

Well, there you go. All you have to do is get a good calibration on the scribes and arrange a somewhat better sliding mount for the prism and you're in business. When the temperature changes, just a remeasurement of three points on the rail with the steel tape (endpoints and mid) should verify the temperature correction.

Hello rfc,

I have a couple of suggestions which Kent may have covered. Please post the un-rounded measurements. Either make a bracket which squares itself against the side of the track or use drilled holes with a locating pin. Holes and a pin will remove the need to use a magnified/vernier arrangement to locate the bracket. But if you cut the front of the bracket on a slight angle you can very accurately locate the prism bracket on your scribed divisions by sliding the prism bracket until your E-W track scribe mark lines up with a N-S scribe mark on your prism bracket.

Lastly, I hope you are scribing your distances and re-measuring the actual distances rather than using the distance you were trying to scribe. For example, using the photo you posted, that would be about 3.0004m for the 'true' distance down the track rather than 3.000m.

> Lastly, I hope you are scribing your distances and re-measuring the actual distances rather than using the distance you were trying to scribe. For example, using the photo you posted, that would be about 3.0004m for the 'true' distance down the track rather than 3.000m.
Thanks for weighing in, Conrad.
By "actual distances" do you mean real, independently measured distances to the TS? In my last setup, I put the 5 meter mark exactly at my pre-setup 100' range, but by the end of that thread (Part 2 or 3; I can't remember), it was stated that the real distance doesn't matter...just the relative .5, 1.0, 1.5 meter distances.

This time I just made the first mark .500 from the end of the tube, and scribed the lines at .500m intervals. I paid no attention to the distance from the TS. It doesn't look like Reuger was interested in that either so far as CYCLIC errors alone go. I'm not doing this test as an absolute check on distances. For that, (if I get the time), set up the range Kent (or you; I can't remember) suggested...a number of stations, then setup on each, measure fore and aft, etc.; reduce into LSA, etc.

But, One last note on the apparent preoccupation with getting the prism perpendicular to the line of sight (because of the refractive index of the glass). Reuger's calculations on this show negligible differences here. At 1 degree, he calculates 0 mm. At 5 degrees, it's .07mm, or .00007m. That's WAY below anything that is likely to affect measuring the cyclic error of the instrument.

I'll try to post the un-rounded data.

> But, One last note on the apparent preoccupation with getting the prism perpendicular to the line of sight (because of the refractive index of the glass).

Actually, my interest was in knowing the actual distance to the prism. What I understood that you did was to make a make at given distance using tape and then extend the mark along a scribed line made using a machinist's square held against the edge of the extruded tube. I'd second Conrad's remarks about drilling holes for locating pins to remove all of the fuss and muss of aligning and centering the prism.

> Actually, my interest was in knowing the actual distance to the prism. What I understood that you did was to make a make at given distance using tape and then extend the mark along a scribed line made using a machinist's square held against the edge of the extruded tube. I'd second Conrad's remarks about drilling holes for locating pins to remove all of the fuss and muss of aligning and centering the prism.

Understood. No, I didn't measure that independently this time (with a tape). But I bet if we did LSA on all these raw numbers, we could come up with the most probably number to any one of the scribe marks.:-D
Here's the stuff right out of the DC. I've given up on the file thing for now. Until I get a chance to look closer at SurvCE and Magnet, with their various export funtions, I'm not trusting what they're doing to the data. Heck I even just tried a LandXML file, but even that rounded these to three digits.

19.7340
19.7342
19.7346
20.2344
20.2340
20.7344
20.7344
21.2338
21.2334
21.7330
21.7336
22.2332
22.2328
22.7332
22.7334
23.2334
23.2326
23.7320
23.7318
24.2328
24.2330
24.7338
24.7338
25.2332

> But I bet if we did LSA on all these raw numbers, we could come up with the most probably number to any one of the scribe marks.

The critical step is actually knowing what the distances between the prism stations on the rail are. Considering that it is only 5m that you're dealing with, that should be very easy to determine with a tape. However, commercial tapes do have errors in their printed graduations that, as Conrad suggested, are minimized by the simple procedure of measuring the distances in opposite directions (which will use different sets of graduations on the tape).

> Here's the stuff right out of the DC.

The stuff "right out of the DC" would be the SDR-format file. I assume that there are some angles, zenith and horizontal, associated with all of the slope ranges measured.

> The stuff "right out of the DC" would be the SDR-format file. I assume that there are some angles, zenith and horizontal, associated with all of the slope ranges measured.

There's no way to upload an SDR file here. Here it is in text format, but I can't make heads or tails of it.
I am pretty sure, however that the SD and HD's were exactly the same. The horizontal angles were within 30" of horizontal.

00NMSDR33 V04-03.00 Mar-21-15 11:34 111211
10NMcyclic5 121111
06NM1.00000000
13NMMAGNET Field Jul 25, 2014 (MAGNET Field V2.5.0.0) Version 2.7.1 (build 150712)
13OOOBS
13NMForesight prism name: 0 Offset
13PCForesight prism const.: 0 mm
13NMBacksight prism name: 0 Offset
13PCBacksight prism const.: 0 mm
05PT 1013.3 20.0
13NMEquipment: Total Station
02TP 00.00000000 0.00000000 0.00000000 0.00000000
03NM0.00000000
08TP 50019.73399978 0.00000000 0.00296587
07TP 0 5000.00000000 0.00000000
13NMBacksight HR:0.000
09F1 0 50019.73400000 89.99138889 0.00000000
09F1 0 5619.73420000 89.99138889 0.00000000
09F1 0 5719.73460000 89.99138889 0.00000000
09F1 0 5820.23440000 89.99138889 0.00000000
09F1 0 5920.23400000 89.99138889 0.00000000
09F1 0 6020.73440000 89.99138889 0.00000000
09F1 0 6120.73440000 89.99138889 0.00000000
09F1 0 6221.23340000 89.99138889 0.00000000
09F1 0 6321.23380000 89.99138889 0.00000000
09F1 0 6421.73300000 89.99138889 0.00000000
09F1 0 6521.73360000 89.99138889 0.00000000
09F1 0 6622.23320000 89.99138889 0.00000000
09F1 0 6722.23280000 89.99138889 0.00000000
09F1 0 6822.73320000 89.99138889 0.00000000
09F1 0 6922.73340000 89.99111111 0.00000000
09F1 0 7023.23340000 89.99138889 0.00000000
09F1 0 7123.23260000 89.99138889 0.00000000
09F1 0 7223.73200000 89.99138889 0.00000000
09F1 0 7323.73180000 89.99138889 0.00000000
09F1 0 7424.23280000 89.99138889 0.00000000
09F1 0 7524.23300000 89.99138889 0.00000000
09F1 0 7624.73380000 89.99138889 0.00000000
09F1 0 7724.73380000 89.99138889 0.00000000
09F1 0 7825.23320000 89.99138889 0.00000000

Okay, that DC file shows that the slope ranges are all colinear and horizontal for the purposes of the test. That's good.

Now, what are the tape readings to the scribes measured in opposite directions and on opposite sides of the scribes (or at points on the centerline of the rail where the prism was)?

Here is a statistical summary of the above EDM ranges.

Note that the standard errors are just a measure of the variability of the repeat measurements, not a measure of the accuracy.

Basically, the resolver on the EDM of your instrument has a standard error of about 0.3mm over these ranges. That means that if you took a long series of twenty repeat ranges to the same prism, the series would probably have a standard error (internal precision) of about 0.3mm. The practical significance of that is that if you measure each range five times, you'll likely have a resulting mean that will be repeatable within about +/-0.13mm.

If you can refine your rail design to be able to know the distances to prism stations on it with an uncertainty of better than 0.25mm, you should be able to generate a smoother plot of the cyclic error function.

[pre]
19.7340
19.7342
19.7346 s=0.3mm
-------------------------
19.7343 = mean

20.2344
20.2340 s=0.3mm
-------------------------
20.2342

20.7344
20.7344 s=0.0mm
-------------------------
20.7344

21.2338
21.2334 s=0.3mm
-------------------------
21.2336

21.7330
21.7336 s=0.4mm
-------------------------
21.7333

22.2332
22.2328 s=0.3mm
-------------------------
22.2330

22.7332
22.7334 s=0.1mm
-------------------------
22.7333

23.2334
23.2326 s=0.6mm
-------------------------
23.2330

23.7320
23.7318 s=0.1mm
-------------------------
23.7319

24.2328
24.2330 s=0.1mm
-------------------------
24.2329

24.7338
24.7338 s=0.0mm
-------------------------
24.7338
[/pre]

> > Lastly, I hope you are scribing your distances and re-measuring the actual distances rather than using the distance you were trying to scribe. For example, using the photo you posted, that would be about 3.0004m for the 'true' distance down the track rather than 3.000m.
> Thanks for weighing in, Conrad.
> By "actual distances" do you mean real, independently measured distances to the TS? In my last setup, I put the 5 meter mark exactly at my pre-setup 100' range, but by the end of that thread (Part 2 or 3; I can't remember), it was stated that the real distance doesn't matter...just the relative .5, 1.0, 1.5 meter distances.

Hello rfc,

No, I'm unconcerned about the actual distances from the instrument. The un-rounded, recorded distances are good enough. I'm concerned about the actual distances down your track. I would like the measured distances down the track, backwards and forwards from each end as if I walked in to your setup and measured them myself with a steel tape, without any knowledge of where they were supposed to be, estimated to the nearest 0.1mm. To increase your precision you could do this by reading on the m side of the tape and the ft-in side, backwards and forwards and reporting both.

I was recommending some kind of guide solely to help get a more consistent location on your track for the distance positioning. Also according to a Leica paper on prisms, at short ranges some of the EDM signal can be reflected off the front of the prism rather than making it to the back of the prism. For this reason the front of Leica's most accurate (and expensive) prism is cut at an angle to avoid direct reflection from the front of the glass. To be safe I would not measure from a position perfectly perpendicular to the prism surface. The further you are from the prism the less likely this would be to happen.