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Tacheometry for a Beginner
Tacheometry for a Beginner
Hi. I??m an architect designing primarily rural-ish high-end homes in Ohio. I work for a builder.
As a way to verify the topo data I??m using in my computer model (I download topo data in ASCII files from OGRIP to construct a mesh), I like to take topo-shots with our GPS unit onsite. Our sites are often wooded and steep with existing buildings, and our GPS unit never performs well in those situations where satellites aren??t easily visible.
As an alternative, I just purchased a Wild T1A theodolite (1959ish model for $100) to take shots using tacheometry. I tried using the stadia hairs with a vertical pole, but it??s too hard/takes too long to read exactly which number I??m looking at, so instead I??m just taking vertical angles at the same two marked points on the pole every time. From there I feed the angles into an excel sheet to do the trig calculations. Typical horizontal distances I shoot would be max 500??.
I know I could probably get faster results with an electronic theodolite or totalstation, but I just like the idea of an instrument that has no software to re-learn, no batteries to forget/die, and no memory or circuits to fail. Just sits there and works the same every time. I??m not taking that many shots anyways.
I??d like to test the instrument to determine it??s maximum accuracy, and I??m wondering if there are any standard methods to do this that don??t require investing in expensive optical testing equipment. Basically what??s the best way to set up a very accurate large square (say 100??) outdoors when all I??ve got is a 200?? tape? Can I rely on the tape to be at least as accurate as the instrument when stretched to make the square? Thanks!
- 18 Replies
There are two NGS control points near you that are intervisible and something more than 600 feet apart. They are AA6166 and AA6198. You can see their data sheets here https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=AA6166 and here https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=AA6198
They are northwest of Danville on highway 44, less than 5 miles.
Perhaps sighting between them will help.
One way to evaluate your performance is to measure against an NGS calibration baseline. I don??t know where you are located but using Math Teacher??s reference to Danville, OH I found the following NGS baseline which includes a 100 foot monument:
https://beta.ngs.noaa.gov/CBLINES/pages/data/OH/oh_coshocton_2.html
Carefully read the descriptive information.
Distances available on the CBL are 100 feet, then 150, 275,425,875,1150 and 1300 meters.
On the map copied below, the blue dots represent NGS CBLs, the red x is Danville, OH.
Good luck,
DMM
Basically what??s the best way to set up a very accurate large square (say 100??) outdoors when all I??ve got is a 200?? tape? Can I rely on the tape to be at least as accurate as the instrument when stretched to make the square?
If you mean a 100′ x 100′ square, use the 200′ tape to set one side of the square. Then occupy each end with the T1A, turn 90?ø from one end and 270?ø from the other end and measure 100′ from those ends. The fourth side should measure close to 100′. Check your diagonal distances. The tape won’t be as accurate as the instrument because the tape stretches.
MH
@geeoddmike That’s NGS Calibration base line (not baseline)
@geeoddmike That’s NGS Calibration base line (not baseline)
Yaroshio If you want to test your theodolite then look at “International Standard” ISO 17123-3
Optics and optical instruments— Field procedures for testing geodetic and surveying instruments—
Part 3:
Theodolites
You can purchase this for a small fee. Go to http://www.iso.ch
Reading the OP again, I realize that I do not understand how he determines distances. I thought he was talking about reading stadia for distances then he mentions using vertical angles to two points on a pole.
Since the title of the OP refers to tacheometry, I imagine he is using the points as a sort of subtense bar. I recollect reference to using an M16 as a subtense bar. Of course they used horizontal angles and insured that the orientation of the subtense bar was perpendicular to the instrument.
Many years (actually many decades) since I did this sort of work.
BTW, on a project in Africa during the mid-1970s I used this instrument:
http://www.dehilster.info/geodetic_instruments/1963_wild_heerbrugg_rds.php
As for baseline v base line, Mr Nolton is correct (twice). I am appropriately chastened.
@geeoddmike Sorry for the post “TWICE”. I did not see it say it had posted so I hit the enter key again.
Congratulations on getting a real bargain on the T1A.
Please explain your procedure in more detail. I, too, am uncertain if you are getting the distance by tape or computation. I hope you have a computation that uses the vertical angles and not just their difference alone.
One important check on the instrument is to read a vertical angle to a well-defined point, turn the instrument 180 degrees and reverse the scope to read the point again. The readings should sum to 360 degrees within a few seconds. If not, the collimation is off and you need to use the average of reading A and 360-B to get really accurate values. Run your computation with each to see if it matters for your work.
.@geeoddmike Sorry for the post “TWICE”.
If you find within some time period that you have posted twice, you can find a delete option near the top of the post to correct the situation.
.My thought was to use the data sheets to calculate horizontal distance and height delta. Then observe and calulate and compare the two.
Here’s the data sheet calculation, note that the geoid heights are virtually the same so I used ellipsoid heights.
I did a stadia project in school. I’ve never done it in the “real world”. But I’ve discussed it with people who did. This is how I understand that it got done on the job:
1. Sighting the rod, you set the bottom hair on an even foot mark and read the interval. The math to get the slope distance distance is easy. Keep in mind that at a 0.01′ error in reading the interval is 1′ error in the distance. At 500′ sight distance you would be lucky to read the interval to ?ñ0.05′. So the distance at that range will be +/-5′
2. Sight the rod at the instrument height, and record the zenith angle. You would typically have a piece of flagging tied around the rod at the height of instrument to facilitate this. This cancels the instrument height / rod height from the height difference calculation. But if you can only read the rod to ?ñ0.05′ at 500′ your elevation error will be that much due to sighting alone. Add other sources of error.
3. Record the horizontal angle.
In other words, by today’s standards, stadia surveying is rather crude.
The tape won’t be as accurate as the instrument because the tape stretches.
If you are using a good surveyors steel tape, handling it expertly, and accounting for tension and temperature, the tape will be more accurate than the EDM at distances of less than a tape length.
Of course you will be hard pressed to get two guys together who ever knew how to handle a tape expertly, and when you do they will be 20 years out of practice.
I??d like to test the instrument to determine it??s maximum accuracy, and I??m wondering if there are any standard methods to do this that don??t require investing in expensive optical testing equipment. Basically what??s the best way to set up a very accurate large square (say 100??) outdoors when all I??ve got is a 200?? tape? Can I rely on the tape to be at least as accurate as the instrument when stretched to make the square? Thanks!
Use your instrument to layout two 100.00′ legs at 90?ø00’00”. By Pythagoras the diagonal measurement will be 141.42′, if the 90?ø angle is correct.
Alternatively, run a 4 sided closed figure. The distances are not material. The angles don’t need to be exactly 90?ø. Setup at each of the four sides and read the interior angles. They should add up to 360?ø exactly. Do not expect perfection. An error in keeping with the least count of your instrument is acceptable.
I sort of figured the T1A might be more accurate than a non-steel tape, and I don’t have access to a steel tape, so the NGS base line and/or control points seem like great places to start. I’ll look into the ISO standard as well (and see if I can find it somewhere for less than the $120 they are asking), and probably used the 4-sided-figure technique to test the horizontal angle accuracy. Thanks very much for all the helpful info, I had no idea most of those things existed.
Here’s an image of the method I’m using. My thought was that the vertical pole (w/ bubble level) would allow the vertical leg of the triangle to be much larger than the typical distance between the stadia hairs (8′ minimum instead of 1′ at 100′ horizontal distance) and therefore be a more accurate trig calc. At least for the distances I typically work over, which are house-sized. Personally, I also find it less mentally taxing to read two separate vertical angles to a high-contrast color boundary instead of squinting at numbers on the pole with the stadia hairs.
And here’s the code which plots points in an x-y-z coordinate system in the modeling software I use.
Other than the stadia method, are there other ways of determining location/elevation that are faster and/or more accurate, given the instrument I have?
2. Sight the rod at the instrument height, and record the zenith angle. You would typically have a piece of flagging tied around the rod at the height of instrument to facilitate this. This cancels the instrument height / rod height from the height difference calculation. But if you can only read the rod to ?ñ0.05′ at 500′ your elevation error will be that much due to sighting alone. Add other sources of error.
You can also use the theodolite like a level, not set up over the elevation reference point. Check the vertical collimation as described above. If it is close, then you can set the zenith angle to 90 (or make a slight correction) and not measure the height of the instrument (another source of error). Just take readings seen on the rod at the elevation bench mark and the unknown points.
.
An architect I know showed me how to topo a small area with a card table, scale, and tape. Sort of like an alidade and plane table. He would measure the distance to building corner or other point of interest then sight down the scale and tick off the distance. It worked reasonably well. Then you use a level and rod to get elevations.
I think the British have a program where they teach ordinary people to “survey” like that, the purpose is they have so many historic sites that it is not possible for professionals to get to them all but the more minor ones can be documented by volunteers. Better than nothing.
I would say if you can’t read the rod then you are going to far. Set some “fly points” around the area to be topo’d, a small spike or wooden stake (the little ones are called “ginees”). Then locate those with the T1A then get topo from each one using the stadia method Mark/Norman outlined above.
You could mount the most basic and compact Leica Disto or similar laser on the telescope and get the slope distance directly to a simple bullseye target on a pole adjustable to match instrument height. You’d still have calcs but only slope dist x cos and sine of the vertical angle to obtain horizontal distance and difference in height. With the laser you can also shoot to building corners, roof points etc.
In the 1970s, I probably put in over a thousand hours shooting stadia topo with a T1 and a T1A. The procedure was much like what Norman Oklahoma describes, except that we didn’t shoot a flag on the rod to cancel out the height of the instrument. We made that adjustment in the office.
We set additional points, as mentioned by Dave Karoly, to keep the maximum shot distance down to about 300 feet. It’s possible to read a rod to 0.01 ft. at 300 feet, but that’s about the maximum range. At those distances it was only necessary to read angles to the nearest minute, which saved time. We ran a level loop through all the setup points rather than carrying elevations by stadia. These were 3-person crews, with the third person being the notekeeper.
Yaroshio, your vertical tacheometry is likely to be more accurate than stadia if the rod is held plumb and steady, and bearing in mind what Bill93 said about the vertical angle collimation. There will probably be a foot or two of tolerance in the horizontal distances and a tenth or two in the elevations. You can find out on the base line.
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