A T2 is an amazing instrument.
What I saw in the results, just like the documentation said, the upper limit of subtense distance accuracy is user defined. In my experiment, although up to 550', a cm was uncommon, 15 mm an outlier.
So in a pre electronic setting, 400' subtense distance could compete with chaining. If circumstances left no plan C. And it's not just take an average. Reliability of the distance is how well you can home in on better than 1/4 second. And that's not outside the ability of T2.
That's the nostalgia of surveying. A very old, highly understood science. But, GPS and total stations have taken a lot skill out the game.
I have a 1925 book by the Royal Engineers. It's in depth, and high science. And surveys didn't get better, just faster cheaper.
Dave Ingram and I authored a story about the American theodolite. The story about how the graduation lines on a glass circles were etched is truly amazing. You cannot see the graduations on a circle with the naked eye. In the story, there is a photo of me holding one.
http://www.amerisurv.com/PDF/TheAmericanSurveyor_PenryIngram-TheAmericanTheodolite_Vol10No9.pdf
For what it is worth.. mathematicians, like to find new ways to express numbers, and equations, that are meaningful.
So, here is my "bring to meaning" post on this subject.
The Average Diameter of the earth is 7917.5 miles.
This makes the radius 3958.75'
Tan of 1 arc second x 3958.75 = 101.34 feet.
So, if you are scaling the USGS quad sheet, and you are off by one arc second, you are off by about 100'.
So, if you set your T-2 and the center of the earth, and turned a 1" angle, that would result in a surface dist of just over 100'. (Depending on elev, of course)
And, so when your GPS system is set on an autonomous point, that is 10' from the real one, how much angular error is introduced, into your survey?
Well, how far are we from the north pole? Well, that varies. But, from Little Rock Arkansas, it is about 3825 miles. Pretty close to the same distance from her to the middle of the earth. So, if were off by 10' with our autonomous GPS base, then we are off by about 1 tenth of a second, with our bearings.
So, for every 10' of EW error, in our Autonomous GPS base, we add 1 tenth of a second.
And, if we take 2 sunshots, that are a mile apart, EW, then the convergence is around 0å¡00' 54" per mile.
Make Math meaningful.
Then, you will remember it.
Nate
It's always been: a minute = nautical mile.
Nautical mile = 6080 ft äö 60 seconds
Divide by 60 äö 1" äö 100 ft
Divide by 100 äö 1 ft äö 0.01 seconds
And latitude is 1" äö 100 ft.
Longitude is 1" äö 100' x cos(Lat)
At 39å¡, 1" longitude äö 78 ft
I have an old text with tables to convert feet of 'latitude and departure' to degrees of latitude and longitude to carry Lat/Long in traversing without trig comps.
And that second of arc when you are pointing at Polaris is about a billion miles.
OK, to take this full circle a second is approx 100 feet at MSL and 1 billion seconds is 31.7 years, so, I am 33,457,600 miles old. No wonder I am tired ...
Larry Scott, post: 364360, member: 8766 wrote: Well, I didn't post the full precision of the resulting angles. And I indicated using a Lufkin Super highway 'chain' which is a tape. Along with a K&E metric tape. And I've never used the verb taping when pulling a tape. Old style T2.
The chains are not calibrated. And they agree with each other at 20 degrees C, 10 pounds, fully supported. They also return 1:20,000 agreement to GPS determined distances. So, the chains, 2 different manufactured, very different ages, are "probably" okay for this exercise. NIST charges $500/ea. I didn't go with that at this time - since they measure approximately the same, fit distances determined by other means, they are only assumed to be suitable. The thermometers are high quality industrial mercury. A pair, returning temperatures so similar I can't tell them apart. And I tested them in an ice bath. The spring balance was tested against a static load of 12 liters of water, easily satisfactory for this application.
In the wild subtense documentation they state the precision can be improved by increased observations. The 25 mm per 100 m is only 1:4000. Not stated in my Wild documentation. In the wild manual that I have, it states 1:10,000 is readily achievable at reasonable effort, and the length and stability of the bar can support 1:20,000 with additional effort. Doubling and quadrupling the number of sets. In the manual they refer to a standard procedure of 10 sets at or below 1" std dev. for the expected 1:10,000. And longer distances simply require more.
Also in my manual it states the obvious: that a 1" second instrument can readily far surpass 0.5" accuracy. Also per the manual: "the inverse square law applicable to errors offers the possibility of holding to a predetermined accuracy by the judicious combination of angle and distance measurement .... ... the figures given in this manual for the mean errors to be expected can be substantially reduced where needed".
And what about (FL+FR)/2 = 0.8"? Is that per set?
It's a matter of statistics. The t2 is quoted as 1", attainable accuracies can easily be better than 1". With larger, consistent data sets, precision improves. Per Wild, and other academic sources, 30, 60, or even more, outliers edited, present better that 0.2" precision. And to reduce that amount of data I use a spreadsheet.
I was trying to see how well I could measure distances with a subtense bar, without doubt. What is the upper limit of precision? So, I set up a parking lot network (10 pts), and turned every possible angle to over determine the network. Using Starnet, a priori angles: 2". Centering was done by transiting 2 instruments (T1, T16) at close range to center the targets better than the optical plumb of the tribrachs. Centering error assumed approx 1 mm. Minimally constrained, angle/direction residuals well distributed (+/-) and 0-5" with exception on the really short sides. 4-8 sets typically, many angle/direction sets repeated.
All distances chained (or taped) multiple times. Tension temperature, with wide swings in ambient temperature. A priori distance error set 50 ppm (1:20,000). Residuals (+/-) 0-0.006 m, with exception on only the longest line, 12 mm.
30 distances. Median distance 85 m, max distance 168.787 m.
Additionally, I incorporated 6 points held to 5 mm std err, determined by GPS, and the residuals to both distance and angles were essentially unaffected. i.e. the chain distances fit the GPS well, very small scalar component, very low noise data. (I then removed the GPS positions so that only chain/subtense/angle data are adjusted.)
Then, I measured all distances by subtense. The long distances, 168 m, several times, with approximately 0.25" day-to-day repeatability. I accumulated repeat measures, and several of the longer lines have 80-100 sets collected from multiple days. Calculated Standard err typically 0.12" and better, std dev <1". And shorter lines 8-16 sets, std dev <1", std err 0.2" - approximately. All in all about 1300 sets.
In the adjustment, the subtense distance residuals were indistinguishable to chain distance residuals. Including the 168 m, (550 foot) legs.
95% confidence regions, semi major axis, 0.000-0.003.
The effort was well beyond a paying job. But Starnet can reveal error, blunders and accuracy so well, that a 2 day goof around became a couple of month investigation.
What I found is that subtense distances, well beyond 75 m, up to the 168 m, repeat easily and reliably at 1:20,000, and several of the distances, those with the most accumulated data 1:30,000.
I've seen a lot a questions about "can a 1" instrument measure a 1" angle?". The answer is yes, but it's a matter of statistics.
All I can say is that, I have repeated measure of subtense angles with 10-20 sets on different days and the angle always repeated less than 1/2 second, often repeated 0.15". A real world observation, not a quote from a text. And that returns about 3 mm in 90 m using a subtense bar. 1:30,000 best, 1:20,000 normal.
I've seen many publications that cite subtense as marginal, and the upper limit as 75 m. And the question "is subtense as good as chaining (taping)?" The answer is: is chaining is as good as subtense? Yes, if fully supported, elevation profile, temperature, tension applied. In catenary, 1:20,000 chaining is difficult. 1:20,000 subtense (less than 168 m) easy. 60 sets, about an hour.
I even checked the length of the bar in blaze sunshine in summer, and again in winter. A temp diff of 50 deg C. I was not able to detect a change in length. I was verifying its temp stability since it was an eBay purchase, and it may have been broken.
So, in a 1965 setting, if you had to cross a 400 ravine 1-2 hrs of subtense wouldn't be the weak link in traverse. Try pulling a 400 ft tape at 1:20,000 in one pull.
If I started on it today, I would use fewer angles. But, I was trying determine: systematic error, scale error, realistic provable accuracy, procedures, and all completely analog. An EDM would not be better, just faster.
I yield on the quarter/mile. A quarter is 3" at a mile.
Holy Crap! I'm not ever going to argue with Mr. Scott.
For: Larry Scott
You say at 39 degree latitude, 1" of longitude is ~ 78 ft.
Where did you get this number?
On the Bessel 1841 ellipsoid at Lat. 39 deg., 1" of longitude = 24.0600 m ~78.9368 US survey feet
On the Clarke 1866 ellipsoid at Lat. 39 deg., 1" of longitude = 24.0635 m ~78.9483 US survey feet
On the GRS 80 ellipsoid at Lat. 39 deg., 1" of longitude = 24.0629 m ~78.9464 US survey feet
These 3 ellipsoid the distance would round to 79 feet not 78.
WHAT ELLIPSOID WERE YOU USING? and what book did you get your information from so I can try to reproduce your number.
A couple of good books on rounding of numbers are:
Numerical Mathematical Analysis by James B. Scarborough and Introduction To Numerical Analysis by F.B. Hildebrand.
Just to list 2 of many.
JOHN NOLTON
Remember it's Imagining the size of a second of arc.
Nautical miles have had many definitions.
A common value was 6080 ft, which was to approximate 1 minute of longitude at the equator, and 1 minute of latitude, for mariners of centuries past.
The nautical mile is not an SI unit. So, pick which ever value suits you.
So, 6080Ìá60 äö 101.3 feet.
Nautical miles serve for navigation. A minute of central angle on the surface of the earth is about a nautical mile. 1/60 nautical is about a hundred feet. Useful with nav charts, tables, and reckoning.
6 significsnt digits isn't really called for with knots and a mag compass.
I can pace a hundred feet. I can't pace 100.00 ft.
Therefore, I can pace about a second.
Imagine that.
Useful in monument recovery and a handheld GPS.
JOHN NOLTON, post: 364350, member: 225 wrote: For: Larry Scott
I just read your post and would like to comment on some things.
1. Wild says that their "Precision invar subtense bar" accuracy is 25mm at 100 m.
2. At a angle of 1d 32m (exact) your distance should be 74.729 m not 74.730 m.
3. The DIN 18723 specification for a Wild T2 theodolite is 0.8 seconds (The Standard deviation of a mean direction measured in
face left and face right (FL+FR)/2 = 0.8 seconds
4. 1 second in a mile is 7.8 mm (a quarter is 24.2 mm in diameter, nickel is 21.24 mm in diameter, penny is 19.01 mm in diameter
and a dime is 17.75 mm in diameter.
5. In your taping of the distance( you say chaining but I know you DO NOT used a Gunter chain) you have close agreement but nothing was said that
the 2 tapes had been calibrated at NIST nor was the tension handle or thermometers calibrated.With #3 above I would think that you could turn less sets and get very good results.
How long have you been turning angles?
What type of T2 (old style or new).
What procedure do you use when you turn your angles?JOHN NOLTON
I had to chuckle.
"5. In your taping of the distance( you say chaining but I know you DO NOT used a Gunter chain)"
Division of National Mapping. Australia
From field practices manual.
1.18 Field Chaining
1.18.1 Chains
Most third order chaining has been done with the 300 foot steel band. However, future chaining will be done with metric bands, probably the 50 metre band. The characteristics of the 50 metre bands currently in use within the Division are:-
