Old Scool traverse question

Old School traverse question

According to my "old school" textbook (Davis, Foote, & Kelly, 1960's) the standard method of traversing would be to hold the tape level and "break tape" as needed according to the elevation change. Whenever the elevation changes too much to manage the tape, use a plumb bob at the high end, held on an even foot mark, over a point on the ground and then move forward to repeat. Taping downhill is easier than uphill.

Stadia has some other corrections to be made when looking at an elevated angle, not just the cosine. See the books to estimate how serious that is for your case.

In any case, the accuracy isn't going to be great by modern standards. My book indicates that casual measurements by stadia may be 1:100 and more careful ones 1:300, with the best hardly approaching 1:1000.

By comparison, reasonably careful taping over smooth ground with temperature and tension/sag correction should be better than 1:1000 and careful expert taping under good conditions (but not using special apparatus:(no taping bucks or magnifiers), can be better than 1:3000.

For slope, your first method would not be old-school because of the complicated calculation. However it might be more accurate than the second.

Your second method would be easier to calculate. Be sure to plumb the rod carefully or you'll get a possibly surprising amount of error.

Now the experts can correct me.

Yesterdai I Could Not Spill "Scool", Tuday I Are A Teecher

Enough fun, back to Surveying 101. "Breed and Hosmer", Elementary Surveying, page 17, first day of class.

Slope measurement = s, difference in height = h, horizontal distance = d.

With todays calculators stick with Pythagoras, d² = s² - h².

"Old school" is a pencil math shortcut, d = s - (h²/2s).

My father first taught me that in the field at 12 years old.

As to stadia, use a plumb rod and do the math. It is too hard for a less experienced crew to rock the rod for shortest reading and communication.

As I said in an different post, I still have my father's Philadelphia rod with 3 targets, for 1000' sightings. Using hand signals, once the targets are set, the instrument man and the rod man, record the readings, comparing notes later.

Paul In PA

You should always read a stadia shot with a plumb rod..... you do not "rock" it. Read all three wires. The stadia intercept is the lowest reading subtracted from the highest. Multiply that difference by the cosine squared of the vertical angle to get the horizontal distance. BTW each 1/100 equals a foot of distance. The center reading can be used to further check your math and the other two readings. This method applies to modern theodolites or any instrument with a 100 stadia coefficient. Keep in mind I am recalling a long ago lesson from my ICS survey correspondence course for the method so it may all be wrong.... if so I am sure someone will correct me.:-)
Good Luck

Yesterdai I Could Not Spill "Scool", Tuday I Are A Teecher

Thanks. I got the math down, but the way you describe it makes it simpler. Don't need to account for HI prior to doing the trig. Just do the trig to ascertain the height difference between the sighted point and the instrument, then add the height of the instrument.

The 1960's book indicates that there is an offset (perhaps part of a foot?) to be applied to even a horizontal stadia reading of the transit to account for the way the optics work, i.e., the position of the focus point.

There's a cosine in converting the reading on a vertical rod into a slant distance and another in converting the slant distance to horizontal.

Horiz = Ks * cos^2(a) + C * cos(a)
Vert = Ks * cos(a) * sin(a) + C sin(a)
where
a is the vertical angle from horizontal,
Ks is about 100
and C is small
Ks and C are to be determined for each instrument by stadia measurement of known distances.

Are any modern total stations set up with a precise 100:1 reticule so you can do stadia if your batteries die?

wouldn't be able to read the angles with no batteries unfortunately.

You Can Read Angles With Low Batteries

But you cannot shoot a distance, or send the angles to a data collector.

I have finished up a few projects with an instrument with no power for distance. Hand write the angles in the filed book, assuming you know what a field book is, and tape the distances. Yes we still carry plumb bobs. I sometimes find it necessary to come back and actually shoot a point or two, but not losing that day before you evaluate your data can make or break a project.

On a cold day it sometimes is necessary o warm up the batteries a few times to milk out the last few shots.

This requires thinking like an owner, not an hourly employee.

Paul in PA

No, But Modern Level Guns Have Stadia Lines.

A level gun is adequate for more than 90% of the topos most surveyors do.

Paul in PA

You Can Read Angles With Low Batteries

Hand write the angles in the field book, assuming you know what a field book is, and tape the distances.

LOL! I'm certainly using a field book! And no batteries or data collector for my Topcon AG2 gun!

Take a look at https://engineering.purdue.edu/~asm215/topics/stadia.html for cases when observing inclined sighting.

Dang you sure brought back old memories. Typically we never traversed w/stadia, but it was very common to do a topographic survey with it. One guy reading "top wire, bottom wire, middle wire, horizontal angle, zenith angle" with the note-taker writing as fast as he could. Esp in the mtn's you could almost never read three wires at a 90 zenith. We would keep as level as we could to avoid introducing more error. If we put a vertical in the gun we would often put the bottom wire on an even foot. The note-taker would make a quick calculation in his head to make sure the center wire was halfway between the top and bottom before calling off the rodman. All day long reading three wires. The notetaker writing till he had cramps in his hand. (Not just all the numbers but noting what the shot was).

Anyway, take note of the extra calculation if you have any steep vertical change as couple of guys have mentioned. Have fun.

rfc, That Comment Was To Squowse

Paul in PA

And the first round results are in...

Well, I'd put it somewhere between "borderline fail", and "promising but no cigar"....
Both stadia readings were long...after reduction, by an average of 1.4%, compared to tape...like 4' or so on one; 7' on the other...both around 400' shots. Not sure what's up with that.

The resulting closure of the original traverse, though, improved to about 1:7600 from below 1:5000 slogging uphill through the woods, using the measurements from the tape.

Using stadia, though, I noted that even at just 400' the stadia lines seemed like they were .05' thick! My old Topcon AG2 has a 25x scope; I note a lot of newer instruments have 30x. Also, I think the optics may need cleaning, because even in perfect focus, there seems to be a haze of sorts. It's just not like looking through my little Nikon binoculars.

Plus, I learned that the shimmering heat off the gravel drive I was working on, fuzzed up the stadia readings too. My eyes were watering by the time I called the measurements. I'm very impressed with what the "old timers" did in their day. This is work!

Cant wait to try EDM next, lol!

And the first round results are in...

Professor Clifford Crandall of Princeton University developed the Crandall Method of traverse adjustment specifically for Transit/Stadia surveys (for Rail Road engineering). His book was published over 100 years ago. "Geodesy"

OK, Report Actual Readings & How You Got Correct Results

So we can check your methods and math.

Also how long a Philadelphia Rod you have.

BTW +/- 1.7% is entirely adequate for a topo survey.

A good check is to lay out 100', 200', 300' & 400' stations. Level is not necessary and some up and down shots are preferable.

BTW, did you shoot forward and reverse as all precise work should be?

F&R averages out your level setup, vertical circle and horizontal errors.

Paul in PA

OK, Report Actual Readings & How You Got Correct Results

>
> BTW, did you shoot forward and reverse as all precise work should be?
>
> F&R averages out your level setup, vertical circle and horizontal errors.
>
> Paul in PA

I was using the first two sections of a three piece wooden rod...about 10 feet and change long.

Uh...on the forward reverse thing...My wife (my "rod man") was baking in the sun, and would have baked even more had I done reverse shots, so I let her off the hook. Finding good help in this business must be very hard.