Old survey data, or, I can't do trigonometry...

[Peggy Renwick]

I work at a state-owned cave in Tennessee, and the cave is a system with 3 entrances: the main, historic entrance is separated from the other 2 by a siphon. My husband and I have surveyed more than half a mile in part of the cave accessible through one of these upper entrances, and our data is entered straight into Compass, so the computer can do all the number-crunching work and all I have to do is draw the map.

I've recently borrowed from work a copy of the survey notes of the historical/commercial section - more importantly, the numbers - with the hopes of entering them into Compass, to see what the rest of the survey looks like and how close ours comes to it. The survey was done in 1977-78, and the data include about 40 pages of Cave Survey Data Sheets, where chunks of the raw data are written and then Cosine is calculated, etc.

I'm trying to figure out how to extract the raw numbers, to plug 'em into Compass. I can't use the actual survey notes, although they are included in what I have, because this packet is a copy of a copy and the actual survey notes are mostly illegible.

So, back to these Data Sheets. The data on the sheet, for each survey shot, are given in both mills/meters, and feet/degrees. I want to use feet and degrees, and the columns are: (Distance) Feet; (Azimuth) Degrees; (Angle) Theta (that's the O w/horizontal line, right?); (Cosine) Theta; (Distance) Horizontal Feet. Great, right? It should be all there...

But, for most survey shots, the (Angle) Theta and (Cosine) Theta columns are empty. It seems they rarely took a vertical angle. Most shots only have Distance, Azimuth and Horizontal Feet Distance.

Does anyone have any clue as to why this would've been done? That is, was it standard practice in the late '70s to forego the inclination reading if the shot "looked" level? Most of what they were surveying was old tourist trail, so it is pretty flat, but still...!!

Then there's the fact that the survey was started at the cave's iron gate - because, apparently, that was "the one point in the cave that won't change." Is it worth the trouble of entering 30 pages of data into Compass?

[Rick Brinkman]

I have similar data sheets and the same problem. Have you tried to track down the surveyors and get the original survey notes??

I haven't tried to do the 'backwards' math because I don't know what they used for declination 30 years ago or even if they put it into their calculations. To make it worse, they apparantly had a large error on at least one survey.

Some of my sheets are even the next step that have only the XYZ coordinates. These are actually better, but again, I don't know what declination was used. Another concern is the number of errors that could have happened while doing all the math by hand.

[Roppelcaver]

There was a fair amount of "flat-taping" in the 70s, where vertical angles were only used to correct a slanted shot. I had seen it mostly around the Mammoth Cave area, but it was probably more pervasive than that. I mostly saw it in wet caves where they were surveyed in long lakes. To this day, we might forego the vertical angles on near-sumps by keeping stations a known distance (measured) above the water surface. In this unique case, this is probably more accurate than using inclinometers.

They did it at Mammoth Cave until about 1980, where you would do no vertical angles by keeping the tape "flat", measuring vertical changes where necessary. These surveys have largely been replaced, or are given nominal weight in closing loops (the old survey might be in something not worth redoing).

Of course, it sounds like you should just resurvey it anyway, if for no other reason than the sketch is probably not very usable.

I used to do this all the time, using cosine tables and a basic calculator to determine "latitude" (N/S) and "departure" (E/W).

I would have to see these data sheets to offer specific guidance.

But, I can offer some basics:

- Where they did not have a vertical angle, you assume the shot if flat (vertical angle = 0).

- For survey data, you calculate the X/Ys doing the following:

For the X Coordinate

X(tsta) = X(fsta) + SIN(azi)*(COS(va)*tape)

For the Y Coordinate

Y(tsta) = Y(fsta) + COS(azi)*(COS(va)*tape)

(If there were no vertical angles, COS(va)*tape = tape (Cos(0)=1))

--

I don't know what data you have, so I cannot offer a solution to reverse the results, but you should be able to fiddle with the equations to come up with the correct construct.

Each vector (shot) makes a right triangle, with the "legs" being the X and Y values (of the shot) and the hypotenuse being the horizontal taped distance. You can use the Pythagorean Theorem to figure out the horizontal tape (X**2 + Y**2 = C**2, where C is the hypotenuse).

If you have the X and Y values, you can easily calculate the polar vector values (C is the horizontal tape).

ARCSIN(X/C)= Azimuth

or

ARCCOS(Y/C) = Azimuth

If the shot was actually measured for a vertical angle, you can do the same thing (the taped distance is the hypotenuse (C), the horizontal tape (X) and vertical height (Y) are the legs.

Hopefully, this is a help.

[Peggy Renwick]

I have similar data sheets and the same problem. Have you tried to track down the surveyors and get the original survey notes??

Besides the fact that ten pages of data sheets are <i>missing</i> from the set I have...Well...we're trying to get a good chunk of data, same cave, from one of its original surveyors and it's kinda like pulling teeth (though we sent him our new data, with copies of everything, months ago). Chalk it up to his long distance from here...

I haven't tried to do the 'backwards' math because I don't know what they used for declination 30 years ago or even if they put it into their calculations. To make it worse, they apparantly had a large error on at least one survey.

In terms of declination - can't a lot of survey software calculate the declination based on the location of the cave, and the date of the survey? Or would using a calculated declination introduce a whole set of new errors?

[Peggy Renwick]

Of course, it sounds like you should just resurvey it anyway, if for no other reason than the sketch is probably not very usable.

For now, we're more interested in a line plot, to help us figure out where they were in relation to where we are - it'd be great to get around the sump, for example.

And my boss is somewhat willing to let me resurvey that section of cave, on work time perhaps! but I've only got 'til the end of the summer and then I'm moving far far away, so we probably wouldn't get through all 3+ miles of cave.

Very helpful numbers, though! Thanks! And the history is equally enlightening...might just plug it all into Compass to see what we end up with.

[Roppelcaver]

Walls certainly calculates declinations based upon dates and Lat/long. Compass, I think, does to.

The only consideration is whether the original surveyors applied the declination somehow when they copied the data onto these sheets. I doubt that they did actually.

Just make sure that the declination is applied in all cases. In may not be automatic and you have to set something. And, the drift over that many years is close to 5 degrees.

So, if you "back out" the polar coordinates, enter them into Compass, Compass can correctly apply the declination.

[Rick Brinkman]

Thanks for the trig formulas!! I'll try to back-calculate my 'old' data too!

Shouldn't be too hard to set up a spreadsheet to do it.

[George Dasher]

My guess, is that once you do the trig, you're going to find that the data isn't much good.

Those supposed horizontal distances are also probably slope distances, although most of them are probably very horizontal.

Given that there is no sketch and the data is suspect, I would give some serious consideration to resurveying the passages.

But Good Luck!!

[George Dasher]

Here's a website to calculate magnetic declination...

http://www.ngdc.noaa.gov/seg/geomag/magfield.shtml

[Peggy Renwick]

Given that there is no sketch and the data is suspect, I would give some serious consideration to resurveying the passages.

But Good Luck!!

...thanks!
I wish I had the time and resources to get really into this project! I'll definitely talk it over with the bosses, just in case they see it as a priority - even if they don't, I might try to at least get the project going in the hopes that it'll continue when I leave.