Understanding the dimensional space of caves

[robjones]

Earth curvature is 78.4mm height difference per 1km at the equator, 78.7mm at the poles. Refraction usually makes this effect less.

Thank you for the correction. So its about two-tenths of an inch in a hundred yards. My dim and distant recollection of basic survey 1981 was out by a factor of five.  :-[

That's a bit under a metre over the c.15km extent of Mammoth Cave mentioned up-thread. In a high grade traditional surface survey to plot entrance locations (and hence to establish a framework on which to base the underground survey) that would be worth taking into account I think - but very few cave surveyors possess instruments to work to such accuracy that curvature becomes worth taking into consideration.

Excellent cartoon about "What your favourite map projection says about you": http://xkcd.com/977/

 

[Les W]

That's a bit under a metre over the c.15km extent of Mammoth Cave mentioned up-thread. In a high grade traditional surface survey to plot entrance locations (and hence to establish a framework on which to base the underground survey) that would be worth taking into account I think - but very few cave surveyors possess instruments to work to such accuracy that curvature becomes worth taking into consideration.

Apart from analy retentive geekdom or severe OCD, why would somebody need a survey that was that accurate? 1 metre over 15km is far more accurate than anybody could ever need in the caving world.
Most people only want an idea of where they went and the more dedicated diggers only want a reasonable indication of what might join some passage to another in the same or different cave...
A show cave needing to drill into an area for a radon fan or to extract water and such like would be very happy with an accuracy or 1m over 15km and they are possibly the most likely use for a super accurate survey.
I expect even somebody tunneling over those distances (15km) would be more than happy with an error that small. (0.0066666666666667% error).  :-\

 

[Roger W]

What I found interesting in Ben's original post was his example of 3-D modelling using crochet.

Do you think this medium could have any possibilities for 3-D cave mapping/modelling?

 

[Amy]

I'd be willing to take a knack at it...I've done crocheting of the knots up through 7 crossings. Crocheting cave space seems fun!! I love the idea!

Uh for those not familiar with knot theory:
http://www.math.toronto.edu/~drorbn/KAtlas/Knots/

 

[TheBitterEnd]

Apart from analy retentive geekdom or severe OCD, why would somebody need a survey that was that accurate? 1 metre over 15km is far more accurate than anybody could ever need in the caving world.
Most people only want an idea of where they went and the more dedicated diggers only want a reasonable indication of what might join some passage to another in the same or different cave...
A show cave needing to drill into an area for a radon fan or to extract water and such like would be very happy with an accuracy or 1m over 15km and they are possibly the most likely use for a super accurate survey.
I expect even somebody tunneling over those distances (15km) would be more than happy with an error that small. (0.0066666666666667% error).  :-\

And no one is going to get a survey that accurate over those distances anyway with conventional cave surveying techniques (that's likely to start a flame war  ).

Re tunneling, I was once a site engineer on a tunnel over 2km long. The tunnel lining was about 2.9m external diameter and we had to hit a shaft eye that was 3m in diameter, we were out by about 15mm when we finished. The max allowable error would have been a bit more than twice what you quote -0.0025%.

 

[robjones]

Simplon met with a horizontal misalligment of 7.87" over 19,755.52m (apologies for mixed units but thats what Sandstrom gives in 'A History of Tunnelling', London, 1963) = about 0.0000012%. The vertical misalligment was 0.087m. Sandstrom states that "In America, the headings [of modest length tunnels] meet on a dime; if the tunnel is not too long a skilled instrument man will hit the dime's edge."