It appears there is a full-specifics article in Science, but I don't have access to it. However, someone on Liftport does, and posted an excerpt:
Especially considering the absence of polymer binder, the mechanical properties of the aerogel-like and densified MWNT sheets are unexpectedly high, which is probably a consequence of the interconnected fibril network (fig. S2). The density-normalized mechanical strength is much more accurately determined than mechanical strength, because the sheet thickness is less reliably measured than the ratio of maximum force to mass-per-length in the stretch direction. Stacks of undensified sheets have an observed tensile strength of between 120 and 144 MPa/(g/cm3) (fig. S5, A and B). A densified stack containing 18 identically oriented sheets had a strength of 465 MPa/(g/cm3), which decreased to 175 MPa/(g/cm3) when neighboring sheets in the stack were orthogonally oriented to make a densified biaxial structure. These density-normalized strengths are already comparable to or greater than the ~160 MPa/(g/cm3) strength of the Mylar and Kapton films used for ultralight air vehicles and proposed for use in solar sails for space applications (21) and those for ultra–high-strength steel [~125 MPa/(g/cm3)] and aluminum alloy [~250 MPa/(g/cm3)] sheets.
Sheets generally have much lower limiting strengths than do fibers of the same material. However, at a value of 465 MPa/(g/cm3), the tensile strength of the densified MWNT sheet is comparable to or exceeds reported values for nanotube fibers and yarns that do not include a binding agent: 575 MPa/(g/cm3) for forest-spun twisted MWNT yarns (12), 500 MPa/(g/cm3) for aerogel-spun yarns (7), 105 MPa/(g/cm3) for SWNT yarns spun from superacids (22), and 65 MPa/(g/cm3) for SWNT yarns spun using an acidic coagulation bath (23). Order-of-magnitude or greater increases in mechanical strength have been observed when internanotube coupling is enhanced by polymer incorporation into nanotube sheets and yarns (23–26), and similar strength increases might be achievable by infiltration of suitable polymers into the present MWNT sheets.
There's also some discussion that at present, the nanotubes in the buckytape appear to be adhering only by Van der Waals forces between neighboring nanotubes.
So, to summarize that for my less technical readers: As stands, without any kind of resin binder, the buckytape appears to be around four times as strong, weight-for-weight, as ultra-high-strength steels, and adding an appropriate polymer binder might increase that to as much as forty times as strong.
There's also some speculation in that Liftport thread that starting with longer buckytubes may yield a proportional or near-proportional increase in tensile strength, something I have speculated on myself. If so, then assuming one could find the correct binder and triple the length of the individual nanotubes, 100 times the tensile strength (weight-for-weight) of the strongest steels currently known ought to be within reach.
Oh yeah, glossary: SWNT = single-walled nanotube, MWNT = multiple-walled nanotube (concentric buckytubes, essentially), MPa = megapascal. One megapascal is approximately 145 pounds per square inch, or approximately 10.44 tons per square foot, so 465MPa/(g/cm3) would mean that, to pick simple numbers, a buckytape cable a foot square with the density of steel (7.8 grams per cubic centimeter, about 4.5 ounces per cubic inch) could support on the order of 39,000 tons. As discussed above, using the correct binder and doubling the nanotube length might increase that to as much as 800,000 tons.
(It should be noted that this density is somewhat improbably high for a carbon cable, but it makes an easily-visualized comparison.)
Update:
rbos has graciously provided a link to a PDF copy of the Science article.
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Next you'll be saying you don't like the idea of sandmen chasing down runners who didn't turn themselves into renewal.
*grin*
Seriously, though, controlling the weather inside cities through transparent domes/tents seems like it would have some positive impacts. And then there's the whole 9/11 thing. What down-sides do you see?
Well, see the previous note about trapped pollution, air exchange, and greenhouse effect, for starters.
It also means any city that wanted a tent and had airports within the city would have to close them and build new ones outside the tent. (It might be possible to build "airlocks" for seaports, but I have severe doubts about it being actually feasible.)
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I'm not terribly worried about trapper air pollution/etc. You've got to suspend the tent on something, and that can have air processing and ventilation units.
In fact, it could make a great way to do a solar tower: the tower holds up the tent, and at the top of the tower is a turbine that extracts kinetic energy from the air that wants to rise out of the top of the tent. (and, even if this material wont help with building the structure of a beanstalk, it might help with building the structure of a solar tower)
And, because the air is trapped, you can actually do more with it, not less, in terms of dealing with air pollution. Depending upon how you segment the tent, you could move the air artificially, and those movement points could involve air filtration to remove nasty things from the air.
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Of course, if we pollute the atmosphere badly enough, we might end up not having a choice....