Bucky Fuller wrote in a couple places (Critical Path, Utopia or Oblivion ) about geodesic structures called tensegrity(tensional integrity) spheres. One of the anomalies of their construction is that the larger they are the less they weigh in relation to the surrounding atmosphere. Fuller claimed that in a sphere with a half mile diameter, a one degree temperature change would cause the structure to float.
Was Bucky just talking out his ass here? Has anyone actually tried to test this theory? Do the materials used in the construction have an effect on the weight ratios?
Of course even if it works I can see problems when the thing equalizes(as it would, eventually).
1/2 mile hemisphere has a volume of 8.73e12 liters
At STP (22.4 l/mol) that’s 3.897e11 moles of gas
Raising the temp by a degree, at constant pressure:
p2v2/p1v1 = t2/t1
v1/v2 = T1/T2 = T1/(T1+1) = 273/274 = 0.9963504
Ignoring all the fidgety units, this is the fractional change in density.
3.897e11 moles X 0.9963504 = 3.883e11 moles under the dome at the new temperature.
Using 29 for the average molecular weight of air:
The atmosphere in the cold dome would weigh 1.13013e10kg
While in the warmer dome it would be 1.12607e10kg
A difference of 4.06e7kg or 44,713 tons of lift.
How much did Mr. Fuller say that a half mile dome would weigh ?
It’s been a while since I read about this, but I don’t seem to recall any concrete weights being given for the spheres, but rather some calculations stating that as the sphere is enlarged, its weight in relation to a similar amount of the surrounding atmosphere becomes less. If I’m remembering this right (which I can’t guarantee), the half mile mark is where the ratio equalizes and the temperature differential between the interior and the exterior of the sphere is enough to provide liftoff.
Of course, assuming this has any grounding in reality, you’re still in a world of hurt should the temperature equalize.
From The Dymaxion World Of Buckminster Fuller, figure 489
Johnny Q Tensegrity is a special discontinuous-compression, continuous tension system. You seem to be confusing that with geodesic structures. Tensegrity
I presume that the calculations assume that the thickness or weight per surface area of the geodesic structure remains constant. At 1/2 mile diameter it would probably be as proportionally flexible as a mylar balloon.
Also, given the height of the sphere, would the difference in air pressure between the bottom and the top make a difference?
Since I barely remember any physical science, could a tensegrity or geodesic sphere be vacuumed of air? So the 100 ft diameter sphere would have just a ton of air inside rather than 7?
Neal Stephson described airships built of nanotech structures full of vacuum in his book, Diamond Age. Any chance of that happening, or would temperature changes be too difficult to moderate
If you read DocCathode’s quote, it actually decreases. It looks like the mass goes linearly with radius (M[sub]ton[/sub] = 4R[sub]100ft[/sub] - 1) instead of quadratically like you’d expect: