Any assessment of the Cloud Structures proposal is plagued by the many arithmetical discrepancies in the source texts.
Both the Architectural Design article of Dec. 1972 and Pawley's book (p.155) make a dog's breakfast of the figures.
Closer examination of Fuller's own calculations also reveals arithmetical difficulties.
For expanding objects, length, areas, and volumes increase at different rates: areas increase in proportion to the square of the length, volume in proportion to the cube. If the length of a cube is doubled, the area is not doubled but quadrupled, whereas the volume increases eightfold. The same applies if a sphere's radius is doubled.
The air weight in the Cloud Structure must be directly proportional to the volume, and if we assume that the shell's thickness and density are constant, then its weight is directly proportional to the area.
Fuller postulates a 50ft radius sphere weighing 3 tons and containing 7 tons of air. Doubling the radius, he says, gives 7 and 56 tons respectively, and doubling again gives 15 and 500. From these figures, he gives the following air : structure weight ratios: 2:1, 8:1, 33:1.
According to the expansion rule given above, the 100ft radius should give 12 and 56 tons, and the 200ft radius, 48 and 448 tons. But then the ratios become 2.3:1, 4.7:1, and 9.3:1.
Fuller claims that a half-mile-wide sphere would yield a ratio of 1000:1, enabling lift-off. But if we start from his premises, such a ratio would only come from a sphere over 16 miles wide.
The initial figure of 7 tons of enclosed air is not demonstrated by Fuller. If we calculate from a basis of 22.4 litres of air weighing 29g, the figure becomes over 18 tons. To reach the 1000:1 ratio, we would then need a sphere "only" about 6 miles wide.
This ratio is itself unexplained, however. Conventional hot-air balloons float with much smaller ratios. The physics of gaseous expansion and buoyancy would presumably reduce the scale arrived at above.
For a general consideration, see Size And Shape.
© Paul Taylor 2001