Fuller designed this megastructure with the help of Shoji Sadao. The geometrical principle behind this design is that for an expanding sphere, the volumetric increase is greater than the surface area increase, so that ratio of volume to area increases with the size of the sphere. For spheres hundreds of feet wide, the weight of the air enclosed may be considerably greater than that of the structure itself.
At a certain critical volume, the weight of air displaced by expansion due to heating by sunlight exceeds the weight of the structure, so the combined weight is now less than an equivalent volume of air at prevailing temperature. Then the sphere floats, being less dense than the air surrounding it. According to Fuller, a half mile sphere would float.
This design is discussed and illustrated on p.235 of Dymaxion World, and p.336 of Critical Path.
It so happens that assessment of this idea is complicated by a surprising amount of inconsistency in the mathematical explanations offered by Fuller and his commentators. This raises issues in design geometry, not to mention numeracy, and these are discussed in Cloud Structures Analysis.
For broader discussion, together with a story about a horse, see Size And Shape.
© Paul Taylor 2001