A one-hundred-foot diameter geodesic sphere weighing three tons encloses seven tons of air. The air to structural weight ratio is 2/1. When we double the size so that geodesic sphere is 200 feet in diameter the weight of the structure goes up to seven tons while the weight of the air goes UP to 56 tons-the air to structure ratio changes to 8/1. When we double the size again to a 400 feet geodesic sphere - the size of several geodesic domes now operating - the weight of the air inside goes to about 500 tons while the weight of the structure goes up to fifteen tons. Air weight to structure weight ratio is now 33/1. When we get to a geodesic sphere one-half mile in diameter, the weight of the air enclosed is so great that the weight of the structure itself becomes of relatively negligible magnitude for the ratio is 1000/1. When the sun shine& on an open frame aluminum geodesic sphere of one-half mile diameter the sun penetrating through the frame and reflected from the concave far side, bounces back into the sphere and gradually heats the interior atmosphere to a mild degree. When the interior temperature of the sphere rises only one degree Fahrenheit, the weight of air pushed out of the sphere is greater than the weight of the spherical frame geodesic structure. This means that the total weight of the interior air, plus the weight of the structure, is much less than the surrounding atmosphere. This means that the total assemblage, of the geodesic sphere and its contained air, will have to float outwardly, into the sky, being displaced by the heavy atmosphere around it. When a great bank of mist lies in, a valley in the morning and the sun shines upon it, the sun heats the air inside the bank of mist. The heated air expands and therefore pushes some of itself outside the mist bank. The total assembly of the mist bank weighs less than the atmosphere surrounding it and the mist bank floats aloft into the sky. Thus are clouds manufactured. As geodesic spheres get larger than one-half mile in diameter they become floatable cloud structures. If their surfaces were draped with outwardly hung Polyethylene curtains to retard the rate at which air would come back in at night, the sphere and its internal atmosphere would continue to be so light as to remain aloft. Such sky-floating geodesic spheres may be designed to float at Preferred altitudes of thousands of feet. The weight of human beings added to such prefabricated "cloud nines" would be relatively negligible. Many thousands of passengers could be housed aboard one mile diameter and larger cloud structures. The passengers could come and go from cloud to cloud, or cloud to ground, as the clouds float around the earth or are anchored to mountain tops. While the building of such floating clouds is several decades hence, we may foresee that along with the floating tetrahedronal cities, air-deliverable skyscrapers, submarine islands, sub-dry surface dwellings, domed-over cities, flyable dwelling machines, rentable, autonomous-living, black boxes, that man may be able to converge and deploy around earth without its depletion.
Text and drawing by: R. Buckminster Fuller