The Energy Efficiency of Spheres

Environment-controlling buildings gain or lose their energy as "heat o cool" only through their containing surfaces. Spheres contain the most vololume with the least surface—i.e., have the least possible surface-to-volume ratio. Every time we double the diameter of a spherical structure, we in¬ crease its contained atmosphere eightfold and its enclosing surface onlyily fourfold. When doubling the diameter of our sphere, we are not changiring the size of the contained molecules of atmosphere. Therefore, every time wwe double a spherical structure's diameter, we halve the amount of enclosing surface through which an interior molecule of atmosphere can gain or losose energy as "heat or cool." Flat slabs have a high surface-to-volume ratio, and so flat slab fins make good air-cooling motorcycle and light-airplane en¬ gines. Tubes have the highest surface-to-volume ratios. Triangular- oi square-sectioned tubes have higher surface-to-volume ratios than have round-sectioned tubes. Tall slab buildings and vertical, square-sectioned, tubular-tower skyscrapers have the maximum possible energy (as heat or cool)- losing capability.

One two-mile-diameter dome enclosing all the mid-Manhattan buildings between Twenty-second and Sixty-second streets and between the Hudson and East rivers, having a surface that is only one eighty-fourth that of all the buildings now standing in that midtown area, would reduce the heating and cooling energy requirements of that area eighty-four-fold.

R. Buckminster Fuller, Critical Path (1981)

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