0 Cartography
THE OCTET TRUSS
1It was indicated earlier that the Vector Equilibrium could be subdivided into tetrahedrons (four-sided pyramids) and octahedrons (eight-sided ‘‘solids’’); actually it is composed of eight tetrahedrons and six half octahedrons.
2 A complex of Vector Equilibriums joined together form a matrix of alternating tetrahedrons and octahedrons. Such structures form what Fuller calls the Octet Truss. A frame built of tetrahedron-octahedron combinations provides an omnidirectional and equal dispersion of load pressures, with no member of the truss duplicating the function of any other. For this reason the truss has an enormous load-carrying ability; and its strength to weight ratio increases as the truss grows in size.
3 In 1953, at the University of Michigan, Fuller load tested an Octet Truss made of 170 slim 33’’ aluminum struts, each weighing one-third of a pound. The entire truss, when riveted, weighed 65 pounds. This frame, no heavier than an ordinary canoe, supported a total load of six tons, the weight of a small army tank.
4 Fuller himself did not expect such a performance from the tetrahedron-octahedron combination. It was a surprise—the behavior of a whole not predicted by its parts. Describing the Octet Truss in a letter to his patent attorney, Donald W. Robertson, Fuller wrote, almost apologetically, ‘‘I am sorry that my whole family of inventions tends, by rational acceleration, to sneak up on you and press you for attention. But isn’t this the nature of invention? Invention is always a surprise.’’
TENSEGRITY
5The Wichita Dymaxion House had been designed to be delivered across the Pacific in a single DC-4. 1927 h°use
6 was to be delivered by dirigible. The passing of two decades had been marked by such improvements in technology that shelter delivery was now possible by heavier-than-air aircraft.
7 After the Wichita House, Fuller concentrated on the problem of air delivery. He had never departed from his 1927–4D assumption that the air is our ultimate ocean, and that man’s ‘‘mobilizing, recirculating, design-regenerating technology’’ will eventually evolve into gossamer. But evolution toward gossamer depends on radical weight reduction; a spider’s web can float in hurricanes only because of its high strength-to-weight ratio. For new design strategies aimed at radical weight reductions and strength intensifications, Fuller once again scanned the premises of his Energetic Geometry; he explored possibilities of intertwining the geometry with the inventory of war-developed technical advances.
8 In the planned 1927–4D house, Fuller had minimized weight by separating compression members from tension members. The central mast was a compression unit, around which hung a multiple-rimmed tensionally-cohered, horizontal wire wheel house structure. Guy wires supporting the mast provided the balancing tension. In developing the Wichita house, however, he discovered that as he increased the diameter of the mast-and-guy-wire complex, the over-all mast complex weight grew less. And ultimately, at its dimension of least weight, the mast complex structure was congruent with the outside shell of the house.
9 When this ‘‘congruent phase’’ had been reached, the inner wall of the shell (the ‘‘mast’’ complex) would be in compression, the outer structure would be in tension. Although to the viewer there would be no visible separation of compression and tension elements, there was nevertheless a universal, comprehensive tension system in operation; this system laced the entire structure into a single, finite, energetic embrace.
10 The universal comprehensive tension system could be interspersed locally with islands of compression, in the form of struts, in such a manner that the islanded compression struts would not touch one another. Yet these struts would force the tension network into outward patterning from the center of the total structural system in precisely the same way that molecules of gas inside a balloon press the balloon bag outwardly from its center.
11 Fuller saw that the gas molecules in balloons were not exploding in a radial pattern from the center of the system, but were bouncing around the inside circumference of the balloon, as sounds bounce around the wall of a circular structure. But if the skin of a plastic balloon is viewed with a microscope, it is found to be full of holes. Therefore it was clear to him that an accurate description of a balloon is a ‘‘network’’—but one in which the holes in the network arc smaller than the molecules of gas. These molecules, coursing independently of one another like so many herrings inside a weir, impinge upon the weir net repeatedly, thus forcing it to balloon outwardly. Thus the action is not the result of a consolidated, group effort of the herrings in a shoulder-to-shoulder radial attack outwardly, in all directions, against the net, but rather of the high frequency ricocheting impingements of each herring.
12 This theoretical consideration of balloons and fish nets, herrings and molecules, suggested that the comprehensive tension network of his structural system could be patterned in such a manner that the individual compression struts would not touch one another, yet would hold the tension network outwardly in firm spherical patterning. That is, Fuller saw that he might be inventing a spherical building in which the bricks, or compression members, did not touch one another. Thus there would be a spherical building of bricks, in which the bricks would be interlaced with ‘‘rubber bands’’; each brick would be in effect restrained from escaping from the pattern only by the rubber bands for no brick would be in direct contact with any other brick.
13 Fuller later concluded, after he had developed and successfully demonstrated a variety of discontinuous-compression, continuous-tension structures, that it was only the habitual tendency to think of all forms of matter in terms of brick-on- brick structuring that led to the assumption that the structure of the atom’s nucleus could not be represented by a model—‘‘even though the nuclear physicists had discovered certain geometric system pattern relationships with respect to the nuclear coherence.’’
14 Fuller called this special discontinuous-compression, continuous-tension system the Tensegrity.
15 What is startling about the conception is its pertinence to fields which ordinarily seem to be unrelated. Tensegrity supplied a generalized approach to the most economic forms of ‘‘man-occupiable’’ structures. And again, as nuclear physicists have suggested, it might provide in fact a true model of the atom’s nuclear structure.
16 To understand how his compression struts could be successfully islanded from one another while thrusting the net outward, it is only necessary to think of a large number of pairs of live herrings, with the members of each pair so close to each other that the two appear as a unit. Each of these unit-couples are approximately evenly spaced away from the other couples but all of these evenly dispersed couples are within a complete spherical fishnet dropped into the ocean by a trawler (the neck of the net has closed after the herring have swum inside and the connecting line to the trawler has been inadvertently severed).
17 Imagine the herring pairs setting up a patterned herring dance; each member of each pair takes a position facing away from the other; then swims away from its partner, and continues in a straight line until it strikes the net—even if only with a glancing blow—thus pushing the net outward. After making a racing swimmer’s turn, each herring races swiftly in a straight line back again to its mate, joins the mate momentarily, and then repeats this out-to-the-net-and-back linear darting, over and over again. Thus, we have a pis cine ballet pushing the net outwardly in all directions.
18 Let us substitute for each pair of herrings, one round rod, whose two ends represent the two members of the couple; and arrange a pattern of these rods, acting as chords within a sphere, pushing at an acute angle in the opposite directions against the net in such a manner that the sum total of chordal patterns provides an omni-triangulated grid wherein the point of impingement of one rod is congruent with the mid arc of the chorded action of the next rod. It will be seen that such triangulated outward-pushing can be independently accomplished by the positive and negative chordal impingements on the net; yet the chords’ ends will not be in continuous array.
19 This Tensegrity network principle could also be demonstrated in a linear manner—as Fuller, enlightened by a linear Tensegrity discovery of his student colleague, Kenneth Snelson, showed by developing a series of Tensegrity masts. From 1949 to 1952 his Tensegrity’ masts were exhibited on the campuses of many universities, including the Massachusetts Institute of Technology, the University of Oregon, the University of Michigan, and North Carolina State College.
20 The Tensegrity principle in its spherical omni-triangulation intensifies the structural integrity of Fuller’s Geodesic structures.
21 It can be seen that Fuller’s Tensegrity geodesics, like fishnets or balloons, could result in highly flexible surfaces. WTien it is desirable to have a Geodesic integrity with a non-mushy exterior, Fuller provides concentric Tensegrity spheres, one of lesser radius than the other, and the inner one of one modular frequency less than the outer. He interlaces the inner and outer spheres respective omni-triangulated point patterns. Each of the inner points connects outward to three of the outer points; and each of the outer points, as a result, is found to be interconnected to three inner points. The resulting inter-triangulating of the concentric Tensegrity spheres provides an Octet Truss.
22 The Octet Truss, in this spherical arrangement, will be seen to be the same finite omni-triangulated patterning of Fuller’s energetic-synergetic geometry, closest-packing Vector Equilibrium layers of any modular radius and frequency.
23 Compression columns have a limit slenderness ratio (the ratio of column length to cross-section diameter). If this ratio is exceeded, the column (strut) will buckle. (The slenderness ratio of a column of ordinary steel is approximately 33 to 1.) On the other hand, tension cables have no inherent limit ratio of section diameter to length. The ‘‘pulling strength’’ of a cable is the same in lengths of two feet or two miles. Thus it can be said that compression is limited and tension unlimited in relative slenderness ratio magnitudes, and their respective structural applications.
24 It followed from this that structures developed according to Tensegrity principles, with discontinuous compression, continuous tension, have no size limit. Theoretically it is possible to dome the entire earth in a Tensegrity envelope. Unlike other structures, Tensegrity domes increase in strength by a factor greater than that governing their growth in dimensions; the larger they are made, the stronger they become. It is only at the toy-size level that their strength-area relation does not show up to dramatic advantage.
25 Even at this writing, Fuller has plans developed for structures now feasible which could dome in all of lower Manhattan, or the site of an entire town. Such a dome, erected in the Antarctic, would give colonizers a temperate environment long before actual living and industrial facilities were installed.