Tensegrity by R. Buckminster Fuller

The revolutionary architect-engineer's own patent revelation about his basic structurial discoveries



Architect, engineer and cosmologist R. Buckminster Fuller and [Following] three of his basic structures: Tensegrity mast, Geodesic dome, octet truss in the Fuller exhibition, Modern Museum, N.Y.
Note from Robert Gray:

This paper appeared in Portfolio and Art News Annual, No.4, 1961. In addition to this article there is an accompanying Introduction by John McHale. Only the Tensegrity article is reproduced here by permission of the Estate of R. Buckminster Fuller.

An attempt has been made to re-produce the illustrations contained in the article. It is clear that I have had varying degrees of success. Please see the original article for the full sized, and possibly clearer, illustrations.


The following two photographs are Copyright 1960 Allegra Fuller Snyder

Courtesy, Buckminster Fuller Institute, Brooklyn, NY

All other figures are Copyright 1961 Allegra Fuller Snyder
Courtesy, Buckminster Fuller Institute, Brooklyn, NY



Tensegrity


by R. Buckminster Fuller
© 1961 R. Buckminster Fuller

It is commonly overlooked that the patrons of architects, engineers and professional craftsmen are inherently the prime designers of their projects. Theirs is the conceptioning, the will to do, the initiative and the statement of limits.
Conceivers of great industries and their trans-national patterning have been the large pattern-designers of the last world century. Those who have been successful world-industry designers have also been powerful anarchistic authorities.

In this last century many conceivers and concept-explorers have been unwilling to submit to patronage lest the patron compromise the potentials of their conceiving. Under the powerful economic network woven by the major industrial conceivers, economic survival was difficult for the untamed artists--for this they were.


In the long evolution of fundamental rights of men and the slow inhibition of these rights into the securing codes of society, the letters patent issuable to individuals who, on their own initiative, succeed in augmentation of the commonwealth have been common to all manner of governments. Absolute monarchs and republics have alike honored their individuals with temporary monopolies to replenish and regenerate their creative resources. Patents are operative in Russia and behind the Iron and Bamboo Curtains; patents are operative in the Western world. Patents are not operative, however, between these two world domains.


Amongst other fundamental experiments which I have been conducting over the last forty years has been the testing of whether the individual may achieve original formulations and initiate their realization in world economic patterning without either the compromising direct patronage or politically-seized dictatorial power. It seemed that the only possibility of so doing lay in the direction of patents secured entirely through the inventor's own economic means. Because I have been fortunate enough to have been befriended by many artists of extraordinary individual and original conceptual initiative, and because I have had the further good fortune to have gained long-time experience, not only in patent-law, but in patent-securing, -maintenance, and the broad economic ramifications of patent-holding in the most recent era of massive government and massive corporation (made more difficult by the shroud of official secrecy embracing the unprecedented technical acceleration of our era), I am eager to discuss the economic security of the artists and their potential joining of forces, as did the medical profession long ago, in the advantageous realizations for world democracy inherent in the artist-joined anticipatory competence.

It is a sad fact that the world of patronized design is the last area of commonly accepted social behavior where piracy is considered ethical. Patrons hire designers to steal their competitors' work. Patrons hire designers to steal other non-professional designers' fresh-new crops of potential economic growth. Only by joining forces will the architect-, scientist-, engineer-artists be able to eliminate this intellectual cancer of the regenerative processes.

I am going to discuss a special case of structural exploration and invention. This published discussion constitutes what is legally called "public disclosure" of an invention which I have "reduced to practice," which latter reduction puts me by common law in the powerful position of holding momentary monopoly of the economic employment thereof. I have fortified this common-law position with patents already obtained, as well as patent applications in process. I fortunately hold several patents covering geodesic structures in America and in almost every other country in the world which subscribes to the Berne (Switzerland) patent convention. If I did not have this patent protection, I am confident that neither the government nor any of the great industrial corporations would in any way have recognized my invention of these structures. Though big government has spent billions in noneffective structural research, I frequently encounter the statement by government and corporation bureaucrats that they consider it their duty to the taxpayer to use their enormous powers of specification and purchase to circumvent my patents covering structures which I had anticipatorily invented at my own expense and developed to satisfy society's needs under just such emergent necessities as those confronting the bureaucrats. The basis of their contention is that the few thousands of regenerative dollars that may be returned to me represent an immoral exploitation by the individual of democracy's emergency needs. They completely overlook the billions of taxpayers' dollars they have already fruitlessly spent in their intra-mural budgetary politics, attempted under the supposition that they will be rewarded by their incumbent masters if they can stretch yesterday's investments to cover tomorrow's evolutionary transformations. How can they justify large research and development budgets for next year if it were visible that the original technical gains were accruing exclusively to society from the individual preoccupations and initiatives existing entirely outside of massive government and massive corporate manufacture and distribution? The self-deceit of democracy at this moment in history by its professionally advertised aggrandisement of the "corporate image" with reputed impeccability of super-inventiveness may be the undoing of democracy's case until another century has washed away this miasmic fallacy. Not only have these professional word- and picture-factories manufactured the greatest and most persuasively erroneous myths, but they also have robbed our heritage of word- and picture-language of its incisively exquisite effectiveness. The primary tools of men have been blunted and misappropriated. Bereft of the age-long developed tools, artists of our day have sought for new and vital means of communication. The beatnik is the anti-body of Madison Avenue. The true artists seek escape from the stale-mated vacuum of the two. History tells us that they will probably be successful. The probability is that the artists will win enjoyment of our whole earth by all the world's people--with the complete emancipation of man's innate freshness and regenerative conceptioning.


PATENTS AND NATURAL PRINCIPLES

One cannot patent geometry per se nor any separate differentiated-out, pure principle of nature's operative processes. One can patent, however, the surprise complex behaviors of associated principles, where the behavior of the whole is unpredicted by the behavior of the parts, i.e. synergetic phenomena. The latter is what is known as an invention, a complex arrangement, not found in nature, though sometimes superficially similar to nature. Though superficially similar in patternings to Radiolaria and Flies' Eyes, geodesic structuring is true invention. The Radiolaria collapse when taken out of water. Flies' Eyes will not provide structural precedent or man-occupiable structures.

The processes of engineering, up to the moment of introduction of my invention of Geodesic structures, are predicated upon the stress analysis of individual beam and column behaviors, as separate components and thereafter upon comprehensively organized beams, columns and cantilevers as a solid compressional over-all integrity of cohesion, aided here and there by tensionally exaggerated sinews--tension being subordinate and local. Therefore, engineering as academically constituted in 1951 could in no way predict the associated behaviors of Geodesics, in which any one, several or many of the components could be removed without, in any way, jeopardizing the structural integrity cohesion of the remaining primary structure.

I have visited approximately all the leading universities and engineering schools in the U.S.A. (only as their spontaneously invited guest, as I allow no promotion or agentry solicitation of engagements ), and I have been a guest of major architectural and engineering societies around the world. I am able to state from the direct testimony of its leaders, that world engineering not only was surprised by the Geodesic behavior but clearly stated that it was unable to explain or predict the unprecedented performance per pound efficacy of the geodesic structures by any of the academically known mathematical principles of analysis. In lieu of an extant and proven theory of Geodesics and their stress analysis strategies, engineers professionally charged with the responsibility of validating my (or my companies') Geodesic dome undertakings have only one recourse, and that is to direct static load testing accompanied by progressive electric strain gauge readings with loading carried through to "failure." Thereafter, formulas are derived, which do not provide any general theory but only special knowledge concerning this particular case. However, I do enjoy a lucid theory of geodesic structuring which I have frequently reduced to successful practice in technical, economic and industrial ways.

For these reasons I have had to develop a completely new strategy of educational exposition of synergetic behaviors.It is because I have developed the Geodesic theory and not only the invention but this effective strategy of exposition, that I am, and have been, invited to conduct original seminars in the primary educational institutions around the world, as well as before the important annual professional conventions of primary engineering-architectural bodies of these countries.

Whereas, engineers told me, before my full-scale demonstrations of Geodesic structures, that Geodesics would not work; now, after one-third of a century of expositional engagements and discourse, there has been produced altogether such an effect upon the general climate of technology that Geodesic componentation is frequently employed by others with satisfactory structural results, though the individuals do not know why. This occurs because of a subconsciously-marshaled approach of the design factors generated by hundreds of news photographs of successfully standing structures, ranging from desk models to the largest clear-span enclosures of all history. Many of these are shown being flown to installation sites, some of which are at the world's formidable polar,mountain and desert regions.




All these Geodesic events were news items simply because they were synergetic surprises, ergo contrary to the obvious. Copied geodesic ventures in higher modular frequency of triangular Geodesic subdivisioning, or other less symmetrical employments of the Geodesic structural integrity than I have as yet undertaken, do not constitute invention.Nor does the variation warrant exemption from the temporary economic authority granted to me as a patent.




There have been recent news references to structures which I have designed for firing to the Moon. Six hundred pounds is the approximate weight of my thirty-six foot diameter sphere self-openable from a thirty-six inch diameter ball. There can, and probably will, be much larger units, which I will discuss later in this disclosure. Of first interest to engineers and artist-conceivers is the fact that my potential prototypes of satellite- and moon-structures are tensional integrity, omni-triangulated, high-tensile-cabled, spherical nets in which local islands of compression act only as local sprit-stiffeners. The local stiffeners are so oriented that they angle inwardly and outwardly between comprehensively finite, exterior and interior, tensional, spherical nets, thus producing positive and negative waves of action and reaction in inter-stabilized dynamic equilibrium.

Recourse to this discontinuous-compression, continuous-tensioning structure was not obvious to man, therefore the following needs to be observed.




Whereas compression members have an inherent limit ratio of section diameter to length, tension members have no inherent ratio of section diameter to length. The Greeks, who built entirely in compression, discovered that a stone column's slenderness ratio was approximately 18 to 1 of length to diameter. Modern structural steel columns with an integral tensional fibering unpossessed by these stone columns have a limit slenderness ratio of approximately 33 to 1.

If we have better metallurgical alloys, we can make longer and longer tension members with less and less section--apparently ad infinitum, but not longer compression columns, ad infinitum.

GENESIS OF SYNERGETIC GEOMETRY



What interested me back in 1927, regarding the limitless ratios of tensional slenderness,was whether we were trending toward bridges which had infinite length and no section dimension at all, or whether this was a nonsensical question. As a sailor I looked spontaneously into the sky for indicated clues. I found myself saying, "It is very interesting to observe that the solar system, which is the most reliable structure that we know of, is so constituted that the earth does not roll around on Mars as would ball bearings, which is to say that the compressional components of celestial structures are astro-islands spatially remote from one another and they are each shaped in the most ideal conformation for highest compressional-structure effectiveness which is the approximately spherical shape. In the spherical condition any aspect of a compressional system is its neutral axis, that is the sphere has an infinity of axes. All other spheroidal (cigar, turnip, egg, potato or spider) shapes have only one most neutral axis. This is why spherical ball bearings are the most ideal compressional system structures of man's devising, as they continuously shift their loads while distributing the energetic effects to the most parts in equal, ergo relatively miniscule shares in the shortest time.


I saw that those astro-islands of compression of the solar system are continuously controlled in their progressive repositioning in respect to one another by comprehensive tension of the system which Newton called "gravity." This effective coherence between island-components varied in respect to their relative proximities and masses, in ratio gains and losses of the second power in respect to the dimensional distance, as stated in the terms of radius of one of the component bodies involved.


I then switched my observation from the macrocosmic to the microcosmic and witnessed that man's probing within the atom disclosed the same kind of discontinuous-compression, continuous-tension apparently governing the atom's structure. That is, the islands of energy concentration of the atom and its nucleus were extraordinarily remote from one another in respect to their measurable local energy concentration diameters,and all were bound together by a comprehensive but invisible tensional integrity.

As a consequence of these macro-, micro-structural reminders, it seemed to me, in 1927, appropriate to ask also whether man, who obviously tended to think only of a solid, brick-on-brick, pile-up law as governing all fundamental forms of structural modifications, i.e., formal, local alterations of the "solid" compressional earth's crust, was congenitally limited to "solid" structural conceptioning, and could therefore never participate in the far more efficient structural strategies evidenced in his (only instrumentally harvested) infra- and ultra-sensorial data of universal patterning. I also saw that man had long known of tensional structures, and had experienced and developed those tensional capabilities but apparently only as a secondary accessory of primary compressional structuring. For instance, he inserted a solid mast into a hole in "solid" earth and rammed it in as a solid continuity of the unitary solid earth.




However, to keep it from blowing over and breaking off when hurricanes raged, he added a set of tension stays triangulated from the top of the masthead to the ground, thus taking hold of the extreme end of the potential mast-lever at the point of highest advantage against motion. But these tensions were secondary structuring actions. So also were they secondary adjuncts in his solidly built compressional-continuity ships. To man, building and earth were alike, compressionally continuous. Compression was that "realistically hard core" that he loves to refer to, and its hard reality was universal, ergo comprehensive.

It followed that tension must be secondary, and local, in all his thoughts, ergo in all his philosophic reasoning. As a consequence, popular conception of airplane flight was, at first, and for a long time, erroneously explained as a compressional push-up force operating under the airplane's wing. It "apparently" progressively compressed the air below it as a ski compresses the snow into a grooved track of icy slidability. The scientific fact remains, as tunnel experiments proved, that 75% of the airplane's weight support was furnished by the negative lift of the partial vacuum created atop the air-foil. This is simply because, as Bernoulli showed, it was a longer way for the air to go around the top of the foil than under the foil, and so the same amount of air in the same amount of time had to be stretched thinner, ergo, vacuously over the top It seemed to me that this stretching thinner, and its concomitant greater effectiveness of inter-positioning of bodies (the plane in respect to earth ), was our same friend, the astro- and nucleic tensional integrity of dynamic interpatterning causality.


THE WIRE WHEEL

As I wondered whether it was now possible for man to inaugurate an era of thinking and conscious designing in the terms of comprehensive tensions and discontinuous compressions, I saw that his structural conceptioning of the wire wheel documented his intellectual-designing break-through into such thinking and structuring That is, the compressional hub of the wire wheel was clearly islanded or isolated, from the compressional "atoll" comprising the rim of the wheel.




As these compressional islands were only interpositioned in structural stability by the tensional spokes, I said that this was dearly a tensional integrity, where tension was primary and comprehensive and compression secondary and local. This reversed the historical structural strategy of man. His first wire wheel had many and varied numbers of spokes. I probed mathematically for generalized laws which might govern this tensional integrity and sought for experimentally proven knowledge governing the minimum number of spokes necessary to wire wheel stability. I found that 12 was the minimum number of spokes. Man had used more, in providing a lightweight wheel, as stays for the frequent support of the resultingly slender rim.

Thus I found a mathematics of natural coordination fundamentally governing the universally constant and alternate minimum of 12 unique vectors of freedom, each of equally minimum energy involvement. Out of the 12 vectors of unique and alternate freedoms of nature's fundamentally accommodating coordinations, there emerged a comprehensive hierarchy of entirely rational mathematical relationships apparently governing all known fundamental transformation behaviors of nature. I named this body of mathematical relationship discovery "Energetic and Synergetic Vectorial Geometry.-' Out of the comprehensive ramifications of Energetic and Synergetic Vectorial Geometry came the eventual, not only to design discontinuous compression structures, and to comprehend in direct, consciously-conceived patterning the gamut of orderly transformal strategies used by nature in her array of evolutionary designing, which also proved to be everywhere the most economically accommodating to the inherently diverse local effects of the sum total universal coordinations, and respective progressions, of local energy investments.


» Read part II starting with 'TENSION vs. COMPRESSION'

| posted in: | help