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dowel and fishing line tensegrity tower

This tower was an outgrowth of my discontent with the wobbly behavior of my first tower, much as Snelson's topologically identical tower design was an outgrowth of his discontent with a mast he'd designed for Buckminster Fuller. I designed and built this tower on June 29, 1981, after reading Hugh Kenner's book Geodesic Math (now back in print!). Kenner doesn't discuss the construction of towers or masts, but gives an approximate technique for designing tensegrity spheres with a diamond topology (see Chapter 3: Complex Spherical Tensegrities). For this structure, I used an underlying geometry of stacked octahedrons and applied the technique in Kenner's book to get the appropriate tendon lengths. Upon assembly I found another set of longitudinal tendons were needed to make the structure taut.

In December 1986, I found out about Kenneth Snelson's topologically identical structure. I found his tower in the exhibition catalog for "Kenneth Snelson" (March 13, 1971 - April 19, 1971) put out by the Kunstverein Hannover which also has photos of construction and assembly instructions for the Needle Tower (1968), an example of which is at the Hirshhorn Museum in Washington, DC. Two sources had stimulated my interest in Snelson's work. The first was Peter Hjerson's book Dome Notes (Berkeley, CA: Erewon Press, 1975). That book had a string of references on Snelson and spoke more on his work than I had seen others do. Then at the Museum of Fine Arts, Boston, I saw a piece of his work (Tall Tale, 1976) in the "Boston Collects: Contemporary Painting & Sculpture" exhibition (October 22, 1986 - February 1, 1987) which made an impression on me.

As far as my tower was concerned, Ken's precedence was more strenuously called to my attention in April 1999 by his email indicating he had patented the technology (see Patent #3,169,611 Fig. 25) and that he differed with the way I presented the structure on my website. Along with the fact that I failed to give him credit for inventing the structure, he didn't like that I was calling it a "mast". I addressed his concerns.

To pursue a line of thought Buckminster Fuller has developed (see Fig. 740.21 from Synergetics), each strut in this tower could be replaced by a miniature tensegrity tower and each strut in those towers could be replaced by an even smaller tower and so on until the collective mass of the struts is as small as you please. Likewise, as the performance per pound of materials in tension increases, the tendons can be replaced with lighter and lighter materials with no sacrifice in performance. Thus the trend is for the mass of the structure to be reduced to zero with no sacrifice in performance. This is what Bucky calls ephemeralization.

To me, Snelson's tower actually fits Bucky's argument better than the one Bucky used due to Snelson's use of simple struts instead of the more-complex four-strut complexes Bucky used. In addition, although I can see the above substitution geometrically, structurally, as I've heard civil engineers point out, it might be tricky to get the same stiffness. Finally, in his response to my email of reconciliation, Kenneth Snelson pointed out to me that in the dictionary ephemeral is a purely time-based concept. Bucky is using the term somewhat idiosyncratically. Being a student of Einstein's space-time, Bucky apparently didn't have much of a problem using a time-based concept to express a volumetric one. I've thought "ethereal" might be a more generally acceptable substitute for "ephemeral" in this context. However, Bucky explicitly rejects this alternative in a footnote on p. 133 of Critical Path. J. Baldwin indirectly suggests "dematerialization" as an alternative on p. 15 of Bucky Works.

In his response to my email of reconciliation, Ken had also indicated he was interested in receiving a copy of my book, so I mailed a copy to him. A short time after getting Ken's response indicating the changes to this page satisfactorily addressed his concerns, I asked his permission to post the patent-montage graphic he had sent me. Ken's response was cautiously positive. His final approval of my presentation of the patent montage had an interesting discussion of his experience "tuning" the tension in tensegrity structures. In my response to his final approval I discussed my own experience with adjusting tension in tensegrity structures.

Years afterwards, I've put together a datasheet for a structure similar to the tower above. I used more-exact computations than I did years ago. Depending on how you attach the tendons to the struts, you may need to make allowance for the dimensions of your connectors, and if you use elastic material, you should remember that the length when you measure will be shorter than the length when the tendon is in place.

Also years afterwards, in response to my email query of January 9, 2006, Ken said he originally developed the "three-way column" around November 1959.

Recently I've been reading Val Gómez Jáuregui's new book on tensegrity, Tensegridad: Estructuras Tensegríticas en Ciencia y Arte (Santander, Spain: Servicio de Publicaciones de la Universidad de Cantabria, 2007) which is mostly a Spanish translation -- with some updates -- of Tensegrity Structures and their Application to Architecture, his Master's thesis (Belfast, Northern Ireland: Queen's University, School of Architecture, 2004). The quote from Bucky's Portfolio and Art News article "Tensegrity" strikes me:

My initial harvest of mathematical structures produced by this new conceptual tool was a family of four Tensegrity masts characterized by vertical side-faces of three, four, five and six each, respectively. The three and four sided masts consisted of discontinuous compression islands of tetrahedronal strut groups mounted only in tension one above the other, while the five and six sided masts consisted of local islands of icosahedronal and octahedronal strut groups mounted vertically above one another, again only by tensional connectors.

I realize I am only familiar with one of these structures -- the one which appears in Fig. 740.21 from Synergetics. I am curious to learn about the other three. Please email me at bobwb@juno.com if you have any information.


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