Daniel López-Pérez Lightness 720 Lightness

720 Issue #: 07 by FunctionLab Daniel López-Pérez Lightness 720 Lightness

“I will devote my first lecture to the opposition between R. Buckminster Fuller (1895 – 1983) was famously known for advocat- lightness and weight, and will uphold the values of ing that “Lighter Means Better.” It was under this heading that his lifelong lightness. This does not mean that I consider the virtues pursuit for lightness was described in a feature in Time magazine (where of weight any less compelling, but simply that I have he also appeared in the cover): “Bucky first turned his new perceptions on more to say about lightness. After forty years of writing the industry he knew best: building. In the era where the aircraft industry fiction, after exploring various roads and making diverse in particular was devising a new technology of lightweight engineering and experiments, the time has come for me to look for an materials, the traditional building methods seemed to him absurd. Tradition- overall definition of my work. I would suggest this: my al buildings depended on compression on their walls to support the roof. But working method has more often than not involved the modern technology has developed tensile materials, which are many times substraction of weight. I have tried to remove weight, stronger in relation to their weight than compression materials. A house sometime from people, sometimes from heavenly designed to use tension as its basic structural principle could be made bodies, sometimes from cities; above all I have tried to infinitely lighter, built with fewer materials, and therefore far more cheaply. If remove weight from the structure of stories and from mass-produced, such houses could solve the world’s shelter problems.”1 language.” The following pages explore Fuller’s pursuit of lightness by tracing his Italo Calvino, “Lightness”, Six Memos for the Next Mil- development of geodesic structural prototypes over time. In the writings lennium (London: Jonathan Cape, 1992), 3. of his Tensile-Integrity Patent from 1963 Fuller had already identified a paradigm shift in structural thinking, one that aimed to minimize compres- “The essence of my invention consists in the discovery sion elements while maximizing those based on tension as a way to arrive of how to progressively reduce the aspect of compres- at a state of minimum weight with maximum structural performance. This sion in a structure so that, to a greater extent than has condition of “doing more with less” through the use of tensile elements been found possible before, the structure will have Fuller coined “Ephemeralization” and defined as “[...] the doing of ever the aspect of continuous tension throughout and the more with ever less, per given resource units of pounds, time and energy.”2 compression will be subjugated so that the compres- Testing the limits of this paradigm shift from a logic of compression to one sion elements become small islands in a sea of tension. of tension, Fuller would spend most of his life in search in search of novel This is to bring the slenderness, lightness and strength and increasingly more complex systems that sought the promise of new and of the suspension bridge cable into the realm previ- unprecedented degrees of lightness. ously dominated by the compression column concept of building. [...] In general, my invention is useful wherever The general time line traces Fuller’s development of geodesic prototypes it is advantageous to make the largest and strongest organized according to three structural systems: compression (“strut”), ten- structure per pound of structural material employed.” sion (“strut + cable”), and plate (“surface”). Each prototype is subsequently [...] “Tensile-Integrity Structures” (Tensegrity), US Patent scaled to a diameter of 9 meters, and measured to obtain an overall com- No.: 3,063,521, Application: August 31, 1959; Serial bined length or area that results from the sum of all of all of its parts. This Number: 837,073; Patented: November 13, 1962.” value of combined length or area becomes the basis from which to rank the geodesic prototypes across time in accordance to their total use of material R. Buckminster Fuller, “15. Tensegrity”, Inventions, the (or weight if a specific material ratio of weight to their specific overall length Patented Works of R. Buckminster Fuller (New York: St. or area is applied). By indexing their intricate form according to a linear or Martin’s Lane, 1983), 179-193. surface logic (or at times also hybrid across both), the development of these geodesic structural prototypes can be understood as Fuller’s pursuit of vary- Issue 7 / Summer 2014 / The Function of Lightness ing degrees of “lightness” over time.

Daniel López-Pérez 1 Miriam Rumwell, “Lighter Means Better”, “The Dymaxion American”, Time, (January 10, 1964) 48. with 2 R. Buckminster Fuller, “RBF DEFINITIONS: Ephemeralization”, Jacob Bruce, Angela Vanella, Katinka Bosch, Lucy Hill Synergetics Dictionary, The Mind of Buckminster Fuller, Volume 1: A-E (New York: Garland Publishing Inc., 1986) 649. Advanced Geodesic Research Unit Department of Art, Architecture and Art History University of San Diego www.sphericalatlas.com

2 3 720 A = 95 m2 Lightness 1 face

“Radome” (1954) 11 “Dome Units for Geodesic Inc.” A = 192 m2 (1950s) 76 faces 16 A = 320 m2 490 faces “Fifty-Foot Radome” “Laminar Dome (1955) 14 Patent a ”

Surface A = 176 m2 “31 Foot 24 (1964) 277 faces Radome” A = 182 m2 (1954) 12 110 faces A = 178 m2 1100 faces “Laminar Dome “Tenting for US Patent b” “Plydome” (1965) Marine Corps” 20 (1959) 25 (1954) 10 A = 190 m2 A = 181 m2 A = 124 m2 64 faces 200 faces 195 faces

“50 Foot “US Marine Core” Radome” “Laminar Dome 15 (1950) (1954) 13 Patent c” A = 162 m2 A = 119 m2 26 (1965) 124 faces 2530 faces A = 179 m2 220 faces

“Pan-Type” “Pine Cone (1947) Dome” 2 “Laminar Dome “Geodesic Tent” 28 (1977) L = 452 m 18 (1957) Patent” 370 struts “Geodesic 23 (1963) L = 226m Patent” L = 353 m 120 struts A = 120 m2 (1954) 347 struts A = 155 m2 240 faces 7 A = 158 m2 L = 1209 m A = 95 m2 110 faces “Geosphere” 105 faces (1951) 4 3073 struts 1 face L = 650 m Strut 802 struts “Raft System” “University of 19 (1959) “4v Parallel Dome” Oregon” (1980) 29 8 (1953) L = 802 m L = 706 m 724 struts A = 156 m2 879 struts “Geodesic Patent 200 faces Fly’s Eye” 22a (1963) Icosadodecahedron’s 40 struts/ Thirty-one faces Great Circle Grid “Egg Crate” (1950) 3 (1947) 1 “Fifty-Foot Magnesium “Paperboard” L = 389 m 17 (1956) L = 452 m Geodesic Hangar” 137 struts (1954) L = 467 m 370 struts 9 L = 428 m 426 struts 255 struts “Geodesic Patent Geodesic Structure” “University of 22b (1963) Minnesota” L= 117 m Strut and Cable (1953) 5 115 struts L = 612 m 523 struts L’ = 750 m 640 cables

“Tensile-Integrity “Discontinuous (Tensegrity) “Non Symmetrical Patent” Tensegrity” Compression” D = All models have been scaled to a diameter of 9m (1953) 6 21 (1962) 27 (1975) L = Total length of struts in meters L = 199 m L = 612 m L’ = Total length of cables in meters L = 137 m 120 struts 523 struts A = Total area of surfaces in square m. 30 struts L’ = 277 m L’ = 201 m L’ = 292 m 254 cables 120 cables 60 cables 1940s 1950s 1960s 1970s 1980s

4 5 720 Lightness

6 Discontinuous Compression Sphere,

School of Architecture Princeton University: b (1953)

TENSEGRITY (1962)

US Patent No: 3,063,521

Application: a August 31, 1959

Serial No.: 837,073

Patented: November 13, 1962

Perimeter = 5A

Projection: The Spherical triangle re- Solid: sults from the inscription Each strut is tied by a wire of a icosahedron into a cable following a number sphere/ - urations, three struts held a together by cables, each a of which forms pentagonal Subdivision: and hexagonal assemblies. The Spherical triangleis subdivided according to the class I schema. Icosahedron

Subdivision:

Class I b

a a Frequency: 4v

A a 4v rate of The 4 frequency Class I subdivision Grid divides this assembly into sub-assemblies in the form of pentagons and hexagons. Each of the resulting pentagonal and hexagonal assemblies is formed by a network of a struts working in compression tied to cables working in tension.

6 7 720 Lightness

21 TENSEGRITY: (1962)

US Patent No.: 3,063,521

Application: August 31, 1959

Serial No.: 837,073

Patented: November 13, 1962 a

Perimeter = 10A + 5B

Projection: Solid This spherical triangle re- This sphere results from an sults from the inscription assemblage of a number and projection of an ico- of linear rigid tubes held sahedron into a sphere. together by tensile network wire cables. The tubes and the wire cables work in tension and compression Subdivision: a to form a discontinuous This spherical triangle is web-like structure. Each subdivided according to tube is tied by a wire cable Icosahedron a the Class I subdivision schema. from triangular, pentagonal, Subdivision and hexagonal assemblies. b b

b b Class I b b

Frequency a b a v b 4

The Tensegrity principle is b b generally described as the physical phenomenon that b b produces a stable geometric structure with solid members that are arranged in tandem with tense metal cables where the solid members of this system do not touch or b support each other directly b 4vrate of subdivision The 4 frequency Class I Grid produce curved edges a and further divides this assembly into sub-assem- a blies in the form of pentagons and hexagons.

8 9 720 Lightness 5 University of Minnesota, School of Architecture, Dome Project, Winter-Spring Quarter: (1953)

Perimeter = 5A

These trusses are held a together with a series of Solid: Projection: cables working in tension This spherical triangle results from across the entire dome in the inscription and projection of a an interlocking, open-web Rhombic Triacontahedron into a network of tension and sphere compression.

Rhombic Triacontahedron Subdivision: a This spherical triangle is b a subdivided according to a c the Class II subdivision Subdivision: schema b a b

Class II

c a Frequency: a a 8v b b This prototype is similar to the Egg Crate design a a c b comes from the assembly of subunits which begin A with the subdivision of an icosahedral face, and a a result in the appearance of a projected rhombic b a a triacontahedral face. 8v rate of c subdivision a The 8 frequency grid subdivision is used to produce curved sections which follow the rhombic b triacontahedron face edges, producing diamond shaped sections of trusses that run parallel to the rhombic triacontahedron face edges, perpendicular- a ly to the icosahedron face edges.

10 11 720 Lightness

9 Fifty-foot Magnesium Geodesic Hangar for the US Marine Corps Dome: (1954)

c Perimeter = 20A

A A

Projection: This Spherical triangle results Solid: from the inscription and projection of an icosahedron into a sphere. The Fifty-Foot Magnesium a Geodesic Hangar for the U.S. Marine Corps Dome is made of linear struts joined together. These struts are held together Subdivision This spherical triangle is intersections at their joints. Each a subdivided according to a of these parts joins at the center Icosahedron the class II subdivision of a number of hexagonal or schema. pentagonal shapes, producing a rigid structural network. Subdivision: b b

b a

b Class II b

b Frequency:

a 4v

a a a

a a c

The 4 frequency grid subdi- d vision is used to produce 4v rate of curved section which subdivision produce diamond shaped A units of aggregation.

12 13 720 Lightness 7 Building Construction, “Geodesic Patent”: (1954)

GEODESIC DOME (1954)*

US Patent No.: 2,682,235

Application: December 12, 1951

Serial No.: 261,168

Patented: June 29, 1954

Perimeter = 10A A

Solid: These tube-like structural elements are held together Projection: a The spherical triangles their joints. Which leads to result from the inscription b them aggregating together of an icosahedron into a to form small sub-assem- sphere. blies of hexagons and pentagons b Icosahedron b Subdivision: a c b b Subdivision: b This spherical triangle is b subdivided according to b the class II subdivision d c schema b b d b b Class II d d b d d e b Frequency: b b e d d b e v b e e b d c 16 d d a d d e b b e b d b d d d b b b e d e b c b b d b d b A a v 16 rate of b subdivision e The 16 frequency class II subdivision is used to produce curves sections which This prototype is similar d follow the icosahedral face to the Eight Sixteen edges producing small Frequency geosphere hexagons and pentagons. for comes from the hex- b agonal and pentagonal division of subunits from an icosahedron.

14 15 720 Lightness

18 Geodesic Tent Patent : (1957)

CATENARY GEODESIC TENT (1959)

US Patent No.: 2,914,074 a

Application: March 1, 1957

Serial No.: 643,403

Patented: November 24, 1959

Perimeter = 5A

Solid:

Projection: This spherical triangle results from the inscrip- This Geodesic Tent Patent tion and projection of an a assembly is made of linear icosahedron into a sphere structural struts, cables, and fabric joined together. Icosahedron These struts are held together in a continuous a - Subdivision: Subdivision: a tions as their joints. This a a This spherical triangle is system of struts, working subdivided according to with the system of sus- the Class I subdivision pended cables in the form schema of catenaries, shapes the a fabric component of the a structure. a Class I a

a Frequency: a v a 6 a a a a a a a a a a

a a

a a a a A The 8 frequency grid subdivision is used to produce triangular shaped section a v a 6 rate of of structure. subdivision

16 17 720 Lightness

16 Dome Units for Geodesics Inc.: (1950s) a

c c

a a b

a d

d d d

Perimeter = 20A A

Solid Projection: This spherical triangle results from the inscription and projection of an This Dome Units for icosahedron into a sphere Geodesics Inc. assembly

joined together. These a faces are held together in Subdivision: multiple layers with folded Icosahedron This spherical triangle is seams as their joint. subdivided according to the Class I subdivisio`n schema Subdivision :

b c Class I b c Frequency:

v a c c 3 c c a

c b

B c a b 3v rate of subdivision

The 3 frequency grid subdivision is used of

a join to gather to producing a hexagonal and pentagonal surfaces. These join together creating a semi sphere.

18 19 720 Lightness

15 US Marine Corps

F.F. 42 1/2 S. Preliminary Dome: (1955)

Perimeter = 20A A

Projection: Solid: This spherical triangle results from the inscrip- This US Marine Corps F.F. tion and projection of an 42 ½ S. Preliminary Dome icosahedron into a sphere a joined together.These faces are held together in a

Subdivision: This spherical triangle is intersections at their edge. Icosahedron subdivided according to the Class II subdivision a schema a Subdivision:

a b b a

a b b Class II b Frequency: b

b v b b a b 4 a

a a

b 4v rate of A subdivision a b

b a The 4 frequency grid subdivision is used to produce

irregular triangle shaped sections resulting in a semi sphere. b

20 21 720 Lightness

20 Self-Strutted Geodesic Plydome Patent: (1959)

PLYDOME (1959)

US Patent No.: 2,905,113

Application: April 22, 1957

Serial No.: 654,166

Patented: September 22, 1959

A a Perimeter = 2A+4B+2C B

Projection: a This spherical triangle This dome is formed by the Solid results from the inscrip- aggregation of a number of tion and projection of an bent rectangular plywood icosahedron into a sphere b structural panels. These panels bend to produce a multi-layered, porous a geometry. Each of these rectangular parts bends to overlap with the corners of b its adjacent panel creating Icosahedron of irregular openings. b Subdivision: This spherical triangle is Subdivision subdivided according to c the Class II subdivision schema.

c b

Class II d a d c c b b a Frequency

b v c 6

c b A

a 4vrate of subdivision The 4 Frequency grid subdivisions are used to produce a grid for bent rectangular plywood producing hexagon and pentagon shaped section.

22 23 720 Lightness

720 #7 / Summer 2014 / Lightness

Daniel López-Pérez is an Assistant Professor and a founding faculty member of the Architec- ture Program at the University of San Diego.

López-Pérez received his Ph.D.. in the History and Theory of Architecture at Princeton Universi- ty, a Master of Science in Advanced Architectural Design (with Honors) from Columbia University, and an AA Diploma from the Architectural As- sociation.

López-Pérez edited R. Buckminster Fuller: World Man, a study of Fuller’s never-before- published inaugural Kassler lecture delivered at Princeton University’s School of Architecture in 1966. Reflecting on the severe challenges facing the global ecology, Fuller delivered an impassioned rallying cry to architects to shape their universe by responding to its underlying principles – a cry that World Man argues to be as relevant today as it was in the visionary de- signer’s own time.

720 is the subject reference number given to architecture in the . The DDS is the proprietary system of library classification developed by Melvil Dewey in 1876.

720 is the occasional pamphlet of FunctionLab, the think tank of Farshid Moussavi Architecture.

www.functionlab.org

Contact: [email protected] +44(0)20 7033 6490

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