Geodesic dome
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A geodesic dome is an almost spherical structure based on a network of struts arranged on great circles (geodesics) lying approximately on the surface of a sphere. The geodesics intersect to form triangular elements that have local triangular rigidity and yet also distribute the stress across the entire structure. It is the only man-made structure that gets proportionally stronger as it increases in size. When completed to form a full sphere, it is known as a geodesic sphere.
Of all known structures made from linear elements, a geodesic dome has the highest ratio of enclosed volume to weight. Geodesic domes are far stronger as complete units than the individual struts would suggest. It is common for a new dome to reach a "critical mass" during construction, shift slightly, and lift any attached scaffolding from the ground.
The design of the geodesic dome is a complicated matter. In part, this is because there is no one standard design. Rather, there are a number of designs based on taking a Platonic solid, such as an icosahedron, and then projecting each face onto the interior surface of the sphere. There is no perfect way to do this, as neither the angles nor the sides can be preserved without one distorting the other. The result of the design compromise is a regular pattern of triangles with their vertices lying approximately on the surface of the sphere. The edges of the triangles create "geodesics," great circles of a sphere, to distribute stress across the sphere.
Geodesic designs can be extended to any curved, enclosed space, although very oddly-shaped designs would require calculating (and fabricating) each strut individually, and thus be expensive and complicated to construct. Because of the expense and complexity of design and fabrication of any geodesic dome, builders have tended to standardize on a few basic designs.
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[edit] History
The second dome that could be called "geodesic" in every respect was designed just after WWI by Walter Bauersfeld,[1] chief engineer of the Carl Zeiss optical company, for a planetarium to house his new planetarium projector. The dome was patented, constructed by the firm of Dykerhoff and Wydmann on the roof of the Zeiss plant in Jena, Germany, and opened to the public in 1922. Some thirty years later R. Buckminster Fuller apparently came up with the idea independently and named the dome "geodesic" from field experiments with Kenneth Snelson and others at Black Mountain College in the late 1940's. Although Fuller cannot be said to be the inventor, he exploited and developed the idea, receiving a U.S. patent.
The geodesic dome appealed to Fuller because it was extremely strong for its weight, its "omnitriangulated" surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area. Fuller had hopes that the geodesic dome would help address the postwar housing crisis. This was in line with his prior hopes for both versions of the Dymaxion House.
From an engineering perspective geodesic domes are far superior to traditional, right-angle post-and-beam constructions. Traditional constructions are a far less efficient use of materials, are far heavier, are less stable, and rely on gravity to stand up.
However, there are also some notable drawbacks to geodesic constructions as well. Although extremely strong, domes react to external stresses in ways that confound traditional engineering. Some tensegrity structures will retain their shape and contract evenly when stressed on the outside, and some don't. For example, a dome built at Princeton, New Jersey (quote needed) was hit by a snowplow. The stress was transmitted through the structure, and popped out struts on the opposite side. To this day, the behavior of tension and compression forces in the different varieties of geodesic structures is not well understood. So, traditionally trained structural engineers may not be able to adequately predict their performance and safety.
The dome was successfully adopted for specialized industrial use, such as the 1958 Union Tank Car Company dome near Baton Rouge, Louisiana and specialty buildings like the Henry Kaiser dome, auditoriums, weather observatories, and storage facilities. The dome was soon breaking records for covered surface, enclosed volume, and construction speed. Leveraging the geodesic dome's stability, the US Air Force experimented with helicopter-deliverable units. The dome was introduced to a wider audience at Expo '67 the Montreal, Canada World's Fair as part of the American Pavilion. The structure's covering later burned, but the structure itself still stands and, under the name Biosphère, currently houses an interpretive museum about the Saint Lawrence River. A dome was constructed at the South Pole in 1975 where its resistance to snow and wind loads is important.
In the 1970s the Cinesphere dome was built at the Ontario Place amusement park in Toronto, Canada.
Residential domes have been less successful, due largely to their complexity and consequent higher construction costs. Fuller himself lived in a geodesic dome in Carbondale, Illinois, at the corner of Forest and Cherry. Residential domes have so far not caught on to the extent that Fuller hoped. He envisioned residential domes as air-deliverable products manufactured by an aerospace-like industry. Fuller's dome home still exists, and a group called RBF Dome NFP is attempting to restore the dome and have it registered as a National Historic Landmark.
[edit] Chord factors
A "chord" is a line segment lying on the surface of a circle or sphere. The chord factor of a dome indicates the number of times the "polyhedral face" is being subdivided when it is being projected onto the interior surface of the sphere. In this context, it is symbolized by "v." The chord in a dome is calculated as twice the sine of half the "central angle of the chord" (the central angle of the chord is the angle between the center point inside the sphere and the ends of the chord). Determining the central angle usually requires some non-trivial spherical geometry. In Geodesic Math and How to Use It Hugh Kenner writes, "Tables of chord factors, containing as they do the essential design information for spherical systems, were for many years guarded like military secrets. As late as 1966, some 3v icosa figures from Popular Science Monthly were all anyone outside the circle of Fuller licensees had to go on." (page 57, 1976 edition) Other tables became available with publication of Lloyd Kahn's Domebook 1 (1970) and Domebook 2 (1971). With advent of personal computers, the mathematics became more accessible. Rick Bono's Dome software, outputs a script that can be used with the POV-ray raytracer to produce 3D pictures of domes. Domes based on differing polyhedrals and differing chord factors produce differing results.
[edit] Advantages of domes
Domes are very strong, actually getting stronger as they get larger. The basic structure can be erected very quickly from lightweight pieces by a small crew. Domes as large as fifty meters have been constructed in the wilderness from rough materials without a crane. The dome is also aerodynamic, so it withstands considerable wind loads, such as those created by hurricanes. Solar heating is possible by placing an arc of windows across the dome: the more heating needed the wider the arc should be, to encompass more of the year.
Today there are many companies that sell both dome plans and frame material with instructions designed simply enough for owners to build themselves, and many do to make the net cost lower than standard construction homes. Construction techniques have improved based on real world feedback over sixty years and many newer dome homes can resolve nearly all of the disadvantages below that were more true of the early dome homes.
[edit] Disadvantages of dome homes
As a housing system the dome can have numerous drawbacks and problems:
The shape of a dome house makes it difficult to conform to code requirements for placement of sewer vents and chimneys. Off-the-shelf building materials normally come in rectangular shapes. There can be considerably more scrap, left from cutting rectangles down to triangles, than with a conventional building approach, thus driving costs up. Fire escapes are problematic; codes require them for larger structures, and they are expensive. Windows conforming to code can cost anywhere from five to fifteen times as much as windows in conventional houses. Professional electrical wiring costs more because of increased labor time. However, even owner-wired situations are costly, because more of certain materials is required with a dome versus conventional construction.
Air stratification and moisture distribution within a dome are unusual, and these conditions tend to quickly degrade wooden framing or interior paneling. Privacy is difficult to guarantee because a dome is difficult to partition satisfactorily. Sounds, smells, and even reflected light tend to be conveyed through the entire structure.
As with any sloping shape, the dome produces wall areas that can be difficult to use and leaves some peripheral floor area with restricted use due to lack of headroom. This can leave a volume needing to be heated that cannot be lived in. Circular plan shapes lack the simple modularity provided by rectangles. Furnishers and fitters usually design with flat surfaces in mind, and so installing a standard sofa (for example) results in a half-moon behind the sofa being wasted. This is best overcome by purpose-built fittings, adding to cost.
Dome builders find it hard to seal domes against rain, because of their many seams and because solar heat flexes the entire structure each day as the sun moves across the sky. The most effective waterproofing method with a wooden dome is to shingle the dome. One-piece reinforced concrete or plastic domes are also in use, and some domes have been constructed from plastic or waxed cardboard triangles that overlapped in such a way as to shed water.
Buckminster Fuller's former student J. Baldwin states that there is no reason for a properly designed, well-constructed dome to leak, and that some designs cannot leak (Bucky Works: Buckminster Fuller's Ideas for Today). However, Lloyd Kahn, after writing two books on the subject (Domebook One and Domebook 2), became disillusioned with domes. He calls domes "smart but not wise" on his website, and has collected many of the criticisms given above.
[edit] Methods of construction
Wooden domes drill a hole in the width of a strut. A stainless steel band locks the strut's hole to a circle of steel pipe. This method lets the struts be simply cut to the exact needed length. Triangles of exterior plywood are then nailed to the struts. The dome is wrapped with several stapled layers of tar paper, from the bottom to the top in order to shed water, and finished with shingles.
Temporary greenhouse domes have been constructed by stapling plastic sheeting onto a dome constructed from 1x1s. The result is warm, movable by hand in sizes less than 20 feet, and cheap. It should be staked to the ground, because it will fly away in strong wind.
Steel-framework domes can be easily constructed of electrical conduit. One flattens the end of a strut, and drills bolt holes at the needed length. A single bolt secures a vertex of struts. The nuts are usually set with removable locking compound, or if the dome is portable, have a castle nut with a cotter pin. This is the standard way to construct domes for jungle-gyms.
Concrete and foam plastic domes generally start with a steel framework dome, and then wrap it with chicken-wire and wire screen for reinforcement. The chicken wire and screen is tied to the framework with wire ties. The material is sprayed or molded onto the frame. Tests should be performed with small squares to achieve the correct consistency of concrete or plastic. Generally, several coats are necessary on the inside and outside. The last step is to saturate concrete or polyester domes with a thin layer of epoxy compound to shed water.
Some concrete domes have been constructed from prefabricated prestressed steel-reinforced concrete panels that can be bolted into place. The bolts are within raised receptacles covered with little concrete caps to shed water. The triangles overlap to shed water. The triangles in this method can be molded in forms patterned in sand with wooden patterns, but the concrete triangles are usually so heavy they must be placed with a crane. This construction is well-suited to domes because there is no place for water to pool on the concrete and leak through. The metal fasteners, joints and internal steel frames remain dry, preventing frost and corrosion damage. The concrete resists sun and weathering. Some form of internal flashing or caulking must be placed over the joints to prevent drafts. The 1963 Cinerama Dome was built from precast concrete hexagons and pentagons.
[edit] Largest geodesic dome structures
Many geodesic domes have been built and are in use. According to the Buckminster Fuller Institute Web site, the largest geodesic-dome structures (listed in descending order from largest diameter) are:
- The Eden Project, Cornwall, UK.
- Fantasy Entertainment Complex: Kyosho Isle, Japan, 710 feet / 216 m
- Multi-Purpose Arena: Nagoya, Japan, 614 feet / 187 m
- Superior Dome: Northern Michigan University. Marquette, MI, USA, 536 feet / 160 m
- Tacoma Dome: Tacoma, WA, USA, 530 feet / 161.5 m
- Walkup Skydome: Northern Arizona University. Flagstaff, AZ, USA, 502 feet / 153 m
- Round Valley High School Stadium: Springerville-Eagar, AZ, USA, 440 feet / 134 m
- Former Spruce Goose Hangar: Long Beach, CA, USA, 415 feet / 126.5 m
- Formosa Plastics Storage Facility: Mai Liao, Taiwan, 402 feet / 122.5 m
- Union Tank Car Maintenance Facility: Baton Rouge, LA, USA, 384 feet / 117 m
- Lehigh Portland Cement Storage Facility: Union Bridge, MD, USA, 374 feet / 114 m
- Spaceship Earth: the symbol of Epcot at Walt Disney World, 165 feet/50m. (Note: this is not a true geodesic dome, as it is a sphere supported on legs. It was, however, derived from the geodesic dome concept.)
- Mitchell Park Domes, Milwaukee, WI, USA. Horticultural Conservatory comprises three domes each 140 feet / 43 m
However, the info in this article is a bit outdated. The staff of wikipedia will update this site as soon as possible.
[edit] Sources
1. From the Arratus Globe to the Zeiss Planetarium, Helmet, Werner, Publ. Gustav Fischer, Stuttgart, 1957. (Available only from Carl Zeiss, N.Y.) 2.http://experts.about.com/e/g/ge/geodesic_dome.htm
[edit] See also
- Concrete dome
- The DHARMA Initiative, related to TV series Lost, involves domes (Note: Spoiler warning!)
- Domed city
- Fullerene
- Hoberman sphere
- Monolithic dome
- Radome
- Silent Running 1971 science fiction film prominently featuring geodesic domes.
- Space frames
- Shell structure
- Truss
[edit] External links
- 1973. Geodesic Domes and Charts of the Heavens. Bolinas: CA. Shelter Publications, Inc. http://www.telacommunications.com/geodome.htm
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- [1] 1000's of pictures and discussion about a 45 x 37" Dome being built now, many links to other dome sites]
- The R. Buckminster Fuller FAQ: Geodesic Domes
- Build Your Own Geodesic dome
- The Mathematics behind Geodesic Domes and Spaceframes
- Build Geodesic Dome Models out of Plastic Straws and Pipe Cleaners
- Designs in Various Frequencies
- Emergency shelter from cardboard dome instructions
- Dome Glossary
- A big list of large-span structures
- Dome software tools
- Photo and article on Fuller's dome home in Carbondale, Ill.
- Preserving Fuller's dome home in Carbondale
- Solardome.co.uk, animated presentation on commercial site about how geodesic domes capture more solar energy than conventional structures
- American Ingenuity A company applying modern Structural insulated panel developments to create a dome that solves some of the problems associated with domes.
- Project geo-dome Dome building techniques, information and instructions for building a paper dome model.
- Origami Geosphere Photo of a geodesic sphere made with origami.
- Geodesic Domes - Apparel and Merchandise Apparel and Merchandise for lovers of Geodesic Domes.
- GeometryDome Non-commercial resource with blueprints for geodesic domes that don't need custom corner connectors.
