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Spaceship Earth at Epcot, Walt Disney World, a familiar geodesic sphere
Spaceship Earth at Epcot, Walt Disney World, a familiar geodesic sphere

A geodesic dome is an almost spherical structure based on a network of great circles (geodesics) lying approximately on the surface of a sphere. Spaceship Earth is the iconic and symbolic structure of Epcot, a Theme park that is part of the Walt Disney World Resort. Epcot is a Theme park at the Walt Disney World Resort. The park is dedicated to international Culture and technological Innovation. Walt Disney World Resort is the most visited and largest recreational resort in the world containing four Theme parks two Water parks twenty-three themed hotels A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe The geodesics intersect to form triangular elements that have local triangular rigidity and yet also distribute the stress across the entire structure. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line Stress is a measure of the average amount of Force exerted per unit Area. It is the only man-made structure that becomes proportionally stronger as it increases in size. Of all known structures made from linear elements, a geodesic dome has the highest ratio of enclosed volume to weight. A dome is a common structural element of Architecture that resembles the hollow upper half of a Sphere. 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. When completed to form a full sphere, it is known as a geodesic sphere.

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. In Geometry, a Platonic solid is a convex Regular polyhedron. In Geometry, an icosahedron ( Greek: eikosaedron, from eikosi twenty + hedron seat /ˌaɪ 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.

Contents

Related patterns

The principle of building strong stable structures out of patterns of reinforcing triangles, called tensegrity, is most commonly seen in tent design. For the movement system created by Carlos Castaneda, see Tensegrity (Castaneda A tent is a shelter consisting of sheets of fabric or other material draped over or attached to a frame of poles or attached to a supporting rope It has been applied in the abstract in other industrial design, but even in management science and deliberative structures as a conceptual metaphor, especially in the work of Stafford Beer, whose syntegration method is based so specifically on dome design that only fixed numbers of persons can take part in the process at each deliberation stage. Industrial design is an Applied art whereby the Aesthetics and Usability of mass-produced products may be improved for marketability and Management science (MS, is the discipline of using Mathematical modeling and other analytical methods to help make better business Management decisions Structure is a fundamental and sometimes Intangible notion covering the Recognition, Observation, nature, and Stability of In Cognitive linguistics, conceptual metaphor refers to the understanding of one idea or Conceptual domain in terms of another for example understanding Quantity Anthony Stafford Beer ( September 25, 1926 - August 23, 2002) was a British Theorist, Consultant and professor This article refers to legal deliberation for other meanings of the word refer to its Wiktionary entry.

History

The Montreal Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, Montreal, Canada
The Montreal Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, Montreal, Canada

The first dome that could be called "geodesic" in every respect was designed just after World War I by Walther Bauersfeld,[1] chief engineer of the Carl Zeiss optical company, for a planetarium to house his new planetarium projector. The Biosphère ( of Environment Canada is a museum in Montreal dedicated to Water and the environment. The 1967 International and Universal Exposition, or Expo 67 as it was commonly known was the World's Fair held in Montreal, Canada from April 27 to October Richard Buckminster “Bucky” Fuller ( July 12, 1895 &ndash July 1, 1983) was an American Architect, Author Saint Helen's Island (French Île Sainte-Hélène) ( is an Island in the Saint Lawrence River, in the territory of the city of Montreal Montreal, or Montréal in French ( pronounced in French, in English) is the largest city in the Canadian province of Quebec Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page Walther Bauersfeld ( January 23, 1879 in Berlin – October 28, 1959 in Heidenheim an der Brenz) was a German engineer employed Carl Zeiss ( September 11, 1816 &ndash December 3, 1888) was an Optician commonly known for the company he founded Carl Zeiss A planetarium is a Theatre built primarily for presenting educational and entertaining shows about Astronomy and the night sky or for training in Celestial navigation 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. Jena (pronunciation ˈjeːna is a university City in central Germany on the river Saale. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Some thirty years later R. Buckminster Fuller further investigated this concept and named the dome "geodesic" from field experiments with Kenneth Snelson and others at Black Mountain College in the late 1940s. Richard Buckminster “Bucky” Fuller ( July 12, 1895 &ndash July 1, 1983) was an American Architect, Author Kenneth Snelson (born June 29, Black Mountain College, founded in 1933 near Asheville North Carolina, was known as one of the leading progressive schools in the United States Although Fuller cannot be said to be the first 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. The Dymaxion House was developed by inventor Buckminster Fuller to address several perceived shortcomings with existing homebuilding techniques

The Climatron greenhouse at Missouri Botanical Gardens, built in 1960, inspired the domes in the science fiction film Silent Running.
The Climatron greenhouse at Missouri Botanical Gardens, built in 1960, inspired the domes in the science fiction film Silent Running. The Missouri Botanical Garden is a Botanical garden located in St Silent Running is a 1972 ecologically-themed Science fiction film directed by Douglas Trumbull which depicts a future in which all Plant life

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 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 do not. For the movement system created by Carlos Castaneda, see Tensegrity (Castaneda For example, when a dome built at Princeton, New Jersey was hit by a snowplow, the stress was transmitted through the structure and popped out struts on the opposite side. See also Princeton Township New Jersey, Borough of Princeton New Jersey Princeton Borough New Jersey Princeton Township New Jersey this The behavior of tension and compression forces in the different varieties of geodesic structures is still 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. Baton Rouge (French Bâton-Rouge ˌbætən ˈruːdʒ in English, and in French) is the capital city of Louisiana. Henry Kaiser may refer to Henry Felix Kaiser (1927&ndash1992 American academic known for the Varimax rotation Henry J The dome was soon breaking records for covered surface, enclosed volume, and construction speed. According to a WAFB-TV of Baton Rouge news report on November 27, 2007, the Union Tank Car Company Dome has been demolished.

Leveraging the geodesic dome's stability, the US Air Force experimented with helicopter-deliverable units.

The dome was introduced to a wider audience as a pavilion at the 1964 World's Fair in New York City. This dome is now used as an aviary by the Queens Zoo in Flushing Meadows Corona Park. The Queens Zoo is a 5 acre (20000 m² Zoo located in the New York City borough of Queens, located in Flushing Meadows-Corona

Another dome from Expo 67 the Montreal, Canada World's Fair as part of the American Pavilion. The 1967 International and Universal Exposition, or Expo 67 as it was commonly known was the World's Fair held in Montreal, Canada from April 27 to October Montreal, or Montréal in French ( pronounced in French, in English) is the largest city in the Canadian province of Quebec Expo (short for "exposition" and also known as World Fair and World's Fair) is the name given to various large public exhibitions held since the 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. The Biosphère ( of Environment Canada is a museum in Montreal dedicated to Water and the environment. A museum is a "permanent institution in the service of society and of its development open to the public which acquires conserves researches communicates and exhibits the Saint Lawrence River (in French: fleuve Saint-Laurent; Kahnawáˀkye in Tuscarora, Kaniatarowanenneh meaning big waterway

In the 1970s the Cinesphere dome was built at the Ontario Place amusement park in Toronto, Canada. This article is about the Decade 1970-1979 For the Year 1970 see 1970. Cinesphere is the world's first permanent IMAX Theatre, built in 1971 Ontario Place is a multiple use entertainment and seasonal amusement park in Toronto, Ontario and owned by the Province of Ontario. Toronto (təˈrɒntoʊ colloquially pronounced or) is the largest city in Canada and is the provincial capital of Ontario Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page In 1975, a dome was constructed at the South Pole, where its resistance to snow and wind loads is important. Description and history The Amundsen-Scott South Pole Station is the southernmost continually inhabited place on the planet

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. Carbondale is a city in southern Illinois in the midwest United States, miles southeast of Saint Louis Missouri 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.

Chord factors


A geodesic sphere and its dual.

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 "ν" (Greek letter nu). Nu (uppercase Ν, lowercase ν; Νι Ni is the 13th letter of the Greek alphabet.

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. Spherical geometry is the Geometry of the two- Dimensional surface of a Sphere.

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. Hugh Kenner ( January 7, 1923 &ndash November 24, 2003) was a Canadian Literary Scholar, Critic 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. For the 1935-1949 film series see Popular Science (film. Popular Science is an American monthly Magazine founded in 1872 " (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. The Persistence of Vision Raytracer, or POV-Ray, is a Ray tracing program available for a variety of computer platforms In physics ray tracing is a method for calculating the path of Waves or Particles through a system with regions of varying propagation Velocity, absorption Domes based on differing polyhedrals and differing chord factors produce differing results.

Advantages of domes

Of course, like all domes, geodesic domes provide an enclosed space free of structural supports. 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. A tropical cyclone is a storm system characterized by a low pressure center and numerous Thunderstorms that produce strong winds and Flooding 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.

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 (e. g. , plywood, strand board) 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 are required for dome 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 that may require heating – representing a cost in energy – but 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 placing a standard sofa (for example) results in a half-moon behind the sofa being wasted. This is best overcome by purpose-built fittings, though it adds to cost.

Dome builders using cut-board sheathing materials find it hard to seal domes against rain, because of their many seams; as well, these seams may be stressed because ordinary 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 are 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). James Tennant Baldwin (born 1933 (whose books and articles have been published under the names J However, Lloyd Kahn, after writing two books on the subject (Domebook 1 and Domebook 2), became disillusioned with domes. Kahn (b 1935 is the founding editor-in-chief of Shelter Publications Inc He calls domes "smart but not wise",[2] and has collected many of the criticisms given above.

Methods of construction

Construction details of a permanently installed tent-type geodesic dome by Buckminster Fuller.
Construction details of a permanently installed tent-type geodesic dome by Buckminster Fuller. Richard Buckminster “Bucky” Fuller ( July 12, 1895 &ndash July 1, 1983) was an American Architect, Author

Wooden domes have a hole drilled in the width of a strut. A stainless steel band locks the strut's hole to a steel pipe. With this method, the struts may be cut to the exact length needed. Triangles of exterior plywood are then nailed to the struts. The dome is wrapped from the bottom to the top with several stapled layers of tar paper, in order to shed water, and finished with shingles. This type of dome is often called a hub-and-strut dome because of the use of steel hubs to tie the struts together.

Panelized domes are constructed of separately-framed timbers covered in plywood. The three members comprising the triangular frame are often cut at compound angles in order to provide for a flat fitting of the various triangles. Holes are drilled through the members at precise locations and steel bolts then connect the triangles to form the dome. These members are often 2x4's or 2x6's, which allow for more insulation to fit within the triangle. The panelized technique allows the builder to attach the plywood skin to the triangles while safely working on the ground or in a comfortable shop out of the weather. This method does not require expensive steel hubs.

Temporary greenhouse domes have been constructed by stapling plastic sheeting onto a dome constructed from one-inch square beams. The result is warm, movable by hand in sizes less than 20 feet, and cheap. It should be staked to the ground to prevent it being moved by 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, wrapped with chicken wire and wire screen for reinforcement. The chicken wire and screen is tied to the framework with wire ties. A coat of material is then 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 that 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. Pacific Theatres ' Cinerama Dome at 6360 Sunset Boulevard in Hollywood of the United States has been a landmark Movie theater Precast concrete is a form of construction where concrete is cast in a reusable mold or "form" which is then cured in a controlled environment transported to the construction

Largest geodesic dome structures

Many geodesic domes built are still in use. According to the Buckminster Fuller Institute Web site, the largest geodesic-dome structures (listed in descending order from largest diameter) are:

See also

References

  1. ^ Bauersfeld, Walter
  2. ^ "Refried Domes" by Lloyd Kahn
  3. ^ "Attractions in Omaha", The New York Times. A space frame or space structure is a Truss -like lightweight rigid structure constructed from interlocking struts in a geometric Pattern. The University of Notre Dame du Lac (or simply Notre Dame) (ˌnoʊtɚˈdeɪm is a private Roman Catholic Research university located in Thin-shell structures are light weight constructions using shell elements. In Architecture and Structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose A tent is a shelter consisting of sheets of fabric or other material draped over or attached to a frame of poles or attached to a supporting rope Retrieved 5/8/08.

External links

Dictionary

geodesic dome

-noun

  1. A domed structure of lightweight straight elements forming interlocking polygons.
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