# geodesic dome

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 becomes 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. (The use of patterns of triangles to approximate either a rougher or smoother shape is also fundamental to computer graphics.)

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.

## Related patterns

The principle of building strong stable structures out of patterns of reinforcing triangles, called tensegrity, is most commonly seen in tent design. 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.

## History

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 WWI by Walther 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 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. 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 Climatron greenhouse at Missouri Botanical Gardens, built in 1960, inspired the domes in the science fiction film Silent Running.
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 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. 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. 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.

In the 1970s the Cinesphere dome was built at the Ontario Place amusement park in Toronto, Canada. In 1975, a dome was constructed at the South Pole, where its resistance to snow and wind loads is important.

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.

## 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 "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.

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. 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.

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). However, Lloyd Kahn, after writing two books on the subject (Domebook 1 and Domebook 2), became disillusioned with domes. 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.
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.

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.

## 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:

## References

1. ^ Bauersfeld, Walter
2. ^ "Refried Domes" by Lloyd Kahn

StRUT (Students Recycling Used Technology) is an organization which provides technology education, resources, and recycling to schools in the United States.
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In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space.
A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3
A triangle is one of the basic shapes of geometry: a polygon with three corners or and three sides or edges which are straight line segments.

In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
Stress is a measure of force per unit area within a body. It is a body's internal distribution of force per area that reacts to external applied loads. Stress is often broken down into its shear and normal components as these have unique physical significance.
dome is a common structural element of architecture that resembles the hollow upper half of a sphere.

## Description

Domes do not have to be perfectly spherical in cross-section, however; a section through a dome may be an ellipse.
In geometry, a Platonic solid is a convex regular polyhedron. These are the three-dimensional analogs of the convex regular polygons. There are precisely five such figures (shown below). They are unique in that the faces, edges and angles are all congruent.
An icosahedron (Greek: eikosaedron, from eikosi twenty + hedron seat; /ˌaɪ.kəʊ.sə.ˈhi.
Computer graphics is a sub-field of computer science and is concerned with digitally synthesizing and manipulating visual content. Although the term often refers to three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
Tensegrity is a portmanteau of tensional integrity. It refers to the integrity of structures as being based in a synergy between balanced tension and compression components.
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A tent is a shelter, consisting of sheets of fabric or other material draped over or attached to a frame of poles and/or ropes.
Industrial design is an applied art whereby the aesthetics and usability of products may be improved for marketability and production. The role of an Industrial Designer is to create and execute design solutions towards problems of engineering, marketing, brand development and
Management science, or MS, is the discipline of using a mathematical model, and other analytical methods, to help make better business management decisions. The field is also known as Operations research (OR) in the United States or Operational Research in the United
In cognitive linguistics, conceptual metaphor refers to the understanding of one conceptual domain in terms of another, for example, understanding time in terms of space (e.g. "time flies"). A conceptual domain can be any coherent organization of experience.
Anthony Stafford Beer (September 25, 1926 - August 23, 2002) was a British theorist, consultant and professor at the Manchester Business School. He is best known for his work in the fields of operational research and management cybernetics.
Walther Bauersfeld (January 23, 1879 in Berlin–October 28, 1959 in Heidenheim an der Brenz) was a German engineer, employed by the Zeiss Corporation, on a suggestion by the German astronomer Max Wolf, started work on the first projection planetarium in 1912.
Carl Zeiss (September 11, 1816 – December 3, 1888) was an optician commonly known for the company he founded, Zeiss. Zeiss himself also made a few contributions to lens manufacturing that have aided the modern production of lenses.
planetarium is a theatre built primarily for presenting educational and entertaining shows about astronomy and the night sky, or for training in celestial navigation. A dominant feature of most planetariums is the large dome-shaped projection screen onto which scenes of stars,
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Richard Buckminster “Bucky” Fuller (July 12, 1895 – July 1, 1983)[1] was an American visionary, designer, architect, poet, author, and inventor.
Kenneth Snelson (born June 29, 1927) is a contemporary sculptor and photographer. His sculptural works, composed of flexible and rigid components, are arranged according to the idea of tensegrity.
Black Mountain College, founded in 1933 near Asheville, North Carolina, was known as one of the leading progressive schools in the United States. It ceased operations in 1957.
Dymaxion House was developed by inventor Buckminster Fuller to address several failures he perceived with existing homebuilding techniques. Fuller designed several different versions of the house at different times, but they were factory manufactured kits, assembled on site,
Tensegrity is a portmanteau of tensional integrity. It refers to the integrity of structures as being based in a synergy between balanced tension and compression components.
Princeton, New Jersey is located in Mercer County, New Jersey, United States. Princeton University has been sited in the town since 1756. Although Princeton is a "college town", there are many other important facilities in the vicinity that enrich the town's character and economic
Baton Rouge, Louisiana
Downtown Baton Rouge

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Location of Baton Rouge in East Baton Rouge Parish, Louisiana
Henry Kaiser may refer to:
• Henry J. Kaiser (1882–1967), American industrialist
• Henry Kaiser (musician) (born 1952), grandson of Henry J. Kaiser