Hyperboloid structures are
architectural structureAn architectural structure is a free-standing, immobile outdoor constructed element. The structure may be temporary or permanent.Structures include buildings and nonbuilding structures . Examples of building structures include houses, town halls, libraries, and skyscrapers...
s designed with
hyperboloid geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer
Vladimir ShukhovVladimir Grigoryevich Shukhov , was a Russian engineer-polymath, scientist and architect renowned for his pioneering works on new methods of analysis for structural engineering that led to breakthroughs in industrial design of world's first hyperboloid structures, lattice shell structures, tensile...
(1853–1939). The world's first hyperboloid tower is located in
Polibino, Lipetsk OblastPolibino is a village in Dankovsky District of Lipetsk Oblast, Russia. A historical estate of Russian aristocrats Nechayevs is located there.The estate is composed of a palace, English park, regular gardens, ponds, and more...
, Russia.
The shapes are
doubly ruled surfacesIn geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone...
(hence can be built with a lattice of straight beams), which can be classed as:
- Hyperboloid of one sheet, such as cooling tower
Cooling towers are heat removal devices used to transfer process waste heat to the atmosphere. Cooling towers may either use the evaporation of water to remove process heat and cool the working fluid to near the wet-bulb air temperature or in the case of closed circuit dry cooling towers rely...
s
- Hyperbolic paraboloids, such as saddle roof
A saddle roof is one which follows a convex curve about one axis and a concave curve about the other. The hyperbolic paraboloid form has been used for roofs at various times since it is easily constructed from straight sections of lumber, steel, or other conventional materials...
s
Properties of hyperboloid structures
Hyperbolic structures have a negative
Gaussian curvatureIn differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way...
, meaning they curve inward rather than outward or being straight. As doubly ruled surfaces, they can be made with a lattice of straight beams, hence are easier to build and, all else equal, stronger than curved surfaces that do not have a ruling and must instead be built with curved beams.
Hyperboloid structures are superior in stability towards outside forces than "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency) and therefore are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features, but their cross section is much more commonly seen in hyperbolic bridges.
With cooling towers, a hyperbolic structure is preferred. At the bottom, the widening of the tower provides higher surface area for water to boil in. As the water first boils and steam rises, the narrowing effect helps accelerate the
laminar flowLaminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents...
, and then as it widens out, contact between the heated air and atmospheric air supports turbulent mixing.
Work of Shukhov
In the 1880s, Shukhov began to work on the problem of the design of roof systems to use a minimum of materials, time and labor. His calculations were most likely derived from mathematician
Pafnuty ChebyshevPafnuty Lvovich Chebyshev was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov, Tschebyshev, Tchebycheff, or Tschebyscheff .-Early years:One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk,...
's work on the theory of best approximations of functions. Shukhov's mathematical explorations of efficient roof structures led to his invention of a new system that was innovative both structurally and spatially. By applying his analytical skills to the doubly curved surfaces Nikolai Lobachevsky named "hyperbolic", Shukhov derived a family of equations that led to new structural and constructional systems, known as hyperboloids of revolution and hyperbolic paraboloids.
The steel
gridshellA gridshell is a structure which derives its strength from its double curvature , but is constructed of a grid or lattice....
s of the exhibition pavilions of the 1896
All-Russian Industrial and Handicrafts ExpositionThe All-Russia industrial and art exhibition 1896 in Nizhny Novgorod was held from May 28 till October 1 , 1896. The 1896 exhibition was the biggest pre-revolution exhibition in Russian Empire and was organized with the money allotted by Nicholas II, Emperor of Russia...
in
Nizhny NovgorodNizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
were the first publicly prominent examples of Shukhov's new system. Two pavilions of this type were built for the Nizhni Novgorod exposition, one oval in plan and one circular. The roofs of these pavilions were doubly curved
gridshellA gridshell is a structure which derives its strength from its double curvature , but is constructed of a grid or lattice....
s formed entirely of a lattice of straight angle-iron and flat iron bars. Shukhov himself called them
azhurnaia bashnia ("lace tower", i.e.,
lattice towerA lattice tower or truss tower is a freestanding framework tower. They can be used as electricity pylons especially for voltages above 100 kilovolts, as a radio tower or as an observation tower....
). The patent of this system, for which Shukhov applied in 1895, was awarded in 1899.
Shukhov also turned his attention to the development of an efficient and easily constructed structural system (
gridshellA gridshell is a structure which derives its strength from its double curvature , but is constructed of a grid or lattice....
) for a
towerA tower is a tall structure, usually taller than it is wide, often by a significant margin. Towers are distinguished from masts by their lack of guy-wires....
carrying a large gravity load at the top – the problem of the
water towerA water tower or elevated water tower is a large elevated drinking water storage container constructed to hold a water supply at a height sufficient to pressurize a water distribution system....
. His solution was inspired by observing the action of a woven basket holding up a heavy weight. Again, it took the form of a doubly curved surface constructed of a light network of straight iron bars and angle-iron. Over the next twenty years, he designed and built close to two hundred of these towers, no two exactly alike, most with heights in the range of 12m to 68m.
At least as early as 1911, Shukhov began experimenting with the concept of forming a tower out of stacked sections of hyperboloids. Stacking the sections permitted the form of the tower to taper more at the top, with a less pronounced "waist" between the shape-defining rings at bottom and top. Increasing the number of sections would increase the tapering of the overall form, to the point that it began to resemble a cone.
By 1918 Shukhov had developed this concept into the design of a nine-section stacked hyperboloid radio
transmission towerA transmission tower is a tall structure, usually a steel lattice tower, used to support an overhead power line. They are used in high-voltage AC and DC systems, and come in a wide variety of shapes and sizes...
for Moscow. Shukhov designed a 350m tower, which would have surpassed the
Eiffel TowerThe Eiffel Tower is a puddle iron lattice tower located on the Champ de Mars in Paris. Built in 1889, it has become both a global icon of France and one of the most recognizable structures in the world...
in height by 50m, while using less than a quarter of the amount of material. His design, as well as the full set of supporting calculations analyzing the hyperbolic geometry and sizing the network of members, was completed by February 1919; however, the 2200 tons of steel required to build the tower to 350m were not available. In July 1919, Lenin decreed that the tower should be built to a height of 150m, and the necessary steel was to be made available from the army's supplies. Construction of the smaller tower with six stacked hyperboloids began within a few months, and
Shukhov TowerThe Shukhov radio tower , also known as the Shabolovka tower, is a broadcasting tower in Moscow designed by Vladimir Shukhov. The 160-metre-high free-standing steel structure was built in the period 1920–1922, during the Russian Civil War...
was completed by March 1922.
Other architects
Antoni GaudiAntoni Gaudí i Cornet was a Spanish Catalan architect and figurehead of Catalan Modernism. Gaudí's works reflect his highly individual and distinctive style and are largely concentrated in the Catalan capital of Barcelona, notably his magnum opus, the Sagrada Família.Much of Gaudí's work was...
and Shukhov carried out experiments with hyperboloid structures practically simultaneously, but independently, in 1880-1895. Antoni Gaudi used structures in the form of hyperbolic
paraboloidIn mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point....
(hypar) and hyperboloid of revolution in the
Sagrada FamíliaThe ' , commonly known as the Sagrada Família, is a large Roman Catholic church in Barcelona, Catalonia, Spain, designed by Catalan architect Antoni Gaudí...
in 1910. In the Sagrada Família, there are a few places on the nativity
facadeA facade or façade is generally one exterior side of a building, usually, but not always, the front. The word comes from the French language, literally meaning "frontage" or "face"....
- a design not equated with Gaudi's ruled-surface design, where the hyperboloid crops up. All around the scene with the pelican, there are numerous examples (including the basket held by one of the figures). There is a hyperboloid adding structural stability to the cypress tree (by connecting it to the bridge). The "bishop's mitre" spires are capped with hyperboloids.
In the
Palau GüellThe Palau Güell is a mansion in Barcelona, Catalonia, Spain designed by the Catalan architect Antoni Gaudí for the Catalan industrial tycoon Eusebi Güell.It is part of the UNESCO World Heritage Site "Works of Antoni Gaudí"....
, there is one set of interior columns along the main facade with hyperbolic capitals. The crown of the famous parabolic
vaultA Vault is an architectural term for an arched form used to provide a space with a ceiling or roof. The parts of a vault exert lateral thrust that require a counter resistance. When vaults are built underground, the ground gives all the resistance required...
is a hyperboloid. The vault of one of the stables at the
Church of Colònia GüellThe Church of Colònia Güell is an unfinished work by Antoni Gaudí. It was built as a place of worship for the people in a manufacturing suburb in Santa Coloma de Cervelló, near Barcelona . Colònia Güell was the brainchild of Count Eusebi de Güell...
is a hyperboloid. There is a unique column in the
Park GüellPark Güell is a garden complex with architectural elements situated on the hill of El Carmel in the Gràcia district of Barcelona, Catalonia, Spain. It was designed by the Catalan architect Antoni Gaudí and built in the years 1900 to 1914...
that is a hyperboloid. The famous Spanish engineer and architect
Eduardo TorrojaEduardo Torroja y Miret, was a Spanish structural engineer, pioneer in the design of concrete-shell structures. His first large project was the Tempul cable-stayed aqueduct in 1926, Guadalete, Jerez de la Frontera, in which he used prestressed girders, and he made his name with the concrete...
designed a
thin-shellThin-shell structures are light weight constructions using shell elements. These elements are typically curved and are assembled to large structures...
water tower in Fedala and the roof of hippodrome "Zarzuela" in the form of hyperboloid of revolution.
Le CorbusierCharles-Édouard Jeanneret, better known as Le Corbusier , was a Swiss-born French architect, designer, urbanist, writer and painter, famous for being one of the pioneers of what now is called modern architecture. He was born in Switzerland and became a French citizen in 1930...
and
Félix CandelaFélix Candela Outeriño was a Spanish architect known for his significant role in the development of Mexican architecture and structural engineering. Candela’s major contribution to architecture was the development of thin shells made out of reinforced concrete...
used hyperboloid structures (hypar).
A hyperboloid
cooling towerCooling towers are heat removal devices used to transfer process waste heat to the atmosphere. Cooling towers may either use the evaporation of water to remove process heat and cool the working fluid to near the wet-bulb air temperature or in the case of closed circuit dry cooling towers rely...
was patented by Frederik van Iterson and Gerard Kuypers in 1918.
The
Georgia DomeThe Georgia Dome is a domed stadium located in Atlanta, Georgia, United States, between downtown to the east and Vine City to the west. It is primarily the home stadium for the NFL Atlanta Falcons and the NCAA Division I FCS Georgia State Panthers football team. It is owned and operated by the...
was the first Hypar-
TensegrityTensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members do not touch each other and the prestressed tensioned members delineate the...
domeA dome is a structural element of architecture that resembles the hollow upper half of a sphere. Dome structures made of various materials have a long architectural lineage extending into prehistory....
to be built.
See also
- List of hyperboloid structures
- Polibino, Lipetsk Oblast
Polibino is a village in Dankovsky District of Lipetsk Oblast, Russia. A historical estate of Russian aristocrats Nechayevs is located there.The estate is composed of a palace, English park, regular gardens, ponds, and more...
- The world's first hyperboloid structure
- Tensile structure
A tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with tensegrity, which is a structural form with both tension and compression elements....
- Lattice mast
Lattice masts, or cage masts, are a type of observation mast common on major warships in the early 20th century. They were used most prominently on American dreadnought battleships and armored cruisers of the World War I era. Observation posts were mounted on the masts and used to direct the fire...
- Thin-shell structure
Thin-shell structures are light weight constructions using shell elements. These elements are typically curved and are assembled to large structures...
- List of thin shell structures
- Cooling tower
Cooling towers are heat removal devices used to transfer process waste heat to the atmosphere. Cooling towers may either use the evaporation of water to remove process heat and cool the working fluid to near the wet-bulb air temperature or in the case of closed circuit dry cooling towers rely...
- Sam Scorer
Sam Scorer FRSA was an innovative architect from Lincolnshire.-Early life:He was brought up in Lincoln, one of five children. His father was a senior partner in a firm of solicitors, and later became clerk to the district council.He read Mechanical Sciences at Corpus Christi College, Cambridge in...
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