Hyperboloid structure
Hyperboloid structures in
architecture were first applied by great
Russian engineer
Vladimir Shukhov (
1853-
1939). 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 Chebyshev'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 hyperboloid roofs of the exhibition pavilions of the
1896 All-Russian Industrial and Handicrafts Exposition in
Nizhny Novgorod were the first publicly prominent examples of Shukhov's new system. The roofs of these pavilions were doubly-curved surfaces formed entirely of a lattice of straight angle-iron and flat iron bars. Shukhov himself called them "metal lace." The patent of this system, for which Shukhov applied in
1895, was awarded in
1899.
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A hyperboloid tower in the port of Kobe, Japan. |
Two pavilions of this type were built for the Nizhni-Novgorod exposition, one oval in plan and one circular. Shukhov also turned his attention to the development of an efficient and easily constructed structural system for a
tower carrying a large gravity load at the top - the problem of the
water tower. His solution was inspired by observing the action of a woven basket holding up a heavy weight. Again, it took the form of a non-Euclidean doubly-curved surface constructed of a light network of straight iron bars and angle-iron.
Shukhov's patent for an
azhurnaia bashnia ("lace tower," i.e.,
lattice tower) was submitted in
1896 and awarded in
1899. The hyperbolic form of the tower is remarkably similar to that of the
pseudosphere used to illustrate explanations of Lobachevskii's disproof of Euclid's parallel postulate. Shukhov built his first
azhurnaia bashnia as a water tower (hyperbolic shell) for the 1896 All-Russian Exposition.
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 15m to 40m. The world's first
hyperboloid tower is located in Polibino of the
Lipetsk region of
Russia.
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 tower for
Moscow. Shukhov designed a 350m tower, which would have surpassed the
Eiffel tower 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 of
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 Tower was completed by March of
1922.
Antoni Gaudi and Shukhov carried out experiments with
hyperboloid structures practically simultaneously in
1880-
1895. They did those experiments independently from each other. Antoni Gaudi used structures in the form of hyperbolic
paraboloid (hypar) and hyperboloid of revolution in the
Sagrada Familia in
1910 [
1]. In the
Palau Güell, there is one set of interior columns along the main facade with hyperbolic capitals. Also, it appears that the crown of the the famous parabolic vault is a
hyperboloid. The vault of one of the stables at the
Church of Colònia Güell appears to be a hyperboloid. There is one unique column of sorts in the
Park Güell that is a hyperboloid. Also, in the
Sagrada Familia, there are a few places on the nativity facade - a design not equated with Gaudi's ruled-surface design, where the
hyperboloid crops up. All around the scene with the pelican, there are numberous 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). And finally, the "bishop's mitre" spires are capped with
hyperboloids.
Le Corbusier and
Félix Candela used hyperboloid structures (hypar).
The
Georgia Dome is the first Hypar-Tensegrity
Dome to be built [
2].
*
Vladimir Shukhov*
Antoni Gaudí,
Sagrada Familia *
Oscar Niemeyer,
Brasília Cathedral *
Ken Shuttleworth,
"The Vortex" *
Le Corbusier,
Parliament Building, Chandigarh*
Le Corbusier,
Iannis Xenakis,
«Poème électronique» Hypar Philips Pavilion*
Ieoh Ming Pei,
Hyperboloid New York*
Gyo Obata, the McDonnell Planetarium in
St. Louis *
Shukhov Tower*
Kobe Port Tower*
Shukhov tower on the Oka River*
Ještěd Tower*
Georgia Dome*
Thin-shell structure*
Tensile architecture*
Tensile and membrane structures* Hyperbolic roof
Olympic Stadium, Munich* Hyperbolic paraboloid roof
Pengrowth Saddledome* Hyperbolic paraboloid roof
Apache Plaza[
3]
*
Shukhov Tower*
Hyperboloid structures of Sagrada Familia*
Gaudi and Shukhov*
Gaudi's vaulted structures*
The Origins of Modernism in Russian Architecture*
Special Structures*
Hyperboloid footbridge *
Shells: Hyperbolic paraboloids (hypar)*
Hyperboloid structures and music.*
EXPO-70 Japan Automobile Pavilion by
Kunio Maekawa*
Hyperbolic Paraboloids & Concrete Shells*
Shukhov Tower Foundation* "The Nijni-Novgorod exhibition: Water tower, room under construction, springing of 91 feet span",
"The Engineer", № 19.3.1897, P.292-294, London,
1897.
*
Rainer Graefe:
"Vladimir G. Šuchov 1853-1939 - Die Kunst der sparsamen Konstruktion.", S.192, Stuttgart, DVA,
1990. [
4]
*
Elizabeth Cooper English:
"Arkhitektura i mnimosti": The origins of Soviet avant-garde rationalist architecture in the Russian mystical-philosophical and mathematical intellectual tradition", a dissertation in architecture, 264 p., University of Pennsylvania, 2000.
