Engineering

"The miniature facets are adjusted by hand... It is sufficient to simply let the sun shine on the miniature reflector and then turn the facets so that the reflected light strikes those parts of the globe corresponding to the region to be irradiated."

"In the north, on the other hand, outside of , there are no such masses of land-ice (however much ice there may be, no danger arises from melting ice that floats in the water), and the glaciers of Greenland will remain because if their high location and because there will be more snowfall on Greenland if the polar sea melts."

"An ideal opaque shield would scatter the Earth bound solar energy into diffuse infrared energy."

"A rocket with the necessary equipment is sent aloft and there given a lateral propulsion which puts it into an elliptical orbit around the earth. I will call this rotation about the earth "revolution". Major axis perpendicular to the ecliptic, perigee in the south 1,000 km above the earth's surface, apogee in the north 5,000 km above the earth's surface."

"Whether we must seek to constantly reflect the light on the earth vertically or are, in fact, able to is another question. I will assume that we can in order to study the single elements which determine the path of the reflector. (s are also used in calculations, although it is known that they do not exist.)"

"Enough of this. They are only dreams of the future. Bold ones? Perhaps, but we have already experienced... bolder ideas. Who would have believed in 1894 that, a few years later, one would see through a person by means of Roentgen rays? PHILANDER's statement (Medical Fairy Tales), "Man will be made transparent like a jelly-fish", was bolder than this dream of the future; that required finding something completely new, while here we are dealing with laws of nature already known.—Accomplishing these things will certainly require the conversion of enormous energies. But were not hundred times greater sums of money expended during the World War? In one year, the nations of Europe spend more on smoking and drinking than the whole sodium reflector would cost. War and narcotics are quite unnecessary things, yet more money is spent on them than on something useful. Should not mankind, in an exceptional case, also save something for constructive work?"

"Oberth... began the book Men in Outer Space: New Projects for Rockets and Space Travel... written in the style accessible to the general reader. ...Published in 1955 in German, it was translated into English, French, Italian, Dutch, and even in Croatian! ...Oberth's new book was indeed "cosmic," and this gave it a cardinal distinction from his classic book of the 1920s. ...A supplemental chapter ...is devoted to "s," a theme which occupied Oberth all his life. A short description ...is already present in the 1923 book. In 1929, when he published his fundamental work, Ways to Space Travel, he included a much more comprehensive description... in the chapter... "Space Stations." ...[A]lmost the entire chapter is devoted to space mirrors. In the 1954 book... a new varient... is presented. Eventually in Bucharest in 1978, an entire book (in German) was devoted to this theme. ...[T]he primary purpose for the space mirror would today be called an ecological one ...At the time ...there was ...no robotics technology, and he assumed all the work after ...erection ...would ...be carried out manually by astronauts."

"The cultural tasks are... possible to fulfill. For example, if a sea route to the ports of Siberia is to be kept ice-free, a route must only be chosen that runs approximately in the direction of the winter wind from the Gulf Stream... light is thrown on a relatively narrow and short strip running from east to west... to the extent that the sky clouds over at this place. ...[T]he direction of the wind and ...the earth's rotation coincide. Hereby the earth always rotates as we need it ...By the time the light patch has passed along the whole stretch, the fog at the beginning will either have settled or been blown away... Then one can begin at the beginning again, Since the clouds hold the heat above the shipping lane... a reflector 100 km in diameter is... sufficient."

"In the south... the main task of large reflectors... of making polar regions arable, is not feasible. If the glaciers of Antarctica were melted, the level of the ocean would rise uncomfortably (6-8 m). Hopefully, by then man will be sensible enough at least to leave a cold zone for the protection of nature."

"A wide range of techniques has been proposed for increasing the planetary , ranging from painting surfaces white to placing mirrors in orbit between the Earth and the sun."

"[H]is belief... a reduction in the cost of building large structures in outer space could be achieved by delivering the necessary materials from the moon... [H]e presupposed the existence of the necessary industrial plants on the moon, but the end result would be a thousand-fold reduction in the cost of building large structures in space."

"Oberth proposed to shade planets located close to the sun... with gigantic cosmic shields... Vice versa, the planets... further from the sun... would be warmed... with... gigantic cosmic mirrors."

"[A] giant net (similar to a trawl) would be erected in outer space, constructed in a hexagonal mesh pattern. This net would be stretched out and a tension sufficient to rotate the entire net would be maintained by . The rotation would be begun by special rockets and... continue because it was in a vacuum. The diameter of each hexagon would be about 10 kilometers, and the entire mirror would have a circular disk shape with a diameter of about 100 to 200 kilometers. Within each hexagon, a round mirror approximately 10 kilometers in diameter, would be installed. ...[Each] single mirror would be capable of being [independently] tilted... initiated by... electric s."

"shields for planets such as Venus or Mars would... be large, complex structures requiring vast amounts of lunar or asteroidal material... and long-range transportation... One... stepping stone to understanding and mastering the technologies and processes... would be the construction of a shield to offset the greenhouse effect on... Earth. Such... would not require interplanetary capabilities."

"The time required for the removal of... [[w:Greenhouse gases|[greenhouse] gases]] from the atmosphere by natural processes is... uncertain: current estimates are several centuries. The uncertainties... [have] led to calls for... restrictions on the generation of greenhouse gases. ...The existence of a possible technical solution could... have a major short-term impact in influencing short term consumption restrictions, even if the solution could not be implemented until the next century."

"Greenhouse warming of the Earth due to human activities is a possibility, moreover one for which mitigative/remedial actions of the types proposed here can be at once deliberate and effective. In contrast, Ice Age-severity cooling... that have occurred quasi-periodically many times during the last 1.2 million years, is a practical certainty. Moreover, a several-decade duration cold snap of Ice Age Maximum temperature-drop is known to have occurred in the Northern Hemisphere with essentially no warning during the last interglacial period, under precursor climatic conditions only slightly warmer than the present-day one."

"can be formed into glass for either a transparent or opaque shield."

"For a given diameter and height of a tower and a given strength, this shape requires less material than any other form. ...Hyperboloidal towers can be built from or as a steel lattice, and is the most economical such structure for a given diameter and height."

"In 1899... V. Shukhov... patented the principle of constructing hyperboloid gridshell structures based on a hyperboloid of revolution. ...A one-sheet hyperboloid is a connected surface having negative at each point. Through any point of this surface, two intersecting [straight] lines can be drawn, completely belonging to it. Thus the... surface can be formed by the set of straight lines. It the steel beams would be placed along these lines the shape... could be retained under... external loading... [I]n Shukhov's towers horizontal rims [rings] were used... located at different levels... The stability... was ensured by numerous riveted connections... During the installation... the straight angles of the metal profile was somewhat deformed... [at] the... intersecting elements in order to ensure maximum contact... by rivets."

"The hyperboloid is the design standard for all nuclear cooling towers and some coal-fired power plants."

"This is an interesting paradox: you get the best local buckling resistance because the beams are straight and the best overall buckling resistance because the surface is double curved."

"When designing... cooling towers, engineers are faced with two problems: I. The structure must be able to withstand high winds and II. They should be built with as little material as possible... The hyperbolic form solves both..."

"The main hazard for high-rise structures is the loads caused by wind gusts. The grid shell design... minimize[d] their influence. Open-work design... ensured... sufficient strength, high stability and low metal consumption. ...[C]onsumption of metal per unit height... was three times less than... the ..."

"The presented orthogonal fitting algorithm can be applied easily for ellipsoid, and sphere also other surface[s] such as paraboloid."

"As hyperboloid structures are double curved, that is simultaneously curved in opposite directions, they are very resistant to . This means that you can get away with far less material than you would otherwise need..."

"The Radio Tower in Moscow is a gridshell which aims for structural efficiency. Its minimal surface and open lattice structure help in reducing the wind load, one of the main challenges in high-rise building design. ...Shukhov's design logic focuses on structural . The rings between the different segments offer additional reinforcement to create an equilibrium between minimal material consumption, structural efficiency and geometry."

"Single curved surfaces, for example cylinders, have strengths but also weaknesses. Double curved surfaces... are curved in two directions and thus avoid... weak directions."

"Grigory Kovelman writes that Shukhov told him he had been thinking about the properties of hyperboloid structures for a long time, that he had studied hyperboloid forms at the Technical School, and that apparently the moment of enlightenment came about when he saw an up-ended wicker wastepaper basket with a focus on top of his desk. According to Shukhov, this was when he understood clearly how a hyperboloid structure with its curved surface [was] generated by straight rods..."

"The water tower was a unique structure of its time... According to Cooper, the idea... came directly from an imaginary hyperboloid geometry, invented by... Lobachevski in 1829..."

"[T]he structure of the lattice tower was a spatial system, where the load was equally spread along the surface. ...Aiming to optimise the design process, soon after building the tower Shukhov presented the standardised elements of the tower structure in a table format... with the aid of which it became possible to design a new water tower according to a client’s requirements in twenty-five minutes..."

"[T]his is the magical part... despite the surface being curved in two directions, it is made entirely of straight lines. Apart from the cost savings of avoiding curved beams or shuttering, they are far more resistant to buckling because the individual elements are straight..."

"... Ještěd in Czechia, Guangzhou in China... and Khan Shatir Shopping-Entertaining Center in Kazakhstan, Aspire Tower in Qatar... are vivid examples of using... the hyperboloid principle... [in] modern buildings."

"In 2010, the journal Detail published an analysis of Shukhov’s constructions, calling his approach to design 'an early example of ’..."

"Alongside Shukhov’s drawings and sketchpads... a typescript produced by Shukhov’s former employee Grigory Kovelman... put together an extensive overview of Shukhov’s inventions and projects, both as a biographer and as a specialist who had worked with Shukhov.... Elena Shukhova... grand-daughter... presents extensive biographical details in Vladimir Grigorevich Shukhov. The First Engineer in Russia... Art of Construction... is a valuable collection of articles about Shukhov and his various inventions, written by... specialists. It includes... examples of his calculations. Shukhov’s own book Rafters... discusses the mathematical investigations which led him to conceptualise the spatial lattice structure, describing it as 'an optimisation process'."

"Vaulted gridshell constructions... were formed with thin metal arches turned away from the frontal position at a particular angle. They thus worked as one continuous resilient truss. ...Each arch was made with rigid metal strips of equal length... during the assembling process, each piece was bent equally. ...It was the first time in the world’s building practice that double-curved spatial vaults were created with single type rod elements ..."

"In this paper, the carbon bond model is built on the symmetry properties of the hyperboloid. These properties allow it to achieve a high ratio of the lateral and longitudinal , therefore the hyperboloid shapes are widely used in the engineering to create lightweight constructions consisting of straight beams that are known for being able to carry a large load while achieving a low use of raw materials."

"[T]here are... approaches that are closer to the field of the classical mechanics... so–called structural or discrete-continuous methods... The most straightforward example... is a modeled by the solid deformable rod... [T]he interatomic bonds are modeled as a deformable body or a construction. ...[T]hese approaches... can be implemented in standard computing packages based on the finite–element, boundary–element, or s. These methods can be considered as the bridges between the s of atomistic and continual models of the material."

"[T]he first hyperboloid tower was built by Russian engineer V.G. Shukhov in (1896)... Being widely demanded in architecture and engineering, such models still haven’t found a wide use in micro- and . It appears that the analogy drawn from the macro level will allow to describe correctly the properties of carbon materials at the micro level."

"Shukhov’s lattice-suspended and vaulted structures represented a carrying surface, which could be shaped in any form. ...The density of the grid made it possible to attach it to the shell without additional structures. ...[T]he grids were two to three times lighter than roofs with conventional frames..."

"Due to the complexity of the building procedure, uncertainties in the material properties as well as differences between the theoretical and the real geometry... reliability analysis... seems... indispensible..."

"In recent years... numerical simulation... has been applied to describe the collapse of structures, e.g., the collapse of cooling towers under blasting demolition... and the collapse of the World Trade Center..."

"This review is a complete collection of the studies done for cooling towers and... [gives] updated and sufficient materials for the researches in this field."

"Noorzaei et al... analyzed the cooling tower–foundation–soil system under vertical and lateral load generated due to self-weight and wind loads. In this study, the unsymmetrical wind pressure distribution in terms of [were] given..."

"Consideration of the soil–structure interaction... is extremely important when the soil or the foundation medium is not very firm. ...[U]nder ...dynamic loadings, the structure interacts with the surrounding soil imposing soil deformations. These... change the response of the structure."

"The collapse of three natural draft cooling towers at the Ferry bridge power station in 1965... [was] due to the inadequate design for the wind forces..."

"We present a new mechanical model of interatomic bonds, which can be used to describe the elastic properties of the carbon allotropes, such as , diamond, , and s. The interatomic bond is modeled by a hyperboloid–shape structure."

"The final and most unusual of the gridshell structures presented at the Exhibition was the 32-metre-tall lattice hyperboloid water tower. Everything was amazing in that first Shukhov tower—everything in it was some structural and geometric puzzle: straight rods and the external silhouette double curvature, the openwork lightness below and the solid heaviness above."

"191 of the Shukhov's Towers (from known near 200...) have been irretrievably lost during... the 20th century... [Some] towers were destroyed because their continued use for water supply has become impractical. To use them for another purpose... large investments were necessary."

"After the sudden collapse of three immense cooling towers at Ferry-Bridge Power Station in England in 1965, experimental and theoretical investigations had been done in... the stability of hyperbolic shells to study the parameters increasing the wind resistance and buckling safety..."

"Wind is the prime lateral load and its combination with self weight of the tower shell can cause the instability leading to catastrophic failure."