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(a) Original concept for the Eiffel Tower sketched by Nouguier and Koechlin, 6 June 1884; (b) final design sketched by Eiffel. [From E. Heinle and F. Leonhardt, Towers: A Historical Survey (Rizzoli International, New York, 1989). Reprinted by permission of La Nouvelle Societe d'Exploitation de la Tour Eiffel—illustrations Pierre Bideau.]

(a) Original concept for the Eiffel Tower sketched by Nouguier and Koechlin, 6 June 1884; (b) final design sketched by Eiffel. [From E. Heinle and F. Leonhardt, Towers: A Historical Survey (Rizzoli International, New York, 1989). Reprinted by permission of La Nouvelle Societe d'Exploitation de la Tour Eiffel—illustrations Pierre Bideau.]

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The design and construction of the Eiffel Tower was based, in part, on a uniform horizontal wind model giving 300 kg m−2 kinematic pressure acting on the surface of the tower. Eiffel received a patent for his method of construction that eliminates the need for diagonal trellis bars used to resist the moment of an oncoming wind. At the end of the 19...

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Context 1
... Koechlin and Emile Nouguier, em- ployed by Gustave Eiffel in his construction company, Com- panie des Etablissements Eiffel, first conceived the idea to build a 1000 ft tower at Champs de Mars for the Paris Ex- position in 1889. The original conceptual drawing for the Eiffel Tower, made by these engineers in Zurich in 1884, is reproduced here in Fig. 1a. To exhibit its extreme 300 m height nearest metric equivalent to 1000 ft, the tower in Fig. 1a is compared with the accumulated heights of Notre Dame, the Statue of Liberty, the Arch de Triomphe, three replications of the Place Vendôme column, and a six-story Paris apartment building. Numerous modifications by Eiffel and his architect ...
Context 2
... des Etablissements Eiffel, first conceived the idea to build a 1000 ft tower at Champs de Mars for the Paris Ex- position in 1889. The original conceptual drawing for the Eiffel Tower, made by these engineers in Zurich in 1884, is reproduced here in Fig. 1a. To exhibit its extreme 300 m height nearest metric equivalent to 1000 ft, the tower in Fig. 1a is compared with the accumulated heights of Notre Dame, the Statue of Liberty, the Arch de Triomphe, three replications of the Place Vendôme column, and a six-story Paris apartment building. Numerous modifications by Eiffel and his architect Stéphane Sauvestre evolved the tower to its final design, shown in Fig. 1b, which was given as ...
Context 3
... to 1000 ft, the tower in Fig. 1a is compared with the accumulated heights of Notre Dame, the Statue of Liberty, the Arch de Triomphe, three replications of the Place Vendôme column, and a six-story Paris apartment building. Numerous modifications by Eiffel and his architect Stéphane Sauvestre evolved the tower to its final design, shown in Fig. 1b, which was given as an at- tachment to the contract to build the tower signed on 18 January 1887. Figures 1a and 1b are taken from Ref. 1. In particular, the 43 panels girdled by six ceintures belts ex- hibited in Fig. 1a were pared down to just 29 panels girdled by three ceintures in Fig. ...
Context 4
... Numerous modifications by Eiffel and his architect Stéphane Sauvestre evolved the tower to its final design, shown in Fig. 1b, which was given as an at- tachment to the contract to build the tower signed on 18 January 1887. Figures 1a and 1b are taken from Ref. 1. In particular, the 43 panels girdled by six ceintures belts ex- hibited in Fig. 1a were pared down to just 29 panels girdled by three ceintures in Fig. ...
Context 5
... evolved the tower to its final design, shown in Fig. 1b, which was given as an at- tachment to the contract to build the tower signed on 18 January 1887. Figures 1a and 1b are taken from Ref. 1. In particular, the 43 panels girdled by six ceintures belts ex- hibited in Fig. 1a were pared down to just 29 panels girdled by three ceintures in Fig. ...
Context 6
... the direction of each upright element de- flects following a curve illustrated in the drawing fig. 1, Pl. 91, and in reality, the exterior curve of the tower reproduces, at a given scale, the very curve created by the bending moments of the ...

Citations

... The wind energy challenge is quite unique in the sense that geophysical turbulent flows interact with machinery whose scales are unparalleled in prior engineering applications of turbulence research. It is known that Eiffel, while designing the tower that bears his name, used the assumption of a constant mean velocity distribution in the atmosphere and that using a more realistic turbulent mean boundary layer profile would have in fact yielded a modified shape [97]. Now imagine the challenges of designing a 'dynamic' Eiffel Tower containing moving parts that speed along five times faster than the wind velocity. ...
Article
The accelerating growth of wind energy in recent years mandates improved understanding of wind turbine, wind farm and atmospheric turbulence interactions. Fluid turbulence plays a vital role in these interactions, motivating the present formulation of several pertinent questions for turbulence research. These questions touch upon the need for better analytical, synthetic and reduced order models of turbulence, better model coupling methods and basic understanding of flow phenomena governing kinetic energy entrainment and limiting power densities. Responding to the formulated questions may lead to improvements in wind energy harvesting.
... This said, on November 13 th 2015, these two of us left for Paris with a pocket seismometer in the backpack and decided to climb the Eiffel Tower to measure its dynamic behavior, since surprisingly nobody has done it before, at least to our knowledge based on bibliographic research. In the literature, several studies about the tower shape [5,11] and its foundations [1] can be found, as well as studies on the tower behavior to wind [3,8,9]. According to the French newspaper Le Moniteur [7], a 2 year project to create a numerical model of the tower was going to be realized by the Société d'Exploitation de la Tour Eiffel but we have not found any further information on this. ...
Article
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The Eiffel tower is the most visited monument in the world. Millions of visitors have taken millions of pictures of it over the last century but apparently a dynamic picture (that is a dynamic characterization) does not exist or is not publicly available. In this paper we show the amount of information that can be extracted from a few recordings of ambient tremor collected on the tower and on the surrounding subsoil with a single pocket seismometer in a few minutes, during a leisure visit. We also propose a numerical model for the tower, capable to fit the observed data. This is interesting because the mass and stiffness distribution of the tower is unique and does not follow any modern construction rule. The dynamic model of the tower would also be important if Paris were a high seismic hazard town, which is not. According to our model, the tower could withstand peak ground accelerations >100% larger than the values prescribed by current seismic hazard estimates. The dynamic model of the tower is also important to better design the future interventions and to monitor the ageing of the structure.
... Note that this is exactly the wind torque considered, in the continuum version, in [11,12] and, in its discrete version, in [10]. ...
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The use of solar chimneys for energy production was suggested more than 100 years ago. Unfortunately, this technology has not been realized on a commercial scale, in large part due to the high cost of erecting tall towers using traditional methods of construction. Recent works have suggested a radical decrease in tower cost by using an inflatable self-supported tower consisting of stacked toroidal bladders. While the statics deflections of such towers under constant wind have been investigated before, the key for further development of this technology lies in the analysis of dynamics, which is the main point of this paper. Using Lagrangian reduction by symmetry, we develop a fully three-dimensional theory of motion for such towers and study the tower's stability and dynamics. Next, we derive a geometric theory of optimal control for the tower dynamics using variable pressure inside the bladders and perform detailed analytical and numerical studies of the control in two dimensions. Finally, we report on the results of experiments demonstrating the remarkable stability of the tower in real-life conditions, showing good agreement with theoretical results. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
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Cet article décrit sommairement la recherche expérimentale de Gustave Eiffel, qui a mis en évidence la forte réduction de la trainée d’une sphère dans un écoulement à grande vitesse, accompagnant le changement occasionné par la transition de la couche limite du corps depuis l’état laminaire vers l’état turbulent (crise de trainée). Cette découverte, mise en question initialement par Ludwig Prandtl, a été rendue possible par la conception et la réalisation par Eiffel d’un ensemble de nouvelles expériences astucieuses et de techniques innovantes créées autour de la tour Eiffel. Un siècle après la découverte de cet effet, la compréhension de la dynamique de transition turbulente intermittente et bistable ainsi que la description des structures cohérentes instables présentes dans cette transition, restent ouvertes.
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Lessons on math and Philadelphia's City design.
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The City design appears to accommodate circles-of-life geometries. Furthermore, the Golden Phi balance, or perfect matching of two length ratios, is observed. Bible verses may have been inscribed to invigorate the Penn-Holme design of the City of Philadelphia grid. This would provide an explanation of the unusual pattern of northern numerical land parcel side-lengths. An investigation to explain why the street width of North-South Broad Street had been widened to 113 feet is presented. Finally, an explanation for the tilt, or angle of the rectangular grid is proposed. One answer is simply the application of Newton's color wheel for a "greene" country towne. Further, it has an alignment association toward Jerusalem on a great circle around the Earth. Isometry transformations of the City grid would generate nets, a quincunx. Foundations for the descriptor, Golden, for the perfect proportion in color vision are presented.
Article
The Eiffel tower is the most visited monument in the world. Millions of visitors have taken millions of pictures of it over the last century but apparently a dynamic picture (that is a dynamic characterization) does not exist or is not publicly available. In this paper we show the amount of information that can be extracted from a few recordings of ambient tremor collected on the tower and on the surrounding subsoil with a single pocket seismometer in a few minutes, during a leisure visit. We also propose a numerical model for the tower, capable to fit the observed data. This is interesting because the mass and stiffness distribution of the tower is unique and does not follow any modern construction rule. The dynamic model of the tower would also be important if Paris were a high seismic hazard town, which is not. According to our model, the tower could withstand peak ground accelerations >100% larger than the values prescribed by current seismic hazard estimates. Regarding the wind, Eiffel could only study its effects from a static planar point of view, while the model allowed us to follow a 3D approach and to assess the expected displacements under different loads. Last, the dynamic model of the tower is also important to better design the future interventions and to monitor the ageing of the structure.
Article
Full-text available
We propose a novel design for a solar updraft tower, wherein the chimney that generates the updraft is a self-supporting, free-standing stack of hollow gas-filled tori. Considerations for the design stabilizing the structure via a combination of shape, overpressure, and buoyancy are presented. Filling the tori with air rather than with a light gas may be advantageous for stability. The chimney shapes are optimized for deformation under wind loading. We also present simple cost calculations and results of CFD modeling to confirm the viability of the design.