ight and reduces the surface area exposed to the wind."
Based on the information, Weidman derived a new equation for the skyline profile -- one that "embraces Eiffel's deep concern for the effects of wind-loading on the tower," he said. Weidman found an exact solution of the equation in the form of an exponential function that closely matches the shape of the tower's upper half.
The tower is composed of four arched, wrought-iron legs tapering inward to form a single column that rises to 300 meters, or 986 feet. The top level was built with a large room that Eiffel used for meteorological studies, capped by a spiral staircase and a television antenna that reaches to 1,052 feet today.
Plotting the actual shape of the tower reveals two separate exponential sections that are hooked together, he said. Since Eiffel did not seem confident in estimating the wind torque on the tower, he "overdesigned" the bottom section, beefing it up for safety reasons.
"The structural factor of safety is responsible for the second exponential equation describing the lower half of the tower," Weidman said.
Weidman and Pinelis presented their findings in a paper titled "Model Equations for the Eiffel Tower Profile: Historical Perspective and New Results."
The paper appeared in the July 2004 issue of the journal, "Comptes Rendus Mecanique," published by Elsevier and the French Academy of Sciences. In addition, the English translation of Eiffel's 1885 communication to the Society of French Engineers by Weidman and Roland recently was accepted for publication in the Architectural Research Quarterly published in Great Britain.
"While the events of the French Revolution are captured by Charles Dickens in his poignant novel, "A Tale of Two Cities," the centennial of the French Revolution is commemorated by Eiffel's graceful tower, the skyline profile of which is "A Tail of Two Exponentials," Weidman and Pinelis wrote in their 2004 paper.
The Eiffel tower, notes Weidman, "is a structural form molded by the wind." This was Eiffel's point more than a century ago, when he wrote about the four stout legs supporting the legendary tower: "Before they meet at such an impressive height, the uprights appear to spring out of the ground, moulded in a way by the action of the wind itself."
Other social bookmarking and sharing tools:
Note: Materials may be edited for content and length. For further information, please contact the source cited above.
Note: If no author is given, the source is cited instead.