Model equations for the Eiffel Tower profile: Historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel\u27s writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel\u27s writings provides a fair approximation to the tower\u27s skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel\u27s concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind . An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved