Model Equations for the Eiffel Tower Profile: Historical Perspective and New Results

A review of mathematical models for the shape of the Eiffel Tower show that they are not consistent with Eiffel's writings. Reported here is a new model derived from Eiffel's concern about wind loads on the tower, as documented in a communication to the French Civil Engineering Society on March 30, 1885. This model reveals an exponential skyline profile, while the actual tower profile closely resembles two piecewise continuous exponentials. This discrepancy is explained by specific safety factors that Eiffel & Company incorporated in the construction of the lower half of the 300 meter tower.