At the time the tower was built many people were shocked by its daring shape. Eiffel was criticised for the design and accused of trying to create something artistic, or inartistic according to the viewer, without regard to engineering. Eiffel and his engineers, however, as experienced bridge builders, understood the importance of wind forces and knew that if they were going to build the tallest structure in the world they had to be certain it would withstand the wind.
Researchers have found that Eiffel used empirical and graphical methods accounting for the effects of wind rather than a specific mathematical formula. Careful examination of the tower shows a basically exponential shape; actually two different exponentials, the lower section overdesigned to ensure resistance to wind forces. Several mathematical explanations have been proposed over the years for the success of the design; the most recent is described as a nonlinear integral equation based on counterbalancing the wind pressure on any point on the tower with the tension between the construction elements at that point.[38][39] As a demonstration of the tower's effectiveness in wind resistance, it sways only 6–7 cm (2–3 in) in the wi