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The Eiffel Tower, Paris, France

48° 51′ 29.88″ N, 2° 17′ 40.2″ E

The Great Men of Science

Most visitors go to the Eiffel Tower because it’s an icon, or they go for the view from the top, or they wait for nightfall to watch the spectacular light show. But scientific travellers should go because the Eiffel Tower is filled with science and technology.

The tower was built between 1887 and 1889 by the French engineer Gustav Eiffel, and was the entrance to the 1889 World’s Fair in Paris. It was designed as a temporary monument and was initially considered an ugly addition to the Paris skyline. It survived because of its scientific utility.

Almost the entire tower is constructed from puddle iron, which has a higher carbon content than wrought iron and therefore more tensile strength. Puddle iron is made by mixing the pig iron from a blast furnace (see page 282) with iron oxide (rust) and puddling it (stirring the molten mixture). Oxidation occurs inside the mixture, removing some carbon and other impurities. Puddling has the additional advantage that the composition of the resulting iron is controllable by adjusting the amount of iron oxide added.

The iron was formed into plates, which were riveted together with hot rivets on site. The rivets contracted as they cooled to tightly clamp the plates together. The tower currently stands 324 meters tall and contains 7,300 tonnes of iron. Visitors who make it to the top (just the long wait for the elevator can put many people off) are rewarded with a spectacular view of Paris, and a reproduction of Gustav Eiffel’s office.

One of Eiffel’s major concerns for the tower was its wind resistance. He had constructed many bridges (and the Statue of Liberty) before building the tower. The tower’s graceful curving shape was designed to prevent it from being adversely affected by the wind (see sidebar). Eiffel himself said that it was the wind that determined the basic shape of the tower.

Around the base of the tower Gustav Eiffel had the names of 72 great French scientists and engineers inscribed just below the first balcony. Here you’ll find Lagrange, Laplace, Lavoisier, Ampère, Navier, Gay-Lussac, Fizeau, Becquerel, Coriolis, Cauchy, Fresnel, Coulomb, Foucault, Arago, Poisson, Daguerre, Fourier, Carnot, and many more. The names are just visible from the ground, although a good pair of binoculars would help.

After the tower was constructed and had served its purpose, it might have been pulled down, but was largely saved by scientists. Eiffel used it for his own experiments, and meterologists found it useful for measuring pressure, humidity, and temperature at different heights. At the time, it was the tallest structure in the world.

In 1898, radio signals were sent from the Pantheon (see Chapter 13) to the Eiffel Tower, and in 1903 the tower was used by the French military for radio communication. In 1921, experimental television signals were sent from the top of the tower. Today the top is covered with radio antennas of various kinds.

A scientific day out in Paris can be had by following the Arago medallions (see Chapter 8), stopping off at the Pantheon, and finishing with the Eiffel Tower.

Practical Information

The Eiffel Tower has a website at http://www.tour-eiffel.fr/. The site is available in English.

The Shape of the Eiffel Tower

Gustav Eiffel wrote that “the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments of the wind.” In effect, Eiffel was saying that he had designed the tower with wind resistance as the guiding factor and that its shape was entirely dictated by the wind itself. It’s perhaps not surprising, then, that the tower has such a graceful, almost natural, silhouette.

In 1885, Eiffel wrote a paper for the French Society of Civil Engineers in which he described the most significant part of the tower’s design—he had eliminated any diagonal bars by ensuring that stress from the wind was transmitted exclusively down the exterior of the tower. This design dictated a specific curving shape.

In his diagram (Figure 18-1), Eiffel imagined the forces of the wind acting on the tower from one direction (PI, PII, PIII, PIV). He then imagined any horizontal cut through the tower (such as MN in the figure) that passed through a pair of the walls. He explained that if the walls cut by the horizontal could be angled such that their imaginary intersection point (where the dotted lines at the top meet) were exactly where the resulting combined wind force was directed, then all the stress would run along the walls with a resulting force of zero across any diagonal. This simple result comes about because for a structure to be in equilibrium, all the moments passing through a point must sum to zero.

Figure 18-1. Eiffel’s diagram

For further details of the mathematics behind the tower’s shape, read the paper “Model Equations for the Eiffel Tower Profile: Historical Perspective and New Results” by P. Weidman and I. Pinelis. The paper shows that the shape of the tower is actually an exponential curve.

Of course the tower is not actually curved—it’s made of a number of approximations to the actual curve dictated by the wind, and Eiffel built in a large safety factor. To this day, the Eiffel Tower stands without being bothered by the Parisian wind—the largest deflection of the tower was measured in 1999 when the top moved 13 centimeters.