The Eiffel Tower is one of the most iconic structures in the World. This lattice iron tower was built in 1889 by Gustave Eiffel as the entrance for the World’s fair. There are so many superlatives about the tower it’s impossible to know where to start: It’s the tallest structure in France. (1,064ft tall). It’s the most visited paid monument in the World. Over a quarter of a people have visited so far, with an average of 25,000 additional people visiting every day.*billion*Before the Eiffel Tower was built, the tallest man-made structure in the World was the Washington Monument (which the tower exceeded by almost a factor of two!). After construction, the Eiffel Tower was the World’s tallest structure for over 40 years; until it the construction of the Chrysler Building in 1930. Then, in 1957, a taller antenna was installed at the top of the Tower, leapfrogging Eiffel’s structure to be taller than the Chrysler building once more! It's still taller than the Chrysler Building today. The tower comprises 18,038 individual metal pieces held together by 2.5 million rivets. There are 1,710 steps to the top of the third floor (today, visitors can only take the steps up to the first two levels). The iron of the tower weighs 7,300 metric tonnes. The height of the Eiffel Tower varies by up to 15 cm (5.9 in) due to thermal expansion. Every seven years, approximately 50 tonnes of paint are applied to prevent rusting.
## TriviaThen there are pieces of trivia: It was designed to only be a temporary structure, and dismantled after the fair. It was initially criticized by some of France’s leading artists and designers. Upon the German occupation of Paris in 1940, the lift cables were cut by the French (they were not repaired until 1946). If Hitler wanted to get to the top, he would have had to walk up; he elected to stay on the ground. As the Germans were being driven out of France, Hitler ordered the tower to be destroyed (along with much of the rest of the city); his order was disobeyed. Gustave Eiffel built himself a small apartment at the top, and a laboratory. Gustave Eiffel engraved on the tower the names of 72 French scientists, engineers, and mathematicians in recognition of their contributions to the building of the tower.
However, the most startling piece of trivia that I’ve heard about the tower is that it weighs less than the cylindrical column of air that it sits in! That’s right, if cylindrical tube were placed over the tower, the weight of the volume if air inside the tube would exceed that of the metal in the tower. (I believe this fact might have been mentioned on Mythbusters). Is it true? Let’s find out … ## IronAccording to the internet, the iron used in the construction of the tower came from Reșița in Romania. The density of wrought iron is approximately: 7.70 g/cm At a weight of 7,300 tonnes, this amount of iron has a volume of approximately: 948 m If melted down into a sphere of iron, this ball would have a radius of just 6.1 m If flattened into a coin with a diameter the circumscribes the base of the tower, it will be just 4 cm thick!
That's not a lot of iron. The lattice structure is pretty efficient. |

Using the dimensions of the foot of the tower, the diameter of the cylinder can be calculated.

The arch at the bottom of the tower is pretty wide. Wide enough, in fact, that it has tempted various pilots to fly underneath the tower. If you search the web there are numerous reported incidents of this happening, including a pair of dog fighting combatants during WWII, a Mosquito celebrating the liberation of France, and even a mystery pilot in a stolen aircraft. Here's a video of a crazy man doing it in a Beechcraft Bonanza. |

Here's what a cylinder sleeeve over the tower would look like: Knowing the height of the tower, combined with the disc diameter we determined above allows us to calculate the volume of the cylinder. There is approximately 7.96 million m The density of air is not a constant, so this next step is only going to be approximate. Air density changes with altitude, local pressure, temperature, and even humidity. The standard figure for the density of air at sea level at 15°C is 1.225 kg/m However, Paris is not a sea level, and the top of the tower (where the air will be a little thinner and colder) certainly isn't. |

The altitude at the base of the tower is approx 35m above sea level, putting the top of the tower at 360m. The mean daytime temperature in Paris is pretty close to 15°C, so we'll use this standard value. We'll also estimate the dewpoint temperature at 5°C (this allows us to calculate the change in density of the air based on water vapor).

The density of air at the

*foot*of the tower under these conditions is 1.216 kg/m^{3}The density of air at the

*top*of the tower under these conditions is 1.169 kg/m^{3}

There's almost a 4% drop in density of the air between the top and bottom (small, but measurable). It's not a linear falloff, but as a first order approximation, considering all the other approximaations we're making, we can take a simple average for the density of the air to give a value of 1.19 kg/m^{3}.

Multiplying by the volume we get a value of approx 9,400 for the mass of the air. Even with our approximations, this is certainly greater than the quoted 7,300 tonnes for the mass of the iron.

*It's true - the mass of the air in the cylinder surrounding the Eiffel Tower, is heavier than the tower itself!*

Lattice structures really are very efficient!

image: Scott Kublin

If you'd like to learn a little more about the stability of lattice structures, click here.

If you'd like to learn a little more about how our atmosphere changes with altitude, click here.

If you'd like to learn what a cloud 'weighs', click here.

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