I’ve got to admit, this is a beautiful skyscraper:
I was never very enamored of the Petronias Towers or the Taipei 101, both of which lacked the architectural panache that supertall structures ought to have. The Burj Khalifa has it. Burj Dubai is a more elegant name, but long story short Dubai really got nuked by the worldwide financial crisis and this Khalifa fellow helped keep Dubai out of bankruptcy. So now he has the world’s tallest building named after him. The Burj Khalifa cost around a billion and a half dollars to construct, and I expect that figure would have been enormously higher if it had been constructed in New York. Among other reasons, the developers of the Burj Dubai have access to what we might politely call cheap labor.
It’s a nice building anyway. Now, the whole point of a tall building is to take stuff that was at ground level and suspend it in the air by means of steel and concrete. As such you can park your desk and do paperwork in what used to be blank air a thousand feet above the ground. It takes energy to move that stuff up the earth’s gravity well, and energy costs money. How much of that $1,500,000,000 was spent in the actual meat of the project – the moving of the parts from the ground to their respective positions in the air?
The energy required to move one floor’s worth of material will be approximately its mass times its height above the ground (call that h) times the acceleration due to gravity (g). The mass of one floor is the linear density (in kilograms per meter or whatever, call it lambda) times the height of the floor itself (say, 15 feet or whatever. Call it dh).
That gives you the energy dE needed to raise one floor up to a height h:
Add that up with the help of calculus for all the floors with a height between 0 and H, the final height of the structure:
Evaluate the integral:
And density times height is just the total mass m:
So the total energy is just the same as is required to move all the mass up half the height, which makes sense as an average. Now the Burj Khalifa is not of uniform density the whole way up, so the real figure for energy will be somewhat less. But it’s a good starting point for an estimate.
What’s the total mass of the building? Wikipedia says 330,000 cubic meters of concrete and 55,000 tons of steel were used, and that’s about 842 million kilograms. Plug in and get a total of 3.4 trillion joules. And that’s about 948,000 kWh. Here in Texas prices of ~$0.10 per kilowatt hour are doable, and so it would have cost about $95,000 to raise the materials.
Obviously most of the cost is not in the raw energy. More of it is the materials themselves, the labor required to move them, and the fact that no use of energy is completely efficient anyway. Similar figures would hold for just about any building anywhere in the world. Still, it’s interesting to see that the raw lifting energy is so small in comparison to total construction costs.