Avenging Science

So, I'm sure many of you have seen the avengers. It was a fun movie, but like all superhero movies, it's not a place that you would expect to go for scientific accuracy. And you would be correct. The main thing that caught my eye, since it couldn't be explained away using either Magic or Tony Stark(see magic) was the giant flying aircraft carrier. This guy here:

That is not a particularly practical looking piece of flying equipment, and I can pretty much guarantee it's only use to is make Samuel L. Jackson look even more badass. The question though is not should you use a giant awesome flying aircraft carrier, of course you should, but is the one depicted physically possible. The first thing we need to look at is the force required to keep that in the air. As you can see in the image, the carrier has 4 ducted turbofans. I have tentatively estimated that the average speed of the air going through the fans it ~.3 times the speed of sound at sea level, or 100 meters per second. Since the mass of the carrier must be assumed to be on the order of the mass of the USS enterprise

(I'll assume 50000 tons for our purposes), we can figure out what surface area of fan is required to move that much air. The force needed to keep a 50000 ton aircraft carrier aloft is about 4.5*10^8 newtons. Now, we have to compare that to the force actually able to be produced by the ducted fans. At the speed discussed, they would produce about 6.4*10^3 newtons of force per square meter, that means you need 69740 or so square meters of area to get your lift. Or 17435 m^2 per fan. Which comes out to a radius of 75 Meters. Unfortunately, as we can see from the image, the radius of those fans is closer to 15 meters, so how fast would the air have to be moving? The answer is something like 1200 meters per second, which is significantly faster than the speed of sound. And sadly impossible. Unfortunate that we have found that this isn't really possible, but let's assume that they can generate the speed needed, how much power is required? That's relatively easy, since we know how much air we are moving at what speed. Assuming we use the larger turbines, that means moving 69740 cubic meters of air at 100 m/s. Since the energy of the air moving past the turbine in 1 second is 1/2 m*v^2, the power required would be about 1 gigawatt, or 5 times the output of the Enterprise. This is actually not terribly impossible, but if you instead assume that they are using the turbines shown, the energy goes up to an impossible 12 gigawatts. Which is unavailable to any craft of that size today. Once again a movie has shown us the impossible. But then again, it did manage to make Samuel L. Jackson look cool using a bluetooth headset, so I suppose we will have to forgive the director.