Flying Aircraft Carriers: Physics and Engineering in The Avengers

CREDIT: Marvel Studios

I saw the Avengers on Memorial Day.  Awesome movie, and if you've read one of my early blog posts, Transformers 3 - Dark of the Moon, you might guess I sometimes think about physics during the movie.  One thing that caught my attention was the flying aircraft carrier.  What would it take to make one fly?

Thanks to Wikipedia, I found some specifications for a modern US navy supercarrier.  They are 333 meters long (1,092 ft) and 78 meters wide (260 ft), and its displacement is 100,000 long tons which is equal to 224,000,000 pounds and 101,600,000 kg.  It is powered by two nuclear power reactors that provide 190 megawatts.

Now for science!

There was a shot in the movie when two of their fans were shut down and the ship was plummeting.  The altimeter read between 17 and 18,000 ft.  So I will begin by assuming they were cursing at 30,000 ft.  This is also where many commercial flights travel.  I will also assume that it takes about 30 minutes to reach cruising altitude.

CREDIT: Marvel Studios

Now I can estimate the acceleration.  Kinematics, the study of motion, says that for a body initially at rest, the acceleration is given by

Plugging in gives a value of 0.006 m/s/s.  For you non-students of physics, this means that for every minute, the carrier goes almost 1 mph faster.

Now for Isaac Newton.  To produce this acceleration, Professor Newton says that unbalanced forces have to act on the carrier.  Newton's 2nd law:

Here I will have to use the ship's displacement as its mass.  The displacement measures how much water an object pushes out of the way.  Rather than trying to calculate the ship's mass, I'll take the shortcut.  The total unbalanced force is about 570,000 Newtons.

There will be two forces acting on the ship - the thrust and the gravitational force (commonly referred to as the weight).  The thrust has to be 570,000 Newtons larger than the weight.  We can find the weight by multiplying the mass by the gravitational field (9.8 N/kg).  Therefore the thrust is approximately 10,000,000,000 Newtons.

The total energy used in both speeding up the ship and raising it can be found by multiplying the thrust by the distance.  

Since power is the rate at which energy is converted, we can take the energy and divide by 30 minutes.  To raise SHIELD's ship requires 5,000,000,000 Watts; that's 5.0 gigawatts!  Earlier I noted that the 2 reactors aboard a US carrier provide 190 megawatts, SHIELD needs 52 nuclear reactors.

Now for those fans providing the thrust.  To try to calculate the thrust of a ducted fan, one needs an extensive knowledge of fluid dynamics and aeronautical engineering plus a powerful computer.  I'll take the quick path to the answer.

With a 0.16 second Google search of "thrust fan specifications", the first result was for Ventry Solutions, Inc.  They sell a 24 inch ventilation fan that supplies 108 Newtons of thrust.  I'll scale that up for the ducted fans seen in the movie.  

Judging from the photo above, the fans have a diameter of about 40 meters (130 ft).  If - a very big if - the thrust is proportional to the diameter, then one fan can give 7100 Newtons.  Uh oh.  7100 Newtons per fan; 10,000,000,000 Newtons needed.  

14 million of them.