Landing on an Aircraft Carrier

Over the break, we were talking about family and I was reminded that my grandfather was in the Navy and that he worked on an aircraft carrier. I actually stayed on an aircraft carrier for a few days when I was younger and they demo-ed how planes are able to land and stop in as little as just 2 seconds. To put this into perspective, the smallest runways are ~245m long (the average is ~1,829 m), but the flight deck of an aircraft carrier can be as small as 78m in length. So, the question is, how do they stop in such a short distance—and in so little time?

Every aircraft carrier has four wires strung across the deck, and every plane has a tailhook. The pilots must catch a wire—ideally the third—using that hook in order to stop. If they miss, they have to take off immediately, so the pilot actually does not slow down during this landing (like commercial aircraft do). This seems counterintuitive, but they accelerate upon landing in case they do need to take off again. Ultimately, the plane decelerating to a stop is due to that wire, and the force of tension exerted by the wire. So, I decided to solve and see what that force of tension could be if the plane is 33,000lbs (14969kg) and landing with an initial velocity of 150mph (67m/s)—a real-case scenario. To make this simple, however, we’re going to pretend that they are moving at a constant velocity upon landing, and the wheels are rolling without slipping (so no friction).

First you find the acceleration:

v_f = v_o + at

0m/s = 67m/s + a(2s)

a = -33.5m/s²

Then, you can find F_T:

F_T = m(a)

F_T = (14969kg) (33.5m/s²)

F_T = 501,462N

And that number is insane. There's a lot of other factors that go into a perfect landing, including the angle you land at, the direction of the wind, and the speed at which you land, but this one is pretty important too. If you’re interested, here’s a short video of a fighter jet landing and catching the wire: https://www.youtube.com/watch?v=-4UBmRNLWAc