Airplane on a Treadmill Explained

Here’s the problem. An airplane is sitting atop a treadmill (conveyor belt). The treadmill has been programmed to match the airplane’s speed, but it operates in reverse, to attempt to keep the plane from moving forward. The question is: can the plane take off, or will it be unable to do so thanks to the treadmill? My first instinct when hearing this question was that obviously, the plane would not be able to take off because if it’s not moving, then it can’t generate the lift it needs to overcome gravity (as you know, airplanes get lift when air passes over and under its wings). The plane needs some velocity relative to the air, and if it doesn’t have that, it isn’t taking off. That’s a rock solid solution with sound physics background. Problem solved…right? Not quite. While the bit about the lift is true, the assumption that the plane is stationary is wrong. In all the conversations, arguments, and debates I’ve seen, what the no-takeoff-sayers fail to grasp is this:

1) We all know that planes need velocity relative to the air to gain lift.

Many who are in the no-takeoff camp stick to the relative airspeed argument, and assume that the takeoff camp just doesn’t understand the concept. Truth is, this point was never up for debate. It’s another concept entirely that’s key to solving this problem.

2) The best way to explain the solution is this: No treadmill in the world can stop an airplane from moving forward.

This is the simplest, most concise way I know to convey the reason why the plane will take off. Think about it. A plane moves because it pulls itself through the air, via propellers, jet engines, rockets, whatever. The wheels are free-rolling; they are not driven at all. Thus, a treadmill on the ground that matches the plane’s speed will not actually stop the plane from being able to propel itself forward. A good analogy is this: Imagine you are on a treadmill, and that you are wearing roller skates. You grasp the handlebars and pull yourself forward. Easy. The treadmill could be off, it could be at walking speed, running speed, whatever, it doesn’t matter. Because the method of your propulsion is not the wheels, but your arms pulling on the handlebars, you move forward regardless of the treadmill speed. Likewise, since a plane is pretty much pulling on the air (like you pull on the handlebars), it will move forward regardless of the treadmill’s activity. If it moves forward, it can take off. Period.