As described in a straitdope.com discussion of the Plain/Treadmill Conundrum, there’s this thought experiment circulating on the Internet right now. I had no idea such a stupid damned thing was making the rounds until I saw the alt text for an xkcd comic that mentioned it.
The supposed conundrum is roughly as follows:
You have a commercial jet. You set it on a huge conveyor belt, of a length arbitrarily great enough to perform your stupid little experiment without problems. The conveyor belt somehow measures the tangential speed of the surface of the wheel’s tire, and accelerates to match that speed relative to the ground. It also magically doesn’t generate air movement to interfere with the experiment. Thus, if you were driving on this conveyor belt in a car, no matter how hard you pressed on the gas pedal, you’d remain in place relative to the ground around the conveyor belt. Would the plane take off?
That’s no damned conundrum at all. It’s a stupid question. The only reason the aircraft might not take off is the fact that the landing gear of the aircraft might fail before it achieved sufficient airspeed to lift off. The wheels and conveyor belt would just accelerate infinitely fast as the aircraft started moving forward, causing obviously unavoidable catastrophic damage to the wheels and/or conveyor belt. As such, if you don’t assume no damage will occur to the various parts involved, I guess the aircraft might not take off since the landing gear and conveyor belt would fail effectively instantly and the nose of the aircraft would plow into the ground. If you do assume no damage will occur and ignore the friction problems of things like the bearings in the wheels so you can have your silly experiment without problems, you’d have tires and belt moving fast enough to suffer absurd relativistic effects while the aircraft just smoothly moved forward and lifted off the ground like nothing was wrong.
Of course, we really don’t know what happens when the tangential speed of a tire’s surface exceeds the speed of light, so . . . who knows what would really happen?
I guess we’re ignoring relativity, too, for this. I guess the plane takes off. Well, glad that’s settled.
Didn’t anyone teach these children that it’s the engine exhaust thrust and airflow over lifting surfaces that makes an aircraft fly, and not the spinning of the wheels?
Can we have a thought experiment that makes sense now, please?