Cecil, always enjoy your column, however you’ve got this “airplane and conveyor belt business” absolutely wrong. . . . –strafe, via the Straight Dope Message Board
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I knew this was going to happen. Everyone else, forgive me. This week’s column is for the geeks. Here’s the original question, as encountered online: “A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”
The implicit assumption is that if the conveyor belt’s speed backward exactly matches the airplane’s “speed” (whatever that means) forward, the plane remains stationary relative to the earth and, more important, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can’t take off.
But what if the treadmill continues to accelerate? Different story. In principle it’s possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply. (This is a departure from the original question, which said the conveyor belt compensated for the plane’s speed, not its force.) The only mathematics needed to demonstrate this is the well-known physics axiom F = ma–that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to equal any forward force F generated by its engines. Result: The plane stands still and doesn’t take off. Welcome to BR #2.
