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Bad Physics at BoingBoing [Dec. 12th, 2006|10:02 am]
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Originally published at Galactic Interactions. Please leave any comments there.

Sigh. Sometimes a huge amount of confusion and misunderstanding about science gets spread by the amateur pontifications of those who don’t fully understand it simply because of a tremendously poorly-phrased and non-sensical question.

BoingBoing is linking to a NYT blog question about whether or not a plane will take off if it’s on a treadmill rather than a runway:

“Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off? “I say no, because the plane will not move relative the the ground and air, and thus, very little air will flow over the wings. However, other people are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.”

Mark Frauenfelder of BoingBoing says yes:

I say yes. Let’s assume the friction in the wheel bearings is negligible. Putting a plane on a treadmill is like putting it on an icy lake. When you fire up the jets, the plane is going to shoot down the lake and take off just like it would on a runway.

Answer : they’re both wrong. Not about the “yes” or “no”, but about the explanations. In fact, the whole question, with the implicit assumptions behind it, doesn’t make any sense whatsoever. It’s a nonsensible question posed as if there were a proper “yes” or “no” answer… and, thus, anybody who writes trying to justify one or the other position is forced into using some misconception.

The picture of the airplane ever accelerating the rolling of its wheels while staying put on the treadmill, but without taking off, is wrong.

The picture of the airplane that accelerates its wheels like a car on the treadmill, and then somehow lifts off into the air, is also wrong.

Here’s the real answer: You wouldn’t be able to keep an airplane on the treadmill. Hence, the attempts to answer the question fall flat on their face. Mark, and others, correctly state that the wheels are ultimately irrelevant to the taking off of an airplane, that it’s the movement of the plane through the air that matters. The thought experiment that is created, however, is an airplane that’s sitll due to the action of the treadmill. This wouldn’t work. As the aircraft’s engines are pulling it through the air, eventually it would start to skid forward along the treadmill. Depending on how the treadmill was set, it would either be more or less efficient in its initial acceleration, but it would move forward across the treadmill.

When an airplane takes off, the friction of the wheels against the road is not negligible. Indeed, even in a perfectly oiled, perfectly bearinged airplane (or car, for that matter), there is friction between the wheels and the road. Think about when your car is on an icy road. You step on the gas. The wheels spin… and you don’t move. The whole reason you move in a car is because of the friction between the wheels and the road.

If the friction between the airplane wheels and the road is negligible, then it becomes irrelevant that they are wheels. The may well be the skis on the icy lake that Mark taks about . But this is very different from the mental image of an airplane that’s somehow held still on a treadmill. The skids on the lake mean no friction, so the airplane is free to move across the ground. If there’s no friction between the wheels and the treadmill, then the treadmill doesn’t know that the wheels are moving, and it becomes completely irrelevant that it is a treadmill! Try sliding a block of ice across a treadmill; the treadmill won’t respond to it. The plane will slide forward relative to the ground, and relative to the treadmill (assuming, of course, that the treadmill is not in some sort of variable-speed wind tunnel, which would obviate the whole confused and nonsensical paradox that the original author tries to set up).

The whole reason a car would stay on a treadmill is that it is the (static) friction between the car’s wheels and the road that provides the motive force for the car. The car then moves relative to the road. If you can arrange for the “road” to be moving backwards — a treadmill — then, yeah, you can make the car stay put. Same thing when you’re walking. But the typical airplane doesn’t have an engine driving its wheels, they’re just rollers. Its engines push against the air. The airplane would move relative to the treadmill, and not stay on it.