I was late to the Airplane on a Treadmill party, so maybe you were too. Not since the famous Monty Hall and the Goat problem has so much hot air been generated by an online puzzler. Stated briefly, here is the problem:
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?
What’s your answer? I must confess that I was seduced by the wrong conclusion for a while. This problem has now been around so long that the Myth Buster guys have had the time to demonstrate it on TV. Even if you have been aware of this problem for a few years, I recommend the writeup on the eponymous airplaneonatreadmill.com site entitled Airplane on a Treadmill Definitive Analysis. It’s a nice piece of writing about physics, and it does what so much of good science writing does: reframe the question using clearer terminology. In particular, look at his rewording of the problem into three separate but related problems.
Simply put, cars grab onto the ground to pull themselves forward. If you move the ground, they can’t go anywhere. Planes, in contrast, grab onto the air to pull themselves forward. If you move the ground, they really don’t care so much.
4 thoughts on “Airplane on a Treadmill Definitive Analysis”
I think the problem everyone has with the problem is the treadmill. Having spent a lot of time answering science question, I’ve seen a lot of “Thought-problem Telephone”, where an intricately worded (often allegorical) problem is posed by some professor in a graduate level class; one of the students repeats it to the undergaduates he’s TAing; the undergraduate becomes an assistant teacher and poses the question to the class; and finally one of the students posts a question to the MadScientistNetwork about why can’t you just use a glass box and watch the cat through the whole experiment (or “why does it have to be a cat?”). This problem sounds more like it should read, “if by some mechanism an airplane could not translate forward relative to the ground, could it take off,” and some reelly smart person sed, “some mechanism?! Why, your describing a treadmill!” and then posted his/her version to the web. From all of the posts and comments, “treadmill” was not what the original problem was describing.
Right! Let’s rephrase it this way: “Suppose the landing gear of an unstoppable rocket plane was encased in immovable cement…”
Is that the one with the egg-shaped cages that spin around? I almost barfed on that once.
I’m with Mike O. When I read the problem, I interpreted it as “Blah-blah-blah-totally-unrealistic-mechanism-blah-blah-blah-there’s-no-airflow-over-the-wings.” Answer: no takeoff.
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