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The Airplane-Treadmill Conundrum

Ruthlessly ripped off from the NY Times via Boing Boing

OK, this one’s driving me crazy. This brain-teaser is ripping around the Internet, plus I actually overheard it THREE TIMES in airport conversations on a recent trip to Canada.

Here’s how I found it presented at http://boards.straightdope.com/sdmb/showthread.php?t=34 8452:

“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.”

Check out all the comments

Comments so far:

Comment by Will

# December 14, 2006,

I read this on bing bong, and if you follow the theory the plane will not take of due to it being stationary, thus no air flow, however what is more likely is that due to the thrust from the engines, the conveyor will be going so fast that it will catch fire and blow up the plane ….. :-D


Comment by Jim

# December 14, 2006,

surely it would take off?  the engines are providing thrust, not turning the wheels.


Comment by Will

# December 14, 2006,

Nope the thrust does not cause the plane to lift, the airflow over the wings causes the plain to lift, the thrust is for forward motion not flight, without forward motion there is no airfloe thus no lift …. fact :-D


Comment by Jim

# December 14, 2006,

but if you stood still with a jet engine in your hands, pointing away from, and turned it on, surely it would knock you over due to the thrust.  its the same thing?


Comment by Jim

# January 8, 2007,

The latest from Boing Boing says that it will:

 

Salon’s "Ask the Pilot" on plane-on-a-treadmill puzzler

Salon’s "Ask the Pilot" columnist, Patrick Smith, wrote a column about the popular plane-on-a-treadmill brain teaser I blogged last month. It neatly sums up the problem, pointing out the impossibility in the setup, and what would actually and theoretically happen if the experiment was carried out.

With the airplane and treadmill, there is, at the outset, friction force capable of rotating the tires at the proper speed to keep the plane stationary. However, as the thrust is increased, that force eventually maxes out. (Two separate frictions are at play here, actually, one between the tires and belt, the other between the plane’s axles/bearings and its wheels. The first will max out before the second.)

"And at that point the wheels no longer roll, they slide," says Camp. "Or rather, they roll and slide at the same time. Tire motion is now decoupled from the belt motion. No matter how much you whiz up the treadmill, you won’t add any more rotational velocity to the wheels because friction is already doing everything it is capable of. The plane skids toward takeoff — likely accompanied by much smoke and a powerful rubbery stink."

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