Actually, that is necessarily true. Even if the wheels are rotating, the friction from the bearings cause a moment on the wheel, and some force from the treadmill is transmitted to the plane. That force moves the plane in the direction the treadmill is moving, as brewha said. Not as fast as the treadmill itself is going, but moving nonetheless.
Yes, but is the river flowing uphill, like the Nile, or downhill?
Well, isn’t this just a poke in the IJ with a sharp Styx.
The January 30, 2008 episode of the Discovery Channel’s Mythbusters will attempt to answer the question.
[http://dsc.discovery.com/video/?playerId=2...tleId=348411075](Mythbusters - Plane on a treadmill)
Cick on link scroll down the list on the left to “60 clips”…
Click on “60 clips” and you will see “Plane on Treadmill”
Just wanted to say that Zut has made some excellent and amazingly well-tempered posts on this thread. As a result of his comments I went away and worked out the theory for exactly how an accelerating treadmill could resist the thrust of an aeroplane by accelerating the wheels. I would like to come up with a figure for the acceleration of the treadmill that would resist the 207 kN thrust of a 747 and keep it stationary. I believe the formula for the acceleration required to be
a = F R^2 / I
Where
F = Thrust of the engines and the force required to be resisted
R= radius of wheels
I = Moment of Inertia of wheels
and for a simplified wheel that can be modelled as a cylinder this reduces to
a = F R^2 / M R^2
= F / M
where M = total mass of all of the wheels of the 747
but I don’t seem able to find the mass of a 747 wheel anywhere! Does anybody know where I could find out ?
Had a thought the other day that the best way to test this is to have wheeled mass on a treadmill attached to a fishing scale anchored on the wall ahead of the treadmill. As you accelerate the treadmill you can see how much force is exerted on the mass.
Programming alert!! This is tonight. Of course, it will be replayed a few times too.
Well, duh. Like the poser of the original question said, the wheels just turn twice as fast.
Seems to me, if the conveyor could somehow hold the plane still, then it would violate the question by not matching the plane’s speed (i.e., nil). One of those paradox thingies.
The take-off into the wind case is actually the opposite. The plane is flying, but the wheels don’t turn at all. I’ve done that myself with an R/C model.
BTW: Back in the '20s or '30s, a character named Martin Jensen built a plane especially for slow flying. One of his windy-day stunts was to fly backwards across the fairgrounds. The Smithsonian has some articles about him on microfiche (or used to).