Can a Plane on a Treadmill Take Off?

"cjcampbell" wrote:

"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward. Does the airplane take off?" (Assuming the tires hold out, of
course.)

Now, there are two references to motion in the problem, and the
correct (IMHO) solution is based on both of those motions being from a
consistent frame of reference, i.e., relative to the ground.

The incorrect (IMHO) solution seems to depend on reading these two
motions as related to inconsistent frames of reference, to wit: "An
airplane on a runway sits on a conveyer belt that moves relative to
the surface of the earth in the opposite direction at exactly the
speed that the airplane is moving relative to the surface of the
conveyer [Not sure how those who read it this way fit the word
"forward" into their interpretation.] This reading leads to the
conclusion that the plane is standing still, but flies in the face of
what really would happen if such a device were built, given how a
plane's propulsion is provided -- i.e., this reading of the problem
assumes facts inconsistent with what conceivably could happen were
such a device built. (BTW, many seem to focus on this practical aspect
of propulsion, but that misses the pure logic of the thought
experiment, it seems to me.)

But think about the opposite inconsistent reading of the statement:
"An airplane on a runway sits on a conveyer belt that moves, relative
to the airplane, in the opposite direction at exactly the speed that
the airplane is moving forward relative to the ground." That
inconsistent frame of reference seems just as justifiable as the
other, and is in fact MUCH easier to imagine actually implementing!

I think we should do something to make sure that all future airports
are built with runways that work like this third interpretation of the
stated problem! g
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.