Can a Plane on a Treadmill Take Off?

On Sat, 4 Feb 2006 08:44:24 -0800, "RST Engineering"
wrote:

Cecil Adams (world's smartest human being) is correct to a first
approximation. The correct answer to a second approximation is that it will
take off normally less some small correction factor for the increased
friction of the tires, wheels, and wheel bearings.

Note the "trick" of the question. It does not say that the conveyor keeps
the AIRPLANE at zero speed relative to the real world, just that it rotates
at a speed equal to the airplane moving forward. The question itself
supposes forward velocity of the aircraft relative to the earth and the only
thing the conveyor belt does is spin the wheels twice as fast.

Jim


Jim, you've got to realize that it must be a tough job being the
smartest man in the world.

I like being the second smartest. But as George Wallace once put it
after a reporter asked him, "You think that you're the smartest man in
the world?" No he said, "but I'm the smartest man in this room."

Mike Weller

And I'm not a George Wallace fan, for many reasons.

The whole problem is confusing because
"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."

Moving forward with respect to what? The conveyor belt? (you gt the
answer that it WONT take off), or the air? (you get the answer that it
WILL take off).

AMBIGUOUS!!!

(Cecil's answer assumes with respect to the air, and that is also how
he gets the tires going at twice the speed of the plane through the
air).

"Doug" wrote:

The whole problem is confusing because
"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."

Moving forward with respect to what? The conveyor belt? (you gt the
answer that it WONT take off), or the air? (you get the answer that it
WILL take off).

AMBIGUOUS!!!

Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified. Two movements are mentioned in the problem. Is
there any reason to suspect that one is movement relative to surface
of the earth (the conveyor) and the other is movement relative to the
first object? Why not th other way around, in which case the conveyor
is just an ordinary runway?

If you are not willing to resolve that ambiguity by assuming
conventional frames of reference, you might as well assume that one is
speaking of velocities relative to a solar system frame, in which case
the plane may be going very very fast forward, backward, sideways, up,
or down, depending on time of day and orientation relative to the
earth. The problem makes a lot more sense assuming conventional use
of "moving".
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified. Two movements are mentioned in the problem. Is
there any reason to suspect that one is movement relative to surface
of the earth (the conveyor) and the other is movement relative to the
first object? Why not th other way around, in which case the conveyor
is just an ordinary runway?

If you are not willing to resolve that ambiguity by assuming
conventional frames of reference, you might as well assume that one is
speaking of velocities relative to a solar system frame, in which case
the plane may be going very very fast forward, backward, sideways, up,
or down, depending on time of day and orientation relative to the
earth. The problem makes a lot more sense assuming conventional use
of "moving".

Yes, the frame of reference has everything to do with the answer ...and the
riddle!
Since the original post refers to an airplane taking off you should conclude
that
"air" (the atmosphere) has to be included in the mix and that an airplane
does it's
flying relative to the world/atmosphere. Then it is not unreasonable to
assume that the riddle
implies that the most logical reference frame is the planet and that the
conveyor and the plane
are moving in opposite directions with respect to that stationary observer.
The only requirement
then is that the airplane move fast enough to take off and that the conveyor
move fast enough "backwards"
to match the airplanes speed (only to satisfy the specified initial
conditions even though the speed of
the conveyor is entirely irrelevant to whether or not the airplane takes
off.) It doesn't even matter if the wheels
need a bearing job or if the plane is on skids or if the brakes are set.
Either the engine generates enough thrust
to overcome resistance and accelerate the plane to take off or it doesn't.

"alexy" wrote in message
...
Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified.

Very amusing.

According to you:

On the one hand, the problem is uninteresting if one removes the ambiguity
in the phrasing.

On the other hand, there is no ambiguity, because if a different frame of
reference were intended, "it is almost always specified".

So, the logical conclusion you arrive it in your post is that the problem is
uninteresting.

For an uninteresting problem, it sure generated a lot of traffic.

Pete

"Peter Duniho" wrote:

"alexy" wrote in message
.. .
Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified.

Very amusing.

According to you:

On the one hand, the problem is uninteresting if one removes the ambiguity
in the phrasing.

On the other hand, there is no ambiguity, because if a different frame of
reference were intended, "it is almost always specified".

So, the logical conclusion you arrive it in your post is that the problem is
uninteresting.

For an uninteresting problem, it sure generated a lot of traffic.

True. Which really surprised me. When I first saw CJ's post, I thought
it was too obvious to draw in this kind of activity.

--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

For an uninteresting problem, it sure generated a lot of traffic.

True. Which really surprised me. When I first saw CJ's post, I thought
it was too obvious to draw in this kind of activity.

Indeed. If it was not a well recognized name posting, it would be a post
more worthy of a troll.

Dang you, CJ! Please refrain, next time!

Or if your post was moving backwards at twice the speed of light, did it
ever appear at all, and did it erase all of the activity before it? g
--
Jim in NC

cjcampbell wrote:
Saw this question on "The Straight Dope" and I thought it was amusing.

http://www.straightdope.com/columns/060203.html

The question goes like this:

"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.)

Cecil Adams (world's smartest human being) says that it will take off
normally.

Assuming the increased tire friction doesn't cause a problem the aircraft
should take off but have twice the normal tire rotation speed when becoming
airborne. That's because the thrust is produced by the prop and it will
accellerate the aircraft into the relative wind. The conveyer belt is just
an entry to confuse the issue. For a car the situation would be completely
different since it produces forward motion by the tires which contact the
moving conveyer belt. The car wouldn't move at all.
--

Darrell R. Schmidt
B-58 Hustler History: http://members.cox.net/dschmidt1/
-

"Darrell S" wrote in message
news:rT6Ff.24873$jR.14387@fed1read01...
[...] For a car the situation would be completely different since it
produces forward motion by the tires which contact the moving conveyer
belt. The car wouldn't move at all.

It might. As "Doug" points out, the presentation is ambiguous as to the
reference point for the speed of the vehicle. If one uses the ground (and
stationary portions of the treadmill) as a reference, then the car would
move, just as the airplane does (it would have to in order to comply with
the description given in the problem), and the car's speedometer would
register a speed twice its actual speed relative to that reference.

Pete

If you tie a 100 foot rope to the tail of an airplane (or some other
part of the airframe), attach it to a good strong post, and run the
propellor up to whatever rpm is available, is anyone claiming the
airplane can then lift up say a feet off the ground?

(Assuming the tail doesn't tear off)

(and, a conveyor belt under the airplane is optional)