Can a Plane on a Treadmill Take Off?

"cjcampbell" wrote in message
oups.com...
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.)


AH! ...here's the problem! Are the airplane and the belt moving at equal
speeds in opposite directions
relative to the world? (-X mph for the belt & +X mph for the plane = eg.
airspeed of 100mph &
wheel speed of 200mph) If so the airplane could take off. The answer to this
question would be easy --
is the airspeed high enough or not?

......OR relative to each other? If so, there could be just enough thrust
applied to overcome frictional
forces and the airplane doesn't move relative to the world so airspeed is 0.

BUT WAIT!!! .... ANY two objects can be said to be moving (or not) at equal
speeds relative to each other. A point
on the conveyer belt moving east at 4mph and a jet moving west at 600mph
each have a relative velocity of 604
with respect to each other and there could be an observer who sees each
object moving in opposite directions
at 302mph. The only real question is how fast is the airplane moving with
respect to the air(world).

Thrust is an external force applied to the conveyer belt/airplane system.


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


He likely had a little more information than is available in the OP.

"muff528" wrote in message
news:OW2Ff.179$DV2.5@trnddc07...

.....OR relative to each other? If so, there could be just enough thrust
applied to overcome frictional
forces and the airplane doesn't move relative to the world so airspeed is
0.

That would have to be either a very underpowered airplane, or wheels with a
lot of friction.

BUT WAIT!!! .... ANY two objects can be said to be moving (or not) at
equal
speeds relative to each other. A point
on the conveyer belt moving east at 4mph and a jet moving west at 600mph
each have a relative velocity of 604

But there's the trick. A treadmill belt isn't really moving at all, it's
turning.
Try this for a brain scrambler. Think about a tire on your car, driving down
the highway. At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed of the
car.

"Michael Ware" wrote in message
. ..

"muff528" wrote in message
news:OW2Ff.179$DV2.5@trnddc07...

.....OR relative to each other? If so, there could be just enough thrust
applied to overcome frictional
forces and the airplane doesn't move relative to the world so airspeed
is
0.

That would have to be either a very underpowered airplane, or wheels with
a
lot of friction.

Yes!..that's why I said "COULD be just enough thrust..." More thrust than is
necessary
to overcome friction would result in the airplane moving forward relative to
the air. Then
it's only a question of how much thrust would be necessary to move the plane
forward fast
enough through the air to overcome gravity :-) A little less thrust would
result in the airplane
going backwards but not as fast as the conveyer. In any case the relative
velocities of the
plane to the conveyer would be equal to observers on either object but NOT
to an observer
standing on dirt.


BUT WAIT!!! .... ANY two objects can be said to be moving (or not) at
equal
speeds relative to each other. A point
on the conveyer belt moving east at 4mph and a jet moving west at 600mph
each have a relative velocity of 604

But there's the trick. A treadmill belt isn't really moving at all, it's
turning.

Again, Yes....but that's why I said "a POINT on the conveyer.." not the
conveyer
system itself.

The trick is that the original question as posted asks a question (will the
plane take off) and gives just enough info
to cause assumptions that aren't specified.

Try this for a brain scrambler. Think about a tire on your car, driving
down
the highway. At the point where the tire contacts the ground, it's speed
is
zero. 180° away, at the top, it is moving forward at twice the speed of
the
car.

Yes, but only for a very brief instant in time. And since velocity is
measured as a function of
time, is that point on the tire really moving at all at that one brief
instant when the measurement
is taken? :-)

In article ,
says...

"muff528" wrote in message
news:OW2Ff.179$DV2.5@trnddc07...

.....OR relative to each other? If so, there could be just enough thrust
applied to overcome frictional
forces and the airplane doesn't move relative to the world so airspeed is
0.

That would have to be either a very underpowered airplane, or wheels with a
lot of friction.

BUT WAIT!!! .... ANY two objects can be said to be moving (or not) at
equal
speeds relative to each other. A point
on the conveyer belt moving east at 4mph and a jet moving west at 600mph
each have a relative velocity of 604

But there's the trick. A treadmill belt isn't really moving at all, it's
turning.
Try this for a brain scrambler. Think about a tire on your car, driving down
the highway. At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed of the
car.

Negative - yer forgetting centripetal force.

http://www.wordiq.com/definition/Centripetal

--
Duncan

"Dave Doe" wrote in message
. nz...
In article ,
says...
At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed of
the
car.

Negative - yer forgetting centripetal force.

? Negative what? Talking about a point on the surface of the tire, not the
wheel as a whole. Centripital force has nothing to do with the forward
velocity of that point (how it travels in one axis).

http://www.wordiq.com/definition/Centripetal

--
Duncan

In article ,
says...

"Dave Doe" wrote in message
. nz...
In article ,
says...
At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed of
the
car.

Negative - yer forgetting centripetal force.

? Negative what? Talking about a point on the surface of the tire, not the
wheel as a whole. Centripital force has nothing to do with the forward
velocity of that point (how it travels in one axis).

Are you talking about a round tire or not - are you then talking about a
big long flat tire of say infinite length. Sorry bud, can't make the
initial assumption that's been made - as it's on a tire, and yep, even
that point, at that time - has the centripetal force.

--
Duncan

"Dave Doe" wrote in message
. nz...
In article ,
says...

"Dave Doe" wrote in message
. nz...
In article ,
says...
At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed
of
the
car.

Negative - yer forgetting centripetal force.

? Negative what? Talking about a point on the surface of the tire, not
the
wheel as a whole. Centripital force has nothing to do with the forward
velocity of that point (how it travels in one axis).

Are you talking about a round tire or not
What other kind of tire is there?
.. Sorry bud, can't make the
initial assumption that's been made -
I'm not your bud,. And what assumption are you talking about?
as it's on a tire, and yep, even
that point, at that time - has the centripetal force.

We aren't talking about the forces at work on the wheel or tire, we are
talking about the forward velocity. I can see this concept is lost on you.

--
Duncan

In article ,
says...

"Dave Doe" wrote in message
. nz...
In article ,
says...

"Dave Doe" wrote in message
. nz...
In article ,
says...
At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed
of
the
car.

Negative - yer forgetting centripetal force.

? Negative what? Talking about a point on the surface of the tire, not
the
wheel as a whole. Centripital force has nothing to do with the forward
velocity of that point (how it travels in one axis).

Are you talking about a round tire or not
What other kind of tire is there?
. Sorry bud, can't make the
initial assumption that's been made -
I'm not your bud,. And what assumption are you talking about?
as it's on a tire, and yep, even
that point, at that time - has the centripetal force.

We aren't talking about the forces at work on the wheel or tire, we are
talking about the forward velocity. I can see this concept is lost on you.

There is no forward velocity - there *is* a change in angular momentum
though. Do you not understand that concept?

--
Duncan

Dave Doe wrote:


Try this for a brain scrambler. Think about a tire on your car, driving down
the highway. At the point where the tire contacts the ground, it's speed is
zero. 180° away, at the top, it is moving forward at twice the speed of the
car.

Negative - yer forgetting centripetal force.

http://www.wordiq.com/definition/Centripetal

Well, I'm impressed that you know of the existence of centripetal
force. But in what possible way do you think it negates the comment
about the speeds (relative to the ground) of points at the top and
bottom of the tire on a moving car?
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Let' say it this way. The airplane is moving forward at 60 kts. Does
that make it more clear?

The airplane is moving forward at 60, the belt, using the model in the
OP, is moving backwards at 60. The wheels are turning at 120 kts. If
it's a 172 it'll lift off into, on a calm day, 60 kts of airspeed over
the wings.

It's a nicely phrased question that caught me at first as well.
Substitute real speeds into what had been posted and the answer becomes
clear to me, although a lawyer in the group might find a (ground) loop
hole.