A harmless little riddle

mandingo, you may have read most of the posts but not very closely. here is the argument: you are entirely correct in saying that if the plane isn't moving it won't levitate up. we're saying that the plane will start moving forwards because the action of a treadmill spinning the wheel under the airplane at the same velocity as the airplane is very weak compare to the thrust of the engines.

if you wanted to stop a toy airplane from lifting off and all you could do was spin some ball bearings on the side of the airplane, it would be very hard. you'd have to slap those babies like i feel like doing to wow right now.

Engineer wrote:

Please read my paragraph or any relavent literature on boundary layer theory. A runway sized treadmill moving at 500 mph would create winds well in excess of 100 mph over the runway. This air moves over the wings creating lift even though the plane is not moving.

What happens when the plane is lifted above this boundary layer caused by the rapidly moving over-sized treadmill?

Ok, so I\'m sure most of folks agree that it takes some wind velocity to generate the lift the plane needs. I think the initial question was just poorly posed. Here\'s why-

When the original post says that \"the treadmill runs in the opposite direction at the same speed the plane is moving\". Is the speed relative to the treadmill or to an inertial reference frame?

Anyone who has taken any elementary mechanics course knows that:

V(p)=V(p/t)+V(t) (vector equation)

where the V\'s are vectors, and (p) denotes absolute velocity of plane, (t) is absolute velocity of treadmill belt, and (p/t) is the velocity of the plane with respect to the belt.

If the original question implied that the speed of the plane with respect to the treadmill was the same as the speed of the treadmill belt (as viewed by an inertial observer) then the plane would not be moving in an inertial frame. Call the speed \'u\'.

That is, V(p/t)=u (in the positive x direction), and V(t)=u (in negative x direction). Think about if you were a particle stuck in the treadmill as you are \'dragged\' backwards (negative x)- the plane would appear to be moving away from you with speed u in the positive x direction.

Adding these vectors gives a vector sum of zero. Thus, as viewed by an inertial frame (someone looking at the treadmill from the ground), the plane is not moving. If the air is stagnant (again, from the inertial frame), then the plane is not moving relative to the stagnant air- thus producing no lift.

If the plane had a V(p/t) that was greater than V(t), then the vector sum would be positive, and the plane would move (as viewed by an inertial observer). Then, if the speed were great enough, you can get lift.

In conclusion- WITH RESPECT TO THE BELT, the plane would have to go it\'s normal takeoff speed (i.e. with no treadmill) PLUS the speed of the treadmill in order to get in flight.

Asterix wrote:

mandingo wrote:

What would the plane do? Levitate up?

What if the plane is a V-22 Osprey?

If that's the proper name of the Harrier Jump jet I think they covered that!

You moron, the Harrier is a Harrier and the V-22 Osprey is a v-22 Osprey.

IS FORD THE PROPER NAME FOR A CHEVY???

i'm glad you feel as if you're slapping me right now. i would suggest slapping yourself, but i feel like that could only lead to further brain damage. you guys are f-ing retarded. the plane needs thrust to stop it from being moved backward by the treadmill. the amount of thrust that it will take to stop the backward movement is EQUAL to the amount of thrust it would take the plane to go the speed of the treadmill if the plane were on a normal runway. that's it. yes it is possible for the plane to accelerate and take off IF IT GOES FASTER THAN THE TREADMILL. unfortunately for all of you, that is not allowed by the question. it's been entertaining, though.

no it isn't.

mandingo wrote:

If that's the proper name of the Harrier Jump jet I think they covered that!

Harrier is the AV-8:

V-22 Osprey is a different aircraft:

the magic breath of life wrote:

You moron, the Harrier is a Harrier and the V-22 Osprey is a v-22 Osprey.

IS FORD THE PROPER NAME FOR A CHEVY???

Just asking! I think he was trying to add some humour to the increasing seriousness of this thread!

There is one runner, Vince Friel, who runs a 4min 1500 as a master and is an Air Canada pilot.The perfect guy for this. If you are not flying right now Vince, answer the riddle!

Well, again, it depends on how you interpret the riddle. If you interpret the riddle to mean the treadmill has the capability to negate ALL forward movement of the plane, then I have to concede that the treadmill must continue accelerating because, obviously, once the plane leaves the surface the only way the treadmill can couterract the thrust of the engines is to whip up enough wind to keep it from moving forward - this acceleration of the treadmill causes the boundary layer to reach even higher - which makes the plane go higher - which requires the treadmill to accelerate, ect...

Actually I'm not positive about this scenario as I can't remember how boundary layer thickness depends on the surface velocity.

If you interpret the riddle to mean that only the friction between the runway and the wheels prevent forward movement, then clearly the plane would rapidly accelerate forward as it lifts off of the runway.

the propulsion doesn't come from the wheels. that is to say that the the push of gravity isn't the driving force like it is for a car that spins it's wheels to move. The propulsion of a plane comes from the transfer of air. Analogy, Air:Airplane :: Water:Swimmer. So the plane will travel at the same speed regardless of the movement of the ground below. Thus the plane will build enough speed to take off. Yes, the plane would take off!

even a sufficiently fast flying car would take off under the conditions of this riddle.

700!

701!

The original poster should elaborate on the question. Technically, if a treadmill is going at the same speed backwards as a plane is moving, the plane has to be moving forward, otherwise its at zero miles an hour and neither the treadmill nor the plane is moving. If this is the case, the plane would be moving forward at x mph while the treadmill spins backward at x mph, so the wheels are actually turning at 2x mph. Here, if x is great enough, the plane WILL take off. HOWEVER, if they meant that the speed of the wheels equals the speed of the treadmill, the plane would stand still and it wouldn't take off.

I think.

Here's the real question. If a tree falls in a forest and springs back up as a joke, do the squirrels freak out?

The only way to justify a contested statement in physics is to write down the equations. So stop being philosophers and do some physics.

I've worked out the exact conditions that need to be met in order for the plane to accelerate. It depends on many factors, and is not identically equal to the acceleration of the plane unless you've got some trippy wheels.

It's got trippy wheels.

argh... wrote:

I've worked out the exact conditions that need to be met in order for the plane to accelerate. It depends on many factors, and is not identically equal to the acceleration of the plane unless you've got some trippy wheels.

http://home.uchicago.edu/~dryu/airplane_treadmill2.pdf

I think that sums it up nicely, particularly since the original post implied (although didn't make it absolutely clear) that the treadmill matches the plane's speed, hence:

"Thus we arrive at the conclusion that the acceleration of the treadmill depends on the force of the engines, the radius of the wheels, and the moment of inertia of the wheels."

We're basically looking at a super-treadmill that can accelerate with whatever force is necessary.

If we only got a second-rate super-treadmill that is not infinitely powerful, then it will be possible for:

"Alternately, this shows that given the behavior of the treadmill, we can calculate uniquely the force needed

from the engines for the plane to be stationary. Any more force from the engines will cause it to accelerate."

LOL you are dumb cause guess what... that forse he was talking about is alot less than the force that the treadmill would be going at, and the point of the riddle is that they are equal