think about this...

[d10]

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SOLVED!!!11

the plane will take off if the conveyor belt gets fast enough. saying that there is no air flow over the wings is retarded. the conveyor belt causes viscous drag on the air above it, and forces the air over the wings corresponding to a velocity profile that is in chapter one of any fluid dynamics book.

it's the same reason your canoe slows down after you row it. if the conveyor belt is acutally going 3000 mph relative to the plane, the air speed right at the edge of the belt is also 3000 mph relative to the plane. (that is a fact, don't debate it.) this speed drops off drastically, but it might be 100 mph by the wing. which would create lift, and the plane would take off and instantly be carried backwards unless it was producing trust of its own.

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The problem with this is that the wind speed would be drastically faster under the wing than it would be a few feet higher above the wing. Although it would be impossible to say for sure without knowing the exact shape of the wing, I have a feeling that this effect will create more downforce than lift.

[diebitter]

I'd take the bus

[4_2_it]

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If only this was posted earlier, we could have saved 40 pages of reading!

[jman220]

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SOLVED!!!11

the plane will take off if the conveyor belt gets fast enough. saying that there is no air flow over the wings is retarded. the conveyor belt causes viscous drag on the air above it, and forces the air over the wings corresponding to a velocity profile that is in chapter one of any fluid dynamics book.

it's the same reason your canoe slows down after you row it. if the conveyor belt is acutally going 3000 mph relative to the plane, the air speed right at the edge of the belt is also 3000 mph relative to the plane. (that is a fact, don't debate it.) this speed drops off drastically, but it might be 100 mph by the wing. which would create lift, and the plane would take off and instantly be carried backwards unless it was producing trust of its own.

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No. We've already stipulated that the whole thing is a completely frictionless system. (Yes thats impossible, but equally as impossible is a plane with magic wheels that somehow move at a different speed from the plane at the moment of takeoff). No friction caused by the conveyer belt moving means no air flow. And what you suggesteed has already been suggested about 20 pages back, and tossed out because of this.

[jman220]

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If only this was posted earlier, we could have saved 40 pages of reading!

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The last 30 pages didn't deal with the fact that you couldn't take off, but with the fact that the OP worded it wrong, and is now trying to support it by saying that, "oh yeah it works as you approach infinity." If Sklansky pulls himself forward the wheels on his skates are moving at a different speed than the treadmill, so actually, you are proving the OP's conditions wrong with this picture. If sklansky merely hold's on, sure the speed of the wheels and conveyer belt are the same, but his speed relative to the ground (read airspeed) is 0, thus no lift, thus no takeoff.

Edit: Nice Picture though.

Edit Edit: I have now surpassed my quota of OOT posts for the year, so I'll leave this topic be. Its clear that the other side will not admit that they worded the problem wrong, and this is pointless.

Edit Edit Edit: And if the fact that he's facing against with the treadmill is meant to imply that the plane could be travelling with the treadmill, well thats not the way the OP was worded.

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final clarification, FBD style:

wheel velocity = conveyor velocity = lim(x) as x -> infinity. this is defined by the OP and the fact that the continual (feedback) acceleration of both is inevitable.

thrust velocity + wheel velocity - conveyor velocity = net velocity

since wheel velocity = conveyor velocity, then net velocity MUST equal thrust velocity

therefore, the plane can take off, as long as thrust velocity is great enough to create lift.

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How is this still going on? Does this require a "proof"?

Here we go.

The plane's wheels are stationary. the runway is stationary, thus satisfying the OP.

there is no net air speed---> no lift.

The engine applies thrust--> wheels speed up faster than runway--> net air speed > 0

-->plane takes off.

However, wheels are moving faster than runway, so OP is not satisfied.



OH By the way, for those unfamiliar with math, infinity + 1 is strictly greater than infinity, but not by much.

[JackWilson]

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final clarification, FBD style:

wheel velocity = conveyor velocity = lim(x) as x -> infinity. this is defined by the OP and the fact that the continual (feedback) acceleration of both is inevitable.

thrust velocity + wheel velocity - conveyor velocity = net velocity

since wheel velocity = conveyor velocity, then net velocity MUST equal thrust velocity

therefore, the plane can take off, as long as thrust velocity is great enough to create lift.

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How is this still going on? Does this require a "proof"?

Here we go.

The plane's wheels are stationary. the runway is stationary, thus satisfying the OP.

there is no net air speed---> no lift.

The engine applies thrust--> wheels speed up faster than runway--> net air speed > 0

-->plane takes off.

However, wheels are moving faster than runway, so OP is not satisfied.



OH By the way, for those unfamiliar with math, infinity + 1 is strictly greater than infinity, but not by much.

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I think this part is wrong. "The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels" does not imply this.

But I'll be the first to admit that I'm no rocket scientist.

[Koss]

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How can the plane move and the wheels stand still?

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The wheels do not move while the plane is flying. My point is forward movement of the plane is not driven by the wheels in any way, shape, or form.

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Oh ok, I don't think anybody is having any trouble with that part. The issue is that it doesn't matter if the plane is moving the wheels or the wheels are moving the plane, (in fact neither is happening).

As the plane moves forward the wheels must move faster than the conveyor belt is moving, even if they are just being taken along for the ride.

Just like pushing a skateboard forward on a treadmill. The only time the wheel speed equals the treadmill speed is when you are holding the skateboard stationary.


Edit: To illustrate imagine the skateboard on a treadmill moving at 1m/s. After one second the wheel will have covered 1m of treadmill track.
Wheel speed 1m/s
Treadmill speed: 1m/s
Skateboard speed: 0m/s

If you push the skateboard forward during that second at a rate of 1m/s the wheel will have covered 2m of track.
Wheel speed 2m/s
Treadmill speed: 1m/s
Skateboard speed: 1m/s

Therefore in order for the skateboard to move forward, wheel speed must be greater than treadmill speed and the conditions of the OP can't be met.

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I've read this whole damned thread and changed my answer about 400 times. I'm sticking with this one though. I'm pretty sure it's right. As long as the planes wheels are physically in contact with the ground and they aren't slipping in anyways, then the plane cannot move forward unless the tangential velocity of the wheels is faster than that of the treadmill.

If there were no friction in the wheels at all, thent he plane would just sit on a runway not going in any direction, and the wheels would just spin in place at whatever speed the conveyer was moving. Once the props or jets or whatever add thrust, the wheels spin faster than the conveyer. If the conveyer speeds up to keep up with the wheels, the whole system diverges.

Sklansky in the DERB helmet had me in tears.

[LetYouDown]

Classic.