think about this...

[MrWookie47]

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It is possible to apply a force via the wheels and have the wheels move at the same speed as the runway. (think of getting a smog check and how they test your car)

It is not theoretically possible to apply a force from the jet engine and have the wheels move at the same speed as the runway. The wheels will speed up, no MATTER how fast you make the runway, the wheels will move at that speed plus more, thanks to the force from the jet.

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This makes no sense, and I'm really starting to think you're just a troll. If the airplane is moving relative to the control tower at a speed +V, and the runway is moving at the same speed +V relative to the tower, the wheels aren't moving because in the frame of the wheels, the runway is stationary.

[Voltron87]

im lost here. i thought the force acting on the plane to the left was the same as the force acting on the plane to the right, the forces on it would cancel each other out and it would stay in place. and if it isnt moving relative to the ground, the air wont pass over its wings and provide lift. no?

[NLSoldier]

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OK, let's put the plane at the end of the runway at rest, just like it normally is. However, we're on a magic runway that can move at whatever speed necessary to meet the condition of OP. So the runway moves at the same speed as the wheels. What part of the wheels? Well, the obvious point is the contact point of the wheels, but I say to hell with that. Let's say the whole [censored] wheel can't have any velocity relative to the runway. So, we fire up the engines. The enines propel air backwards and the plane forwards. But, holy [censored]! That means the wheels are moving! We gotta get that runway going! So the runway accelerates too, and the wheels remain motionless. Mean while, the plane is still accelerating. Holy [censored]! We can't have the wheels moving! Heap some more magic dust into the runway motor so it speeds up! And the wheels don't move. And now the plane speeds up again. Holy [censored]! But this time, the plane has reached 88 miles an hour (relative to the air traffic control tower) and goes back in time. Wait til [censored] OOT hears about this!

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I fully understand what you are saying. However, think about this-- I mean really think it over.

It is possible to apply a force via the wheels and have the wheels move at the same speed as the runway. (think of getting a smog check and how they test your car)

It is not theoretically possible to apply a force from the jet engine and have the wheels move at the same speed as the runway. The wheels will speed up, no MATTER how fast you make the runway, the wheels will move at that speed plus more, thanks to the force from the jet.

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THIS ISN'T A [censored] CAR! The jet engines have no connection to the wheels whatsoever. They do not drive the wheels, the wheels just spin. The jets provide a thrust force. That's it. There's no driveshaft down to the wheels. The thing that spins the wheels is friction with the ground and relative motion between the plane and the runway. How [censored] stupid are you?

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patrick, 1 question that may or may not be relavent and is likely retarded.

would it be theoretically possible for the plane to take off with its wheels spinning in reverse?

[Redd]

Not directed at wookie, but OP is too far away:

Looks like we're not the first to have trouble with this

[Voltron87]

updated, one last detail

[Oblivious]

Assuming you have no friction in the wheels axls, the effect of the conveyor does nothing to impede the plane. The effect of the conveyor only accellerates the wheels.

Here's the sequence of events:

1. The planes prop generates enough force to break the static friction (usually caused my the wheels axils, but in this case---&gt caused by the atmosphere.

2. The plane moves forward some distance DELTA.

3. The wheels on the plane rotate some angular distance DELTA.

4. The conveyor rotates some distance DELTA.

BUT! This causes the wheels to rotate some distance DELTA+DELTA or 2DELTA, which causes the convyor to move some amount greater and so on and so forth.

The thing is, events 1 through 4 actually all happen at the same time, and as soon as the plane moves forward some distance greater than zero, the wheels will be spinning at an infinite rate. Youve basically created a feedback loop between the wheels and the conveyor. But just because theres no solution for the rate at which the wheels should be rotating, doesnt mean there is some force impeding the plane. The plane will accellerate according to the force generated by its props and take off within its normal distance.

Sorry if Ive repeated anybody, but I didnt want to read infinity pages before posting.

[Hiding]

My interpretation is that the outer edge of the wheel has a rotational velocity equal and opposite to the linear velocity of the conveyor. The hub of the wheel (or center of the plane) is moving forward with an equal and opposite force of the thrust.

[Patrick del Poker Grande]

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OK, let's put the plane at the end of the runway at rest, just like it normally is. However, we're on a magic runway that can move at whatever speed necessary to meet the condition of OP. So the runway moves at the same speed as the wheels. What part of the wheels? Well, the obvious point is the contact point of the wheels, but I say to hell with that. Let's say the whole [censored] wheel can't have any velocity relative to the runway. So, we fire up the engines. The enines propel air backwards and the plane forwards. But, holy [censored]! That means the wheels are moving! We gotta get that runway going! So the runway accelerates too, and the wheels remain motionless. Mean while, the plane is still accelerating. Holy [censored]! We can't have the wheels moving! Heap some more magic dust into the runway motor so it speeds up! And the wheels don't move. And now the plane speeds up again. Holy [censored]! But this time, the plane has reached 88 miles an hour (relative to the air traffic control tower) and goes back in time. Wait til [censored] OOT hears about this!

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I fully understand what you are saying. However, think about this-- I mean really think it over.

It is possible to apply a force via the wheels and have the wheels move at the same speed as the runway. (think of getting a smog check and how they test your car)

It is not theoretically possible to apply a force from the jet engine and have the wheels move at the same speed as the runway. The wheels will speed up, no MATTER how fast you make the runway, the wheels will move at that speed plus more, thanks to the force from the jet.

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THIS ISN'T A [censored] CAR! The jet engines have no connection to the wheels whatsoever. They do not drive the wheels, the wheels just spin. The jets provide a thrust force. That's it. There's no driveshaft down to the wheels. The thing that spins the wheels is friction with the ground and relative motion between the plane and the runway. How [censored] stupid are you?

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patrick, 1 question that may or may not be relavent and is likely retarded.

would it be theoretically possible for the plane to take off with its wheels spinning in reverse?

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You're right. I said this a long time ago. The wheels can do whatever the hell they want because they have nothing to do with the plane taking off. The only thing the wheels do in this scenario is enforce a minimum altitude (they hold the plane up off the ground when it's just sitting there).

[LAGmaniac]

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I'm no physics expert, but I think I have an example that might satisfy Nasty/Crazy/goofball.

Imagine that there is no friction at all involved with the wheels and the conveyor belt. The wheels and the belt are moving at the same rate, but this is not necessarily because of friction.

Imagine that the conveyor belt and the wheels are both completely stationary. You expect the wheels to spin faster as the plane moves forward because of the effects of FRICTION BETWEEN the wheels and the conveyor belt. If there is no friction, then the wheels will remain stationary - regardless of the speed of the plane (and, incidentally, of the conveyor belt).

This is a specific hypothetical situation in which the plane clearly accelerates under the conditions outlined in the OP (there is no suggestion that the identical speeds of the wheels/belt are due to friction).

I'm not 100% sure how this situation works if the speed of the runway and wheels scale linearly due to friction, but I don't think it's relevant. Even if we imagine the speed of the wheels and the speed of the conveyor belt to be completely independent (they just happen to be identical), the principle of the solution stands.

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It was assummed and I believe the OP specified a no-slip condition between the wheels and runway. I don't believe that condition can be reconciled with the condition that the wheel's speed = runway speed if the wheel has a tangential acceleration with respect to the runway.

[LetYouDown]

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would it be theoretically possible for the plane to take off with its wheels spinning in reverse?

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Yes. No difference.