Leaving on a jet plane (or, how smart are you again?)

one more point. certainly the original author intended for "wheel speed" to designate the speed the wheels AND plane move relative to the ground, not the conveyor belt.

However suppose, as some have, that "wheel speed" was intended to mean the speed at which the surface of the tires move relative to the conveyor belt. Then the conveyor belt would achieve a speed equal to and opposite the the newly defined "wheel speed" simply by not moving at all (relative to the ground), or by moving at any speed in either direction! It is a question of relativity. And of course, the plane takes off STILL!
 
Just got to this thread... what a ridiculous waste of time. The whole controversy arises because the problem is very poorly and misleadingly defined:

<i>The conveyer belt is designed to exactly match the speed of the wheels, but moving in the opposite direction.</i>

Do you mean the speed of the hub, the speed of the rubber in contact with the runway, or the speed of the top of the wheels? 3 different speeds.

1) Hub. This is the same as the speed of the rest of the plane, since the wheel hub is rigidly attached to the plane. In this case there's obviously no way the conveyor belt can keep the plane stationary, because if the plane isn't moving then the conveyor belt isn't moving. A motionless conveyor belt cannot impose a force on the plane. The only question is whether the conveyor belt would slow the plane down slightly through friction in the wheel bearings (probably insignificant) or accellerate its liftoff through induced wind / ground effect (probably also insignificant) or disrupt takeoff through ground effect turbulence (IMHO, probably). None of these questions can really be answered definitively without detailed technical information and/or CFD modelling.

2) Contact patch. The contact patch on a vehicle's wheels NEVER MOVES relative to the ground, unless the vehicle is skidding. In this case the conveyor belt does not move at all, even when the plane is going down the runway at 100mph. The takeoff would be absolutely normal.

3) Top of wheel. This is physically impossible. The moment the plane starts to move, the top of the wheel is moving faster than the conveyor belt by definition. This is the only situation in which the plane "can't" move but that's only because it violates the impossible terms of the problem.

Martin
 
I asked a couple guys from work and we all got the answer immediately.

As the initial post is phrased:

1. The plane would take-off as normal.

2. The wheels would not be spinning during take-off.

3. The conveyor would be travelling the same direction of the plane at the same speed the plane is travelling until the plane leaves the ground.
 
Let him have it Turok. We've got another disembodied plane... The plane is moving the same direction as the conveyor belt, but "as the initial post phrased," the wheels move in the opposite direction.



Quote from Cache Landing:

I asked a couple guys from work and we all got the answer immediately.

As the initial post is phrased:

1. The plane would take-off as normal.

2. The wheels would not be spinning during take-off.

3. The conveyor would be travelling the same direction of the plane at the same speed the plane is travelling until the plane leaves the ground.
More...
 
Quote from bellman:

Let him have it Turok. We've got another disembodied plane... The plane is moving the same direction as the conveyor belt, but "as the initial post phrased," the wheels move in the opposite direction.
More...

The initial post said the belt moves opposite the wheels, not the plane.

If the engine pushes the plane forward, the free spinning wheels consequently roll in a forward direction. The belt must then move in a forward direction to offset the forward spinning wheels. As the plane is not driven by the wheels during takeoff, they need not spin during takeoff. As it is stated, they remain motionless during takeoff, even though the plane moves forward like normal.
 
To state it more clearly..

The base of the wheel moves toward the back of the plane at the same speed the plane is moving relative to the ground. This is not because the wheels are driven, but rather because they are free spinning and the plane is moving relative to the ground.

Thus, the belt moving opposite the wheels would require that the belt be moving toward the front of the plane at the exact rate of speed the plane is travelling.

This would render the wheels motionless and the plane would leave the ground as usual.

Conversely, if the plane's take-off was driven by the wheels, the plane wouldn't be able to take-off, but rather the entire plane would remain motionless.
 
Quote from Cache Landing:

The base of the wheel moves toward the back of the plane at the same speed the plane is moving relative to the ground.
More...

The base of the wheel -- the point where it is in contact with the ground -- is always stationary during the entire takeoff run. This is also true for cars, or any other vehicles, unless they are skidding.

You seem to be measuring velocity relative to the plane's reference frame. In that frame, the bottom of the wheel is moving backwards, the hub is stationary, and the top of the wheel is moving forwards.

However, you have no basis to assume the plane's reference frame rather than the ground's reference frame. You also have no basis to assume that we are talking about the bottom of the wheel rather than the hub.

The original statement is underspecified and deceptive. If it were sufficiently precise, the answer would be obvious. It's like a rorschach blot, everyone sees something different because there's actually nothing there.

Martin
 
sparo:
>The original statement is underspecified and deceptive.
>If it were sufficiently precise, the answer would be
>obvious. It's like a rorschach blot, everyone sees
>something different because there's actually nothing there.

(author of original statement unknown -- it was emailed to me)

Don't agree that the original statement is "deceptive".

Do agree that if the problem was better stated, there would be less varied answers.

Just after starting this thread, I saw the wildly differing answers and rewrote the problem to my satisfaction and reposted in a new thread.

http://www.elitetrader.com/vb/showthread.php?s=&threadid=107520

That thread never took off like this one.

JB
 
I just want to know what airline this experiment is taking place on, and if there is a piliot on board... so that I never fly that company.
 
sparo:
>The original statement is underspecified and deceptive.
>If it were sufficiently precise, the answer would be
>obvious. It's like a rorschach blot, everyone sees
>something different because there's actually nothing there.

Just one more point sparo --

Since seeing (and posting) that orginal email problem, I have seen several other versions around the net -- some of them "sufficiently precise". Turns out for most people, the answer is not more obvious.

Most folks simply won't believe that a plane can take off from a treadmill.

JB

Again, my more precise version:
http://www.elitetrader.com/vb/showthread.php?threadid=107520
 
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