what mythbusters *SHOULD* have done.

[gsh]

Airplane on conveyor belt. As with many word problems, the exact wording becomes important, so google "plane conveyor belt" hit "I'm feeling lucky" and get:


Here's the original problem essentially as it was posed to us: "A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?"

Mythbusters showed two examples of the plane taking off, and declared the myth busted. However, I don't think they did the myth right. The basic physics is that as long as the plane isn't moving with respect to the wind, there is no lift. However, as long as the plane's propeller is providing thrust, there will be an acceleration of the plane. Any conveyor belt that doesn't accelerate doesn't describe what is listed in the myth. As long as the belt accelerates to match (and cancel) the acceleration of the plane, the plane doesn't generate lift. Eventually the conveyor belt reaches its maximum velocity, stops accelerating, the plane surges forward, starts generating lift, and then can take off.

What, me OCD on this issue?

Comments

[elkor.livejournal.com]

This conveyor has a control system that tracks the plane speed

The myth as I read it pertains to the speed of the airplane.

Speed is a relative measure of the motion of an object against some (nominally) stationary reference. In most cases, we use the ground to measure speed (which is why there is a "ground speed" and an "air speed" when discussing airplanes, birds and other such objects).

Typically, when the plane is on the ground, it uses ground speed. When it is in the air, it uses air speed.

So, as long as the plane is on the "runway" they go by ground speed.

Also, it is the propeller that is moving the air. In order to negate the air speed of the plane, it would end up moving backwards on the conveyor.

At which point the plane is no longer stationary relative to an observer.

[gsh]

Also, it is the propeller that is moving the air.

In general, that is not true. Most of the air flow over a wing hasn't been moved by the propeller.

I agree the distinction between ground speed and air speed is important, but the conveyor belt can (for a period of time) cancel out the air speed (but not the ground speed). Once the belt reaches its maximum velocity, the plane will have both a non zero groundspeed and a non zero airspeed.

[elkor.livejournal.com]

Once the belt reaches its maximum velocity, the plane will have both a non zero groundspeed and a non zero airspeed.

Assuming that the conveyor is infinitely fast, but not infinitely long, at some point the plane will roll off the back of the conveyor.

I guess my point is that:
1) In either situation, the myth is busted.
2) Your interpretation is at odds with the lay persons interpretation (using ground speed)
3) Your proposal of a belt that matches the air speed of the plane is infeasible for a sustainable test.

[gsh]

The plane should never roll off the back of the conveyor. Once the belt reaches the maximum velocity, the plane will roll off the front.

The myth is true as long as the setup is correct. I don't put much stock in the lay person's interpretation, most lay persons don't do physics correctly.

The third point is what I consider the beauty of it, as long as the belt can accelerate under strict command, the plane won't lift off. But eventually it can't, and then the plane will. So both sides are correct, in the limits of the assumptions.

[elkor.livejournal.com]

I don't put much stock in the lay person's interpretation, most lay persons don't do physics correctly.

Yet most lay persons are the ones that create the myths in the first place, by simplifying the situation and applying their own logic to it. Because the knowledgable people already know the answer.

We're going to have to agree to disagree. I believe the ground speed interpretation is the correct one.

[gsh]

While we may need to agree to disagree, I simply don't know what you mean by "the ground speed interpretation is the correct one". Do you mean that you think the amount of lift developed by a plane is based on the ground speed?

[elkor.livejournal.com]

Do you mean that you think the amount of lift developed by a plane is based on the ground speed?

No, that the myth says the conveyor the plane rests on would counteract the ground speed of the plane.

So the plane remains stationary relative to a ground point not on the conveyor.

[drcruel.livejournal.com]

But then...wouldn't you still need the same amount of runway space minus what was needed to accelerate the plane to the point at which there was sufficient air under the wing to create lift? In other words, the plane would leave the conveyor belt at take-off velocity, I agree, but then you would still have the problem of needing the engines fired and synched to sustain that velocity and you'd still be moving at exactly take-off velocity, from which you would need space to accelerate and achieve more lift before achieving crusing altitude. In other words, I think it works, but it doesn't seem to solve the problem of shortening take-off.

I think. Right? Maybe?

[mtnwlf.livejournal.com]

That banging sound you hear is the sound of the wife bonking her head on the monitor. He just can't handle it that I said the plane would fly and he said it wouldn't. ROTFLOL

[whitebird.livejournal.com]

And now, how much wind velocity is generated under/over the wings as the conveyor belt travels under the plane? There is a variety of ground effects with wind which could easily come into play for increasing the amount of lift the plane is subjected to while on the conveyor.