Tuesday, January 29, 2008

Plane on a Conveyor Belt

Apparently, the following question has inspired a lot of passionate debate throughout the Internet:
A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?
The comment threads springing from the mention of this problem are, for the purposes of any normal human being, endless, and there is only one fact that is beyond dispute: people who believe the plane takes off think that those who believe it doesn't take off are complete idiots (and vice-versa).

After thinking about this on the train ride home, I'm in the no-takeoff camp. I understand that a plane's thrust is not derived from its wheels, but if the treadmill can match the wheel speed, I just don't see how air flow over the wings could be generated for takeoff. And, to my surprise, with only fifteen minutes of consideration, I've become dogmatic in this belief.

It helps me to compare the following situation. Put a seaplane in one of those swimming pools with the jets that enable you to swim full strokes without moving. If you calibrate the jets to exactly counteract the thrust provided by the plane's propeller, it seems evident that the plane will not move relative to the air. Is this not the same situation as the treadmill?

Luckily, I've discovered this debate at exactly the right time. Set your tivo to record Mythbusters tonight, because they're going to put a plane on a giant treadmill to settle the debate for all time.


Matt O said...

My thought is that vertical take off and land, which is what the Harrier is, does rely solely on engine thrust. However, it is combination of vertical and horizontal thrust. So, in the end I have no idea. Let us know how this works out. We will be watching Spongebob and Power Rangers.

Matt said...

Right. The hypothetical should be more specific. I'm assuming a plane with no vertical thrust that can only achieve flight by producing air flow over the wings.

Anonymous said...

If there is no airflow across the wings (creating a low pressure region above the wing and high pressure below it - creating a pressure difference called lift) - then the thing is dead weight.

If you chained the tail of a 747 to the runway and then applied full power, the plane would not lift. If you tilted the engine upward (like a Harrier Jet), then the plane would become airborne.

If a plane was in a hurricaine, then it could be hovering directly above a stationary point on the earth with plenty of lift. It would be not moving relative to the observer on the ground, yet there would be plenty of airflow around the wings (what matters most)-fred

Anonymous said...

And another thing to add - having a conveyor belt under the plane's wheels will do absolutely nothing significant to counteract the thrust of the plane. The wheels will simply turn 2x as fast while the thrust of the engines act on the air.

The plane will take right off with no discernable difference from normal conditions.

Imagine standing on a conveyor belt while wearing roller skates. You are holding a rope connected to the wall in front of you. Would it be more difficult to pull yourself to that wall? Not at all.


Matt said...

Well, I just watched the Mythbusters episode, and their plane took off. It was pretty unsatisfying, though. They tested a proposition that I find self-evident: a plan can overcome a treadmill and take off. They used a conveyor belt that traveled at a constant rate.

The question I thought we were asking was this: can a plane overcome a treadmill that is specially tuned to speed up exactly in time with the plane?

Anonymous said...

OK Matt - I changed my mind. It would not take off. Here's why.

I think that the rolling resistance of the wheels would be relatively small. Therefore, if one wanted to counteract the thrust of a plane's propeller (or jet) with a moving treadmill underneath, the speed of the treadmill would have to far exceed the speed of the wheels.

The question states that the treadmill would counteract the wheel speed perfectly. If this is a perfect system then as soon as the thrust of the engines pulled the plane then the treadmill (and the wheels) would speed up immediately. Almost instantaneously the treadmill would achieve an tremendous speed - until the force of the engine is matched with the opposing force being exerted on the system from the wheels.

This is not practical in the real world, as the bearings would melt from the intense heat produced (remember the conservation of energy - no energy is lost due to friction, but converted to heat). -f

Thomas Petillo said...

i too thought the plane would not take off. the hypothetical seemed so specific about the belt matching the speed of the wheels, that i thought the plane would stand still. i've come to realize (mythbusters didn't state this clearly enough) that the belt, no matter how fast it can go, has no effect whatsoever on the thrust of the plane.

Thomas Petillo said...

also, as far as your whirlpool analogy goes, that would hold true if the vehicle were a boat with a prop in the water. but you're right, the plane would not take off from the hot tub, it's thrust would probably propel it out of the tub and onto the ground in front of the pool.

Anonymous said...

The friction exerted by the wheels, however minute it may be, must not be overlooked. There is some friction there, therefore the treadmill would perpetually increase in speed until the force exerted on the place by the wheels would exactly counteract the force exerted by the jet engine. When this happens, those wheels may be spinning at 5 million miles per hour - but the plane would not have moved at all.

Remove the landing gears and place the belly of the plane on a treadmill. Now state that "any forward motion of the plane would instantaneously be countered by the treadmill". The plane would never move, and therefore would never take off.

These two scenerios are analogous - only one has more friction (belly on treadmill) than the other (wheel bearings).

Matt O said...

Let's go back to vertical take off planes. I didn't make my point well. Forget the Harrier, take an Osprey, which has rotating props. I can't reconcile the no take off argument with the way this plane takes off. The instant the props go fully forward I do not see how the plane has generated the speed anything like a plane moving down the run way at the point of take off. Seems to me the engines pull the craft (or air over wings), as the take off crowd asserts, otherwise it would drop like a rock. In fairness, this plane has dropped like a rock before. So, I still don't know. Admitting up front that this all over my head, I am moderately pro take off.

Thomas Petillo said...

forget about the treadmill for a second. imagine that each wheel of the plane is placed on its own set of rollers, sort of like those used by cyclists when they can't ride their bicycles outside. those rollers spin extremely free, nearly effortless. now, the plane initiates thrust. what happens next?

Anonymous said...

If the plane is placed on a "dynometer" like contraption, then thrust applied from the jet engines would likely cause the plane to bump off of the dynometer. It's like powering up with those wheel blocks in place (those yellow ones that the ground crew places at the gate).

The treadmill is actively and dynamically countering the force of the jet engine from the time that the thrust is applied. If there is any friction at all in the wheel bearings, then the plane does not move.

The dynometer only gives a static amount of resistance (or friction) in a passive manner. The plane would eventually produce enough force to overcome the system.

-anonymous fred (sorry for forgetting to sign my last post).

Thomas Petillo said...

right, exactly. to say that a treadmill could produce enough counter force to keep the plane from moving is analogous to attaching a rope to the back of the plane and adding people to hold the rope as the plane ramps up thrust. the plane is going to take off.

Matt said...

I like your people-holding-a-rope image, Tom - but I don't think it illustrates the point you're making. Given enough people, you really could hold back a jet airplane with ropes.

For me, it's coming down to this: could an airplane take off of a dynometer or a treadmill? Sure, but not without violating one of the premises that we set for ourselves: the wheels of the plane will either spin faster than the treadmill or skid across the treadmill.

Matt said...

I watched the video. I love the do-it-yourself fervor that this question has inspired across the world.

We can't say that the plane wheels will always move faster than the treadmill. In our definition of the problem, we say that the treadmill matches the wheel speed. In the video you linked (and in Mythbusters), they show that a plane can overcome a treadmill moving the other way. They're proving that a plane can overcome a moving treadmill. But those experiments don't offer support for the statement that "no matter how fast the treadmill is moving," the plane will take off.

Anonymous said...

"if a guy can lift 10x his weight with the same force required to lift 4x his weight, he could probably lift anything."- newton is turning in his grave. remember, force=mass x acceleration.

"you said the treadmill would have to be spinning at much much more than 10x the take off speed before enough counter force would occur." -true statement. we agree that an opposite force is indeed acting on the plane through the wheels (and treadmill). That's right - it's going to be a fast-moving treadmill to negate those big airplane blades (or jets).

"until then the plane would move forward, and it would take off once the take off speed is achieved."
- well, then we are not using the treadmill as initially stated in the question. get a better treadmill (that has no time delay in applying the treadmill speed to counteract the wheels instantly) and the jet goes nowhere. -F

Anonymous said...

i'm not sure what this guy proved with his home video

he proclaims that "the forces are equal" out of nowhere.

I want to see him put maple syrup in the wheel bearings of that model airplane (to increase the friction of the wheel system) and then try it out. -F

Matt O said...

I sat with a retired airline pilot this evening on flight from Dallas to Washington. As we were landing I posed Matt's conveyor belt hypothetical. He very quickly laid out why the plane would not take off. His reasoning was precisely what Matt said.