I mentioned this "debate" to an aerospace professor down the hall and we had a good chuckle about some of the responses here.

I stand by the fact that it's irrelevent in this discussion.

Well, it's irrelevant only if you also find the magical moving runway also irrelevant.

I guess I read too much into the original question. Scott posed it as such: "The conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction)."

I guess if by "plane speed" you mean the speed the plane would normally achieve on stationary ground, given a thrust of XYZ, then yes, that'd never be enough to affect the miniscule amount of friction between the wheels and belt.

If the conveyor moved so fast (again, it'd have to be a magical conveyor that moved thousands of miles per hour) as to keep the plane stationary with relation to the Earth/ground, then it would go nowhere. I guess traditional wheel bearings and tires would melt before that point. So again, I was making some assumptions as to what was being proposed in the initial question.

Problem with this teaser is in the wording.

Plane takes off because it moves forward and creates airflow over the wings.

Unlike a car, which when in gear, the forward power is applied thru the wheels, a plane generates thrust via airflow (whether prop or jet).

If a car is going 50 mph on this magical treadmill that is going backwards at 50 mph then it stays stationary because the force put down by the car's wheels is counteracted by the treadmills reverse motion applied to the SAME wheels putting down the power (preferrably rear wheels :) ).

BUT with a plane, once it generates thrust to get to this same 50mph, the only thing that the counter acts this force is wind resistance and the minimal friction on the wheels so it will MOVE forward while the wheels spin at close to twice the rate (because this magical treadmill) because the wheels spin freely and are in no way associated with the plane's engines unlike the car example.

Just because the treadmill is moving backwards at the same speed that the plane is moving forward, the only thing this does is spin the wheels faster while the plane moves forward b/c the wheels are not creating any force, they are just allowing the plane to roll rather than be dragged on the ground. Even a magical conveyor belt that moved at a infinite speed in the reverse direction would simply spin the wheels faster while the engines continued to make thrust and move the plane forward.

Bottom line, you set us up for failure by asking a bunch of car guys about planes.

Yeah, now an example of a plane with pontoons taking off from the water, you'd have much more friction, but you'd still need an incredibly strong current to make the plane stationary in the water.

If the planes lift-off airspeed is typically ~100kts, you might need, say, ~300kts of water current speed in the opposite direction.

Couldn't have said it better myself.

Edit - Atlanta, I'm also sharing a good chuckle about this "debate"

Everyone keeps saying that "the wings won't generate lift, because the plane is stationary."

But that's just it, the plane isn't stationary. It is generating thrust relative to the surrounding air, which is not moving. Therefore, the plane will move itself through the air regardless of what the treadmill is doing.

Remember that the treadmill is only moving as fast as the airplane is moving, with regard to a fixed point of reference external to the airplane/runway combination. We'll assume that this reference is the atmosphere.

Consider what would happen if, with the engine off, we start the treadmill rolling backwards at 5MPH and fix it at that speed. Since the airplane is not generating any thrust, it will remain stationary with regard to the treadmill, and thus begin to move backwards at 5MPH relative to the fixed point of reference.

Then we fire up the engine and run it up to takeoff power. The airplane will begin to move forward with regard to the treadmill. When it gets to 5MPH treadmill speed it will now be stationary with regard to the fixed point of reference. And it will continue to accelerate, until it is moving at takeoff speed with regard to the fixed point of reference, which is the atmosphere. This means that air will be flowing over the wings sufficient to generate lift and allow rotation. The treadmill will be scrolling backwards at takeoff speed, sure. But all this means is that the wheels will be spinning at twice takeoff speed (actual airspeed, plus reverse groundspeed.)

How is this?

Well, how did the airplane manage to start moving forward in the first place? At the beginning of the run, the treadmill was running backwards even faster than the airplane was moving forwards, and yet the airplane produced enough thrust to overcome this and begin moving. At the point that the airplane crosses over 5MPH relative to the external reference its doing 10 MPH relative to the treadmill, but the important fact, and the one that seems to be causing people grief, is that the airplane is still moving through the air.

If the plane was generating thrust, it would run off of the treadmill long before any actual takeoff occured, invalidating the experiment.

Besides, any air moving would be moving through the turbines, NOT over the wings. Since the treadmill is stationary, and so is the plane, lift will not be achieved. Period.

drag.... not friction.

And, in relation to my last post. My friction equation isn't the correct one. After thinking it over there would be a rolling resistance of the tire to the surface... but it wouldn't be nearly that high. The friction you'd need to account for would be in the wheel bearings which is related to speed. It would still be too small of a force to counter the thrust of the engines and the airplane would still lift off.

Umm... you're wrong too.

kotomile - I think we're laughing for different reasons.

But the plane is not standing still. You are assuming that the plane is stationary.

The original question only says that the conveyor belt tracks the speed of the airplane and moves at the same speed in the opposite direction. It does not say that the plane is stationary, you are assuming this.

Think about it this way, what force is keeping the plane stationary? The planes engines are generating thrust which pushes the plane forward. Although the wheels move backwards because of the conveyor belt, they would just spin and not keep the plane from moving. The conveyor belt simply causes the plane's wheels to spin, but aside from some friction in the plane's wheels, there is minimal backwards force on the plane.

For example, if you wear rollerblades on a treadmill, aside from the friction within the wheels of the rollerblades, the treadmill would not make you go backwards because the wheels would just spin. The only force you need to apply from going backwards is overcoming the force caused by friction of the wheels spinning. The plane is the same way, but the engines are applying a hell of a lot more force in the forwards direction so the plane moves forward relative to the ground and takes off.

Care to elaborate?

Yes, the plane would take off, but the only way it would happen would be to let the plane move relative to the ground (off of the treadmill).

So then, since the plane cannot take off without moving through the atmosphere (read: moving relative to the ground) no airflow, no bernoulli's principle, and no lift.

Also, EVEN IF the plane could take off without moving relative to the ground (which it can't) in order to sustain flight the plane would have to be moving forward fast enough to keep aloft. So, the plane's going to go from 0 mph on a treadmill to cruising speed in an instant? Not likely..

It's necessary to read and completely appreciate the original puzzle. I mis-read it originally, and came up with a needlessly long and incorrect answer.

For one thing, we are assuming that the treadmill is at least as long as a standard runway.

For another, you're overlooking how airplane engines work, be they prop or jet.

We'll assume this is a jet aircraft with one engine. If the plane is sitting on a normal (stationary) runway and the engine is run up to power, air is drawn in the front and exhausted out the back. So air is moving through the turbine, and the turbine is doing work against the air to generate force (which we call thrust). The moving air coming out of the back of the turbine is colliding with the stationary air behind the engine, and this causes a force to be applied to the entire turbine / moving air combination, relative to the stationary air that makes up the rest of the atmosphere. This is Newton's third law, governing reciprocal actions.

Now, the turbine mechanism itself wishes to move forward with regard to the air, which is stationary. Because the turbine has an airplane attached to it however, the turbine has no choice but to drag the rest of the plane along with it as it moves forward through the air. Thus, the wings of the airplane will be moving with regard to the air, and lift will be produced.


None of this changes as you start to move the runway. Because the airplane has wheels which are able to freely rotate, the runway cannot exert sufficient force upon the airplane to counteract the thrust being exerted upon the air by its engines.

The important thing is that, if we assume that the air and the ground (external to the treadmill) are both stationary, then the airplane WILL be moving relative to these, regardless of what the treadmill is doing. Because the airplane engine is not exerting force upon the treadmill, it's exerting force upon the air!

But it will be moving relative to the ground and the stationary atmosphere, see my longer post on the last page... I don't understand wtf you are trying to argue so it's hard for me to elaborate... you are just wrong.

How can the plane be moving relative to the ground AND be running on a treadmill at the same time?

Kotomile, I think you and I both read into it the same way...perhaps we should celebrate our differences with respect to the rest of the crowd here :D

Amen brother.

How about a situation in which the friction of the moving surface plays a much bigger role...like, say, my pontoon'd airplane taking off against an opposing current in water.

Again, Koto and I appear to have read into the teaser that the conveyor belt could move so quickly as to cause the thrust by the jet engine/propeller/rocket/etc. to be opposed through the friction/drag/whatever between the tires and the conveyor surface. The whole point of bearings, as Philip so eloquently put it, is that they have little friction, though.