This is first time I saw this kind of topic. My answer is "YES". The plane can fly on a moving conveyor which travel at the same speed in the opposite direction.

I think we need to read the statement again. Can a plane take off on a conveyor belt moving at the speed in opposite direction?. It didn't mention that the plane will be stationary. Reason why there is a large number of people in the "no camp" because they misinterpret that the airplane will be stationary when the conveyor is moving in the opposite direction. Allow me explain a bit.

Cheesenium has post an extensive lift principle, so I'll skip that. For my explaination, you need to know at least the definition of newton's third law.

In newton's third law, every action has a reaction in the opposite direction. On a moving conveyor, an object will remain stationary (to a third eye) if there is a force in the opposite direction reacting on the object. For example, a car. The reaction force will be driving the car at the same speed of the conveyor, in the opposite direction. Because the conveyor is moving, the car appear stationary, like a dyno machine. Agree?

Now, in airplane, the reaction force comes from the thrust of the engine. When we run the engine, the engine move air from the suction to the exit. Basically it doesn't move air on top and below the wing, but across and within the engine. So there is plenty of thrust generated, but without air moving across the wings, it will never fly.

Next, imagine we mount the engine on a trolley, or cart (just the engine, without the wing). The thrust generated will transfer the force to the trolley, and hence pushing the trolley forward. The same effect can also be achieved with fan on a trolley. As the trolley travel forward, air travel across it. Although trolley cuts through the air, it don't fly because there is no wing. Now, we exchange the trolley with a hull and wings, so we get an airplane.

WHEN a plane travel forward (on the runway), only will, the air move across the wing, and create lift. (Hope everyone can keep up with this.)

Now, we upgrade the experiment a bit. We put a conveyor at the bottom. By running the airplane on a conveyor, the engine actually create thrust onto the hull. Despite whatever the ground speed maybe, the thrust generate force onto the stationary air. If the ground travel at light speed yet the air above it remain stationary, the thrust will generate force onto the air, unlike car which generate thrust onto the ground. So, the airplane will just keep moving forward.

When it gain enough speed, sufficient air movement across the wing, the airplane will take off. In fact, it will still require the same runway length disregard of whatever speed the conveyor maybe. Mythbuster is right.

If it generates thrust towards the hull, doesn't that create drag and result in force going in the backwards direction, working against the airplane?

And besides, the point of the conveyor is to match the airplane's forward speed but in the opposite direction, so "keep moving forward" won't happen unless the wheels loose frictional contact with the belt.

Yup, the hull is actually holding the engine from moving forward. However given enough thrust, it will overcome this resistance and start moving forward. If you take a close look at Boeing, you will notice a "lump" at the bottom of the hull, which connect to the wing.

When it starts moving forward, the conveyer belt spins backwards faster (e.g. hook it up in a closed feedback loop), keeping the plane where it is.

How does the plane overcome this and move forward?

Thanks bgeh, I'm an ass for not reading your first post here, because it started with ".. doesn't take off .." and was freakin long. I now understand the importance of Aurora's statement that a car generates thrust into the ground while a plane generates thrust into the air, because when put together with freely-moving wheels it leads to the result that the conveyor belt can never hold a plane back*.

* - taking this at face value, in all honesty i am probably never going to cross-check with the equations coz i'm not a physicist

It's an empirical equation, so yeah at best we take it as some approximation (which will probably fail at some limit). Actually if you used the same linear approximation, given powerful enough engines, you would reach the same conclusion that a plane on wheels with brakes applied will also fly off given the same condition of a conveyor belt.

Also, the above explaination only explains the first part of my post, where I claim that in the ideal case with friction and no rolling resistance, the plane simply doesn't move when the conveyor belt moves.

The question is that can a plane take off on a conveyor belt moving at the same speed in opposite direction?

actually la. the videos posted so far, we can't conclude what exactly is the Mythbuster test about since we'll need more info from the starting. they always explain.

so if we go by the thought of the propeller's thrust finally overcoming the speed of the conveyor belt then I wouldn't disagree on anything. surely it'll reach a point where airflow creates sufficient lift to takeoff.

however in the case of what seagates mentioned............
then clearly it's no.

why? because it's no different from tying the plane to a solid object - it's not moving, thus won't takeoff.

yes, from my POV - the wheels don't matter.

i'm imagining that if the thrust generated results in a 75km/h forward motion, the wheel will spin the other direction with the conveyor belt at 75km/h.

in the end it's like running on a treadmill. power is used to go forward but the object remains stationary due to the area that the object is moving on, is moving backwards. and just like running on a treadmill, you can run at 12km/h and still don't feel any air going around your body.

so if we were to go with Seagate's 1st post - clearly there's only 1 answer.

No, because the treadmill analogy fails to compensate for the fact that we're no longer talking about cuboid like objects, which experience massive friction that literally causes us to stop, but wheels instead, where the friction instead speeds up the wheel's velocity. Try this question then. Take a roller skater moving at say 5km/h. Let him skate to a walkalator moving in the opposite direction, at also 5km/h. Guess what will happen when he reaches the walkalator? [You could also substitute the walkalator with a treadmill, as long it's perfectly horizontal and stuff]

Solution in the form of an edit, after you reply (will take a while though)

Edit: 2nd analogy I just thought of: (True story)

When I was a kid, I always wanted to do roller skating/roller blading, and spent quite some time admiring and looking at my neighbour and cousin's skates. Naturally with my itchy hands I liked to roll the wheels using my hands by running my palm across the wheels. I hope you've done this too, but I noticed that the faster you move your hand across the wheels, the faster they rotate. Why? Same principle applies to the walkalator question, and same principle applies to the 'free spinning wheels' on the plane

after putting some thought of what you mentioned, i think i finally understood your point.

so assuming i get your point right, we're talking about..........

conveyor belt moving backwards at X speed. Free wheel also will spin at that speed to counter belt's backward movement. that effectively nullifies the speed, while the propeller is still giving the thrust. if that's the case, then it's clear that in the end as long as the thrust provides forward movement, the plane will take off when the air pressure generates sufficient lift.

short version - the free wheel spins to the speed of the conveyor belt, reducing the total effect of the conveyor belt on the plane's forward motion.

after putting some thought of what you mentioned, i think i finally understood your point.

so assuming i get your point right, we're talking about..........

conveyor belt moving backwards at X speed. Free wheel also will spin at that speed to counter belt's backward movement. that effectively nullifies the speed, while the propeller is still giving the thrust. if that's the case, then it's clear that in the end as long as the thrust provides forward movement, the plane will take off when the air pressure generates sufficient lift.

short version - the free wheel spins to the speed of the conveyor belt, reducing the total effect of the conveyor belt on the plane's forward motion.

do plane really need a wheel to move forward??
i mean, let say the body of the plane is on ice, the thrust from engine is enough to make the plane go forward.

i don't think you get what i was saying. btw never once did i mention using wheel to move forward.

try to understand what me and bgeh talked about in this page, we've come to an agreed understanding already.

i'll try to make it even more simple

the counter movement of the conveyer belt at the same speed of the thrust has no effect on the plane as the contact point between the plane and the belt is the wheel, where the wheel will spin according to the speed of the belt thus having little to no effect on the thrust.