A plane sits on a conveyor belt

*cough* no lift *cough*

If it's a Malaysia Airlines plane it will disappear.

The wheels on a plane do not provide forward thrust. The wheels are there only to facilitate the plane moving along the ground while the engine thrust moves the plane forward.

The plane will take off more or less as normal. There will be some minor loss of propulsion due to the friction between the axle and wheels as they turn faster than normal, but that will not have sufficient effect to stop the plane from achieving takeoff.

People get confused with this problem because they think of the plane's forward motion on the ground much like they think of a car's motion on wheels. A car on a treadmill that matches its speed will not move forward. However, a plane on the ground is not just a car with wings. It's still an airplane, and its forward thrust does not come from the wheels.

The only gotcha will be that the airplane is initially moving backwards on the treadmill at some speed. When the engines are throttled up, it will gradually "slow down" in the negative direction, come to a stop relative to the world, then accelerate forward in a normal manner.

One other potential problem is that the wheels will be spinning twice as fast as they should before it takes off. Hopefully the bearings and the tires can take that.

Mythbusters covered this one. They achieved lift.

The end of their segment is here.
https://www.youtube.com/watch?v=YORCk1BN7QY

Hmmm...That's as dodgy a Mythbusters experiment as ever I've seen.

ETA: I'd use a Harrier.

When I read the title I thought this thread was gonna be a good joke. You know, something like "Guy walks into a bar..."

Myrealana said:

The wheels on a plane do not provide forward thrust. The wheels are there only to facilitate the plane moving along the ground while the engine thrust moves the plane forward.

The plane will take off more or less as normal. There will be some minor loss of propulsion due to the friction between the axle and wheels as they turn faster than normal, but that will not have sufficient effect to stop the plane from achieving takeoff.

People get confused with this problem because they think of the plane's forward motion on the ground much like they think of a car's motion on wheels. A car on a treadmill that matches its speed will not move forward. However, a plane on the ground is not just a car with wings. It's still an airplane, and its forward thrust does not come from the wheels.

Click to expand...

But the conveyor belt isn't matching the wheel speed; it's matching the airspeed.

It would not rise because the lift comes from air passing above and below the wings at different speeds.

So put a plane with no wheels in a really strong wind tunnel...

This question (along with the one about a person running in a train) has sparked some of the longest and most heated threads I've ever seen. (Both are exceeded by the 'should people keep cats in Australia' threads, which invariably end in threat of violence. But I digress.)

But the question has always been about wheel speed. In this one, Albedo's asking about air speed, as Kuwi's pointed out. So if the air's moving fast enough to register 300km/h on the indicator, presumably there'll be some lift. If that's how airspeed indicators work. I dunno. I always avoided those threads, because they do my head in. (And the xkcd forum has banned them, I believe.)

Based entirely on intuition and a few beers, here's my answer:

The plan would eventually achieve lift. This is ultimately because the conveyor belt is matching its current speed rather than its acceleration. And assumes that instantaneous acceleration is impossible.

Consider its velocity at a few instantaneous points in time:
1. The plane accelerates and achieves 1 m/s.
2. The conveyor belt accelerates and matches -1 m/s.
3. The plane is now at 0 m/s and the conveyor belt decelerates to 0 m/s.
4. The plane continues to accelerate, achieving 1 m/s again.
5. The conveyor belt accelerates and matches -1 m/s.
6. The plane is now at 0 m/s and the conveyor belt decelerates to 0 m/s.

Throughout this, the plane continues to accelerate.

If one plots the speed of the plane, this process results in a sinusoidal curve.

I propose that because the plane is continuously accelerating, while the conveyor belt is both accelerating and decelerating to match speed, that the plane's acceleration will eventually overtake the conveyor belt, i.e., the amplitude of the sinusoidal curve will grow larger and larger over time, until at some point, the instantaneous speed of the plane is enough to achieve flight.

Angry Guy said:

The only gotcha will be that the airplane is initially moving backwards on the treadmill at some speed.

Click to expand...

I don't see that, whether in the OP's statement or in the problem statement(s) I recall from so many years ago. But whatever, I don't think that matters.

One other potential problem is that the wheels will be spinning twice as fast as they should before it takes off. Hopefully the bearings and the tires can take that.[/QUOTE]
I heard this thing discussed on the radio maybe ten years ago. It seems a lot of the argument and confusion are about how the problem is stated, and then a lot more argument and confusion are about how the problem is interpreted.

One way I (apparently incorrectly) interpreted the problem so many years ago was that as the airplane started to move forward, the treadmill would start moving fast enough so that wheel resistance would stop it. So if the plane were moving at 5mph the treadmill might have to move backwards at 90mph for the wheel friction to be enough to bring its speed back to zero. I assumed bearings-and-tires could take this, otherwise it gets even MORE overly complicated.

Of course, the airplane's ability to fly has nothing to do with groundspeed, wheelspeed or treadmill speed, but only with sufficient airspeed. I'll let others figure out whether the plane flies based on that (or based on whatever else they may consider pertinent).

yes it will

Helix said:

Hmmm...That's as dodgy a Mythbusters experiment as ever I've seen.

ETA: I'd use a Harrier.

Click to expand...

If I recall the whole segment, they tried it small scale first with a model plane on a conveyor belt and it had no trouble lifting off. But trying to scale up they ran into a "how do we build a conveyor belt big enough and strong enough on our budget"... hence the truck and fabric.

There should be videos of the whole segment somewhere, I just found the tail end.

kuwisdelu said:

But the conveyor belt isn't matching the wheel speed; it's matching the airspeed.

Click to expand...

Doesn't matter, because the wheels are nothing but friction mitigators.

The answer is "Batman wins."

That answer is never wrong, regardless the question.

The thing that's always worried me about this question is this:

Seaplanes.

the plane would take off as it normally would but it wouldn't go anywhere.





















*locks thread*

Still waiting for an evaluation of my answer...

Is it a black-and-blue plane, or a gold-and-white plane?

Belts and planes are non sequitur. The plane is free to use its propeller to generate whatever force it can to accelerate while the surface contacts provide minimal friction due to their passive design.

Windtunnels and planes do follow.