Well the basis of the problem is that it's a plane that's sitting, gear down, on a conveyor belt that's programmed to move backwards at the same speed that the plane moves forwards.

So really, the belt is immaterial, the only thing different is that you'll get to takeoff speed and the wheels will be spinning twice as fast as they normally would. It'll introduce a small amount of friction, but nowhere near enough to actually stop the plane from taking off.

A lot of people assume that the plane would remain stationary, which would be true for a car that gets its forward motion from the wheels. But since a plane flies by thrusting through the air, the conveyor belt can't stop it. If there was a big fan instead of a big conveyor belt, that blew air forward at the same velocity as the propellor was blowing it backwards, then it wouldn't be able to take off.

Maybe the mythbusters should do this one. Oh well. At very least you can get around the problem by assuming a VTOL airplane like the Osprey or Harrier. :p

i'll research this later when i have the time, but no-one knows how planes stay in the air
airfoil lift only accounts for a slight percentage of the lift, all other explanations are theories, my dad(who is a pilot) showed me when he was studying for his exam, i also saw it in a magazine called 'fly'.

i'll research it later

WTF are you on? Of course the airfoil is what provides all the lift. What else would it be?

no-one knows how planes stay in the air

i'll research this later when i have the time, but no-one knows how planes stay in the air
airfoil lift only accounts for a slight percentage of the lift, all other explanations are theories, my dad(who is a pilot) showed me when he was studying for his exam, i also saw it in a magazine called 'fly'.

i'll research it later

i'll research this later when i have the time, but no-one knows how planes stay in the air

Intelligent Design is what keeps planes flying.

It's not rocket science. They're not the same number. Surely that's enough to satisfy everyone.

Isn't it just the difference in time for the air to travel under/over the wing that makes them fly? I always thought it was.

Is it just me who can see how simple and obvious that is?

About the numbers:
I'm not genius but 0.8888 sure as hell doesn't make 2.

0.99999 = 0.99999

1 = 1

It's not rocket science. They're not the same number. Surely that's enough to satisfy everyone.

0.999.... only EVER = 1 when you round up. That's it. It's not complicated, otherwise it remains 0.999.... etc.

Is it just me who can see how simple and obvious that is? I think people are digging too deep to make up some silly theory.

t's not like, debatable. That's why this thread was silly in the first place.

About the numbers:
I'm not genius but 0.8888 sure as hell doesn't make 2.

0.99999 = 0.99999

1 = 1

It's not rocket science. They're not the same number. Surely that's enough to satisfy everyone.

0.999.... only EVER = 1 when you round up. That's it. It's not complicated, otherwise it remains 0.999.... etc.

Is it just me who can see how simple and obvious that is? I think people are digging too deep to make up some silly theory.

About the planes:

Isn't it just the difference in time for the air to travel under/over the wing that makes them fly? I always thought it was.

WTF are you on? Of course the airfoil is what provides all the lift. What else would it be?

Next theoretical problem: is the number of bloated egos on this thread finite?

Yeah, if the plane did somehow take off because it's speed relative to the belt was equal to the necessary flight velocity, then the plane would still have zero air velocity. The plane would be magically floating stationary in the air when observed by anyone on the ground.

You can put a matchbox car on a piece of paper and then accelerate the paper at a low enough rate that the car stays in place. Once the paper reached it's final velocity, the "driver" of the car could accelerate so that the car was staying in place relative to whatever the paper is sitting on. The car would not be moving relative to what the paper was on, but would be moving relative to the paper.

Planes typically take off and land facing the wind. This gives them a larger air velocity without having to have such a large land velocity. The plane on the conveyor belt would have very little air velocity and high conveyor belt velocity. That won't help the plane get into the air.

If you would argue that the friction of the wheel assembly plus the friction of the wheel and belt wouldn't be enough to keep the plane at the same speed as the belt, then the issue is the physics of the inertia and friction reaction and not whether the plane can fly. The flight issue is secondary to the relative motion issue.

First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.

A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

I don't even have any idea how anyone is getting either of these questions wrong.

.99999... equals 1.

The plane will take off.