Who said anything about the tires maintaining a solid grip?

BTW
Here is a translation of the oldest version
“Russian to English translation
“The aircraft (jet or screw) stands on the tarmac with a movable cover (type transporter). Dvigaetsya coating may be against the direction of take-off aircraft. It has a control system that monitors and adjusts the speed of cloth so that the wheel speed aircraft was equal to the speed blade motion. Question: Can the plane take a run on the track and take off?”

I think the whole problem has been not the precise set up. The problem is with the question.
The first English translation changed it to “can the plane take off”

The stubborn “no” people later changed it to “can the plane take off without moving forward”.

I think there would have been no major controversy if the question has always clearly been “can the plane move”.

I really want to agree with you. I agree with 1st and 2nd concepts – yes the aircraft has to move forward relative to the ground in order to generate lift sufficient to fly.

But, I think I can see a way to make it fly. Lets look at your variations:

1. You agree in this case (fixed belt speed) the plane will take off, so lets go to 2
2. Belt moving at same speed as the aircraft but opposite direction. Here’s some thoughts first:
a. If the effect of a backward moving belt creates a frictionless (or at least very low friction) surface, then why can aircraft take off on ice? How do hovercraft move forward?
b. If you put a car on ice with smooth plastic wheels(ie – no grip at all), would it move? No – movement relies on friction and is relative to the ground only. What about if you strapped a rocket to it? Would it move then? Yes – Rocket – like a prop – provides thrust relative to the air, not the ground.
c. Is the belt matching the rotation speed of the wheels? or is the belt matching the forward speed of the aircraft relative to the ground? (The question seems to state the belt is matching aircraft’s forward speed to the ground).

Let me explain why that is relevant. If the belt is matching the speed of the aircraft over the ground (or even say doubling it), the net effect is frictionless wheels – like a hovercraft. If it were a car, it would go nowhere, but like a hovercraft, aircraft use a prop for forward speed, and because the prop is pulling the aircraft forward relative to the AIR around it, the plane will still move forward, irrespective of what speed the wheels are spinning.

Example: the aircraft moves forward 1mph. The belt moves backwards at 1mph, but then the wheel revolves at 2mph (1mph caused by the aircraft pulling it forward, and 1mph caused by the belt). Because the wheels are not driving the forward motion – the aircraft is still pulled by the prop – the wheels just turn twice their speed. Aircraft accelerates and wheels go twice their speed, but this hardly bothers the plane at all, and it takes off, wheels spinning twice the speed of takeoff. Making the wheels spin faster is NOT the same as locking the plane to the ground. Free spinning wheels (like a dynamo) would prevent a car (driven by wheels) from moving forward, but not an aircraft that is pulled by the prop. The wheels can do whatever they like (as long as they keep spinning and don’t lock up).

Now, let me throw in what I first imagined when I read this puzzle (and said to myself it wouldn’t take off):

Instead of the belt moving backwards at the same speed as the aircraft, rather the belt moving backwards at the same speed as the spinning wheels.

OK. Aircraft going forward at 1mph. Belt goes backwards at 1mph. Wheels spin at 2mph. Belt then matches 2mph. Wheels then hit 3mph (1 from aircraft moving forward, 2 to counter belt). Belt then hits 3mph. As you can see, this will very quickly escalate to either wheels falling off or belt disintegrating. However, irrespective of what is happening to the belt or the wheels, the aircraft will still move forward. At 1mph aircraft forward speed the wheels might be doing 500, but that has no impact (other than marginal friction) on the prop pulling the aircraft forward.

Here’s another example. Imagine you are standing on a treadmill wearing roller skates (I really don’t want to test this one). If there is no friction, there is no way you could move forward – right? But let’s say you had something you could pull on – like a rope. No matter how fast the treadmill goes, you can pull yourself forwards – infact, the speed of the treadmill will make almost no difference to the effort needed to pull yourself forwards. The aircraft has this piece of string – the prop – which is attached to something outside the conveyor belt (air in this case), which it can use to pull itself forward.

1st concept(How does a plane achieve lift): An airplane achieves lift by moving enough air over the wings to achieve a thrust greater than the weight of the airplane.

2nd concept(How does the plane accelerate): The airplane must accelerate with it’s engines and propell the plane forward in relation to the air, if there is no wind then the velocity of the air is, for all intents and purposes, equal to that of the ground.

3rd concept(How does a conveyor belt affect acceleration):
This is where the argument generally becomes confusing and is the basis for such a conflicted array of answers. There are variations to this riddle that affect the outcome so I will work through the two variations.

Variation 1:
The belt is moving at a fixed rate of speed that is independent of the planes movement. If this is the case the airplane will achieve a state of equilibrium with the forces acting upon it and will eventually begin moving in relation to the ground(air) and CAN take off. The wheels will begin to move at a faster pace than the belt because the belt remains at a static speed. Conclusion, the plane will take off in an ideal situation.

Variation 2:
The belt is moving at a speed equal to the wheels of the plane in the opposite direction. This variation gets tricky but bear with me. In an ideal situation where friction is not a factor. The plane will not take off. Here’s why; in order for the plane to move forward the wheels MUST move at a pace faster than the belt. If the belt is constantly speeding up. The force of the wheels will keep the plane from moving forward. In a less than ideal environment, the friction created by the wheels would most likely be overpowered by the engine and the the wheels would begin to skid on the belt, like pushing a car with the wheels locked up.

The entire basis is that the wheels are indeed connected to the plane. In order for the plane to move forward with the wheels maintaining solid grip with the belt they have to move faster than the belt. The only other way to move it forward is to overcome the friction provided by the wheels and the ground.

Wheels spinning at 40mph are offering little resistance compared to the thrust of the plane’s propeller, so acceleration will be minimally affected. Once the plane reaches 20mph relative to the ground the wings are providing enough lift to fly. At this point the wheels are actually spinning at 40mph, despite the plane’s “true” speed of 20mph.

The plane’s propeller, on the other hand, relies only on being surrounded by air. It doesn’t matter what the tyres are doing, that propeller will still be exerting the same forward force on the plane.

So you can have your wheels spinning away at 800kph (500mph) on a conveyor belt and that propeller will still be exerting the same force and accelerating the plane in the same manner relative to the stationary ground (as long as the tyres and bearings can handle that speed).

Lift one of a car’s drive tyres off the ground and see how little pedal depression it takes to have that wheel spinning at 200kph. That is how little resistance a spinning plane wheel is offering against the significant force applied by the propeller.

The plane will take off. Jamie could have been driving that truck along at 100mph and the same result would have occurred.

Place the aircraft on a conveyor belt with only the wheels contacting and it will plunge directly into the sea.

The earliest version I found was
“A plane is standing on 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 opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off? ”

notice the question includes “will it be able to run up”.
That would not be part of the question and an assumption that it would not run up.

all the “depends on what you measure relative to” argument is based on the assumption that plane stands still. But it is not a given in the question, it is the point of the question.

It’s clearly what the speed is relative to. if the plane is going 20mph right and the tarp 20mph left the plane won’t move, HOWEVER the planes speed is relative to the speed of the tarp… so simply said if you calculate from the starting point on the tarp the plane will be going 20mph…

On the other hand if you calculate everything relative to the ground the plane will be going (truely) 40mph, therefore moveing 20mph compared to a point on the ground.

So I believe the myth is true that the plane will not move in relation to the starting point on the ground.

To explain why mythbusters found this busted… one their tarp wasn’t a great surface to pull the plane on (but in all respect what else could they have used) two they can’t have the plane 100% on the ground so the tarp wasn’t completely pulling the plane, and finally three event thought the plane and truck when 20mph in opposite dirrections if you weren’t exactly perfect with the increase of speed on both, the plane would have been skipping over parts of the tarp therefore giving them the result they had…. i 100% understand this myth and for those who say the plane is strictly 20mph from start, going right.. and the tarp is strictly 20mph from start, going left you are CORRECT… Please ask questions if you don’t understand

the myth needs to be refined to make it more pure and therefore provable

Q2: Can conveyor belts be used to reduce runway lenghts at airports?
Answer: NO.

Someone should call the navy on this one. They could save a lot of money on their carriers.

ABC your second sentence is just plain wrong. Why do you think that the wheels make any difference? They don’t move the planes forward.

If you understand the question you realize the setup would stop a car from moving forward but not a plane.

People made a wrong assumption and can’t get past it. People like Joe and ABC

And Joe you fell for the “IF” trap.
For what you said to be relevent the part after the “if” must be true. It isn’t. Air is moving over the wings like normal.

But I agree that the plane will move forward and once its air speed is sufficient it will take off. The wheel “speed” is irrelevent and will always match the speed of the conveyor belt provided the wheel is not skidding.

The “gotcha” is the misconception that by spinning the conveyor belt you will somehow prevent the plane from moving. You will not. No matter how fast you spin it.

I think asking the following questions whose answers are more obvious cover the concepts wrapped up in the original question/scenerio:

Q1: Can an airplane take off on a frictionless surface, for example ice?
Answer: YES
Q2: Can conveyor belts be used to reduce runway lenghts at airports?
Answer: NO.

Both of these point to the same concept that the wheels and wheel speed have nothing to do with creating and supporting flight.

That’s not the case. The plane does take off because it does move forward and this causes the air to move over the wings.

It doesn’t matter how fast or slow the conveyor belt moves (aside from a small amount of friction)…the plane will move forward at the same rate.

ABC you’re missing the point. You think because the plane moved forward that the truck didn’t match the speed. Until you grasp what stephen has written you won’t get why the plane moves forward AND takes off regardless of the conveyor belt.

Mythbusters did a show on this, where they dragged cloth the other way while the plane sped of the other way. The plane did manage to take off, but that’s because they weren’t matching the speed of the conveyor.

Good job, asshat.