This old chestnut

[Munkul]

The original question only says that the conveyor is moving hence my original response that wheel speed is not important. At first reading I took it that they were asking if the plane would fly if the conveyor got the wheels up to speed. What it actually requires you to infer is that if the plane IS getting to take-off speed but the conveyor is holding the wheels stopped by it's motion will the plane take off? If you do take that as the question then yes it will of course, otherwise seaplanes would be boats.

The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.

Speed obviously being surface speed, as you cannot equal the rotational speed of the wheels with a surface speed of the conveyor belt

 

[Munkul]

I've always read this question (this version anyway) as a red herring.

The ignorant focus on the wheels and say its not possible.
The partly-knowledgeable focus on the lack of importance of the wheels as an aeroplane uses thrust, not drive to the wheels, and say yes it can.
The engineers focus on the losses due to friction of the "incredibly fast" conveyor and wheels and say it possibly can, with lots of debate.

Then the mathematical person comes along and points out the theoretical impossibility of the situation due to the unbalanced infinite acceleration of wheels and conveyor.

(I was in the 2nd category until the teacher pointed out the maths to us all)

 

[rtcosic]

Engines supply thrust
Wings supply lift
As long as an aircraft’s engines are producing more thrust than the total drag the aircraft is experiencing it will accelerate, (Airspeed) once the airspeed matches the calculated speed for take off (weight and altitude dependent) it can then take off, the wings will produce enough lift in order to overcome gravity.
It will then take off leaving the hypothetical conveyor belt behind irrespective of what speed the wheels are travelling at

Can I change my vote, please?

As this is a thought experiment the conveyor belt is infinitely long.

I reimagined the conveyor belt as an infinitely long aircraft carrier sailing at the take-off speed of an aircraft. The aircraft will take off whilst moving at zero speed relative to the carrier but take-off speed relative to the air and the sea. The wheel speed of the aircraft will be zero.
Turn the aircraft around on the aircraft carrier and takeoff will still be take-off speed relative to the air and sea but twice take off speed relative to the carrier.

In the latter case, if the aircraft is moving relative to the air and sea at half takeoff speed then the wheel speed and carrier speed will be equal and the aircraft will just trundle along the infinitely long flight deck. In the other direction, it will have taken off before the wheels have ever turned.

Or have I got THAT wrong as well!

 

[daleyd]

I read the question as the conveyor moves in the opposite direction, ie the wheels would “appear” stationary when the plane moves forward on the “ground” (which is obviously unimportant as its air speed over wings which provide lift) - not that the conveyor somehow doubles the speed of the wheels To do that the conveyor would have to be travelling in the same direction as the wheels.

 

[Munkul]

I read the question as the conveyor moves in the opposite direction, ie the wheels would “appear” stationary when the plane moves forward on the “ground” (which is obviously unimportant as its air speed over wings which provide lift) - not that the conveyor somehow doubles the speed of the wheels To do that the conveyor would have to be travelling in the same direction as the wheels.

Wrong way around in your head! For the wheels to be stationary, the conveyor would match the exact forward speed of the plane itself, and go forward!

 

[Munkul]

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the plane, moving in the opposite direction.

Can the aeroplane take off?

- Change one key word there and then the scenario becomes theoretically possible, and also yes the plane can of course take off at its normal takeoff speed, the wheels will be going twice as fast.

 

[daleyd]

Wrong way around in your head! For the wheels to be stationary, the conveyor would match the exact forward speed of the plane itself, and go forward!

No - as soon as the wheel starts to rotate the conveyor moves in the opposite direction so the wheel would appear stationary. It makes no reference to the plane moving only the wheel. If the conveyor was going in the same direction (as the wheel - not plane, this is important) then wheel speed would increase, but not opposite

 

[Porkypine]

Reminds me of those daft "fancy" bling wheel trims a good few years back that continued spinning when the car stops.. It was a bit of a WTF? moment the first time i saw a set on a car in traffic

 

[Munkul]

No - as soon as the wheel starts to rotate the conveyor moves in the opposite direction so the wheel would appear stationary. It makes no reference to the plane moving only the wheel. If the conveyor was going in the same direction (as the wheel - not plane, this is important) then wheel speed would increase, but not opposite

nope.

 

[Burdekin]

I hate when the pilot applies the brakes to the wheels when flying to stop the plane.

 

[Burdekin]

The wheels just spin backwards while the jet engine propels the plane forward. The wheels don't drive the plane in any manner. They are just a bearing.

 

[daleyd]

The wheels just spin backwards while the jet engine propels the plane forward. The wheels don't drive the plane in any manner. They are just a bearing.

This ^ - the wheels are of no consequence (I still think that as the question is worded they would appear not to rotate)

 

[Maker]

I've always read this question (this version anyway) as a red herring.

The ignorant focus on the wheels and say its not possible.
The partly-knowledgeable focus on the lack of importance of the wheels as an aeroplane uses thrust, not drive to the wheels, and say yes it can.
The engineers focus on the losses due to friction of the "incredibly fast" conveyor and wheels and say it possibly can, with lots of debate.

Then the mathematical person comes along and points out the theoretical impossibility of the situation due to the unbalanced infinite acceleration of wheels and conveyor.

(I was in the 2nd category until the teacher pointed out the maths to us all)

I've got another "engineers" answer;

This infinitely fast conveyor will quickly develop a boundary layer of atmosphere moving fast enough to make the plane take off vertically.

 

[Munkul]

I've got another "engineers" answer;

This infinitely fast conveyor will quickly develop a boundary layer of atmosphere moving fast enough to make the plane take off vertically.

Yes! I have heard that one before

 

[daleyd]

Plane moves forward, wheel rotates as per arrow above conveyor. To match the speed of the wheel the conveyor moves in opposite direction.

 

[Munkul]

This is actually impossible.



Scenario with conveyor matching wheel speed - if the vessel moves forward at a rate of 1 m/s, the wheel will also rotate with a surface speed of 1 m/s. But the conveyor also matches the wheel speed, which as the vessel forward speed is independent of the wheel speed, this would cause the wheel to double in surface speed. The conveyor matches this speed, and the wheel speed doubles, and so on... infinite acceleration to an infinite speed.

 

[daleyd]

This is NOT supposed to represent my original question.

View attachment 328605

It's not specified whether it matches the wheel forward speed or rotational speed, I have read it as the wheels rotational speed, so the conveyor speed goes the opposite way.

 

[Munkul]

This scenario is possible. Both as steady state and instantaneous.

 

[Seadog]

Then the mathematical person comes along and points out the theoretical impossibility of the situation due to the unbalanced infinite acceleration of wheels and conveyor.

Why will the wheels and conveyor move at infinite speed? Once the areoplane has lifted there is no longer contact.

This is actually impossible.

Imagine the plane have a massive telescopic ram holding it in position on the runway. this ram has no contact with the runway. If it starts to move the plane forwards, what happens? The wheel rotates and the conveyor moves. As the ram accelerates the plane the wheels and conveyor move faster. At the point where sufficient forward speed is achieved the plane loses contact. The ram is a direct parallel with the thrust generated by the engine.

 

[Munkul]

It's not specified whether it matches the wheel forward speed or rotational speed, I have read it as the wheels rotational speed, so the conveyor speed goes the opposite way.

I can see where you are coming from. 99% of people would read it as the wheel surface speed. The possible confusion would be about the MOVEMENT of the wheel as a whole (ie the plane speed), not the surface speed.

Rotational speed is an incorrect assumption because revolutions or angular speed cannot equal surface speed, it's a non starter.