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The old "plane on a conveyor belt" debate

This one is (again) doing the rounds of the internet

Currently it is on some group on FB and someone did a poll, which shows a big majority saying the plane will never take off. I am not surprised by that in terms of the general public but what is scary is that, on a quick look at their profiles, most appear to have a PPL. And here’s one comment from a UK PPL instructor:

There is no way this plane can take off. If the conveyor matches the wheels there is no forward motion. As such there is no airflow so it will not generate any lift. Therefore it stays put. Lift is a function of airflow over the wings and has NOTHING to do with the speed of the wheels . I find it hard to understand how the Yes group actually passed a POF exam…..if they did

I suppose it is possible to get a PPL with no understanding of mechanics or physics. I just wonder whether the pilot will find flying to be full of weird and frequently scary surprises.

Administrator
Shoreham EGKA, United Kingdom

Well, the tyres exploding at some point before V1 might inhibit the takeoff (as the wheels will end up rotating twice as quickly as they normally would as the plane accelerates down the conveyor belt, so the wheels will be rotating well above their maximum rated speed by the time you’re approaching takeoff speed).

Andreas IOM

It depends on what you mean by “wheel speed”. If you mean the speed of the tyre at the point it makes contact with the conveyor belt, then I agree that the aircraft will make a normal take off. The speed of the tyre at the contact point is always zero (unless the wheel is skidding) so the conveyor belt would not move at all.

On the other hand, if “wheel speed” means the speed of the wheel as a whole, then the question is difficult or impossible to answer, as it has several unrealistic premises. If we assume that there are no physical limitations to either the aircraft or the conveyor, then the premises are even impossible to satisfy simultaneously.

But assuming that

- the aircraft is a real aircraft as far as physical limitations go
- the conveyor has no physical limitations, i.e. it can match any wheel speed and is able to essentially instantaneously react to changes in wheel speed

then I agree that the aircraft would never take off.

As the aircraft attempts to move the conveyor belt will start moving in the opposite direction with rapidly increased speed until one of the following happens:

- The wheel friction equals the engine thrust and we have a stable situation with no movement of the aircraft and a constant wheel/conveyor belt speed
- The tyre(s) burst at which point bad things will happen, but no take off.
- The wheel bearing(s) fail at which point again bad things will happen, but no take off.

ESKC (Uppsala/Sundbro), Sweden

I think the intent of the question is that you disregard second order effects and disregard “pedantic” language interpretations e.g.

  • disregard tyre rpm limits (above post #2)
  • disregard general friction (wheel bearings etc)
  • not interpret the question as saying that the wheel as a whole, i.e. the whole landing gear assembly remains stationary because then obviously the plane will never take off because the landing gear is screwed to the airframe, and thus no airspeed will ever be achieved
  • disregard the portion of the engine power which gets used to spin up the wheels (resulting in a very slightly longer takeoff roll on the backwards-moving conveyor belt, because the wheels are getting spun up to 2x the normal rpm)
  • disregard the local airflow effects which a large conveyor belt moving at 120kt would produce (resulting in a slightly shorter takeoff roll because you are in effect getting a bit of headwind)

etc

Administrator
Shoreham EGKA, United Kingdom

Peter wrote:

not interpret the question as saying that the wheel as a whole, i.e. the whole landing gear assembly remains stationary because then obviously the plane will never take off because the landing gear is screwed to the airframe, and thus no airspeed will ever be achieved

I think that’s the interpretation of most people who answered that the aircraft wouldn’t take off, and frankly that’s the reasonable interpretation of the speed of the wheel as different parts of the wheel have different speeds (and velocities).

ESKC (Uppsala/Sundbro), Sweden

I think that’s the interpretation of most people who answered that the aircraft wouldn’t take off,

If you saw the endless discussions on this one, you would find that most people get it wrong because they think of it like a car on a rolling road. Whereas a plane is more like a jet powered car on a rolling road, and you cannot run a jet powered car on a rolling road because it will just run straight off it – because it is not driven through the wheels.

If you assume the landing gear doesn’t move then the Q is just silly

Administrator
Shoreham EGKA, United Kingdom

Mythbusters busted this one some time back.



Fly safely
Various UK. Operate throughout Europe and Middle East, United Kingdom

Airborne_Again wrote:


I think that’s the interpretation of most people who answered that the aircraft wouldn’t take off, and frankly that’s the reasonable interpretation of the speed of the wheel as different parts of the wheel have different speeds (and velocities).

Fully agree with this statement. I am still unsure what Peter means though, how would the plane take off?

Low-hours pilot
EDVM Hildesheim, Germany

OK, think of this another way and the aircraft is a glider on a winch launch where the winch and cable have replaced the propeller to provide forward ‘thrust’.

Same scenario – will the aircraft take off? Of course it will because the winch is winding-in the cable with is pulling the aircraft over the ground or, more relevantly, through the air which, with a bit of 1/2RhoV2S, will provide lift. The speed over the ground (in this case moving ground) is irrelevant.

Fly safely
Various UK. Operate throughout Europe and Middle East, United Kingdom

The other trick in this question is that it causes people to think that the backwards moving belt will prevent the plane developing any forward motion relative to the earth i.e. relative to the air and that is wrong.

The belt is irrelevant. You could replace the landing gear with magnetic levitation, etc.

Administrator
Shoreham EGKA, United Kingdom
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