Can a Jet Plane Take Off on a Treadmill?

[Dalton Peters]

So I have heard this around the internet before but thought is was a question worth exploring if a jet plane is sitting on a treadmill and the treadmill moves backwards at the same rate the plane is moving forward will it take off? I think no because the plane would have to be moving forward for air to go over the wings to provide lift right? unfortunately there is a lot that disagree with me and was wondering if I could get a reply from some more qualified people. (sorry if there is ignorance in this post I still haven't started under grad physics yet)

 

[mfb]

and the treadmill moves backwards at the same rate the plane is moving forward

That is ill-defined.
Only the speed of the aircraft relative to the air matters.

 

[Dalton Peters]

That is ill-defined.
Only the speed of the aircraft relative to the air matters.

basically if the airplane has zero velocity can it still achieve lift

 

[A.T.]

the treadmill moves backwards at the same rate the plane is moving forward

To be meaningful, you have to state relative to what the speeds are measured.

unfortunately there is a lot that disagree with me

Probably because everyone understands such vague question differently.

 

[russ_watters]

basically if the airplane has zero velocity can it still achieve lift

No, it can't.

Note, this is a very easy question that is made difficult only by the fact that it is worded as a seeming self contradiction and also physically difficult to achieve:

1. You said "...the plane is moving forward..." (without stating with respect to what) when you really meant the plane is stationary with respect to the ground.

2. If the plane isn't moving forward with respect to the ground, then something unspecified is holding it in place.

We have gotten this question a bunch of times, always with similar poor wording, which is what causes the arguments/confusion. Run a search and you'll find somee...

 

[lekh2003]

So I have heard this around the internet before but thought is was a question worth exploring if a jet plane is sitting on a treadmill and the treadmill moves backwards at the same rate the plane is moving forward will it take off? I think no because the plane would have to be moving forward for air to go over the wings to provide lift right? unfortunately there is a lot that disagree with me and was wondering if I could get a reply from some more qualified people. (sorry if there is ignorance in this post I still haven't started under grad physics yet)

The plane does not generate lift from speed; it generates lift from the speed of the air it is entering. The fast air hitting it can lift the plane.

If the plane is simply standstill relative to the air, then it won't move. This is the case in your example, the plane is moving forwards and the treadmill is moving backwards with the same speed. Relative to the moving ground on the treadmill, the plane is moving. BUT remember that to generate lift the plane needs to be moving relative to the air. So it will not lift upwards.

 

[lekh2003]

basically if the airplane has zero velocity can it still achieve lift

Not using the correct terminology is resulting in your confusion. The plane's velocity can be 30000 m/s relative to the sun. It could also be 300000000 m/s relative to the light around it. The only thing that matters here is the velocity relative to the air. That velocity is definitely NOT zero.

 

[Dalton Peters]

Not using the correct terminology is resulting in your confusion. The plane's velocity can be 30000 m/s relative to the sun. It could also be 300000000 m/s relative to the light around it. The only thing that matters here is the velocity relative to the air. That velocity is definitely NOT zero.

but its not moving its essentially fixed to one point because of the backwards movement of the treadmill i just want to know if it will ever lift up off of the treadmill

 

[Bystander]

to know if it will ever lift up off of the treadmill

What part of "No" are you not understanding.

 

[russ_watters]

but its not moving

Then it doesn't takeoff! Simple!

However:

its essentially fixed to one point because of the backwards movement of the treadmill

That is physically impossible. If the airplane's engines are firing, the treadmill alone can't stop the plane from moving with respect to the air.

I suggest you draw yourself a diagram and label all the motions and forces. If the forces don't sum to zero, the plane has to move.

 

[jbriggs444]

but its not moving its essentially fixed to one point because of the backwards movement of the treadmill

This partially clarifies your interpretation of the question. The airplane is stationary relative to the ground while a treadmill beneath it moves.

Further questions:

Is there any wind? A plane can take off at zero ground speed if there is sufficient wind.

Are we to neglect the wind induced by the plane's own engine(s)? I suspect that a plane could take off in its own slip-stream if one were to tether it inside a big doughnut-shaped wind tube.

What is causing the plane to move forward relative to the treadmill? One assumes that its engine is on and the prop spinning.

What is restraining the plane from moving forward relative to the ground? One assumes that its prop is only spinning fast enough to counter the rolling resistance of the tires.

 

[A.T.]

plane is moving forward

but its not moving

Make up your mind.

 

[Dalton Peters]

Make up your mind.

it has speed but is not moving from its point due to the movement of the treadmill counteracting its forward movement

 

[Dalton Peters]

I have updated the post with a diagram

 

[russ_watters]

is not moving from its point due to the movement of the treadmill counteracting its forward movement

How? What is the cause of the force in your diagram?

 

[Dalton Peters]

How?

sorry for any vagueness I added a diagram that can probably explain it better than me

 

[russ_watters]

sorry for any vagueness I added a diagram that can probably explain it better than me

The diagram shows three forces. The thrust force is obvious. What is the cause of the other two?

 

[Dalton Peters]

How? What is the cause of the force in your diagram?

the conveyor turns in the opposite direction of the thrust force of the plane. The plane is sitting on a conveyor belt

 

[russ_watters]

the conveyor turns in the opposite direction of the thrust force of the plane. The plane is sitting on a conveyor belt

I know the conveyor moves and the wheels spin, but motion is not force. Indeed, in constat speed motion, forces must sum to zero. So what causes the forces? Consider that the spinning wheels don't stop a plane from taking off on a runway, so ordinarily there is essentially no force exchange between runway and wheels. Why does the conveyor change that?

 

[Dalton Peters]

I know the conveyor moves and the wheels spin, but motion is not force. Indeed, in constat speed motion, forces must sum to zero. So what causes the forces? Consider that the spinning wheels don't stop a plane from taking off on a runway, so ordinarily there is essentially no force exchange between runway and wheels. Why does the conveyor change that?

yeah that's where my question basically lies is if the plane is not moving there is not as much air flowing over the wings therefor less thrust is created so I was wondering if the plane could still take off even though it's wings are not gliding through the air creating that downward thrust

 

[Dalton Peters]

I know the conveyor moves and the wheels spin, but motion is not force. Indeed, in constat speed motion, forces must sum to zero. So what causes the forces? Consider that the spinning wheels don't stop a plane from taking off on a runway, so ordinarily there is essentially no force exchange between runway and wheels. Why does the conveyor change that?

I'm sorry I didn't include a diagram that represents the air flow that I am referring to

 

[A.T.]

if the plane is not moving

That's a big "if", when you can't name the force that would prevent it from moving.

 

[sophiecentaur]

if the plane is not moving there is not as much air flowing over the wings

If it is not moving through the air then there will be no lift. How many times must this be stated and an how many different ways, before you take that message on board. Whatever the wheels and the treadmill are doing will have no effect on the lift if the plane is not moving forward, relative to the air. There are no 'loopholes' to make your idea suddenly work.
PS the thrust from the engines that's required to keep the plane stationary relative to the Earth is very small - just enough to overcome the rolling friction of the wheels over the treadmill. Do not try to make your intuition govern your way of thinking here. Try to apply the laws of Physics, as have been stated in the other posts in this thread.

 

[Dalton Peters]

If it is not moving through the air then there will be no lift. How many times must this be stated and an how many different ways, before you take that message on board. Whatever the wheels and the treadmill are doing will have no effect on the lift if the plane is not moving forward, relative to the air. There are no 'loopholes' to make your idea suddenly work.
PS the thrust from the engines that's required to keep the plane stationary relative to the Earth is very small - just enough to overcome the rolling friction of the wheels over the treadmill. Do not try to make your intuition govern your way of thinking here. Try to apply the laws of Physics, as have been stated in the other posts in this thread.

Alright, thank you

 

[russ_watters]

yeah that's where my question basically lies is if the plane is not moving there is not as much air flowing over the wings therefor less thrust is created so I was wondering if the plane could still take off even though it's wings are not gliding through the air creating that downward thrust

Well, ok. At this point whether the plane takes off or not and why is really up to you. You're making assumptions in order to correct the deficiencies in the problem statement. You don't necessarily need to correct all of them, I guess, so you are left with:

Q: A plane doesn't move. Does it take off?
A: No. (Obviously)

You've decided that's the answer you want and are filling in details to make it true. That's fine. These details of why (engine is at idle now apparently...) aren't important and don't necessarily need to be developed if you don't want to.

However, my personal preference is to fix it to be a more realistic and non trick question scenario, in which case the plane takes off.

[Edit] Also, I think you will find that except as a logical trick, the presence and behavior of the treadmill is irrelevant to whether the plane takes off. In your diagram, you included a force applied by the treadmill, but the treadmill isn't capable of providing that force on its own.

 

[sophiecentaur]

yeah that's where my question basically lies is if the plane is not moving there is not as much air flowing over the wings therefor less thrust is created so

This is a complete non-sequitur. There can be as much thrust as you like when the plane happens to be stationary. You are totally confusing cause and effect. The thrust is not 'because of' airflow so your "therefore" is the wrong word.

yeah that's where my question basically lies is if the plane is not moving there is not as much air flowing over the wings therefor less thrust is created so I was wondering if the plane could still take off even though it's wings are not gliding through the air creating that downward thrust

You mean lift? "Thrust is conventionally taken to be the force that the engines produce. The only way you can get lift with aircraft not moving through the air is to use vectored thrust. VT has not been mentioned so far in the thread so it would be better not to move the goalposts by introducing it.

I think it's time for you to re-read this thread and to see how so many of your posts have not addressed the other comments. What do you actually want out of this exercise? You are not going to change the theory. Why not learn the theory and then you will be able to answer the questions yourself.

 

[rcgldr]

Going back to the original question.

if a jet plane is sitting on a treadmill and the treadmill moves backwards at the same rate the plane is moving forward will it take off?

The planes tires will spin twice as fast, which won't have much effect on the plane accelerating forwards due to thrust, and the plane will be able to take off, only using bit more distance to compensate for the relatively small increase in angular kinetic energy of the wheels.

The TV show myth busters did an actual demonstration, by pulling a "conveyor belt" backwards:

 

[russ_watters]

Going back to the original question.

The planes tires will spin twice as fast, which won't have much effect on the plane accelerating forwards due to thrust, and the plane will be able to take off, only using bit more distance to compensate for the relatively small increase in angular kinetic energy of the wheels.

The TV show myth busters did an actual demonstration, by pulling a "conveyor belt" backwards:

This is fine for your, my and Mythbusters' assumptions, but fails for the OP's assumptions, which define the plane to be at rest and include other necessary assumptions like an engine at idle.

 

[CWatters]

If the aircraft has wheels there is very little or no friction between the aircraft and the conveyor belt. So the moving conveyor belt applies very little rearward force on the aircraft. This force is easily overcome by the thrust from the engine so the plane accelerates and takes of normally.

The only difference is that the wheels rotate faster.

If in doubt draw a free body diagram of the aircraft showing the force acting on it.

 

[OCR]

Airplanes and Lift

This again, really... all over, again... ?