Will a plane on a treadmill take off?

[Who_me_1]

I’ve skipped the last few pages… sue me.

The best way to get the plane to take off and not violate the rules of the OP is to lock the wheels in place so that they don’t turn at all.

Otherwise, I feel that the OP is an impossibile situation and uses impossible suppositions. The treadmill will have a negligable effect on the plane and its ground speed and any plane on a treadmill would take off normally, however fast the treadmill is going. Any consideration of a treadmill that would speed up to match the wheels spinning is like asking if God can make a rock so big so that he cannot lift it…

[Who_me_1]

[QUOTE=Who_me?]

The best way to get the plane to take off and not violate the rules of the OP is to lock the wheels in place so that they don’t turn at all.

[\QUOTE]

Forgot to add that these wheels have frictionless surfaces, just like all the other frictionless things mentioned in the thread.

[matt]

@David Simmons

I still have difficulty seeing how the turning of the wheels would apply a linear force to the axle through a frictionless bearing.

Me too! But it has to be the case. For another way to think about the situation, imagine a drum in space, with a single rocket mounted on its surface and firing tangentially. Does the drum simply rotate around its axis, or does it accelerate as a whole,albeit with a changing vector?

@David Simmons

In addition, the OP wasn’t imagining some outlandish monstrosity of an airplane for the test.

Absolutely, but this is more fun!

RaftPeople, I’ll have to think about that a while.

@Seven

If the engine DID have enough thrust to lift the airplace without wings it would be called a rocket.

@matt

No it wouldn’t. A harrier jump jet can do it. A fair few military fighters can do a vertical climb.

@Seven

If we’re talking about a Harrier on a treadmill, then the answer is yes.

What answer? A Harrier is a rocket?

@Seven

But I don’t think that’s that point of the question. It would be the same as asking if a helicopter could take off on a treadmill

No, it’s not the point of the question. It was just a snarky reply on my part, provoked by your statement “For those of you having a hard time understanding this, let’s set up a slightly different situation”, which I percieved as patronising. Perhaps I’m over sensitive.

[David_Simmons]

@zut

Because you disbelieve the fact that force can be transmitted through a bearing.

Oh please. The force of the treadmill results in a torque on the wheel which turns it. Seehere.

@matt

… imagine a drum in space, with a single rocket mounted on its surface and firing tangentially. Does the drum simply rotate around its axis, or does it accelerate as a whole,albeit with a changing vector?

And that changing vector first points forward, then down, then backward, the up, then forward, etc. For a real rocket the thing will rotate around the center of mass of the drum and rocket with some wobble as a result of inevitable misalighnents and unbalances. What it will most certainly not do is take off in a straight line.

[RaftPeople]

@lissener

I think what’s kept this thing going for a hilarious 7 pages is that the question being answered is not the OP. The question being answered is,

“Can you posit a scifi treadmill, outside of the laws of physics or rationality, that could make it impossible for an airplane to take off?”

The resulting thought experiment seems to have imagined a treadmill which manages to absorb ALL of the “equal and opposite reaction” of the jets’ or propellors’ actions.

Since this is not really possible, again I say the OP has been answered. The only way to believe otherwise, IMO, is to consider the OP to be a question along the lines of, “Is god so omnipotent that he could create a mountain that was too big for him to move?”

You’re getting closer to the actual problem.

The problem is not that the OP created the “mountain too big” type of problem for sure.

The problem is trying to determine, “did the OP create an impossible situation or not?”.

And the only way to determine that is to work through all of the details of wording, physics, etc.

So the question back to you is, why do you think the OP created a treadmill that manages to absorb ALL of the engines thrust? The only thing the OP said was it would match speed, is that enough to counteract thrust?

[RaftPeople]

@Hombre

Would anyone like to address the issue of the treadmill matching the wheel speed exactly?

If the wheel speed is matched exactly by the treadmill, how could the plane move foreward al all?

Anyone?

Yes it has been discussed.

If you interpret speed to mean the linear speed of the circumference of the wheel as it moves past the point of contact with the belt, then you are correct, no forward motion is possible.

Most of the discussion is assuming that “speed” means forward movement of the wheel (which is really the same as the speed of the plane).

[Who_me_1]

@RaftPeople

The only thing the OP said was it would match speed, is that enough to counteract thrust?

Of course not, the treadmill has no effect on the thrust. The plane WILL move, no matter what the treadmill does or doesn’t do, how fast the wheels and the treadmill move have no bearing on the speed the plane is moving in relation to where the treadmill is sitting.

[treis]

@David Simmons

Oh please. The force of the treadmill results in a torque on the wheel which turns it. Seehere.

You are still looking at the wrong friction. Its not the friction between the bearings and the axle its the friction between the tire and the ground.

Look at this picture:

Now, if Ffriction is not zero and assuming as you contend that Faxle is 0 then the wheel will accelerate to the right. Looking at the bike FBD if Faxle is 0 then that portion of the bike does not accelerate. Since the wheels are attached to the bike it is impossible for them to accelerate while the bike has a non-zero acceleration. Therefore, there must be a force between the axle and the wheel.

@Who_me?

Of course not, the treadmill has no effect on the thrust. The plane WILL move, no matter what the treadmill does or doesn’t do, how fast the wheels and the treadmill move have no bearing on the speed the plane is moving in relation to where the treadmill is sitting.

This is wrong.

[treis]

@David Simmons

And that changing vector first points forward, then down, then backward, the up, then forward, etc. For a real rocket the thing will rotate around the center of mass of the drum and rocket with some wobble as a result of inevitable misalighnents and unbalances. What it will most certainly not do is take off in a straight line.

No, the drum will not only rotate but it will travel in a circle around a point in space and that point will move linearly. Its tough to explain it just through words but what happens is that there is a rotation from the rocket being off of the center of mass. In addition to that the drum will accelerate linearly becuase there is an unbalanced force on the drum. But since the drum is rotating the direction of this acceleration is constantly changing and results in circular motion. However, since the drum is angularly accelerating the amount of time through a portion of its rotation is continually decreasing.

Assume that at 0 degrees rotation the rocket is at the bottom of the drum and the exhaust is pointing to the left. Lets say that it starts at rest and takes 1 second to go from 0 degrees to 90 degrees. Over that 90 degrees there is an acceleration both to the right and up from the changing direction of the rocket. Now, the movement from 90 degrees to 180 degrees would cause an equal acceleration to the left and down except for the fact that our drum’s angular speed is increasing. Since it is angularly accelerating this takes a shorter time and thereforce has less linear acceleration.

This is very complicated acceleration and it would take a lot of vector and calculus to get an answer for a stationary reference frame.

@David Simmons

I still have difficulty seeing how the turning of the wheels would apply a linear force to the axle through a frictionless bearing.

I missed this before, its not the turning of the wheels that apply a linear force through the axle. You are right, a wheel just spinning on an axis does not apply a force to the axle (other than the weight of the wheel). When the wheel does apply a force is when there is a linear acceleration on the wheel. For linear acceleration it does not matter where the force is applied. It just so happens that when you apply a force through a point other than the center of mass the wheel rotates.

In the case of the treadmill the key point to take away is that the force from friction between the wheel and the treadmill exactly opposes the force from the engines. Once we know that you can describe the acceleration of the treadmill by looking at the wheels.

[treis]

@treis

No, the drum will not only rotate but it will travel in a circle around a point in space and that point will move linearly. Its tough to explain it just through words but what happens is that there is a rotation from the rocket being off of the center of mass. In addition to that the drum will accelerate linearly becuase there is an unbalanced force on the drum. But since the drum is rotating the direction of this acceleration is constantly changing and results in circular motion. However, since the drum is angularly accelerating the amount of time through a portion of its rotation is continually decreasing.

Assume that at 0 degrees rotation the rocket is at the bottom of the drum and the exhaust is pointing to the left. Lets say that it starts at rest and takes 1 second to go from 0 degrees to 90 degrees. Over that 90 degrees there is an acceleration both to the right and up from the changing direction of the rocket. Now, the movement from 90 degrees to 180 degrees would cause an equal acceleration to the left and down except for the fact that our drum’s angular speed is increasing. Since it is angularly accelerating this takes a shorter time and thereforce has less linear acceleration.

This is very complicated acceleration and it would take a lot of vector and calculus to get an answer for a stationary reference frame.

I’d like to add that eventually the angular acceleration becomes very small compared to the angular velocity. When that circling of the drum around a point and the net linear acceleration becomes negligible. At that point it will continue to accelerate angularly but will more or less travel linearly at a constant velocity.

[David_Simmons]

Will you guys stop talking about bicycles and autos? What you are both saying is that if I jack up a non driving wheel of a car and push backwards on the bottom of the wheel I can push the car off the jack. Nonsense.

That’s it. I’m done.

[EvilGhandi]

Why do we assume the treadmill is moving against the direction of the wheels? Could we assume that for a moment that the treadmill was moving with the directin of the plane. The rotation would be exactly zero. It wouldn’t matter if the brakes were on or not.

[treis]

@David Simmons

Will you guys stop talking about bicycles and autos? What you are both saying is that if I jack up a non driving wheel of a car and push backwards on the bottom of the wheel I can push the car off the jack. Nonsense.

You can call it nonsense all you would like but its the truth. For linear acceleration it doesn’t matter where the force is applied on the body. You can apply it at the bottom of the wheel, through the center of mass or the top. That car is going to accelerate at a rate of A=F/M in the direction of the force.

How do you think a car accelerates? It does so by a frictional force applied at the base of the tire.

[treis]

Look, you agree that the bike will slow down going from the ice to the pavement. That means there must be a force on the rider from somewhere. If not from the friction between the tire and pavement where does the force come from to slow the rider?

[Who_me_1]

@treis

This is wrong.

No… it isn’t.

[treis]

@Who_me?

No… it isn’t.

Yes it is. You find me a plane which engines produce a force Fengines and a treadmill that can accelerate at the rate of 2*Fengine/Mtires and I will show you a plane that goes nowhere. The math is in the pdf file linked in post 255.

[GusNSpot]

Just to be sure I’m part of history, I’m gonna post some more…

Now lets stop all this magic stuff and do this right. ( This can actually be physically done with the technology and engineering we have today. Be a bit of a $$ waste but it could actually be done. )

We have a 10,000 foot treadmill that will take the weight of an airplane.

I am in control of the treadmill speed.

I am sitting facing the treadmill with 98% of the treadmill to my left as I face it.
I have a sight to look at the airplane through and can tell if it moves in relation to the hangers in the background or relative to me sitting off to the side.

First test.
Park the airplane on treadmill facing my left with engines off.
I move the treadmill to the right with my controller and since I moved it too quickly, the inertia of the airplane allowed the plane to roll forward a few feet as I brought the treadmill into motion. Due to friction, rolling resistance etc., the plane becomes stationary on the treadmill belt and moves off to the right until I slowly stop the belt.

*::: bring plane back to start position. ::: *

Second test.
The engine of the airplane is fired up and the plane begins to move to my left down the treadmill at 1.0 mph. I can see this in my sight so I bring the plane back to the start position by running the belt at 1.1 mph and slowing it to 1.0 mph to keep the plane in my sight. But I needed to actually go a bit faster with the treadmill because as soon as I started moving the plane to the right, the force of the thrust was increased by the plane stopping and moving to the right so it’s net thrust is higher than if it was in a steady 1.0 mph run down the runway.

But… this is a bigger load on the propeller ( lets use a propeller because it might be easier to see what is happening to the air being
pushed backwards. ) so the engine need a fraction more fuel to keep the same RPM.

This added power makes the plane move to the left again and I see this and speed up the treadmill more to keep the plane in position. This will sun reach an state of equilibrium when everything will balance out .

Now, the plane adds power to the propeller and I keep adding speed to the belt and keeping the plane stationary relative to me. Again we reach equilibrium at say 10 mph of belt speed but the plane is gaining much help from being stationary and so it’s actual ‘push’ to move is getting bigger and it is taking more and more belt speed to keep it there because the transferee of energy through the wheels and to the plane to counter act the force of the propeller is actually got the belt moving at 50 mph to the right to make enough force to hold against the plane’s countering force of pushing on the air.

Now I have a problem. Did we make the belt strong enough and fast enough to transfer enough force to the plane to counter act the engines at full power.

Depends on the speed we can move the belt and the strength of the landing gear and all it’s components.

For a Cessna 150 with small wheel, we might could build a treadmill fast enough to destroy the wheels and keep the plane on the ground.

An A1-E Skyraider or a C-130 super Herc, or F-18 in full after burner…?? Well that would be some belt because I have seen what those planes can do. Some brute force there. ( They don’t need wheels in some cases… Scary powerful they are. )

I don’t think we can build a belt that good for a big and powerful airplane.

Now we can amend this with all the magic you want and it still comes down to speed of light constraints if we have frictionless and infinite speed belts and mass less wheels.

Just remember how you’ve seen powerful airplanes skid with their brakes locked when at full power. That is a lot of force to restrain with just the normal transfer of force through a landing gear assembly.

This of course does not apply to those who want to play the " But if ( magic, magic, magic ) " game.

Which of course is silly.

That pastime is not a thought experiment, but a contest to see who can come up with the most outlandish set of impossible circumstances and IMO, has no mental bar bell qualities to it at all.

[treis]

@GusNSpot

First test.
Park the airplane on treadmill facing my left with engines off.
I move the treadmill to the right with my controller and since I moved it too quickly, the inertia of the airplane allowed the plane to roll forward a few feet as I brought the treadmill into motion. Due to friction, rolling resistance etc., the plane becomes stationary on the treadmill belt and moves off to the right until I slowly stop the belt.

When you say that you moved the treadmill too quickly do you believe it is possible for the plane to remain motionless with its engines off while the treadmill is accelerating?

You said that the airplane is facing left and moves forward when you bring the treadmill into motion. Does this mean the plane is going to your left and the treadmill is going to your right?

[Who_me_1]

@treis

Yes it is. You find me a plane which engines produce a force Fengines and a treadmill that can accelerate at the rate of 2*Fengine/Mtires and I will show you a plane that goes nowhere. The math is in the pdf file linked in post 255.

There is no math involved since the only force the treadmill imparts to the plane is from the friction of the wheel and bearings.

Due to the way te OP is set up, there are some impossibilities involved, such as what device determines what speed the airplane wheels are turning and increases the treadmill to match? What do we get? A feedback loop where everything runs to infinity? Seems that way to me… of course I’m thinking about this logically because I don’t have the math to decsribe everything.
Sorry, but I’m at work and the math and diagram PDF is blocked.

[Cervaise]

I’m still having trouble with the whole angular momentum thing (as I mentioned above, I know little of physics). So I’m going to propose a variation on the scenario that, I hope, expresses similar interactions of force.

Let’s say the airplane is coming in for a landing on the treadmill. The treadmill is moving backward relative to the airplane at whatever ludicrous rate has been calculated to “absorb” the forward velocity of the airplane via angular momentum in our original scenario.

While the plane is in the air, there’s no interaction between it and the treadmill, and the latter has no effect on the former. But the moment the plane touches down, its wheels spin backward at dizzying speed, sucking up all the plane’s kinetic energy, and the plane stops instantly dead.

Right?