Plane on a Treadmill

[CadetProgramGuy]

Thanks Capt!!

Unless you have a force that will counteract the force of the treadmill, the aircraft will move backwards.  The propeller will counteract that force.

[tsrup]

I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

I think I read someone else who put it best. 
Stand on a treadmill wearing roller blades, then using your arms pull yourself forward.  Guess what, you will move forward.  You can play with the speeds all you want, but the outside force will over come the two opposing forces.

Simple physics.  You have two opposing forces in equilibrium, as soon as you introduce a third, equilibrium will cease to exist.  The treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction). 

[ßτε]

I still believe that the aircraft will not fly.

In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

Now can someone tell e how much relative wind is moving over the airfoil (wing) with a relative speed of Zero?

The premise of the question in my understanding is that the treadmill speed was matched by the wheels of the aircraft.  Equal forces applied, Does the aircraft move anywhere? No it does not.

I'll take the $100, and keep my Yeager.

The thing is that the treadmill cannot "work against the force of the propeller."

In order for the treadmill to move at the same rate as the wheels, there must be zero velocity (relative to an observer not in the plane and not on the treadmill.) That means the net force on the plane is zero.  If power is applied creating force in the forward direction, something has to apply force in the opposite direction. However, the treadmill cannot be the source of this force. The force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

[CadetProgramGuy]

Let me try to make my answer simpler.  Let us propose the following:

The four forces on an airframe in level unaccelerated flight are Lift vs Weight (gravity), Thrust vs drag.

The treadmill is drag on the airframe.
in aviation to fly, one needs to counteract drag with thrust.

Drag (treadmill) is 60kts.

To acheive equilibrum thrust needs to be 60kts.

To acheive flight lift must be created by wind flowing over the wing.  It must be sufficient lift to overcome the weight of the aircraft or gravity. The wing cannot create lift if it is standing still with no wind flowing over it.

[N Harmon]

The treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction).

Ah hah! 

See, some of us are dealing with friction, and some of us are not. Yet another reason why the original problem sucks.

[N Harmon]

The force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

Are you asserting that if the propeller was not turning, and the treadmill began turning,... the aircraft would remain stationary and only its wheels move? If so, you may be assuming zero friction at the wheels, which is not part of the problem.

[tsrup]

The treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction).

Ah hah! 

See, some of us are dealing with friction, and some of us are not. Yet another reason why the original problem sucks.

Null factor, The propeller was designed to overcome the friction from a start on a stationary surface therefore it doesn't factor in to the problem. 
friction is only an issue if the treadmill was started before the engine.  In that case the plane, as pointed out before, would simply move backwards until the engine is started.

[ßτε]

No, I am saying if the wheels are turning at the same speed as the treadmill, something else must be acting on the airplane other than the treadmill.

[tsrup]

The force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

Are you asserting that if the propeller was not turning, and the treadmill began turning,... the aircraft would remain stationary and only its wheels move? If so, you may be assuming zero friction at the wheels, which is not part of the problem.

You'll find that when dealing with physics problems the norm is to assume a non friction environment.  It helps simplify the problem and is usually not necessary until dealing with applied physics anyways. 

[N Harmon]

You'll find that when dealing with physics problems the norm is to assume a non friction environment.  It helps simplify the problem and is usually not necessary until dealing with applied physics anyways.

I didn't find that in my physics classes. When we were dealing with mechanics, once we learned how to include friction in our calculations we included friction quite regularly. In fact, we were not allowed assume a frictionless environment unless the problem stated as such. YMMV, obviously.

The propeller was designed to overcome the friction from a start on a stationary surface therefore it doesn't factor in to the problem. friction is only an issue if the treadmill was started before the engine.  In that case the plane, as pointed out before, would simply move backwards until the engine is started.

The propeller, while able to overcome friction on a stationary surface, may not be able to overcome friction on a moving surface, especially when the velocity limit of that surface is not bounded.

[N Harmon]

Say we have a Cessna 182 with a Lycoming engine that puts out 230 horsepower. Let's also say that its wheels require 50 pounds force (lbf) to keep it rolling.

Assuming a ideal prop, I simply need to run my treadmill at -1,725 miles per hour, to keep the aircraft stationary. Less if the prop is not ideal.

[tsrup]

The propeller, while able to overcome friction on a stationary surface, may not be able to overcome friction on a moving surface, especially when the velocity limit of that surface is not bounded.

Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

[CadetProgramGuy]

Say we have a Cessna 182 with a Lycoming engine that puts out 230 horsepower. Let's also say that its wheels require 50 pounds force (lbf) to keep it rolling.

Assuming a ideal prop, I simply need to run my treadmill at -1,725 miles per hour, to keep the aircraft stationary. Less if the prop is not ideal.

Umm not to nitpick, but your answer is in the negative.....

[N Harmon]

Umm not to nitpick, but your answer is in the negative.....

It's a power vector in the opposite direction the aircraft's engine power is being directed.

Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Except the work being performed by the treadmill is in the opposite direction as the work being performed by the propeller. So, the treadmill isn't taking work away from the propeller, but adding to it's burden.

[davidsinn]

Major Lord isn't interested in any serious conversation on the subject and is just trolling.

I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

This is the second time you have said the wheels will spin faster than the treadmill, which is NOT what the original problem said the treadmill is designed to do. The original problem said the treadmill will "exactly match the speed of the wheels, moving in the opposite direction". It doesn't say it will match them "once the airframe starts to move", or at half of the speed of the wheels. It says it will MATCH the the speed, EXACTLY.

I would appreciate if you, and some of you others tone down the condescending "you are completely failing to grasp the concepts at work here". I do grasp them. You are violating the conditions of the original problem by saying the velocity magnitude of the wheels and treadmill are unequal.

I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

I never stated the wheels spin faster than the treadmill. Unless the wheels are in a skid that's not possible. The tangential velocity of the wheels always exactly matches the velocity of the treadmill. I stated that the only way to make the wheels spin at all is to move the airframe via thrust from the prop. Thus I have imparted forward rotation to the wheel at a tangential velocity of X. Since common sense as well as every physics problem I have ever seen states that the wheel the surface they run over are always matched unless in a skid the only way to meet the premise of the problem is to make the treadmill's velocity be X in the opposite direction which leads us to a wheel tangential velocity of 2X.

You need to remember that the only way to add any kind of velocity into the system at all is for the airframe to start moving in reaction to prop thrust. You are missing that point.

[Major Lord]

I would like to point out that the conditions of the original problem are impossible to replicate in the real world. That might be the biggest impediment to understanding here.

Well, if by this, you mean there is no way an actual experiment could be conducted that would validate your findings, I would have to agree. As for your "Troll" comment, I think you may want to have a chat with your professor ( or high school physics teacher) about your position on this particular test question. My experience leads me to believe the madder you get, the more likely you are to be wrong,  and its time to reconsider the problem without emotion. Chill.

Major Lord

[Major Lord]

The question as originally posed:

Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

[N Harmon]

I never stated the wheels spin faster than the treadmill. Unless the wheels are in a skid that's not possible. The tangential velocity of the wheels always exactly matches the velocity of the treadmill.

What? You did too state the wheels spin faster than the treadmill. You even stated it again in this very post; in the final sentence of your first paragraph (underline mine)...

Since common sense as well as every physics problem I have ever seen states that the wheel the surface they run over are always matched unless in a skid the only way to meet the premise of the problem is to make the treadmill's velocity be X in the opposite direction which leads us to a wheel tangential velocity of 2X.

I'm afraid that I simply can not follow your reasoning here. You seem to be contradicting the problem in one instance while contesting you are not in another.

Are you measuring the tangential velocity of the wheels relative to the treadmill, and comparing that to the velocity of the treadmill relative the ground? In other words, are you using different points of reference for each velocity and from that concluding the premise of the question, that the treadmill is designed to match the speed of the wheels, is satisfied?

If so, then I would have to say your interpretation does not seem at all reasonable to me. While I will gladly lay the blame for this on the poor wording of the original problem, it would go far in bringing us together to realize that most of us took that to mean that the treadmill would match the speed of the wheels as both are compared to the ground.

You need to remember that the only way to add any kind of velocity into the system at all is for the airframe to start moving in reaction to prop thrust. You are missing that point.

Not really. Forces can be introduced without the airframe starting to move, causing the wheels and treadmill to spin. Remember the premise of this question has all of this occurring instantaneously.

[CadetProgramGuy]

ok, let me ask this question. In order for the airplane to fly, you need lift.  Where is your lift created in this theory?

[tsrup]

Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Except the work being performed by the treadmill is in the opposite direction as the work being performed by the propeller. So, the treadmill isn't taking work away from the propeller, but adding to it's burden.

Wrong, If you want to talk about friction then you have to isolate the wheels and the treadmill, as soon as the treadmill starts running it will try to break the friction of the wheels.  Just as a powered wheel tries to break the friction of the ground, the powered ground will try to break the friction of the wheel