Plane on a Treadmill

[Major Lord]

YES. The Airplane will fly

I don't think anyone is arguing that if the airplane is not actually moving into the wind, the airplane will not take off. If someone is thinking that the wheel RPM makes the airplane fly, they are not thinking clearly.

The overriding question is whether the airplane will continue to accelerate into the wind despite the treadmill rotating its wheels "backwards" in relationship to the forward movement of the aircraft. When the magician slides the table cloth out from under the dinnerware, the dinnerware is not instantly accelerated to the velocity of the tablecloth. The amount of energy coerced onto the dinnerware is a function of the critical coefficient of drag. If introduced too slowly, the frictional forces are sufficient to allow the table cloth to drag the dinnerware off the edge of the table, but if introduced at a rate that is "magic"; That is to say, a rate at which the frictional forces are induced and overcome quickly enough so that inadequate force is transmitted to the plates, the table cloth slides clear.

The force of the counter-rotating treadmill is not sufficient to overcome the thrust of the aircraft, which will accelerate regardless of the tiny amount of additional drag introduced by the counter-rotating treadmill's action on the wheels. The wheels will just roll faster that the aircraft is actually moving forward. The model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate. If the aircraft was accelerating by virtue of engines turning its wheels directly, you would be right ( a car for instance, would remain static in relation to the treadmill) but since the airplane is driven by a column of compressed air, it matters not how fast the wheels are turning, only that the aircraft is accelerating to the velocity required to achieve lift sufficient to leave the treadmill.

Now, I am an engineer too, but the electronic kind, not the aero type, so I think we need the input of a bona fide aeronautical engineer to put this one to bed, not just another civil engineer. My $100.00 bet is still open. ( first come, first serve)

Major Lord

[N Harmon]

The model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate.

Did you even read the article I linked to in re: #46?

The problem with the original question is that as stated the question is paradoxical. The plane can't fly because the treadmill will somehow always match the velocity of the wheels. How it does this is not stated in the problem, only that it does it.

You talking to us about movement coming from power to its wheels or power to a column of air...we get it.

I am positing that the paradox may be solved by assuming that the bounds on engine thrust means the treadmill and wheels do not spin to infinity but rather at some pyschotic high speed whereby the rolling resistance of the wheels create enough force in the negative direction to cancel the positive force from the engines.

[Major Lord]

Nathan,

I fully understand your point, but we are not talking about a frictionless model in a vacuum. There is no "accelerate to infinity" possibility here. I just think you are wrong. I have asked a group of aviators I deal with to find an AE to answer the question in fully real world terms. So you accept my wager?

Major Lord

[N Harmon]

Wow, you don't understand my point at all.

[lordmonar]

The model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate.

Did you even read the article I linked to in re: #46?

The problem with the original question is that as stated the question is paradoxical. The plane can't fly because the treadmill will somehow always match the velocity of the wheels. How it does this is not stated in the problem, only that it does it.

You talking to us about movement coming from power to its wheels or power to a column of air...we get it.

I am positing that the paradox may be solved by assuming that the bounds on engine thrust means the treadmill and wheels do not spin to infinity but rather at some psychotic high speed whereby the rolling resistance of the wheels create enough force in the negative direction to cancel the positive force from the engines.

Nathan,

You can't solve the paradox....the breakdown is that the wheels freely spin.  The plane moves forward at 5m/s the tread mill moves back at 5m/s....there is not enough Resistance in the wheel bearings to produce enough drag to counter act the thrust of a real airplane.  Because they are designed that way.  In theory you could move the treadmill at sufficient speed that drag from the wheels counter acts the thrust....and keeping the aircraft stationary (or at least keeping below take of speed) but the original question posted that the treadmill only moves at the same speed of the wheels.

Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

The treadmill can not go to some high speed because it can only go the same speed at the wheels.  If the take off speed of the plane is 100 KIAS then the relative speed of the wheel and the treadmill will only be 200 Knot....and that is not high enough to induce enough drag to counter act the thrust of the powerplant.....About the only thing that may happen is the wheels would fail under such speed....but let us assume for the sake of argument, these wheels can take those sort of speeds.....the reality of the equation is that the wheels are designed to roll freely and reduce the amount of drag between the ground and the aircraft during the take off roll.  Yes there is drag, yes in theory you could develop enough drag to counter thrust (say you had a ski-plane on tarmack! or you forgot to pull the chocks)....but that is introducing new variable to the problem.

A properly maintained, balanced and loaded, production plane has more then enough thrust to overcome any drag introduced by the wheels in contact with the ground.  If anything the treadmill may actually help the plane get airborn as the backward motion helps reduce the inertia of the wheels themselves and allows the aircraft to use that much more power to accelerate the airplane.

[Major Lord]

Nathan,

Lets try this as a fundamental step-off point. " The rotational velocity of the wheel is the sum of the velocities of the aircraft and the treadmill" agree , or disagree?

Major Lord

[lordmonar]

Please read this:
http://tinyurl.com/Stupid-Airplane-On-Treadmill-Q

Where the author of that article claims there is no physical mechanism that would cause the plane to have nonzero speed, I say there is: kinetic friction. And kinetic friction is precisely what stops the treadmill from spinning up to infinity as the thrust of the plane's engine is bounded so is the limit of the speed of the treadmill. If you want to argue against THAT portion of my argument, I would be glad to do so.

I looked at this again and I found some errors.

In Case 1 he states that V_b=v_c that is the speed of the bottom of wheel V_b (as it turns) is equal to the speed of threadmill V_c

The problem is that the speed of the bottom of the wheel (v_b) is developed by the forward motion of the aircraft V_w and Resistance with the ground.  If the ground is also moving (v_c) then you have to factor that in as well.  The equation should actually be V_b=(v_w+v_c)*R where R is the coefficient of resistance between the bottom of the wheel and the treadmill.

In Case 3 he wants the tradmill to move a the speed of the sum of the aircraft speed and the speed of the spinning tire V_s=V_b+V_w. 

So the equation would be V_c=V_b+V_w.  However I have already shown that V_b=(V_c+V_w)*R so you end up with an equation where the product of the equation is also one of the variables in the equation V_c=(V_c+V_W)*R+V_w

Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

And all of this has no bearing on the ability of the aircraft to fly...as the only velocity the wings care about is V_w and nothing as been presented that v_c can affect this in any meaningful way.

[Major Lord]

Excellent work there, my friend. You may keep the coveted Yaeger Aerospace award! :clap:

Major Lord

[N Harmon]

Oh, so close, yet so far.

Major Lord, if your troll can't even spell Yeager correctly, then would you kindly leave it at home?

Okay, lordmonar. You said,...

Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

And then you also said,...

Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

Now, consider this posit: Small forces like that of your highly efficient ball bearings (which are oiled, right? thus travelling in a fluid, right?) that increases with velocity....become very LARGE forces as a result of very LARGE velocities (large as in,...approaching infinite).

And since the amount of thrust the airplane can provide is finite, then at SOME point, those LARGE velocities scaling small forces into LARGE forces will create a sufficient force equal and opposite of thrust....creating equilibrium.

[Major Lord]

Oooh, nasty! Didn't know it was your maiden name! Focus on the physics Nathan. I see you have still not accepted my $100.00 wager, so I assume you rest on the courage of your proffered opinion. So you are sticking with the force exerted on the bearings being so large at near infinite velocities, that they overcome the thrust of the aircraft at takeoff  velocities. Check. "Yaeger" or "Yeager"  by the way is the anglicized version of the German name "Jaeger" meaning "Hunter".

Major Lord

[Major Lord]

A more complete Mythbusters video: http://www.youtube.com/watch?v=YORCk1BN7QY

Major Lord

[flynd94]

Who cares if it flies, the most important questions are:

How much does it pay?
How senior will it be?

[Major Lord]

The obvious answer is that pilots can do anything....just ask one!

Major Lord

[FW]

^And that, my friends, is the answer to all our questions.  Thanks. 

[lordmonar]

Oh, so close, yet so far.

Major Lord, if your troll can't even spell Yeager correctly, then would you kindly leave it at home?

Okay, lordmonar. You said,...

Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

And then you also said,...

Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

Now, consider this posit: Small forces like that of your highly efficient ball bearings (which are oiled, right? thus travelling in a fluid, right?) that increases with velocity....become very LARGE forces as a result of very LARGE velocities (large as in,...approaching infinite).

And since the amount of thrust the airplane can provide is finite, then at SOME point, those LARGE velocities scaling small forces into LARGE forces will create a sufficient force equal and opposite of thrust....creating equilibrium.

No....an equilibrium will NOT be met....you are forgetting the Three things.  One.....by the original premise the fastest the treadmill can travel is the speed the aircraft is moving.  Two...The feed back loop I describe shows that the math is wrong.  You cannot set up a system with the set up that he describes the math does not support it.  Third...you still assume that there sufficient drag induced through the wheels and the hub bearings to counter act the thrust of the power plant.

As I said....in theory that could be the case....flat tires, seized bearings, float plane pontoons on hard asphalt......but not a properly maintained aircraft.  The plane will have gotten to take off airspeed long before the any drag induced by the treadmill got high enough to noticeably counter act the thrust of the power plant.

[flynd94]

The obvious answer is that pilots can do anything....just ask one!

Major Lord

Allen,

I am glad to see you finally understand that pilots are "god's".  It sure took you a long time to realize that and, who would of thought that a ground pounder can be taught things.   

[lordmonar]

The obvious answer is that pilots can do anything....just ask one!

Major Lord

Allen,

I am glad to see you finally understand that pilots are "god's".  It sure took you a long time to realize that and, who would of thought that a ground pounder can be taught things.   

Yeah.....but with out maintenance.....a pilots is just pedestrian with a lether jacket and cool sun glasses! 

[raivo]

I'm starting to think this is one of those things that we can never really know for sure, since it can't effectively be proven under the circumstances given in the original post...

[N Harmon]

you are forgetting the Three things.  One.....by the original premise the fastest the treadmill can travel is the speed the aircraft is moving.  Two...The feed back loop I describe shows that the math is wrong.  You cannot set up a system with the set up that he describes the math does not support it.  Third...you still assume that there sufficient drag induced through the wheels and the hub bearings to counter act the thrust of the power plant.

One: The original premise is that the treadmill travels at the speed of the wheels, not the aircraft. This is an important distinction because wheel speed is independent aircraft speed (we agree here). Thus, the speed of the wheels is (theoretically) unbounded, as is the speed of the treadmill.

Two: The math mirrors the way the problem is worded. If it creates a paradox in doing so, then that means the problem is paradoxical. It is not evidence that the math is wrong, and by no means evidence that the plane takes off.

Three: I offer it as a possible solution to the paradox. The the "feedback loop" reaches some terminal velocity where the rolling resistance matches engine thrust, and the speed of the wheels and speed of the treadmill stop accelerating. Is it possible? I've found surprisingly little information on how rolling resistance changes with relativistic speeds, so I don't know. But if it isn't possible, then that again, doesn't mean the airplane flies. It just returns us to this paradox where the treadmill is designed to keep the aircraft at zero speed by virtue of spinning the wheels, but doesn't say how.

[lordmonar]

Your solution to the paradox breaks the premise of the question.

I agree......it is theoretically possible to spin the treadmill fast enough to keep the plane from flying.....but the question says it only goes as fast as the wheels move.  I don't think the 100 MPH that the treadmill is moving will be enough to keep a Cessna from flying! 

The math mirrors the way that question is worded.  That shows that the person asking the question does not understand physics, math or how to word questions.

Either way....the plane will fly.  Mythbusters did it.....even if they too did not understand the physics behind it.