Comments on Airplane on a Treadmill: Airplane on a treadmill

As mentioned in the original post, it's a matt...

2011-09-10T13:33:54.423-04:00

As mentioned in the original post, it's a matter of semantics. If we manipulate our interpretation of what the thought experiment is asking, we can come up with any answer we're comfortable with.

Q: A Boeing 787 Dreamliner is sitting on a NordicTrack Commercial 1750. The 787 throttles up for takeoff and the NordicTrack attempts to match its acceleration. Does the dreamliner take off?
A: The NordicTrack is crushed under the Dreamliner's 300,000 kilos and the plane takes off without any trouble.

Q: A Pegasus Quantum 145-912 ultralight trike is sitting on an interplanetary treadmill with the mass of 4 Jupiters. The ultralight fires up its propeller for takeoff and the treadmill begins moving to counteract the ultralight's acceleration. Does the ultralight take off?
A: The ultralight suffers severe structural failure on the runway and the pilot is crushed under the weight of the collapsing high performance Rogallo wing. It does not take off.

This is why it's pointless to have an internet debate about it...

I agree with the "conspiracy theory", in...

2011-09-09T18:58:17.708-04:00

I agree with the "conspiracy theory", in which the pilot and treadmill operator conspire to keep the plane still, with ONE exception, which I will get to in the third paragraph.

The "conspiracy theory" works, as the author postulates, because the ordinarily negligible friction in the wheel bearings created by the treadmill can be used to counter-act the force the engines exert on the air, if the engines were adjusted to use a very weak force. The force that keeps the airplane in place in this example is called rotary inertia, where the rolling friction in the wheel bearings can create an equilibrium despite the fact that the engines are pushing on the air and not the ground, simply because the airplane is in initial contact with the ground.

However, assuming the treadmill is powerful enough, and the "conspiracy theory" scenario is in effect (the plane is at a standstill with minimal engine thrust and extreme treadmill speed) then the pilot could gradually ramp up the engine and I could increase the treadmill to keep the plane in equilibrium. The pilot increases the engine thrust at the same time I increase the treadmill speed. Eventually, assuming the treadmill is powerful enough (it would need a power output much much greater than the jet engine), the plane's jet engine could be at full throttle with the treadmill spinning at an extreme speed to keep the plane at a standstill. The treadmill speed would be many orders of magnitude faster than any takeoff speed of the plane. If the tires and bearings are strong enough, the plane would sit there all day, with the bearings glowing red hot, soaking up the energy from the jet engines and transferring it into heat.

This is overlooked by the crowd that considers itself more intelligent than the crowd that merely thinks of this in terms of a plane acting like a car on the treadmill. It's obvious that a plane exerts a force on the air and not the ground, but because the plane's wheels are always touching the ground until it can get enough momentum for the wings to work, the tires, wheels and bearings all play a factor in it's ability to move forward relative to the ground.

It's with this example that I can nullify the author's first stipulation, in which he suggests there's a scenario in which he can accelerate and I can't keep him on the ground. If I have enough power as a treadmill operator, and his engines have an upper bound thrust limit, I can always keep him on the ground.

I like the way the no-flys rely on an ideal treadm...

2011-06-13T02:34:11.281-04:00

I like the way the no-flys rely on an ideal treadmill (ie unconstrained acceleration and velocity) but non-ideal wheels and bearings (ie with friction, relativistic effects). If you ignore relativity and friction in the treadmill, you must also ignore them in the wheels / bearings.

The tires would melt, followed by the wheels, bear...

2011-05-03T16:32:14.093-04:00

The tires would melt, followed by the wheels, bearings and landing gear... After that, it is not pretty. :)

But it's not relevant to the question at hand,...

2011-04-04T02:46:57.517-04:00

But it's not relevant to the question at hand, is it?

if you could somehow make a giant fan to make the ...

2011-04-04T00:41:56.432-04:00

if you could somehow make a giant fan to make the air surrounding the plane match the speed and direction of the plane it would also not be able to take off

As long as some posters are allowing treadmills th...

2011-03-30T23:21:36.800-04:00

As long as some posters are allowing treadmills that can accelerate infinitely, and invoke laminar flow of the air to create a headwind and thus let the plane take off while remaining stationary to the ground.

Then why not have this infinitely accelerating treadmill move in the same direction as the plane's desire and thus the laminar flow creates a tail wind preventing the plane from achieving take off air speed.

And since I am presuming impossible things, I prefer to do all this in Newton's Universe where there are no black holes to collapse into.

Once again, sufficiently twisted thought can force the thought experiment to turn out which ever way you want. ;-)

But... will it blend?

2011-03-23T09:29:45.819-04:00

But... will it blend?

"Increasing the speed doesn't increase th...

2011-03-19T14:09:34.698-04:00

"Increasing the speed doesn't increase the friction force, true, but it does increase the power needed by the engines to keep up, since power = force*velocity.
The throttle controls power, not force."

Actually, that is not true. The throttle controls the power and velocity of the engine, wich is attached to the propeller, wich in turn converts the power and velocity into thrust/force. This force is not applied against ground, but the air, and as such, the speed of the ground under the aircraft is, as always, irrelevant.

"If you run the treadmill at 5mph and turn on...

2011-03-18T16:30:13.725-04:00

"If you run the treadmill at 5mph and turn on the plane's engines just slightly, they will provide enough thrust, pushing against the air, to keep the plane still. If you then increase the treadmill speed to 500 mph, you won't need to adjust the throttle on the airplane - it will remain stationary."

Increasing the speed doesn't increase the friction force, true, but it does increase the power needed by the engines to keep up, since power = force*velocity.
The throttle controls power, not force.

You accuse others of looking at the question as a ...

2011-01-26T23:09:16.487-05:00

You accuse others of looking at the question as a trick, yet your are as guilty yourself. You ignore the spirit of the problem, and go off on tangents about how if the pilot conspires not to fly he won't. Yes, in that wording the pilot would make no attempt to fly, but just get the the nexus of the problem and forget such ridiculous and overall minute word logical fallacies.

Not that it really matters, since the problem really is just the verbal equivalent of the stone of Spartoi.

2011-01-26T21:55:24.791-05:00

This comment has been removed by the author.

groundspeed makes no difference to an airplanes wi...

2011-01-13T22:21:05.042-05:00

groundspeed makes no difference to an airplanes wings, airspeed does and the wheels " freespin ' the engines thrust against the air, not the ground. the plane will always take off, no matter what the treadmill does. If a planes takeoff airspeed is 50 mph it can take off with a 50 mph headwind and no groundspeed. If it has a 50 mph tailwind it will have to have a 100 mph groundspeed to take off. There is an object something like your giant treadmill that planes use all the time, its called an AIRCRAFT CARRIER.

That is some assumption... Can you name one plane...

2010-11-11T07:45:19.026-05:00

That is some assumption...

Can you name one plane that has as little as 11 knots margin between topspeed and takeoffspeed?

Even the cute little underpowered slow-flying plane that was tested on Mythbusters (Rans S-5 Coyote) has a margin of about 50 knots...
The larger S-6 Coyote II (that i used as a reference earlier in this discussion) has a margin of about 75 knots...

Basically, you're assuming that the plane is so underpowered that any increase in friction would keep it from taking off, but in reality, no normal aircraft has that little power, because it would be dangerous...

KIAS = Knots Indicated Air Speed.

2010-11-09T05:06:13.034-05:00

KIAS = Knots Indicated Air Speed.

This article seems to assume that the airplane nee...

2010-11-09T05:04:09.043-05:00

This article seems to assume that the airplane needs to be kept stationary relative to ground in order not to lift-off. This is simply not true.

The airplane needs to be kept under its take-off speed, which is an order of magnitude easier task to do, since as an airplane approaches its takeoff speed, aerodynamic drag tends to arrest most of its forward acceleration.

Suppose a plane, if let to accelerate on an infinitely long runway, can reach a top speed of 160 KIAS, but it's lift-off speed is 150 KIAS. The treadmill only needs to reduce that plane's speed by 11 KIAS, not 150 KIAS.

How hard is it to move a REAL life stationary plane on a giant-ass tread mill at 11 KIAS backwards?

Certainly significantly less than 500 mph.

I'm sorry Nathan, but i have a hard time under...

2010-10-13T19:50:51.604-04:00

I'm sorry Nathan, but i have a hard time understanding both your logic, and your claim to accept your arguments...

Your chain of logic are all based on the assumption that the airplane is in fact stationary, but that is only your assumption, not a fact.

You can theorize all you want, with cars or airplanes driven by wheels, but the fact is(!) that the problem is called "Airplane on a treadmill", and as such the vehicle in the problem is in fact an airplane, not a car. If they intended you to theorize about a wheel-driven vehicle, i'm sure they would have selected a car rather than an airplane.

Defining it as a "thought experiment", it sure is convenient to be able to suspend the laws of physics to be able to reach a predetermined conclusion that the aircraft will not takeoff, the universe will implode, and so on...

However, like many other contributors to this debate, i prefer to include the laws of physics, and treat this as a real problem, not one where important factors can be left out just because they do not suit my preconceived answer.

The fact is, that in this reality, the laws of physics will let the airplane take off.

"Here is an explanation of the principle of c...

2010-10-13T19:43:42.796-04:00

"Here is an explanation of the principle of charity"

My comment about begging was a joke - hence the winking smiley. I do actually understand the principle of charity, I just disagree that the thought experiment interpretation is the more logical.

The first thought experiment interpretation basically asks - if we hold a plane motionless, will it be able to generate lift? - and asks us to assume for the sake of argument that the treadmill is capable of holding the plane still. Anyone asking this must not know much, if anything at all, about the mechanics of flight, much less the physics of how a plane and a treadmill would interact. Not only is the answer trivial, but choosing this interpretation seems to contradict your Principle of Charity, in that it assumes the worst of the questioner.

The second thought experiment interpretation asks if a treadmill can be manipulated into preventing the motion of the plane, knowing that doing so will prevent the flight of the plane. This is interesting from a physics perspective, but ultimately uninteresting because it is known that preventing the motion of the plane will prevent the plane from taking off.

The riddle interpretation relies on human nature to trick the reader into the wrong answer. We naturally make assumptions about the behavior of a car/treadmill system, and mistakenly apply those assumptions to the plane/treadmill system. This is similar to such riddles as "a plane crashes on the border of Turkey and Iraq - where do they bury the survivors?".

Applying Occam's Razor leads me to the conclusion that the riddle interpretation is the simplest, most logical, and thus more probably correct interpretation.

Here is an explanation of the principle of charity...

2010-10-13T18:32:14.695-04:00

Here is an explanation of the principle of charity, I assume that my explication of the thought experiment will be rather clear if you take the time to understand this basic presupposition of all rational debate:
http://www.csus.edu/indiv/m/mayesgr/phl4/Tutorial/phl4charity.htm
http://en.wikipedia.org/wiki/Principle_of_charity

"The move we must make, to make sense of this...

2010-10-13T12:28:44.893-04:00

"The move we must make, to make sense of this thought experiment, is simply to work from the idea of a plane that uses a motor to turn its wheels and create the speed necessary for lift"

So, in other words, to arrive at the answer we want - that the plane won't fly - we must first assume that the plane is, in fact, a car (or, bolt the plane to the ground).

Planes don't use their motors to turn their wheels to create their speed. End of story.

"to put it another way, my claim is simply adherence to the principle of charity."

So... you're begging us to accept your interpretation. What are you, a socialist? ;)

People put too much credence in these "thought experiments", in my opinion. Sure, a treadmill could be manipulated to prevent the motion of the plane - if you ignore all of reality accept the mass of the wheels. Why is this an acceptable answer?

Again, it's so much simpler, and requires so much less suspension of reality, to accept that the author intended to take advantage of the reader's misapplication of the effects of a treadmill on a car or runner onto the plane to lead them to the wrong answer, and to force them to abandon their preconceptions (a difficult task for most people) to arrive at the correct answer - that the plane will fly.

"Moving the ground backwards under a plane do...

2010-10-13T12:07:12.531-04:00

"Moving the ground backwards under a plane does nothing to prevent the plane from moving forward."
Of course not, with an actual plane. That's my whole point--the only way to read intelligibility into this thought experiment is to take up the mantle of interpretive authority.
We ask: what is the point of this thought experiment? How can we read the meanings of the terms used such that the thought experiment doesn't fall apart due to merely accidental facts?

Now, as who I am is clearly unimportant to whether or not I'm right about our hermeneutic orientation to this problem, I'm going to ignore your worry about worry about what kind of authority I am. I am a philosopher, but that doesn't give me any special bearing here. The move we must make, to make sense of this thought experiment, is simply to work from the idea of a plane that uses a motor to turn its wheels and create the speed necessary for lift(or the idea of a treadmill that connects to a portion of the plane that won't minimize the resistance the treadmill is to create such that the treadmill is capable of matching, negatively, whatever forces are created which move the plane forward). This kind of plane would not lift off on a treadmill that could keep up with its tire speed and this is not unintelligible.

The thought experiment works on these grounds, and that's all the authority I need--to put it another way, my claim is simply adherence to the principle of charity.

"In treating the thought experiment as if it ...

2010-10-03T13:13:53.737-04:00

"In treating the thought experiment as if it need deal with the design of actual planes, you do damage to the proper interpretation of said thought experiment's purpose"

Who are you do declare what is the proper interpretation of the riddle?

It is a much more reasonable interpretation that the author of the riddle intended to play upon the reader's natural inclination to misapply the effects of a treadmill on the motion of a runner or a wheel-driven vehicle to the motion of the airplane - thus leading to the incorrect assumption that the plane is to remain motionless. Once the reader can abandon their preconception, they can quickly arrive at the correct conclusion, that the plane will not remain motionless.

"Under a reasonable interpretation of 'plane' and 'treadmill', the plane would not take off. Simple as that."

What a ridiculous assertion. A treadmill prevents the motion of a car or runner by moving the ground backwards so that the car or runner doesn't move forwards. Moving the ground backwards under a plane does nothing to prevent the plane from moving forward. No reasonable interpretation of "treadmill" would ever prevent a reasonable interpretation of "plane" from taking off.

In treating the thought experiment as if it need d...

2010-10-03T11:07:59.746-04:00

In treating the thought experiment as if it need deal with the design of actual planes, you do damage to the proper interpretation of said thought experiment's purpose. Hypothetically, of course, we can list all the possible interpretations and deal with them in uncontroversial ways (I take you to have done this partially and innadequately). Our job, as interpreters, is not simply to list all the meanings that COULD be relevant, we must also try to make sense of which one of these the thought experiment actually is--for this task, understanding the purpose of those who employ it is crucial.

The reason that actual plane designs and actual treadmills are unimportant is that planes and treadmills are only mentioned to pump intuitions about certain FUNCTIONAL roles that each of these are to play. Thus, because the question is one of liftoff while remaining stationary relative to the environing atmosphere(a question, that is, about the way that wings create lift) we must treat of the plane/treadmill such that remaining stationary is the result. This need not require one's not trying to take off (as you suggest), as a plane that only achieves lift on the basis of a kinetic chain through its wheels is not inconceivable (of course, it would not be able to fly after take-off, but this is not PRIMARILY a thought experiment about planes and treadmills) and, in the case of this thought experiment, perhaps necessary for maintaining the intelligibility of the intuition we're trying to pump.

Under a reasonable interpretation of 'plane' and 'treadmill', the plane would not take off. Simple as that.

Sorry, this all might be correct, but the plane wo...

2010-10-01T10:38:07.049-04:00

Sorry, this all might be correct, but the plane wouldn't take off.
Ok, it depends on the question, but if the treadmill runs exactly as fast as the wheels are turning, than we have a bigger Problem. The engine of the airplane starts moving the plane, this caused rotating wheels and the treadmill starts running. This accelerate the wheel, that let the belt run faster ...
In a very short time it reaches the speed of light, gain mass and all collapse into a black hole - the plane did not take off.

@what you call "fact" C: well you say &q...

2010-09-27T12:28:22.945-04:00

@what you call "fact" C: well you say "The most powerful conveyor belt in the world couldn't do it. David Copperfield couldn't do it. It can't be done."

and I object: Chuck Norris could do it.