Will it fly?

Curtis, I think you're giving the questioner a little too much credit. It's not philosophical, it's just "I don't know how physics work". 

Keith Tanner said:

Curtis, I think you're giving the questioner a little too much credit. It's not philosophical, it's just "I don't know how physics work". 

Normally I would agree, but it was posed originally in 2003 by a Russian/American Physicist

Here is the original post, as researched by multiple internet sleuths

Again, I respectfully disagree.  There is an answer here, but as you noted, interpretation of the question is the actual "question" here.  I think it is reasonable to interpret:

"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction" that the treadmill moves at the speed the wheels would move along the ground (which of course is just, speed) in the opposite direction.  You can interpret that as matching the rotation, but the results are the same (just allows you to know the rpm of the wheels). 

The wheel speed on an airplane, when it is on the ground, is directly tied to the speed of the plane over the ground (airspeed if you assume no wind).  That rotation is, in RPM, ft/minute (of the plane) divided by (pi multiplied by the diameter of the tire).  E.g. 3140 ft / minute = 100 rpm on a 10 foot (!) diameter tire.  But the rotation is generally irrelevant (other than the exploding thing), it's all about the speed of the tread rolling across the ground (no mater what size the tire is).

 You stated: "If the treadmill exactly matches the wheel speed, it is impossible for forward motion to occur."  That is fundamentally untrue, and I think that is where your confusion is.  It is entirely true with a car driven by the wheels, but with a plane, the wheel do nothing for the motion of the plane other then keep it from scraping on the ground.  E.g. no acceleration forces.  As noted, there will be some drag generated by wheel speed, but it will be comparatively very small.

Am I wrong?  I am entirely open to the argument that I am. 

As noted, there is a bit of an opening for interpretation (what does "speed of the wheels" exactly mean), so there may not be an obviously "always correct" answer.  My suspicion is that it was worded (would be interpreted) slightly differently in Russian.

Of note (not relevant to this question): If you put a fan capable of blowing 50 mph wind over the entire surface of the wing (only the top is needed, and actually more effective) of a Piper Cub, in front of it, it will take off with zero ground speed and zero wheel speed.  You may ask:  what if that "fan" was attached to the plane?  Yes, it will still take off!  It just presents some difficulties in getting the "wind" to blow over the entire wing.  NASA actually had a plane (jet) that almost did this, I think it still required maybe 10 or 20 mph of forward speed.

Curtis73 (Forum Supporter) said:

Keith Tanner said:

Curtis, I think you're giving the questioner a little too much credit. It's not philosophical, it's just "I don't know how physics work". 

Normally I would agree, but it was posed originally in 2003 by a Russian/American Physicist

Maybe it was a first year physics test question for engineers to thin the herd :) Or maybe they just weren't a very good physicist. I've seen engineers argue really stupid things.
 

And then random people started taking it very seriously.

I subscribe to Hanlon's Razor. 
"Never attribute to malice that which can be adequately explained by stupidity."

Keith Tanner said:

I've seen engineers argue really stupid things.

I've argued this for 15-20 pages on another forum.

Not my fault that the initial question was phrased as "the runway moves at the same speed as the plane" and they heard the more common "the runway moves at the same speed as the wheels"

The argument is generally summed up in this link someone else posted:

https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

In interpretation #3 they state:

What if we hook up a speedometer to the wheel, and make the treadmill spin backward as fast as the speedometer says the plane is going forward?

If you did that, the wheel and treadmill speed quickly go to infinity (as they state).  I think this is (sort of) what Curtis's interpretation is.  As such, it doesn't make any sense, thus I reject it as a possibility for a reasonable interpretation.

Don't worry Curtis, I don't reject you, just your interpretation. 

You can fly a plane in a wind tunnel. 

What if at the end of the treadmill are 5 people who will be struck by the plane, but if you pull a lever to shift to another runway only one person will be struck?  That man is holding a box inside that box is a cat.  It may be alive or dead.  Does it make a sound?

Mr_Asa said:

Keith Tanner said:

I've seen engineers argue really stupid things.

I've argued this for 15-20 pages on another forum.

Not my fault that the initial question was phrased as "the runway moves at the same speed as the plane" and they heard the more common "the runway moves at the same speed as the wheels"

Is google translate leading me astray? (Unpossible!) That link that Curtis posted sounds like it says exactly. Runway moves at opposite wheel speed. But again, it's using google translate so is the translation wrong?

"The surface can move against the direction of takeoff of the aircraft. It has a control system that monitors and adjusts the speed of the belt so that the speed of rotation of the aircraft's wheels is equal to the speed"

Fueled by Caffeine said:

You can fly a plane in a wind tunnel. 

Not true.  

Maybe they will let you, but they certainly won't let me!

In reply to aircooled :

Ha.. There have been some very strange but true stories of early developemnet of tethered planes inside giant wind tunnels

aircooled said:

 You stated: "If the treadmill exactly matches the wheel speed, it is impossible for forward motion to occur."  That is fundamentally untrue, and I think that is where your confusion is.  It is entirely true with a car driven by the wheels, but with a plane, the wheel do nothing for the motion of the plane other then keep it from scraping on the ground.  E.g. no acceleration forces.  As noted, there will be some drag generated by wheel speed, but it will be comparatively very small.

Am I wrong?  I am entirely open to the argument that I am. 

As noted, there is a bit of an opening for interpretation (what does "speed of the wheels" exactly mean), so there may not be an obviously "always correct" answer.  My suspicion is that it was worded (would be interpreted) slightly differently in Russian.

Of note (not relevant to this question): If you put a fan capable of blowing 50 mph wind over the entire surface of the wing (only the top is needed, and actually more effective) of a Piper Cub, in front of it, it will take off with zero ground speed and zero wheel speed.  You may ask:  what if that "fan" was attached to the plane?  Yes, it will still take off!  It just presents some difficulties in getting the "wind" to blow over the entire wing.  NASA actually had a plane (jet) that almost did this, I think it still required maybe 10 or 20 mph of forward speed.

If the plane moves forward relative to the "real" ground, then the question has been violated as one of two things must happen:  1) the speed of the wheels has to exceed the speed of the treadmill, or 2) the treadmill will match the speed of the tires, but will have to move at the square of the acceleration of the airplane.  It has nothing to do with driven wheels vs non-driven wheels.  

Basically, in order for the hypothetical question to be satisfied toward the conclusion that the plane will successfully move forward, the phrase "exactly match..." must be violated - either because the belt is not keeping up, or the belt can keep up but lags behind.  Since that is not what the question poses, in order for the plane to move forward, the premise of the question must be violated.

In the real world, (assuming that the two forces of the thrust and the belt are completely independent... that is to say, the thrust isn't pushing on the belt like it would in real practice) what would happen is this:  First, let's assume that you believe that the plane would not move.  You would apply, let's say, 10 tons of thrust.  As the wheels passively began to roll forward, the treadmill would have to roll backward at a speed that generated 10 tons of frictional restriction in the opposite direction in order to prevent forward motion relative to real ground.  If, however, you believe it won't affect the plane taking off, that means the wheels are accelerating faster than the treadmill and therefore violates the premise of the question.

Regarding "speed of the wheels," my only interpretation that (I think) lives within the spirit of the simply-phrased question is that the speed of the circumference of the tires is the same as the speed of the treadmill.  Otherwise we're getting into tire slipping, coefficient of friction, yadda yadda.

Edit to add this corollary:  If we were to assume zero friction in the tires/bearings, and an infinite speed capacity of the treadmill, then the plane would take off just like a plane on the tarmac next to it.  It would have zero effect on the plane's ability to accelerate and lift off.  I'm not saying that the treadmill would actually prevent the plane from taking off... I'm saying that for the plane to accelerate and move forward relative to real ground, the premise of the question must be violated.

Isn't it fun to argue about stupid questions without enough information to come to a conclusion?

I think minimum wage should ahhghh urf crash wheeze not the patio!!!

aircooled said:

Don't worry Curtis, I don't reject you, just your interpretation. 

All good.  But this kind of points out my previous statement.  In the scientific world, these questions are just questions to which you can attribute assumptions and calculations.

It's like if someone asks you on a game show "do you want what's behind curtain number 1 or curtain number 2."  You can't ask "well, what's the value of what's behind them?"  What you can do is deliberate on the size of the curtain, which one is closer to your favorite color, etc.  In the same way with this airplane question, you can't ask "what's the coefficient of friction in the bearings?" or assume "how fast can the treadmill go?"  Its a face value, literal question to which you apply equations.  The Russian physicist who asked the question initially (speculating) wasn't actually wondering if the plane would take off or not, he may have just had some force/acceleration things in his head and came up with the metaphor... in the same way that you might be looking at a new Miata and debating buying it.  You can't decide, so you ask yourself a wild question:  "If I had a spare million dollars, would I buy this car?"  If the asnwer is "no" then you've made your decision.  You came up with a wild hypothetical notion to answer a question you couldn't do without a different perspective.

These questions are not "answered" in the scientific world in the same way that 2 x 6 = 12, or what happens when you mix vinegar and baking soda.  These are the kinds of questions that the big-brained people ask to give them a springboard for theoretical mathematics.  Propose a metaphorical scenario to demonstrate the thing you wish to prove.

I think if that Russian physicist were in this conversation, he would be laughing until we got to page 6, then he would chime in and say, "Guys... I was just helping a friend decide whether or not to buy a new Miata by asking a hypothetical question, but thanks for the entertainment."

Streetwiseguy said:

Isn't it fun to argue about stupid questions without enough information to come to a conclusion?

I think minimum wage should ahhghh urf crash wheeze not the patio!!!

You actually just won.

The point of these questions is not to come to a conclusion!

I remember seeing the movie IQ with Walter Matthau and laughing so hard at the scene where the professors are all sitting around discussing atoms bumping into atoms.  Everyone was wondering why I was laughing.  It's because of THIS.  They sometimes don't ask the questions because "yes" or "no", they ask because it's how they get ideas and make discoveries.

I think you're reading a lot into a machine translation of some random Russian post. The only reason this discussion gets traction is because people don't understand the difference between ground speed and air speed or because it's a fun hook for a TV show that likes to build insane apparati. It's not because it expands the theoretical bounds of human knowledge because it's clearly not true, and the only way to make a discussion about it is to dissect very specific wording which is not actually the wording of the person who initially proposed the question. 

I'm all for hypotheticals that force to you think about how things work or to come at an idea from a different angle in order to make discoveries. This isn't one unless you start talking about how to build the world's biggest, fastest treadmill.

Note: studied three years of pure mathematics in university, so I definitely get the handwavy questions.

Curtis73 (Forum Supporter) said:

 

If the plane moves forward relative to the "real" ground, then the question has been violated as one of two things must happen:  1) the speed of the wheels has to exceed the speed of the treadmill, or 2) the treadmill will match the speed of the tires, but will have to move at the square of the acceleration of the airplane.  It has nothing to do with driven wheels vs non-driven wheels.  ....

This is where I don't understand about how you are interpreting the question.  How is the plane moving violating the "match the speed in the opposite direction requirement"?, it seems to require it.  How can the wheels exceed the speed of the treadmill, it's supposed to be moving in direct oppostion, so they should be the same speed, just opposite (ignoring the infinity issue).  And, how do you get to the square of the acceleration (where does that come from)?  You know, other than that, I totally understand your interpretation... 

The way I see it, the treadmill matching the "speed" of the tires, but directly opposite, either results in infinite speed (as the belt increases speed, so does the tires, so does the belt, so do the tires.....), or it somehow uses airspeed, and it would double the speed of the tires (which is what I assume, since it's the only one that makes any sence or even possible). E.g.  airspeed is 10 mph, thus rolling speed of tire is 10 mph, so treadmill runs 10 mph in the opposite direction (resulting in 20 mph wheel speed).

I also don't understand this statement "that is to say, the thrust isn't pushing on the belt like it would in real practice". The only thrust that would be on the belt would be the result of rolling resistance of the tires and bearings (which of course would be very small).  Is that what you are refering to?  You also seem to imply that (in one case) the threadmill must match the thrust (acceleration) and not the speed (velocity) which doesn't seem to be in the question.

Quote for reference: "The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction" 

Honestly, you don't have to explain your interpretation if you don't want to (I am not disagreeing with you, I just don't understand your basis).  Again, stupid question, in many ways....

BTW - yes it is fun to argue such things, for me at least.  I think this would be more of a "discussion" than an "arguement".  We have not yet attacked each other (internet law, I know), so...

Keith Tanner said:

I think you're reading a lot into a machine translation of some random Russian post.

Perhaps it's not as common knowledge as I thought it was.  This theoretical physics question has been around for decades.  It's not quite as old as "tree falls in the woods... sound," but almost as ubiquitous.

This airplane question was actually a discussion we had in Physics class back in the early 90s.  It's a pretty common hypothetical... or at least I thought it was.  I'm judging by the responses in this thread that it maybe not as common as I thought.  From my perspective, this airplane/treadmill thing is nearly as recognized as the tree/sound/woods hypothetical.  Have you guys not really heard of it?  That's not an insult, I'm just genuinely curious since my physics background may be clouding my perception. 

But a discussion about the world's fastest treadmill would be awesome.

I've heard of it mostly due to the Mythbusters episode, but I've spent enough time working on airplanes that I never considered it much of a deep thought. To me, it isn't something like defining what sound is or the nature of perception with that lonely fallen tree. It's a simple answer and it has a definite answer.

I suspect it's primarily a good illustration of how important frames of reference are. You need to look at the airplane from the point of view of the air, not the surface it's sitting on. The treadmill is just there to provide a moving surface without affecting the air, to separate the two frames. I don't think it's intended to blow your mind about how it's actually impossible for the treadmill to function because the plane is not driving the wheels.

Somewhere, there is a world's fastest treadmill. And even better, somewhere someone is trying to figure out how to make the world's second-fastest treadmill go faster.

aircooled said:

Curtis73 (Forum Supporter) said:

 

If the plane moves forward relative to the "real" ground, then the question has been violated as one of two things must happen:  1) the speed of the wheels has to exceed the speed of the treadmill, or 2) the treadmill will match the speed of the tires, but will have to move at the square of the acceleration of the airplane.  It has nothing to do with driven wheels vs non-driven wheels.  ....

This is where I don't understand about how you are interpreting the question.  How is the plane moving violating the "match the speed in the opposite direction requirement"?, it seems to require it.  How can the wheels exceed the speed of the treadmill, it's supposed to be moving in direct oppostion, so they should be the same speed, just opposite (ignoring the infinity issue).  And, how do you get to the square of the acceleration (where does that come from)?  You know, other than that, I totally understand your interpretation... 

The way I see it, the treadmill matching the "speed" of the tires, but directly opposite, either results in infinite speed (as the belt increases speed, so does the tires, so does the belt, so do the tires.....), or it somehow uses airspeed, and it would double the speed of the tires (which is what I assume, since it's the only one that makes any sence or even possible). E.g.  airspeed is 10 mph, thus rolling speed of tire is 10 mph, so treadmill runs 10 mph in the opposite direction (resulting in 20 mph wheel speed).

I also don't understand this statement "that is to say, the thrust isn't pushing on the belt like it would in real practice". The only thrust that would be on the belt would be the result of rolling resistance of the tires and bearings (which of course would be very small).  Is that what you are refering to?  You also seem to imply that (in one case) the threadmill must match the thrust (acceleration) and not the speed (velocity) which doesn't seem to be in the question.

Quote for reference: "The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction" 

I'm digging the discussion.  Zero argument from me.  Just counterpoint.

I can see where our interpretations differ.  Let me ask you this.  Let's assume that the force it takes to move the treadmill is equal to the force it takes to move the tires/wheels/bearings on the plane.  Now, lock the brakes on the plane and try to take off.  Will the plane take off?

BTW, there's a reason for my question.  First, because this is how physicists and theoretical mathmaticians arrive at the theories behind, and second because your answer will be an indicator of my own theory... that we're both arguing the same basic point.  I'm not discussing the physics of the situation, nor am I saying whether or not the plane will fly, I'm simply saying that the way the question is worded, it is a non-answerable paradox.  It can't be answered without more data, nor was its intent to elicit an answer in the first place.

Keith Tanner said:

I've heard of it mostly due to the Mythbusters episode, but I've spent enough time working on airplanes that I never considered it much of a deep thought. To me, it isn't something like defining what sound is or the nature of perception with that lonely fallen tree. It's a simple answer and it has a definite answer.

I suspect it's primarily a good illustration of how important frames of reference are. You need to look at the airplane from the point of view of the air, not the surface it's sitting on. The treadmill is just there to provide a moving surface without affecting the air, to separate the two frames. I don't think it's intended to blow your mind about how it's actually impossible for the treadmill to function because the plane is not driving the wheels.

Somewhere, there is a world's fastest treadmill. And even better, somewhere someone is trying to figure out how to make the world's second-fastest treadmill go faster.

 

We're in agreement.  I'm simply saying that this airplane/treadmill question has no more answer than Schrodinger's cat box.  Schrodinger didn't actually put a cat in a box with radioactive material and a vial of poison to see what happened.  His cat in the box idea was simply a metaphor which launched a direction of theory and math that was in some ways considered the birth of modern theoretical physics, or what we call quantum mechanics.  The point was not to test whether or not the cat dies in a box.

The airplane/treadmill question was not born to test airplanes and treadmills, it was a small-scale Schrodinger's cat theory.

The "if I had a million dollars" theoretical question we ask ourselves to help us move forward with a critical purchase is also a miniature cat box.  We didn't actually put a million dollars in our account just to test what we do with it.  We just pose an implausible question to gain perspective.  Well, implausible to me anyway.

I didn't see the mythbusters thing, but that would have ruined it for me.  It would be like Mythbusters solving why the chicken crossed the road - or - which came first the chicken or the egg.  Those aren't answerable questions.  They're philosopical conundrums designed to make you think, not have an empirical answer.

The point of wheels is to decouple the motion of the airplane from the ground. Stipulations about the wheels' and treadmills' speed that have no mechanism to apply... don't apply.

It's a nonsensical question, as folks have already pointed out quite well.

It's really on the level of "When will I get to lunch if my instantaneous speed is always half my instantaneous speed?" run through the Car Talk radio show's Puzzler obfuscation process.

And because I can't help addressing the logical flaw more viscerally: We should all agree that a plane sitting on unlocked wheels on a treadmill should be able to move a little, yes? That seems obvious. The issue isn't that it physically can't move; the issue is that the problem says that the instant the plane moves AT ALL then the wheels have traveled faster than the treadmill, thus breaking the stipulation. The treadmill doesn't affect the plane, the prescription does.

I know I'm not bringing any new info here; *possibly* just pointing out the logical break in a slightly different light.

It seems flawed as a thought exercise, unless you're just talking about spotting inherent contradictions.

Curtis73 (Forum Supporter) said:

aircooled said:

I'm digging the discussion.  Zero argument from me.  Just counterpoint.

I can see where our interpretations differ.  Let me ask you this.  Let's assume that the force it takes to move the treadmill is equal to the force it takes to move the tires/wheels/bearings on the plane.  Now, lock the brakes on the plane and try to take off.  Will the plane take off?...

.... It can't be answered without more data, nor was its intent to elicit an answer in the first place.

Regarding the locked brakes:  I would say absolutely.  You are replicating the exact forces for a normal takeoff except that the wheels are not turning.   Assuming I am interpreting your question correctly, and the treadmill is long enough of course.

I totally agree there is not enough information to "solve" the problem as presented, that is why I need to make an assumption of what the question can reasonably be actually asking.  Much like my comment about them not letting me fly a plane in the wind tunnel.  Clearly I knew what (as most would) he actually meant, even if he did not expicitely say it.

Jesse Ransom (FFS) said:

... the issue is that the problem says that the instant the plane moves AT ALL then the wheels have traveled faster than the treadmill, thus breaking the stipulation.....

Explain this part.  This is the part that does not seem to be in the question (to me).  (Curtis can also, you seem to think alike... maybe that's good...)

I guess I could also ask what your interpretation of "moving in the opposite direction" means in the question.

We will get to the bottom of this... then we need to talk about your relationship with your mother....