- Pretty much everybody knows that.
- It’s also been covered before.
- But this is a thought experiment.
- So it really depends on what your assumptions are.
Then why is it not treated as a thought experiment? Assume the treadmill is exactly as capable as the question poses. That is a thought experiment. “What if…?”
So what if an airplane was on this perfect treadmill, as per the question? You can even assume that it is 1000 times as capable and spins the tires near their maximum speed rating in the other direction, from the moment the aircraft taxis. The aircraft will take off anyway.
Your comment to Paradoxic that “the belt will supply a force to the plane to counteract the engine thrust” if the belt could practically be built is BS. The engines pull or push (depending on aircraft design) the aircraft until enough positive lift is generated to leave the ground and continues moving that aircraft until the thing comes to a stop. The belt spins the wheels. Whoop-di-doo. Spinning wheels wont stop take off. In many cases (as per my examples) having NO wheels wont stop take off.
It is not a thought experiment to imagine an aircraft so weak in thrust that the pilot having a heavy lunch will keep it on the ground, and consider that aircraft sitting on your treadmill. The question involved a normal aircraft in this extaordinary situation of being on this perfect treadmill. In that situation, you will always have take off. Always.
What assumptions are you working from?
Oh, and EvilTOJ, having read many of the arguments from those that could not see that the aircraft would fly and those that either could not convince the unconvinced, or who twisted the question to meet some peculiar purpose (superman, etc.) that did not help the unconvinced, I thought I would use my experience on aircraft (and not any plagarism, as you allege) to try to demonstrate why the aircraft will fly.
Perhaps you should go back one page, even and read JoeSixPack’s posts to see that not everyone gets it. But, you know, I think you were better off attacking me for trying to help than in trying to help, yourself. At least you made yourself feel better.
Nary D, you have to understand. This issue has been covered by members of this board since before even Uncle Cece first tackled it, if I’m not mistaken. There are numerous threads besides this one. We very thoroughly understand the issue here.
How you answer the question depends on how the question is posed. Posed one way, the thought experiment attempts to draw exactly the distinction you mention. We understand and acknowledge that, though there are, indeed, posters who pop up now and again and make it clear that they do not. Posed another way, however, the thought experiment appears to draw a totally different distinction: that it is, indeed, possible to prevent the plane from taking off, though it cannot be done in the real world. We also understand this, which you, apparently, do not.
As to which of the two questions is “correct,” we will probably never know. If you read the link and discussion that was occurring just prior to your arrival in the thread, you would see that the question apparently comes to us via a group of Russians, and finding out who originated the issue in Russia may be something we cannot accomplish. Unless and until we do, we won’t know which is the “correct” answer.
And if you understand enough physics, you will learn that there are, indeed, situations in which the belt can prevent the plane from taking off. They just don’t exist in the real world, in all likelihood. 
Well, I treat it like a thought experiment. Browse through this post earlier in the thread for some different scenarios and sets of assumptions.
Unless you assume massless and frictionless wheels (which isn’t necessarily bad, this being a thought experiment an all), you’re incorrect. If the treadmill, or any other source, delivers a force to the plane which counteracts the thrust of the engines, the plane won’t move forward. If the plane doesn’t move forward, the wings won’t develop lift (except for some very specific scenarios which I think we can ignore for now).
With normal, non-massless wheels, the acceleration of the wheels will impart a force on the plane. With high enough acceleration, the force is large enough to balance the thrust of the engine. Of course, this relies on having a treadmill capable of high acceleration rates, but if it’s a thought experiment…
Whether the plane will take off depends on your assumption. If you assume a perfect “magic” treadmill capable of large acceleration, and a normal aircraft, the tires on the aircraft will overheat and it will crash and burn. With magic tires (still massy), force will be transferred to the airplane and it will be held stationary. Again, this depends on the assumptions up front–I’m fine with whatever assuptions you want to make about the problem, but be aware that different assumptions lead to different conclusions.
Whether or not the plane will fly depends on yor assumptions. Normally the issue with this problem is that people interpret the problem to mean one thing or another and reason out the answer (usually, but not always, correctly), and then don’t understand how anyone else could possibly come to a different conclusion.
There’s been a number of threads about this problem in the past three or four years, and the lengthiest arguments are between two people who each think they’re right, but come to different conclusions. And the reason the arguments are so lengthy is that both people are right, they just have different unstated assumptions about the problem. And when everyone realizes that, the arguments devolve into semantic arguments about what the problem was “supposed to” mean. However, there are occasionally people who are simply wrong because they don’t understand the physics of airplane lift.
In any case, let me apologize for the snarkiness of my colleague. Not everyone’s seen multiple arguments about this problem, and these threads can be pretty rife with misunderstanding. Welcom to the Dope, Nary D.
I did feel better, thanks. Why should I help? Anything I would say has been covered in this thread over and over and over and over… and over.
Thanks for the link, but before I check it out, I’ll try one more time to address your thoughts on this. I promise I will follow the link in the next few days, but not right this sec. This really interests me how one can have thoughts like this. Here it goes:
What you say could only be true if the treadmill applied it’s motion against or at least closer to the axis. Unless the wheel was submerged and you had to slog against this moving belt, unless that is the assumption you are referring to, the aircraft is unimpeded by the moving belt and flies no problemo.
I have worked on aircraft for 18.5 years now, so I would never assume that a 200 lb tire under a 120000 lb aircraft was massless or frictionless. I do know enough about physics and mechanics in general that something rubbing against the bottom edge of a spinning object could never ever ever apply enough force to arrest the movement of the object. How does the friction of the treadmill against the underside of the tire compare to the 60 tons of weight on top of the axle? If the engines can throw this weight up into the sky, how can you say that bearing friction due to a tangental force being applied to the outside surface of the tire can stop it. Unless you apply that force to the wheel hub (which is the way brakes work) you are not counteracting the thrust of the engine. You are merely providing the direction that the engine thrust causes the aircraft to go.
That is too true. If the plane **doesn’t **move forward, it certainly wont be because of bearing friction, though. Unless you are applying friction against the progress of the wheel hubs, or some other fixed part of the aircraft, you are not stopping it. You might as well hold a paint roller against the skin as it taxis by, to try to stop it.
Wrong, the force of the plane imparts acceleration on the wheels. The airspeed, while the wheels drag on the ground, rolling as wheels do when they are moved against a surface is what makes them turn.
Again, no.
No. The 60 ton aircraft I work on takes off at 140 mph and has tires rated at 350mph. The engines will pull the aircraft at 140 knots and the tires will end out in this thought exercise, spinning at 280 in a desperate attempt to keep it on the ground. The AIRspeed gives it lift and off it goes. Fast spinning tires would have no effect.
Apply your force to the the aircraft and you’re right. Apply it under the tires and you’re still wrong.
Nope, the aircraft will fly unless your assumption involves a treadmill that goes up to the axle.
Well, I really did not want this to go on even this long, but I’m gravitated by your assumption that the tarmac puts a direct force against the axle. Your argument is tantamount to saying that if everyone drove around the equator opposite to the direction of rotation of the earth, that the earth would stop rotating around the sun. It truly does not work.
I do thank you for your welcome, and despite not being able to support your assertations at all, I do appreciate the challenge of changing your assumptions. It’s not likely that I will try very hard or very much longer, I will check out the link later, but I really wish you’d give this some deeper thought and see that a tangental force on the outside of a disk, mounted on a free-spinning axis point below an aircraft with built to fly with more than enough force to get it airborne is not the same as the same aircraft with your opposing force applied to an immobile part of it instead. The tires deflect your treadmill’s force away from the aircraft and the aircraft takes off. No assumption short of a thick, mushy, squishy, adhesive surface to your treadmill will change that.
Cheers!
Ah. This is where stating your assumptions is useful. You’re apparently assuming that when the treadmill matches the plane’s speed, that means that the treadmill moves at the same speed with respect to the ground that the plane moves (and thus the wheel will spin twice as fast). In that case, you;re correct: the plane will take off. However, not everyone makes that assumption. Some people assume that this means that treadmill will accelerate at whatever rate is required to keep the plane stationary.
This is simply false. If the plane’s wheels have mass, the accelerating treadmill will apply a force causing rotational acceleration. That force will be transferred to the axle of the plane.
My argument is tantamout to Newton’s law: F=ma. If the treadmill applied abackwards force to the wheel, the wheel must accelerate backwards unless there is an opposing force. In the case where the plane takes off, there’s still an opposing force from the axle. This has nothing to do with the Earth’s rotation.
Tires do not “deflect” forces.
Yay, we finally get to your assumptions. Until now, your only defence was that things depended on one’s assumptions with no admission of what your own were.
This is the way I see the picture, and you tell me if it matches your picture. The aircraft is going from a stop to full takeoff mode. (I’m assuming there’s no cheating here, as in turn in the treadmill while the aircraft is stationary just to crash it.) The engines start, and as the engines begin applying power and draw the aircraft forward, you start sending the treadmill belt in the other direction. Not so fast as to send the aircraft flying off the end of the ramp, but whatever is perceived to be required to result in zero forward motion with respect to a fixed point. The faster the forward thrust, the greater the belt speed to keep the aircraft in place.
In your mind’s eye, the rapidly spinning wheels equal a force against the hub which is the same as a force against the whole aircraft because they are attached, which, despite any amount of thrust that the aircraft exhibits, results in zero forward movement ergo zero airflow ergo zero lift ergo no flight.
I will work from that, since I have no other info from you. Please advise if it wasn’t what you meant.
Now here is why things wont work your way: The aircraft is going from a stop to full takeoff mode. The engines start, and as the engines begin applying power and draw the aircraft forward, you start sending the treadmill belt in the other direction. Same rules apply: Not so fast as to send the aircraft flying off the end of the ramp, but whatever is perceived to be required to result in zero forward motion with respect to a fixed point.
Your error is that you are not pushing the aircraft backwards, you are spinning the tires in the same direction that they would need to travel to move the aircraft forward. As you drag the bottom of the tires toward the rear of the airplane, you are forcing the tops of the tires forward. Any perceived force on the mass of the tire away from the direction of travel is counterbalanced by the mass of tire moving in the direction of travel, because, needless to say, the tire is round.
An experiment: Take your bicycle and balance it on the rear tire with the seat and handlebars against a tree and the front wheel facing you. Spin the front tire by hand as rapidly as you can without yanking the tire. No matter how fast it spins, the bike will not change it’s position. It will stay there while you play with the tire, all day long. That is because in a spinning circle, all forces are distributed evenly. The momentum experienced at the back of the circle equals the momentum experienced at the front, going in the opposite direction, is the same at any moment in the arc of it’s circle, going in any tangental direction.
Your formula is not F=ma, as you said, it is F= (mv2)/r, Newton’s law of centrifugal force.
The wheels have no effect on the airplane in question because the forces applied to it are evenly distributed and energy is expended by it in all directions simultaneously. The faster you spin the bottoms of the tires away equals the faster you are spinning the whole tire forward.
The force you use via the belt, to spin the wheels, being both for and against moving the aircraft forward cancels itself out. The force applied by the engine, as it pulls the aircraft forward is not centrifugal in nature. It has direction: forward. That is why, with your belt’s efforts are ineffective in retarding the aircraft’s progress and the engine is very effective in applying its force going forward. Your belt will never be able to compensate for the advance of the aircraft because it truly has no effect, and into the clear blue sky it goes, safe and sound.
If you decided to compensate for the forward rolling tendencies of the tires by making the belt travel in the direction of travel, you’d just achieve takeoff with stationary tires. You can’t win. The belt speed or direction will hardly even change the point of takeoff unless you cheat and crash the plane.
Your one hope is to stack the cards in your favor, plus cheat. Put crappy wheelbearings on the aircraft. If you don’t cheat, but play fair, even if you managed to overheat and fuse the bearings, you’d be responsible to slow down the belt as the bearings fail and the wheels cease. At full wheel stop, though, the engines would still have thrust, and the friction of the stationary wheels on the belt would end out in the aircraft moving forward because the thrust would cause the belt to inch forward just like walking on a motorized treadmill with the power off makes that belt move. It would be slow going at first, but thrust plus inertia would win the day. Before you knew it, the aircraft would be airborne with fused wheelbearings underneath. I’d hate to be there for the landing, though.
Now can you see? No matter how you look at this question, no matter how magic or unmagic things are, flight will happen and the tires truly truly have no effect. Give it a good, honest, openminded evaluation. I know you’ll see and then we can both move on to some even cooler puzzle together.
Natch, if you still don’t agree, I’ll be here. If you have any other assumptions to throw my way, toss them over. I’ll always give them an honest, open review.
Cheers!
Nary D, I believe you need to learn some physics, or relearn it if you once knew it. I’ll leave it to people like zut to point out the flaws in your understanding.
But the basic, underlying issue has to do with how fast the treadmill is allowed to go. If the treadmill is allowed to speed up as fast as you need, there is some point that it can go so fast that the resulting spin of the wheels as they attempt to keep up with it will impart a force on the plane sufficient to overcome the thrust of the engines. And yes, that is possible.
Perhaps if you did follow the link, right this sec, it would avoid much re-rehashing of a fully hashed subject.
Just sayin’.
This is bullshit. zut posted in this very thread a list of 13 possible sets of assumptions one could make from the original vague wording of the question. He also specifically directed you to that post. Don’t blame zut for your lack of diligence.
I don’t really have a preferred set of assumptions, I try to work with whatever assumptions other people make. However, it’s important to realize that not everyone makes the same assumptions, and that different assumptions lead to different conclusions. That’s why it’s important to state your assumptions up front.
Like I said, I’m fine with whatever assumptions you’d like to make. So in this case, let’s assume that we have a “magic” treadmill that will accelerate at whatever rate is required to keep the plane stationary, and that we have some regular-looking wheels that have mass, but will withstand extremely high speeds.
No, you’re mistaken. This is basic mechanics, and has been discussed previously.
- If the wheels have mass and do not slip, motion by the treadmill will impart a force on the bottom of the wheel. This force will be whatever is required to rotationally accelerate the wheel (Fr = I[symbol]a[/symbol])
- If the wheel were not connected to the axle, this force, in addition to rotationally accelerating the wheel, with accelerate it translationally backwards, at an acceleration of F=ma.
- However, the wheel is connected to an axle. This axle imparts a forward force on the wheel which is exactly equal to the rearward force from the treadmill. (In the case that the plane itself remains stationary. If you assume that the plane moves forwards, the axle force is greater.)
- The higher the force from the treadmill, the higher the acceleration of the wheel, and the larger the force transmitted to the axle is.
- If the force from the treadmill is large enough, it will equal the thrust from the engine.
- This required high acceleration of the treadmill, but since we’ve assumed it’s magic, that’s fine.
The reason the bicycle doesn’t move is because the acceleration you can apply with your hand, and the inertia of the tire, produces a relatively small force compared to that required to overcome the friction of the seat against the ground.
As a counter-experiment, set a roll of tape on a tablecloth and pull the tablecloth firmly (but without jerking it). The tape will both rotate and move in the direction you pull the cloth.
This is completely incorrect. Draw a free body diagram.
You’re changing your assumptions so that the treadmill will not move at whatever speed is required. There’s nothing wrong with different assumptions, but different assumptions lead to different conclusions.
I’m afraid you fundamentally misunderstand basic mechanics, in particular forces external and internal to a body. I’d be happy to explain (and I have before), but I’m not quite ceratin where to start.
I can’t agree. I’ve read all your points and I still find the same flaws. Your accelerating treadmill will always only suceed at trying to overcome the forward momentum. It is reactive to the motions of the aircraft, so the aircraft will always be one step, however minute, ahead of the treadmill. Unless you throw in another assumption that the treadmill is clairvoyant and accelerates in anticipation of what the aircraft is about to do, your scenario will not do what you envision. The aircraft moves forward at 5 mph, the belt moves back at 5, but by then the airplane is moving at 6 or 8 or 10, and so on, and as the acceleration mounts (and it mounts REALLY quickly) the gap between what the aircraft puts forward and what the belt sends back grows. There is no linear climb in acceleration in aircraft during takeoff, so unless you are adding a new assumption that you have a precogniscent belt that can anticipate what is coming next, the aircraft has to gain on the treadmill and the aircraft wins.
I’ve watched thousands of takeoffs. Your belief that an effect applied to the tires will overcome the horrendous amount of thrust given off by the engines just isn’t realistic. Put the aircraft on ice or some imaginary zero friction surface, if you like, where the aircraft gets no purchase on the ground and it will still and always take off. Not that those surfaces are actively opposing it, but the result is the same. I’d love to see the math, using real values and not assumptions, to back up your views. I’m sure I wont, but I’d love to.
Yep.
The wheel is not connected to an axle, it is connected to a hub. The hub is stationary and the bearings race around it. There is nothing mobile connecting the tire on one side of the landing gear to the one on the other. There is a hollow metal tube about 3" in diameter and the bearing race circles the outside of the tube.
That is absolutely wrong. You’re forgetting again that the engines pull the aircraft. You’re instead stating this like the engine power is diverted to a drive mechanism that moves the tires. The hub is stationary and does not impart any force other than any minute frictional opposition to the bearings racing through the grease around it. Nothing turns the wheel other than the forward motion of the aircraft. It it did not move forward because of the engines were not pulling the aircraft forward, the wheels would not move.
The only force being transmitted to the stationary hub is friction, but I contend that the aircraft will be airborne before that is even an issue.
Not in any of the scenarios that your link put forward.
Now put a string through the middle and have a friend pull it in the other direction while you try to anticipate the speed at which he’ll pull it forward to simulate the non-ground related effect of the engines and see what it gets you.
No I’m not. Your stated intent was to prevent the aircraft from advancing, not to move it backwards from the starting point, but to keep it there. I am, however, making assumptions that the bearings would fail at the same time, in the same way, so you did not get any sideways motion, but since we’re playing with magic and assuming no breakdown in the conveyor belt, it seemed fair at the time. One point for you.
I feel EXACTLY the same way about your understanding of aircraft construction and performance. I will concede that a clairvoyant magic treadmill with no air movement over to the conveyor belt because it’s so magic, could work at keeping the aircraft still, and maybe that’s what you were assuming. It seems like a lot of postulations to put forward to overheat some bearings, though, but whatever floats your boat.
I believe the “instantaneousness” of the treadmill is indeed part of the original problem as posted on this board. (I could be mistaken because it’s been a while but that is how I remember it).
Questions: If you had a plane on a treadmill and the engines were not turned on, it was just sitting there, and the treadmill was moving at a constant 5mph, would the plane move? What about if the treadmill was steadily but slowly accelerating from 0 to 100mph, would the plane move?
I took another look and the “original” problem that I read (which may be different than yours) and it read that there was a sensor that measured the forward speed of the aircraft and then caused the belt to travel on the opposite direction at the same speed.
There is always a lag time between detection and reaction, however small, and I’d bet dollars to donuts that it exceeds the speed loss due to friction that so many have made a big deal of.
I have read so many posts on this that I may be guilty of blending fantasy scenarios in this. What I thought was in the original post, several hundred posts ago, was that the experiment would keep the aircraft stationary. That it would remain at it’s starting point. Not that it could be send back of the starting point, that it would be kept there.
You have to agree that the thought is flawed. Until the aircraft’s engines pull the aircraft forward, there is no speed to compensate for. As the aircraft goes through it’s power curve the belt keeps trying to keep up. The design of the thing is to play catch up. You can’t play catch up and simultaneously hold something back. The only way to defeat the aircraft is to overcompensate but if you go too far you fail at your stated goal of keeping the aircraft at it’s starting point.
I’m not clear on what you’re getting at. Are you wondering if the air motion would cause lift? Not enough on the ones I work on. Are you puzzling as to whether the wheels would turn? Are the brakes on? The tires would definitely not rotate, but the plane sure moves in relation to the surroundings although not in relation to the patch of treadmill that it is on. Are they off? Likely no tire movement, but same deal for the a/c. Why? What is the point of your question?
Nary D, your basic problem is that you fail to understand the effect of shifting the assumptions, an effect created by restating the problem in different ways. Your failure to stay true to the assumptions is evidenced in your post #273, where you say, “Your belief that an effect applied to the tires will overcome the horrendous amount of thrust given off by the engines just isn’t realistic.” This is an indication you are not accepting the basic underlying assumption of the restatement that zut is discussing: the treadmill is “magic”, capable of delivering unrealistic (indeed, if need be, infinite) results. EVERYONE (with the exception of the occasional poor soul who doesn’t understand simple physics) agrees that, if the problem is stated so that the speed of the treadmill matches the forward speed of the plane, the plane takes off. This isn’t in issue, it’s not the dispute, it’s not what zut is talking about. But the problem doesn’t have to be stated such that this is true; indeed, the problem (translated into English from Russian, as it appears happened) can be worded very awkwardly so that this simple scenario isn’t possible, based upon the wording (simply word the problem so that the treadmill matches the speed of the rotating tires (Nitpick here: the “wheels” don’t touch the runway at all, the tires do)).
It’s not clear to me that you’ve read what Uncle Cece said that sparked the whole furor to begin with (and I note it was never linked in the first post of this particular thread). So I’ll link Cecil’s two columns here. You should read them before continuing:
The follow-up. Note that zut was one of the people Cecil references in this follow-up.
zut’s excellent analysis of the situation, posted numerous times previously.
I’ve read all of those things. The first article from Cecil puts it that the belt speed matches the aircraft speed, but up it goes anyway. No problemo, as you say.
The second one poses a what if the belt just keeps getting faster. As I put to Raftpeople, I seem to have been guilty of blending “original” questions that I have read. My recollection that I got from 4 different sites and spent a fair bit of time reading responses on each, was that a keystone to the scenario was that the airplane was kept at it’s starting point.
What I put forward toward the first scenario is that unless the aircraft is allowed to come forward, there is no measurable speed to compensate for and each compensation then must lag every advance and up goes the airplane.
What I put forward to the second one is that you end out with the same result. Unfortunately, that is dependent on whether my keystone holds true. If it is true, then you are not attempting to send the aircraft hurtling backwards into the scrub at the end of the runway, you are trying your damndest to keep that aircraft where it started. As such, despite the infinitely capable belt, it would never get that far because the necessity to keep the aircraft where it is would have to be managed while being able to monitor it’s speed to keep from whipping the aircraft off the runway. The belt must accelerate along exactly as the aircraft does, but without the powers of precognition, how could it? If the pilot hesitates or flinches on his power levers, it’s either into the rhubarb or up in the sky he goes. The game is, by necessity, a game of catch up and I move that the belt can’t win.
If, however, the belt is able to come up to a speed that the aircraft can’t manage before the aircraft and hold that speed, the aircraft can definitely not get into the air. Again, with my keystone in place, I move that it is impossible to keep the aircraft at its starting point and neither backwards nor forwards of it, without precognisence, and that may be magic but the word becomes a pretty broad stroke then. Going back to Cecil’s blog, I see that it was one of the other blogs that mentioned the starting point and I’ll have to find out which one it was.
If I hadn’t thought it was part of the original post (and didn’t have aircraft as my life), I would never have argued so strongly on the impossibility since, obviously, you could simply whip the aircraft well beyond the starting point, controlling it’s progress by overcompensating the whole way, and when it finally maxes out at top speed, you can ease it into whatever location you wish.
You know, you try to read up on a topic, especially when you read some of the insane notions some people have on things. You try to ensure your ducks are in a row. Sometimes you just get them mixed from different ponds.
Still, if you’ve ever been plastered to a wall while the aircraft you’re in goes balls-to-the-wall hurtling down a runway, or watched fighter jets take off with full afterburners in nothing flat, you wouldn’t hold so strong to your beliefs either. Zero to mach in nothing flat and ducted exhaust… it’s still taking off and all you have is a melted treadmill.
What I’m getting at is that you made this statement:
“As you drag the bottom of the tires toward the rear of the airplane, you are forcing the tops of the tires forward. Any perceived force on the mass of the tire away from the direction of travel is counterbalanced by the mass of tire moving in the direction of travel, because, needless to say, the tire is round.”
So I wanted to hear what you thought would happen if the engines were out of the picture and you simply had a plane sitting on a treadmill and the treadmill was moving, would the plane move (either with constant treadmill motion or with constant treadmill acceleration).
DSYoungEsq posted some links regarding the column but the original thread prior to the column is this:
http://boards.straightdope.com/sdmb/showthread.php?t=348452&highlight=plane+treadmill
Ah, thanks for the clarification. I don’t see how your question pertains to anything discussed, but maybe we’ll get to that.
If you don’t mind, I’ll be specific to my aircraft in my answers to your questions. I realize I answered this before, but I wasn’t really thinking about real life scenarios.
For the first one, I don’t think any aircraft including an ultralite would budge.
As for the second, though, I have to completely change what I had told you before. I was just rattling things off and wasn’t thinking.
Even though my aircraft weighs 60 tons, we chain it down whenever the winds exceed 35 knots. Over 55, we double chain it or hangar it. I spoke to some aircraft mechanics in California once because their aircraft was chained down in the hangar. During winds they had one of their aircraft lift completely off the ground inside the hangar and was deposited 90 degrees off. They work on the same airframe type that I do. With a half load of fuel, that was a 100,000lb aircraft pointing into the hangar lifted by 50 to 60 knot winds that whipped inside an open hangar door. No ground speed. No engines. Nose away from the open door. 100 mph, gradual or not, and that bird is on the verge of takeoff.
A quick google shows that a Cessna 150 needs 63 mph. Jetliners 150-180 mph. STOLs need 46 or less and will lift with a strong wind. So, okay, with no specific aircraft mentioned, your 100 mph will launch more than half the aircraft in the world without engines.
What’s next? You asked if the aircraft would move? In every sense of the word, the answer is yes. It goes up, it comes down not where it started, it is not near whatever it started near alongside the belt. Cool. I’m glad I gave it a second thought. Thanks. On a treadmill going forward, even if you had your brakes on, you’d fly at 100mph with most aircraft.
Okay, now to refer to why you asked the question. Remember, the wheels on an aircraft have no motive force applied to them, other than being taken along for the show by an airplane that is being pulled through the air. So the treadmill is attempting to create drag on the aircraft, to pull it backwards so fast that it cannot get lift. However, the only reason the wheels began rolling is that the engines are starting to pull that aircraft off of the ground. It is pulling it forward, which is the first step in getting it off the ground. It is no longer sitting on it’s haunches. It comes up on the landing gear like a slow-motion explosion. It’s awesome.
The treadmill spins the tires the tires in the direction they’re going anyway, and they are going that way because the engines are pulling and lifting the aircraft. Tell me if that helps you.
So in a thought experiment it’s ok to think about massless wheels and frictionless bearings, but not ok to imagine instantaneously responding control systems and a treadmill capable of nearly infinite acceleration?
None of the people responding to you thinks that any situation remotely corresponding to reality the plane will fail to take off. They are not "hold(ing) so strong to (their) beliefs ".
The plane will take off in almost all of the different scenarios based on the different assumptions. We all know this. There is one set of assumptions, however, that can stop the plane. And that includes a treadmill that can accelerate continuously and essentially instantaneously up to infinite speeds.
And it’s the acceleration of the treadmill that imparts force to the axle of the plane, not the speed.
If I understand correctly, no steady speed of the tradmill, regardless of how fast, will impart a backward force to the plane. But while the rotational speed of tires is changing, there is a force. Negligible for any real world acceleration, and it’s going to require truly ludicrous acceleration to hold that plane back, but the numbers are there.