That /\ was in the post you quoted but you chose to delete it for some reason. But that is what I am interested in as stated previously. Forget engines, just think of a new situation in which the airplane does not have any engines, now we are just discussing whether a treadmill can cause a vehicle with wheels to move relative to the ground. If so then there is a net force in one direction, if the answer is no then there is no net force.
Ok, so an ultralight that doesn’t even have any engines (we removed them) that is sitting on a treadmill, and the treadmill is moving at 5 miles per hour steady speed would not cause the plane to move relative to the ground, the plane would just sit in the same place relative to the ground but the wheels would spin.
Question #1 answered.
Question #2 was the same plane on a treadmill such that the treadmill gradually speeds up to 100mph. In this case would the plane (which has no engines) stay motionless relative to the ground, just sitting there with wheels spinning, or would it begin moving relative to the ground due to the treadmills motion?
I actually only considered the aircraft tires that I’ve worked with. The aircraft comes in at 170, hits the ground and the tires go from deadstop and no load to 170 and full load plus the force of hitting the ground, and after a brief taxi they’re often not even warm. That’s with real life and no “ideals”. That’s why I can so easily shrug off claims of frictional effect. Any heat comes from braking action, not from rotation. Lots of hot brakes, no hot hubs.
I never claimed massless wheels. That was an assumption that zut made. I imagined the behavior of the tires I work with, ie 3 feet tall and 200 lbs or so and aircraft grease. I imagined the aircraft and the hubs and all the things I have experience with applied to this fantasy scenario. Even though I was not assuming any cheating on my end, I was willing to consider any scenario so long as it was stated outright.
Among the things not stated was a treadmill so massless that it could accelerate on demand. Another was that it had no lag. Another was that it was so massless and had so little lag and yet so magical that it could apply enough force without any of those things that it could turn the wheels fast enough to slow an aircraft on takeoff. Another was that this amazing treadmill might even avoid whipping up a hellacious wind when attempting to travel at infinity.
I realize that these things might still count as assumptions to zut and the boys, but if stating assumptions is so important, it’s a two-way street. If the belt is very long, it must have lots of mass to accelerate and acceleration must take time. If the aircraft has already accelerated and the belt is attempting to hold back the aircraft it can’t win. IF your infinity belt can whip the aircraft backwards until it is constantly going faster than its possible forward speed, I would think that is worth stating, don’t you?
Is it really a thought experiment if it is so one-sided? The belt can instantly accelerate, calirvoyantly even, but the aircraft cannot and has heat-intollerent bearings, and the belt can send the aircraft miles the other way to countermeasure the advance due to the engines and and and… I mean why don’t you postulate that someone has disconnected the battery so that the ground power unit can’t deliver bleed air to the engines so it can’t turn a prop? Or that a sniper is aiming at the pilot?
At some point thought becomes not-thought. When things must be so unequal to achieve a goal, it would be like the US military going full bore against Trinidad or proving that owning Mediterranean Ave alone against the rest of the board could result in your loss. Duh.
I just don’t see the point as to claiming even the theorhetical victory. In every situation where both sides are treated equally, the aircraft wins. Even the impossible ones. That’s pretty cool. Really cool even. Almost miraculous. But there it is.
So long as the acceleration of the belt is reactionary to the aircraft, the aircraft wins. I know I’m on a rant. I’ve had some beer and I might be a little pissy right now, but I ask you to prove me wrong.
Well crapola. I know I posted a response to this thread around 7 pm. Except I guess I just previewed. :smack:
Much of what I was going to say has been said.
Here’s the rub. When we posit the thought experiment with a car on the treadmill, we propose a car that starts from 0 and accelerates to a set speed (60 mph?). The treadmill is a powered treadmill, not a response treadmill. Somehow it must accelerate at the same profile to keep the car at the same place on the treadmill. Yet we accept that premise, because that is the stated premise.
The same condition is suggested by those who interpret the question that way. They read the question not as saying
An airplane is on a powered treadmill that accelerates at exactly the same profile as the airplane throttle. Can the treadmill keep the airplane from taking off?
They read it as saying
An airplane is on a powered treadmill that accelerates however it needs to to keep the airplane in the same location with respect to the ground. Can the treadmill keep the airplane from taking off?
In other words, they are assuming the answer to the question. They are interpreting the question in such a way that they are not asking about how an airplane responds to a treadmill, they are interpreting the question as the treadmill can do anything it takes to keep the airplane in one place. That was what zut’s mega post was all about - spelling out all of the objections that he could conceive being offered that allow the person to get to the point where their interpretation “works” and they get the result they want.
Actually, the point is that the folks who are making the claim are not stating assumptions, they are just assuming and then arguing with folks who don’t have the same assumptions. That’s why zut’s post is all about “what are your assumptions?”
Yes, you’ve got it. It’s not-thought. It’s assumption by interpretation. They have interpreted the original problem in such a way that the plane does not move with respect to the ground. That is their assumption. Ergo, they reach the logical conclusion that the plane does not take off, because there is no airspeed.
The reason why zut mentioned magical treadmills is precisely because he agrees with you that any real world scenario is going to allow the plane to take off, and it takes a string of precisely worded assumptions to counteract all the ways that physics says that the plane will take off, in order to reach the condition that has been interpreted - the treadmill somehow keeps the plane from moving with respect to the ground.
One more time: please state what your assumptions are about the problem.. Most of what you’re saying is simply noting that if you changed your assumptions, then the result would be different. I know that. The above quote is a good example. Trying to pin you down, I explicitly said “let’s assume that we have a ‘magic’ treadmill that will accelerate at whatever rate is required to keep the plane stationary.” Your response was that “the aircraft will always be one step, however minute, ahead of the treadmill.” That’s a change in the assumptions. It’s fine to have different assumptions (in fact, that’s my whole point), but you have to state them up front.
From a practical point of view, it’s not really difficult to build a control loop that measures plane velocity and controls the treadmill to keep it at zero. There will be some dither in actual velocity, but building a control system to keep the dither small isn’t an unusual engineering problem. With better control, the dither can be decreased, and the problem reduces to the semantics of “how ‘close’ to stationary is close enough?”
More to the point, this is a thought experiment. You seemed to accept a thought experiment that posited a “magic treadmill” capable of nearly infinite speed, but you won’t accept a control loop? If your point is that we couldn’t actually build a treadmill that performs like that, so clearly the plane will take off if put on any reasonable treadmill, everyone in this thread knows that. This is why you have to state your assumptions up front.
What exactly, would you like to see? I’m happy to go through it (and I have before), but you’re fundamentally misunderstanding the mechanics, as shown below.
Even ignoring a powered treadmill, the ground imparts a force on the wheel to spin it, once the plane moves. How, exactly, would a force on the center of the wheel cause it to spin?
If you add a powered treadmill into the mix, the treadmill is capable of producing a force on the wheel without the plane moving.
This, to be blunt, is a pretty good example of where you’re fundamentally misunderstanding basic physics. Even in a situation where the plane is taking off from the ground, the wheels have mass, and are being accelerated forward. To be accelerated, a force must be applied. This is Newton’s law: F = ma.
One more time: what, exactly, are your assumptions? If your point is that we couldn’t actually build a treadmill that performs like that, so clearly the plane will take off if put on any reasonable treadmill, everyone in this thread knows that. You could have saved a lot of typing by stating that up front.
However, not everyone reads the question the same way. For example, people ask questions like, “what would happen if you fell into a tube through the Earth?” or “what would gravity be like on the inside of a donut?” With these, it’s perfectly valid to point out that we can’t build a tube through the Earth or a donut planet. But that’s not necessarily the point of the question. Likewise, it’s perfectly valid to point out that we can’t build a magic treadmill. But that’s not necessarily the point of the question.
What makes a question a thought experiment, and what makes this particular question interesting, is that examining the question reveals some interesting scenarios. To change to something neutral, “what happens if a spaceship accelerates to 99.99% the speed of light?” makes an interesting thought experiment, because you’re forced to think about how relativity affects time and space, and what the pilot sees v. what happens on the ground, and so forth. “What happens if the engines of a spaceship don’t work so it can’t accelerate to 99.99% of the speed of light?” is a much less interesting question. For the original spaceship question, pointing out that we can’t build such a spaceceship, and the difficulties of storing fuel, are legitimate arguments, but saying, “let’s assume we have a magic spaceship that accelerates on command” doesn’t make this a one-sided thought experiment where the deck is stacked and the forces of reason can never win.
And, just to point out: this isn’t true, even from a practical point of view. Control systems to maintain constant speed are built all the time. Cruise control in a vehicle is one example. There’s no reason one can’t build a control system to maintain zero speed. Now, if you demand exactly zero error, that’s likely to be a problem, but given that the point is to keep the plane below its takeoff speed, I would think some dithering is acceptable and not worth discussion.
So your contention is that under anything like real world circumstances, the plane will take off. Let me tell you what we all think about that:
WE KNOW.
Let me restate that:
WE UNDERSTAND AND AGREE. Anyone with a basic high school education who thinks the problem through should come to the same conclusion. And most do.
All these things were stated in the post zut linked to that you say you’ve read. And once again, it’s not the speed of the wheels here that may make a difference, it how much they can be accelerated.
Once again, we’re not disagreeing with you about your conclusion based on the assumptions you’re making about the problem**.
It is not the case that you’re dealing with a bunch of people here who simply refuse to listen to reason and bow to your superior knowledge. WE KNOW that under anything like real world conditions the plane will take off. WE KNOW that under normal conditions the treadmill just can’t put anything like enough force on the plane to slow it down significantly without simply spinning the tires to the speed where they explode.
WE KNOW ALL THIS. But that’s a boring question. Too simple. Childishly easy, even.
So then we say, what kind of conditions could be imagined that might make it a more interesting question? What force can the treadmill exert, even if normally negligible, and what conditions could increase that force to a usable level? Now that becomes an interesting question.
** I will say that your contention that a control system can’t possibly react fast enough to control the planes speed is silly. I’ve worked with (and even designed) control systems for years and it is fairly trivial to design a system that will react to a change in rate and counteract it fast enough to keep a system running within a specified speed range. It happens all the time. The trick is to find a way that the treadmill can exert enough force, not find a way to control it.
When you click on the Quote button to quote the post and respond, it only quotes the one you are responding to, not the quotes they are quoting. Try it, you’ll see that your above quote disappears in your response to me.
Okay, you have a new scenario. Now when you say “move relative to the ground” do you mean the ground surrounding and under the treadmill, or the surface of the treadmill itself? Unless there is a force (inertia, being tethered, being propelled) that is so strong that the gentle nudge of the treadmill can’t move the body (the aircraft in this case) but only the wheels, then the treadmill just carries the body away with it. Put a dinky car or wagon or whatever you wish on a home treadmill and start it slowly and if you start gradually enough you should even be able to avoid rocking the wheels, let alone spinning them.
When designing the Tokyo subway years back, one of their stated goals was that the entire journey, including start & stop, should be smooth enough to allow one to hold a glass of water and not have it slosh at all. You said “gradual” on your first post in your second question. That’s gradual to me. Did you define it differently?
I should have been clearer then. The aircraft would not budge from it’s location on the belt but would go wherever the belt would carry it. No wheels would turn even if you lurched to such a low speed. There would be no sustained acceleration applied to the wheels to make them brake their stasis. As you say:
To further add to my previous response to Q2, incase that wasn’t clear either, I don’t think the wheels would spin in this case either. They might move incidentally due to bouncing up & down on the treadmill as lift is gained and then lost since the treadmill was acting as it’s surrogate engines by accelerating it to that speed, but no continual rotation would occur, probably. I can only say probably because when it decelerates in the air and comes down, the treamill is already at speed, so potentially it might catch and spin the wheels before the entire weight of the aircraft settles on it and it may change things, but that depends on too many factors for me to puzzle out right now. I’ll think about it though.
As it stands, you have no spinning wheels, one aircraft moving with the treadmill and one being launched by it. Please go on.
Nary D, perhaps you can quote zut’s excellent post covering 12 sets of assumptions and critique each one, then add any sets of assumptions you think he hasn’t covered. Here’s the post, I challenge you to find flaws in it; be specific.
Now you are misunderstanding. Nary D is talking about force being transmitted to the hub from the wheels. He is ignoring the force applied to the hub by virtue of the hub being attached to the airplane structure.
There is a force transmitted to the hub from the wheels that is equal and opposite the force transmitted to the wheels from the hub. The force to the wheels from the hub arises because the wheels are being accelerated forward. F = ma
There’s also a vertical force due to weight, but I assume we’re all ignoring that, as it doesn’t have a direct affect on the forward motion of the plane.
True, but in my original I quoted you by copying and placing your words into the post and merely adding double quotes around it, I assumed the software does not consider that a quote (as in the type with brackets around it). That’s why I was confused.
Ok, a couple more questions:
Would a faster but steady speed treadmill cause the plane’s wheels to rotate? Say, 50mph or 100mph?
1b) If the answer is yes to either, would the plane remain motionless relative to the ground (ground as in the ground that we observers are standing on) but the wheels are spinning? If not, what would happen?
In the 2nd case, would greater acceleration cause the plane’s wheels to rotate? Say 0mph to 100mph in 1 minute or maybe 10 seconds?
2b) If the answer is yes to either, would the plane remain motionless relative to the ground (from outside observer perspective) but the wheels are spinning? If not, what would happen?
Nary D, I hope you’ve taken the opportunity to draw a free-body diagram, as zut has suggested. Just stick with a wheel sitting on the ground, and some frictional force acting backwards upon the bottom of the tire (say a rug being pulled out from underneath it, or a treadmill starting up underneath it)
You’ll find that there’s an unbalanced force in the x-direction, that can only be solved by including a corresponding mass-acceleration vector, acting on the cg of the wheel. (Additionally, there is an unbalanced moment produced by the same frictional force that is creating an angular acceleration on the wheel, causing it to spin)
The Plane will propel itself forward but will it take off?
Hey i’m back…ok so we all agree I think that “the wheels are along for the ride” and the plane will propel itself forward because it uses thrust from the jets not the wheels etc… To use Cecils analogy of a pulling yourself forward on a treadmill by a rope while on rollerblades…but I believe if you were racing someone doing the same on pavement then they would pull ahead of you.
Can the plane reach V1 or V2 (Vr) without having the wheels take the weight & inertia (momentum) to assist in propelling the plane forward?
Let’s say there are three doors, and behind these three doors are nine yards of fabric in a full Scottish kilt, a plane on a treadmill, and a 9-11 conspiracy…
I never posted to any of the other threads regarding this. My brother and I read about it in a Flying or maybe **Pilot **magazine c. 2 months before the Greatest Thread Known Ever. He’s a pilot and I’m a physicist, and our guess to the “trick” was that rolling resistance is not negligible,
As it turns out the fun of the thread was the very nice dissection of all the assumptions in the wording of the problem. I loved that whole pesky thread. I feel better for, at least, making one post on the subject.
Armchair Aviator, I am trying to follow your question, but am having difficulty. In what way are the wheels not taking the weight or inertia?
The wheels are providing the structural support to hold the plane up. The wheels are spinning such that the difference in speed between the belt and the airframe is accounted for. The only difference is that the wheels are spinning faster than the airspeed would suggest they should be spinning with respect to a non-moving ground.
Well I guess my question is if you brought the (treadmill) plane up to speed and cut the engines, will it roll the same distance as it would on pavement?
Just popping in to say that I read the article and skimmed most of the thread. This thought experiment is making my brain melt.
If the treadmill is going backwards at the same speed the wheels are spinning forward, doesn’t that mean that the plane is stationary? And yes, I know that the plane doesn’t use the wheels to move forward, but still, the wheel speed would be dependent on how fast the plane is moving.
But if the plane can take off in this situation, why can’t it take off while remaining stationary in other situations?
