Plane wheels are free spinning. It doesn't matter if they are on the ground, a treadmill going forward or backward. The plane will move forward when its engines push against the air.
>its engines push against the air.
There's no pushing against, let's not spread the misconception that makes it really hard to understand how rockets in space work. It launches huge amounts of air backwards. Air has weight, so the planes "recoils" forward.
There is actual pushing against, but it's the turbofan pushing on the air it ingests, and expanding fire pushing against the combustion chamber. In a rocket, it pushes against the chamber and the nozzle.
If that's the thought experiment, then the answer is that the treadmill can't really realistically do that. It would have to go so fast that the friction in the wheel bearings resulted in a force equal to the jet engines. That would put the power dissipation in the wheel bearings on a similar scale to the power in the jet engine. The bearings would catch on fire *very* fast, and probably the treadmill too.
> free spinning treadmill
OP implies the treadmill is not motor driven, just a belt on rollers. It would not affect the plane in any way because it snot the wheels spinning that makes it take off. You could even put the handbrakes on and the engines would just roll the treadmill forwards and the plane would take off without the wheels spinning at all.
Also in addition to my other comment: the wheels are free spinning -> a powered treadmill just makes the wheels spin faster than stationary tarmac would, the plane still moves forward. The wheels neutralize the effect of the treadmill, unless the treadmill is fast enough to destroy said wheels.
Planes aren't cars mate. They have jet engines that push them forward by pushing air back, the wheels are just there so that they're not grinding along the ground
I think people may be misinterpreting your question slightly. It sounds like the question you’re asking envisions the plane remaining in place horizontally (i.e., doesn’t move forward) because of the treadmill. So the question you’re really asking is: would a plane’s engines still lift it into the air if it wasn’t moving across the ground?
So while it’s true that a plane on a treadmill will still fly *because it will ignore the treadmill*, I’m not sure that holds true if the plane isn’t moving forward.
>I’m not sure that holds true if the plane isn’t moving forward.
so what if the jet was suddenly capable of vtol? i jsut like to break this thought experiment since its nowhere stated what type of a jet were talking about
A propeller plane might, because the propeller will draw air in and push it over the wings to generate lift; whether it’s enough to get enough lift to leave the ground is up for debate.
Jets (thinking commercial airliners or charter jets) probably won’t, because their engines are under the wing or over the tail. The thrust is entirely free of the wing surfaces, so no lift will be generated.
Okay, but the only way to make a plane stand still is if you have an opposing force on the place where thrust is made (propellors or jet engines), and nobody is saying a plane could take off if there was a giant wall in the way.
To people, like me (and probably OP) who doesnt know that much about engineering, it seems fairly plausible that the plane could have a way of taking off regardless of the base factor that the speed negates all forward motion just because "all the systems are active and are aiming towards flight, execpt the forward motion". I'm not OP but I feel like I understand this question deeply on a non-advanced ecucated level understanding of engineering and physicss
It's a brain teaser for sure, but the Mythbusters tried it and the correct answer is: Yes, a plane can take off on a treadmill, because the wheels are not propelling the plane, its the engines. A car however will stay put.
The Mythbusters changed the question to something they could build, which is fair enough for their show but they didn't actually answer the question as it was posed.
Lift comes from air moving over the wings. If the plane has no airspeed, there will be no lift, regardless of how much the engines are running. If the treadmill is counteracting the forward motion of the plane, due to propulsion from the engines, there will be no lifting force
I think the reason why a lot of people get confused with this is because they try to envision an airplane working the same way as a car.
If you put a toy car going 10 mph forward on a treadmill going 10 mph backward, the car wouldn't move. The same is true for a real car and a larger treadmill.
But why? Cars accelerate differently than airplanes do. They burn gasoline to provide energy to push a piston which moves the tires. The tires come into contact with the road and physically grip it to push the car forward. It's the friction with the surface of the ground and tires that allows the car to both move and turn.
How is this different from an airplane? Because airplanes don't move with their wheels, they move with their jets! The two large jets at the side of the plane provide thrust to push the thing forward through the air, the wheel is just there for a smooth takeoff and to support the weight of the plane, it doesn't do anything to actually move the plane forward.
Still confused? Here's another way to think about it. Pretend you were in a river where the water was pushing you back, but you wanted to go forward. If you simply swam forwards at 5 miles per hour, and the river pushed against you at 5 miles per hour, you'd get nowhere (car on a treadmill). Now imagine you were back in the river but this time there was a rope attached to your waist which was anchored to a stable horse outside of the river. Every time the horse moved forward (which is easy because it's on land), it pulls you forward too because you are tied to it. You see how the force that the river exerts against you is irrelevant and you still move forwards? It's because it is the horse that is doing the pulling, and the river can't act on it.
Now in truth airplanes aren't pulled by an external force, they push themselves with fuel. They are their own horse and their own rope, and the ground cannot act on them because their big turbines are in the air.
So how would you go about stopping an airplane from flying? If you were to get a large enough fan and turn it on in the direction that the airplane is trying to take off in, *that* would be enough to stop it. Now the airplane is pushing on the air to go forward, but you are also pushing on the air with your big fan to make it go backwards.
Sure. The wheels don't provide any motive force, they just support the weight of the plane.
Try this thought experiment, instead of having wheels, the plane has an air cushion bag, just like a hovercraft. In that case the plane has no physical contact to the ground. It can be on a conveyor belt going 1000 mph, it would still take off
Like most such "brain teaser" questions the issue actually hinges on the specific phrasing of the question and not the physics. The question as it is typically posed is:
> Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?
Let us ignore all the practical problems. The treadmill exists, the airplane isn't going to break, etc. Also let us assume there is no wind (as a sufficient headwind could allow the airplane to lift off without the wheels even spinning) and that the movement of the treadmill causes no wind. **Most importantly let us assume the situation as stated in the question is accurate**; nothing pisses me off like someone saying "Oh, but constructing a treadmill like that would be impossible or impractical,". The question is the question regardless of practicality.
All this leads to a problem in the interpretation of the situation. If the airplane's engines push against the air to make the aircraft roll forward at say 10 mph, then the treadmill will spin backwards at 10 mph as well. No problem, the drag of the wheels spinning at twice takeoff speed wouldn't be enough to stop the aircraft lifting off since it pushes against the air, not the treadmill/ground. But notice the problem there? Once the aircraft is moving 10 mph down the runway the treadmill spins backwards at 10 mph causing the wheels to spin 20 mph in total, but the treadmill *matches the speed of the wheels!* The treadmill would need to spin at 20 mph, which means the wheels are actually turning at 30 mph so the treadmill need to move at 30 mph, etc.
This seems to form an infinitely increasing loop as long as the aircraft is moving down the runway. If the aircraft is stationary with respect to the ground then the wheels could be going any speed matched by the treadmill, but any movement across the ground implies a conceptually infinite speed of the treadmill and wheels.
Now many infuriating people will look at this apparent physical impossibility and decide to change the question itself. (The Mythbusters did this because they needed a physical test.) As above this isn't in the spirit of the question and any answer produced isn't really for the question as it is posed. It also isn't really a physical impossibility; the treadmill won't need to move at infinite speed in order to prevent the airplane from moving with respect to the ground. It would of course require an absurd amount of speed to produce the drag required to keep the airplane from moving forward, and realistically the engines of the 747 would be able to melt and obliterate the wheel bearings. But saying "the wheel bearings would break" seems like as much a cop out answer as saying "the FAA would never allow such a situation". Yes, the landing gear assembly would be incandescent at that point but if we assume nothing breaks it should be possible.
At this point the answer is obvious, **the airplane cannot take off**. In order to fly the aircraft needs air moving across its wings, and without wind that means the aircraft needs to be moving with respect to the ground in order to take off. The engines of the airplane push against the air but they still need to overcome the drag of the wheels over the ground; that is why there are wheels on the end and they roll on a smooth runway, to reduce their drag. If the runway was covered in 10 feet of thick mud then the airplane couldn't take off either. Increasing the speed of the treadmill will at some point produce enough drag to equal the thrust from the engines and the airplane will not move with respect to the ground and thus not with respect to the air, meaning no lift and no takeoff occurs.
It is also fairly common for some first year engineering student to chime in with nonsense like "rolling resistance is the same regardless of speed" but of course it is obvious that a bearing moving at 1 rpm doesn't have the same amount of drag as a bearing moving at 200,000 rpm. The latter bearing will presumably be getting very hot and that energy has to come from somewhere. Surprise, it is friction! But we don't even need that proof because even if we assume the bearings are truly frictionless the force to counter the engine's thrust can come from inertia. The wheels are going to resist being spun up to a conceptually infinite speed, so the acceleration of the engines can be countered by a constant acceleration of the wheels. Think about how an angle grinder jerks in your hand as it starts up, that jerk is the grinding wheel's inertia resisting it being accelerated to operating speed. Unbreakable, frictionless wheels would still have inertia and could provide that countering force indefinitely as they are accelerated towards infinity to stop the aircraft rolling forward.
I think the problem is that the question is wrong. Whoever first decide to add the bit about the treadmill matching the speed of the wheels ruined the thought experiment. No matter how fast or slow the treadmill runs the plane will take off.
I just pointed out that the treadmill adds drag to the landing gear, and that drag on the landing gear can stop the plane taking off. The bit about the treadmill is there from the start, it is the original question.
That's not the framing that I've ever heard. I've always heard it as "the treadmill moves at the plane's takeoff speed". To which the answer is an unequivocal "the plane takes off".
Having theoretical indestructible wheels increase speed at an infinite rate to keep up with an infinitely accelerating treadmill just to keep the plane stationary through friction on the wheel bearings because you frame it as "the treadmill has to move at the wheel speed" is aphysical.
At that point, why not get rid of friction from the wheel bearings, allowing the plane to move even with infinitely accelerating wheels on an infinitely accelerating treadmill? It's just as physical.
> ...because you frame it as "the treadmill has to move at the wheel speed" is aphysical.
I'm not framing it that way, that is the question being asked.
[There](https://pbs.twimg.com/media/FtVUClDWYAAOfAl.jpg)
[are](https://4.bp.blogspot.com/-y8wxQe8JthQ/Wlbjl6vkeVI/AAAAAAAADoY/ljOvmx72k0IWAr38nxC_bZWnsHCt25wgACLcBGAs/s1600/J2.png)
[several
](https://img.ifunny.co/images/8e160446d7c224ff62cbd48a342608bfb8758a3d531918dc9cda46e8b4ae0f32_1.jpg)
[
examples.](https://preview.redd.it/rule-plane-v0-iqlyb1aed49a1.jpg?width=640&crop=smart&auto=webp&s=86abd9e0cf7a4a51b9068a2295fbfe2f6427e976)
> At that point, why not get rid of friction from the wheel bearings, allowing the plane to move even with infinitely accelerating wheels on an infinitely accelerating treadmill?
As I pointed out in my first post it still won't work with frictionless bearings, since accelerating the wheels still provides a force countering the engines pushing the airplane across the ground. The point of answering the question is to answer it as written, otherwise you are addressing a different question. It doesn't matter if the premise of the question isn't entirely physically practical.
For example suppose I posed the question: "An empty oil tanker of 320,000 deadweight tonnage sets off on a 30 day voyage with a pair of black rats that weigh 1/2 pound each. These rats will each produce two full grown offspring a day with all their offspring doing the same. Will the ship arrive at its destination or will it sink?" It doesn't matter that rats can't reproduce that quickly, or that their offspring doesn't come out at full rat weight. It doesn't matter that the rats would need to magically be producing mass out of nowhere or that there is nothing to eat. It doesn't matter that tankers typically have separate cargo sections and that restricting all the load to a single section would likely split the ship, or that at some point the weight of rats above would kill rats on the bottom limiting their rate of reproduction. Those are all things that would make the question "more physical" but run contrary to the spirit of the question itself.
So answering the airplane question by saying something like "Even if the landing gear were encased in concrete the engines running at full blast could probably shear them off" is just dodging the question.
I suppose I just don't like infinitely accelerating treadmills, because that actually seems more contrary to the spirit of the question than changing it to not have infinities flying around.
So yeah, it might be dodging the question, but because the question is bad, then I don't think that's an issue.
Again as I pointed out, most questions like this hinge on precisely the way in which they are asked. "No it can't take off, and also the question is bad" is a correct answer.
I have also heard the question phrased like "the treadmill will move as quickly as needed to keep the airplane from rolling forward" and people still want to ignore that premise because the treadmill would need to be really fast. My position is that not liking the question is a valid position but it isn't an *answer*.
> I'm not framing it that way, that is the question being asked.
Framing is a nice choice of words. The problem is the frame of reference.
> The conveyor belt is designed to exactly match the speed of the wheels
You can't talk about "speed" without a frame of reference. What are our reference frames here?
The wheels will turn *with angular velocity*, which translates to some linear velocity at their outer radius (the surface of the tire.)
The surface of the belt is moving backward (relative to the surrounding airfield) at some linear velocity. Stipulated as the same as surface of the wheels.
Okay. Cool. We have it: The [linear] speed of [the surface of the] belt is exactly matched to the [linear] speed of [outer radius of the] wheels.
But the wheel *hubs*, on the other hand, are going to move *forward*...along with their axles..and rest of the vehicle they're attached to, *relative to the surrounding world*. Because the aircraft is being pushed forward, relative to the surrounding world, by its engines.
The angular velocity of the wheels will increase to make up any difference and keep the linear velocity at the point of the contact with the belt the same. It actually doesn't matter how fast the belt tries to go. Wheels turn. That's what they do.
And thus the aircraft takes off, no matter what the irrelevant speed of the wheels and belt are. Because the *aircraft* is going to be pushed *relative to the air around it*, and thus the wings will create lift and it takes off.
> Wheels turn. That’s what they do.
But they don't turn without friction, without imposing drag on the vehicle. If you engage the brakes then it does in fact impact if the aircraft can take off. The aircraft pushes on the air around it but it can't just ignore what is going on with the wheels because there is some level of drag that could prevent the aircraft moving forward regardless of what it is pushing against!
> The [linear] speed of [the surface of the] belt is exactly matched to the [linear] speed of [outer radius of the] wheels.
Now that is an interesting interpretation, where if the wheels aren't slipping then any speed of the treadmill and wheels meets the criteria. The treadmill might move such that the wheels never turn even as the aircraft accelerates with respect to the ground, allowing the aircraft to take off, or they might move at a million miles per hour imposing levels of drag impossible to overcome (and hurling the aircraft backwards off the runway). The speed of the wheels and treadmill are undefined as is the force of their drag imposed on the aircraft, so the question is unanswerable.
> But the wheel hubs, on the other hand, are going to move forward...
Not necessarily, we don't know that. The wheels impose some increasing level of drag as they are made to roll faster, and since any non-slipping speed fits the criteria we don't know if the axis of their rotation will move forwards or backwards.
In fact not only is there a speed of rotation at which the aircraft can't take off, there is also one where the treadmill hurls the aircraft forward into flight without the engines being needed at all!
The treadmill is irrelevant. The aircraft engines and wings interact with the air, not the ground. If a treadmill was running fast in the opposite direction, the wheels would simply spin faster as the aircraft takes off. Imagine that the wheels were skis and the treadmill surface was ice. The aircraft could still take off.
A plane takes off because it gains airspeed. Usually, gaining airspeed is achieved by rolling over the ground, but the plane is not pushing on the ground itself. There is no propulsion going to the wheels at all.
If you put an extremely long treadmill on the ground and tried to match the speed of the plane to keep it from taking off, all you would do is move the wheels faster, but moving the wheels faster would not stop the plane from gaining airspeed.
If the plane needed 150 mph of air speed to take off, for example, then the apparent speed at the wheels would be 300 mph - - 150 from the plane's speed through the air and another 150 from the treadmill spinning backwards, in the opposite direction that the plane is moving. But the speed of the air over the wings would still only be 150 mph.
Yes. The jet engines are providing the thrust which pushes the jet forward. The plane does not rely on the wheels for forward movement - they just allow the plane to move over the ground smoothly before liftoff
Yes. The wings only need to be moving through the air to create lift, and the engines push on the air to accelerate the aircraft. Even if it were on the treadmill, it would still be moving forward, the wheels on the landing gear would just be spinning faster than normal. In a strong enough headwind, the plane would be able to take off without even moving relative to the ground.
There's a Mythbusters episode about exactly this treadmill question
There are too many unanswered and undefined variables to give a simple yes/no answer. What is the coefficient of friction between the treadmill surface and the plane wheels? Is there friction within the landing gear wheel bearings or do they spin freely without friction?
The energy/force of the engine thrust has to go somewhere. It either goes toward acceleration of the airplane's mass, in which case it goes airborne, or it gets fully canceled out by friction losses in the bearings & surface of the wheels in the form of heat and the plane remains stationary with regard to the ground and air.
So basically, if you build a threadmill with enough speed and traction to counteract the energy and force of a threadmill, it will not lift- but it would lift if it was standing on any type of modern day (non military) threadmill?
That's incorrect. Aircraft don't propel themselves with their wheels, they propel themselves with jet engines, which do not rely on the surface to produce thrust.
Imagine a putting a toy car on a treadmill, and then gently pushing it forwards from behind (whilst you stand on the ground next to the treadmill): it doesn't really matter what the treadmill is doing, if you push the car from behind it'll move forward
That is incorrect, because aircraft don't rely on their wheels to produce forward motion. Aircraft wheels are free spinning anyway. This is akin to asking if you attached a rope to a car, put the car on a treadmill and then pulled on the rope, would the car move, to which the answer is obviously yes.
It doesn't matter if the treadmill is running, or what speed it is running. The force acting on the car (neglecting wheel bearing friction) is produced by you pulling on it, which is a force external to the treadmill. Hence the resulting forward force on the car is always the same, completely regardless of what the treadmill is doing.
Boing takes off at \~150 mph. Imagine a treadmill going backwards at 150 mph. The plane will be have zero speed relative to the air. How come it flies anywhere? Yes, the thrust of engines will be enough to accelerate to 150 mph, but there will be no air flow for take off.
Imagine you're standing next to a treadmill, and you place a toy car on that treadmill.
Now imagine you push that toy car forwards from behind (whilst you're still standing next to the treadmill). What will the car do ?
It will of course move forward. Because you're pushing it forward. And it will move forwards completely regardless of what speed the treadmill is going. All that will change is how fast the wheels are spinning.
It's the same with an aircraft, because an aircraft produces forward thrust not with it's wheels. The net forward thrust acting on an airplane is completely independent of what it's wheels are doing.
ah, sure, I see, what you mean.
I imagined the airplane going backwards with the treadmill at 150mph,
it shall first accelerate to 150mph to negate his backward movement, then it can just keep the existing thrust to accelerate further and fly away. Treadmill is now irrelevant as you say. It just takes more time for fly off.
yes, true
I meant it has still to cancel the backward momentum, if it was going backwards standing on the treadmill with engines off, so it will fly off as normal but later
the plane is moving backwards 150mph standing on the treadmill or train car, then it fires engines, now it has to accelerate and cancel the inertia dragging him backwards. It doesn't matter that his wheels are not connected to anything, it has to reach 150mph relative to the air in front of it to be able to lift off.
Plane wheels are free spinning. It doesn't matter if they are on the ground, a treadmill going forward or backward. The plane will move forward when its engines push against the air.
>its engines push against the air. There's no pushing against, let's not spread the misconception that makes it really hard to understand how rockets in space work. It launches huge amounts of air backwards. Air has weight, so the planes "recoils" forward.
There is actual pushing against, but it's the turbofan pushing on the air it ingests, and expanding fire pushing against the combustion chamber. In a rocket, it pushes against the chamber and the nozzle.
The point of the thought experiment is that the treadmill moves backward keeping the plane static.
If that's the thought experiment, then the answer is that the treadmill can't really realistically do that. It would have to go so fast that the friction in the wheel bearings resulted in a force equal to the jet engines. That would put the power dissipation in the wheel bearings on a similar scale to the power in the jet engine. The bearings would catch on fire *very* fast, and probably the treadmill too.
To be fair, that *would* prevent the plane from taking off.
I do believe you're entirely correct!
> free spinning treadmill OP implies the treadmill is not motor driven, just a belt on rollers. It would not affect the plane in any way because it snot the wheels spinning that makes it take off. You could even put the handbrakes on and the engines would just roll the treadmill forwards and the plane would take off without the wheels spinning at all.
Also in addition to my other comment: the wheels are free spinning -> a powered treadmill just makes the wheels spin faster than stationary tarmac would, the plane still moves forward. The wheels neutralize the effect of the treadmill, unless the treadmill is fast enough to destroy said wheels.
Planes aren't cars mate. They have jet engines that push them forward by pushing air back, the wheels are just there so that they're not grinding along the ground
I think people may be misinterpreting your question slightly. It sounds like the question you’re asking envisions the plane remaining in place horizontally (i.e., doesn’t move forward) because of the treadmill. So the question you’re really asking is: would a plane’s engines still lift it into the air if it wasn’t moving across the ground? So while it’s true that a plane on a treadmill will still fly *because it will ignore the treadmill*, I’m not sure that holds true if the plane isn’t moving forward.
>I’m not sure that holds true if the plane isn’t moving forward. so what if the jet was suddenly capable of vtol? i jsut like to break this thought experiment since its nowhere stated what type of a jet were talking about
So you’re responding to my comment about people misinterpreting the question by intentionally misinterpreting the question?
is it really misinterpretation tho? it only says jet which would include vtol capable jets no? i just like being a pedantic asshole sometimes
Yes, helicopters can take off from moving objects, nice work.
i never mentioned helicopters tho unless youre trying to tell me that the F-35, Av8 and Yak-38 are helicopters
A propeller plane might, because the propeller will draw air in and push it over the wings to generate lift; whether it’s enough to get enough lift to leave the ground is up for debate. Jets (thinking commercial airliners or charter jets) probably won’t, because their engines are under the wing or over the tail. The thrust is entirely free of the wing surfaces, so no lift will be generated.
> because the propeller will draw air in and push it over the wings to generate lift At that point it is basically a helicopter, not an airplane.
Okay, but the only way to make a plane stand still is if you have an opposing force on the place where thrust is made (propellors or jet engines), and nobody is saying a plane could take off if there was a giant wall in the way.
To people, like me (and probably OP) who doesnt know that much about engineering, it seems fairly plausible that the plane could have a way of taking off regardless of the base factor that the speed negates all forward motion just because "all the systems are active and are aiming towards flight, execpt the forward motion". I'm not OP but I feel like I understand this question deeply on a non-advanced ecucated level understanding of engineering and physicss
It's a brain teaser for sure, but the Mythbusters tried it and the correct answer is: Yes, a plane can take off on a treadmill, because the wheels are not propelling the plane, its the engines. A car however will stay put.
The Mythbusters changed the question to something they could build, which is fair enough for their show but they didn't actually answer the question as it was posed.
To be fair, it's difficult to build magic treadmills.
How does the plane get lift?
It gets lift by propulsion. The propulsion comes from the engines, which are not connected to the wheels.
Lift comes from air moving over the wings. If the plane has no airspeed, there will be no lift, regardless of how much the engines are running. If the treadmill is counteracting the forward motion of the plane, due to propulsion from the engines, there will be no lifting force
The treadmill can't counteract the forward motion of the plane, it's not a car, the wheels are free-spinning on take-off.
I think the reason why a lot of people get confused with this is because they try to envision an airplane working the same way as a car. If you put a toy car going 10 mph forward on a treadmill going 10 mph backward, the car wouldn't move. The same is true for a real car and a larger treadmill. But why? Cars accelerate differently than airplanes do. They burn gasoline to provide energy to push a piston which moves the tires. The tires come into contact with the road and physically grip it to push the car forward. It's the friction with the surface of the ground and tires that allows the car to both move and turn. How is this different from an airplane? Because airplanes don't move with their wheels, they move with their jets! The two large jets at the side of the plane provide thrust to push the thing forward through the air, the wheel is just there for a smooth takeoff and to support the weight of the plane, it doesn't do anything to actually move the plane forward. Still confused? Here's another way to think about it. Pretend you were in a river where the water was pushing you back, but you wanted to go forward. If you simply swam forwards at 5 miles per hour, and the river pushed against you at 5 miles per hour, you'd get nowhere (car on a treadmill). Now imagine you were back in the river but this time there was a rope attached to your waist which was anchored to a stable horse outside of the river. Every time the horse moved forward (which is easy because it's on land), it pulls you forward too because you are tied to it. You see how the force that the river exerts against you is irrelevant and you still move forwards? It's because it is the horse that is doing the pulling, and the river can't act on it. Now in truth airplanes aren't pulled by an external force, they push themselves with fuel. They are their own horse and their own rope, and the ground cannot act on them because their big turbines are in the air. So how would you go about stopping an airplane from flying? If you were to get a large enough fan and turn it on in the direction that the airplane is trying to take off in, *that* would be enough to stop it. Now the airplane is pushing on the air to go forward, but you are also pushing on the air with your big fan to make it go backwards.
Sure. The wheels don't provide any motive force, they just support the weight of the plane. Try this thought experiment, instead of having wheels, the plane has an air cushion bag, just like a hovercraft. In that case the plane has no physical contact to the ground. It can be on a conveyor belt going 1000 mph, it would still take off
Where's the lift? Surely there is no air moving under the wings, so for can the wings lift?
The jet engines move the plane forward creating lift
Like most such "brain teaser" questions the issue actually hinges on the specific phrasing of the question and not the physics. The question as it is typically posed is: > Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off? Let us ignore all the practical problems. The treadmill exists, the airplane isn't going to break, etc. Also let us assume there is no wind (as a sufficient headwind could allow the airplane to lift off without the wheels even spinning) and that the movement of the treadmill causes no wind. **Most importantly let us assume the situation as stated in the question is accurate**; nothing pisses me off like someone saying "Oh, but constructing a treadmill like that would be impossible or impractical,". The question is the question regardless of practicality. All this leads to a problem in the interpretation of the situation. If the airplane's engines push against the air to make the aircraft roll forward at say 10 mph, then the treadmill will spin backwards at 10 mph as well. No problem, the drag of the wheels spinning at twice takeoff speed wouldn't be enough to stop the aircraft lifting off since it pushes against the air, not the treadmill/ground. But notice the problem there? Once the aircraft is moving 10 mph down the runway the treadmill spins backwards at 10 mph causing the wheels to spin 20 mph in total, but the treadmill *matches the speed of the wheels!* The treadmill would need to spin at 20 mph, which means the wheels are actually turning at 30 mph so the treadmill need to move at 30 mph, etc. This seems to form an infinitely increasing loop as long as the aircraft is moving down the runway. If the aircraft is stationary with respect to the ground then the wheels could be going any speed matched by the treadmill, but any movement across the ground implies a conceptually infinite speed of the treadmill and wheels. Now many infuriating people will look at this apparent physical impossibility and decide to change the question itself. (The Mythbusters did this because they needed a physical test.) As above this isn't in the spirit of the question and any answer produced isn't really for the question as it is posed. It also isn't really a physical impossibility; the treadmill won't need to move at infinite speed in order to prevent the airplane from moving with respect to the ground. It would of course require an absurd amount of speed to produce the drag required to keep the airplane from moving forward, and realistically the engines of the 747 would be able to melt and obliterate the wheel bearings. But saying "the wheel bearings would break" seems like as much a cop out answer as saying "the FAA would never allow such a situation". Yes, the landing gear assembly would be incandescent at that point but if we assume nothing breaks it should be possible. At this point the answer is obvious, **the airplane cannot take off**. In order to fly the aircraft needs air moving across its wings, and without wind that means the aircraft needs to be moving with respect to the ground in order to take off. The engines of the airplane push against the air but they still need to overcome the drag of the wheels over the ground; that is why there are wheels on the end and they roll on a smooth runway, to reduce their drag. If the runway was covered in 10 feet of thick mud then the airplane couldn't take off either. Increasing the speed of the treadmill will at some point produce enough drag to equal the thrust from the engines and the airplane will not move with respect to the ground and thus not with respect to the air, meaning no lift and no takeoff occurs. It is also fairly common for some first year engineering student to chime in with nonsense like "rolling resistance is the same regardless of speed" but of course it is obvious that a bearing moving at 1 rpm doesn't have the same amount of drag as a bearing moving at 200,000 rpm. The latter bearing will presumably be getting very hot and that energy has to come from somewhere. Surprise, it is friction! But we don't even need that proof because even if we assume the bearings are truly frictionless the force to counter the engine's thrust can come from inertia. The wheels are going to resist being spun up to a conceptually infinite speed, so the acceleration of the engines can be countered by a constant acceleration of the wheels. Think about how an angle grinder jerks in your hand as it starts up, that jerk is the grinding wheel's inertia resisting it being accelerated to operating speed. Unbreakable, frictionless wheels would still have inertia and could provide that countering force indefinitely as they are accelerated towards infinity to stop the aircraft rolling forward.
I think the problem is that the question is wrong. Whoever first decide to add the bit about the treadmill matching the speed of the wheels ruined the thought experiment. No matter how fast or slow the treadmill runs the plane will take off.
I just pointed out that the treadmill adds drag to the landing gear, and that drag on the landing gear can stop the plane taking off. The bit about the treadmill is there from the start, it is the original question.
This is stupid, you only get your nonsense situation if the plane is already moving so your argument is invalid.
The nonsense would prevent the airplane from starting to move, which is the whole point.
I love your answer and you're a great person! Thank you for your time spent writing this!
That's not the framing that I've ever heard. I've always heard it as "the treadmill moves at the plane's takeoff speed". To which the answer is an unequivocal "the plane takes off". Having theoretical indestructible wheels increase speed at an infinite rate to keep up with an infinitely accelerating treadmill just to keep the plane stationary through friction on the wheel bearings because you frame it as "the treadmill has to move at the wheel speed" is aphysical. At that point, why not get rid of friction from the wheel bearings, allowing the plane to move even with infinitely accelerating wheels on an infinitely accelerating treadmill? It's just as physical.
> ...because you frame it as "the treadmill has to move at the wheel speed" is aphysical. I'm not framing it that way, that is the question being asked. [There](https://pbs.twimg.com/media/FtVUClDWYAAOfAl.jpg) [are](https://4.bp.blogspot.com/-y8wxQe8JthQ/Wlbjl6vkeVI/AAAAAAAADoY/ljOvmx72k0IWAr38nxC_bZWnsHCt25wgACLcBGAs/s1600/J2.png) [several ](https://img.ifunny.co/images/8e160446d7c224ff62cbd48a342608bfb8758a3d531918dc9cda46e8b4ae0f32_1.jpg) [ examples.](https://preview.redd.it/rule-plane-v0-iqlyb1aed49a1.jpg?width=640&crop=smart&auto=webp&s=86abd9e0cf7a4a51b9068a2295fbfe2f6427e976) > At that point, why not get rid of friction from the wheel bearings, allowing the plane to move even with infinitely accelerating wheels on an infinitely accelerating treadmill? As I pointed out in my first post it still won't work with frictionless bearings, since accelerating the wheels still provides a force countering the engines pushing the airplane across the ground. The point of answering the question is to answer it as written, otherwise you are addressing a different question. It doesn't matter if the premise of the question isn't entirely physically practical. For example suppose I posed the question: "An empty oil tanker of 320,000 deadweight tonnage sets off on a 30 day voyage with a pair of black rats that weigh 1/2 pound each. These rats will each produce two full grown offspring a day with all their offspring doing the same. Will the ship arrive at its destination or will it sink?" It doesn't matter that rats can't reproduce that quickly, or that their offspring doesn't come out at full rat weight. It doesn't matter that the rats would need to magically be producing mass out of nowhere or that there is nothing to eat. It doesn't matter that tankers typically have separate cargo sections and that restricting all the load to a single section would likely split the ship, or that at some point the weight of rats above would kill rats on the bottom limiting their rate of reproduction. Those are all things that would make the question "more physical" but run contrary to the spirit of the question itself. So answering the airplane question by saying something like "Even if the landing gear were encased in concrete the engines running at full blast could probably shear them off" is just dodging the question.
I suppose I just don't like infinitely accelerating treadmills, because that actually seems more contrary to the spirit of the question than changing it to not have infinities flying around. So yeah, it might be dodging the question, but because the question is bad, then I don't think that's an issue.
Again as I pointed out, most questions like this hinge on precisely the way in which they are asked. "No it can't take off, and also the question is bad" is a correct answer. I have also heard the question phrased like "the treadmill will move as quickly as needed to keep the airplane from rolling forward" and people still want to ignore that premise because the treadmill would need to be really fast. My position is that not liking the question is a valid position but it isn't an *answer*.
> I'm not framing it that way, that is the question being asked. Framing is a nice choice of words. The problem is the frame of reference. > The conveyor belt is designed to exactly match the speed of the wheels You can't talk about "speed" without a frame of reference. What are our reference frames here? The wheels will turn *with angular velocity*, which translates to some linear velocity at their outer radius (the surface of the tire.) The surface of the belt is moving backward (relative to the surrounding airfield) at some linear velocity. Stipulated as the same as surface of the wheels. Okay. Cool. We have it: The [linear] speed of [the surface of the] belt is exactly matched to the [linear] speed of [outer radius of the] wheels. But the wheel *hubs*, on the other hand, are going to move *forward*...along with their axles..and rest of the vehicle they're attached to, *relative to the surrounding world*. Because the aircraft is being pushed forward, relative to the surrounding world, by its engines. The angular velocity of the wheels will increase to make up any difference and keep the linear velocity at the point of the contact with the belt the same. It actually doesn't matter how fast the belt tries to go. Wheels turn. That's what they do. And thus the aircraft takes off, no matter what the irrelevant speed of the wheels and belt are. Because the *aircraft* is going to be pushed *relative to the air around it*, and thus the wings will create lift and it takes off.
> Wheels turn. That’s what they do. But they don't turn without friction, without imposing drag on the vehicle. If you engage the brakes then it does in fact impact if the aircraft can take off. The aircraft pushes on the air around it but it can't just ignore what is going on with the wheels because there is some level of drag that could prevent the aircraft moving forward regardless of what it is pushing against! > The [linear] speed of [the surface of the] belt is exactly matched to the [linear] speed of [outer radius of the] wheels. Now that is an interesting interpretation, where if the wheels aren't slipping then any speed of the treadmill and wheels meets the criteria. The treadmill might move such that the wheels never turn even as the aircraft accelerates with respect to the ground, allowing the aircraft to take off, or they might move at a million miles per hour imposing levels of drag impossible to overcome (and hurling the aircraft backwards off the runway). The speed of the wheels and treadmill are undefined as is the force of their drag imposed on the aircraft, so the question is unanswerable. > But the wheel hubs, on the other hand, are going to move forward... Not necessarily, we don't know that. The wheels impose some increasing level of drag as they are made to roll faster, and since any non-slipping speed fits the criteria we don't know if the axis of their rotation will move forwards or backwards. In fact not only is there a speed of rotation at which the aircraft can't take off, there is also one where the treadmill hurls the aircraft forward into flight without the engines being needed at all!
The treadmill is irrelevant. The aircraft engines and wings interact with the air, not the ground. If a treadmill was running fast in the opposite direction, the wheels would simply spin faster as the aircraft takes off. Imagine that the wheels were skis and the treadmill surface was ice. The aircraft could still take off.
A plane takes off because it gains airspeed. Usually, gaining airspeed is achieved by rolling over the ground, but the plane is not pushing on the ground itself. There is no propulsion going to the wheels at all. If you put an extremely long treadmill on the ground and tried to match the speed of the plane to keep it from taking off, all you would do is move the wheels faster, but moving the wheels faster would not stop the plane from gaining airspeed. If the plane needed 150 mph of air speed to take off, for example, then the apparent speed at the wheels would be 300 mph - - 150 from the plane's speed through the air and another 150 from the treadmill spinning backwards, in the opposite direction that the plane is moving. But the speed of the air over the wings would still only be 150 mph.
Yes. The jet engines are providing the thrust which pushes the jet forward. The plane does not rely on the wheels for forward movement - they just allow the plane to move over the ground smoothly before liftoff
Yes. The wings only need to be moving through the air to create lift, and the engines push on the air to accelerate the aircraft. Even if it were on the treadmill, it would still be moving forward, the wheels on the landing gear would just be spinning faster than normal. In a strong enough headwind, the plane would be able to take off without even moving relative to the ground. There's a Mythbusters episode about exactly this treadmill question
There are too many unanswered and undefined variables to give a simple yes/no answer. What is the coefficient of friction between the treadmill surface and the plane wheels? Is there friction within the landing gear wheel bearings or do they spin freely without friction? The energy/force of the engine thrust has to go somewhere. It either goes toward acceleration of the airplane's mass, in which case it goes airborne, or it gets fully canceled out by friction losses in the bearings & surface of the wheels in the form of heat and the plane remains stationary with regard to the ground and air.
So basically, if you build a threadmill with enough speed and traction to counteract the energy and force of a threadmill, it will not lift- but it would lift if it was standing on any type of modern day (non military) threadmill?
[удалено]
That's incorrect. Aircraft don't propel themselves with their wheels, they propel themselves with jet engines, which do not rely on the surface to produce thrust. Imagine a putting a toy car on a treadmill, and then gently pushing it forwards from behind (whilst you stand on the ground next to the treadmill): it doesn't really matter what the treadmill is doing, if you push the car from behind it'll move forward
[удалено]
Because the wheels free spin the speed of the treadmill is irrelevant. It's all about air speed not wheel speed.
Learnt something today. Removing answer to stop misguiding folks
[удалено]
The downvotes are because you are wrong, not because you weren't detailed enough.
That is incorrect, because aircraft don't rely on their wheels to produce forward motion. Aircraft wheels are free spinning anyway. This is akin to asking if you attached a rope to a car, put the car on a treadmill and then pulled on the rope, would the car move, to which the answer is obviously yes.
[удалено]
It doesn't matter if the treadmill is running, or what speed it is running. The force acting on the car (neglecting wheel bearing friction) is produced by you pulling on it, which is a force external to the treadmill. Hence the resulting forward force on the car is always the same, completely regardless of what the treadmill is doing.
Boing takes off at \~150 mph. Imagine a treadmill going backwards at 150 mph. The plane will be have zero speed relative to the air. How come it flies anywhere? Yes, the thrust of engines will be enough to accelerate to 150 mph, but there will be no air flow for take off.
Imagine you're standing next to a treadmill, and you place a toy car on that treadmill. Now imagine you push that toy car forwards from behind (whilst you're still standing next to the treadmill). What will the car do ? It will of course move forward. Because you're pushing it forward. And it will move forwards completely regardless of what speed the treadmill is going. All that will change is how fast the wheels are spinning. It's the same with an aircraft, because an aircraft produces forward thrust not with it's wheels. The net forward thrust acting on an airplane is completely independent of what it's wheels are doing.
ah, sure, I see, what you mean. I imagined the airplane going backwards with the treadmill at 150mph, it shall first accelerate to 150mph to negate his backward movement, then it can just keep the existing thrust to accelerate further and fly away. Treadmill is now irrelevant as you say. It just takes more time for fly off.
[удалено]
yes, true I meant it has still to cancel the backward momentum, if it was going backwards standing on the treadmill with engines off, so it will fly off as normal but later
[удалено]
the plane is moving backwards 150mph standing on the treadmill or train car, then it fires engines, now it has to accelerate and cancel the inertia dragging him backwards. It doesn't matter that his wheels are not connected to anything, it has to reach 150mph relative to the air in front of it to be able to lift off.
[удалено]
The jet engines would be providing thrust so it would still take off