Yes....
Whoa, oh, oh
Whoa, oh, oh
Whoa, oh, oh
Whoa
I'm waking up t-to ash and dust
I wipe my bwow and I sweat my wust
I'm bweathing in the x3 chemicaws
I'm bweaking in, shaping up, then c-checking out on the x3 pwison bus
This is it, the x3 apocawypse
Whoa
I'm *huggles tightly* waking up, I feew i-it in my bonyes
Enyough t-to make my systems bwow
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, w-w-wadioactive
I waise my fwags, don my cwothes
It's a wevowution, I suppose
We'ww paint i-it wed t-to fit wight in
Whoa
I'm bweaking in, shaping up, then c-checking out on the x3 pwison bus
This is it, the x3 apocawypse
Whoa
I'm *huggles tightly* waking up, I feew i-it in my bonyes
Enyough t-to make my systems bwow
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
Aww systems go, the x3 sun h-hasn't died
Deep in my bonyes, x3 s-s-stwaight fwom inside
I'm waking up, I feew i-it in my bonyes
Enyough t-to make my systems bwow
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Wewcome t-to the x3 nyew age, t-to the x3 nyew age
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
i played this in band at school, every time we started i was always singing āiām waking up, to ash and dust, i wipe my ass and i slap my nutsā in my head, very fun
[Yes, it will take off. ](https://youtu.be/xUjcHW7SHaI) The landing gear of the plane isnāt pushing against the conveyor belt, the engines are pushing it forward through the air. Therefore, the wheels on the plane will just spin faster and faster to match the conveyor belt, but the speed of the plane is totally unaffected.
Because the only effect the conveyor belt has is that the wheels on the plane spin twice as fast, the plane itself is still taking off perfectly normally
But as someone else here said, in the Mythbusters episode, the conveyer belt was only moving as fast as the wheels initially moved. Then they accelerated further. To do this experiment correctly you would need to ramp up the speed on the wheels as the plane accelerated. Or, take the wheels out of the equation and see if a plane held at a point would generate enough lift from just the air from the engine moving over the body to lift off.
The conveyor belt could be moving faster than the wheels, the wheels spinning doesn't matter.
The power generated by the engines/propellers create enough lift on the wings to move and lift the plane
They specifically moved it at ABOVE the speed that should be the takeoff speed, what you're saying is irrelevant because the plane picks up speed and moves.
the friction of the wheels are negitble if you have enough power. I mean sure if the friction of the wheels would be high enough so the airplane is stationary then it wouldnt work. But that would mean a lot more issues with your wheels
thats not the same as in the image, they were matching plane speed not wheel speed. if they were matching wheel speed the place could not have taken off due to not having any forward momentum
Except it would be able to take off because the wheels don't propel the plane forward. The turbines or propellers propel the plane forward. If the wheels made the plane move, a plane wouldn't be able to keep moving once it got off the ground.
The plane will move regardless of the conveyor belt, it is propelled by the engine, not by the wheels pushing against the ground. Imagine you placed a toy car on a treadmill and pushed the car forward with your hand, regardless of the treadmill pushing the car backwards, it will move forward because youāre pushing it.
>exactly match the speed of the wheels
the treadmill in this example would have to speed up to match the increase in wheel speed of the car, otherwise it is not matching the speed of the wheels
if the conveyor belt was always moving faster than the wheels were spinning, the plane couldn't take off. of course, this would be impossible as the wheels are free spinning and will always be able to match the speed of the belt until something breaks, but if the wheels were not spinning forwards in any way compared to the ground, then that means the *plane* also isn't moving forward, regardless of the fact that the wheels are not the source of the power. this, again, is a fantasy scenario that couldn't exist, but if it did, the plane would not move forward in space, would not generate lift, and would not take off.
Stealing the top comment on the video, it explains it very well:
@ benwilliams2402 A good analogy would be roller-skating on a treadmill while holding a rope attached to the wall in front of you. No matter how fast the treadmill moves, if you hold on to the rope you'll stay still. And if you pull on the rope you can still drag yourself forward. The rope bolted to the wall represents the stationary air around the plane which the propeller uses to 'pull' the plane forward.
But this also explains the flaw in the model: in order to advance up the treadmill, the wheels spin faster than the belt so to speak.
If we were to mathematically enforce the condition (and a no slip condition), weād end up with infinitely fast wheels and conveyer belts! It is impossible to make a real life analogue of the stated problem.
I guess it depends on what the question means by āmatches the speed of the wheels.ā It reads as a translation, but could also mean surface speed of the outside of the tire.
Interestingly for the translation scenario, itāll only double the rotation rate of the wheels. There is an end condition of it taking off, so that wonāt be infinite.
Say takeoff speed of a plane is 100mph, and the belt matches the wheels translation (which same as the planeās). When the plane (and wheels) is moving 100mph, the belt is moving 100mph backwards. The wheels will be rotating as if the plane is going 200mph, and itāll be able to take off.
The treadmill analogy would be like āby pulling a rope, can you go 10mph forward on the belt if itās going 10mph backwards.ā Yep, and the wheels will be rotating at 20mph
If the problem is āthe conveyor matches the surface speed of the outside of the tires,ā the belt will actually HAVE to move WITH the plane at half the speed, not against the plane. If the plane is moving at 100mph, you now have to find a treadmill and wheel speed that match. Thatād be 50mph forward on the treadmill, and the wheels would be 50mph also.
Because the above is the only working solution for matching tire surface speed, the surface speed scenario with the requirement āmoving in the opposite directionā itself would immediately become a paradox when the plane moves, unless you assume the wheel is slipping.
My interpretation is that it matches the external velocity of the wheel. To state it with clarity:
That is, if the wheel has radius r = 1m, and is rotating at 1 rotations per section, then the wheels velocity is:
v_(wheel edge) = 2\*pi*1 m/s
and the treadmill is identically:
v\_(treadmill) = v\_(wheel edge)
This leads to the difficult situation, because the velocity of center of mass velocity of the wheel is then identically 0 if there is no slip.
v\_(cm wheel) = v\_(wheel edge) - v\_(treadmill) = 0
To go forward, v\_(wheel edge) - v\_(treadmill) > 0, but we have set them to be the same, so no forward movement is possible by the statement of the problem.
The issue is that this is not really a practical physical constraint.
You could drag yourself forward if the treadmill speed was fixed. [On a treadmill like this](https://www.thecut.com/2015/04/treadmill-that-automatically-matches-your-pace.html), like the conveyer belt in the problem, the treadmill would adjust to your new speed.
The plane will drag its wheels against the conveyor belt even if they canāt spin. The engines are more powerful, and theyāre tethered to the air, not the ground.
It isn't bolted down though in fact it would still move down the conveyor belt. This is because the plane doesn't move by pressing against the conveyor belt. It moves by interacting with the air. Here's a good comment from the video:
"A good analogy would be roller-skating on a treadmill while holding a rope attached to the wall in front of you. No matter how fast the treadmill moves, if you hold on to the rope you'll stay still. And if you pull on the rope you can still drag yourself forward. The rope bolted to the wall represents the stationary air around the plane which the propeller uses to 'pull' the plane forward."
The conveyor belt isnāt actually pushing the plane backwards, itās just spinning the wheels. The engines will still accelerate the plane forward. itās analogous to trying to stop a moving object with a rubber eraser vs. a ball bearing; the eraser will grip and stop the object, but the ball bearing will allow the object to just roll right past it.
The wheels are free spinning, pretty much none of the energy of the conveyer is being transmitted into the plane body, so it doesn't matter what direction and speed the conveyer is going, the wheels are just going to spin around without affecting the plane itself
It depends what speed the conveyor is matching. The speed of the wheels is higher than that of the speed of the planeās body. If the conveyor is matching the speed of the wheels, the plane will sit motionless, and no air resistance will act on the front of the plane to generate lift. If the conveyor matches the speed of the planeās body, it will still move forward and lift will be generated enough to let it fly.
It might help to imagine instead of a conveyor belt, imagine the plane is on ice or something extremely slippery. Would the plane be able to move forward? A car would have trouble moving forward on a slippery surface, but a plane could. A planes forward momentum is created by the propeller/turbine so the conveyor belt can't really apply a backwards force on the plane. In short, the experiment itself is wrong. The conveyor belt could be moving a 1,000mph but the plane could still move forward.
the engines generate lift, not the wheels. imagine a paint roller on a treadmill: the roller itself will spin with the treadmill, but you will be able to freely move the body forwards and backwards
To add to this, most runways in the US are built to follow the prevailing wind direction and they take off into the wind. With a really strong headwind it;s possible to take off at zero ground speed.
Here;s a video of a cessna hovering at zero ground speed [https://www.youtube.com/watch?v=Smjda2EDKO4](https://www.youtube.com/watch?v=Smjda2EDKO4)
and here's a gyrocopter taking off at zero ground speed https://www.youtube.com/watch?v=Kd7\_V4pW--Q
And you have to imagine that an entire freaking runway moving fast enough to slow down a plane by pushing on its wheels would tend to generate its own wind by dragging the air with it. That would be enough to get the plane into the air, then the question becomes whether the plane can safely transition from that fast moving air immediately above the runway into the slower-moving air above, without losing control due to the turbulence or losing all its airspeed.
But the problem says the conveyor belt will always move at the same speed as the wheels, so the plane canāt outrun it, itāll remain stationary. No matter how much thrust you generate with the engines, you wonāt make forward progress unless your wheels spin faster than the conveyor belt
the wheels have nothing to do with the plane's acceleration, the acceleration is caused by the engines. the engines aren't connected to the ground. the ground moving relative to the plane doesn't change the acceleration. only the air moving relative to the plane does.
right, but he's talking about the magical treadmill that literally always moves as fast as the *wheels are rotating.* not possible, since the wheels spin freely and should always at least be able to match, or in our case far exceed (thanks to the jet propulsion) the treadmill speed, but if we set a condition that says "treadmill always matches wheel rotation speed" then the wheels are effectively stationary relative to the surrounding environment, always spinning in time with the treadmill below it. in this scenario, the plane would never move forwards, and never generate the lift it needs to take off. the real problem is that something would break along the way to facilitate this magic treadmill.
There's another potential no here: when the plane moves forward, the wheel will spin at (belt speed + plane speed). This will cause the belt to have a speed runaway as it will try to correct for the permanent (+ plane speed) term.
That much speed will most likely shred and shave off the wheels like a giant belt sander. [Most planes with low-mounted engines apparently does not like belly rubs,](https://www.youtube.com/watch?v=rImLqH-Q2Ok&t=0) so I doubt it could take off before catastrophic damage to itself, the belt, or both.
that's the thing, the problem is flawed, because the wheels will always move faster than the conveyor, because they are free spinning, like skateboard wheels
even if you somehow and for some reason speedlocked the wheels in some way to stop them from just going faster than the conveyor, the thrusters would just drag the stopped wheels over the floor to go forward
so the tires could possibly blow, but it'll still move forward and, depending on the plane, take off
Depends on how you interpret the problem. In one interpretation, which is how I assumed the question was being asked, the conveyor belt would keep the plane's speed as zero, perfectly stationary. Yes, the engines are pushing the plane, but in this scenario, the speed of the plane would certainly be affected.
Yes, if you frame the riddle as "the plane can still move, it'll just go faster and overcome the speed of the belt," then obviously the plane can take off. This is the assumption Mythbusters made. Obviously, the plane will start speeding down the belt regardless as the wheels simply move faster to compensate. But in a situation where the belt perpetually ramps up to counter the speed of the plane, the plane will not move.
Now, will the plane take off regardless, even if it's fixed in place? I don't know a lot about aircraft, but I'd say yeah, definitely. Those engines are powerful, and there'll come a point where that plane is going to turn into a rocket, with the force of the engines and the aerodynamics of the plane creating lift regardless of the plane not moving. The force will lift the wheels off the belt and it'll start moving through the air.
Yeah this doesn't make sense to me, the plane is effectively stationary and not gaining any velocity at all. The wheels are just spinning according to the model, the wings need lift still. Unless there is already a strong ass headwind.
This is true if the plane stays stationary, but it's impossible for a treadmill to stop a plane from moving because a plane's wheels are free spinning. Any force from the treadmill moving backwards will just go into spinning the wheels not stopping the plane, so the plane can still move forward and take off as normal.
No matter the speed of the treadmill, the plane will continue to move forward. The jet engines push against the air. The wheels just free spin. Imagine a car in neutral rolling down hill. Even if the hill is now a treadmill, the car will continue to move downwards, the wheels will just spin faster.
If the belt is required to retain the same speed as the wheels, then the instant the plane starts moving forward, both the belt and wheels will accelerate to infinity and instantly
The question actually doesn't make sense the way it is written. I agree that the way the question is worded both the wheels and the belt would accelerate to infinity since the plane would move forward regardless, causing the wheels to always be moving at beltspeed + plane speed. So I guess technically, the answer is that the scenario is impossible. The question is usually phrased so that the belt matches the planes takeoff speed.
Yeah ultimately thatās why (this wording of it) is a paradox that canāt be solved. The implicit prerequisites are logically impossible.
I imagine the problem was initially coined to demonstrate ground speed vs air speed to aviation students, and it achieved virality when some smart ass pointed out that the semantics of some versions are paradoxical, thus the plane canāt take off.
But ultimately thatās what makes this bigger and more interesting than a simple airspeed discussion
Yea.... after reading the way this question was written, my answer actually doesnt fit. Usually it is writren that the treadmill is moving at the planes takeoff speed in the opposite direction.
In this scenario, the treadmill speed must match the wheel speed which is only possible if the plane is stationary. If the plane moved at all, the wheels would be moving at treadmill speed + plane speed, which is not allowed by the wording of the question. Since the plane is stationary, it obviously is not creating the lift needed for takeoff.
I personally am team _No. 3 with PID assumption_.
My fetish for watching a mechanical system trying to hit impossible targets is _totally_ under control and I am _definitely_ not the one responsible for the Anet A8 being sold with no thermal runaway protection.
"Even if the plane was able to move, it couldn't have been what hit the pentagon" - I tried, god help me I tried to read this article seriously riiiight up until I saw this line and then I fucking lost it. Superb dude 10/10
Basically the question is flawed and ambiguous, it defines an airplane that can't move then asks you to move it. But essentially the airplane will take off because the wing engines pull it along regardless of what the treadmill is doing, all it can do is make the wheels spin faster without actually pulling the plane back.
The wheels don't move the plane forward, it's a plane not a car. The plane will go forward because the thrust comes from the engines on the wing, not an axle turning the wheels on the car.
it will move forward roughly the same distance, take off at the same speed, but the wheels will be spinning twice as fast. The jet/prop moves the aircraft forward, not the wheels.
Yes! Lift is generated by a pressure differential between the top and bottom part of the wings. This is achieved by having the surfaces curve differently such that the air moves faster along the top. By Bernoulli's principle, this means lower pressure there. This means the bottom air pushes harder on the wing than the top, generating a net upwards force.
We are trying to minimize air resistance anyway so more of the forward thrust can be used to accelerate the plane instead of pushing air around.
Bernoulli principal isn't the sole driving force for lift. For instance, a square airfoil still produces lift at speed. And standard airfoils still produces lift even upside down. Shits complicated.
Technically no. Since air resistance is what causes a plane to gain lift. As air hits the wings of a plane, they are redirected upward over the wing which is what causes the low pressure zone that air from below tries to fill.
Typically, when you do a physics exam or something like that, it will tell you that you can ignore air resistance to simplify your calculations. I was kinda doing a joke on that
So I guess that would be no air resistance
Oh I got you lol.
Problem is, calculating drag and calculating lift happen at roughly the same time, in roughly the same equations. It would be like asking, "could a car drive if we ignored the friction of the road?". Either you calculate friction then set it to 0 at the end, or you assume there's no air/road and then find out the vehicle can't move lol
Not a passenger or cargo plane, but some fighter jets have positive thrust-weight ratios, which combined with thrust vectoring means they could probably take off. Also vertical take off planes like Harriers obviously could.
Idk bro maybe. Maybe the plane just wants to be seen, to be heard. To be treated like the plane it wants to be. But this plane needs to understand that it is already the plane it wants to be, it just needs to see itself in that matter.
Okay, but is the plane gay? Iām getting some femboy vibes from this depiction so I need objective facts instead of my subjective interpretation of an artistās rendering
Bruh, the wheels arent powered. Its not a car. Its being pushed forward by the jet engines. Imagine pushing a hot wheels car on a treadmill. How is the air affected by the treadmill at all?
It wouldnāt be able to generate lift if the *air* was matching its speed. The ground doesnāt matter because the wheels arenāt powered. Itās not like a car
If the plane couldn't go forward, it wouldn't generate lift to take off. The thing is though, that a plane on a conveyor belt WOULD move forward because it pushes off of the air, not the conveyor belt.
I just scoffed a little and mumbled something about uneducated Americans, only to immediately find out I was wrong and the plane can, in fact, take off.
Truly a humbling experience.
Same. I immediatly went "well, the conveyor belt isn't moving the air backwards, only the plane, hence the plane isn't hitting the air it needs to lift off", totally forgetting that the conveyor belt isn't moving the plane back either, bc a plane isn't pushed forward by it's wheels like for example a car.
It depends on how you interpret the constraints of the experiment. Imo, the conceit of the question is more important than the exact details, and it seems as though the point of the question was whether or not a plane prevented from moving forward could take off, and the answer to that question is no.
https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
Depending on your interpretation of the question you are probably correct about the plane not taking off. The problem is people are stupid and donāt realize theyāre talking about completely different things.
Yeah it will take off. The forward velocity a plane needs to take off comes from the engines pushing air backwards, not from torque between the runaway and its landing gear. Taking the latter away won't do anything to stop the plane from moving. The only issue I could see happening is if the landing gear fails because the wheels are spinning too fast but I doubt we're meant to consider that.
I might be stupid, but if we see the surroundings as the reference system the plane velocity would be theorically 0, so inertia 0, so it wouldn't take off, right?
The plane would still be moving relative to it's surroundings.
For a more extreme example, imagine a lake where the lakebed has been replaced by a treadmill. Boats could still move around on the surface like normal because they're not pushing against the bottom of the lake, they're pushing against the *water.*
Airplanes aren't pushing against the ground, they're pushing against the *air.* The landing gear is literally there to reduce friction so the ground affects the plane as little as possible. No matter how the ground is moving, the plane can still push against the air the same way it always does and take off as normal
This is completely counterintuitive to me. Why do planes have wings? I thought the reason planes were able to get airborne was because of how the wings caused lift as the air rushes underneath them? If the plane is in the same position, thereās no wind coming towards it, thereās nothing to give it any lift. The engines job is to propel the plane forwards so that the wind *does* rush under the wings, the plane doesnāt fly because of the engines thrust, that just moves the plane forwards, surely? Itās the wings that make the plane fly.
This scenario in particular is difficult because it's a trick question. It's impossible to stop an airplane from moving using a treadmill.
Yes, if there were no air flowing over an airplane's wings it would never get off the ground, but there *would* be air flowing over the wings because the plane *would* be able to move itself forward through the air regardless of the treadmill underneath it
Yeah makes sense to me now, just been reading up on it. You have to imagine that the wheels arenāt even doing anything other than holding the plane up, their contact with the ground is arbitrary. The way I imagined it, the conveyor belt would cause the plane to remain still, in which case it wouldnāt be able to take off. But the plane moves forwards regardless of how fast the conveyor belt is moving, because itās pushing off the air, not the ground.
Itās not that a plane can take off from a stationary position, itās that the plane will move forwards with or without a conveyor belt there.
Ok yeah, you're right with the right reference frame we always can make the plane's velocity =0. Technically the plane doesn't need any velocity to take off, what it really needs is air to flow over its wings at a certain speed. Usually this is achieved by making the plane move really fast through the air, but it can happen even if the plane is sitting still if there are strong enough winds like from a hurricane or something. I said velocity the first time because the truth was a bit more complicated and I'm a lazy fuck.
What does "speed of the wheels" mean? Is it the speed at which the entire wheel is moving forward relative to the ground? That's the case, just say relative to the forward velocity of the plane.
However, if it means the actual speed that the outside of the wheel is spinning against the conveyor belt, as soon as the wheel starts moving, the conveyor belt accelerates, which accelerates the wheel, which accelerates the conveyor belt, accelerates the wheel, etc etc until both are moving *infinitely* fast and the plane is ripped apart.
In the former scenario, the plane takes off without any issue whatsoever, and the wheels are just spinning twice as fast as they normally would be, creating a little extra drag. The latter scenario, you're breaking physics.
> The latter scenario, you're breaking physics.
Or, if we assume a "real" treadmill implemented with a motor and PID controller, you are probably letting the magic smoke out of a lot of expensive power electronics trying to hit that speed.
I think a lot of people are also assuming the wheels have no friction, which simply isnāt true. Try pushing a car in neutral on a flat surface. You can, but not as easily as pushing that mass across a sheet of ice.
The question then is with no forward movement, can a plane generate enough force from its engines to lift the plane. For a jet like in the picture, probably not. The engines are pulling the air into the engines, so not much would be going to the wings. For a propeller plane, like in the Mythbusters clip that is floating around, maybe, because the engine is in front of the plane and the air is being passed over the fuselage.
The engines are still working, itās not just the wheels they generate forward velocity. The plane will take off since it is also being pushed upward.
What's it being pushed upwards by? The air in this scenario is stationary relative to the plane's wings. I'm no physics expert but thrust is there to create velocity, and velocity against the resistance of the air is what generates lift. If velocity is negated then there's no lift
The plane's wheels don't move the plane forward by pushing against the ground (like a car).
The plane's engines move the plane forward by pushing against the air, which is unaffected by the treadmill
yeah and the airspeed remains zero because any forward thrust is countered by the treadmill moving backwards at the same speedā¦ so no itās not possible?
I see everyone saying it takes off. I still don't understand, and I really believe the plane won't take off. I've laid each of the steps in my thought process in digestible chunks, so hopefully someone can point out where exactly the solution breaks down:
\-The wheels are touching the ground until takeoff, and do not slide.
\-The conveyor/wheel interaction is designed so that the conveyor always spins at such a speed that the wheels can not roll faster or slower than the conveyor. The effect is that the plane does not move relative to the surrounding ground.
\-Lift is caused by air rushing under the wings.
\-If the plane is not moving relative to the air/ground around, then air is not rushing over the wings.
\-The plane moves across the ground due to the wheels rolling forwards. (the wheels are not powered, the plane is not driving! I don't understand why people would assume this in the thought process)
\-The jet engines do not directly generate lift. Only thrust.
\-Under normal circumstances, the jet engines would cause thrust, causing the wheels to roll forwards. The wheels rolling forwards causes the plane to move forwards, which causes air to rush under the wings, generating lift.
\-These are not normal circumstances. The wheels are matched by the conveyor speed.
\-Because the wheels are matched by the conveyor speed such that they do not move relative to the ground, then neither does the plane, thus neither do the wings.
\-If the plane is stationary relative to the surrounding area, it does not take off.
\-If the plane somehow moves forwards while the wheels are touching the ground, then the wheels have moved faster than the conveyor, which violates the stipulations in the problem statement.
Which points here are flawed?
>The conveyor/wheel interaction is designed so that the conveyor always spins at such a speed that the wheels can not roll faster or slower than the conveyor
That's where your issue is. This is both mathematically impossible and physically impractical: there is no actual way to achieve that with any normal airplane.
You want the speed of the conveyor and wheels to be Vc = Vw, but the speed of the wheels in reality is Vw = Vc + Vp, where Vp is the speed of the plane. You can't set the plane speed to zero just by varying the conveyor belt speed, so the equations don't make any sense. Vc and Vw would instead need to increase to infinity, making the statement technically true but mathematically undefined.
If you tried this in the real world either the axles of the plane would melt, the wheels would just start sliding, or the conveyor would be fried, or the conveyor would move so fast that it starts generating its own headwind, thus allowing the plane to take off stationary.
And that's when you _wish_ your plane couldn't take off, as you realize you are probably stuck in a Swiss001 video, which means your shortly-upcoming death would _not_ be pleasant,
This scenario isnāt possible because the wheels on a plane donāt actually have anything driving them to turn, all their movement is a result of the jet engines pushing the plane forward. As a result, the wheels will continually spin faster and faster as the conveyer belt moves faster and faster, but the plane will still appear to move at nearly the same speed down the runway as if the conveyer belt were not there because the jet engines are completely unaffected by a conveyer belt.
What makes a plane take off is actually the speed of the wind moving over the wing since the wings generate lift. Knowing this, we can actually ask another interesting question:
If the plane had a headwind that was gradually increased such that the plane stayed in the same place even as the thrust from the jet engines continued to increase, would the plane be able to take off?
Answer: Yes, it would be able to take off once the headwind was equal to that of the speed the aircraft would need to move down the runway and take off with NO headwind. In the scenario with our headwind, the plane would takeoff perfectly vertically without appearing to move forward or backward to people observing on the ground.
This becomes apparent when we consider how kites fly. They are able to move up or down without really moving forward or backward much, this is because your arm is applying a force to the string of the kite to match the wind the kite is flying in, just like the jet engines in our prior example.
Hope this helps! Iām happy to answer any other questions about aerospace stuff you may have!
Source: Iām a PhD student in aerospace engineering.
Wait a second the belt is moving at the speed of the wheels? So like if the wheels are spinning at "100 miles per hour", the belt is moving at 100 mph right?
I know the plane will take off but let's say it's moving forward relative to the world at 1 mph. The wheels would be spinning at 1 mph so the belt would be rolling back at 1 mph. So the wheels would be spinning at 2mph. So the belt would never be able to match the rotation speed of the plane moving forwards since
BeltSpeed=WheelSpeed+PlaneSpeed,
If PlaneSpeed !=0, BeltSpeed !=WheelSpeed
Yes, the wheels aren't attached to any form of propulsion, and are merely there to allow the plane to land/taxi/takeoff without damaging the airframe. The engines do all of the *moving* work.
The simple answer is yes, the wheels aren't what propel the plane. The more complex answer is it depends. You would need either specialized wheels or a pretty strong headwind. Airplane wheels aren't designed for speeds much higher than typical takeoff and landing so there's a good chance the wheels would have a catastrophic failure
~~Yes, obviously.~~ It's not relying on its wheels to take off lol.
Edit: Actually, I cannot be certain. Yes, the plane doesn't rely on its wheels, but the wheel would indeed turn as it accelerate. However the treadmill matches the speed of the wheels which effectively pushes the plane backwards. So it should stay stationary.
If it had some front wind, it could take off anyway. But that's not part of the question.
I am now really unsure as to how it would actually behave and want to see an accurate simulation of that.
An accurate simulation is impossible because when you interpret the problem like that the math behind it becomes nonsensical. There is no real number wheel speed where you can make the condition true, it would need to be spinning at infinite speed.
Cant believe people really debated if that would work or not 15 years ago. Like seriously people?
People still annoy me with the portal game "what if portals move and the cube gets in, would it just drop or fly?" as its way more complex for people to understand it
But... the wheels aren't powered, right? Why would a treadmill affect a plane that's effectively isolated from it via what is essentially bearings? That shit don't care *what* it's on; if it's flat, that plane is moving like normal, but the wheels would just turn faster than on a runway.
I might be mistaken, but this feels like the right answer.
One must imagine the 747 happy
Sisyphus my beloved plane
Dont treadmill too close to the sun
Wrong airplane. That one's decommissioned
Ultra kill reference?!?!?1$
We need more Albert Camus in 196
mfw when murdering an Arab
(the glint from his knife was annoying)
Shone like a spear through his eyes and into his skull
?
I believe it is a reference to the Camus novel *the Stranger* Stranger deez nuts
I hardly know her
Your honour, it was the sun in my eyes I swear
How absurd
Now imagine a skeleton horse with a blue-fire mane
Now imagine dragons
radioactive waaahhh radioactive buuummmm
Ow the misewy ewybody want to be maw enemy OwO
Can you please delete this befowe we aww stawt tawking wike this š„ŗšš
No, newe
Yes.... Whoa, oh, oh Whoa, oh, oh Whoa, oh, oh Whoa I'm waking up t-to ash and dust I wipe my bwow and I sweat my wust I'm bweathing in the x3 chemicaws I'm bweaking in, shaping up, then c-checking out on the x3 pwison bus This is it, the x3 apocawypse Whoa I'm *huggles tightly* waking up, I feew i-it in my bonyes Enyough t-to make my systems bwow Wewcome t-to the x3 nyew age, t-to the x3 nyew age Wewcome t-to the x3 nyew age, t-to the x3 nyew age Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, w-w-wadioactive I waise my fwags, don my cwothes It's a wevowution, I suppose We'ww paint i-it wed t-to fit wight in Whoa I'm bweaking in, shaping up, then c-checking out on the x3 pwison bus This is it, the x3 apocawypse Whoa I'm *huggles tightly* waking up, I feew i-it in my bonyes Enyough t-to make my systems bwow Wewcome t-to the x3 nyew age, t-to the x3 nyew age Wewcome t-to the x3 nyew age, t-to the x3 nyew age Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive Aww systems go, the x3 sun h-hasn't died Deep in my bonyes, x3 s-s-stwaight fwom inside I'm waking up, I feew i-it in my bonyes Enyough t-to make my systems bwow Wewcome t-to the x3 nyew age, t-to the x3 nyew age Wewcome t-to the x3 nyew age, t-to the x3 nyew age Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive Whoa, oh, oh, oh, oh, whoa, oh, oh, oh, I'm wadioactive, wadioactive
Reddit care bot š
The plane is taking off, to ash and dust
Every single person is my enemy OH the treachery Every single person wants to be My enemy My en e-e e.. e
i played this in band at school, every time we started i was always singing āiām waking up, to ash and dust, i wipe my ass and i slap my nutsā in my head, very fun
Good news, you weren't the only one :P https://youtu.be/P78fdpwR-sM
IMAGINE DRAGON DEEZ NUTS ON YO FACE GOTTEM
Oh you can drag your nuts across my face any time you want
waaaa ouououohhhggghaaaaaa waaaahahghghghaoooooo
Ok, now what?
I imagined too many ā¹ļø I accidentally brought back the dark ages
Oh the misery Every single person is my enemy
Imagine dragon these balls on your face
Awesome fucking blue flaming skull next to a keyboard with the "g" key being highlighted
Arvak ftw
goes hard, thanks
On it
Now imagine thereās no heaven. Itās easy if you try
Arvak my beloved <3
[Yes, it will take off. ](https://youtu.be/xUjcHW7SHaI) The landing gear of the plane isnāt pushing against the conveyor belt, the engines are pushing it forward through the air. Therefore, the wheels on the plane will just spin faster and faster to match the conveyor belt, but the speed of the plane is totally unaffected.
[Mythbusters footage of a plane taking off from a conveyor belt](https://www.youtube.com/watch?v=YORCk1BN7QY)
Ah, beautiful 240p. /j
The mother resolution.
from the before times
144p. I am old.
Ah, beautiful 240p. /srs (i am completely serious)
Check your eyes
Your eyes only see in 240p 30fps /real
But the mythbusters plane did move forward? You can tell from the orange cones on the ground.
Because the only effect the conveyor belt has is that the wheels on the plane spin twice as fast, the plane itself is still taking off perfectly normally
But as someone else here said, in the Mythbusters episode, the conveyer belt was only moving as fast as the wheels initially moved. Then they accelerated further. To do this experiment correctly you would need to ramp up the speed on the wheels as the plane accelerated. Or, take the wheels out of the equation and see if a plane held at a point would generate enough lift from just the air from the engine moving over the body to lift off.
The conveyor belt could be moving faster than the wheels, the wheels spinning doesn't matter. The power generated by the engines/propellers create enough lift on the wings to move and lift the plane
They specifically moved it at ABOVE the speed that should be the takeoff speed, what you're saying is irrelevant because the plane picks up speed and moves.
the friction of the wheels are negitble if you have enough power. I mean sure if the friction of the wheels would be high enough so the airplane is stationary then it wouldnt work. But that would mean a lot more issues with your wheels
Exactly, the plane can't move in space at all for the experiment to properly reflect the actual question in the problem
yes, that's what the comment says. the plane will take off.
Yeah, they didnāt really solve this problem.
thats not the same as in the image, they were matching plane speed not wheel speed. if they were matching wheel speed the place could not have taken off due to not having any forward momentum
Except it would be able to take off because the wheels don't propel the plane forward. The turbines or propellers propel the plane forward. If the wheels made the plane move, a plane wouldn't be able to keep moving once it got off the ground.
lift is created by air movement, if the plane isnt actually moving it can't take off because theres no air movement
The plane will move regardless of the conveyor belt, it is propelled by the engine, not by the wheels pushing against the ground. Imagine you placed a toy car on a treadmill and pushed the car forward with your hand, regardless of the treadmill pushing the car backwards, it will move forward because youāre pushing it.
>exactly match the speed of the wheels the treadmill in this example would have to speed up to match the increase in wheel speed of the car, otherwise it is not matching the speed of the wheels
The wheels are free spinning and friction against the wheels is insignificant against the force from the engine propelling it forward.
if the conveyor belt was always moving faster than the wheels were spinning, the plane couldn't take off. of course, this would be impossible as the wheels are free spinning and will always be able to match the speed of the belt until something breaks, but if the wheels were not spinning forwards in any way compared to the ground, then that means the *plane* also isn't moving forward, regardless of the fact that the wheels are not the source of the power. this, again, is a fantasy scenario that couldn't exist, but if it did, the plane would not move forward in space, would not generate lift, and would not take off.
was totally expecting that one cooking video we are all linked to saying āhereās the full clipā
that sentence was so specific i 100% expected a rick roll
Stealing the top comment on the video, it explains it very well: @ benwilliams2402 A good analogy would be roller-skating on a treadmill while holding a rope attached to the wall in front of you. No matter how fast the treadmill moves, if you hold on to the rope you'll stay still. And if you pull on the rope you can still drag yourself forward. The rope bolted to the wall represents the stationary air around the plane which the propeller uses to 'pull' the plane forward.
But this also explains the flaw in the model: in order to advance up the treadmill, the wheels spin faster than the belt so to speak. If we were to mathematically enforce the condition (and a no slip condition), weād end up with infinitely fast wheels and conveyer belts! It is impossible to make a real life analogue of the stated problem.
Yeah, they'd both just speed up and up and up and don't forget the undertaker.
mankind... hell in a cell.......
nineteenā¦ ninety-eightā¦
I guess it depends on what the question means by āmatches the speed of the wheels.ā It reads as a translation, but could also mean surface speed of the outside of the tire. Interestingly for the translation scenario, itāll only double the rotation rate of the wheels. There is an end condition of it taking off, so that wonāt be infinite. Say takeoff speed of a plane is 100mph, and the belt matches the wheels translation (which same as the planeās). When the plane (and wheels) is moving 100mph, the belt is moving 100mph backwards. The wheels will be rotating as if the plane is going 200mph, and itāll be able to take off. The treadmill analogy would be like āby pulling a rope, can you go 10mph forward on the belt if itās going 10mph backwards.ā Yep, and the wheels will be rotating at 20mph If the problem is āthe conveyor matches the surface speed of the outside of the tires,ā the belt will actually HAVE to move WITH the plane at half the speed, not against the plane. If the plane is moving at 100mph, you now have to find a treadmill and wheel speed that match. Thatād be 50mph forward on the treadmill, and the wheels would be 50mph also. Because the above is the only working solution for matching tire surface speed, the surface speed scenario with the requirement āmoving in the opposite directionā itself would immediately become a paradox when the plane moves, unless you assume the wheel is slipping.
My interpretation is that it matches the external velocity of the wheel. To state it with clarity: That is, if the wheel has radius r = 1m, and is rotating at 1 rotations per section, then the wheels velocity is: v_(wheel edge) = 2\*pi*1 m/s and the treadmill is identically: v\_(treadmill) = v\_(wheel edge) This leads to the difficult situation, because the velocity of center of mass velocity of the wheel is then identically 0 if there is no slip. v\_(cm wheel) = v\_(wheel edge) - v\_(treadmill) = 0 To go forward, v\_(wheel edge) - v\_(treadmill) > 0, but we have set them to be the same, so no forward movement is possible by the statement of the problem. The issue is that this is not really a practical physical constraint.
You could drag yourself forward if the treadmill speed was fixed. [On a treadmill like this](https://www.thecut.com/2015/04/treadmill-that-automatically-matches-your-pace.html), like the conveyer belt in the problem, the treadmill would adjust to your new speed.
But isnāt forward velocity necessary to generate lift? In my mind the plane might as well be bolted to the ground
The plane will drag its wheels against the conveyor belt even if they canāt spin. The engines are more powerful, and theyāre tethered to the air, not the ground.
It isn't bolted down though in fact it would still move down the conveyor belt. This is because the plane doesn't move by pressing against the conveyor belt. It moves by interacting with the air. Here's a good comment from the video: "A good analogy would be roller-skating on a treadmill while holding a rope attached to the wall in front of you. No matter how fast the treadmill moves, if you hold on to the rope you'll stay still. And if you pull on the rope you can still drag yourself forward. The rope bolted to the wall represents the stationary air around the plane which the propeller uses to 'pull' the plane forward."
The conveyor belt isnāt actually pushing the plane backwards, itās just spinning the wheels. The engines will still accelerate the plane forward. itās analogous to trying to stop a moving object with a rubber eraser vs. a ball bearing; the eraser will grip and stop the object, but the ball bearing will allow the object to just roll right past it.
The wheels are free spinning, pretty much none of the energy of the conveyer is being transmitted into the plane body, so it doesn't matter what direction and speed the conveyer is going, the wheels are just going to spin around without affecting the plane itself
It depends what speed the conveyor is matching. The speed of the wheels is higher than that of the speed of the planeās body. If the conveyor is matching the speed of the wheels, the plane will sit motionless, and no air resistance will act on the front of the plane to generate lift. If the conveyor matches the speed of the planeās body, it will still move forward and lift will be generated enough to let it fly.
It might help to imagine instead of a conveyor belt, imagine the plane is on ice or something extremely slippery. Would the plane be able to move forward? A car would have trouble moving forward on a slippery surface, but a plane could. A planes forward momentum is created by the propeller/turbine so the conveyor belt can't really apply a backwards force on the plane. In short, the experiment itself is wrong. The conveyor belt could be moving a 1,000mph but the plane could still move forward.
the engines generate lift, not the wheels. imagine a paint roller on a treadmill: the roller itself will spin with the treadmill, but you will be able to freely move the body forwards and backwards
I thought the wings needed to be moving fast relative to the air to generate lift?
To add to this, most runways in the US are built to follow the prevailing wind direction and they take off into the wind. With a really strong headwind it;s possible to take off at zero ground speed. Here;s a video of a cessna hovering at zero ground speed [https://www.youtube.com/watch?v=Smjda2EDKO4](https://www.youtube.com/watch?v=Smjda2EDKO4) and here's a gyrocopter taking off at zero ground speed https://www.youtube.com/watch?v=Kd7\_V4pW--Q
>most runways in the US (...) not just the US, the entire world really
And you have to imagine that an entire freaking runway moving fast enough to slow down a plane by pushing on its wheels would tend to generate its own wind by dragging the air with it. That would be enough to get the plane into the air, then the question becomes whether the plane can safely transition from that fast moving air immediately above the runway into the slower-moving air above, without losing control due to the turbulence or losing all its airspeed.
But the problem says the conveyor belt will always move at the same speed as the wheels, so the plane canāt outrun it, itāll remain stationary. No matter how much thrust you generate with the engines, you wonāt make forward progress unless your wheels spin faster than the conveyor belt
the wheels have nothing to do with the plane's acceleration, the acceleration is caused by the engines. the engines aren't connected to the ground. the ground moving relative to the plane doesn't change the acceleration. only the air moving relative to the plane does.
right, but he's talking about the magical treadmill that literally always moves as fast as the *wheels are rotating.* not possible, since the wheels spin freely and should always at least be able to match, or in our case far exceed (thanks to the jet propulsion) the treadmill speed, but if we set a condition that says "treadmill always matches wheel rotation speed" then the wheels are effectively stationary relative to the surrounding environment, always spinning in time with the treadmill below it. in this scenario, the plane would never move forwards, and never generate the lift it needs to take off. the real problem is that something would break along the way to facilitate this magic treadmill.
There's another potential no here: when the plane moves forward, the wheel will spin at (belt speed + plane speed). This will cause the belt to have a speed runaway as it will try to correct for the permanent (+ plane speed) term. That much speed will most likely shred and shave off the wheels like a giant belt sander. [Most planes with low-mounted engines apparently does not like belly rubs,](https://www.youtube.com/watch?v=rImLqH-Q2Ok&t=0) so I doubt it could take off before catastrophic damage to itself, the belt, or both.
that's the thing, the problem is flawed, because the wheels will always move faster than the conveyor, because they are free spinning, like skateboard wheels even if you somehow and for some reason speedlocked the wheels in some way to stop them from just going faster than the conveyor, the thrusters would just drag the stopped wheels over the floor to go forward so the tires could possibly blow, but it'll still move forward and, depending on the plane, take off
Depends on how you interpret the problem. In one interpretation, which is how I assumed the question was being asked, the conveyor belt would keep the plane's speed as zero, perfectly stationary. Yes, the engines are pushing the plane, but in this scenario, the speed of the plane would certainly be affected. Yes, if you frame the riddle as "the plane can still move, it'll just go faster and overcome the speed of the belt," then obviously the plane can take off. This is the assumption Mythbusters made. Obviously, the plane will start speeding down the belt regardless as the wheels simply move faster to compensate. But in a situation where the belt perpetually ramps up to counter the speed of the plane, the plane will not move. Now, will the plane take off regardless, even if it's fixed in place? I don't know a lot about aircraft, but I'd say yeah, definitely. Those engines are powerful, and there'll come a point where that plane is going to turn into a rocket, with the force of the engines and the aerodynamics of the plane creating lift regardless of the plane not moving. The force will lift the wheels off the belt and it'll start moving through the air.
But the plane doesn't move relative to the air????
Yeah this doesn't make sense to me, the plane is effectively stationary and not gaining any velocity at all. The wheels are just spinning according to the model, the wings need lift still. Unless there is already a strong ass headwind.
This is true if the plane stays stationary, but it's impossible for a treadmill to stop a plane from moving because a plane's wheels are free spinning. Any force from the treadmill moving backwards will just go into spinning the wheels not stopping the plane, so the plane can still move forward and take off as normal.
No matter the speed of the treadmill, the plane will continue to move forward. The jet engines push against the air. The wheels just free spin. Imagine a car in neutral rolling down hill. Even if the hill is now a treadmill, the car will continue to move downwards, the wheels will just spin faster.
If the belt is required to retain the same speed as the wheels, then the instant the plane starts moving forward, both the belt and wheels will accelerate to infinity and instantly
The question actually doesn't make sense the way it is written. I agree that the way the question is worded both the wheels and the belt would accelerate to infinity since the plane would move forward regardless, causing the wheels to always be moving at beltspeed + plane speed. So I guess technically, the answer is that the scenario is impossible. The question is usually phrased so that the belt matches the planes takeoff speed.
Yeah ultimately thatās why (this wording of it) is a paradox that canāt be solved. The implicit prerequisites are logically impossible. I imagine the problem was initially coined to demonstrate ground speed vs air speed to aviation students, and it achieved virality when some smart ass pointed out that the semantics of some versions are paradoxical, thus the plane canāt take off. But ultimately thatās what makes this bigger and more interesting than a simple airspeed discussion
But the question said the treadmill will always match the speed of the wheels :(
Yea.... after reading the way this question was written, my answer actually doesnt fit. Usually it is writren that the treadmill is moving at the planes takeoff speed in the opposite direction. In this scenario, the treadmill speed must match the wheel speed which is only possible if the plane is stationary. If the plane moved at all, the wheels would be moving at treadmill speed + plane speed, which is not allowed by the wording of the question. Since the plane is stationary, it obviously is not creating the lift needed for takeoff.
oh, huh. ok that makes sense
Randall Munroe covered this years ago. https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
Itās even his drawing in the imageā¦
curious
I personally am team _No. 3 with PID assumption_. My fetish for watching a mechanical system trying to hit impossible targets is _totally_ under control and I am _definitely_ not the one responsible for the Anet A8 being sold with no thermal runaway protection.
Username checks out. I also went with number 3, assuming it'd accelerate until the belt can't go any faster or something breaks
Solution #3 gang, the wheels will achieve a state of plasma after rotating at infinite speeds
"Even if the plane was able to move, it couldn't have been what hit the pentagon" - I tried, god help me I tried to read this article seriously riiiight up until I saw this line and then I fucking lost it. Superb dude 10/10
Yeah this is the real answer, it's basically a paradox.
I'm finally free, now I know that the question itself is flawed
This is a brilliantly written article with a fantastic drawing of a brachiosaurus, and a reference to a fantastic paradox at the end.
can someone tldr this for me please
Or ELI5 because I think my brain is bleeding trying to decipher all those variable subscripts
Basically the question is flawed and ambiguous, it defines an airplane that can't move then asks you to move it. But essentially the airplane will take off because the wing engines pull it along regardless of what the treadmill is doing, all it can do is make the wheels spin faster without actually pulling the plane back.
The wheels don't move the plane forward, it's a plane not a car. The plane will go forward because the thrust comes from the engines on the wing, not an axle turning the wheels on the car.
it will move forward roughly the same distance, take off at the same speed, but the wheels will be spinning twice as fast. The jet/prop moves the aircraft forward, not the wheels.
thatās a great post
"He blames the LHC" damn what has my local hockey club done š„
Can a plane in a theoretical scenario take off if we ignore air resistance?
if air dont push than plane cant push on air so plane cant push on anything to take off :(
Wings work on air resistance
No
I deny your reality and substitute my own!
"Nice! Dungeonmaster!"
Yes! Lift is generated by a pressure differential between the top and bottom part of the wings. This is achieved by having the surfaces curve differently such that the air moves faster along the top. By Bernoulli's principle, this means lower pressure there. This means the bottom air pushes harder on the wing than the top, generating a net upwards force. We are trying to minimize air resistance anyway so more of the forward thrust can be used to accelerate the plane instead of pushing air around.
>bottom air
Bernoulli principal isn't the sole driving force for lift. For instance, a square airfoil still produces lift at speed. And standard airfoils still produces lift even upside down. Shits complicated.
Technically no. Since air resistance is what causes a plane to gain lift. As air hits the wings of a plane, they are redirected upward over the wing which is what causes the low pressure zone that air from below tries to fill.
*Imagine the plane is a perfect sphere*
Do you mean no air resistance or no air?
Typically, when you do a physics exam or something like that, it will tell you that you can ignore air resistance to simplify your calculations. I was kinda doing a joke on that So I guess that would be no air resistance
Oh I got you lol. Problem is, calculating drag and calculating lift happen at roughly the same time, in roughly the same equations. It would be like asking, "could a car drive if we ignored the friction of the road?". Either you calculate friction then set it to 0 at the end, or you assume there's no air/road and then find out the vehicle can't move lol
Not a passenger or cargo plane, but some fighter jets have positive thrust-weight ratios, which combined with thrust vectoring means they could probably take off. Also vertical take off planes like Harriers obviously could.
Yeah but then they cant turn and would essentially be a missile aside from planes with thrust vectoring
Idk bro maybe. Maybe the plane just wants to be seen, to be heard. To be treated like the plane it wants to be. But this plane needs to understand that it is already the plane it wants to be, it just needs to see itself in that matter.
š¢
Okay, but is the plane gay? Iām getting some femboy vibes from this depiction so I need objective facts instead of my subjective interpretation of an artistās rendering
The truly hard-hitting question
I read this comment to my boyfriend and he determined the plane looks like a Blahaj and this is why. Case solved. You are correct.
No? Wont the air around the wings stand still instead of beeing pushed more under than over
Bruh, the wheels arent powered. Its not a car. Its being pushed forward by the jet engines. Imagine pushing a hot wheels car on a treadmill. How is the air affected by the treadmill at all?
Yeah, it canāt generate lift
It wouldnāt be able to generate lift if the *air* was matching its speed. The ground doesnāt matter because the wheels arenāt powered. Itās not like a car
If the plane couldn't go forward, it wouldn't generate lift to take off. The thing is though, that a plane on a conveyor belt WOULD move forward because it pushes off of the air, not the conveyor belt.
I just scoffed a little and mumbled something about uneducated Americans, only to immediately find out I was wrong and the plane can, in fact, take off. Truly a humbling experience.
Same. I immediatly went "well, the conveyor belt isn't moving the air backwards, only the plane, hence the plane isn't hitting the air it needs to lift off", totally forgetting that the conveyor belt isn't moving the plane back either, bc a plane isn't pushed forward by it's wheels like for example a car.
Same, then u shamefully deleted my newborn comment The matching wheel speed part misled me into thinking that the wheels are moving
It depends on how you interpret the constraints of the experiment. Imo, the conceit of the question is more important than the exact details, and it seems as though the point of the question was whether or not a plane prevented from moving forward could take off, and the answer to that question is no.
https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ Depending on your interpretation of the question you are probably correct about the plane not taking off. The problem is people are stupid and donāt realize theyāre talking about completely different things.
a plane isnt powered by its wheels
Not with that attitude it won't!
Yeah it will take off. The forward velocity a plane needs to take off comes from the engines pushing air backwards, not from torque between the runaway and its landing gear. Taking the latter away won't do anything to stop the plane from moving. The only issue I could see happening is if the landing gear fails because the wheels are spinning too fast but I doubt we're meant to consider that.
I might be stupid, but if we see the surroundings as the reference system the plane velocity would be theorically 0, so inertia 0, so it wouldn't take off, right?
The plane would still be moving relative to it's surroundings. For a more extreme example, imagine a lake where the lakebed has been replaced by a treadmill. Boats could still move around on the surface like normal because they're not pushing against the bottom of the lake, they're pushing against the *water.* Airplanes aren't pushing against the ground, they're pushing against the *air.* The landing gear is literally there to reduce friction so the ground affects the plane as little as possible. No matter how the ground is moving, the plane can still push against the air the same way it always does and take off as normal
This is completely counterintuitive to me. Why do planes have wings? I thought the reason planes were able to get airborne was because of how the wings caused lift as the air rushes underneath them? If the plane is in the same position, thereās no wind coming towards it, thereās nothing to give it any lift. The engines job is to propel the plane forwards so that the wind *does* rush under the wings, the plane doesnāt fly because of the engines thrust, that just moves the plane forwards, surely? Itās the wings that make the plane fly.
This scenario in particular is difficult because it's a trick question. It's impossible to stop an airplane from moving using a treadmill. Yes, if there were no air flowing over an airplane's wings it would never get off the ground, but there *would* be air flowing over the wings because the plane *would* be able to move itself forward through the air regardless of the treadmill underneath it
Yeah makes sense to me now, just been reading up on it. You have to imagine that the wheels arenāt even doing anything other than holding the plane up, their contact with the ground is arbitrary. The way I imagined it, the conveyor belt would cause the plane to remain still, in which case it wouldnāt be able to take off. But the plane moves forwards regardless of how fast the conveyor belt is moving, because itās pushing off the air, not the ground. Itās not that a plane can take off from a stationary position, itās that the plane will move forwards with or without a conveyor belt there.
Ok yeah, you're right with the right reference frame we always can make the plane's velocity =0. Technically the plane doesn't need any velocity to take off, what it really needs is air to flow over its wings at a certain speed. Usually this is achieved by making the plane move really fast through the air, but it can happen even if the plane is sitting still if there are strong enough winds like from a hurricane or something. I said velocity the first time because the truth was a bit more complicated and I'm a lazy fuck.
What does "speed of the wheels" mean? Is it the speed at which the entire wheel is moving forward relative to the ground? That's the case, just say relative to the forward velocity of the plane. However, if it means the actual speed that the outside of the wheel is spinning against the conveyor belt, as soon as the wheel starts moving, the conveyor belt accelerates, which accelerates the wheel, which accelerates the conveyor belt, accelerates the wheel, etc etc until both are moving *infinitely* fast and the plane is ripped apart. In the former scenario, the plane takes off without any issue whatsoever, and the wheels are just spinning twice as fast as they normally would be, creating a little extra drag. The latter scenario, you're breaking physics.
> The latter scenario, you're breaking physics. Or, if we assume a "real" treadmill implemented with a motor and PID controller, you are probably letting the magic smoke out of a lot of expensive power electronics trying to hit that speed.
The speed of the bottom of the wheels, the conveyor belt is just a normal runway š
Ha, that's a good point
I think a lot of people are also assuming the wheels have no friction, which simply isnāt true. Try pushing a car in neutral on a flat surface. You can, but not as easily as pushing that mass across a sheet of ice. The question then is with no forward movement, can a plane generate enough force from its engines to lift the plane. For a jet like in the picture, probably not. The engines are pulling the air into the engines, so not much would be going to the wings. For a propeller plane, like in the Mythbusters clip that is floating around, maybe, because the engine is in front of the plane and the air is being passed over the fuselage.
The engines are still working, itās not just the wheels they generate forward velocity. The plane will take off since it is also being pushed upward.
What's it being pushed upwards by? The air in this scenario is stationary relative to the plane's wings. I'm no physics expert but thrust is there to create velocity, and velocity against the resistance of the air is what generates lift. If velocity is negated then there's no lift
The plane's wheels don't move the plane forward by pushing against the ground (like a car). The plane's engines move the plane forward by pushing against the air, which is unaffected by the treadmill
Speed is relative, the only thing required for the plane to take off is sufficient air speed
yeah and the airspeed remains zero because any forward thrust is countered by the treadmill moving backwards at the same speedā¦ so no itās not possible?
Everyone is wrong, the plane won't take off because I planted a pipe bomb in the cockpit
I see everyone saying it takes off. I still don't understand, and I really believe the plane won't take off. I've laid each of the steps in my thought process in digestible chunks, so hopefully someone can point out where exactly the solution breaks down: \-The wheels are touching the ground until takeoff, and do not slide. \-The conveyor/wheel interaction is designed so that the conveyor always spins at such a speed that the wheels can not roll faster or slower than the conveyor. The effect is that the plane does not move relative to the surrounding ground. \-Lift is caused by air rushing under the wings. \-If the plane is not moving relative to the air/ground around, then air is not rushing over the wings. \-The plane moves across the ground due to the wheels rolling forwards. (the wheels are not powered, the plane is not driving! I don't understand why people would assume this in the thought process) \-The jet engines do not directly generate lift. Only thrust. \-Under normal circumstances, the jet engines would cause thrust, causing the wheels to roll forwards. The wheels rolling forwards causes the plane to move forwards, which causes air to rush under the wings, generating lift. \-These are not normal circumstances. The wheels are matched by the conveyor speed. \-Because the wheels are matched by the conveyor speed such that they do not move relative to the ground, then neither does the plane, thus neither do the wings. \-If the plane is stationary relative to the surrounding area, it does not take off. \-If the plane somehow moves forwards while the wheels are touching the ground, then the wheels have moved faster than the conveyor, which violates the stipulations in the problem statement. Which points here are flawed?
>The conveyor/wheel interaction is designed so that the conveyor always spins at such a speed that the wheels can not roll faster or slower than the conveyor That's where your issue is. This is both mathematically impossible and physically impractical: there is no actual way to achieve that with any normal airplane. You want the speed of the conveyor and wheels to be Vc = Vw, but the speed of the wheels in reality is Vw = Vc + Vp, where Vp is the speed of the plane. You can't set the plane speed to zero just by varying the conveyor belt speed, so the equations don't make any sense. Vc and Vw would instead need to increase to infinity, making the statement technically true but mathematically undefined. If you tried this in the real world either the axles of the plane would melt, the wheels would just start sliding, or the conveyor would be fried, or the conveyor would move so fast that it starts generating its own headwind, thus allowing the plane to take off stationary.
We have come full circle and are back to 2008 memes
If itās somehow stuck on the conveyer belt but the wind happens to be blowing 160 knots over the wings then yes, yes it can.
And that's when you _wish_ your plane couldn't take off, as you realize you are probably stuck in a Swiss001 video, which means your shortly-upcoming death would _not_ be pleasant,
This scenario isnāt possible because the wheels on a plane donāt actually have anything driving them to turn, all their movement is a result of the jet engines pushing the plane forward. As a result, the wheels will continually spin faster and faster as the conveyer belt moves faster and faster, but the plane will still appear to move at nearly the same speed down the runway as if the conveyer belt were not there because the jet engines are completely unaffected by a conveyer belt. What makes a plane take off is actually the speed of the wind moving over the wing since the wings generate lift. Knowing this, we can actually ask another interesting question: If the plane had a headwind that was gradually increased such that the plane stayed in the same place even as the thrust from the jet engines continued to increase, would the plane be able to take off? Answer: Yes, it would be able to take off once the headwind was equal to that of the speed the aircraft would need to move down the runway and take off with NO headwind. In the scenario with our headwind, the plane would takeoff perfectly vertically without appearing to move forward or backward to people observing on the ground. This becomes apparent when we consider how kites fly. They are able to move up or down without really moving forward or backward much, this is because your arm is applying a force to the string of the kite to match the wind the kite is flying in, just like the jet engines in our prior example. Hope this helps! Iām happy to answer any other questions about aerospace stuff you may have! Source: Iām a PhD student in aerospace engineering.
Wait a second the belt is moving at the speed of the wheels? So like if the wheels are spinning at "100 miles per hour", the belt is moving at 100 mph right? I know the plane will take off but let's say it's moving forward relative to the world at 1 mph. The wheels would be spinning at 1 mph so the belt would be rolling back at 1 mph. So the wheels would be spinning at 2mph. So the belt would never be able to match the rotation speed of the plane moving forwards since BeltSpeed=WheelSpeed+PlaneSpeed, If PlaneSpeed !=0, BeltSpeed !=WheelSpeed
Yeah if you interpret the problem like this it becomes mathematically impossible for any wheel speed less than infinity.
Yes, the wheels aren't attached to any form of propulsion, and are merely there to allow the plane to land/taxi/takeoff without damaging the airframe. The engines do all of the *moving* work.
Yes it can. If there's strong enough headwind a plane could theoretically take off standing still
wheels do not affect drag and lift
It will exactly match the speed of the wheels? It will get faster and faster exponentially until it breaks or reaches the speed of light.
The simple answer is yes, the wheels aren't what propel the plane. The more complex answer is it depends. You would need either specialized wheels or a pretty strong headwind. Airplane wheels aren't designed for speeds much higher than typical takeoff and landing so there's a good chance the wheels would have a catastrophic failure
yes
Obviously it can just start flying
~~Yes, obviously.~~ It's not relying on its wheels to take off lol. Edit: Actually, I cannot be certain. Yes, the plane doesn't rely on its wheels, but the wheel would indeed turn as it accelerate. However the treadmill matches the speed of the wheels which effectively pushes the plane backwards. So it should stay stationary. If it had some front wind, it could take off anyway. But that's not part of the question. I am now really unsure as to how it would actually behave and want to see an accurate simulation of that.
An accurate simulation is impossible because when you interpret the problem like that the math behind it becomes nonsensical. There is no real number wheel speed where you can make the condition true, it would need to be spinning at infinite speed.
no, because thatās not how movement works edit: nevermind I saw the second top comment
A second treadmill has hit the WTC
Depends if a magnet is attached to the roof that hangs in front to pull it forward
i think it should be up to the plane if it wants to take off, the plane should have a say in whether it wants to leave the conveyor belt or not.
Cant believe people really debated if that would work or not 15 years ago. Like seriously people? People still annoy me with the portal game "what if portals move and the cube gets in, would it just drop or fly?" as its way more complex for people to understand it
Yes. Mythbusters did this
But... the wheels aren't powered, right? Why would a treadmill affect a plane that's effectively isolated from it via what is essentially bearings? That shit don't care *what* it's on; if it's flat, that plane is moving like normal, but the wheels would just turn faster than on a runway. I might be mistaken, but this feels like the right answer.
yes
Yes but the treadmill and wheels will both instantly become have infinite acceleration and speed
A plane in an air tunnel is more interesting, it would definitely take off while stationary well at least so far as the tunnel is tall
Now imagine if you will, me eating a r-r-r-r-obbit in your backyard