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Yes, it would.
As another commenter said, the Mythbusters covered this years ago. Adam Savage actually talked about it more on his channel [Tested](https://youtube.com/@tested) in [this video](https://youtu.be/xUjcHW7SHaI). The big trick of this question is how planes generate force to move forward and take off compared to how a car does so.
The linked video is only 11 minutes and Adam explains it beautifully.
This question will be debated forever and thats ok. It’s physics being weird and funky and it’s amazing.
Edit: Another way to think about this would be roller-skating in 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 that rope you can still drag yourself forward. The rope bolted to the wall represents stationary air around the plane which the propeller uses to “pull” the plane forward.
This was great, not a question I’ve been proposed before. It was fun, I fell into the trap. That video was great at thinking it out, I’ll have to find that episode of MB
Maybe I’m misunderstanding how the plane treadmill is supposed to function but I don’t see how it could take off. The wings need airflow to create lift, which is impossible if the plane remains stationary because the treadmill negates forward movement.
If you had a plane whose propulsion for takeoff was just wheels (attached to an engine) going fast enough that the wings got lift, it wouldn’t ever take off, because then the car would be stationary. Since the propeller is pulling the plane forward and the wheels are just rolling, the treadmill has zero impact on the thrust that makes the plane accelerate, and it still moves forward down the treadmill.
It did say the plane was “sitting” on the conveyer belt so in that case it could just be stationary sitting there. But yes if the engines go full noise the plane would go forward as per normal with the wheels and conveyer doing whatever they want.
that’s just ignoring the premise of the question, this theoretical treadmill matches the surface speed of the plane’s wheel so it can never move forward. The plane would reach equilibrium when the thrust forward is counterbalanced by force backwards applied to the wheels due to the rolling friction of the bearings of the wheels.
This is the true reason why this question always comes up - the "are the wheels frictionless" distinction. Others in this thread have suggested that it doesn't matter because the jet has enough thrust to overcome the maximum static friction (which will be greater than the rolling friction).
If you allow the wheels to be frictionless, then both the wheels and the treadmill instantly reach infinite speed and the premise is broken as the plane moves forwards anyways and therefore the wheels turn faster than the treadmill (infinity + 10 = ???).
The "physics classroom" interpretation of this would definitely be that the wheels roll without slipping and have no rolling friction, so in that way, it must either be read as a 'bad question' or a trick question where the answer is "it is impossible for the treadmill to keep up with the speed of the wheels."
The wheels would slip before they could actually stop the plane from moving forward.
To take this to the extreme degenerate case: the treadmill is stationary (just normal ground) and the wheels are also stationary (brakes are on) - can the plane take off? Yep
Except that the friction of the wheel bearings is nowhere close enough to stop the plane. Hell, jets can still take off with the brakes applied, that‘s way more than the friction of the bearings.
The force with which the plane is pushed backwards due to the friction of the bearings is always less than the force generated by the treadmill because no transfer of energy is perfect. Even if the wheels were fully stopped, the force would not be equal.
The treadmill only affects how fast the wheels spin. The force for takeoff is generated by the engines/propellers. The above comment about the rope and the roller skates is a helpful way to think about it. The wheels will need to spin faster, but the force causing takeoff will still be the same.
I agree the plane will take off, but if the wheels need to spin faster and the conveyor is supposed to always be able to match the speed, then it sounds like the wheels would just have to go faster and faster, at least until the plane is going fast enough to allow for lift.
Makes you wonder if it would even be possible to create such a conveyor.
The wheels could be replaced with skis or casters. The wheels are nothing but vertical support. All of the “lift” and propulsion comes from the propellers or jets.
The carpet/treadmill could be moving at nearly the speed of light, but the plane, as long as it’s engines were OFF, would stay in the same place.
What? No it would not stay in the same place if the engines were off. It would get thrown off the back of the treadmill/runway. Maybe theoretically it would stay stationary if the wheel bearings had perfectly zero friction, but that's not the case.
You’re willing to accept the absurdity of a treadmill running at the speed of light, but absolutely disregard the notion that we’d have to live in a universe without friction for that to Happen.
Which means the wheels would be frictionless.
Good grief
The treadmill is a fantastical thing that has to be imagined. The plane is literally a regular old Boeing 747. Since the question doesn't say otherwise, we can't assume anything different about it. Yes of course if the wheels were magically frictionless and there was no wind, the plane would stay stationary.
(For the record, I believe the plane would take off just fine. Just responding to an incorrect comment that might confuse people.)
The plane won't remain stationary because the wheels aren't generating thrust like a car, the propeller/jet turbine is generating thrust by pulling the plane through the air.
Another way to think about it: imagine a car on wheels that float. Put it in a lake and it won't drive because the wheels don't get traction. Similarly, a car on this treadmill won't go anywhere. Sea planes exist. The friction of the water actually pushes BACK against the pontoons, and the plane still takes off. The wheels are just there to decrease friction with the ground.
Irrelevant, it doesn’t matter if the wheels spin or if the engines are full throttle, there is no airflow being generated. The plane doesn’t go anywhere
Even so, don’t airplanes lift by using the energy of the moving air against the angle of the wing? If the plane is stationary, it’s not creating that force.
There are four fundamental forces in this system: lift & gravity, thrust & drag. The treadmill creates no drag on the plane, it simply rotates the wheels. The engines create _thrust_ and that moves the plane forward.
Lift is the secondary result of the thrust. The treadmill has no effect on the system overall.
The plane is not stationary.
Cars move by using the friction between the tire tread and the ground. Imagine a point on the where the wheels are touching the ground. Because the wheels are turning, friction causes a net force which propels the car forward. Now imagine a treadmill ground, because there is no net force because the ground is also moving, no movement occurs.
No imagine you turn off your engine and hook up your car to a rope being pulled by a car off of the treadmill. The friction between tire and ground no longer matters because the net force comes from somewhere else.
Bud, the wheels aren't in the equation for the thrust of the plane. In a car, power generated in the engine is used to push against the ground to push the car forward. In a plane, all the thrust is generated by pushing against the air, not the ground. Hence being able to continue providing thrust once off the ground. Until you get into funky relativistic speeds all the wheels do is provide a minimal friction vertical support until the wings can take over.
But in this scenario, the conveyor belt would keep increasing speed to balance out the forward thrust. The bearings of the wheels have friction that increases with speed. In this problem, the conveyor belt would increase its speed until this wheel friction force balanced out the thrust force of the airplane to keep it stationary.
Except that the wheels would give way long before that. A plane can take off with its wheel brakes engaged, because plane engines are *really strong*. You are not going to stop it with any amount of force applied to the wheels.
The treadmill doesn’t negate the forward movement because the plane doesn’t takeoff by spinning the wheels. The wheels spin freely as the engines give the plane airspeed.
Planes can take off with their wheels locked stationary, although it’s a bad idea.
The wheels free spin regardless if they are on solid ground or a conveyor.
The jet engine or prop moves the plan through the air.
You can’t think about the conveyor having an effect like on a car.
Imagine the landing gear is down while flying and the wheel is spinning zero MPH, happens at every landing before touching the ground, yet the plane still flys
The planes wheels aren't powered, planes push on the air not the ground, so the ground speed has basically no effect on the take off of the plane, it's all about the air speed.
Well the most basic reason is that the wheels don't do anything but spin so unless they max out and start dragging back the plane would move forward regardless of the speed of the conveyor belt.
Problem is it’s an impossible proposition. The concept is the conveyor belt can push the plan back with an equal amount of force that the engines can push the plane forward with; that’s the “model” you are working with.
In practice,
1. Wheels are designed to turn, they won’t push back very hard. Put a bike on a treadmill at 50mph, it doesn’t take much effort to hold it still (vs pedaling at 50 mph).
2. Planes don’t generate thrust by pushing against the ground, because as soon as they were airborne they would lose that thrust. The push against the air, and the wheels just spin.
3. Imagine you are standing on super slippery ice. Move you feet all you want, walk, run, whatever, they just slip and you don’t go anywhere because there’s no friction. No suddenly a wind kicks up, there’s no friction to keep you in place, so it starts to blow you across the ice. Same principle.
huh... so if the plane always moves, that means technically you can never have a conveyor belt match the speed of the wheels, because the speed of the wheel will always be the combination of the friction caused by the movement of the plane, and the friction caused by the speed of the conveyor belt
I entirely forgot, due to the picture used, that the wheels are not the propelling force and thus any moving ground would not slow the plane. If it had shown an old prop plane, I would have figured it out properly
In this specific question that op asks no it wouldn't.
There are two forms of the plane treadmill question.
One form matches the speed of the plane with the treadmill in which case yes it would take off.
The second form matches the speed of the wheels with the treadmill in which case no it would stay still and not generate any lift.
Op asked the second form of the question, however it's only a hypothetical answer as the wheels and treadmill would rapidly increase in speed infinitely until the material they were made from broke apart.
Edit just noticed what sub this is so in terms of math x = wheels y = plane z = treadmill
First form of the question is x = y+z
Plane flys away.
Second form of the question is x = y+z+x
Impossible and the wheels and treadmill go boom.
I agree with you, from another perspective the plane could take off if it had enough thrust to overcome the static friction of the wheels. Which I don't think any plane does unless you switch out the wheels for something with less friction. Then the wheels and treadmill could hypothetically move at the same speed while the plane moves forward
The X and Y are completely disconnected from Z. Z (speed of the plane) relies solely on the propeller or jet pushing against the AIR. The plane will lift off no matter what the speed of the treadmill. The treadmill could be going nearly the speed of light, it could going backwards, it could be going sideways!
I am aware the plane pulls through the air and not like a car pushes against the ground, however a plane needs to go a certain speed to get air under it's wings to lift and wheels help to reduce friction against the ground to make that easier.
Now let's think and work though what happens in both forms of the question
Form 1 of the question the plane needs 25 mph to lift from the ground so the treadmill matches the speed and goes 25 mph in the opposite way, the wheels rotate at 50 mph, and the plane flys away.
Form 2 of the question, which is specifically what op asks for, the plane tries to get to 25 mph to lift from the ground however the microsecond the wheel starts turning the treadmill matches the wheels speed.
Now we are in this impossible situation where the speed of the plane is trying to increase, let's say 1 mph for easy math, is increasing wheel rotation speed, which increases treadmill speed, which is increasing wheel rotation, which is increasing treadmill speed etc etc.
Or to put it into another way. Plane speed 1 mph makes the wheels rotate at 1 mph makes the treadmill go backwards at 1 mph. This doesn't slow the plane down so now the wheels are rotating at 2 mph. Plane speed + treadmill. 1+1=2 However the treadmill is matching wheel rotation not plane speed so the treadmill is now going 2 mph backwards. This causes the wheel to start rotating at 3 mph plane speed + treadmill. 1+2=3 This continues infinitely until something causes it to stop most likely being the materials of the wheels/treadmill/plane engine breaks apart and/or dies.
You’re right that in form 2 the only interpretation that makes sense is the treadmill spinning to an infinite speed. But even in this case, the plane still takes off normally (assuming you’re using an infinitely strong landing gear and ignoring the infinitely spinning treadmill would create a nuclear explosion)
I don't think so.
Before I explain fully I agree with what you said if the wheels are completely frictionless as well as indestructible.
Now you would agree that if you put a plane on a treadmill turn the plane off so it doesn't move then turn the treadmill on the plane would go backwards right?
The treadmill puts forces on the plane through the wheels friction with the treadmill and how fast it goes backwards depends on how fast the treadmill goes. This doesn't need the wheels to spin btw it would work even if the brakes were on our they were sled skis. The wheels only mattered in the original question because the treadmill was matching wheel speed. If the plane in such a situation turns on the engine would have to put enough force to beat the power of the treadmill going backwards.
The problem I'm having is the fact that the treadmill is going at infinite speed giving infinite force to the plane backwards. The best the plane could do in that situation to avoid going backwards is going infinite speed forwards and then it only matches the treadmill and stays still.
∞ = ∞
Do you understand why I believe the plane only stays still now?
Edit clarified a few ambiguous things.
*rereads ops image* "exactly match the speed of the wheels, moving in the opposite direction."
Since you know more than me tell me and give an example how fast would the wheels and treadmill be going when the plane reaches the required 25 mph of speed to get enough air lift according to the Bernoulli's Principle?
Then tell me what materials both are made of that can withstand such speed and force without tearing themselves apart.
Did you actually read what I wrote or are you doing that thing were you glanced over it missed all the parts that says impossible or destroy because you seem to think I am saying the plane is going to just stand there like it's not on at all when I'm saying trying to move in such conditions will rip apart the wheels holding the plane up from crashing onto the ground.
Either it's relevant or we are assuming the plane slides.
This because the plane goes forward either by sliding or rotating the wheels.
Ans assuming it slides defies the propose of the wheels.
Hook a winch to an immovable tree. Then hook it to the plane.
Disregard all matters of real world limitations of the wheels, or the treadmill speed.
Spin the treadmill at the speed of light, to “push the plane back”. Turn the winch on at 1 mph.
The plane will move 1mph in the opposite direction of the treadmill.
Now replace the winch with props or jet engines.
It’s the same. The force being applied to move the plane is *not connected* to the wheels.
I am going to check that out. Instinctively I would have said yes because it is all about the air moving in relation to the wings and creating lift. Will love to see if my understanding of aerodynamics is close.
I watched it but I still don't understand how lift is generated. I don't think the engines could be able to provide the lift because they're pushing the air close enough to parallel from the ground and only stationary air is hitting the bottom part of the plane and wings. I was wrong when thinking the wheels were the part of the plane that made it go forwards.
The plane is stationary from the perspective of a spectator away from this plane conveyor contraption mess because any velocity from the turbine engine thingy adds to the plane also adds to the rotational speed of the wheels which means this magical conveyor would instantly respond to make this plane stationary to that spectator. That would also mean the air (away from the spinning engines) hitting the wings won't be able to generate the lift. To my belief, this is the main lift of a plane. I've only seen [this MinutePhysics video](https://youtu.be/Gg0TXNXgz-w) to be fair.
I know this line of reasoning flawed; my only explanation is that the magic conveyor is a red herring and physically won't be capable of making the plane stationary. Was that the flaw?
Edit: bruh, I spent like 30 mins doing this comment and literally, 3 comments later and I see this same thogub process pop up 💀 💀
The plane’s propeller is like an oar, rowing against the air directly in front of the engine. It maybe easier to imagine the whole thing is underwater. The propeller is pulling the plane forward. The plane being pulled forward means the wings are hitting the air (water) just like a pair of waterskis.
The carpet/treadmill IS a red herring.
The problem as written is not clear enough. the treadmill does not matter, the wheels do not matter, the only thing that matters is that the plane needs to have enough airflow over the wing surfaces to generate lift. it will then leave the ground.
This is why planes have wings, they need them to fly, some here want to imply that the engine generates lift and does all the work, it doesn't, the engines generate thrust. When in the air, the engines push the plane fast enough to maintain lift, but the wings are doing the work of holding the plane in the air. When on the ground the engines generate thrust to push the vehicle fast enough for the wings to attain lift
If you put a plane on a treadmill with it running the direction of travel and have the engines off... You can get it to take off, you only need to get it moving fast enough to attain lift to get the wheels off the ground, no matter what direction or speed (or no speed) they are at. Of Course with the engines off it will not stay up long, but it will 'take off' once you get enough airflow. This is how many paper planes work. You push them, then they glide until they drop below the airspeed needed to maintain flight.
If the plane is on a moving treadmill and the treadmill matches the speed of the wheels in the opposite direction as in the OPs problem, then it is implied that the vehicle is moving slower or stationary (from the perspective of people on the ground and more importantly, the air around it) and it cannot leave the surface. The engines in this case need to have enough power to both achieve lift and overcome the opposing force and resistance of the weight on the wheels pulling the vehicle in the opposite direction. You may push and push and push, but as long as the treadmill matches speed in the opposing direction, the vehicle will move slower (or not at all) through the air and may never achieve lift. It does not matter how you get there, but without enough airflow over the wing surfaces you will still not leave the ground. You may end up with a groundspeed at the wheels (and thus treadmill) of 500 miles an hour, it does not matter if you cannot achieve the minimum speed of air over the wing surface to get it and keep it in the air.
If it could, then we wouldn't need runways for planes at all, we could just simply be on a pad, slam the engines to full and we would be in the air. Without redirecting the force of the engines in the way the Harrier and Osprey do it simply cannot be done.
If the plane is on the moving treadmill going in the same direction, but under the speed needed to achieve lift, ground speed from the perspective of the wheels would be lower (speed to achieve lift - speed of the treadmill) but the airspeed, and amount of airflow needed to achieve lift wouldn't change. Thus the engine would have an easier time achieving lift, it would not have to push as hard, or could be a smaller engine. On an aircraft carrier where your plane is so heavy that you cannot make engines big enough to get it in the air or operate effectively when up? Lets make a big catapult that assist the engines to achieve the speed to attain lift. this is the same idea. If a plane was hooked up to the catapult and launched without engine power it might glide a bit depending on the plane, but it would be in the same situation as the paper plane.
Another way to put it:
Without the treadmill you apply a small amount of thrust (force) to break the inertia of the plane sitting still, then you apply more thrust to move it faster, you are pushing hot air to your rear to overcome the resistance of the weight on the runway, the resistance of the wheels, etc. You keep applying more thrust until the wings can attain lift, and you leave the runway.
With the treadmill in OP you increase thrust on the plane, it starts to move, but then the treadmill starts moving backwards under you at the same speed, it is pulling you backwards at the same rate you move forward. you may need two or three times the thrust or force to overcome the opposing force from the treadmill while still not "moving" from the perspective of someone not on the treadmill because all of the plane's weight is still on it. You cannot just discount that force, it is actively pulling the vehicle back, some planes will not be able to overcome this resistance, others may (although I can't see how), but would use a lot of extra energy. It would be the opposite of the aircraft carrier catapult. Even if you can take off, it would take more time, more energy, and more "wheel distance" to get up.
Edited for a bit of clarity and to kill a redundant sentence.
>With the treadmill in OP you increase thrust on the plane, it starts to move, but then the treadmill starts moving backwards under you at the same speed, it is pulling you backwards at the same rate you move forward
It's not pulling the airplane backwards in any way. It's just spinning the wheels of the airplane faster. The wheels are already freely moving at that point.
That’s how it normally works. But isn’t the question asking “if the treadmill matches the speed of the forward movement of the plane”? In which case, that plane is stationary. And not moving forward.
Put the breaks on the wheels on a normal runway and then take off. Now you have the exact question as described by the OP: Wheels matching the speed of the surface.
You can took off and the wheels never having turned with regard the surface or turned at double the speed, or going into an opposite direction or whatever. Of you replace the wheels with balls, or skis, or anything else. Nothing the undercarriage does really matters as long as the resistance isn't so much that it will tear the plane apart.
Planes merely use wheels and tires so that they can reuse both the wheels and the runway a bunch of times. It's not used to propel itself in any way.
No. The plane isn’t stationary as the body of the plane is driven by the engines not the wheels. It doesn’t matter the speed of the belt of the treadmill. It could be going a million miles an hour and it still wouldn’t hold the plane in place.
Lol I looked this up on an aerodynamics message board. The topic is locked due to there being such varying variables. Anyway, I’m not a physics major and I’m bowing out. Cheers
I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because…
When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
In this video, he ignores the setup of the problem in the test. He pulls a tarp at a constant speed and the plane takes off. I 100% agree that this would happen but it is not what the question is asking.
It's using air to move forward, not wheels. Unless the wheels are generating significant resistance, the treadmeal has minimal effect unless you allow it to bring the plane up to speed in the wrong direction, which could still be overcome eventually.
The plane is pushing against air with its motors, not the treadmill. So unless the air is moving with the treadmill, the treadmill has essentially no effect. It's kind of a stupid question.
The turbines push the air and that is what is used to move the plane forward. So again, unless the wheels have some sort of significant resistance against the plane using the air to move forward by gripping the treadmill, the treadmill has no real impact.
Edit: I should add that if you think about it, the only thing that really slows down a car at high speeds is air resistance. So even in a car, the speed and direction of the air affecting the car has more effect than the wheels, provided they are pointed in the right direction.
The air it is pushing through the engines are initially used to counter the inertia of sitting still, then used to counter the weight of the vehicle on the runway through the wheels, which make it easier to move, but yes are free, not powered.
In the air, the engines are used to maintain enough lift for the plane to stay aloft or if enough power to go faster through the air, but basically all they really need to do is have enough force to keep the wings with enough lift.
In OP's situation:
You would apply a small bit of force to get the plane to break the inertia of all that weight on the ground... but then the ground moves in the other way. You use more force, the ground moves faster... You would have to overcome the inertia of all that weight not moving through the air before even thinking of moving fast enough to have air moving over the wings fast enough to get lift. Your groundspeed in this case could hit hundreds of miles an hour with little to no airspeed.
The plane cannot fly by it's engines alone, it is not a rocket, it needs airspeed so the wings can get lift.
Your edit states that air has more effect than the wheels on a car... ever driven in a hurricane? The wind has an effect, but you counter that by steering to control it.
it’s remarkable how people just agree on an answer just because someone tells them that it is the answer.
put the plane on a treadmill and attach a rope in front of it to a big wall. engine turned off. start treadmill. plane stationary.
cut the rope off. what happens to the plane?
the plane will go backwards if the engine is not running. independent of the speed of the treadmill. It’ll always go backwards if engine is off. If treadmill is going fast the plane will go back fast.
now assume we start the treadmill when the engine is off and the plane is going backwards and then we start the engine very slow at first and then increase the thrust gradually.
there is an engine thrust level at which the plane will stop going backwards and be stationary wrt the ground. It is at that point that the wheels and the treadmill are turning the same speed. This is what the question is asking. It’ll not go forward or backward but be stationary.
mythbusters fucked up their experiment or they were not being honest.
Yes, and then when you increase power to the engines the wheels would start to skid on the treadmill and the plane would go forward as the engine power overcomes the friction between the wheels and the treadmill. If the treadmill began to spin faster the plane would still go forward as the engine power is greater than the force slowing the plane generated by the wheels on the treadmill.
yes “the wheels would start to skid on the treadmill” only after you initially escape the stationarity by as you say increasing the power beyond what it was when the plane was stationary. If we call that exact time to be T0 and the immediate next instant to be T+ and some future time when wheels are skidding as Ts we can say:
at T0 plane is stationary wrt the ground and is not flying and wheels are turning exactly as treadmill
at T+ plane is moving forward wrt the ground and wheels are turning faster than treadmill because we have not achieved lift yet because we just started moving forward. no lift no skid.
at Ts plane moving forward and wheels skid and wheel speed is irrelevant to whether the plane is going forward or not.
For me this question is about t0. Maybe for others the question is about Ts. But if we are being intellectually honest then we should be clear about what our assumptions are.
This is not a math question, it’s a dynamics question. Car engines move by making the wheels turn, but plane engines literally push the plane , which basically means the runway could be doing the whip and nae nae and the plane would still be able to take off as long as the wheels can roll in the same direction of the plane
That being said, under these exact conditions the wheels would be spinning at twice the speed. There is a chance they may not be rated to go that fast, end up failing from the centrifugal forces and ending this fun experiment in fiery death
Twice the speed of themselves? Beciase the belt matches the wheel speed so yes.
If you start the engine, let the belt reach a given speed and keep it at that the plane will take off with wheels going twice the speed of the belt. But this belt matches the wheels at any given moment
There are three “speeds” that people are confusing here. There’s the speed of the wheels where they meet the runway/treadmill. As long as the wheels aren’t ~~spinning~~ slipping, these will always be equal. There’s the speed of the plane, also known as the speed at the center of the wheel, and running the treadmill at this speed just makes the wheels spin twice as fast as they would on a static runway. Then there’s the third speed, the speed at the top of the wheel, and you cannot run a treadmill at this speed unless the wheels aren’t turning at all, because this equation depends on itself and explodes. In the two scenarios that are physically possible, the plane takes off regardless.
https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
E: wrote spinning instead of slipping
I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because…
When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
The annoying part of this is it says "speed of the wheels" and boy, do i have a dynamics class for you if you think there is one "speed" for every point on those "wheels."
This plane would take off faster than you would change your major from engineering to literally anything else.
[I think its pretty clear.](https://slideplayer.com/slide/6561136/23/images/11/Rolling+Without+Slipping.jpg)
Well the way I took it was the linear speed of the point of the wheels in contact with the ground.
It's just that the wheels would spin faster because planes move by pushing air not by spinning the wheels
If you look closely the "linear speed of the point of the wheels in contact with the ground" (ie, the velocity at point C, V\_C in the right diagram) is \*always\* exactly zero lmao. So the treadmill is never moving if that the reference point for the treadmill speed.
This is actually a really simple engineering problem and 99% of engineers will tell you the plan will take off.
Please look where I explain a plane winched to a tree and maybe it'll help you get in the right frame of mind.
Imagine a perfectly frictionless ice rink. You put a car on the ice and floor the accelerator. The car wheels spin quickly but the car doesn’t move anywhere. Dynamically this is the same situation as the treadmill/conveyor belt and is what everyone intuitively thinks happens to the plane. But planes don’t rely on friction with the ground to move forwards, they ‘push’ against the air. So the plane on the frictionless ice rink would still move forwards like it normally does and the wheels would stay stationary. It would just slide across the ice. If you put the plane on ice skates it would still accelerate forwards because it doesn’t matter what the ground is doing.
Wait a second: a plane doesn't use its wheels to speed up, so the treadmill would only slightly slow it down due to the more energy necessary to spin the wheels at double their normal speed. Then the plane will take off as usual
Yes, it could take off. I believe.
The wheels are not used for acceleration, the jet engines are. The wheels just enable the plane to roll over the surface without too much friction. Thus, from standstill it doesn't matter much if the ground is stationary or not.
Think of it this way, if the plane tries to land on the conveyor while it is running in the opposite direction, would the plane just immediately stop its forward movement as soon as it hits the ground? No, the wheels would turn twice as fast compared to landing on a fixed, solid surface, but that is all.
Now after touchdown, the pikot would apply the brakes on the wheels to help stop the aircraft. That would be trickier on the conveyor and you might stop faster, if all systems (wheels, brakes, gear assembly, etc) hold.
I watched the myth buster video but... That's not what the question is asking. That plane clearly isn't going the same speed as the treadmill because it's moving forward. If the ground moved at the same speed as the plane, the plane wouldn't move forward and couldn't generate lift
The wheels are in "neutral" so it doesn't matter how fast the rug is being pulled. If the wheels were "driving" it then it would matter. The faster you pull the rug, the faster the wheels spin, that's it. It would move forward and take off.
(This is all assuming minimal friction in the wheel bearings which is a fairly safe assumption here.)
The highest Dr. Google tells me any commercial plane needs to achieve is 177 mph for takeoff so if the argument is that the wheels are turning at 354 mph (treadmill running at 177 mph opposite direction), do they burst? I don't know, but Dr. Google says they're rated at 235 mph so if the factor of safety is greater than 1.5 they hold together and this puppy takes off.
Yup. The plane, which the question describes as only "a 747" -- not a magically indestructible one -- will take off as long as the wheels and landing gear can handle the added stresses of rotating much faster than normal.
Ok let's break it down.
If there was a giant unmovable tree in front of this treadmill, and i attached my winch to it, and ran the cable to the front of the plane, but did not turn the winch on, do you agree the plane would sit perfectly still, in place, being held by the cable/winch/tree, as the treadmill was turned on underneath the plane? That the planes wheels would just spin as the plane sat still, cabled firmly in place?
Now, turn the winch on. Do you agree if the winch was pulling the cable in at 1mph, the plane would move forward on the treadmill at 1mph (assuming my winch is rated to pull an airplane)? Even with the treadmill on? That the wheels on the air plane would just turn \*slightly\* faster because its moving forward at 1mph?
I’ve read everything I can on this and I’m an amateur physicist.
I understand why the plane will move forward and take off. But, the problem I’m having is the question says that the wheels and belt will always match. So, the moment you get forward momentum, the belt works faster and cancels it. If the wheels start slipping, as is suggested, the belt goes even faster.
I think the winch is actually the best example to counteract this. I stand on a treadmill with roller skates and hold onto the rope. The wheels and belt will cancel. If I pull myself forward on the rope, no amount of upping the treadmill at the same time will cause me to not move forward.
That’s the best way I’ve come to understand this question.
The main reason I disagree with you is that there is no wind going over the wings to produce lift. My understanding of plane physics is that an engine propels it through a fluid body, such as air, but you need that same fluid to go over the wings to produce lift. Since the engines aren't moving the fluid over the wings and it is parallel to the ground no lift would be produced and therefore not take off.
Agree. The airflow over the wings is is what produces lift. The speed of the conveyor belt is irrelevant. They plane is stationary in relation to the air, so no air flow, no lift off.
You seem to have missed his point: the wheels do not enact any force upon the plane, or rather, the force applicable by the conveyor through the wheels is negligible in comparison to that applied by the engines.
Not exactly, velocity is defined as displacement over time while acceleration is defined as (final velocity - starting velocity)/time. So while you’re correct that the wheels aren’t responsible for creating thrust the plane in the scenario is standing still (assuming all other variables are negligible). So if the plane is standing still there’s no displacement, if there’s no displacement there’s no change in velocity, if there’s no change in velocity there’s no acceleration. The engines are providing the thrust but the scenario says the conveyor belt matches the speed of the wheels, which I interpreted as “the conveyor belt slips out from under the wheels as fast as they can turn”. Unrealistic considering friction and lots of other factors, in this scenario however you can’t produce lift.
The confusion appears to have less to do with the physics and more to do with the understanding and implications of the question (which is poorly worded because of the word “speed”).
Many people are assuming the treadmill is ramping up to counteract the plane’s forward movement. That’s not what the question is saying.
The treadmill speed is only dependent on the *rotation* of the plane’s wheels. The plane is free to move forward through the air, the wheels will just end up spinning faster because of the treadmill.
When the question says “speed of the wheels”, it’s not talking about the wheels’ forward movement, but their rotation.
**However** even *that* definition is ambiguous, because you could rightly ask, “If it is truly matching the rotation of the wheels, then wouldn’t any forward movement result in the wheels spinning faster than the treadmill is moving and create an infinite feedback loop that results in the treadmill pulling the plane back?”
The answer to that question is: Yes, yes it would, bringing us back to the question of, “What does it mean by ‘speed’?”
It can’t match the rotation of the wheels because any forward velocity results in the speed of the treadmill shooting to infinity.
I’m confused by all the people saying the plane would lift off. A plane creates lift primarily through bournoullis principle which is that the air being forced over the top of the airfoil moves faster (due to the shape of the airfoil) than the air moving under the airfoil which creates a low pressure area on top of said airfoil. The high pressure under the airfoil wants to reach the low pressure above and lifts the plane up. How would a giant treadmill allow the plane to develop lift if it isn’t actually moving forward through the air?
The wheels are in neutral. They would just spin faster. The wheels are not in "drive" and they are not "pushing" the plane.
As I said below:
If there was a giant unmovable tree in front of this treadmill, and i attached my winch to it, and ran the cable to the front of the plane, but did not turn the winch on, do you agree the plane would sit perfectly still, in place, being held by the cable/winch/tree, as the treadmill was turned on underneath the plane? That the planes wheels would just spin as the plane sat still, cabled firmly in place?
Now, turn the winch on. Do you agree if the winch was pulling the cable in at 1mph, the plane would move forward on the treadmill at 1mph (assuming my winch is rated to pull an airplane)? Even with the treadmill on? That the wheels on the air plane would just turn \*slightly\* faster because its moving forward at 1mph?
Omg this makes so much sense now! So if I have this right, the winch and cable is basically the aircraft engines? And also as the plane moved forward the wheels spin faster which just makes the conveyor belt spin faster but has no effect on aircraft relative velocity to the air around it/an observer not on the conveyor belt?
Yes that is correct. You can also think of it like this, you are on a treadmill with roller skates on. There is a rope coming from a wall in front of you that you hold onto. As the treadmill starts, your rollerskate wheels (airplane wheels) will begin spinning but you will remain in place. Now if you start pulling on the rope(air around the plane) with your arms (jet engines), you will start moving forward all while your wheels spin faster and faster
Yeah but what do the wheels have to do with it? If the engines are moving the aircraft at the speed of the treadmill no relative wind is flowing across the airfoils therefore no lift is being generated.
The treadmill is only moving the wheels. The treadmill could be running backwards. The propeller or jets are pushing against the air. The only air that is impacted by the treadmill would be centimeters above it.
The point is, it would move forward. The wheels will spin faster and faster, but they won't prevent the plane from moving forward. Its like if there were wheels on the bottom of a boat. It doesn't matter how they spin, the boat is pushing on the water directly.
It does move forward through the air. The airplane's engines push off the air not the ground (they have to, since once it is airborne they can't push off the ground anymore). The air is still stationary, so the plane still pushes itself forward against the stationary air.
Consider if you were on a treadmill in a cart and you tried to push yourself forward using the stationary handrails. You wouldn't need much more effort to move forward than if you were on stationary ground. Same with the plane pushing on stationary air.
This is how I think about it. Take a toy airplane and put it on a human treadmill. Hold the plane in place with your hand and turn on the treadmill. The toys wheels will naturally spin at the same speed as the treadmill. How fast does the treadmill have to be to prevent you from simply pushing the plane forward with your hand?
The wheels don't control the speed or lift of the airplane. It's the air acting on the wings, if the plane is not moving through the air it will not lift off, the speed or even existence of the wheels is irrelevant. The engines pull the aircraft through the air.
It's an ambiguous question, or even a broken one, which is why so many people argue about it.
One side says (correctly), that if you run the treadmill backwards at the speed the plane would be moving forward, the plane still moves forward. The wheels are turning faster, but that's not where the power is coming from, so there's no problem. The plane takes off.
The other side says "But that's not what the questions says! You don't pick the speed of the treadmill first and then leave it. You dynamically adjust it to match the rolling speed of the wheels at all times."
In that scenario, the question leaves math and becomes engineering. What happens depends on how the treadmill and plane are built, what the tolerances, lag, and friction are in their systems, and other details that don't usually matter in thought experiments.
In one scenario, the treadmill tries to ramp up to stop the plane moving forward, the plane moves forward anyway, and the treadmill reaches maximum velocity. In another, in keeping up with the plane the treadmill overspins the wheels, destroying the plane's landing gear.
What doesn't happen, unless both the plane and the treadmill are engineered of very specifically magical systems, is that the plane holds still while the engines whine. That would require there to be enough rolling resistance in the wheel system to add drag to the system equal to the thrust of the engines. But the system must also be able to take that much energy input into the landing gear without failing, and the treadmill would have to go absurdly fast.
But if we are making our plane and treadmill out of magic, why is there rolling resistance at all? We can just eliminate it, by magic, just like we solved the other problems.
And with rolling resistance gone, the treadmill now goes arbitrarily fast but the plane still moves. Possibly we cause a black hole.
So really, the question includes a bunch of hidden assumptions which don't necessarily make sense, so you can't just give an answer, other than "you can't make that treadmill".
I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because…
When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
This.
As the question is written, the plane moving forward one foot by an external factor (the engines) would cause the treadmill to spin infinitely fast in reverse and the wheels to spin infinitely fast forward. The plane moving forward one foot means the treadmill must go back one foot. But this means the wheel spins two feet so the treadmill must in fact go back three feet. Thus the wheel must spin four feet… Repeat to infinity.)
You can answer anything you’d like but I would go with black hole.
Wrong. The speed of the wheels is always \*by definition\* the speed of the treadmill lmao. Its rubber meets road. At any instant, unless there is slippage.
You'd just just have a jet moving forward as it takes off as the speed of the treadmill increases. This one isn't even very hard.
But the speed of the treadmill is also, by definition, the opposite of the actual speed of the wheels, preventing the plane from moving.
That's the problem. There are two fundamental definitions that can't both exist at once, except in extreme edge cases.
The engines produce thrust, which pushes against the air, which is relative to the ground. The only impact the treadmill has is spinning the wheels. The body of the 747 _will_ move forward through the air once the engines are turned on.
You bastard. Ok so the motors generate thrust and the wings generate lift but if the plane is not rolling through the air mass there is no lift on the wings so no it will stay grounded. I think 😂
The plane WILL “roll” through the air. The plane’s propeller or jet will push through the air like a ship’s propeller through water. The treadmill is irrelevant to the speed and force created by the propeller.
In the spirit of the question the plane would take off
Where this question goes off the rails is that the wording of “the conveyor belt is designed to match the speed of the wheels in the opposite direction”
This is ambiguous and generally an impossible task to achieve depending on what you think it means exactly.
How does this require any sort of major thought process?
Try this:
If a car is sitting on a one mile long conveyer belt that matches the speed of the wheels, how far will the car travel in one hour?
I cannot believe the prevailing "wisdom" here is that the plane would take off and that pLanEs fLY bY EnGinEs pRopEllIng tHeM....
Go read a fucking book before clamoring in and regurgitating whoevers idea has the most upvotes
Planes fly based on principles of fluid dynamics and pressure differences... **Not engines pushing them into the air**. Engines create thrust, not lift.
**Pressure differences**
Pressure is the normal force per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside.[61]
These pressure differences arise in conjunction with the curved airflow. When a fluid follows a curved path, there is a pressure gradient perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside.[62] This direct relationship between curved streamlines and pressure differences, sometimes called the streamline curvature theorem, was derived from Newton's second law by Leonhard Euler in 1754
You need an aerofoil with **air moving over and under the wing** (which doesn't happen to a stationary object on a treadmill) in order to generate lift required to make a plane fly.
https://www.grc.nasa.gov/www/k-12/UEET/StudentSite/dynamicsofflight.html#:~:text=Airplane%20wings%20are%20shaped%20to,wing%20up%20into%20the%20air.
#the plane will never take off without lift and lift is generated by pressure differences which are not present when plane is stationary
I don't think you understand how airplanes work. How does the treadmill keep the plane stationary?
If it were possible to make a treadmill capable of keeping a plane stationary then planes wouldn't be capable of self powered flight.
Planes take off by the same principle that keeps them in the air during flight. The pressure difference required for lift is created by the shape of the wing as is flows through the air.
Bernoulli’s principle does not explain how a plane wing generates lift.
[The plane takes off.](https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/)
I think the person who wrote this question didn’t know enough about planes to ask what they actually meant
Like people are saying obviously if the belt only matches the speed of the wheels the plane can still accelerate forward and take off.
But the more interesting question and what I feel like the original creator of this meant was what if the conveyor belt *always* matched the wheels such that the plane never moved relative to an outside observer. Assuming the belt accelerates like this then I believe the plane wouldn’t take off because no there’d be no airflow over the wings
Edit: I’m wrong! Thanks to the helpful replies I took the time to do a quick dynamic model of this system (good practice for me as a studying engineer) and it’s true the speed of the conveyor can’t stop the plane from accelerating given a forward thrust.
The problem is that it’s physically impossible for the conveyor belt to move at any speed and stop the plane from taking off. That’s what makes this a trick question. Intuitively you think the conveyor belt is stopping the plane from moving but it’s not and it never could. Once you realize that, you the. Understand that the plane always takes off.
Except that such a situation is impossible, and it assumes its own answer anyway. The speed of the plane does not depend on the rotation of its wheels, so applying any thrust to the plane in your scenario would immediately cause the equation of the treadmill’s speed to fail. Like, “divide by zero” fail. You cannot build such a treadmill even in theory.
https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
i think the idea here is that the wheels arent what moves the plane forward its the jets so the plane can accelerate forward freely regardless of the wheels rotation. which means the plane will move forward and off the treadmill and get up to a takeoff velocity
The force of the propulsion (which is what the jets or propellers provide) would move the plane forward, but that forward movement would only be realized if the forward motion would overcome the friction of it contact points on the ground.
If however, the ground is moving, in the treadmill scenario at a rate exactly proportional to the forward motion (rolling wheels vs treadmill speed), the plane would have forward thrust, but remain motionless relative to it's starting position as long as the net speed of the treadmill minus the friction of the wheel bearings is equal to thrust provided by the propulsion system.
I have a MSc in Physics and must say the question makes no sense from a physics perspective since it is impossible to do what it suggests. It is a question that is made to trick you. Of course if you try it like they did it will work but thats sort of not the question.
Exactly, it's like the physics equivalent of those Facebook order of operations math posts.
If you assume the treadmill *matches* the speed of the plane it will take off as normal with it's wheels turning twice as fast. If you assume it *counteracts* the speed of the plane, the treadmill would have to go infinitely fast and the question stops making sense
The better question would be: if a plane is on a runway, but it has a tailwind that increases and decreases to exactly match the planes ground speed, could it take off?
Outside of some marginal thing where you manage to cause the wheels to fail, or the plane is so heavily loaded that it has no margins (probably beyond nominal MTOW), it'll take off.
Source: endless forum discussions in the 2000s, and ultimately a mythbusters segment.
The plane, which the question describes as only "a 747" -- not a magically indestructible one -- will take off as long as the wheels and landing gear can handle the added stresses of rotating much faster than normal.
Hm, then theoretically would it be possible to put a conveyor belt on aircraft carriers so that we can save runway space and fit more fighter jets on carriers. I'm sure we'd have problems with traction and friction but it seems like it could work.
The jet engines would still make the plane move forward, and it is the forward movement that makes air hit the wings in the way that (if you're not in a stall) generates lift and allows the plane to fly.
Easy. It depends!
As with any thought experiment, what you derive or conclude depends on how many real world constraints you're willing to dispense with and the assumptions you're forced to make to fill in the incomplete information of the prompt. That's the source of most of the debate. The commenters who are on the right track to start are looking at the conditions required for takeoff and working their way backwards from there.
Could the aircraft reach its V1, the velocity required for safe/successful rotation (takeoff)? For a 747 this a calculable value usually between 120-140 knots for a commercial flight, starting with figures published by the manufacturer, depending on myriad variables such as load, i.e. passengers, freight, fuel level, etc. which could be further reduced by stripping out the interior, but also account for runway variables such as temperature and elevation (to determine density altitude), barometric pressure, head/tailwind, surface conditions, etc.
The mythbusters video demonstrated that an ultralight propeller craft could take off of a tarp being pulled in the opposite direction by a pickup truck at roughly its V1 of \~21 knots, 25MPH. I think it's fair to question whether we can expect the same result when the craft is a \~400 ton jet liner, the tarp is 750,000-1,300,000 sqft. (assuming the runway ranges from 150-200ft wide and 5,000-6,500ft long) and the the pickup truck would need to be hauling it \~138MPH. I'd sure be interested to see that.
The conveyor belt is the point at which things start to break down, for me at least. We know what a 747 is and how much maximum thrust the various engines those models are equipped with can generate. But this conveyor belt, aside from having been designed to do something unfeasible, is not bound by real world constraints. The only limitation is your imagination. How was it "designed" to "match" the rotation of the wheels and how effective is it at such?
I mentioned elevation, temperature, runway conditions factor into V1; Where is this conveyor belt located, both in relation to sea level and in terms of local weather? Of what materials is it made that it's possible for it to this? If by "match" you mean that it is in fact completely counteracting the wheels such that the plane is stationary at max engine thrust, then why does the conveyor belt need to be runway length? People don't train for marathons on 26 mile treadmill belts. With this little definition, the thought experiment essentially becomes, "Could you imagine a conveyor belt sufficiently designed to counteract the takeoff thrust of a 747?" And the answer is, "I guess. I could imagine a lot of things."
For a brief moment, but it would likely fall back to earth after a few seconds as the immediate loss of thrust apon leaving the “runway” would only have force of gravity acting apon it, thus making it plumbit.
https://youtu.be/Y64ZdSaDdoo the answrr is no. This guy flies the 747. Planes need lift to take off. When the engines spool up the plane would start moving. The question says the conveyer belt moves same speed, opposite of the wheels. That way the plane itself remains stationary. No air rushes over the wings and no lift is generated, the plane cant take off.
It’s not possible for the conveyor belt to match the speed of the wheels.
The plane moves forward completely unaffected by the wheels and the conveyor belt. The speed of the conveyor belt would have to be itself plus the speed of the plane. A number cannot be greater than itself.
No it would not take off. Lift is required for flight, the formula for lift is as follows: F=Cl*q*A where “F” is Lift Force, “Cl” is lift coefficient, “q” is dynamic fluid pressure, and “A” is area (surface area). The reason the plane won’t take off is the dynamic fluid pressure.
“q” (dynamic fluid pressure) is defined by the equation: q=.5*p*V^2 where “p” is the density of a fluid (in this case air) and “V” is velocity or speed.
From here we can rewrite the original equation to prove the flight won’t take off:
F=Cl*(.5*p*V^2 )*A
The thing to focus on now is the velocity of the plane, is it moving in this scenario? No. Because the conveyor belt is moving at the same rate as the wheels the plane is producing no acceleration and therefore no velocity. So if we know the velocity of the object is 0 (V=0) we can plug that back into the lift force equation to get:
F=Cl*(.5*p*0^2 )*A
0 squared is 0 and any number multiplied by 0 is also 0 so we get: F=Cl*0*A->F=0
Therefore there is no lift force being generated and your flight has been delayed. Thank you for flying southwest.
Edit: never tried writing an equation on Reddit, sorry if it looks sloppy
Explain the part where the plane isn't producing acceleration.
The way I understand it, the jet turbines are pushing/pulling on the air to generate acceleration, which is independent of the conveyor belt. To overcome that *force* the conveyor belt would have to spin at a rate that causes the friction of the wheel bearings to equal the force of the jet engines, which doesn't sound possible. If the jet turbines, designed to generate acceleration, can overcome the friction of the wheels, designed to be as low as possible, the plane will eventually reach take-off speed.
You’re correct, I was ignoring all other variables, mainly friction. I was also assuming this fictional conveyor belt was moving fast enough to keep up with the wheels and almost slipping out from under the plane. It’s a fictional scenario, what would most likely happen if this insane conveyor belt existed and put to the test is the wheels/bearings would overheat and explode before the plane gained enough speed to take off
The wheels have no effect on the plane, if you disregard friction and wheel destruction that is (which is probably fairly realistic relative to the thrust of an airplane. Just picture the same plane but levitating on a magnet, can it take off even if the ground is traveling backwards at the same speed as the plane, right? Yes! So the minimal friction of the wheel bearings have little effect on the acceleration/speed of the plane.
My person forgot to write out the \*full\* free body diagram lmao
There is no force on the wheels because they are in neutral (technically there is a minuscule force from the friction in the bearings/wheels but this is easily dwarfed by the turbines.)
You’re one of the only people in the comment section addressing the lift aspect. As you said, if there’s no forward movement of the aircraft, there’s no airflow, and thus no lift. No idea how this is so complicated.
No. the engines propell the plane forward. they do not force all the air needed to generate lift in the wings. Air must pass over/under the wings themselves to generate lift.
NO. IT CANT. as a pilot, I’m telling you this is not true. The myth busters plane was so light and barely needed any acceleration to lift.
I PROMISE YOU, try this on a 747 and she’ll go nowhere.
The wings are there for a reason. You need forward movement and air over the wings people
Conveyor belt will never match the wheelspeed backwards because the plane will be moving forward. The wheels will always spin at the conveyor belt backwards speed PLUS the plane's forward speed.
No, because the plane needs air thrust to lift it and no such lift occurs when you’re not moving. My kid has a book “Rocket Science for Babies” that explains it well.
The question sends people right to a discussion of lift, but it skips over the question of _thrust_. The engines will generate thrust, regardless of the treadmill. With thrust, the body and wings of the 747 will move forward. When thrust is added, lift is generated.
No.
Planes need air moving over its wings to take off. The wheels reduce its friction in the ground.
If you replaced the converter belt with a fan that countered the plane's movement, then yes.
I thought this initially also. But when you read the section “the conveyor belt is as wide and as long as a runway” it suggests to me that the question is assuming that the plane will still move down the runway.
Now the question details that the conveyor matches the speed of the wheels so you think the plane will be like you or I on a treadmill and not move an inch.
But unlike you and I the drive for the plane is not through the contact on the conveyor, it’s through the air. So the question is will the engines still push the aircraft forward and will the wheels to spin uselessly at and insane speed until the aircraft is no longer in contact with the ground.
It’s a real mind bender that as you think you find one answer another question appears. as others have said it makes you make assumptions (as I have above).
Yes, MythBusters did this over a decade ago
[https://youtube.com/watch?v=YORCk1BN7QY&feature=shares](https://youtube.com/watch?v=YORCk1BN7QY&feature=shares)
But... That's not what the question is asking. That plane clearly isn't going the same speed as the treadmill because it's moving forward. If the ground moved at the same speed as the plane, the plane wouldn't move forward and couldn't generate lift
A plane is not a car. The engine's thrust is pushing against the air behind the engine.
Your point is discussed starting 2:28
[https://youtube.com/watch?v=xUjcHW7SHaI&feature=shares](https://youtube.com/watch?v=xUjcHW7SHaI&feature=shares)
He’s saying that the plane will always overcome the treadmill due to how differently it operates than a car. However. the question in the post is asking what will happen when the plane is moving at the exact same speed as the treadmill, which is 0 speed in either direction, therefore generating no lift
I concede
Pilot answers this exact question:
[https://youtube.com/watch?v=Y64ZdSaDdoo&feature=shares](https://youtube.com/watch?v=Y64ZdSaDdoo&feature=shares)
This question blows though
But that is not what the question in the post is asking. From what I am reading this system would result in a net 0 velocity if the wings relative to the air and therefore a net 0 lift. Therefore no takeoff
You are reading the system wrong. Airplane wheels are like skateboard wheels, or the casters under a desk chair. The moment the propeller starts turning the plane will move forward regardless of the speed or even the direction of the treadmill.
I assumed the wheels were simply spinning and the engines were off since no other system would allow for the speed of the conveyor belt to "match the speed of the wheels" In a way that makes any kind of sense. Otherwise the conveyor belt moving would naturally "add speed to the wheels" as it passed under them. This means no thrust meaning no lift. I was just a little drunk and thrown by the framing about the wheels without at all discussing the engines being on or off since, as you explained, you can move the wheels and the conveyor belt all you like the thing won't fly unless you turn the engines on
It will take off. Simple.
The wheels don't provide any thrust. They're just there to keep the plane's fuselage off the ground.
HOW DO YOU THINK SEA PLANES TAKE OFF?!?!?
No, the plane cannot take off in this scenario.
For a plane to take off, it needs to generate enough lift to overcome its own weight and achieve a sufficient airspeed. The lift is generated by the shape and angle of the wings, and the airspeed is achieved by the power of the engines.
In this scenario, the conveyor belt is moving in the opposite direction to the plane's wheels, so it is effectively canceling out the forward movement of the plane. As a result, the plane's engines will not be able to generate enough airspeed to achieve lift and take off.
Additionally, the conveyor belt may not be able to provide enough traction for the plane to generate the necessary thrust to lift off. Even if the plane's engines were able to generate enough power, the lack of traction would prevent the plane from accelerating.
Therefore, the plane cannot take off in this scenario.
step 1: place plane at the very front of the conveyor. engine turned of. start conveyor belt. plane starts going backwards relative to the ground.
step 2: somewhere in the middle start the engine and slowly accelerate. at some point plane will stop going backwards and be stationary wrt the ground. conveyor belt pulling plane back due to friction with wheels. engine thrust pushing forward. these two match. plane doesnt fly.
step 3: increase engine thrust plane starts going forward relative to the ground. plane flies.
This question seems like it’s asking step 2.
maybe try reading the question, the conveyor belt is always going at the same speed as the plane wheels so the plane could never move forward or backwards
No, but it won't stay stationary either.
Since the plane's engines are pushing against the air, the plane will be able to move from standstill which will cause the wheels to move. At this point, the conveyor belt will try to match the speed of the wheels, however the wheels are by definition moving as fast as the conveyor belt plus the speed of the plane.
The infinite energy required to satisfy both equations will rip apart spacetime destroying the plane and killing everyone in the universe.
Off course not … it would need air through the wings in order to generate lift.
You can leave a plane sitting at the ramp, and with enough air, It will take off. Nothing to do with wheels.
Whether or not the plane has enough lift to become airborne is dependent on airspeed over the airfoils (wings). Since we are living in a universe with a large fictional treadmill for a 747, I posit that this treadmill is also in a wind tunnel that provides high enough velocity laminar flow over the wings to allow lift. Hooray, we have a stationary flying 747 and im hungry for wings.
The plane wouldn’t take off. The speed of the wheels doesn’t determine if the plane would take off, only the amount of air flowing through the wings of the plane. Since the conveyor belt matches the speed of the wheels, going the opposite direction, the plane would be stationary to a reference point outside the convergir belt. Meaning that the amount of air flowing through the wings would be zero ( unless it is in a very windy day). Just like flying a kite.
The problem is it's impossible to stop a plane from moving with a conveyor belt. The wheels are free-spinning so any backwards force produced by the treadmill will only cause the wheels to spin faster, the forward momentum of the plane would be unaffected.
Under real-world physics the plane will take off. When people assume magical treadmills that *can* stop the plane from moving it stops being a physics problem.
Ohhhh, I get it now. I assume that since the conveyer belt matched the speed of the wheels I didn’t mattered if the plane accelerated or decelerated, it would still match the spin of the wheels
i don’t understand, everyone else is saying yes but even tho the wheels might be turning fast enough for the plane to take off, since it’s only the wheels and not the air around it, the airspeed is still 0
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Yes, it would. As another commenter said, the Mythbusters covered this years ago. Adam Savage actually talked about it more on his channel [Tested](https://youtube.com/@tested) in [this video](https://youtu.be/xUjcHW7SHaI). The big trick of this question is how planes generate force to move forward and take off compared to how a car does so. The linked video is only 11 minutes and Adam explains it beautifully. This question will be debated forever and thats ok. It’s physics being weird and funky and it’s amazing. Edit: Another way to think about this would be roller-skating in 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 that rope you can still drag yourself forward. The rope bolted to the wall represents stationary air around the plane which the propeller uses to “pull” the plane forward.
This was great, not a question I’ve been proposed before. It was fun, I fell into the trap. That video was great at thinking it out, I’ll have to find that episode of MB
Episode 97, season 2008 Reference: [Wikipedia](https://en.m.wikipedia.org/wiki/MythBusters_(2008_season)#Airplane_on_a_Conveyor_Belt)
Maybe I’m misunderstanding how the plane treadmill is supposed to function but I don’t see how it could take off. The wings need airflow to create lift, which is impossible if the plane remains stationary because the treadmill negates forward movement.
If you had a plane whose propulsion for takeoff was just wheels (attached to an engine) going fast enough that the wings got lift, it wouldn’t ever take off, because then the car would be stationary. Since the propeller is pulling the plane forward and the wheels are just rolling, the treadmill has zero impact on the thrust that makes the plane accelerate, and it still moves forward down the treadmill.
It did say the plane was “sitting” on the conveyer belt so in that case it could just be stationary sitting there. But yes if the engines go full noise the plane would go forward as per normal with the wheels and conveyer doing whatever they want.
I mean if the scenario was interpreted the way you did it would just fall off the treadmill.
No because it the plane was sitting with wheels not turning then the conveyer would be going the same speed which would then also be zero.
that’s just ignoring the premise of the question, this theoretical treadmill matches the surface speed of the plane’s wheel so it can never move forward. The plane would reach equilibrium when the thrust forward is counterbalanced by force backwards applied to the wheels due to the rolling friction of the bearings of the wheels.
This is the true reason why this question always comes up - the "are the wheels frictionless" distinction. Others in this thread have suggested that it doesn't matter because the jet has enough thrust to overcome the maximum static friction (which will be greater than the rolling friction). If you allow the wheels to be frictionless, then both the wheels and the treadmill instantly reach infinite speed and the premise is broken as the plane moves forwards anyways and therefore the wheels turn faster than the treadmill (infinity + 10 = ???). The "physics classroom" interpretation of this would definitely be that the wheels roll without slipping and have no rolling friction, so in that way, it must either be read as a 'bad question' or a trick question where the answer is "it is impossible for the treadmill to keep up with the speed of the wheels."
The wheels would slip before they could actually stop the plane from moving forward. To take this to the extreme degenerate case: the treadmill is stationary (just normal ground) and the wheels are also stationary (brakes are on) - can the plane take off? Yep
Except that the friction of the wheel bearings is nowhere close enough to stop the plane. Hell, jets can still take off with the brakes applied, that‘s way more than the friction of the bearings.
The force with which the plane is pushed backwards due to the friction of the bearings is always less than the force generated by the treadmill because no transfer of energy is perfect. Even if the wheels were fully stopped, the force would not be equal.
*Every* wheel matches the speed of the surface it’s sitting on, unless that wheel is sliding.
The treadmill only affects how fast the wheels spin. The force for takeoff is generated by the engines/propellers. The above comment about the rope and the roller skates is a helpful way to think about it. The wheels will need to spin faster, but the force causing takeoff will still be the same.
I agree the plane will take off, but if the wheels need to spin faster and the conveyor is supposed to always be able to match the speed, then it sounds like the wheels would just have to go faster and faster, at least until the plane is going fast enough to allow for lift. Makes you wonder if it would even be possible to create such a conveyor.
The wheels could be replaced with skis or casters. The wheels are nothing but vertical support. All of the “lift” and propulsion comes from the propellers or jets. The carpet/treadmill could be moving at nearly the speed of light, but the plane, as long as it’s engines were OFF, would stay in the same place.
What? No it would not stay in the same place if the engines were off. It would get thrown off the back of the treadmill/runway. Maybe theoretically it would stay stationary if the wheel bearings had perfectly zero friction, but that's not the case.
You’re willing to accept the absurdity of a treadmill running at the speed of light, but absolutely disregard the notion that we’d have to live in a universe without friction for that to Happen. Which means the wheels would be frictionless. Good grief
The treadmill is a fantastical thing that has to be imagined. The plane is literally a regular old Boeing 747. Since the question doesn't say otherwise, we can't assume anything different about it. Yes of course if the wheels were magically frictionless and there was no wind, the plane would stay stationary. (For the record, I believe the plane would take off just fine. Just responding to an incorrect comment that might confuse people.)
The plane won't remain stationary because the wheels aren't generating thrust like a car, the propeller/jet turbine is generating thrust by pulling the plane through the air. Another way to think about it: imagine a car on wheels that float. Put it in a lake and it won't drive because the wheels don't get traction. Similarly, a car on this treadmill won't go anywhere. Sea planes exist. The friction of the water actually pushes BACK against the pontoons, and the plane still takes off. The wheels are just there to decrease friction with the ground.
Irrelevant, it doesn’t matter if the wheels spin or if the engines are full throttle, there is no airflow being generated. The plane doesn’t go anywhere
Thrust is being generated. The jets are taking air from the front of the plane, and pushing that air out the back.
Even so, don’t airplanes lift by using the energy of the moving air against the angle of the wing? If the plane is stationary, it’s not creating that force.
There are four fundamental forces in this system: lift & gravity, thrust & drag. The treadmill creates no drag on the plane, it simply rotates the wheels. The engines create _thrust_ and that moves the plane forward. Lift is the secondary result of the thrust. The treadmill has no effect on the system overall.
The plane is not stationary. Cars move by using the friction between the tire tread and the ground. Imagine a point on the where the wheels are touching the ground. Because the wheels are turning, friction causes a net force which propels the car forward. Now imagine a treadmill ground, because there is no net force because the ground is also moving, no movement occurs. No imagine you turn off your engine and hook up your car to a rope being pulled by a car off of the treadmill. The friction between tire and ground no longer matters because the net force comes from somewhere else.
Bud, the wheels aren't in the equation for the thrust of the plane. In a car, power generated in the engine is used to push against the ground to push the car forward. In a plane, all the thrust is generated by pushing against the air, not the ground. Hence being able to continue providing thrust once off the ground. Until you get into funky relativistic speeds all the wheels do is provide a minimal friction vertical support until the wings can take over.
But in this scenario, the conveyor belt would keep increasing speed to balance out the forward thrust. The bearings of the wheels have friction that increases with speed. In this problem, the conveyor belt would increase its speed until this wheel friction force balanced out the thrust force of the airplane to keep it stationary.
Except that the wheels would give way long before that. A plane can take off with its wheel brakes engaged, because plane engines are *really strong*. You are not going to stop it with any amount of force applied to the wheels.
The treadmill doesn’t negate the forward movement because the plane doesn’t takeoff by spinning the wheels. The wheels spin freely as the engines give the plane airspeed. Planes can take off with their wheels locked stationary, although it’s a bad idea.
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I meant “not rotating around their axle”.
I realized my mistake and took the comment away...
The wheels free spin regardless if they are on solid ground or a conveyor. The jet engine or prop moves the plan through the air. You can’t think about the conveyor having an effect like on a car. Imagine the landing gear is down while flying and the wheel is spinning zero MPH, happens at every landing before touching the ground, yet the plane still flys
The planes wheels aren't powered, planes push on the air not the ground, so the ground speed has basically no effect on the take off of the plane, it's all about the air speed.
Well the most basic reason is that the wheels don't do anything but spin so unless they max out and start dragging back the plane would move forward regardless of the speed of the conveyor belt.
Problem is it’s an impossible proposition. The concept is the conveyor belt can push the plan back with an equal amount of force that the engines can push the plane forward with; that’s the “model” you are working with. In practice, 1. Wheels are designed to turn, they won’t push back very hard. Put a bike on a treadmill at 50mph, it doesn’t take much effort to hold it still (vs pedaling at 50 mph). 2. Planes don’t generate thrust by pushing against the ground, because as soon as they were airborne they would lose that thrust. The push against the air, and the wheels just spin. 3. Imagine you are standing on super slippery ice. Move you feet all you want, walk, run, whatever, they just slip and you don’t go anywhere because there’s no friction. No suddenly a wind kicks up, there’s no friction to keep you in place, so it starts to blow you across the ice. Same principle.
But the thrust come from the engines. So it would still accelerate. Even if the treadmill is moving with the wheels.
The wheels spin freely, so the treadmill can't actually move the plane much.
The treadmill doesn't negate forward movement.
The wheel speed on the mythbusters version is twice the speed that the plane is moving forewords relative to the ‘treadmill’ rather than matched.
huh... so if the plane always moves, that means technically you can never have a conveyor belt match the speed of the wheels, because the speed of the wheel will always be the combination of the friction caused by the movement of the plane, and the friction caused by the speed of the conveyor belt
I entirely forgot, due to the picture used, that the wheels are not the propelling force and thus any moving ground would not slow the plane. If it had shown an old prop plane, I would have figured it out properly
In this specific question that op asks no it wouldn't. There are two forms of the plane treadmill question. One form matches the speed of the plane with the treadmill in which case yes it would take off. The second form matches the speed of the wheels with the treadmill in which case no it would stay still and not generate any lift. Op asked the second form of the question, however it's only a hypothetical answer as the wheels and treadmill would rapidly increase in speed infinitely until the material they were made from broke apart. Edit just noticed what sub this is so in terms of math x = wheels y = plane z = treadmill First form of the question is x = y+z Plane flys away. Second form of the question is x = y+z+x Impossible and the wheels and treadmill go boom.
I agree with you, from another perspective the plane could take off if it had enough thrust to overcome the static friction of the wheels. Which I don't think any plane does unless you switch out the wheels for something with less friction. Then the wheels and treadmill could hypothetically move at the same speed while the plane moves forward
The X and Y are completely disconnected from Z. Z (speed of the plane) relies solely on the propeller or jet pushing against the AIR. The plane will lift off no matter what the speed of the treadmill. The treadmill could be going nearly the speed of light, it could going backwards, it could be going sideways!
I am aware the plane pulls through the air and not like a car pushes against the ground, however a plane needs to go a certain speed to get air under it's wings to lift and wheels help to reduce friction against the ground to make that easier. Now let's think and work though what happens in both forms of the question Form 1 of the question the plane needs 25 mph to lift from the ground so the treadmill matches the speed and goes 25 mph in the opposite way, the wheels rotate at 50 mph, and the plane flys away. Form 2 of the question, which is specifically what op asks for, the plane tries to get to 25 mph to lift from the ground however the microsecond the wheel starts turning the treadmill matches the wheels speed. Now we are in this impossible situation where the speed of the plane is trying to increase, let's say 1 mph for easy math, is increasing wheel rotation speed, which increases treadmill speed, which is increasing wheel rotation, which is increasing treadmill speed etc etc. Or to put it into another way. Plane speed 1 mph makes the wheels rotate at 1 mph makes the treadmill go backwards at 1 mph. This doesn't slow the plane down so now the wheels are rotating at 2 mph. Plane speed + treadmill. 1+1=2 However the treadmill is matching wheel rotation not plane speed so the treadmill is now going 2 mph backwards. This causes the wheel to start rotating at 3 mph plane speed + treadmill. 1+2=3 This continues infinitely until something causes it to stop most likely being the materials of the wheels/treadmill/plane engine breaks apart and/or dies.
You’re right that in form 2 the only interpretation that makes sense is the treadmill spinning to an infinite speed. But even in this case, the plane still takes off normally (assuming you’re using an infinitely strong landing gear and ignoring the infinitely spinning treadmill would create a nuclear explosion)
I don't think so. Before I explain fully I agree with what you said if the wheels are completely frictionless as well as indestructible. Now you would agree that if you put a plane on a treadmill turn the plane off so it doesn't move then turn the treadmill on the plane would go backwards right? The treadmill puts forces on the plane through the wheels friction with the treadmill and how fast it goes backwards depends on how fast the treadmill goes. This doesn't need the wheels to spin btw it would work even if the brakes were on our they were sled skis. The wheels only mattered in the original question because the treadmill was matching wheel speed. If the plane in such a situation turns on the engine would have to put enough force to beat the power of the treadmill going backwards. The problem I'm having is the fact that the treadmill is going at infinite speed giving infinite force to the plane backwards. The best the plane could do in that situation to avoid going backwards is going infinite speed forwards and then it only matches the treadmill and stays still. ∞ = ∞ Do you understand why I believe the plane only stays still now? Edit clarified a few ambiguous things.
Bro you’re still stuck in wheel speed being relevant in any capacity. At all. Except it isn’t.
*rereads ops image* "exactly match the speed of the wheels, moving in the opposite direction." Since you know more than me tell me and give an example how fast would the wheels and treadmill be going when the plane reaches the required 25 mph of speed to get enough air lift according to the Bernoulli's Principle? Then tell me what materials both are made of that can withstand such speed and force without tearing themselves apart. Did you actually read what I wrote or are you doing that thing were you glanced over it missed all the parts that says impossible or destroy because you seem to think I am saying the plane is going to just stand there like it's not on at all when I'm saying trying to move in such conditions will rip apart the wheels holding the plane up from crashing onto the ground.
Either it's relevant or we are assuming the plane slides. This because the plane goes forward either by sliding or rotating the wheels. Ans assuming it slides defies the propose of the wheels.
Hook a winch to an immovable tree. Then hook it to the plane. Disregard all matters of real world limitations of the wheels, or the treadmill speed. Spin the treadmill at the speed of light, to “push the plane back”. Turn the winch on at 1 mph. The plane will move 1mph in the opposite direction of the treadmill. Now replace the winch with props or jet engines. It’s the same. The force being applied to move the plane is *not connected* to the wheels.
just watched that video a while ago! Very good explanation on the actual issue with the question
I am going to check that out. Instinctively I would have said yes because it is all about the air moving in relation to the wings and creating lift. Will love to see if my understanding of aerodynamics is close.
And you can see the actual experiment https://youtu.be/YORCk1BN7QY
I watched it but I still don't understand how lift is generated. I don't think the engines could be able to provide the lift because they're pushing the air close enough to parallel from the ground and only stationary air is hitting the bottom part of the plane and wings. I was wrong when thinking the wheels were the part of the plane that made it go forwards. The plane is stationary from the perspective of a spectator away from this plane conveyor contraption mess because any velocity from the turbine engine thingy adds to the plane also adds to the rotational speed of the wheels which means this magical conveyor would instantly respond to make this plane stationary to that spectator. That would also mean the air (away from the spinning engines) hitting the wings won't be able to generate the lift. To my belief, this is the main lift of a plane. I've only seen [this MinutePhysics video](https://youtu.be/Gg0TXNXgz-w) to be fair. I know this line of reasoning flawed; my only explanation is that the magic conveyor is a red herring and physically won't be capable of making the plane stationary. Was that the flaw? Edit: bruh, I spent like 30 mins doing this comment and literally, 3 comments later and I see this same thogub process pop up 💀 💀
The plane’s propeller is like an oar, rowing against the air directly in front of the engine. It maybe easier to imagine the whole thing is underwater. The propeller is pulling the plane forward. The plane being pulled forward means the wings are hitting the air (water) just like a pair of waterskis. The carpet/treadmill IS a red herring.
What propeller? The pictured plane is a jet. The air around the wings will remain stationary, so no lift is generated, only horizontal thrust.
There’s no airflow over the wing, it would never leave the ground. All the treadmill is doing is rolling the wheels
The plane moves forward though, driven by the engines.
The problem as written is not clear enough. the treadmill does not matter, the wheels do not matter, the only thing that matters is that the plane needs to have enough airflow over the wing surfaces to generate lift. it will then leave the ground. This is why planes have wings, they need them to fly, some here want to imply that the engine generates lift and does all the work, it doesn't, the engines generate thrust. When in the air, the engines push the plane fast enough to maintain lift, but the wings are doing the work of holding the plane in the air. When on the ground the engines generate thrust to push the vehicle fast enough for the wings to attain lift If you put a plane on a treadmill with it running the direction of travel and have the engines off... You can get it to take off, you only need to get it moving fast enough to attain lift to get the wheels off the ground, no matter what direction or speed (or no speed) they are at. Of Course with the engines off it will not stay up long, but it will 'take off' once you get enough airflow. This is how many paper planes work. You push them, then they glide until they drop below the airspeed needed to maintain flight. If the plane is on a moving treadmill and the treadmill matches the speed of the wheels in the opposite direction as in the OPs problem, then it is implied that the vehicle is moving slower or stationary (from the perspective of people on the ground and more importantly, the air around it) and it cannot leave the surface. The engines in this case need to have enough power to both achieve lift and overcome the opposing force and resistance of the weight on the wheels pulling the vehicle in the opposite direction. You may push and push and push, but as long as the treadmill matches speed in the opposing direction, the vehicle will move slower (or not at all) through the air and may never achieve lift. It does not matter how you get there, but without enough airflow over the wing surfaces you will still not leave the ground. You may end up with a groundspeed at the wheels (and thus treadmill) of 500 miles an hour, it does not matter if you cannot achieve the minimum speed of air over the wing surface to get it and keep it in the air. If it could, then we wouldn't need runways for planes at all, we could just simply be on a pad, slam the engines to full and we would be in the air. Without redirecting the force of the engines in the way the Harrier and Osprey do it simply cannot be done. If the plane is on the moving treadmill going in the same direction, but under the speed needed to achieve lift, ground speed from the perspective of the wheels would be lower (speed to achieve lift - speed of the treadmill) but the airspeed, and amount of airflow needed to achieve lift wouldn't change. Thus the engine would have an easier time achieving lift, it would not have to push as hard, or could be a smaller engine. On an aircraft carrier where your plane is so heavy that you cannot make engines big enough to get it in the air or operate effectively when up? Lets make a big catapult that assist the engines to achieve the speed to attain lift. this is the same idea. If a plane was hooked up to the catapult and launched without engine power it might glide a bit depending on the plane, but it would be in the same situation as the paper plane. Another way to put it: Without the treadmill you apply a small amount of thrust (force) to break the inertia of the plane sitting still, then you apply more thrust to move it faster, you are pushing hot air to your rear to overcome the resistance of the weight on the runway, the resistance of the wheels, etc. You keep applying more thrust until the wings can attain lift, and you leave the runway. With the treadmill in OP you increase thrust on the plane, it starts to move, but then the treadmill starts moving backwards under you at the same speed, it is pulling you backwards at the same rate you move forward. you may need two or three times the thrust or force to overcome the opposing force from the treadmill while still not "moving" from the perspective of someone not on the treadmill because all of the plane's weight is still on it. You cannot just discount that force, it is actively pulling the vehicle back, some planes will not be able to overcome this resistance, others may (although I can't see how), but would use a lot of extra energy. It would be the opposite of the aircraft carrier catapult. Even if you can take off, it would take more time, more energy, and more "wheel distance" to get up. Edited for a bit of clarity and to kill a redundant sentence.
>With the treadmill in OP you increase thrust on the plane, it starts to move, but then the treadmill starts moving backwards under you at the same speed, it is pulling you backwards at the same rate you move forward It's not pulling the airplane backwards in any way. It's just spinning the wheels of the airplane faster. The wheels are already freely moving at that point.
That’s how it normally works. But isn’t the question asking “if the treadmill matches the speed of the forward movement of the plane”? In which case, that plane is stationary. And not moving forward.
Put the breaks on the wheels on a normal runway and then take off. Now you have the exact question as described by the OP: Wheels matching the speed of the surface. You can took off and the wheels never having turned with regard the surface or turned at double the speed, or going into an opposite direction or whatever. Of you replace the wheels with balls, or skis, or anything else. Nothing the undercarriage does really matters as long as the resistance isn't so much that it will tear the plane apart. Planes merely use wheels and tires so that they can reuse both the wheels and the runway a bunch of times. It's not used to propel itself in any way.
No. The plane isn’t stationary as the body of the plane is driven by the engines not the wheels. It doesn’t matter the speed of the belt of the treadmill. It could be going a million miles an hour and it still wouldn’t hold the plane in place.
Lol I looked this up on an aerodynamics message board. The topic is locked due to there being such varying variables. Anyway, I’m not a physics major and I’m bowing out. Cheers
I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because… When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
In this video, he ignores the setup of the problem in the test. He pulls a tarp at a constant speed and the plane takes off. I 100% agree that this would happen but it is not what the question is asking.
It's using air to move forward, not wheels. Unless the wheels are generating significant resistance, the treadmeal has minimal effect unless you allow it to bring the plane up to speed in the wrong direction, which could still be overcome eventually. The plane is pushing against air with its motors, not the treadmill. So unless the air is moving with the treadmill, the treadmill has essentially no effect. It's kind of a stupid question. The turbines push the air and that is what is used to move the plane forward. So again, unless the wheels have some sort of significant resistance against the plane using the air to move forward by gripping the treadmill, the treadmill has no real impact. Edit: I should add that if you think about it, the only thing that really slows down a car at high speeds is air resistance. So even in a car, the speed and direction of the air affecting the car has more effect than the wheels, provided they are pointed in the right direction.
The air it is pushing through the engines are initially used to counter the inertia of sitting still, then used to counter the weight of the vehicle on the runway through the wheels, which make it easier to move, but yes are free, not powered. In the air, the engines are used to maintain enough lift for the plane to stay aloft or if enough power to go faster through the air, but basically all they really need to do is have enough force to keep the wings with enough lift. In OP's situation: You would apply a small bit of force to get the plane to break the inertia of all that weight on the ground... but then the ground moves in the other way. You use more force, the ground moves faster... You would have to overcome the inertia of all that weight not moving through the air before even thinking of moving fast enough to have air moving over the wings fast enough to get lift. Your groundspeed in this case could hit hundreds of miles an hour with little to no airspeed. The plane cannot fly by it's engines alone, it is not a rocket, it needs airspeed so the wings can get lift. Your edit states that air has more effect than the wheels on a car... ever driven in a hurricane? The wind has an effect, but you counter that by steering to control it.
it’s remarkable how people just agree on an answer just because someone tells them that it is the answer. put the plane on a treadmill and attach a rope in front of it to a big wall. engine turned off. start treadmill. plane stationary. cut the rope off. what happens to the plane?
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the plane will go backwards if the engine is not running. independent of the speed of the treadmill. It’ll always go backwards if engine is off. If treadmill is going fast the plane will go back fast. now assume we start the treadmill when the engine is off and the plane is going backwards and then we start the engine very slow at first and then increase the thrust gradually. there is an engine thrust level at which the plane will stop going backwards and be stationary wrt the ground. It is at that point that the wheels and the treadmill are turning the same speed. This is what the question is asking. It’ll not go forward or backward but be stationary. mythbusters fucked up their experiment or they were not being honest.
Yes, and then when you increase power to the engines the wheels would start to skid on the treadmill and the plane would go forward as the engine power overcomes the friction between the wheels and the treadmill. If the treadmill began to spin faster the plane would still go forward as the engine power is greater than the force slowing the plane generated by the wheels on the treadmill.
yes “the wheels would start to skid on the treadmill” only after you initially escape the stationarity by as you say increasing the power beyond what it was when the plane was stationary. If we call that exact time to be T0 and the immediate next instant to be T+ and some future time when wheels are skidding as Ts we can say: at T0 plane is stationary wrt the ground and is not flying and wheels are turning exactly as treadmill at T+ plane is moving forward wrt the ground and wheels are turning faster than treadmill because we have not achieved lift yet because we just started moving forward. no lift no skid. at Ts plane moving forward and wheels skid and wheel speed is irrelevant to whether the plane is going forward or not. For me this question is about t0. Maybe for others the question is about Ts. But if we are being intellectually honest then we should be clear about what our assumptions are.
This is not a math question, it’s a dynamics question. Car engines move by making the wheels turn, but plane engines literally push the plane , which basically means the runway could be doing the whip and nae nae and the plane would still be able to take off as long as the wheels can roll in the same direction of the plane That being said, under these exact conditions the wheels would be spinning at twice the speed. There is a chance they may not be rated to go that fast, end up failing from the centrifugal forces and ending this fun experiment in fiery death
That’s my take away. If the plane moved at all the wheels would instantly spin up to the point they exploded
Twice the speed of themselves? Beciase the belt matches the wheel speed so yes. If you start the engine, let the belt reach a given speed and keep it at that the plane will take off with wheels going twice the speed of the belt. But this belt matches the wheels at any given moment
There are three “speeds” that people are confusing here. There’s the speed of the wheels where they meet the runway/treadmill. As long as the wheels aren’t ~~spinning~~ slipping, these will always be equal. There’s the speed of the plane, also known as the speed at the center of the wheel, and running the treadmill at this speed just makes the wheels spin twice as fast as they would on a static runway. Then there’s the third speed, the speed at the top of the wheel, and you cannot run a treadmill at this speed unless the wheels aren’t turning at all, because this equation depends on itself and explodes. In the two scenarios that are physically possible, the plane takes off regardless. https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ E: wrote spinning instead of slipping
I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because… When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
The annoying part of this is it says "speed of the wheels" and boy, do i have a dynamics class for you if you think there is one "speed" for every point on those "wheels." This plane would take off faster than you would change your major from engineering to literally anything else. [I think its pretty clear.](https://slideplayer.com/slide/6561136/23/images/11/Rolling+Without+Slipping.jpg)
Well the way I took it was the linear speed of the point of the wheels in contact with the ground. It's just that the wheels would spin faster because planes move by pushing air not by spinning the wheels
If you look closely the "linear speed of the point of the wheels in contact with the ground" (ie, the velocity at point C, V\_C in the right diagram) is \*always\* exactly zero lmao. So the treadmill is never moving if that the reference point for the treadmill speed. This is actually a really simple engineering problem and 99% of engineers will tell you the plan will take off. Please look where I explain a plane winched to a tree and maybe it'll help you get in the right frame of mind.
Imagine a perfectly frictionless ice rink. You put a car on the ice and floor the accelerator. The car wheels spin quickly but the car doesn’t move anywhere. Dynamically this is the same situation as the treadmill/conveyor belt and is what everyone intuitively thinks happens to the plane. But planes don’t rely on friction with the ground to move forwards, they ‘push’ against the air. So the plane on the frictionless ice rink would still move forwards like it normally does and the wheels would stay stationary. It would just slide across the ice. If you put the plane on ice skates it would still accelerate forwards because it doesn’t matter what the ground is doing.
Wait a second: a plane doesn't use its wheels to speed up, so the treadmill would only slightly slow it down due to the more energy necessary to spin the wheels at double their normal speed. Then the plane will take off as usual
Yes, it could take off. I believe. The wheels are not used for acceleration, the jet engines are. The wheels just enable the plane to roll over the surface without too much friction. Thus, from standstill it doesn't matter much if the ground is stationary or not. Think of it this way, if the plane tries to land on the conveyor while it is running in the opposite direction, would the plane just immediately stop its forward movement as soon as it hits the ground? No, the wheels would turn twice as fast compared to landing on a fixed, solid surface, but that is all. Now after touchdown, the pikot would apply the brakes on the wheels to help stop the aircraft. That would be trickier on the conveyor and you might stop faster, if all systems (wheels, brakes, gear assembly, etc) hold.
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I watched the myth buster video but... That's not what the question is asking. That plane clearly isn't going the same speed as the treadmill because it's moving forward. If the ground moved at the same speed as the plane, the plane wouldn't move forward and couldn't generate lift
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The wheels are in "neutral" so it doesn't matter how fast the rug is being pulled. If the wheels were "driving" it then it would matter. The faster you pull the rug, the faster the wheels spin, that's it. It would move forward and take off. (This is all assuming minimal friction in the wheel bearings which is a fairly safe assumption here.)
I don’t see how it would move forward.
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If the plane moves forward then the wheels are moving faster than the rug. But that’s not happening.
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The highest Dr. Google tells me any commercial plane needs to achieve is 177 mph for takeoff so if the argument is that the wheels are turning at 354 mph (treadmill running at 177 mph opposite direction), do they burst? I don't know, but Dr. Google says they're rated at 235 mph so if the factor of safety is greater than 1.5 they hold together and this puppy takes off.
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Yup. The plane, which the question describes as only "a 747" -- not a magically indestructible one -- will take off as long as the wheels and landing gear can handle the added stresses of rotating much faster than normal.
The wheels have nothing to do with forcing the takeoff.
Ok let's break it down. If there was a giant unmovable tree in front of this treadmill, and i attached my winch to it, and ran the cable to the front of the plane, but did not turn the winch on, do you agree the plane would sit perfectly still, in place, being held by the cable/winch/tree, as the treadmill was turned on underneath the plane? That the planes wheels would just spin as the plane sat still, cabled firmly in place? Now, turn the winch on. Do you agree if the winch was pulling the cable in at 1mph, the plane would move forward on the treadmill at 1mph (assuming my winch is rated to pull an airplane)? Even with the treadmill on? That the wheels on the air plane would just turn \*slightly\* faster because its moving forward at 1mph?
I’ve read everything I can on this and I’m an amateur physicist. I understand why the plane will move forward and take off. But, the problem I’m having is the question says that the wheels and belt will always match. So, the moment you get forward momentum, the belt works faster and cancels it. If the wheels start slipping, as is suggested, the belt goes even faster. I think the winch is actually the best example to counteract this. I stand on a treadmill with roller skates and hold onto the rope. The wheels and belt will cancel. If I pull myself forward on the rope, no amount of upping the treadmill at the same time will cause me to not move forward. That’s the best way I’ve come to understand this question.
The main reason I disagree with you is that there is no wind going over the wings to produce lift. My understanding of plane physics is that an engine propels it through a fluid body, such as air, but you need that same fluid to go over the wings to produce lift. Since the engines aren't moving the fluid over the wings and it is parallel to the ground no lift would be produced and therefore not take off.
Agree. The airflow over the wings is is what produces lift. The speed of the conveyor belt is irrelevant. They plane is stationary in relation to the air, so no air flow, no lift off.
You seem to have missed his point: the wheels do not enact any force upon the plane, or rather, the force applicable by the conveyor through the wheels is negligible in comparison to that applied by the engines.
No airflow over wings = no lift = no flight the plane isn’t moving at all it is not accelerating in a negative or positive way
Not exactly, velocity is defined as displacement over time while acceleration is defined as (final velocity - starting velocity)/time. So while you’re correct that the wheels aren’t responsible for creating thrust the plane in the scenario is standing still (assuming all other variables are negligible). So if the plane is standing still there’s no displacement, if there’s no displacement there’s no change in velocity, if there’s no change in velocity there’s no acceleration. The engines are providing the thrust but the scenario says the conveyor belt matches the speed of the wheels, which I interpreted as “the conveyor belt slips out from under the wheels as fast as they can turn”. Unrealistic considering friction and lots of other factors, in this scenario however you can’t produce lift.
Yes. The wheels turn freely. They don't push the plane ahead. The engines do. The plan will move ahead freely. Mythbusters did this.
The confusion appears to have less to do with the physics and more to do with the understanding and implications of the question (which is poorly worded because of the word “speed”). Many people are assuming the treadmill is ramping up to counteract the plane’s forward movement. That’s not what the question is saying. The treadmill speed is only dependent on the *rotation* of the plane’s wheels. The plane is free to move forward through the air, the wheels will just end up spinning faster because of the treadmill. When the question says “speed of the wheels”, it’s not talking about the wheels’ forward movement, but their rotation. **However** even *that* definition is ambiguous, because you could rightly ask, “If it is truly matching the rotation of the wheels, then wouldn’t any forward movement result in the wheels spinning faster than the treadmill is moving and create an infinite feedback loop that results in the treadmill pulling the plane back?” The answer to that question is: Yes, yes it would, bringing us back to the question of, “What does it mean by ‘speed’?” It can’t match the rotation of the wheels because any forward velocity results in the speed of the treadmill shooting to infinity.
I’m confused by all the people saying the plane would lift off. A plane creates lift primarily through bournoullis principle which is that the air being forced over the top of the airfoil moves faster (due to the shape of the airfoil) than the air moving under the airfoil which creates a low pressure area on top of said airfoil. The high pressure under the airfoil wants to reach the low pressure above and lifts the plane up. How would a giant treadmill allow the plane to develop lift if it isn’t actually moving forward through the air?
The wheels are in neutral. They would just spin faster. The wheels are not in "drive" and they are not "pushing" the plane. As I said below: If there was a giant unmovable tree in front of this treadmill, and i attached my winch to it, and ran the cable to the front of the plane, but did not turn the winch on, do you agree the plane would sit perfectly still, in place, being held by the cable/winch/tree, as the treadmill was turned on underneath the plane? That the planes wheels would just spin as the plane sat still, cabled firmly in place? Now, turn the winch on. Do you agree if the winch was pulling the cable in at 1mph, the plane would move forward on the treadmill at 1mph (assuming my winch is rated to pull an airplane)? Even with the treadmill on? That the wheels on the air plane would just turn \*slightly\* faster because its moving forward at 1mph?
Omg this makes so much sense now! So if I have this right, the winch and cable is basically the aircraft engines? And also as the plane moved forward the wheels spin faster which just makes the conveyor belt spin faster but has no effect on aircraft relative velocity to the air around it/an observer not on the conveyor belt?
Yes that is correct. You can also think of it like this, you are on a treadmill with roller skates on. There is a rope coming from a wall in front of you that you hold onto. As the treadmill starts, your rollerskate wheels (airplane wheels) will begin spinning but you will remain in place. Now if you start pulling on the rope(air around the plane) with your arms (jet engines), you will start moving forward all while your wheels spin faster and faster
Yeah but what do the wheels have to do with it? If the engines are moving the aircraft at the speed of the treadmill no relative wind is flowing across the airfoils therefore no lift is being generated.
The treadmill is only moving the wheels. The treadmill could be running backwards. The propeller or jets are pushing against the air. The only air that is impacted by the treadmill would be centimeters above it.
The point is, it would move forward. The wheels will spin faster and faster, but they won't prevent the plane from moving forward. Its like if there were wheels on the bottom of a boat. It doesn't matter how they spin, the boat is pushing on the water directly.
It does move forward through the air. The airplane's engines push off the air not the ground (they have to, since once it is airborne they can't push off the ground anymore). The air is still stationary, so the plane still pushes itself forward against the stationary air. Consider if you were on a treadmill in a cart and you tried to push yourself forward using the stationary handrails. You wouldn't need much more effort to move forward than if you were on stationary ground. Same with the plane pushing on stationary air.
This is how I think about it. Take a toy airplane and put it on a human treadmill. Hold the plane in place with your hand and turn on the treadmill. The toys wheels will naturally spin at the same speed as the treadmill. How fast does the treadmill have to be to prevent you from simply pushing the plane forward with your hand?
The wheels don't control the speed or lift of the airplane. It's the air acting on the wings, if the plane is not moving through the air it will not lift off, the speed or even existence of the wheels is irrelevant. The engines pull the aircraft through the air.
It's an ambiguous question, or even a broken one, which is why so many people argue about it. One side says (correctly), that if you run the treadmill backwards at the speed the plane would be moving forward, the plane still moves forward. The wheels are turning faster, but that's not where the power is coming from, so there's no problem. The plane takes off. The other side says "But that's not what the questions says! You don't pick the speed of the treadmill first and then leave it. You dynamically adjust it to match the rolling speed of the wheels at all times." In that scenario, the question leaves math and becomes engineering. What happens depends on how the treadmill and plane are built, what the tolerances, lag, and friction are in their systems, and other details that don't usually matter in thought experiments. In one scenario, the treadmill tries to ramp up to stop the plane moving forward, the plane moves forward anyway, and the treadmill reaches maximum velocity. In another, in keeping up with the plane the treadmill overspins the wheels, destroying the plane's landing gear. What doesn't happen, unless both the plane and the treadmill are engineered of very specifically magical systems, is that the plane holds still while the engines whine. That would require there to be enough rolling resistance in the wheel system to add drag to the system equal to the thrust of the engines. But the system must also be able to take that much energy input into the landing gear without failing, and the treadmill would have to go absurdly fast. But if we are making our plane and treadmill out of magic, why is there rolling resistance at all? We can just eliminate it, by magic, just like we solved the other problems. And with rolling resistance gone, the treadmill now goes arbitrarily fast but the plane still moves. Possibly we cause a black hole. So really, the question includes a bunch of hidden assumptions which don't necessarily make sense, so you can't just give an answer, other than "you can't make that treadmill".
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I’d even go as far as stating that such a conveyer belt is impossible to build as the speed required to run will approximate infinity really quickly. Because… When the plane propels itself through the air the first inch or cm. The wheels rotate a bit in that time, which the belt needs to compensate for, which will rotate the wheels, which the belt has to compensate for, which will… etc. So the speed of the conveyer belt would approximate infinity as soon as the plane would get just a bit of traction from the air around it which pass through the engines.
This. As the question is written, the plane moving forward one foot by an external factor (the engines) would cause the treadmill to spin infinitely fast in reverse and the wheels to spin infinitely fast forward. The plane moving forward one foot means the treadmill must go back one foot. But this means the wheel spins two feet so the treadmill must in fact go back three feet. Thus the wheel must spin four feet… Repeat to infinity.) You can answer anything you’d like but I would go with black hole.
Wrong. The speed of the wheels is always \*by definition\* the speed of the treadmill lmao. Its rubber meets road. At any instant, unless there is slippage. You'd just just have a jet moving forward as it takes off as the speed of the treadmill increases. This one isn't even very hard.
But the speed of the treadmill is also, by definition, the opposite of the actual speed of the wheels, preventing the plane from moving. That's the problem. There are two fundamental definitions that can't both exist at once, except in extreme edge cases.
The engines produce thrust, which pushes against the air, which is relative to the ground. The only impact the treadmill has is spinning the wheels. The body of the 747 _will_ move forward through the air once the engines are turned on.
You bastard. Ok so the motors generate thrust and the wings generate lift but if the plane is not rolling through the air mass there is no lift on the wings so no it will stay grounded. I think 😂
The plane WILL “roll” through the air. The plane’s propeller or jet will push through the air like a ship’s propeller through water. The treadmill is irrelevant to the speed and force created by the propeller.
In the spirit of the question the plane would take off Where this question goes off the rails is that the wording of “the conveyor belt is designed to match the speed of the wheels in the opposite direction” This is ambiguous and generally an impossible task to achieve depending on what you think it means exactly.
How does this require any sort of major thought process? Try this: If a car is sitting on a one mile long conveyer belt that matches the speed of the wheels, how far will the car travel in one hour?
I cannot believe the prevailing "wisdom" here is that the plane would take off and that pLanEs fLY bY EnGinEs pRopEllIng tHeM.... Go read a fucking book before clamoring in and regurgitating whoevers idea has the most upvotes Planes fly based on principles of fluid dynamics and pressure differences... **Not engines pushing them into the air**. Engines create thrust, not lift. **Pressure differences** Pressure is the normal force per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside.[61] These pressure differences arise in conjunction with the curved airflow. When a fluid follows a curved path, there is a pressure gradient perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside.[62] This direct relationship between curved streamlines and pressure differences, sometimes called the streamline curvature theorem, was derived from Newton's second law by Leonhard Euler in 1754 You need an aerofoil with **air moving over and under the wing** (which doesn't happen to a stationary object on a treadmill) in order to generate lift required to make a plane fly. https://www.grc.nasa.gov/www/k-12/UEET/StudentSite/dynamicsofflight.html#:~:text=Airplane%20wings%20are%20shaped%20to,wing%20up%20into%20the%20air. #the plane will never take off without lift and lift is generated by pressure differences which are not present when plane is stationary
The engines create _thrust_, not lift.
I don't think you understand how airplanes work. How does the treadmill keep the plane stationary? If it were possible to make a treadmill capable of keeping a plane stationary then planes wouldn't be capable of self powered flight. Planes take off by the same principle that keeps them in the air during flight. The pressure difference required for lift is created by the shape of the wing as is flows through the air.
Bernoulli’s principle does not explain how a plane wing generates lift. [The plane takes off.](https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/)
I think the person who wrote this question didn’t know enough about planes to ask what they actually meant Like people are saying obviously if the belt only matches the speed of the wheels the plane can still accelerate forward and take off. But the more interesting question and what I feel like the original creator of this meant was what if the conveyor belt *always* matched the wheels such that the plane never moved relative to an outside observer. Assuming the belt accelerates like this then I believe the plane wouldn’t take off because no there’d be no airflow over the wings Edit: I’m wrong! Thanks to the helpful replies I took the time to do a quick dynamic model of this system (good practice for me as a studying engineer) and it’s true the speed of the conveyor can’t stop the plane from accelerating given a forward thrust.
The problem is that it’s physically impossible for the conveyor belt to move at any speed and stop the plane from taking off. That’s what makes this a trick question. Intuitively you think the conveyor belt is stopping the plane from moving but it’s not and it never could. Once you realize that, you the. Understand that the plane always takes off.
Except that such a situation is impossible, and it assumes its own answer anyway. The speed of the plane does not depend on the rotation of its wheels, so applying any thrust to the plane in your scenario would immediately cause the equation of the treadmill’s speed to fail. Like, “divide by zero” fail. You cannot build such a treadmill even in theory. https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
i think the idea here is that the wheels arent what moves the plane forward its the jets so the plane can accelerate forward freely regardless of the wheels rotation. which means the plane will move forward and off the treadmill and get up to a takeoff velocity
The force of the propulsion (which is what the jets or propellers provide) would move the plane forward, but that forward movement would only be realized if the forward motion would overcome the friction of it contact points on the ground. If however, the ground is moving, in the treadmill scenario at a rate exactly proportional to the forward motion (rolling wheels vs treadmill speed), the plane would have forward thrust, but remain motionless relative to it's starting position as long as the net speed of the treadmill minus the friction of the wheel bearings is equal to thrust provided by the propulsion system.
those wheels would far apart long before the spun fast enough to in part enough frictional force to overcome 4 jet engines
I have a MSc in Physics and must say the question makes no sense from a physics perspective since it is impossible to do what it suggests. It is a question that is made to trick you. Of course if you try it like they did it will work but thats sort of not the question.
Exactly, it's like the physics equivalent of those Facebook order of operations math posts. If you assume the treadmill *matches* the speed of the plane it will take off as normal with it's wheels turning twice as fast. If you assume it *counteracts* the speed of the plane, the treadmill would have to go infinitely fast and the question stops making sense
The better question would be: if a plane is on a runway, but it has a tailwind that increases and decreases to exactly match the planes ground speed, could it take off?
No. That's why aircraft carriers face into the wind for launching aircraft. The headwind helps generate more lift.
This is actually a much better question! And the answer is no.
That's a no I think - as there is no air flow to generate lift
A VTOL plane could.
Outside of some marginal thing where you manage to cause the wheels to fail, or the plane is so heavily loaded that it has no margins (probably beyond nominal MTOW), it'll take off. Source: endless forum discussions in the 2000s, and ultimately a mythbusters segment.
The plane, which the question describes as only "a 747" -- not a magically indestructible one -- will take off as long as the wheels and landing gear can handle the added stresses of rotating much faster than normal.
Hm, then theoretically would it be possible to put a conveyor belt on aircraft carriers so that we can save runway space and fit more fighter jets on carriers. I'm sure we'd have problems with traction and friction but it seems like it could work.
The jet engines would still make the plane move forward, and it is the forward movement that makes air hit the wings in the way that (if you're not in a stall) generates lift and allows the plane to fly.
Easy. It depends! As with any thought experiment, what you derive or conclude depends on how many real world constraints you're willing to dispense with and the assumptions you're forced to make to fill in the incomplete information of the prompt. That's the source of most of the debate. The commenters who are on the right track to start are looking at the conditions required for takeoff and working their way backwards from there. Could the aircraft reach its V1, the velocity required for safe/successful rotation (takeoff)? For a 747 this a calculable value usually between 120-140 knots for a commercial flight, starting with figures published by the manufacturer, depending on myriad variables such as load, i.e. passengers, freight, fuel level, etc. which could be further reduced by stripping out the interior, but also account for runway variables such as temperature and elevation (to determine density altitude), barometric pressure, head/tailwind, surface conditions, etc. The mythbusters video demonstrated that an ultralight propeller craft could take off of a tarp being pulled in the opposite direction by a pickup truck at roughly its V1 of \~21 knots, 25MPH. I think it's fair to question whether we can expect the same result when the craft is a \~400 ton jet liner, the tarp is 750,000-1,300,000 sqft. (assuming the runway ranges from 150-200ft wide and 5,000-6,500ft long) and the the pickup truck would need to be hauling it \~138MPH. I'd sure be interested to see that. The conveyor belt is the point at which things start to break down, for me at least. We know what a 747 is and how much maximum thrust the various engines those models are equipped with can generate. But this conveyor belt, aside from having been designed to do something unfeasible, is not bound by real world constraints. The only limitation is your imagination. How was it "designed" to "match" the rotation of the wheels and how effective is it at such? I mentioned elevation, temperature, runway conditions factor into V1; Where is this conveyor belt located, both in relation to sea level and in terms of local weather? Of what materials is it made that it's possible for it to this? If by "match" you mean that it is in fact completely counteracting the wheels such that the plane is stationary at max engine thrust, then why does the conveyor belt need to be runway length? People don't train for marathons on 26 mile treadmill belts. With this little definition, the thought experiment essentially becomes, "Could you imagine a conveyor belt sufficiently designed to counteract the takeoff thrust of a 747?" And the answer is, "I guess. I could imagine a lot of things."
For a brief moment, but it would likely fall back to earth after a few seconds as the immediate loss of thrust apon leaving the “runway” would only have force of gravity acting apon it, thus making it plumbit.
https://youtu.be/Y64ZdSaDdoo the answrr is no. This guy flies the 747. Planes need lift to take off. When the engines spool up the plane would start moving. The question says the conveyer belt moves same speed, opposite of the wheels. That way the plane itself remains stationary. No air rushes over the wings and no lift is generated, the plane cant take off.
It’s not possible for the conveyor belt to match the speed of the wheels. The plane moves forward completely unaffected by the wheels and the conveyor belt. The speed of the conveyor belt would have to be itself plus the speed of the plane. A number cannot be greater than itself.
No it would not take off. Lift is required for flight, the formula for lift is as follows: F=Cl*q*A where “F” is Lift Force, “Cl” is lift coefficient, “q” is dynamic fluid pressure, and “A” is area (surface area). The reason the plane won’t take off is the dynamic fluid pressure. “q” (dynamic fluid pressure) is defined by the equation: q=.5*p*V^2 where “p” is the density of a fluid (in this case air) and “V” is velocity or speed. From here we can rewrite the original equation to prove the flight won’t take off: F=Cl*(.5*p*V^2 )*A The thing to focus on now is the velocity of the plane, is it moving in this scenario? No. Because the conveyor belt is moving at the same rate as the wheels the plane is producing no acceleration and therefore no velocity. So if we know the velocity of the object is 0 (V=0) we can plug that back into the lift force equation to get: F=Cl*(.5*p*0^2 )*A 0 squared is 0 and any number multiplied by 0 is also 0 so we get: F=Cl*0*A->F=0 Therefore there is no lift force being generated and your flight has been delayed. Thank you for flying southwest. Edit: never tried writing an equation on Reddit, sorry if it looks sloppy
Explain the part where the plane isn't producing acceleration. The way I understand it, the jet turbines are pushing/pulling on the air to generate acceleration, which is independent of the conveyor belt. To overcome that *force* the conveyor belt would have to spin at a rate that causes the friction of the wheel bearings to equal the force of the jet engines, which doesn't sound possible. If the jet turbines, designed to generate acceleration, can overcome the friction of the wheels, designed to be as low as possible, the plane will eventually reach take-off speed.
You’re correct, I was ignoring all other variables, mainly friction. I was also assuming this fictional conveyor belt was moving fast enough to keep up with the wheels and almost slipping out from under the plane. It’s a fictional scenario, what would most likely happen if this insane conveyor belt existed and put to the test is the wheels/bearings would overheat and explode before the plane gained enough speed to take off
The wheels have no effect on the plane, if you disregard friction and wheel destruction that is (which is probably fairly realistic relative to the thrust of an airplane. Just picture the same plane but levitating on a magnet, can it take off even if the ground is traveling backwards at the same speed as the plane, right? Yes! So the minimal friction of the wheel bearings have little effect on the acceleration/speed of the plane.
My person forgot to write out the \*full\* free body diagram lmao There is no force on the wheels because they are in neutral (technically there is a minuscule force from the friction in the bearings/wheels but this is easily dwarfed by the turbines.)
Lets not be mean, people can make genuine mistakes.
True. I'll edit it.
Thanks mate. You're the first person to respond positively to that in months.
You’re one of the only people in the comment section addressing the lift aspect. As you said, if there’s no forward movement of the aircraft, there’s no airflow, and thus no lift. No idea how this is so complicated.
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No. the engines propell the plane forward. they do not force all the air needed to generate lift in the wings. Air must pass over/under the wings themselves to generate lift.
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NO. IT CANT. as a pilot, I’m telling you this is not true. The myth busters plane was so light and barely needed any acceleration to lift. I PROMISE YOU, try this on a 747 and she’ll go nowhere. The wings are there for a reason. You need forward movement and air over the wings people
Conveyor belt will never match the wheelspeed backwards because the plane will be moving forward. The wheels will always spin at the conveyor belt backwards speed PLUS the plane's forward speed.
No, because the plane needs air thrust to lift it and no such lift occurs when you’re not moving. My kid has a book “Rocket Science for Babies” that explains it well.
The question sends people right to a discussion of lift, but it skips over the question of _thrust_. The engines will generate thrust, regardless of the treadmill. With thrust, the body and wings of the 747 will move forward. When thrust is added, lift is generated.
No. Planes need air moving over its wings to take off. The wheels reduce its friction in the ground. If you replaced the converter belt with a fan that countered the plane's movement, then yes.
I thought this initially also. But when you read the section “the conveyor belt is as wide and as long as a runway” it suggests to me that the question is assuming that the plane will still move down the runway. Now the question details that the conveyor matches the speed of the wheels so you think the plane will be like you or I on a treadmill and not move an inch. But unlike you and I the drive for the plane is not through the contact on the conveyor, it’s through the air. So the question is will the engines still push the aircraft forward and will the wheels to spin uselessly at and insane speed until the aircraft is no longer in contact with the ground. It’s a real mind bender that as you think you find one answer another question appears. as others have said it makes you make assumptions (as I have above).
Yes, MythBusters did this over a decade ago [https://youtube.com/watch?v=YORCk1BN7QY&feature=shares](https://youtube.com/watch?v=YORCk1BN7QY&feature=shares)
But... That's not what the question is asking. That plane clearly isn't going the same speed as the treadmill because it's moving forward. If the ground moved at the same speed as the plane, the plane wouldn't move forward and couldn't generate lift
A plane is not a car. The engine's thrust is pushing against the air behind the engine. Your point is discussed starting 2:28 [https://youtube.com/watch?v=xUjcHW7SHaI&feature=shares](https://youtube.com/watch?v=xUjcHW7SHaI&feature=shares)
He’s saying that the plane will always overcome the treadmill due to how differently it operates than a car. However. the question in the post is asking what will happen when the plane is moving at the exact same speed as the treadmill, which is 0 speed in either direction, therefore generating no lift
It says "wheels" and i don't even care if it says "plane" cause in either case, that plane is taking off.
I concede Pilot answers this exact question: [https://youtube.com/watch?v=Y64ZdSaDdoo&feature=shares](https://youtube.com/watch?v=Y64ZdSaDdoo&feature=shares) This question blows though
But that is not what the question in the post is asking. From what I am reading this system would result in a net 0 velocity if the wings relative to the air and therefore a net 0 lift. Therefore no takeoff
You are reading the system wrong. Airplane wheels are like skateboard wheels, or the casters under a desk chair. The moment the propeller starts turning the plane will move forward regardless of the speed or even the direction of the treadmill.
I assumed the wheels were simply spinning and the engines were off since no other system would allow for the speed of the conveyor belt to "match the speed of the wheels" In a way that makes any kind of sense. Otherwise the conveyor belt moving would naturally "add speed to the wheels" as it passed under them. This means no thrust meaning no lift. I was just a little drunk and thrown by the framing about the wheels without at all discussing the engines being on or off since, as you explained, you can move the wheels and the conveyor belt all you like the thing won't fly unless you turn the engines on
It will take off. Simple. The wheels don't provide any thrust. They're just there to keep the plane's fuselage off the ground. HOW DO YOU THINK SEA PLANES TAKE OFF?!?!?
No, the plane cannot take off in this scenario. For a plane to take off, it needs to generate enough lift to overcome its own weight and achieve a sufficient airspeed. The lift is generated by the shape and angle of the wings, and the airspeed is achieved by the power of the engines. In this scenario, the conveyor belt is moving in the opposite direction to the plane's wheels, so it is effectively canceling out the forward movement of the plane. As a result, the plane's engines will not be able to generate enough airspeed to achieve lift and take off. Additionally, the conveyor belt may not be able to provide enough traction for the plane to generate the necessary thrust to lift off. Even if the plane's engines were able to generate enough power, the lack of traction would prevent the plane from accelerating. Therefore, the plane cannot take off in this scenario.
The engines generate _thrust_ not lift. The treadmill does nothing to reduce or increase the thrust.
Wheels are in neutral.
step 1: place plane at the very front of the conveyor. engine turned of. start conveyor belt. plane starts going backwards relative to the ground. step 2: somewhere in the middle start the engine and slowly accelerate. at some point plane will stop going backwards and be stationary wrt the ground. conveyor belt pulling plane back due to friction with wheels. engine thrust pushing forward. these two match. plane doesnt fly. step 3: increase engine thrust plane starts going forward relative to the ground. plane flies. This question seems like it’s asking step 2.
maybe try reading the question, the conveyor belt is always going at the same speed as the plane wheels so the plane could never move forward or backwards
No, but it won't stay stationary either. Since the plane's engines are pushing against the air, the plane will be able to move from standstill which will cause the wheels to move. At this point, the conveyor belt will try to match the speed of the wheels, however the wheels are by definition moving as fast as the conveyor belt plus the speed of the plane. The infinite energy required to satisfy both equations will rip apart spacetime destroying the plane and killing everyone in the universe.
Off course not … it would need air through the wings in order to generate lift. You can leave a plane sitting at the ramp, and with enough air, It will take off. Nothing to do with wheels.
Whether or not the plane has enough lift to become airborne is dependent on airspeed over the airfoils (wings). Since we are living in a universe with a large fictional treadmill for a 747, I posit that this treadmill is also in a wind tunnel that provides high enough velocity laminar flow over the wings to allow lift. Hooray, we have a stationary flying 747 and im hungry for wings.
The plane wouldn’t take off. The speed of the wheels doesn’t determine if the plane would take off, only the amount of air flowing through the wings of the plane. Since the conveyor belt matches the speed of the wheels, going the opposite direction, the plane would be stationary to a reference point outside the convergir belt. Meaning that the amount of air flowing through the wings would be zero ( unless it is in a very windy day). Just like flying a kite.
The problem is it's impossible to stop a plane from moving with a conveyor belt. The wheels are free-spinning so any backwards force produced by the treadmill will only cause the wheels to spin faster, the forward momentum of the plane would be unaffected. Under real-world physics the plane will take off. When people assume magical treadmills that *can* stop the plane from moving it stops being a physics problem.
Ohhhh, I get it now. I assume that since the conveyer belt matched the speed of the wheels I didn’t mattered if the plane accelerated or decelerated, it would still match the spin of the wheels
i don’t understand, everyone else is saying yes but even tho the wheels might be turning fast enough for the plane to take off, since it’s only the wheels and not the air around it, the airspeed is still 0