ELI5, If a large passenger jet was trying to take off on a free spinning treadmill, would it take off?
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I think people may be misinterpreting your question slightly. It sounds like the question you’re asking envisions the plane remaining in place horizontally (i.e., doesn’t move forward) because of the treadmill. So the question you’re really asking is: would a plane’s engines still lift it into the air if it wasn’t moving across the ground?
So while it’s true that a plane on a treadmill will still fly *because it will ignore the treadmill*, I’m not sure that holds true if the plane isn’t moving forward.
I think the reason why a lot of people get confused with this is because they try to envision an airplane working the same way as a car.
If you put a toy car going 10 mph forward on a treadmill going 10 mph backward, the car wouldn’t move. The same is true for a real car and a larger treadmill.
But why? Cars accelerate differently than airplanes do. They burn gasoline to provide energy to push a piston which moves the tires. The tires come into contact with the road and physically grip it to push the car forward. It’s the friction with the surface of the ground and tires that allows the car to both move and turn.
How is this different from an airplane? Because airplanes don’t move with their wheels, they move with their jets! The two large jets at the side of the plane provide thrust to push the thing forward through the air, the wheel is just there for a smooth takeoff and to support the weight of the plane, it doesn’t do anything to actually move the plane forward.
Still confused? Here’s another way to think about it. Pretend you were in a river where the water was pushing you back, but you wanted to go forward. If you simply swam forwards at 5 miles per hour, and the river pushed against you at 5 miles per hour, you’d get nowhere (car on a treadmill). Now imagine you were back in the river but this time there was a rope attached to your waist which was anchored to a stable horse outside of the river. Every time the horse moved forward (which is easy because it’s on land), it pulls you forward too because you are tied to it. You see how the force that the river exerts against you is irrelevant and you still move forwards? It’s because it is the horse that is doing the pulling, and the river can’t act on it.
Now in truth airplanes aren’t pulled by an external force, they push themselves with fuel. They are their own horse and their own rope, and the ground cannot act on them because their big turbines are in the air.
So how would you go about stopping an airplane from flying? If you were to get a large enough fan and turn it on in the direction that the airplane is trying to take off in, *that* would be enough to stop it. Now the airplane is pushing on the air to go forward, but you are also pushing on the air with your big fan to make it go backwards.
A plane takes off because it gains airspeed. Usually, gaining airspeed is achieved by rolling over the ground, but the plane is not pushing on the ground itself. There is no propulsion going to the wheels at all.
If you put an extremely long treadmill on the ground and tried to match the speed of the plane to keep it from taking off, all you would do is move the wheels faster, but moving the wheels faster would not stop the plane from gaining airspeed.
If the plane needed 150 mph of air speed to take off, for example, then the apparent speed at the wheels would be 300 mph – – 150 from the plane’s speed through the air and another 150 from the treadmill spinning backwards, in the opposite direction that the plane is moving. But the speed of the air over the wings would still only be 150 mph.
Like most such “brain teaser” questions the issue actually hinges on the specific phrasing of the question and not the physics. The question as it is typically posed is:
> Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?
Let us ignore all the practical problems. The treadmill exists, the airplane isn’t going to break, etc. Also let us assume there is no wind (as a sufficient headwind could allow the airplane to lift off without the wheels even spinning) and that the movement of the treadmill causes no wind. **Most importantly let us assume the situation as stated in the question is accurate**; nothing pisses me off like someone saying “Oh, but constructing a treadmill like that would be impossible or impractical,”. The question is the question regardless of practicality.
All this leads to a problem in the interpretation of the situation. If the airplane’s engines push against the air to make the aircraft roll forward at say 10 mph, then the treadmill will spin backwards at 10 mph as well. No problem, the drag of the wheels spinning at twice takeoff speed wouldn’t be enough to stop the aircraft lifting off since it pushes against the air, not the treadmill/ground. But notice the problem there? Once the aircraft is moving 10 mph down the runway the treadmill spins backwards at 10 mph causing the wheels to spin 20 mph in total, but the treadmill *matches the speed of the wheels!* The treadmill would need to spin at 20 mph, which means the wheels are actually turning at 30 mph so the treadmill need to move at 30 mph, etc.
This seems to form an infinitely increasing loop as long as the aircraft is moving down the runway. If the aircraft is stationary with respect to the ground then the wheels could be going any speed matched by the treadmill, but any movement across the ground implies a conceptually infinite speed of the treadmill and wheels.
Now many infuriating people will look at this apparent physical impossibility and decide to change the question itself. (The Mythbusters did this because they needed a physical test.) As above this isn’t in the spirit of the question and any answer produced isn’t really for the question as it is posed. It also isn’t really a physical impossibility; the treadmill won’t need to move at infinite speed in order to prevent the airplane from moving with respect to the ground. It would of course require an absurd amount of speed to produce the drag required to keep the airplane from moving forward, and realistically the engines of the 747 would be able to melt and obliterate the wheel bearings. But saying “the wheel bearings would break” seems like as much a cop out answer as saying “the FAA would never allow such a situation”. Yes, the landing gear assembly would be incandescent at that point but if we assume nothing breaks it should be possible.
At this point the answer is obvious, **the airplane cannot take off**. In order to fly the aircraft needs air moving across its wings, and without wind that means the aircraft needs to be moving with respect to the ground in order to take off. The engines of the airplane push against the air but they still need to overcome the drag of the wheels over the ground; that is why there are wheels on the end and they roll on a smooth runway, to reduce their drag. If the runway was covered in 10 feet of thick mud then the airplane couldn’t take off either. Increasing the speed of the treadmill will at some point produce enough drag to equal the thrust from the engines and the airplane will not move with respect to the ground and thus not with respect to the air, meaning no lift and no takeoff occurs.
It is also fairly common for some first year engineering student to chime in with nonsense like “rolling resistance is the same regardless of speed” but of course it is obvious that a bearing moving at 1 rpm doesn’t have the same amount of drag as a bearing moving at 200,000 rpm. The latter bearing will presumably be getting very hot and that energy has to come from somewhere. Surprise, it is friction! But we don’t even need that proof because even if we assume the bearings are truly frictionless the force to counter the engine’s thrust can come from inertia. The wheels are going to resist being spun up to a conceptually infinite speed, so the acceleration of the engines can be countered by a constant acceleration of the wheels. Think about how an angle grinder jerks in your hand as it starts up, that jerk is the grinding wheel’s inertia resisting it being accelerated to operating speed. Unbreakable, frictionless wheels would still have inertia and could provide that countering force indefinitely as they are accelerated towards infinity to stop the aircraft rolling forward.
There are too many unanswered and undefined variables to give a simple yes/no answer. What is the coefficient of friction between the treadmill surface and the plane wheels? Is there friction within the landing gear wheel bearings or do they spin freely without friction?
The energy/force of the engine thrust has to go somewhere. It either goes toward acceleration of the airplane’s mass, in which case it goes airborne, or it gets fully canceled out by friction losses in the bearings & surface of the wheels in the form of heat and the plane remains stationary with regard to the ground and air.
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