Easiest to just imagine the plane is on a sheet of zero-friction ice with the engines off, then imagine the engines turning on, what happens to the plane when the engines come on?
Yāall crack me up. Iām over here thinking aerodynamics and everyone else is worried about tires.
Btw, airplane tires are incredibly tough and overdesigned.
Let me present the opposite theoretical to try to explain why it will fly.
The takeoff velocity of a plane is calculated based on weight and lift.
If the takeoff velocity of a plane is 100 mph, it can move forward at 99mph forever and never lift off. The 100 mph is determined by how much lift is needed to get off the ground. Not by how much forward motion of the plane, but by the LIFT on the wings. Yes they are connected but lift is king.
100mph is a convenient way to describe a complex equation because, as this argument shows worldwide, most people canāt disconnect two perpendicular force vectors in their brains, which is normal because most people donāt study this stuff
I believe I am describing the situation as worded by the question. If thatās a paradox then that explains why I canāt wrap my head around it.
If I say given the wheel and the treadmill are supposed to always be matching in speed, does the wheel speed increase to infinity as the plane takes off? If not, then how fast are the wheels turning when the plane takes off?
This seems like a disagreement over what the question is supposed to mean. I did not really understand your explanation other than I think I agree with it but itās a rebuttal to something I donāt think I said.
The question is poorly posed, and demonstrates the need for accurate and clearly-stated assumptions in engineering discourse and design
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I think people are confused by how much lift there can be on the wings if the purpose of the conveyor belt is to hold the plane stationary to the air surrounding it.
If you have a plane chained to a fixed point so that it cannot move forward and you blast the engines (and the combination of tire and surface prevent it from blowing a tire and add anything else that makes this possible), given sufficient power to the engines, will it leave the ground?
Of course the speeds canāt match if the plane moves forward, thatās why itās poorly written.
Yes
If a plane could lift off of a treadmill why arenāt aircraft carriers just fitted with treadmills instead of that slingshot? Because the treadmill thing is impossible
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If the center of mass of a wheel is going forward at 185 knots (relative to the ground) on a treadmill thatās going backwards at 185 knots (relative to the ground), then the bottom of the wheel is going backwards at 185 knots relative to the ground, and the top of the wheel is going forwards at 555 knots relative to the ground.
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Iāll read this again and likely understand it, but at first glance itās a claim about the temperature at which jet fuel burns and the melting point of steel beams.
Itās not poorly written, itās just doing something different than what you think it is. If thereās no friction in the wheels and the tires, plane, and treadmill are all indestructible then the wheels ramp up to an arbitrarily high speed instantly and as suzzer points out, relativistic effects cause the plane becomes infinitely heavy and cannot take off.
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When I put my Tonka truck on my moving treadmill, itās cool how the truck doesnāt move, and just stands still, because of the truck wheels
Thatās the actual question.
If the plane is based on reality but the treadmill is magical, the question is unanswerable.
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And if, as the question implies, itās a magical treadmill that can instantly ramp up to arbitrarily high speeds and a regular old 747, then the regular 747 is just going to get eaten by the magic treadmill like belt sander.
Quick scan, but are the two sides of this argument really being taken up by this forumās traditional adversaries?
ETA: need to find out where CN and JalFreezi stand imo
OK, but what does this mean to you, because youāre not thinking of the meaning in enough detail. Does it mean the center of mass of the wheel relative to the ground vs. the treadmill relative to the ground?
Because even in the case of a car, the parts of the wheel arenāt all moving at the same speed, and we have to consider speed relative to what?
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No. The air and ground are not moving with respect to each other. The plane has to move relative to both to create enough airflow to generate lift.
If anything, the airflow around the wings due to the operation of the engine causes a downward force on the plane, since air is taken into the engine at the front of the wing and ejected at the back.
Edit: I take back the downward force comment since itās the shape of the wings that matters, probably not so much the direction of the airflow. I donāt think a 747 would generate much lift this way though.
I say the answer is NULL
Uhā¦no.
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Fly, yes. Take-off?
Iām assuming the conveyer is on the ground and the air and ground are not moving.