But that’s irrelevant. You have told me that the treadmill and wheels move at the same speed in opposite directions. We cannot just throw that condition out. So you have to explain what the speed of the wheels and treadmill is, and how that’s possible while the plane moves forward, if you are asserting that the plane is moving forward.
I used to watch Monty Hall when I was a kid and he was always tipping off the right choice, sometimes very obviously. Absolutely drove me nuts when folks made a bad pick. Studio audience of that show reliably the dumbest people on Earth. .
I understand that speed relative to air is the important factor generating lift. The question is whether the plane’s engine causes the air to flow around the wings with sufficient speed when the plane is at a standstill vs ground.
This seems to prove my point. We’re talking about current planes with current technology
Heard this paradox the other day, which was new to me. Here are two very smart people disagreeing about it.
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Takeoff weight?
Let’s go with average, which is around 185 mph.
This speed of “treadmill” is not infeasible. I’d change the question to “dynometer” instead of treadmill. F1 synod can easily handle those speeds.
Edit: Oops, sorry, I meant this reply for @ThisGuy.
I can’t say I’m 100% sure I’m not missing something. Maybe I don’t really understand the question. Here is what I think:
There’s nothing weird going on with the plane’s tires.
To try to be clear, what I picture is that, in the drawing, the wheels will turn counterclockwise. The top surface of the conveyer moves from left to right. The conveyer responds to the motion of the wheels, which turn because of the forward (right to left) motion of the plane, which is due to thrust from the engines. As long as there is no slipping, the tangential velocity of the tires at the point where they contact the conveyer is the same in direction and magnitude as the top of the conveyer. The plane will take off when it acquires sufficient speed relative to the ground/air. At that moment, the rotational speed of the wheels will be what it would normally be if the plane were taking off from an ordinary runway; the conveyor will match the wheels, as required by the question, but that makes no difference.
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The engines accelerate the plane forwards, so it will not be at a standstill relative to the ground except at t0.
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So the spirit of the question is that the plane is not moving forward as fast as it would on solid ground, unless you’re asserting that a plane with no engines just stays in the same place while the treadmill is on
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If the plane is static on the treadmill, then its wheels aren’t rolling.
De plane is risen
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“Assume it’s frictionless” is really bad advice unless the treadmill cannot move an engineless plane, due to magic wheels or no gravity or something
Will the plane take off if the treadmill is going at exactly the takeoff speed of the plane? Yes, of course. Say it’s a calm day. How fast will the surface of the wheels be turning in that circumstance? Twice the takeoff speed. So that doesn’t meet the conditions laid out in the problem statement. It’s not poorly written, it’s written in a way that necessitates a magic treadmill that doesn’t move at a fixed rate, but an exponentially increasing rate that will only be kept from instantly being infinite by the friction in the wheel bearings.
I think the spirit of the question distills down to:
If the airspeed required for takeoff is 185 knots, will the plane take off of a treadmill going 185 knots in the opposite direction?
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Ahh excellent thought experiment. I remember this also was posted on 2p2 at some point.
Which do you go for?
- Both A and B
- Only box B
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voters
Will the plane not move in the treadmill’s direction if the engines are off?
The treadmill in your question is slowing the engines-on plane down unless it’s magic.
Sorry, I didn’t mean to imply you didn’t know. I think you were there for the previous discussion, which I vaguely recall was about Bernoulli not really working and even Navier-Stokes not quite agreeing with experiment or something like that.
The treadmill would have zero effect on the engines.
The surface of the wheel is going 370 knots when it takes off! The spirit of the question is the treadmill is going the same speed as the surface of the wheel. This leads to some problems.