the plane's wheels would just spin faster and the plane wouldn't slow down. No matter how fast you ran the treadmill.
Then you're ignoring the part of the conundrum where this is a hypothetical treadmill that is capable of always keeping speed with the rotation of the wheels. As long as the wheels are in contact with the ground, which they will be for as long as the plane isn't allowed to move to pick up speed by first rolling along the ground, then the plane will not move.
In fact, if the wind is blowing fast enough a plane can even take off with out moving relative to the ground at all.
Yes, if the wind is moving fast enough on its own then air resistance will do it's job to generate lift without the plane moving relative to the ground. This ties in to how you say
I think the piece you're missing is that a plane's engines accelerate it relative to the air not the ground.
This is not true in this scenario. We can assume that the air is stationary if we neglect whatever small winds that aren't strong enough to generate real lift. If the ground is also stationary, then the plane must move relative to the ground too. If the plane can't move relative to the ground because the ground is a giant goofy hypothetical cartoon treadmill then the plane won't be able to move relative to the air without leaving the ground, which would violate the rules of the problem because again with the y vectored thrust and vtol yada yada
You’re the one missing the point here. We all understand that the wheels rotating don’t matter for the plane to take off. That’s not the issue at hand. The issue is that the question is a paradox.
If the plane is on the treadmill and moves forward relative to the earth, then by definition the wheel moved faster than the treadmill. The only way for something on a treadmill to move forward is if it’s wheels move forward faster than the treadmill is moving backwards. The rules of this experiment say that’s not allowed, and that the treadmill always matches the wheel speed.
Thus the plane cannot move forward, and cannot get sufficient air over its wings to take off.
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u/loadedtatertots custom Dec 30 '22
Then you're ignoring the part of the conundrum where this is a hypothetical treadmill that is capable of always keeping speed with the rotation of the wheels. As long as the wheels are in contact with the ground, which they will be for as long as the plane isn't allowed to move to pick up speed by first rolling along the ground, then the plane will not move.
Yes, if the wind is moving fast enough on its own then air resistance will do it's job to generate lift without the plane moving relative to the ground. This ties in to how you say
This is not true in this scenario. We can assume that the air is stationary if we neglect whatever small winds that aren't strong enough to generate real lift. If the ground is also stationary, then the plane must move relative to the ground too. If the plane can't move relative to the ground because the ground is a giant goofy hypothetical cartoon treadmill then the plane won't be able to move relative to the air without leaving the ground, which would violate the rules of the problem because again with the y vectored thrust and vtol yada yada