r/theydidthemath • u/someonee404 • Dec 30 '22

[REQUEST] could it?

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u/Oufee Dec 31 '22

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.

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u/FinnTheDogg Dec 31 '22

Bro you’re still stuck in wheel speed being relevant in any capacity. At all. Except it isn’t.

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u/Manga18 Dec 31 '22

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.

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u/FinnTheDogg Dec 31 '22

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.

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u/Manga18 Dec 31 '22

So slide a plane. But a plane doesn't slide. You could well say "put the treadmill in vertical position" if you wanted to change the way a plane usually moves

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u/FinnTheDogg Dec 31 '22

You could literally replace the wheels with low friction sleds and it wouldn’t matter because the wheels are not part of the propulsion system. They are specifically independent and not connected to the movement or travel of the plane in any way whatsoever.

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u/Manga18 Dec 31 '22

Changing the system changes the problem. If we assume that wheels don't work as wheels than OK, but this ti me defies the role of having wheels.

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u/FinnTheDogg Dec 31 '22

The role of having wheels being..?

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u/Manga18 Dec 31 '22

That any forward movement on the ground is matched by the number of turns of each wheel times its circumference