Science!! Fucking magnets, how do they work?

Ancient it's fucked if the treadmill is rolling back at around 470 (It'd likely be less than that because the rolling resistance would increase as the plane moved forward, so it'd be in at equilibrium somewhere between 0 and takeoff speed). Where that number is exactly because of the decrease in weight due to lift I dunno, but it never generates lift at 470mph if it can't achieve positive velocity relative to the ground.

What we really need is a plane that can take off backward.

I think in our scenario it's best to assume that either:
1. The plane is artificially held in place until the treadmill and the propeller are running at fullspeed.
2. While the plane is moving forward relative to ground the treadmill will continue to accelerate up to 470mph.

In either of these cases you won't need to worry about the plane going backward at high speeds.

Tea_sl said:

The equation you are using is a simplified version for some car X, and it's extremely unlikely those values apply to airplanes. Road tires at 200 mph are going to encounter significant deformation and oscillation problems whereas aircraft tires will not, and that is among the several dozen reasons why your number is far too low. The speed required to prevent take off is likely to be at a point of catastrophic failure.

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Then find evidence of a better equation or a better rolling resistance coefficient.

Also from a quick google it looks like we're not far off:
http://books.google.com/books?id=XMp...icient&f=false

Guys, guys, guys! I have a degree in aeronautical engineering, I can fix this!

Ok seriously, I do have that degree, but nothing can make people understand this problem until the part about the wheels not mattering finally clicks in their head. I've tried to explain this to several people over the years, so let me see if this will help at all.

Take a toy airplane with a propeller and an engine. Set it on a treadmill (engine off at first). Start that treadmill up, but hold the plane in position with your hand. No matter how fast you make that treadmill go, you can hold the plane in place without moving, right (assuming you don't rip off the wheels due to friction)? To the extent that you can probably even hold it there with a pinky finger, because all the wheels are doing is spinning in place, not exerting any real force except the negligible amount due to friction (the fact that you can offset it with one finger is showing you how negligible it is). Speed up or slow down the treadmill and it makes no difference, the wheels just spin and spin.

Ok, now pick that airplane up and hold it in your hand, and start the engine. What happens? The propeller starts to exert a force on your arm, wanting to pull the airplane forward through the air. Do the wheels do anything at all while you are holding it in your hand? No, they don't, they just sit there. That's because the engine is in no way connected to the wheels, just the propeller.

Now, put that airplane back down on the spinning treadmill, holding it in place again. The wheels start to spin again, but only because of the reason it spun in the first place when the engine was turned off. The engine on or off is doing nothing to the wheels, at all. However, that slight pull on your arm that you felt while holding it in the air is still there, because the propeller is trying to pull the airplane forward through the air. If you let go, the plane will start to slowly move forward on the treadmill because of that pull on the air. No matter how fast the treadmill is going, that propeller is pulling the plane through the AIR. Assuming you haven't hit the maximum structural velocity of the wheels, the speed you set the treadmill at doesn't matter. The wheels are just spinning, and they spin like they just don't care. The plane will slowly start to accelerate THROUGH THE AIR, until it reaches a speed at which the airfoil shape of the wing generates enough lift to start flying. Assuming they don't blow up, the wheels can be going 10 mph or 1000 mph when it finally takes off. All that matters is how fast the air goes over the wing.

Did that help at all?

Hey Vvoid stop dicking around with using too many words to describe the treadmill problem and show the math on how fast the treadmill would have to go to cock over a cessna.

Sterling_sl said:

What sort of surface on the treadmill?

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Concrete. It's really noisy.

Eomer_sl said:

Like Tea has been saying, I'd imagine the wheels fail due to spinning too fast before their rolling resistance has any appreciable effect on the plane's ability to move forward.

But that's just what you're getting at, anyways.

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That was my assumption too, but after OB demonstrated that the equilibrium would occur at around 470mph I'm not convinced that's true. 470mph is of course an incredible speed for a wheel to move at and I'm sure a real plan would just wobble/burn and crash but whatever.

Skanda_sl said:

I thought we learned back during the HM days to never take anything he says seriously?

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We don't have to take him seriously, but the information shown appears to be correct.