Here you go.

Now, personally I'd say the plane would take off, but I skated through college physics with grades just passable enough for graduation. But, my Aerospace engineer friend has conclusively said the plane cannot move with how the problem is phrased. His arguments make some sense, you just have to think about it. You just can't take the easy answer and say that the wheels spin freely and have no affect on forward movement. Now, if you wanted to change the problem from "wheel speed" to "ground speed of the place" then yes, the plane will take off.

I'm just taking the argument (the plane won't take off) here as I understand it for the sake of discussion.

Basically, the two angular velocities (wheel and belt) have to be opposite and equal as per the question, and the only condition that satisfies that equation is when they are zero, which means no airspeed. No one measures wheel speed as the speed of the aircraft with respect to the ground. Think of it this way: if the wheels *have* to spin at the same speed as the belt, there's no way for the wheel's axles to *ever* move relative to the ground around the belt, and therefore there's no way for the plane to ever move.

The reason the question is poorly posed is because if the wheels could move even a micron the belt would start to accelerate to match the speed of the wheel, it will start to exert a force onto the wheel, which will change the wheels velocity. Which means the belt has to go faster to catch up to it, which means it exerts a different accelerative force on the wheel. Etc, etc. You have to consider speed AND acceleration in this question. Unless, of course, you have treadmill that never accelerates (or has instaneous acceleration), it only has velocity.

(ps. this post brought to you by plagarism. like I said, I think the plane would take off, but I'm cut'n'pasting the argument against)

 

Okay, somone explain this to me and my lowly mechanical engineering degree. While the plane is generating thrust, it is not moving through space due to the converyor. If it's not moving through space, how can it generate lift? Without air flowing under the wings, the plane can't take off.

 

omg...


2,200 reply thread about this on nasioc...

900 reply thread about this on nasioc...


this has been beaten to death over there and we still dont have an answer. a LOT of name calling and harassment though :rotfl:

 

Give it up, Mike. He's a better mechanical engineer, it's his name!




Yeah, there's not really a right answer given the simple question, just lots of intellectual noodling. Fun, though

 

i guess a similar question would be how does a sailboat go forward against a current?

 

wouldn't the energy going in one direction be canceled out by the energy of equal force being applied in the opposite direction?

 

Absolutely.

Here's an example of a similar situation...

During a parachute jump in the military we'd sometimes go out to the dirt drop zone instead of the AFB and load-up onto the C-130 Hercules, C-17 (whatever) there. We'd then take off from the very short, hard-packed dirt runway known as an FLS (field landing strip).

The pilot would get on the far end of the strip, hold the brakes, then accelerate to full throttle. Once full throttle was achieved they'd let go of the brakes and whiplash every paratrooper and crew to takeoff on the short runway.

You just have to substitute the conveyor for something else that cancels out the force from the throttle. In this case the brakes act as the converyor and the throttle is still the throttle. The conveyor is only there to throw you off because you think it generates wind and lift when it doesn’t in this case. If the conveyor suddenly stopped then the plane would take off much quicker than normal.


EDIT: I do know that the relative speed of an aircraft to the speed of an aircraft carrier is important when taking off. They take off to the front (with the carrier moving forward or at stop) and into the wind in order to create added lift.

 

/thread

 

Yeah, that's why we're saying it wont move.

 

if you take the bold part of the quote into consideration, the plane will in fact take off. by tracking the plane speed, it is implied that the plane is moving. the conveyer will run at double the speed of the plane, but the only result is that the wheel speed will increase.

a car on a conveyer that matches the speed in reverse will not move because the motive force is the drive wheels in contact with the belt. a airplane will move because the motive force is the propeller acting on the air around it.

 

The plane would take off quicker than normal just like any plane does when you hold the brakes or use JATO. But if it is completely stationary as Ed implied and at full throttle, it is going nowhere. Your example and the original question/my response are apples and oranges.

All the brake holding method does is hold the plane while the engines get to full throttle so that when the plane starts to roll, the engines are already at max. That's as opposed to rolling down the runway while the engines spool up. It's no different than dropping the clutch as 6k or power braking in an auto tranny car.

As for your edit, that is exactly true and it's the same reason planes launch into the wind on runways also.

 

But Russ, how are you generating lift? Planes take off from the ground due to lift under the wings. Your are correct, props and turbofans force air backwards, but they don't force it under the wings of a plane. No matter how much air you push backwards (i.e.: thrust) your relative speed remains zero (unless I read the question wrong).

 

No offense intended. I apologize for my condescending tone. I've just argued about this plane problem too many times and I get a little fired up.

Short answer is the plane takes off equivalently to that of the plane on a normal runway with wheels of twice the inertia.

Even in the case of a car driving on a treadmill, the car will move forward. The solution to the coordinate transformation of the problem is simply that the wheels spin at twice the normal speed. So in the case of a car, if you were sitting on the car on a treadmill, your speedo would say 30 mph, but the car would actually be moving forward at 15 mph. It's just an interesting brain teaser.