Beating a Dead Horse - Airplane on a Treadmill

[BuffCyclist]

Okay, so to stop threadjacking that other post, I want to explain to people where I was coming from, in my thinking that a plane CAN NOT take off on a treadmill. There are two answers to this question, both of them are correct, but they are based on the initial conditions of the problem.

Scenario 1:

Can a plane take off if placed on a treadmill? This answer is NO. Everyone who thinks of this problem, thinks of this:



Which is literally, a plane on a treadmill. In this scenario, the plane does not have enough room to move forward and since the wheels can spin freely, the plane will just sit there (assuming the engines power the plane at the same speed as the treadmill, so as to keep the plane stationary). The wheels do not generate forward thrust and thus, if a blindfold is put on this plane, they will be at rest relative to the air surrounding them.

Now, if you want to look at the actual scope of the problem, which took me quite a bit of googling to actually find the DETAILED, well written problem, it is this:


Scenario 2:

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

In this scenario, because the wheels spin freely, as long as the engines are turned on and powering the plane, will it be able to take off? YES. This is because the engines see speed relative to the air, and therefore the wheels can spin at 500mph and the plane will still be able to take off because the air is not moving at 500mph.

And here is the MythBusters' episode on this situation:




Conclusion:

So there you have it, two scenarios where the plane is able to both take off and not take off from a treadmill. This was not a matter of the plane being able to take off or not, it was a matter of the initial conditions of the problem and the problem not being explained correctly.

Lastly, for the record, I have absolutely no idea how I have never heard of this problem before. It appears to have been floating around like crazy in 2006, when I was in college for my first degree.



And now I'm ready:

[00tec]

Mythbusters tested it

[BuffCyclist]

Mythbusters tested it

Yes, mythbusters tested Scenario 2. And they saw exactly what I saw I described (editing first video to include the video).

But Scenario 1 is still a valid scenario of this problem.

[merl]

but what about a sea plane in an endless pool?

[BuffCyclist]

but what about a sea plane in an endless pool?

Do you mean Scenario 1 or Scenario 2? An "endless pool" is a brand name for a pool that has a turbine at one end to simulate a current in the 20ft long pool. If the plane is a normal sized plane, then NO, the plane will not take off.

Here is their website: http://www.endlesspools.com/

How do I know about them? My Dad had one installed at our house so we could train for triathlons easier than having to go biking around our house, stop at the YMCA for the pool (and leave the bike there), then run around the neighborhood. With the Endless Pool, we could go on our swim, hop out of the pool and get on our bikes, then end up back home and head our running.


If however, by "endless pool" you mean a pool that is simple endless in nature (ie an ocean) then YES, the plane will take off.

[Ridge]

It's not about how fast the wheels are moving, or how fast air is moving through the engines. It's about how fast air is moving across the WING.

[BuffCyclist]

It's not about how fast the wheels are moving, or how fast air is moving through the engines. It's about how fast air is moving across the WING.

(video removed to lessen clutter)

Correct, but the two scenarios I laid out are both correct in and of themselves. You are furthering my explanation as to the reason why a plane can or can not take off.

If there was a fan in front of the treadmill in scenario 1, that changed speed according to the tread, would the plane be able to take off? YES. The airspeed over the wings would reach the 80mph or whatever speed required to achieve lift and it would become airborne. However whether or not the plane would start moving forward once it got out of the way of the plane is an entirely different question. It would depend on the achievable acceleration
of the plane (in that if you drop a plane at 30k feet with its engines at max speed, it will still fall below 30k feet before moving forwards).

[Ridge]

Yes, that is true. At least until the plane moved out of the fan's area of influence, at which point it would probably stall and crash and burn.

[asmo]

Please god make it stop..

[BuffCyclist]

Yes, that is true. At least until the plane moved out of the fan's area of influence, at which point it would probably stall and crash and burn.

Yes, that is what I was trying to say after I said YES. The plane would have no lift but the engines would be at their max capacity, it would probably fall down but if put high enough into the atmosphere, it would be no different from the engines stalling and could, in theory, recover. If the plane was able to accelerate at an ungodly high rate (think UFO going from stop to superfast in a second), then it could fly.

This type of problem is exactly how a lot of problems in special relativity are laid out.

For example, two twins are on earth and one gets on a spaceship, to fly at the speed of light, towards a star that is 4 light years away. When she gets there, she realizes there are no planets and returns the 4 light years to earth. When she gets there, she has aged only 8yrs, however her twin sister on earth aged something like 20yrs. But the twin on earth sees it a different way. Long story short, the spaceship is in an accelerating reference frame, because it is physically impossible to travel the speed of light from one point to another and return without accelerating and therefore is not the valid reference frame to use for this situation. But this type of problem gives hundreds of physics students a run for their money every semester.