MythBusters tackles "plane on a conveyor belt problem"

[The_Decryptor Veteran]

Yes, it's that old conundrum, we had a lively discussion about it on the IRC, and i thought the forum would be a good place for a discussion on it (IRC doesn't exactly lend it's self to long lengthy discussions with multiple participants). Anyway, question is as such.

A plane (jet engine or propeller based) is sitting on a treadmill, the treadmill will always speed up to match the rotation of the wheel's, in reverse, no matter how fast the wheel's turn, the treadmill will match*.

Now, will the plane be able to take off?

* Ignoring such issues like the treadmill and wheel's spinning up to infinity, or the wheel's blowing or melting, or such.

(i know this has been discussed before, but i can't find the thread)

Update: The post about Mythbusters can be found here: https://www.neowin.net/forum/index.php?show...amp;p=589169105

[Caleo Global Moderator]

Yes, the engines on the jet create the thrust, not the wheels... So, it'd overcome the treadmill & the wheels would probably explode doing so, but it would still take off.

[sundayx Veteran]

ah this question again, well i voted no, unless there is enough wind going through the wings from the thrust of the engine to be able to lift the plane....

the engine propels the wings through the air to create lift, but seeing the airplane is stationary, i dont see how the plane could fly

[davemania]

Yes and pls don't bring back that thread :p

An analogy would be a model car on a treadmill with free axle being pulled by a string. If you pull the string, the car will move forward irregardless of the speed of the treadmill

[Caleo Global Moderator]

Yes and pls don't bring back that thread :p

An analogy would be a model car on a treadmill with free axle being pulled by a string. If you pull the string, the car will move forward irregardless of the speed of the treadmill

And bingo was his name-o.

[Mr. Chronopoulos]

Decryptor, I explained this in great detail on IRC. Don't make me do it again. It will NOT take off. In fact, the plane will not move at all. Trust the third year physics student. Please.

[davemania]

http://www.straightdope.com/columns/060203.html

http://answers.yahoo.com/question/index?qi...15213700AAaWyTK

the general consensus in other search results seems to indicate that it does. The plane doesn't remain stationary inregardless of the matching speed.

[vincent]

**** here we go again :no:

[Rob2687]

Just wait for them to do it on Mythbusters.

I say it does.

[Blues]

the plane can only take off if there is sufficient lift

if there is no wind to get under the wings (ie the plane either isnt PHYSICALLY moving, or there isnt wind blowing) it will not take off

i hate to burst someones bubble but this is less of a physics question and more of an aeronautics question

[The_Decryptor Veteran]

If you think the plane isn't moving, explain why you think it isn't moving, it isn't tethered to the ground or anything.

[sundayx Veteran]

ok so i think i have both sides to the arguement, some may suggest that the plane does not fly, this is correct given the plane remains at stationary throughout acceleration. but keep in mind that the thrust of the plane will eventually reach a speed that it does not require forces induced from the treadmill, but actually the plane would accelerate such taht it is not in stationary (however the is the variable of air resistance), therefore the plane is NOT in stationary, it is accelerating forwards and need not the treadmill, and air would be moving through the wings and eventually propelling the plane to lift. i think thats the case, but i argued that if the plane in fact remains in stationary throughout the acceleration then it does not fly.

edit: ok nevermind the treadmill still matches the speed of the wheels, so that the plane will in fact remain at stationary all the time, think of it as friction less vaccume, wait, should we regard this as a friction less surface or vacume? that would be the absolute answer to the question...

edit: aite i got it, in the realistic case, it should be a friction less surface, therefore the engines would propell the plane forward and it may probably reach a speed with enough lift for flight. im out

[beh]

The plane still moves because the plane is being pushed forward NOT by the wheels, but by the thrusters or propellers. The wheels just reduce friction between the plane and the ground. If the treadmill matches the speed of the wheels, then the plane will take off pretty much like normal except the wheels will be spinning twice as fast.

So the plane WILL take off.

[_sphinx_]

We've already been over this

Would it be efficient on aircraft carriers though?

[Echilon]

Been asked before, and I'm still not convinced the plane would take off :p

[jackwanders]

Ugh. Ok, let's end this quickly and put this to bed, shall we?

First off, we have to assume that the treadmill is of sufficient length, say the length of a runway.

That said, we can immediately negate the treadmill factor altogether. If the treadmill and the wheels are always travelling at equal but opposite velocities, than their velocities cancel out and there is no relative motion. It is as if the plane is standing on a regular runway, wheels not moving.

Ok? Are you with me? We've now reduced the problem to this:

If a plane is on a runway, and its wheels have been locked so that it's impossible for them to spin, can the plane take off?

The answer, quite obviously, is yes. Of course the plane will take off. A plane needs thrust to create lift, and it needs lift to fly. A plane's thrust is not provided by its wheels. The thrust is provided by the propeller(s) or jet engine(s). If you take a plane with locked wheels and start the engines, thrust will still be created, and the plane will still move forward. It won't be pretty, the friction between the wheels and pavement would cause a lot of smoke, but the plane will move forward, lift will be created, and the plane will take off.

Don't believe me? I submit to you, the pontoon plane:

This plane takes off from water. Does the plane push against the water to move forward? No. The propellers push air past them, providing thrust. This is the exact same situation as a plane on a treadmill.

Decryptor, I explained this in great detail on IRC. Don't make me do it again. It will NOT take off. In fact, the plane will not move at all. Trust the third year physics student. Please.

Third year? Good job. You're forgetting the fact that a plane's thrust is not provided by the wheels.

Take a RC car and put it on the same magical treadmill we're using for this problem. No matter how hard you push the car's engine, the treadmill will match the speed of the wheels and the car will sit there, stationary.

Now, take your hand, grab the back of the car, and push it forward on the treadmill. The wheels will skid and make an awful noise, but the car moves forward, relative to the treadmill. Why? The new source of thrust is you, not the wheels pushing against the surface of the treadmill.

Replace your hand with a jet engine and the car with a plane.

PS - Let's not forget that the treadmill could never match the wheels' speed, because as soon as the plane starts to move, the wheels will always be travelling at (X+Y) where X is the speed of the plane and Y is the speed of the treadmill. A treadmill cannot possibly go faster than itself.

Edited December 8, 2006 by Jack31081

[_sphinx_]

Doesn't it depend on the speed of the conveyor belt?

Usinng the bernouli equation P1v1 = P2v2, as you see, velocity is a factor...so to answer the question, partially, yes; the plane will take off if the physics are right. Otherwise, no way.

Yes, Jack. Thrust is a major factor here, but remember that the force of the thrust isn't going to moving the plane; it's overcoming the opposing force of the conveyor belt. The real reason isn't thrust, it's the rotation of teh wheels and their unorthodox friction with the ground, which I won't get into again.

[jackwanders]

Ok. Part of the problem is as I mentioned before, it's impossible for the treadmill to match the wheels' speed. If the plane goes 10mph, the wheels will be going 10mph. So the treadmill speeds up to 10mph. But now the wheels will be going 20mph. So the treadmill speeds up again, which makes the wheels spin faster, which makes the treadmill speed up, etc, etc.

The only logical way out of this is to have the treadmill match the plane's speed.

So let's do this to start the experiment. Cut the runway in half. The first half is asphalt, the second half is a treadmill. The plane starts at the end of the runway and speeds up to 100mph. The treadmill is churning away at 100mph. Now the plane hits the treadmill at 100mph.

What will happen? The plane will continue to move at 100mph and the wheels will speed up to 200mph. The plane won't stop because the wheels are not the source of propulsion. A car moves by pushing the road backwards. A plane moves by pushing the air backwards.

[Fred Derf Veteran]

A truly advanced treadmill, capable of anticipating and compensating for the engine's thrust, would not allow the plane to take off because no wind would pass over its wings.

[jackwanders]

The wheels on a plane are free-rolling. There is no connection between a plane's overall velocity and that of its wheels.

If the ground underneath a plane begins moving, the wheels simply spin faster to compensate. The plane itself does not slow down.

[Fred Derf Veteran]

The wheels on a plane are free-rolling. There is no connection between a plane's overall velocity and that of its wheels.

If the ground underneath a plane begins moving, the wheels simply spin faster to compensate. The plane itself does not slow down.

Well, that makes sense then. I guess we're ignoring wheel friction and all that.

[jackwanders]

Well, that makes sense then. I guess we're ignoring wheel friction and all that.

We don't have to.

I made a mistake in my first post when I talked about locked wheels and smoking and such.

Like I said after realizing my error, the wheels of any plane will always move at Z = X+Y, where

X = forward velocity of plane

Y = backward velocity of ground

Normally, the ground doesn't move, so Y = 0. Therefore, Z = X.

However, if the ground is moving, as with the treadmill, Y is larger than zero, and the wheels will spin at X+Y.

plane = 100mph

treadmill = 100mph

wheels = 200mph

The wheels are still spinning 100mph faster than the ground is moving, just as if the plane were on solid ground. There is no additional friction between the ground and the wheels. At least I don't think so. Either way, I don't believe there is any additional friction that would slow the plane's forward progress.

[_sphinx_]

I wish we had a definitive mathematical answer. I feel if the case was that simple, they would've at least tested it to see if it solves the runway probelm, but they haven't which means that it's probably not even theoretically possible.

Wait a second...it is theoretically possible!!!

But it can never be done in reality because the tires will blow up. Yep, that's it. Imagine the wheel spinning at about 1000 mph; that's it.

Edited December 8, 2006 by _sphinx_

[Fred Derf Veteran]

I wish we had a definitive mathematical answer. I feel if the case was that simple, they would've at least tested it to see if it solves the runway probelm, but they haven't which means that it's probably not even theoretically possible.

Wait a second...it is theoretically possible!!!

But it can never be done in reality because the tires will blow up. Yep, that's it. Imagine the wheel spinning at about 1000 mph; that's it.

The normal necessary runway speed required for takeoff would only need to be doubled.

[n3wt]

Wouldn't a plane with a prop mounted on its nose wash air over the wings regardless of whether it had any foreward momentum?