Comments on: The Goddamn Airplane on the Goddamn Treadmill

By: Bryan

Bryan — Fri, 06 Nov 2009 20:04:21 +0000

Forget about the airplane and the treadmill. Instead, consider whether a truck with a model helicopter in the enclosed cargo area will weigh the same whether the copter is hovering or powered off and sitting on the floor. In my aeronautics classes, I found this scenario much more interesting than the plane/treadmill.

Extra Credit: what if the truck has an open top?

By: Mostly Harmless

Mostly Harmless — Tue, 27 Oct 2009 03:24:56 +0000

NO —> plane will CRASH and most likely kill people inside too stoopid to believe it will be able to takeoff.

Ok the speed is as in #2, the 747 tires spin at about twice the speed.
And there is no wind to affect takeoff. Air being blown along the conveyor not counted.

The plane will go forward to takeoff speed, which is 175-185 mph

Being accurate about the takeoff speed won’t matter too much, well because:

THE 747 TIRES HAVE A SPEED RATING OF 235 MPH!

At umm, 160mph the tires are going at about 320 mph.
Lets see if they’ll fail, YES, remember what happened to concord when its tire(s) shredded?

A couple tires will shred, hits from the high speed chunks of tire whacking into other tires, about to pop too, causing a domino effect and a CATASTROPHIC FAILURE.

That’s the right answer. The solution to make it fly is to get landing gear that can take over 360 mph for a normal takeoff, (skis?). The stall speed of a 747 is about 160 mph, but the absolute minimum speed some nut could take off at…

By: tom

tom — Sun, 25 Oct 2009 01:35:28 +0000

Jason:
Although you are correct that wheels with non-zero angular mass would allow the treadmill to apply horizontal force to the plane…

1) The problem never mentions “a plane with wheels of angular mass ‘I’.” Which is what any physics book would do if the author wanted you to take the angular mass into account.
2) The problem is obviously set up to test beginners who are just getting their first experiences with free body diagrams. And at this level “wheel” means frictionless contact unless otherwise stated.

Thus I believe Sriracha is either trying to stir up trouble, or desperately wants attention and thinks he’s super smart by bringing up angular mass.

OR you and Sriracha are one and the same person, in which case Sriracha is indeed a successful troller.

I hate the internet so much sometimes.

By: E. Wyatt

E. Wyatt — Fri, 23 Oct 2009 09:09:10 +0000

Well, of course, there are ambiguities in the question that make the problem confusing. But in the the xkcd examination of the problem there are further issues. In his equations, he’s using V, which is usually shorthand for a vector, when he’s usually referring to the speed, which is not a vector, so I’m not sure what his math is saying.
But back to the problem. “The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” The “conveyor belt” speed is in the opposite direction as the wheels. What is the speed of the wheels? The speed of the axel relative to the ground, or the to conveyor? The speed of the point on the wheel where it touches the conveyor, relative to the ground, conveyor, or plane?
The problem needs to be rewritten.
Suppose we just said, “the conveyor moves horizontally such that the plane stays still relative to the ground (until it flies.)” What then? I assume the plane won’t leave the ground (or move at all) unless the upward thrust from the engines is sufficient to overcome the weight of the plane, which is possible if they are pointed correctly.
Also the question assumes a perfect conveyor control system which can instantly counter the forward motion of the plane. This is impossible. Any control system has errors and delays. Thus the plane will achieve horizontal motion of some sort, and once this is accepted, the problem breaks.
Back to xkcd Case 1: Vb=Vc: Suppose the pilot locks up the breaks, but supplies full power to the engines. The plane leaves a lot of rubber behind, but eventually achieves flight by skidding down the unmoving conveyor until liftoff. Case closed.

By: Jason

Jason — Thu, 08 Oct 2009 04:22:50 +0000

Sriracha is correct. If we consider the mass of the wheels, it is possible for the treadmill to put a backwards force on the plane, and therefore to keep the plane stationary.

This is an interesting physical point, not trolling, Tom, unless you think it’s against the point of the discussion for some people to learn something.

TLDR explanation: This effect doesn’t kick in until the wheels of the plane have mass and the treadmill is constantly accelerating at some very fast rate (not just running at the same constant speed). Therefore, you probably don’t have to worry about it.

And finally before I get into a real explanation, I’ll repeat Randall’s sentiment: *practically* the plane is going to take off (or possibly burn up). We’re operating without the constraints of practicality for the purpose of figuring out some basic principles of mechanics.

A longer explanation:
The plane’s engine provides a force pushing the plane forward. This forward force exists regardless of what the treadmill is doing. Unless the treadmill can exert an equal backwards force on the plane, the plane will move forward and take off.

If the wheels are massless and their axles are frictionless, the treadmill cannot put any force on the plane, and cannot stop the plane from taking off.

However, consider just a (initially stationary) bowling ball on a treadmill (or test it at home if you don’t trust your mental picture). If the treadmill starts running backwards, the ball will also travel backwards, starting to roll as it does so. The direction of the roll will be forwards, but not fast enough to keep the ball stationary.

Now put an frictionless axle through the ball, stand next to the treadmill, and hold the ball stationary, preventing it from rolling backwards. How do you do this? By putting a force on the ball through the axle.

Now let go. The ball remains stationary. Once the ball is spinning forward fast enough to become stationary, it can keep stationary without any additional force. If you increase the speed of the treadmill, though, the ball will start moving backwards again.

Now pretend that axle is connected to an airplane. The plane can keep ball from moving backwards just like the person standing next to the treadmill: by putting a force on it. The plane needs to run its engines to do this–only barely, though, since it doesn’t take nearly a full jet-engine worth of force to keep a bowling ball stationary on a treadmill.

Even if the treadmill is really, really fast–fast enough to really send that bowling ball shooting back–the plane just needs to apply enough force for long enough to accelerate the ball from a backwards velocity to a forwards velocity, and then to a forward velocity large enough to take off.

But if the treadmill keeps speeding up, it will accelerate the bowling ball backwards, more than the plane can keep up with using its engines. Then the plane will never take off.

By: tom

tom — Sun, 04 Oct 2009 02:29:30 +0000

Sriracha:
Wrong: You are a troll.

Anyone who thinks that the rotational mass of the wheels is intended to be a part of this problem is grossly mistaken. Or trolling.

By: Claude

Claude — Wed, 23 Sep 2009 21:24:56 +0000

Ryan, it is possible you misread my comment. I said that the plane *would* take off due to the effect of the treadmill inducing air movement over the wing via friction between the treadmill and the air.

Once the plane left the treadmill it might remain within the quickly flowing boundary layer for a short time, until the plane’s jets moved the plane out of the layer.

We must all remember: this problem has nothing to do with reality. There are no engineering constraints.

By: Fraser Jones

Fraser Jones — Tue, 22 Sep 2009 15:02:51 +0000

Here, I have proved the answer in finality because this problem was /actually/ resolved by the military in the late 60’s

http://www.youtube.com/watch?v=-Sn5JL9t_C4

This is absolutely, 100% proof.

By: bandsma

bandsma — Mon, 21 Sep 2009 15:36:34 +0000

To simplify – the engines move the plane forward causing the air to move over the wings. It is the movement of air over the wings that creates lift. If the treadmill couteracts any forward movement created by the engines then there is no air going over the wings, therefore no lift.

By: Prof. Yuvleaux

Prof. Yuvleaux — Mon, 21 Sep 2009 07:24:44 +0000

airplane. just picture it as a closed system with basic forces acting on the plane. the air is still. no matter how fast the plane is moving on the spedometer it has to be moving that fast relative to air to achieve lift. now given jet engines force vectors cannot be matched oppositely practically with a conveyor belt (to my knowledge). not only that, but they pull air so quickly off the wings that lift is achieved. so to idealize make it some sort of plane with no propeller or engine. if a glider is pushed fast enough it will achieve lift, like a kite. but to get a kite to fly it must move relative to the AIR not the GROUND. so a glider on a treadmill will never ever take off if it is stationary relative to the ground, no matter what is pushing on it. THAT is basic physics. however, the problem does say a plane and given that yes it will take off because the propellers and jets make the air move relative to the plane, producing lift. if mythbuster’s force calculations were correct then the plane would not have moved relative to the ground, can’t believe they didn’t realize that this neglects the conditions of the problem. thought experiment that helped me: if a giant grabbed a plane with the wheels spinning just as fast as his giant treadmill, i.e. no forces involved as both objects don’t need to accelerate, the plane will not move relative to the air which is ideally still relative to the ground. my students are die hard plane will take off fanatics initially but they all seem to come around to logic once the numerous ambiguities are removed from the problem.
Prof. M.T.Y.