The "Plane on a Treadmill" Question

[Happy Monkey]

Originally Posted by Spexxvet

Now, concerning Labrat's ass ... I mean bicycle analogy, one thing is missing. The airport moving walkway would speed up to counteract the push that you give the bike.

No it can't. The only thing the runway can do is speed up the wheels. A push will still move the bicycle forward.

[glatt]

Originally Posted by SteveDallas

I'm so tempted to make six consecutive posts, but I'll be nice and leave it at one.

I was expecting someone to do that. You surprised me, Mr. Dallas, with your restraint. Unlike the treadmill, which provides no restraint for the plane.

[Flint]

Originally Posted by glatt

Unlike the treadmill, which provides no restraint for the plane.

[LabRat]

Originally Posted by Spexxvet

Now, concerning Labrat's bicycle analogy, one thing is missing. The airport moving walkway would speed up to counteract the push that you give the bike.

Yeah, and in doing so, make the wheels turn faster. But the bike would keep on keepin' on with you pushing it.

Here is something you can test--if you're near a large airport.

If you are pulling one of your airport bags with the wheels on it down the airport terminal, then walk onto (or next to with the bag still on the thingie) a moving walkway thingie, and continue to walk at the same speed what happens? The bag does not stop moving because the tread underneath it is going in the opposite direction. It continues forward because YOU are pulling it, while the wheels spin faster than they were when they were on solid ground. You=the plane's thrusters. the bag = the plane on wheels.

TRY IT!!!!!!!

[LabRat]

And with that, this thread is finished

[Torrere]

Can the treadmill possibly exert enough force on the plane to counteract the force of the thrust?

1) Pie is correct that any force exerted on the wheels is subsequently exerted on the plane (although LabRat's drawing is better).

2) By SteveDallas' example, we know that
Fthrust => Ftreadmill
otherwise the plane would be pushed backwards. If Fthrust > Ftreadmill, the plane must accelerate forward and then eventually take off.

3) The force exerted by the treadmill on the wheels is a friction force, and therefore limited to:

Ftreadmill <= μR * Weight of plane

Where μR is the coefficient of rolling friction.

There are three different coefficients of friction that we could use: static, rolling, and kinetic. Static means that the plane is not moving at all w/r to the treadmill. With kinetic friction, the plane and the wheels are sliding forward, as in Maggie's story of brakes on ice.

μK < μR < μS

I'm not sure what the coefficient of rolling friction is for a 747, but the largest μR listed on Wikipedia is 0.03, and that's for a bus on asphalt. I assume that μR for a plane would be much smaller, but I'll use 0.03 for effect. According to Boeing's site, for a 747-400, the maximum takeoff weight of the plane is 3886 kN. Each of the 4 engines produces a maximum of 281 kN of thrust, for a total of 1124 kN of thrust.

So

Ftreadmill <= 3886 kN * 0.03 = 116.6 kN
Fthrust = 1124 kN

1124 kN > 116.6 kN

I'm not entirely sure, but it looks like this plane is going to move forward, and the treadmill can't go fast enough to stop it, because the plane will just start sliding. Since the plane is moving forward, air goes over the wings, and the plane takes off.


Can anyone get μR for a plane wheel?

[Spexxvet]

Originally Posted by Happy Monkey

No it can't. The only thing the runway can do is speed up the wheels. A push will still move the bicycle forward.

Nuh-uh.:p

[Torrere]

Originally Posted by LabRat

And with that, this thread is finished

/me didn't get the memo in time

[Spexxvet]

Originally Posted by LabRat

...TRY IT!!!!!!!

Woops! The walkway doesn't speed up.

[hideouse]

The wheels effectively disconnect the plane from the treadmill. the movement of the plane is relative to the planet they are both sitting on. the treadmill can spin any direction and rate you want it to and will have _no_ effect on the airplane or it's ability to move forward at an increasing rate and eventually generate enough lift to fly.

[Flint]

Originally Posted by LabRat

TRY IT!!!!!!!

Interpretation #1: The question doesn't allow you to move forward, relative to the treadmill.
Interpretation #2: The question does allow you to move forward, relative to the treadmill.
Interpretation #3: In this variation of Interpretation #1, you slide forward, relative to the treadmill.

Originally Posted by hideouse

...the treadmill can spin any direction and rate you want it to and will have _no_ effect on the airplane or it's ability to move forward...

It has exactly that effect, if you interpret the question as stating that the plane's forward motion is relative to the treadmill.

[hideouse]

But now aren't we back to the flaw in the premise?

[barefoot serpent]

aren't we back on the treadmill?

[Kitsune]

Originally Posted by barefoot serpent

aren't we back on the treadmill?

Nope -- landing is an entirely different problem.

[Torrere]

Originally Posted by barefoot serpent

aren't we back on the treadmill?

We're running a rat race on a treadmill with a LabRat