The "Plane on a Treadmill" Question

[Happy Monkey]

Originally Posted by Phage0070

The other interpretation is not internally consistent as it requires the treadmill to be simultaneously stationary and moving. (If the plane rolls forward and the treadmill is matching speed as compared to the ground, to keep it stationary would imply that the treadmill is stationary as well, but also moving at twice the speed the plane is attempting to accelerate) I chose the one that made sense.

Where are you getting the highlighted bit, from the question?

Plane moves forward, relative to the ground, at speed X.
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2 X as plane takes off.

The question tries to trick you into thinking that the "spirit" of the question is that the plane is held stationary relative to the ground, but the words of the question make no such claim.

[Phage0070]

Originally Posted by Happy Monkey

Where are you getting the highlighted bit, from the question?

Plane moves forward, relative to the ground, at speed X.
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2 X as plane takes off.

The question tries to trick you into thinking that the "spirit" of the question is that the plane is held stationary relative to the ground, but the words of the question make no such claim.

Plane moves forward, relative to the ground, at speed X.(wheels spin at X, unless you are suggesting chunks of them are departing the plane)
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2X - so the treadmill must be moving at 2X.
Wheels spin at 4X - so the treadmill must be moving at 4X.
Wheels.....

And thus the problem with the statement. Obviously someone was trying to say something else.

[Happy Monkey]

Originally Posted by Phage0070

Plane moves forward, relative to the ground, at speed X.(wheels spin at X, unless you are suggesting chunks of them are departing the plane)
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2X

Yes...

- so the treadmill must be moving at 2X.

No.

Or, more accurately, the treadmill is moving at 2X, relative to the plane. It it still, however, only moving at X relative to the ground, matching the plane.

The treadmill matches the plane speed, both speeds relative to the ground. The plane moves at X, the treadmill moves at X in the other direction, and the wheels spin as if the plane were moving at 2X.

[HungLikeJesus]

Originally Posted by Happy Monkey

Yes...

No.

Or, more accurately, the treadmill is moving at 2X, relative to the plane. It it still, however, only moving at X relative to the ground, matching the plane.

The treadmill matches the plane speed, both speeds relative to the ground. The plane moves at X, the treadmill moves at X in the other direction, and the wheels spin as if the plane were moving at 2X.

But then it's a circular question. For those saying that the plane doesn't move, relative to the ground, X = 0 and 2X = 0, so the treadmill doesn't turn and the plane can't take off. But if the treadmill doesn't turn, the plane can move as normal and will take off as from a normal runway. Which proves that the plane will take off.

[glatt]

Originally Posted by Phage0070

Plane moves forward, relative to the ground, at speed X.(wheels spin at X, unless you are suggesting chunks of them are departing the plane)

I disagree. The wheels don't spin at X. As soon as the plane begins to move forward, the treadmill instantaneously kicks into gear, and the wheels have to move 2X just to keep up with the plane. The plane moves X, but the wheels instantaneously move at 2X.

Treadmill moves backward, relative to the ground, at matching speed X.

Yes.

Wheels spin at 2X - so the treadmill must be moving at 2X.

I disagree again. The wheels move at 2X, but the treadmill moves at X. This is why the plane is moving forward relative to the ground.

[Griff]

Treadmills are activated by the force applied to their surface. There is no drive power coming from the wheels. No force
= no treadmill movement. The plane will lift off but won't clear the Universal Gym.








Dirty Damn SteveDallas

[Flint]

Let's just read the question and decide what we're being asked about:

First, the plane "begins to move forward." So, forward motion is possible, although it isn't stated whether this forward motion is relative to the surface of the treadmill, or relative to the ground.

Next, the treadmill is described. It is "made to match the forward speed of the plane, only in the opposite direction." What the forward speed of the plane is relative to remains unspecified. The treadmill is said to "move backwards beneath the aircraft as the aircraft moves forward." What the forward motion of the plane is relative to remains unspecified.

Thus, when the treadmill is said to "match the forward speed" of the plane, it isn't stated how this speed is determined. When the treadmill is said to "move backwards...as the aircraft moves forward" it isn't stated how this motion is determined.

So, for step number one, to read the question and determine the parameters of what is being described, we cannot describe the treadmill because we cannot describe the plane, therefore we certainly cannot describe their relationship.

When Mythbusters tests this scenario, I will be curious to see what is tested. Because the question as stated here isn't something you can test.

[Happy Monkey]

Originally Posted by Flint

Next, the treadmill is described. It is "made to match the forward speed of the plane, only in the opposite direction." What the forward speed of the plane is relative to remains unspecified.

Right. That's what makes it a trick question. The first instinct of someone who knows how wings work is to assume that the spirit of the question is that the plane is held stationary. That assumption is not present in the question. Phage0070's wheel friction interpretation is the most grounded in reality of the ways to follow that line of thought, but even that requires the additional assumption of landing gear that can survive the friction (against the road, and internally on the bearings) required to counter an airplane engine, which would likely be several times the speed of sound.

The "relative to the ground" interpretation can actually be done with a real plane, so I'm guessing that that's the one the Mythbusters will do.

[tw]

Originally Posted by Flint

First, the plane "begins to move forward." So, forward motion is possible, although it isn't stated whether this forward motion is relative to the surface of the treadmill, or relative to the ground.

Go right back to Kitsume's post #1.

Originally Posted by Kitsune

A plane is standing on a runway that can move, like a giant treadmill. When the plane's engines throttle up, it begins to move forward, ...

That means the plane moves forward relative to air - independent and irrelevant to a treadmill.

Between plane and the treadmill are wheels. Wheels spin as slow or fast as necessary so that plane and treadmill remain completely independent of each other. Grasp the major significance of the word independent. Tread mill moving forwards or backwards will only affect how fast and which direction wheels spin. Tread mill will have no affect on the plane.

I am still completely mystified why this is not obvious to everyone. In post 104, Happy Monkey again and accurately answered. He is answering to others who remain confuse in post 196.

Meanwhile, the question was answered in maybe five different ways - all coming to the same conclusion - in post 152.

First - what is the purpose of wheels (landing gear)? Velocity of a plane is totally irrelevant to ground. Wheels will spin as slow or as fast as necessary so that volocity of the runway and velocity of plane stay totally independent.

Does not matter what speed or direction (a one dimensional problem) a treadmill moves. It is that simple. Some still have difficulty after 305 posts and 13 months later? I am completely baffled why something so simple has been made so difficult.

It's this simple. Wheels mean the plane is not affected by the treadmill (except by some trivial bearing resistance that is made 100% irrelevant by the planes jet engines). Wheels and jet engine means the treadmill can be replaced by a runway (a treadmill moving as 0 Km/sec) and have the exact same answer.

[Flint]

Originally Posted by Flint

When Mythbusters tests this scenario, I will be curious to see what is tested. Because the question as stated here isn't something you can test.

Originally Posted by Episode 97: Airplane on a Conveyor Belt

An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff.

Busted. I love how they phrased the question so they could bust it. If the myth had been "the plane can take off" it would have been confirmed.

[Happy Monkey]

Originally Posted by Flint

Busted. I love how they phrased the question so they could bust it. If the myth had been "the plane can take off" it would have been confirmed.

Right. "Plane can't take off": Busted. "Plane can take off": Confirmed.

[Flint]

Originally Posted by Flint

Busted. I love how they phrased the question so they could bust it. If the myth had been "the plane can take off" it would have been confirmed.

Originally Posted by Happy Monkey

Right. "Plane can't take off": Busted. "Plane can take off": Confirmed.

Right. This is usually a question: "Can a plane on a treadmill take off?"
But since they are the mythbusters they phrased it so they could score a "bust."

Also (separate point here) they phrased the scenario to specify "ground speed."