A harmless little riddle

Short answer: You're wrong.

Long answer: Read my posts.

late comer wrote:

As an aside, I like the comment that stated if this did work, why wouldn't the navy use treadmills on aircraft carriers instead of the slings that they currently use. Maybe they just don't know ...

I just realized that the analogy of the aircraft carriers is a perfect example of why the plane will take off. Think about it, the aircraft carrier is the treadmill belt, while the water is the ground. Airplanes take off from aircraft carriers all the time, sure, not carriers going 150 MPH, but surely that analogy will help some folks see why the plane will take off, right?

david bowie wrote:

As long as you're admitting that according to the restraints of the question, the plane will take off, I'm happy.

No, nevermind, the plane won't take off. : )

OK think of it like a knot. Theoretically, when you tangle some rope around itself, you should just be able to pull on it and the rope will slide back through. But more often than not the friction from the rope grips itself and you have a knot. It's the same situation here; it looks like the plane can take off in theory but it just won't.

Seriously, this isn't that complicated.

I will end this wrote:

OK think of it like a knot. Theoretically, when you tangle some rope around itself, you should just be able to pull on it and the rope will slide back through. But more often than not the friction from the rope grips itself and you have a knot. It's the same situation here; it looks like the plane can take off in theory but it just won't.

Seriously, this isn't that complicated.

Holy shit that makes no sense at all. I'll give you half credit for originality though.

Seriously though, if that makes sense to you, you're f***ed in the head.

It is not worth my time since your conclusion is incorrect. I have to imagine that your logic is confounded as well. Check out this link and get back to me:

http://www.allstar.fiu.edu/AERO/airflylvl3.htm

It is not the same thing. Why do you think that carriers always head INTO the wind when planes are taking off. Lift, baby!! In the treadmill example there is no air moving over the wings no matter how fast the treadmill goes. On the carrier example the air is traveling over the planes wings at the speed of the plane relative to the air, which is increased if the carrier is headed into the wind.

In the treadmill riddle, the only things moving are the treadmill belt and the wheels. They cancel each other out.

Seriously, go back and read some of the other posts. The plane will move relative to both the ground and air. There will be lift. It will be created exactly as you described.

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

See the link above. Seriously.

thank you david bowie! all this time i was advocating peaceful persuasion, and then you come here and lay down the law. the plane will take off!!! yay!!!

a good (read: relativity-breaking) treadmill is capable of stopping the plane, though. as was stated before, the two main forces opposing the plane are FRICTION IN THE WHEELS and RESISTANCE FROM THE FORCE ACCELERATING THE WHEELS. if the treadmill keeps speeding up phemonenally quickly, and if the wheels still don't slip, the wheels have to accelerate very quickly, and the treadmill could stop the plane, and get some weird relativity effects going on too.

I am going to put an end to this thread.

This is the riddle: "An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

The critical part is where it says, "the treadmill runs in the opposite direction at the same speed the plane is moving."

IMPORTANT

To answer the riddle, we have to know exactly how the "speed the plane is moving" is defined. Is it defined as the airplane's speed relative to the ground (surface of the treadmill) or its speed relative to the air around it? We do not know. The riddle is ambiguous. Therefore, there are two possible answers.

For simplicity, we will assume that the plane's take off takeoff speed is 150 mph

Let us consider the first situation, in which the airplane's speed is defined as speed relative to the ground (surface of the treadmill).

The plane accelerates to 150 mph relative to THE SURFACE OF THE TREADMILL. The treadmill, in accordance with the riddle, moves backwards at 150 mph. If the treadmill is moving at negative 150 mph, and the plane is moving at positive 150 mph RELATIVE TO THE TREADMILL, then the plane is not actually moving forward relative to the air around it. There is no air flowing over the wings. The wings do not generate lift. The plane does not fly.

Let us now consider the second interpretation of the riddle, in which the plane's speed is defined as speed relative the the air around it.

The plane accelerates to 150 mph relative to the air around it (airspeed). The treadmill goes backwards at 150 mph, but it doesn't matter. The wheels are spinning at 300 mph, and the plane's engines have to work roughly twice as hard as they normally would to get up to 150 mph (the plane's entire weight is resting on a surface that is moving backwards at 150 mph), but the plane is still moving forward at 150 mph relative to the air around it. The air is flowing over the wings at 150 mph, and the wings generate enough lift for the plane to take off. The plane flies.

There is not a right or wrong answer to the riddle. There are two different interpretations, because the riddle is ambiguously worded. The two interpretations lead to two different answers.

End of argument.

I am not too big a man to admit that I am wrong, although I have to say that it stems from the ambiguity of the question. The lift arguement stands. However you are right since the plane is propelled forward by pushing on the air, unlike a car that is propelled by pushing on the treadmill. The plane will move relative to both the treadmill and the air, thereby generating lift and taking off (assuming that the plane can generate enough thrust). That is gonna be one big treadmill though.

Sorry guys.

Well, you're half right.

The problem with your first interpretation is that you're assuming there is infinate variability in the speed at which the airplane wheels will spin while the airplane remains stationary to the ground.

I submit to you that there are limited speeds at which this will happen - only the speeds at which the rolling resistance and friction added up equal the thrust provided by the engine.

Assume we are at this state when the plane wheels are moving at 50 MPH and the treadmill is moving at -50 MPH. If we speed up the plane by providing additional thrust, at some point, the thrust from the plane at each incremental MPH is going to outweigh the additional rolling resistance and friction imparted by the treadmill/wheel interface.

In other words, yes the plane CAN fly under these parameters, which is what the question asks. If the question asked, "is there a speed at which the plane's wheels will rotate but the plane will not move relative to the ground?" then yes, your explanation would be correct.

late comer wrote:

the plane is propelled forward by pushing on the air, unlike a car that is propelled by pushing on the treadmill. The plane will move relative to both the treadmill and the air, thereby generating lift and taking off (assuming that the plane can generate enough thrust). That is gonna be one big treadmill though.

Sorry guys.

The engines don't work by "pushing on air." They mix air with fuel, light it on fire, and it comes out the back as thrust. The engines are moving backwards with the treadmill, so they have to work twice as hard to get up to speed.

And the riddle doesn't ask if it's possible, it asks if it would happen given a specific set of circumstances. See my post above.

You're not paying attention to the wording of the riddle. Under the first interpretation, the plane is ALWAYS stationary relative to the air, because the treadmill speed is always cancelled out by the plane's speed relative to the treadmill. They have to stay equal.

Under your interpretation, you're assuming that the forces imparted by a treadmill can keep the plane stationary to the ground, which they cannot. Under your interpretation, the riddle is pointless.

Now that I think about it, under any interpretation the riddle is pointless. I can't believe I've wasted this much time on it.

david bowie wrote:

Under your interpretation, you're assuming that the forces imparted by a treadmill can keep the plane stationary to the ground, which they cannot. Under your interpretation, the riddle is pointless.

Now that I think about it, under any interpretation the riddle is pointless. I can't believe I've wasted this much time on it.

I'm glad you realised how ridiculous it is to question the capabilities of a giant treadmill, but not the existence of the giant treadmill.

Yeah, the riddle is pointless. Once you understand the interpretations, the question is "can an airplane take off if it is standing still?" and then "can an airplane take off if it is going down a runway at takeoff velocity?"

DK wrote:

I'm glad you realised how ridiculous it is to question the capabilities of a giant treadmill, but not the existence of the giant treadmill.

I disagree with your comment on the logic behind questioning the capabilities of such a treadmill. Of course said treadmill is impossible. BUT with simple adjustments to basic laws of friction and pressure, the treadmill can in fact "keep up" with the plane regardless of any other of the plane's properties and can still maintain the physics that make flight possible. In this situation, the plane will travel at the same speed as the magical treadmill, while the air around it will be still relative to the plane.

Discussion over.

DK: either way you look at it, the plane can take off. if you look at the link i posted earlier, i calculated the necessary behavior of the treadmill to keep the plane from moving. i didn't plug any numbers in, but the upshot is that the treadmill has to always be accelerating above a certain threshold acceleration to keep the plane from moving. that threshold is above both the relative acceleration of the plane and the treadmill, and the plane and the air.

the riddle would be better worded as follows:

a particular plane accelerates at a rate of 1m/s^2 (1 meter per second per second) until it takes off. if a person were to put this plane on a treadmill, whose belt, going in the opposite direction accelerated at 1m/s^2, and the plane's thrust and weight were excatly the same as they were in all previous take-offs, would the plane accelerate forward, relative to the ground, and take off?

worded this way, it is obvious, to anyone with a basic understanding of the law of equal and opposite reaction that yes, the plane would accelerate and take off. the wheels would accelerate at a speed of 2m/s^2, but given that the thrust applied backwards is the same, the opposite reaction of the plane going forward must be the same, and it would accelerate, just the same, and take off, just the same.

if the problem is worded to say "the treadmill matches the wheel speed of the plane," it is an impossible conundrum. as the plane tries to go forward, the wheeels would accelerate, accelerating the treadmill, which in turn would make the wheels go faster (since thrust is continually applied backwards, so the plane will go forward at the same acceleration), making the treadmill go faster, and so on and so forth, until we begin to experience relativistic effects such as mass increase, rendering it completely impossible to supply the energy necessary to continue this process.

in short, in any possible conceivable scenario, yes, the plane would take off.

remember newton's law:

EVERY ACTION REQUIRES AN EQUAL AND OPPOSITE REACTION.

if we assume negligible friction in the bearings of the wheels of the plane, the answer is obvious to any intelligent person.