A harmless little riddle

Wow, that's an ironic response. Read my post again.

Engineer - Do you agree that there can be a second interpretation of the riddle that makes a difference as to the outcome of the riddle?

no i do not as a matter of fact its pretty hard to take it as anything but what it is.

Asterix wrote:

In science and engineering, you can't arbitrarily say something is moving without stating what that movement is relative to. That is a pretty fundamental principal.

Simple puzzles don't give hints. That would defeat the purpose. We aren't talking about generic science and engineering; we are talking about the specific field of aeronautics, so we can assume it is a given that the movement of the plane is relative to the air. That piece of info is specifically left out and the treadmill is put in to trick people.

I'd hardly envisage the boss of Boeing running up to his top engineers and posing them a simplistic riddle like that. But after a basic class in aeronautics the instructor might pop something to catch the sleepy ones out.

What do you mean by tangential?

you dork! the spinning of the airplane's wheels is also due to the treadmill. if you turn the treadmill on, will the plane just move with it? no, because there is a torque being applied to the wheels.

"As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving."

There is no ambiguity in this statement, unless you are somehow under the impression that speed = force.

The so-called "second interpretation" is not a reasonable interpretation of the riddle at all. It is simply an explanation of why the "no fly" people got the answer wrong.

"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?"

Why is it so hard believe that a person could interpret the "speed the plane is moving" as being relative to the treadmill?

Also, if the question was written:

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 relative to the treadmill. Can the plane take off?

Would you be a "no fly" guy?

Ok, I think everyone except wow, who is most likely a troll, now understands why the plane would fly if the riddle is interpreted to mean:

The treadmills belt spins at a rate of speed equal to, but in the opposite direction of, the speed of the plane relative to a stationary observer outside the frame of reference of the treadmill, otherwise know as the planes airspeed if we assume a still wind (the planes speed relative to the surface of the treadmill is its groundspeed).

This is the locigal, "real world", interpretation of the riddle based on the actual observatble behaviour of both treadmills (obviously on a smaller scale) and planes. It has been explained to death by everyone on this board and by several outside sources why the plane would take off under this interpretation. This is infact the correct interpretation in that if one were somehow able to construct such an experiment it would correctly predict the result.

Now to the other possible interpretation of the riddle, which I will state as:

The treadmill belt's tangential velocity matches the tangential velocity of the wheels.

First, off I do not believe this is a valid interpretation of the riddle because in order to the conditions of the riddle to be satisfied at all times one would have to assume both a treadmill and airplane engines capable of infinite acceleration. This is obviously not a real world interpretation of the riddle as we have yet to build airplanes or treadmill belts capable of traveling at the speed of light (that whole mass becomes infinite thing is a b!tch).

However, given despite my misgivings of the second interpretation, I will concede that someone could possibly interpret the riddle this way. However, it makes no difference as the plane will still fly. Not in a conventional or controlable manner, but it will infact get airborne.

The reason the plane will still fly was stated earlier when someone talked about velocity boundary layers. As the treadmill moves it entrains some of the air in contact with its surface to move along with it - this is called a boundary layer. Were you to actually construct a treadmill capable of the infinite acceleration necessary to keep a plane with infinitely powerful engines from taking off, the boundary layer of air it would entrain would cause an enormous hurricane of moving air traveling in the direction of the treadmill and over the wings of the plane, throwing the plane into the air. This could only be prevented if both the treadmill and plane were in a vacuum, but then the plane would have no chance to fly even without the treadmill which isn't really fair to the plane now is it.

THE PLANE WILL FLY!!! VIVA LA REVOLUTION!

Note: The last possible interpretation - that the treadmill matches the groundspeed of the plane relative to the surface of the treadmill - is invalid as it postulates a non-inertia frame of reference.

making false statements and saying it's the truth and then closing by saying you're a dumbass gains you absolutely nothing.

the engines "pushing on air" is not the same as the exhaust pushing on the airplane. i'm sorry. in your world, the airplane gets its thrust from planting its invisible feet against this surface of air and pushing, or by pulling itself along this rope of air suspended above the ground. in the real world, however, the exhaust trying to escape the confines of the engine pushes on the engine housing, which is connected to the rest of the airplane, and the plane goes forward. this thrust has absolutely ZERO vertical component, and so the weight of the plane still rests on the wheels, which DOES provide enough friction so that the treadmill can carry the plane. have you ever seen one of those rocket-powered cars? the ones that go like 600mph across the salt flats in the desert? well, don't their engines "push on air" too? and they don't get airborne. this is because there is no lift to overcome gravity.

i will say it again, the only difference between the plane being on a normal runway versus the treadmill runway is that the whole thing starts out moving backwards relative to a stationary observer. the plane's wheels don't magically start moving faster because the section of ground that they're on is moving relative to the ground beyond. does the earth just spin by underneath the wheels while the plane hovers over the earth on a normal runway? i don't think so. this is really getting absurd.

wow. wrote:

okay, the only way that the plane moves forward and takes off is if it's going faster than the treadmill. that can't be that hard to comprehend. the riddle said same speed. it seems pretty open and shut. i don't know why people are trying to make up impossible scenarios and say the plane is actually going 200mph when it's going 100, and all this bs about how no treadmill can be as powerful as a jet engine. that has nothing to do with this riddle. you know, the only reason it's even a "riddle" is because the person who wrote it used language just ambiguous enough to give some people cause to say "it only says SPEED, it doesn't say speed of what," and blah blah blah.

what do you mean, "bs about how no treadmill can be as powerful as a jet engine"? it's clear that the treadmill acts through friction, which has limited maximum value, whereas the jet engines can be arbitrarily powerful. unless you're proposing that the airplane has some sort of velcro or something on the wheels that make the coefficient of friction arbitrarily large. but in that case, the velcro would stick the plane to the runway, preventing it from taking off anyways.

hi all wrote:

What do you mean by tangential?

If something is rotating, you could express its "speed" in two ways: 1) Angular velocity, and 2) Tangential velocity.

1) Angular velocity is expressed as Rad/s, RPM, etc.

2) Tangential velocity is the linear velocity tangential to something rotating, and is a function of angular velocity and the radius of the rotating object. (MPH, m/s, etc.)

Engineer wrote:

no i do not as a matter of fact its pretty hard to take it as anything but what it is.

Look, I've been in the "it flies" camp since I started reading this thread. But I have realized that if you interpret the speed to be wheel speed, then it doesn't fly. And I have also argued previously that the "it flies" answer is still more likely (because plane speed is generally measured in air speed), and so I think that is the more correct answer.

But if you don't agree that if you assume that "speed of plane" means wheel speed, the plane will not take off, then you are as much of a moron as the "no fly only" people.

[quote]cgaites wrote:

The treadmill belt's tangential velocity matches the tangential velocity of the wheels.

/quote]

If we assume that the wheels don't slip, then this is always true. Of course, this is not a valid assumption, since friction is a limited force.

The two interpretations of the riddle are:

1. The treadmill's velocity is equal in magnitude to the plane's velocity relative to the air

2. The treadmill's velocity is equal in magnitude to the plane's velocity relative to the treadmill.

That the surface of the treadmill is a noninertial frame of reference is irrelevant-you can still define a velocity relative to a noninertial frame, it just doesn't behave as nicely when you try to calculate forces and whatnot. But it is manageable.

wow. now i know you are i troll i just explained to you how the wheels work yet you still called it magic. i have never said the word rope once so i dont know where you getting it from. and lastly i never said that the planes engines make the plane fly up in the air. but if the planes engines do make the plane move forward. and once that happens the wings give it lift and it takes off into the air.

"which is connected to the rest of the airplane, and the plane goes FORWARD. this thrust has absolutely ZERO vertical component"

this is what you said. notice how i capped the word FORWARD which you used. tell me then what happens when an air plane moves forward???? so basically i was right and you were wrong without that FORWARD(theres that word again) thrust there would be no vertical component now would there. so it is safe to assume that the thurst does have an effect on the vertical component and you are a dumba$$

KnowItAll wrote:

Engineer wrote:

no i do not as a matter of fact its pretty hard to take it as anything but what it is.

Look, I've been in the "it flies" camp since I started reading this thread. But I have realized that if you interpret the speed to be wheel speed, then it doesn't fly. And I have also argued previously that the "it flies" answer is still more likely (because plane speed is generally measured in air speed), and so I think that is the more correct answer.

But if you don't agree that if you assume that "speed of plane" means wheel speed, the plane will not take off, then you are as much of a moron as the "no fly only" people.

Well, if the plane is to remain stationary, the treadmill must provide an acceleration equal to (F_(engines)*I/r^2), as argh... has posted (what a smart guy! probably the only one who bothered to work this out on paper). Which means that the treadmill will soon become relativistic, making the treadmill shrink, eventually so much that the plane falls off the treadmill and starts to roll. By that time, though, most of the air on the planet will have been flung into far space, the rubber surfaces in question would have vaporized, and the material of the treadmill surface would have contorted as it rapidly accelerates around the corners.

in any case, my conclusions are:

1. wow is a troll

2. Engineer needs to realize that the assumption that v(treadmill)=v(plane relative to treadmill) is equivalent to assuming that the plane doesn't move in the air, which is equivalent to saying that a_{treadmill}=F_(plane)*I/r^2.

3. wow has done nothing in this argument except contribute to the aggravation of both sides. congratulations-even if you don't want to be a troll, you are. dumba$$.

Pherekydes wrote:

Simple puzzles don't give hints. That would defeat the purpose.

Simple puzzles also don't leave any ambiguities open. That would make them not-so-simple (or even solvable).

We aren't talking about generic science and engineering; we are talking about the specific field of aeronautics, so we can assume it is a given that the movement of the plane is relative to the air.

Why do we have to assume the movement is relative to the air? Air is mentioned nowhere in the original post.

What if there was a big fan in front of the plane so we've got several references frames: plane relative to treadmill; plane relative to rest of the world; and plane relative to airflow. All have different values and all could be justifiably used when saying "the treadmill moves at the same speed as the plane is moving".

yes knowitall i will agree with you on that account. but that would mean that only the treadmill would be moving. because in order for the wheels speed to be the same speed as the treadmill you can have no force coming from the plane which means it is not on. and that the treadmill is the only force acting on the wheels. ill agree with you but anyone who looks at it that way needs to get punched in the face for not wearing their special helmet to school.

Why are you even responding to "wow.'s" posts? Its obvious he's 1) and idiot, 2) a troll, or 3) both.

If a person can't see how the plane is able to fly under what has become known as "the first interpretation" then God help them.

The more important matter is helping you to understand "the second interpretation."