A harmless little riddle

I'm just 14 and this stuff is going way over my head. (insert you're an idiot, should have learned it in 7th grade comments now) Can someone explain how the wheels are free rolling etc? How does a plane move on the tarmac if the wheels are free rolling, wouldnt they just spin while the plane stays in place?

OK,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?

1. Plane on treadmill. Neither treadmill nor plane is moving.

2. "As the plane starts its engines" modifies what comes after the comma, namely "the treadmill runs in the opposite direction at the same speed the plane is moving." At this moment the plane is moving at 0 mph, so the treadmill is moving at 0 mph.

3. Can the plane take off? Yes! The riddle does not say that the treadmill matches speed with the plane! The treadmill never moves. The treadmill is moving at 0 mph. Thus the plane takes off as if it were on a normal runway.

We can't assume that the author meant that the speed of the treadmill macthes the speed of the plane. If he meant that, he would have written it that way. We are stuck with what is there. And what is there only describes the speed of the treadmill as the plane starts it's engines.

BTW: if the treadmill was moving, as some have suggested, the plane would still take off.

An airplane does not drive itself foward on the tarmac (or in the air obviously) using its wheels. Instead air is forced through its jet engines (or pushed by its propellor) toward the back of the plane at a high speed, driving the plane foward at a slower speed. This works because in a closed system (in this case the closed system is the plane and the air) momentum must be conserved. Momentum equals mass X velocity. If the air has mass & velocity (M1 & V1) and the plane has mass and velocity (M2 & V2), then it follows from the principle of conservation of momentum that:

(M1 X V1) + (M2 X V2) = A Constant (equation 1)

If both the plane and air are initially at rest then:

(M1 X V1) + (M2 X V2) = 0 (equation 2)

or

(M1 X V1) = - (M2 X V2) (equation 3)

So if V1 is increased (that is the air is given a velocity by the planes engines), then (M1 X V1) also increases because the mass of the air has not changed. Because M1 X V1 has increased then (M2 X V2) must increase to satify equation 3. Since the mass of the plane does not change and there is no such thing as a negative mass, its velocity must increase (that is the plane must start moving in the opposite direction as the air).

Ah, not so!

E=MC2

Think about it.

the riddler wrote:

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?

It's almost unbelieveable that this (UNRELATED TO RUNNING) riddle is still going. I think it's a good sign. I think runners are natural "solution seekers". I majored in Physics in college, so at first I thought that was why I responded to the riddle (incorrectly), intially. Then after a few more days it became obvious that alot of other people enjoyed "taking a stab at it".

I agree, our educational systems need to be improved. Maybe riddles are the answer. Ever hear of the "Socratic Method"?... By asking (intellegent) questions Socrates was able to turn out some brillant students, at his school.

Riddler, are you going to post one last comment on your thread?

Braavo Furgi wrote:

I agree, our educational systems need to be improved. Maybe riddles are the answer. Ever hear of the "Socratic Method"?... By asking (intellegent) questions Socrates was able to turn out some brillant students, at his school.

Yeah, but he so annoyed the rest of Athens that they put him to death.

but now a history guy

Here’s my reasoning, but I have to say that I could be completely wrong.

Assuming that the air is still relative to the earth, the plane should not be able to take off. One aspect of generating lift is the velocity of the air going past the wing. This is initially created by the thrust of the engines. Once the airplane is in the air, the engine simply counteracts the drag (so you move at constant velocity and stay at the same altitude). That is one reason why you slow down when landing and speed up when taking off.

To take off, either the air has to move or the plane has to move. Usually the engine provides the thrust to move the plane relative to the air, which creates lift. If both are still relative to the earth (thus they have a velocity of 0 relative to each other), then no lift will be generated even if the engine is running. Now one might argue that the friction of the treadmill would create a movement of air, thus generating a wind. But the likelihood of friction creating a uniform velocity in one direction that is large enough to create lift seems small and is certainly extremely complicated if not impossible to calculate.

Here’s a quote from a NASA website:

Aerodynamic forces are generated by an object moving through a fluid (liquid or gas). A fixed object in a static fluid does not generate aerodynamic forces. Hot air balloons "lift" because of buoyancy forces and some aircraft like the Harrier use thrust to "lift" the vehicle, but these are not examples of aerodynamic lift. To generate lift, an object must move through the air, or air must move past the object. Aerodynamic lift depends on the square of the velocity between the object and the air. (

http://www.grc.nasa.gov/WWW/K-12/airplane/move.html

or check out

http://www.grc.nasa.gov/WWW/K-12/airplane/bgp.html

)

xbcha1 wrote:

Since you have crashed planes, maybe it's you who shouldn't have the pilot's licence.

If you had been throught the same education system as most of the people who say it will fly then maybe you would have the intelligence to avoid crashing a plane.

When your engine fails away from a landing area... you crash. Logic doesn't enter the equation. And when your plane has an airspeed of zero... it can't go up. I guarantee you that if you ever fly a plane, you'll get it.

From the way the riddle was initially written, it can take off.

But assuming the riddler meant that the airplane never moves forward with respect to the ground, becasue as the jets "propel" the airplane, the treadmill covers the "speed," the lift would never occur.

I have not read everything, but I think people are looking at this in 2 ways, and most of the posts that I have read are actually correct depending on semantics.

This may have already been brought up but I am not reading 19 pages. Get a toy plane that will glide like those old styrofoam ones. Hold it out to your side and run with it on the road. It will pull up. Now do the same thing on a tread mill. It will just stay where it is.

More importantly, as someone early on pointed out, if a plane could stay take off from a tread mill we would have put them on aircraft carriers.

dan patrick wrote:

This may have already been brought up but I am not reading 19 pages. Get a toy plane that will glide like those old styrofoam ones. Hold it out to your side and run with it on the road. It will pull up. Now do the same thing on a tread mill. It will just stay where it is.

That's because you are not moving on the treadmill.

A plane develops its own thrust with its engines. The engines move the plane relative to the air, so it develops lift.

For those who are trying to worm out of it by using semantics, the riddle was developed to test the knowledge of people who already have a modicum of knowledge of aeronautics. If you like, change the surface to a frozen lake with zero friction.

As the riddle is written the plane will move relative to the air - THE TREADMILL CANNOT PREVENT THE PLANE FROM MOVING RELATIVE TO THE AIR. I have already posted several of my own explanations as well as an expert explanation as to why this is true, and why consequently the plane will take off. The net effect of the treadmill will be to double the groundspeed of the plane (its speed relative to the treadmills surface) while leaving the airspeed (its speed relative to the air) unchanged. I'll say it again for the cheap seats - the treadmill will have absolutely no effect on the plane's air speed.

The reason there are not treadmills on aircraft carriers is because the treadmill would have to be exactly the same length as a normal runway for the plane to take off and there would be no point to this. The plane would have to travel the same distance along the treadmill as it would on a normal runway for the plane to take off.

The only way to prevent the plane from taking off would be to move the air surrounding the plane at the same speed as the plane the same direction that the plane is traveling thereby removing the planes ability to generate airspeed. This cannot be done by moving the ground via a treadmill.

Riddler, are you going to post one last comment on your thread?

Yes, I will.

Inspired by the great philisophical thinkers of the past, I posted this thread in the hopes that through debate and critical thinking we, the population of Letsrun.com, would become a microcosm of glorious harmony.

Not really though; I'm just a high schooler from dyestat who wanted to see a bunch of adults prove their idiocy. Thanks to many of you for living up to my expectations.

Simply put, you are an idiot and fail to grasp any basic physics. You also fail to follow simple logic. We are all now dumber for having read your post, may God have mercy on your soul.

How is the propeller generating forward motion if the wheels which are what connects the airplane to the ground before it goes fast enough to take off are being allowed to move on a treadmill? How is the airplane able to roll off the treadmill and then begin accelerating forward fast enough to generate airflow over the wings? The Propeller will continue to keep biting into the air, pulling it past the airplane, not pulling the air over the entire surface of the wings, and meanwhile the wheels will be cancelling all forward momentum because they are already moving on the treadmill, thus the airplane is not actually moving forward through the air.

If this airplane is jet powered, then the thrust generated by the engines, in keeping with the scientific law used for rocketry(a jet engine uses the same principle as a rocket engine)that every action has an equal and opposite reaction, is being cancelled by the moving treadmill under the wheels. The thrust of the engines doesn\'t \"HIT\" anything making the rest of the plane move forward, it sends burnt fuel under pressure out the back of the engine, making the rest of the plane move in the opposite direction. Whether this treadmill is powered or not, doesn\'t matter. The airplanes engines first generate the thrust, the wheels then move, and then airflow is generated over and under the wings creating lift and then the plane takes off. If the engines are generating thrust sufficient for 150 mph, and the treadmill moved under the wheels in direct proportion to the engines thrust accelerating all the way to 150 mph, the wheels are moving at 150 mph, not 300, not anything else.

The speed of the treadmills motion does not add to the forward thrust of the engine. They simply cancel each other out and the plane, meanwhile has still not travelled a single foot forward in relation to the ground, and air, around the airplane, and thus no liftoff can be achieved. It doesn\'t even matter if the airplane sitting on the treadmill is sitting on an incline one way or the other. The treadmills motion is cancelling this forward thrust, by moving the surface of the treadmill the wheels are in contact with, because of the earths gravity. Until the wings can generate lift the aircraft is still connected to the ground, through this treadmill because of gravity. If the treadmill is powered to move by itself, or if the treadmill is set to roll freely, the wheels will begin turning and the thrust will keep thrusting, meanwhile the airplane is not getting any forward motion through the air because the treamdill is cancelling any forward motion because it is turning, or being turned underneath the wheels.

This is basic laws of physics 101 everyone. And airplane cannot take off until it\'s wings are moving through the air at a sufficient speed to generate lift. If the treadmill moves in the direction to simulate forward motion, then the airplane is not getting any forward motion through the air. And thus, the propeller or jet engine can thrust or pull all they can with every bit of power they have and still the wings will not be moving forward because the treadmill is providing the motion under the wheels that gets the airplane moving.

The only way this could work is if the airplane were attached by cable to another airplane that is not sitting on a treadmill. This other airplane would then pull the airplane that is sitting on the treadmill off the treadmill, and then onward to a forward motion sufficient to generate lift on it\'s wings.

At first I also made the mistake of thinking that the plane could not generate airspeed and take off, but I eventually realized that since the wheels spin freely, the plane is essentially disconnected from the treadmill. In other words, if we neglect friction in the wheels, the treadmill cannot generate any lateral force upon the plane to slow its acceleration. So the treadmill will run faster and faster but the plane will accelerate relative to the ground (and air) anyway.

dan patrick wrote:

Simply put, you are an idiot and fail to grasp any basic physics. You also fail to follow simple logic. We are all now dumber for having read your post, may God have mercy on your soul.

(dan) Rather than just calling me names, why don't you come up with what is wrong with my "basic physics"?

The problem is aimed at aeronautic types. Your HS physics isn't going to cut it at this level. It's a bit beyond that.

"This is Basic laws of physics 101 everyone"

What is the matter with you? Please just read some of the earlier post!

It has already been established that the plane generates force against the air not the surface of the treadmill. The wheels are not powered by the engines, there is no drivetrain.

The propulsion system is based on the engines propelling against air so the airplane will move in the horizontal plane across the treadmill (no matter how fast the treadmill goes) and eventually reach a speed to to create enough force on the bottom of the wing to move in the verticle plane