The effect (no horizontal velocity) is the same.

0 + X + (-X) + 0 = 0

How does a plane move forward through the air, once it is off the ground? What gives it forward motion if the wheels are not passing all forward motion on the ground? How do you explain forward motion without the ground contact you are defending?

By your definition, the plane should not be able to progress once the forward motion on the ground is no longer going through the wheels....

The wheels would be moving forward at Okay, I guess then they would be spinning at 999,996.8 mph

Sorry.

At that point, they would not be moving at the same speed as the treadmill, which is a requirement of this scenario.

Jet engines are UNDER the wings. They have absolutely no chance of producing enough lift to take off.

You know, $BILLIONS are spent on airports with runways. Think of all the savings if actual engineers were as smart as Mythbusters. We could just put the planes' wheels on a couple treadmills like at the emissions testers - presto, instant VTO.

The plane is no longer contacting the ground at that point. It's held up by air (much, much less friction*). The wheels don't have to roll.


*In fact, for ideal rolling friction between the ground and the wheel is infinite.

The assumption is the shot one is shot level with a surface with no trajectory via elevation added.

OK, now we are making progress. We've established that there are situations in which wheels and a treadmill cannot match speeds.

Back to the original airplane/treadmill case. There are two areas of slippage relative to the plane. The air slipping over the wings and the wheels and tread mill creating a similar plane of slippage between the plane ground. The jet engines are very powerful and are the driving force of the plane. After you account for the slippage of wind over the wing, they externally set the acceleration of the plane relative to the ground just as surely as the the tow rope sets the speed of the the person. You could speed the tread mill up, slow it down, run it backward, it would not affect the speed of the plane because the prime mover of the plane are the jet engines pushing against the air. The wheels will just free spin (slip) to compensate for the treadmill as needed to give whatever velocity needed to make the plane move at the correct velocity given the acceleration imparted by the force of the jet engines.

Heres the original quote

"Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

All it says is exactly match the speed of the wheels. It doesn't say anything about velocity or what kind of speed?

I know that sounded reeruned, but IMO the wheels have 2 different speeds.

The speed in which they are traveling in a straight line, forward, connected to the plane, and the speed in which they are spinning.

So which speed are we talking about here?

Help me out.
The problem says he takes $2 (from $30) leaving $27. How is that math correct?

If the wheels compensate speed at any point, the treadmill will do the exact same. Due to the structure of the question, the speed of the plane will always be zero relative to the ground. Unless there is wind, there is no lift being created by the wings. 0 + X + (-X) + 0 = 0

If you want to want to discuss the problem in terms of force, the force counteracting the engine thrust comes from the wheel bearings. They would be spinning at an unbelievably unrealistic speed to generate that type of force, but that's why this question is theoretical. Therefore, the engines do not externally set the acceleration of the plane, as you must consider all forces acting on the plane.

So you're building a critical flaw into the test. Way to get the answer you want.

Perfect rolling = no slippage

As I understand it, the speed of an atom of rubber at the very bottom dead center of the wheel at any given instant is equal to the speed of the surface of the top of the treadmill.

The correct problem has the plane sitting on a free-spinning treadmill that will absorb all the energy the wheels impart to it.

That original quote by MagicHef is more or less the way Mythbusters stated the problem.

It's not the correct problem. Read the objection here:

Troy Allen • Jan 30 2008 • 10:53PM
I am completely disappointed at Mythbusters handling of this experiment. The science they used and the “explanations” were both completely flawed. The original myth, and ALL of the discussion, centered around one central conceit: The plane would have NO FORWARD MOTION RELATIVE TO THE GROUND because of the conveyor belt matching the speed of the plane. NOT the “speed of the WHEELS of the plane” or any other contrived version.

Of course the plane is going to take off if it has enough forward motion RELATIVE TO THE GROUND to create the Bernoulli effect required to lift the wing because of the airflow over the wing.

I really expected more “science” from MythBusters. They almost explained it properly with the “model car example”. I guess it was the original Myth that was flawed, or my understanding of the Myth. I guess in their mind the myth is that no plane on a conveyor belt can take off if the “speeds are matching in opposite directions”. That is far too simplistic to make a determination, so it is flawed from the get-go.

Those of us who claimed the plane would not take off without forward motion relative to the ground due to the laws of physics are still correct. The planes both had significant forward motion relative to the ground. I just hope everyone involved in the debate understands these distinctions, otherwise this will just dumb down the TV watching public a bit more. It sure was fun though!

Thats not answering my question.

Are you talking about the atoms Speed going forward or speed rotating?

With frictionless wheel bearings, the only function of the wheels on the conveyor is to provide a normal force separating the plane from the ground by the width of the tires. In all other respects this situation is identical to flying with the landing gear extended.

The only possible other outcome is to say '**** frictionless, these wheels have so much friction, their rolling resistance is more powerful than 4 jumbo jet engines.' But that's kind of a cheat, because unless otherwise indicated, friction is generally assumed to be non-existent or negligible in hypos like this.

When did that ever come in to the question?

Let's try once more from physics.

The plane is initially at zero velocity. To start moving, it needs to accelerate. The acceleration of the plane a = F/m where F is the force and m is the mass of the plane.

The jet engines are one source of force. They push on the air. It is what makes a normal plane move forward.

To keep velocity zero, we need to keep acceleration zero. In order to do that we need a force that opposes the jet engine. The only place it can come from is the tread mill. The tread mill transmits it's force to the wheel and the wheel to the bearing. If the bearing were frictionless, there would be no force on the airplane from this spinning wheel. But in real life, there is friction. The friction would impart a force something like friction force = m*g*k where k is a friction coefficient. Regardless the friction force is small relative to the force of the jet engines. If it were not, the plane couldn't roll in the first place. The velocity of the wheel has very little to do with the amount of friction in the bearing. You can't spin the wheels fast enough to keep the plane stationary by generating more friction at the wheel. It is like the example of a person holding on to the tow rope.

If you take an infinitesimally small amount of time, they will be the same. In other words, speed going forward.

Except for one critical difference - you're NOT airborne. Where did you get the initial lift to get off the ground?

There are two COMPLETELY DISTINCT STATES. Plane sitting on ground - plane moving in air.

Perfect rolling = pure slippage.

I'm not a physics guy, and once someone's posts go into more than about 15 words or start using formulas, I go into a brief coma.

However, this treadmill thing sound impossible. Once the jet kicks in, there must be forward movement for the wheels to even begin to move against this imaginary treadmill...meaning there will always be forward movement.

Am I wrong?

So since the wheels on the plane are going the same speed traveling forward as the rest of the plane, the question is:

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the plane, moving in the opposite direction. Can the plane take off?

I changed the word Wheels to Plane.

Thats the real question I guess.

Of course it's impossible. That's not the point.

I'm not sure how you're using the word. Let me give you my understanding.


Circumference of wheel = 1
Circumference of treadmill = 1

Ideal (1.0) roll of wheel produces (1.0) roll of treadmill
Non-ideal (1.0) roll of wheel produces (1.0 - x) roll of treadmill; x = slippage

the wheel

In approximations pertaining to ideal friction, velocity has nothing to do with frictional force. Explain to me how the plane moves if the parameters of the question hold.

Actual wheels could not be spun fast enough to generate enough friction to overcome the thrust of jet engines.

I'm just saying, niether the wheel nor the treadmill would ever move in this scenario...right?

No, the wheels can be moving at 5 ft/sec with the treadmill moving at 5 ft/sec in the opposite direction, and the plane will be moving at 0 ft/sec.

That is true.

The net speed (plane plus conveyor belt) must equal 0.

The plane will never move forward, there will be no lift generated and it won't take off.

The wheel said nothing about being frictionless.

The wheels dont affect the plane moving, so the real question is if the treadmill is going the same speed as the plane, not the wheels.

No. Ideally the wheel only has move forward one point (0 distance) to start rolling.

Extrapolate from my answer in #185. As the wheel rotates, the plane's hypothetical forward speed equals circumference/(time/rotation); the conveyor belt's speed must equal this.

The wheels are solidly attached to the plane, so they affect the motion of the plane in the sense that the speed of the plane in relation to the speed of the treadmill will always be equal to the speed of the wheels.

So at some point the wheels are moving faster than the treadmill? And the treadmill must catch up?

And is also identical to a pontoon plane on water, or a ski plane on ice.
The lift comes from the rearward thrust pushing the plane body forward as it 'skates' on the conveyor surface.

If the plane isn't moving forward relative to the ground, then its speed is 0, meaning the treadmill's speed is also 0, but that cannot be the case. The speed of the wheels in the original question was referring to the speed in which they were spinning.

Am I wrong here?

No. Let's say the wheel starts out with point A in contact with treadmill point X. The next instant wheel point A+1 makes contact with treadmill point X+1. Both are in simultaneous motion, both bits are driven back to position A and X.

The plane's speed has no effect on the treadmill's speed.

The plane is only 'skating' relative to the conveyor surface - which is also 'skating' at equal and opposite speed. Neither water nor ice is a perfect treadmill (certainly not ice which doesn't move at all - ski plane on ice relies on relatively frictionless contact with "the ground").

The plane is NOT moving forward relative to the atmosphere and produces no lift.

Motion is relative, remember?


The "plane" INCLUDES the wheels. The wheels are moving. That's where all the energy is going. Spinning the wheels. The wheels are resisted by friction against the treadmill. The treadmill absorbs that energy and moves in the opposite direction.

What makes the treadmill begin to move?

I think this problem is set up with an impossible tautology, just like my rollerskate, moving sidewalk, and tow rope example. You cannot match the speed of the wheels and the conveyor belt because the speed of the airplane is externally set. I believe the author of the problem has done this intentionally to get people to talk past one another.

I will defend this to the end of time:

Put a jet on a tread mill. Once the jet starts rolling, run the tread mill at any real speed and direction (it hast to be a real speed, but even 500 mph would be okay). The jet will take off.

Theoretically, no, unless someone came up and pushed on the treadmill or something.

Ok, am going to word this differently, again.

The planes wheel's clearly have 2 different speeds. The speed in which the plane is moving forward, which I'm going to label as its static speed, and the speed in which the wheels are spinning, which I'm going to call their rotating speed.

If the question is

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the static speed of the plane (you can substitute the word wheels for plane here because the wheels, as part of the plane have the same static speed of the plane), moving in the opposite direction. Can the plane take off?

then you have a case.

If the question is

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the rotating speed of the wheels, moving in the opposite direction. Can the plane take off?

then, you have no case, because the rotating speed of the wheels has no affect on whether or not the plane can move forward or take off.

LOL
i just read a comment here about the plane crash in the ocean near Brazil. Which one of you posted it? LMAO reerun?

That's perhaps the most succinct way of putting it exactly right.

As the thrust comes from the jets exerting force on the air behind, everything concerning the wheels and conveyor are just variations on what happens to molecules in the atmosphere as the jet flys by, or molecules in a lake or ice slab as a pontoon or ski plane takes off.

The speed of the airplane is absolutely not externally set. What is the limit to real speeds? I'll say S(100).

The red part is where I disagree with you. That's like saying that the rotating speed of a shopping cart wheel has no effect on the speed of the shopping cart.

http://upload.wikimedia.org/wikipedi...Resistance.PNG

http://en.wikipedia.org/wiki/Rolling_resistance

So you are telling me that if you lock up the wheels on a shopping cart so they cannot rotate, you cannot make the cart move forward just as fast?

Also a shopping cart has no way to propel itself, unlike a plane.

the conveyor has no ability to counteract the momentum produced by the engines because of the broken link caused by the wheels. because of this, a conveyor of any speed will only cause the wheels to spin faster, while the plane is unaffected

Externally set by the thrust of the jet.
Put it this way, you're standing over a hockey puck sitting on an infinite frictionless conveyor. The conveyor can sense if the puck starts to move in one direction and spin the frictionless surface in the opposite direction. You flick the puck with your finger, what happens?


[and yes, I'm familar with your 'rolling resistance stronger than 4 jet engines gambit' but you know and admit it's BS]. Frictionless/negligible is a very safe assumption.

Well, you can have the wheels skidding across the floor. The issue of whether or not the wheels are skidding on the treadmill is not addressed in the problem, but I have been assuming that they are not. The shopping cart is being pushed by someone rather than being propelled by its wheels, which is somewhat analogous to a jet engine.

Try this MagicHef.

Take a pen and a roll of tape, or a toilet paper roll.

Put the roll over the pencil. Do not spin the roll.

Move the pencil from your left to right. Thats your static speed.

Now bring the pencil back to the left, spin the roll. Thats your rotating speed.

Now do both at the same time. The rotating speed doesn't affect the static speed because there is an outside force moving it (your arm).

This is the same w/ the rotating speed of the wheels. While they are spinning, there is an outside force (the jets or propellers) pushing the plane forward.

Thats the difference between static and rotating speeds (combined with an outside force), and whether or not they affect the plane moving.

Of course, I'm no expert.

No, frictionless is not a safe assumption, and I freely admit that the whole problem is BS. But, if there were a system that met the criteria of the question (which there isn't, and could never be) the plane would not take off.

My plane disintegrated. Is that your argument?

I'm going to take a 400,000 lb 747 and apply 200,000 lbs of thrust to it. What speed do you want to run your conveyor belt at to keep it from taking off?

Do the same with the toilet paper roll being pressed against the ground enough to keep it from slipping. The rotating speed and linear speed are linked quite concretely.

Whatever speed it takes.

But now you are using the ground to push off of to move forward, the plane doesn't use the ground to push off of to move forward, so the rotating speed in this case isn't linked to the linear speed, especially because you are asking what if the linear speed is 0.

If the linear speed is 0, then the rotating speed can be x, y, z, or whatever other number you want to throw out there.

I have no idea what you really mean. The plane's momentum is 0.

p = mv

The plane has no velocity. We start up the engines, energy drives the plane forward. It tries to move forward but it is in contact with the ground. The contact points are the wheels. Friction at the points of contact (i.e. where the rubber meets the road) resists any forward motion of the plane, basically pushing back. Since the contact points can't move forward the wheels spin so a new bit of wheel now contacts a new bit of road.

On the conveyor belt, the "road" also spins like the wheels. The new bit of road is in the same place as the first bit of road. There are now new contact points between new bits of wheel and new bits of road, but the position of these points relative to the surrounding ground is the same as the original position. The plane has not moved relative to the surrounding ground - and more importantly air. The plane's velocity remains 0. The plane's momentum remains 0. The energy that was spent spun the wheels and the conveyor belt.

Rinse and repeat.

No, I'm only using the ground to press down on, much like the weight of the plane is pressing the wheels down on the treadmill. The linear speed does not have to be zero, you can change the linear speed of the pen and you will see the rotating speed change accordingly.

If the Linear speed of the plane is not 0, then it can either move forward and take off, or it will move backwards and fall off the treadmill, and the whole experiment is flawed.

YES YES YES.

Tie a shopping cart to a fixed object. Put it on a tread mill. Run the tread mill at any speed. The wheel speed has nothing to do with the speed of the shopping cart. The speed of the shopping cart is set independently of the wheel speed by the balance of the forces.

Wheel speed (depends on) = treadmill speed (independently set) + velocity of shopping cart (determined by force balance which is mostly independent of treadmill speed and wheel speed)

You can't set the treadmill speed to equal the wheel speed.

I only had time to skim this thread. Could someone give me the Cliff's notes on the Donkey fans' argument on why it won't take off? Is it because the spinning wheels have matching friction that matches the thrust of the engine or is because the spinning wheels can't transfer the force of the engines to the ground to get the plane moving?

Try turning on a treadmill, holding the pen still, but pushing the roll down on the treadmill. The linear speed and rotating speed are still linked, but in relation to the speed of the treadmill, not the speed of the ground (0). That is much more similar to the question.

that's what i thought at first, too. but the first step in all of this is that the engines turn on. there's now a force that has to be counteracted, and the conveyor will try move to keep the plane in the same spot.

I get that. when the conveyor tries to do this it causes the wheel to spin faster. but because how fast the wheel spins has no effect on the speed of the plane, it doesn't matter.

Neither.

In order to move forward while contacting the ground, the wheels must roll - which puts a new piece of wheel in contact with a new piece of ground. The conveyor belt is matching this rolling (in the opposite direction) so the new piece of ground is in the same place as the original.

Your example is dependent on one force (rope) being vastly superior to another force (friction in wheel bearings). If you tied it with a single thread of cotton and managed to set the treadmill to run at 500 mph, would you expect the same result?

The force is counteracted by the treadmill spinning in the opposite direction.

It's really simple. In order to go forward, the wheels have to roll or slide along the ground. What else, teleport? Our ideal treadmill allows no sliding. And it matches the wheels' rolling in the opposite direction.

Okay, I see that.

So basically the question is can a Plane take off without moving forward relative to the ground? Regardless of whether or not it is moving relative to the treadmill, its not moving relative to the ground, so of course it cant.

But the original question just asked about the speed of the wheels relative to the treadmill, not the plane.

The force of the jet engine is vastly superior to the friction in the jet wheel bearing. A jet engine would easily break the rope I need to hold the shopping cart.

Yes. The question could certainly be worded much better. I probably should have edited it when I copied it.

Why must it roll for the plane to take off? The force is against the air. If I blow up a balloon and hold it in the air and let go, it takes off just fine without needing friction against the ground. The plane's engines act the same way.

No matter what speed the wheel is spinning at?

No. The plane's engines provide horizontal force. The airflow over the wings provide vertical force.

Simply stated, it cannot.

find x:

x = x +5