[Guest]

This is a very highly debated topic, even though scaled tests have been conducted. The popular Mythbusters show on discovery did it full scale, but some still dispute the way they did it. You can probably find thousands of forums that host this same question, and I wouldn't be suprised if it has even been posted here before. So here goes!

A large passenger jet sits on a tredmill the size of a normal runway that they would normally take off on. When the jet starts up, it climbs in speed slowly. The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well.

The grand question: Will the plane take-off?

Assume that:

The wind is at 0 MPH

The Jet is powered by turbines

Edited September 6, 2008 by RedRum

[Guest]

You haven't actually attacked any of the points that I've made either. You've just asked me questions, and then gotten mad at me. If you see something that I have said that is wrong just point that out to me.

Are you kidding? I've attacked your points several times. Would you like me to point out where? I assure you, I'll point out multiple examples. I've "gotten mad at you" (not really) because you have to be asked repeatedly to answer questions. And you're still not answering them!

As I said before, the wheels are spinning because the treadmill is moving underneath them.

Why don't you answer the question? What is determining the speed of the treadmill? I asked you that in my last post and once again, you don't answer. Actually, you said the treadmill is moving to match wheel speed. I copied and poster your statement several times. If you said it backwards by mistake, how could you not have picked that mistake up with all the times I quoted you, and asked you questions about the statements which you avoided multiple times? Are you bothering to fully read my posts?

By you:

"So if the conveyor speed matches the wheel speed the plane won't take off".

Now I guess you're going to claim you wrote that backwards? What is it that's causing the belt to move so fast? I asked you that before and you once again ignored me. Isn't it possible that we'd get to the bottom of this if you'd just answer my questions?

Why does the belt have to be constantly accelerating? Please give a reason! If the speed of the belt is not determined by the wheels, what determines the speed of the belt?

As long as there is equal force pushing the plane forward and backward the plane will not move. The engines start up and at the exact same moment that the treadmill starts moving.

Why? How is that the converter speed matching the wheel speed? Why does it need to go 10,000 m/s?

Please, hmmmm..., address all my questions point by point for a change.

[Guest]

[moderating]

Okay, guys, I'm going to put a stop to this. Understanding the answer to the OP's riddle is confusing enough for plenty of people just the way it's written; it's not fair for them to have to wade through pages of discussion on what would happen under much different circumstances, which after multiple pages are still not clear. Any further discussion should be in regards to a plane taking off as the OP described: "The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well. "

hmmmm..., I don't think it's unfair for me to not allow further rebuttals at this point as the questions you've just been asked are repeats and you've had multiple opportunities to answer them.

Back on topic...

[/moderating]

[Prime]

[moderating]

... "The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well. " ...

[/moderating]

What does that mean though? Every mile per hour with respect to the ground? Treadmill?

If OP stipulates the plane accelerates with respect to ground, what's the riddle?

[Guest]

[moderating]

Okay, guys, I'm going to put a stop to this. Understanding the answer to the OP's riddle is confusing enough for plenty of people just the way it's written; it's not fair for them to have to wade through pages of discussion on what would happen under much different circumstances, which after multiple pages are still not clear. Any further discussion should be in regards to a plane taking off as the OP described: "The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well. "

hmmmm..., I don't think it's unfair for me to not allow further rebuttals at this point as the questions you've just been asked are repeats and you've had multiple opportunities to answer them.

Back on topic...

[/moderating]

Thank you. But that actually makes me more confused...the first line "the tredmill matches the jet's speed EXACTLY" seems to mean that the speed of the treadmill = the speed of the jet. However, the second line, "For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as well." seems to mean that the speed of the treadmill = the acceleration of the jet, which is a different situation?

[Guest]

What does that mean though? Every mile per hour with respect to the ground? Treadmill?

"The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well. "

Think of it this way:

A plane moves in one direction, while the conveyor belt moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

So yes, with respect to the ground.

If OP stipulates the plane accelerates with respect to ground, what's the riddle?

It's been explained in this thread already. You mentioned what you thought was trying to be accomplished on MythBusters, so I assume you saw the episode. They were attempting to duplicate the conditions I mentioned above. Why? Because plenty of folks don't think the plane can take off. That's it; that's the riddle.

Thank you. But that actually makes me more confused...the first line "the tredmill matches the jet's speed EXACTLY" seems to mean that the speed of the treadmill = the speed of the jet. However, the second line, "For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as well." seems to mean that the speed of the treadmill = the acceleration of the jet, which is a different situation?

See above.

[Guest]

jet stand still treadmill standstill, plane goes faster and treadmill goes faster... matches speed

I the plane is accelerating and aproches a take off speed off it goes, why? because it does not gain forward, backward or any motion from the wheels - it is the equivalent of it being suspend on string above the ground, the jets/propeller will provide the propulsion and it will move forward

That must be clr, you doubters need to get your head around the treadmill speed and aircraft speed, not the wheel speed - that has been simply explained and I'm not repeating it

Can there be any useful examples of the treadmill acting as a frictionless surface as in this case it is not affecting the jets propulsion, just moves the free spinning wheels - surely that is simple

Tal put it perfectly at the beginnig - can we stop the bickering and pushing of ideas, adn shed any ignorance by learning, much less admitting it cls be another way - no one has convinced me of any difference yet

[Guest]

jet stand still treadmill standstill, plane goes faster and treadmill goes faster... matches speed

I the plane is accelerating and aproches a take off speed off it goes, why? because it does not gain forward, backward or any motion from the wheels - it is the equivalent of it being suspend on string above the ground, the jets/propeller will provide the propulsion and it will move forward

That must be clr, you doubters need to get your head around the treadmill speed and aircraft speed, not the wheel speed - that has been simply explained and I'm not repeating it

Can there be any useful examples of the treadmill acting as a frictionless surface as in this case it is not affecting the jets propulsion, just moves the free spinning wheels - surely that is simple

Tal put it perfectly at the beginnig - can we stop the bickering and pushing of ideas, adn shed any ignorance by learning, much less admitting it cls be another way - no one has convinced me of any difference yet

I think you are right. for plane the power of movement is generated by the turbine, with the hi-speed if even there is friction at the wheels, they will just slides instead of spin. If that manner, regardless of the treadmill move forward, still or move backward, the plane will go forward and take off soon.

But the story will be different for a car, right?

[Guest]

I think you are right. for plane the power of movement is generated by the turbine, with the hi-speed if even there is friction at the wheels, they will just slides instead of spin. If that manner, regardless of the treadmill move forward, still or move backward, the plane will go forward and take off soon.

But the story will be different for a car, right?

Yes, A car wont move.

A car applies it's force from the engine through the wheels to the ground. If the car was applying force forwards through the ground, in this case a treadmill. And the treadmill is applying an equal force in the backwards direction. These two equal forces in opisite direction cancel each other out. Leaving the car stationary on the treadmill..

Same same will apply to a bike/skateboard/walking/trucks and any other object which applyies force through the ground.

The difference with the Aircraft is its force is applied though the air, and because of this it doen't interact (or cancel out) with the force of the treadmill..

[Guest]

Yes, A car wont move.

A car applies it's force from the engine through the wheels to the ground. If the car was applying force forwards through the ground, in this case a treadmill. And the treadmill is applying an equal force in the backwards direction. These two equal forces in opisite direction cancel each other out. Leaving the car stationary on the treadmill..

Same same will apply to a bike/skateboard/walking/trucks and any other object which applyies force through the ground.

The difference with the Aircraft is its force is applied though the air, and because of this it doen't interact (or cancel out) with the force of the treadmill..

Thats given me an idea - Dog fight Mafia .... those that cant get there plane off the treadmill loose their vote - I know its off topic, but a little humor pls

[Guest]

Yes, A car wont move.

I beg to differ.

[Guest]

I beg to differ.

it's not moving - wait there is no treadmill that's why it is stuck! good one CR

Edited September 9, 2008 by Lost in space

[Guest]

Let us assume that there is a point A a few meters infront of the plane. As the turbine is turned on, a huge volume of air is sucked in and then exhausted from the engine. What happens here is that, at point A there is a low pressure created and from the exhaust a high pressure. This will make the plane tend to move towards point A irrespective of the tredmill. The actual movement will start when the forward force overcomes the weight of the plane x 10 (mass x gravity), this is the downward force on the tredmill. As the action of sucktion and exhaust increases, at a stage, it will make the plane to move towards point A thus making air move over and under its wings. The plane will only fly when the Lift (the upward force) becomes more than the Drag (the downward force) - Bernoulli's Principle.

[Guest]

Let us assume that there is a point A a few meters infront of the plane. As the turbine is turned on, a huge volume of air is sucked in and then exhausted from the engine. What happens here is that, at point A there is a low pressure created and from the exhaust a high pressure. This will make the plane tend to move towards point A irrespective of the tredmill. The actual movement will start when the forward force overcomes the weight of the plane x 10 (mass x gravity), this is the downward force on the tredmill. As the action of sucktion and exhaust increases, at a stage, it will make the plane to move towards point A thus making air move over and under its wings. The plane will only fly when the Lift (the upward force) becomes more than the Drag (the downward force) - Bernoulli's Principle.

The speed of the treadmill = the speed of the aircraft.

If ground speed = 0

And wind speed = 0

Then lift will = 0

See ya later accelerator

[Guest]

I beg to differ.

Awesome... It still won't take off though X-P

[Guest]

Let us assume that there is a point A a few meters infront of the plane. As the turbine is turned on, a huge volume of air is sucked in and then exhausted from the engine. What happens here is that, at point A there is a low pressure created and from the exhaust a high pressure. This will make the plane tend to move towards point A irrespective of the tredmill. The actual movement will start when the forward force overcomes the weight of the plane x 10 (mass x gravity), this is the downward force on the tredmill. As the action of sucktion and exhaust increases, at a stage, it will make the plane to move towards point A thus making air move over and under its wings. The plane will only fly when the Lift (the upward force) becomes more than the Drag (the downward force) - Bernoulli's Principle.

Um... not quite.

"at point A there is a low pressure created and from the exhaust a high pressure."

The pressure in front and behind the engine are the same (both are exposed to the local atmosphere). The thrust is generated by the difference in momentum of the working fluid (air) between the inlet and outlet.

"The actual movement will start when the forward force overcomes the weight of the plane x 10 (mass x gravity), this is the downward force on the tredmill."

Like anything else, the aircraft will begin to accelerate as soon as there is a net force acting on it. The force does not have to exceed its weight.

"The plane will only fly when the Lift (the upward force) becomes more than the Drag (the downward force) - Bernoulli's Principle."

You are correct that the lift is the upward force (generated by airflow over the wings). The downward force, however, is the aircraft's weight. Drag is the force opposing the forward movement of the aircraft (hopefully mostly due to skin friction). Neither is a statement of Bernoulli's principle, which is really a statement of conservation of energy, under some special conditions.

[Guest]

I didn't read everything that was mentioned, so this might have already been covered.

The planes wheels do not propell it forward, they just roll, unless the plane is braking. So if the planes engines were not propelling it forward, and it was on a treadmill, the wheels would not rotate and the plane would drift backwards at the rate of the treadmill untill it came to the end of the treads. same as any other non-moving object that you put on a treadmill.

If the engines were propelling it and the plane was not on a treadmill, it would go forward, like usual, and the wheels would rotate relative to the speed of the thrust from the engines. Once it reaches the needed V it takes off.

Put the plane on the treadmill, regardless of any speed the treads move, the planes engine will propell it forward and the wheels will just spin faster to keep up with the moving ground under them. They do not contribute to the forward thrust, so it wont matter what happens to them. It might take a little longer to reach the needed V, but only because of an increase in friction and drag from the wheels.

[Guest]

I beg to differ.

You went trough a lot of effort to prove me wrong lol Love the post though

[Guest]

I went through the first half of this thread thinking "Of course the plane take off". Then I got it. It doesn't. All of those arguing against that, please suspend your immediate "he just doesn't get it" response and read.

There are three phases of understanding this question. 1) "It doesn't move, like a car". 2) "oh yeah, it DOES move, because the wheels are free spinning!" 3) "oh damn, it actually doesn't move". Let me elaborate.

Let's take the same experiment, but do it with a car (please bear with me). What would the answer be? The car stands still right? If that is your answer, you've betrayed what you think this question is actually saying. Most people here are saying the treadmill goes as fast as the external (not treadmill) groundspeed. If you apply this to a car, weirdly enough, the car DOES move. For, if the conveyor is moving at the GROUNDSPEED of the car (10km/h) the car can move forward by spinning its wheels at 20km/h. This makes the groundspeed of the car 10km/h, the conveyor 10km/h, and the wheels 20km/h.

But we all know that isn't the intent of the puzzle. The intent is to match the WHEELSPEED of the vehicles. This means the car, no matter how fast it goes, goes nowhere.

Now let's move to a plane. I think we can all agree there is friction in the wheels. Everyone has said "negligable" well, in this case, any non-0 value is not negligable. So, we will say the treadmill speeds up to match the wheels speed in a near-instantaneos fashion. Let's start at time 0.

Plane fires up engines, wheels begin to move, treadmill moves. Here we hit a crazy logorithmic function. As the treadmill speeds up to match the wheels motion, the wheels speed up by the same amount, so we always have WS (wheelspeed) = TMS(treadmillspeed) + PS (planespeed, which is very small, but not 0). Since the TMS must almost instantly equalize with the WS, this continues until we hit ridculously large numbers.

This is where friction comes in. Eventually, the friction (which is dependend on the wheel speed) will equal the maxiumum output of the plane. This will cause the wheels to act as a sort of anchor to the ground. Think of what would happen if you replaced the wheels with iron anchors. The plane would not move (but a lot of force would be on the connectors). Yes, it's counter intuitive, but that's what would happen.

Now, if you assumed 0 friction, it's a paradox. Essentially you're dividing by 0. You get to infinity and beyond and the world explodes. I wouldn't recommend that.

[Guest]

I went through the first half of this thread thinking "Of course the plane take off". Then I got it. It doesn't. All of those arguing against that, please suspend your immediate "he just doesn't get it" response and read.

There are three phases of understanding this question. 1) "It doesn't move, like a car". 2) "oh yeah, it DOES move, because the wheels are free spinning!" 3) "oh damn, it actually doesn't move". Let me elaborate.

Let's take the same experiment, but do it with a car (please bear with me). What would the answer be? The car stands still right? If that is your answer, you've betrayed what you think this question is actually saying. Most people here are saying the treadmill goes as fast as the external (not treadmill) groundspeed. If you apply this to a car, weirdly enough, the car DOES move. For, if the conveyor is moving at the GROUNDSPEED of the car (10km/h) the car can move forward by spinning its wheels at 20km/h. This makes the groundspeed of the car 10km/h, the conveyor 10km/h, and the wheels 20km/h.

But we all know that isn't the intent of the puzzle. The intent is to match the WHEELSPEED of the vehicles. This means the car, no matter how fast it goes, goes nowhere.

Now let's move to a plane. I think we can all agree there is friction in the wheels. Everyone has said "negligable" well, in this case, any non-0 value is not negligable. So, we will say the treadmill speeds up to match the wheels speed in a near-instantaneos fashion. Let's start at time 0.

Plane fires up engines, wheels begin to move, treadmill moves. Here we hit a crazy logorithmic function. As the treadmill speeds up to match the wheels motion, the wheels speed up by the same amount, so we always have WS (wheelspeed) = TMS(treadmillspeed) + PS (planespeed, which is very small, but not 0). Since the TMS must almost instantly equalize with the WS, this continues until we hit ridculously large numbers.

This is where friction comes in. Eventually, the friction (which is dependend on the wheel speed) will equal the maxiumum output of the plane. This will cause the wheels to act as a sort of anchor to the ground. Think of what would happen if you replaced the wheels with iron anchors. The plane would not move (but a lot of force would be on the connectors). Yes, it's counter intuitive, but that's what would happen.

Now, if you assumed 0 friction, it's a paradox. Essentially you're dividing by 0. You get to infinity and beyond and the world explodes. I wouldn't recommend that.

I think the real intent of the riddle is to imagine an identical plane on a non-treadmill runway next to the treadmill. The speed of the treadmill is set to match the speed of the non-treadmill plane as it accelerates down the runway. The two planes' engines work exactly the same way at the same time. This wording gives us the expected answer if you replace "airplane" with "car" (the treadmill car doesn't move), and still allows the treadmill plane to take off.

[Guest]

I think the real intent of the riddle is to imagine an identical plane on a non-treadmill runway next to the treadmill. The speed of the treadmill is set to match the speed of the non-treadmill plane as it accelerates down the runway. The two planes' engines work exactly the same way at the same time. This wording gives us the expected answer if you replace "airplane" with "car" (the treadmill car doesn't move), and still allows the treadmill plane to take off.

I disagree. It never said anything about matching the power output, it said matching the speed. That can mean only two things, either the speed of the plane in relation to the ground, or the speed of the wheels in relation to the ground. If it is the plane, as I showed in my car example, it makes no sense. If it is the wheels, the plane doesn't move.

Personally, I think this is what makes the puzzle interesting. If it were as simple as "the same (ground) speed as the plane", it is a simple and boring puzzle with the answer being the wheels move twice as fast as the plane.

[Guest]

You could preform an experiment.

Get a balloon, fill it with air and attach it to a hotwheels car with the end pointing backwards.

This is needed because the thrust doesnt come from the wheels.

Put it on a treadmill that is set at the lowest speed and see if it moves forward, or if so, by how much compaired to a control test done on the treadmill while its off. I know that the conditions will not even come close to the problem we're talking about, but it will give some insight.

The plane cannot take off with it moving forward, thats how lift works, if the car can move forward, then so could a plane.

[Guest]

Now let's move to a plane. I think we can all agree there is friction in the wheels. Everyone has said "negligable" well, in this case, any non-0 value is not negligable. So, we will say the treadmill speeds up to match the wheels speed in a near-instantaneos fashion. Let's start at time 0.

[etc...]

This is where friction comes in. Eventually, the friction (which is dependend on the wheel speed) will equal the maxiumum output of the plane. This will cause the wheels to act as a sort of anchor to the ground. Think of what would happen if you replaced the wheels with iron anchors. The plane would not move (but a lot of force would be on the connectors). Yes, it's counter intuitive, but that's what would happen.

--sigh--

This is for those of you who believe it is a realistic possibility to keep an aircraft, operating its engines at full throttle, motionless by way of wheel friction.

Let's take a typical aircraft engine: the PW 4000 series. These have a maximum thrust of at least 50,000 lb (up to 100,000 lb for some variants). This is one of the types of engine currently used on the Boeing 747-400. It has four of them. Since they will normally be taking off at full throttle, is reasonable to assume that they are, at the very least, producing some 200,000 lbs of thrust. Yes, that's right, I said two-hundred-thousand pounds of thrust, and likely more. For those of you who live in the metric world, that's roughly 1 MN. That's right: one mega-Newton. Which is a very large force. If you don't believe me, ask 500 sumo-wrestlers to sit on you.

Wheel friction, on the other hand, is a very small force. This is frequently demonstrated in land vehicles by astute passengers who notice that you can coast a really long way with the transmission in neutral. Aircraft are no different. If they were were, they would not need to install them with wheel-brakes and reverse thrust buckets to prevent them from crashing at the end of the runway after landing. Typical values of rolling friction coefficient for properly inflated rubber tires on concrete are as much as 0.01. The maximum takeoff weight of a 747-400 is about 800,000 lbs, so the rolling friction is probably less than 8,000 lbs, or 20 sumo-wrestlers. "At most 20" is a significantly smaller number than "at least 500". If you don't believe me, ask 480 mathematicians.

Finally, we have bearing friction. Under normal circumstances, bearing friction is negligible compared to other sources of loss. This is demonstrated by children around the world who like to spin the front tire of their bicycles and observe how long, with good bearings, it keeps going. A bearing loss, at its rated speed I estimate to be of the order of 5% of rolling friction (or 1 sumo wrestler). "At most 21" is still significantly smaller than "at least 500." Now, if I remember correctly, bearing friction increases approximately with the square of speed. So, in order for bearing friction to account for our remaining 480 sumo-wrestlers, the treadmill would have to be zipping along at 4,000 kts -- slightly more than 20 times the takeoff speed of the aircraft, and roughly 7 times the speed of sound at sea level and 68F.

Now, I'm no expert on such things, but I suspect that if you tried to roll a 747 along a treadmill at 4,000 kts, you might run into some kind of tire, or possibly bearing, problem. But yes, theoretically, if you had bearings made of magic fairy dust, tires stretched from Superman's scrotum, and a freaking huge hamster operating a hypersonic treadmill, you could keep a 747, with all engines at full power, completely motionless.

To conclude:

* in the universe in which we, and all other beings, live, the airplane takes off and soars through the sky;

* in Candy-coated Sugar bon-bon La-La land, where acid-flashbacks come alive, it is possible that the airplane is unable to take off.

[Guest]

The planes wheels do not propell it forward, they just roll, unless the plane is braking. So if the planes engines were not propelling it forward, and it was on a treadmill, the wheels would not rotate and the plane would drift backwards at the rate of the treadmill untill it came to the end of the treads. same as any other non-moving object that you put on a treadmill.

If the engines were propelling it and the plane was not on a treadmill, it would go forward, like usual, and the wheels would rotate relative to the speed of the thrust from the engines. Once it reaches the needed V it takes off.

Put the plane on the treadmill, regardless of any speed the treads move, the planes engine will propell it forward and the wheels will just spin faster to keep up with the moving ground under them. They do not contribute to the forward thrust, so it wont matter what happens to them. It might take a little longer to reach the needed V, but only because of an increase in friction and drag from the wheels.

Don't shoot the messanger (because I know nothing of aeronautics) but I submitted this query to my husband who is the Director of Engineering at an avionics company and here was his reply:

Bogus answer.

This explanation assumes that the treadmill can’t keep up with the thrust of the aircraft. If, as I presume the original puzzle stated, the treadmill is capable of unlimited speed, then the plane would never move. Think about examining it in a microcosm. The plane is sitting there. The engines turn on. The plane moves an inch. The treadmill moves it an inch backwards. How far has it moved? Zero. What is it’s speed? Zero. Without reaching the appropriate lift velocity, the plane would never take off.

Another analogy: Think of a toy boat. It has a propeller (similar to the aircraft wheels) but no motor. As the water begins to flow toward you (the treadmill), but you blow into the sail (the engines/thrust) thus resulting in the propeller spinning freely as the water moves past it (like the wheels). The force or thrust is independent of the propeller, yes. But as long as the water continues to flow as fast as you can blow, the boat will not move. If it doesn’t move, there’s no relative velocity and thus no possibility for lift (in the case of an aircraft).

The only way this could be overcome is if the thrust of the engines had a vertical component of force. (i.e. a vertical takeoff).

Another perspective: a helicopter can stay aloft because it pushes down on the air, which then pushes back with a force that equals that of gravity on the helicopter. If the rotor spins faster, it pushes down on the air harder, the air equals that force which is now greater than the weight of the aircraft and the helicopter rises. Now, throw in the treadmill. In this case it would be analogous to blowing on the helicopter from above. If you can blow down as hard as the helicopter’s rising force, it will not go anywhere.

Edited September 10, 2008 by puzzlegirl

[Guest]

--sigh--

This is for those of you who believe it is a realistic possibility to keep an aircraft, operating its engines at full throttle, motionless by way of wheel friction.

My final post on this topic- NO ONE has claimed it is a realistic possibility to keep an aircraft stationary at full throttle. HOWEVER!! And again, I dont care if it is a car, a skate board on a rope, a plane with a prop or jets or the space shuttle - the moment the vehicle moves forward - it is exceeding the speed of the tread mill!!

The entire breakdown in this argument is how we define the speed of the plane. If it is 1> In relation to the ground - ie the plane moves forward at 300 mph in relation to a fixed point on the ground. Then yes the plane takes off.

If it is 2> In relation to the speed of the treadmill - ie the plane stands still in relation to a fixed option on the ground then no, no wind no lift - It would obviously require the plane to be at less than full throttle for this to happen....

I believe the OP is clearly setting up the scenario #2 - again, because as long as the planes wheels are on the treadmill and it is moving forward - the plane is moving faster than the treadmill - therefore breaching the OP.

[Guest]

But we all know that isn't the intent of the puzzle. The intent is to match the WHEELSPEED of the vehicles. This means the car, no matter how fast it goes, goes nowhere.

No, the intent of the puzzle is just what it says:

"The tredmill matches the jet's speed EXACTLY."

"Jet" here is synonymous with "plane".

Let's stick to the puzzle as it was intended and as we were instructed to do.

I disagree. It never said anything about matching the power output, it said matching the speed. That can mean only two things, either the speed of the plane in relation to the ground, or the speed of the wheels in relation to the ground. If it is the plane, as I showed in my car example, it makes no sense. If it is the wheels, the plane doesn't move.

The treadmill can not match the speed of the wheels as I've shown in a few posts. This has nothing to do with an inability of a plane to take off with a treadmill moving, it has to do with the set-up of a paradoxical situation.

But lets get back on topic.

Bogus answer.

This explanation assumes that the treadmill can’t keep up with the thrust of the aircraft. If, as I presume the original puzzle stated, the treadmill is capable of unlimited speed, then the plane would never move. Think about examining it in a microcosm. The plane is sitting there. The engines turn on. The plane moves an inch. The treadmill moves it an inch backwards.

The treadmill moves an inch backwards, it doesn't move the plane an inch backwards. The plane moves forward an inch and because the treadmill has moved an inch in the opposite direction, the wheels spin twice as fast as it would have if the plane were on a normal runway.

Another analogy: Think of a toy boat. It has a propeller (similar to the aircraft wheels) but no motor. As the water begins to flow toward you (the treadmill), but you blow into the sail (the engines/thrust) thus resulting in the propeller spinning freely as the water moves past it (like the wheels). The force or thrust is independent of the propeller, yes. But as long as the water continues to flow as fast as you can blow, the boat will not move. If it doesn’t move, there’s no relative velocity and thus no possibility for lift (in the case of an aircraft).

Bad analogy. This is more an analogy to a car on a treadmill, not a plane. Wheels on a car move to propel it forward. Props on a boat propel water to move it forward.

the moment the vehicle moves forward - it is exceeding the speed of the tread mill!!

No, it's the treadmill's job to keep up exactly with the speed of the plane, so it can't exceed it.

The entire breakdown in this argument is how we define the speed of the plane. If it is 1> In relation to the ground - ie the plane moves forward at 300 mph in relation to a fixed point on the ground. Then yes the plane takes off.

That's not what you said earlier. You said:

"I don't care if the wheels are spinning 2000 mph, if the the treadmill is responding in kind - the forward velocity of the airplane is still net 0 mph - therefore no wind and no lift...."

and

"On myth busters, the propeller was pushing air over the wings. in a jet - that is not the case.. I am no expert in flight physics, but this seems like a no brainer - the answer is NO - it will not take off..."

Your argument was that the plane would not have taken off on MythBusters had it been a jet and it was the wind from the props that gave the plane lift and not it's forward motion. Wrong.

The entire breakdown in this argument is how we define the speed of the plane. If it is 1> In relation to the ground - ie the plane moves forward at 300 mph in relation to a fixed point on the ground. Then yes the plane takes off.

If it is 2> In relation to the speed of the treadmill - ie the plane stands still in relation to a fixed option on the ground then no, no wind no lift - It would obviously require the plane to be at less than full throttle for this to happen....

The plane moving forward and the treadmill keeping up with the speed in the opposite direction is all we need to be told. It doesn't matter if you want to look at it as in relation to the ground or the treadmill. Same thing:

In relation to the ground:

The plane goes forward at 20 MPH in relation to the ground. The treadmill goes in the opposite direction at 20 MPH in relation to the ground. The plane and treadmill are moving away from one another at 40 MPH.

In relation to the treadmill:

The plane moves forward and the treadmill moves in the opposite direction. The plane and treadmill are moving away from one another at 40 MPH. The plane is moving at 20 MPH in relation to the ground. The treadmill goes in the opposite direction at 20 MPH in relation to the ground.

Same thing.

I believe the OP is clearly setting up the scenario #2 - again, because as long as the planes wheels are on the treadmill and it is moving forward - the plane is moving faster than the treadmill - therefore breaching the OP.

No, the plane's wheels are moving faster than the treadmill; the plane is not moving faster than the treadmill. The plane moves at 20 MPH in relation to the ground and 40 MPH in relation to the treadmill. The treadmill moves at 20 MPH in relation to the ground and 40 MPH in relation to the plane. The plane's wheels are spinning 40 MPH.