The airplane can move forward. Forget the original question, and thing about this:Can a treadmill stop a powered aircraft from moving forward? Think of a 747 just at taxi speeds. 4 jets are pushing it forward at say 10 kts, while the treadmill is moving at the same speed in the opposite direction. Assuming the wheel brakes are off, the plane will taxi forward at 10 kts, while the treadmill will spin the wheels in the opposite direction. The wheels spin 20 kts. Now at takeoff speeds, the wheels might not handle the extra friction and may fail, which makes the original question tough. It depends on the airplane and the amount of extra spin the wheels can handle.

>I didn't see this posted already so I thought I'd go ahead>and post it.>>>http://pogue.blogs.nytimes.com/2006/12/11/...mill-conundrum/>>"Imagine a plane is sitting on a massive conveyor belt, as>wide and as 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?">>I was surprised there is so much debate on this. Unless I'm>missing something, the plane would easily take off. Airplanes>produce thrust not torque so the wheels are completely>irrelevant in this problem. It wouldn't be any different than>a plane accelerating on ice or in mid-air. >>I think people are also becoming confused because they think>the question is suggesting the plane would being to hover>while appearing stationary. The plane would consume the same>length of runway whether it was on the treadmill or concrete.>>>Is this correct?>>JohnIs it just me, or am I wrong to assume the aircraft would take off only if the propeller supplied enough airflow over the wings to create lift. No airflow is being created by the forward movement of the aircraft.Dandog

>It's obvious you have no experience in aircraft wheels and>tires as the speed of the wheels IS the limiting factor ;-) .>The wheels, bearings and landing gear will more than likely>hold up to the rotational stresses but the tire will fail>before taking off. As an example, the speed restriction on the>727 tires is 225 MPH. An avarage loaded 727-200 lift-off speed>is around 150 MPH. Assuming the treadmill is going at 150MPH>in the opposite direction, the wheel speed will be 300 MPH at>lift-off. That's 75 MPH over the tire limit giving a high>probability of failure.Sorry, but "more than likely" doesn't count :) The question only involves factors stated- there is no implication whatsoever as to the type of wheels/tires involved.It's a simple question, and only unanswerable to people who aren't able to think outside the box. I'm not implying stupid- but it's very easy to overthink this question.Does an airplane obtain thrust from wheels? No, the wheels have no bearing on the plane's ability to move forward- we can't assume any limitations because they are not stated. When dealing with automobiles, it's clear the answer could be no. But there is no aircraft type, flap setting, headwind component, or anything else given.No-one could argue that the plane would be able to move forward. Even in your scenerion the plane would reach 117 mph IAS before the tires give out. On a light plane, in a good headwind it could certainly take off.So that fully qualifies the answer- YES it is possible.This is just a trick question- the original writer was clearly wrong in his observation for the very same reason most people would be.The answer comes much more clearly even than most people realize- if the airplane is able to obtain ANY forward airspeed whatsoever, then takeoff is possible.

>Except that the question postulates that the aircraft wheels'>and the treadmill wheels' rotation have to match. Again, who cares what speed the wheels or treadmill move at? It is irrelevant to the underlying problem. When a plane is in flight, what direction are the wheels rotating? It doesn't matter. This question does not state any given components for friction, so I don't care if the wheels are moving 100,000 RPM backward. They have no effect on the airplane's thrust. The right wheel, and the left wheel can be moving at different speeds for all I care. This question is meant to be overthought.You are>absolutely right with regard to a real world treadmill though.> But you need to read the question a little more carefully. >Arguing this question is like arguing whether the chicken or>egg came first. Like that question, this one actually has no>answer. If you think that the plane should takeoff, then you>violate the requirement for the wheels to rotate at the exact>same velocity, What requirement? What exactly is the theoretical relationship between thrust and wheel rotation? RPM is irrelevant in this scenerio. Think the tires will burst at 225 mph? Just envision tires with 1/3 larger diameter. Problem solved.and if you think that the plane should not>takeoff, then you violate the fact that the airplane wheels>are free rolling and that the thrust of movement come from>engine thrust not connected to the treadmill surface. There>is no answer to this question. To argue either side means>you've been duped.There is an answer, don't over think it. Pose the same scenerio where the surface of the runway was ice. Nobody would question it then- the only factor people are taking into account is surface/mechanical friction from the tires- and since there is no specific requirement stated, then there is no way the answer could qualify as "not possible".

>>Except that the question postulates that the aircraft>wheels'>>and the treadmill wheels' rotation have to match. >>Again, who cares what speed the wheels or treadmill move at? >Because that is the fun part of the question. Yes, everybody knows that a real plane can takeoff from a real runway that is a real treadmill regardless of the underlying speed of the treadmill. That's basic. The fun begins when the question is posed with stipulations not possible in real life. That is the whole point of these kind of questions. What would hypothetically happen on a hypothetical something that can hypothetically do something completely hypothetical. When you declare "who cares" about certain stipulations made in the question and ignore them, then you've just cheesed out of having to deal with the real question.

I think Kevin is referring to this line in the question "The conveyor belt is designed to exactly match the speed of the wheels". As stated by Murmur before, the treadmill will instantly reach an infinate speed as the relationship between the wheels and the treadmill is recursive (like the reflection of a mirror in a mirror).However, the assumption is that technology is not relevant, only the theory is relevant and is applicable to these throught experiments unless specific constraints are stated. That being the case, system latency, bearing friction, lubrication, sidewall strenght, etc, are all irrelevant to answering the question. If you applied technology across the board to the question, the treadmill would self-destruct and the manufacturer's warrenty declared void!Therefore, it isn't an issue that the wheels spin at light speed. I agree, all you need to know is that the aeroplane would take-off, because there isn't anything stated to limit this.

>>>Except that the question postulates that the aircraft>>wheels'>>>and the treadmill wheels' rotation have to match. >>>>Again, who cares what speed the wheels or treadmill move at?>>>>>Because that is the fun part of the question. Yes, everybody>knows that a real plane can takeoff from a real runway that is>a real treadmill regardless of the underlying speed of the>treadmill. That's basic. The fun begins when the question is>posed with stipulations not possible in real life. That is>the whole point of these kind of questions. What would>hypothetically happen on a hypothetical something that can>hypothetically do something completely hypothetical. When you>declare "who cares" about certain stipulations made in the>question and ignore them, then you've just cheesed out of>having to deal with the real question.I didn't ignore the question, I solved it as it should be solved. You should never make assumptions- and assuming the wheels rotational speed will have a bearing on the aircraft's forward movement wrong unless the question ACTUALLY stipulates there is a relationship. It's a trick question. It's worded to make the average person (like the editor) assume an aircraft's thrust is related to it's wheels. I don't understand how you think I cheesed out of the question when I answered it exactly as it should- without assumptions. This isn't a riddle, it's a simple question.

>>I didn't ignore the question, I solved it as it should be>solved. You should never make assumptions- and assuming the>wheels rotational speed will have a bearing on the aircraft's>forward movement wrong unless the question ACTUALLY stipulates>there is a relationship. It's a trick question. It's worded>to make the average person (like the editor) assume an>aircraft's thrust is related to it's wheels. >>I don't understand how you think I cheesed out of the question>when I answered it exactly as it should- without assumptions.>This isn't a riddle, it's a simple question.You cheese out because you haven't explained how the aircraft can move forward along the treadmill when its wheel speed is the same as the treadmill's speed as STIPULATED in the question.

You are making an assumption. There is no corelation between "wheel speed" and the movement of the aircraft relative to the wind. Remember, as far as the question is concerned, friction is not a factor. So effectively, the wheel/conveyor relationship is a SEPERATE SYSTEM from the Aircraft/thrust/airflow system. In physics each system has distinct boundaries- that is avoid overcomplicating a problem, as well as to avoid outside influences. For example, when dealing with a thermodynamics system the boundaries of the system conduct no heat, so the system will have a well defined entropy- or overall temperature. If your thermos were 100% efficient your coffee would never cool down- the hotter and cooler parts would all mix together into equilibrium, and the system would remain that temperature indefinitely.So that is how you have to think of this question- with no defined relationship between wheel speed and aircraft (such as mechanical friction on the plane from the wheel spinning, or friction from the wheel pushing the landing gear strut) then you can look at the wheel/conveyor as a seperate system entirely.There is no reason for the aircraft not to move forward along the treadmill because there is nothing stopping it from moving forward.

>>This is easy->>>>The speed of the wheels is completely irrelevant.>>>>The problem arises due to rotational and mechanical friction>>from the wheels on the landing struts. Even still, an>>airplane recieves it's thrust (like stated previously) not>>from the wheels but from the the propellor. If the forward>>thrust is greater than the friction on the struts, then yes>it>>could probably take off. It is possible anyway.>>>It's obvious you have no experience in aircraft wheels and>tires as the speed of the wheels IS the limiting factor ;-) .>The wheels, bearings and landing gear will more than likely>hold up to the rotational stresses but the tire will fail>before taking off. As an example, the speed restriction on the>727 tires is 225 MPH. An avarage loaded 727-200 lift-off speed>is around 150 MPH. Assuming the treadmill is going at 150MPH>in the opposite direction, the wheel speed will be 300 MPH at>lift-off. That's 75 MPH over the tire limit giving a high>probability of failure.>>Cheers,>>John>>Boeing 727/737 & Lockheed C-130/L-100 Mechanic>http://www.sstsim.com/images/team/JR.jpg>www.SSTSIM.comIt's obvious you have no experience with small aircraft (the question does not state any aircraft type). A Piper Warrior can fly in ground effect when lightly loaded around 40 knots. The tires could easily handle 80, or even 120 knots. Problem solved. Naturally, there are aircraft that fly even slower.

>You are making an assumption. There is no corelation between>"wheel speed" and the movement of the aircraft relative to the>wind. Remember, as far as the question is concerned, friction>is not a factor. So effectively, the wheel/conveyor>relationship is a SEPERATE SYSTEM from the>Aircraft/thrust/airflow system. >>In physics each system has distinct boundaries- that is avoid>overcomplicating a problem, as well as to avoid outside>influences. For example, when dealing with a thermodynamics>system the boundaries of the system conduct no heat, so the>system will have a well defined entropy- or overall>temperature. If your thermos were 100% efficient your coffee>would never cool down- the hotter and cooler parts would all>mix together into equilibrium, and the system would remain>that temperature indefinitely.>>So that is how you have to think of this question- with no>defined relationship between wheel speed and aircraft (such as>mechanical friction on the plane from the wheel spinning, or>friction from the wheel pushing the landing gear strut) then>you can look at the wheel/conveyor as a seperate system>entirely.>>There is no reason for the aircraft not to move forward along>the treadmill because there is nothing stopping it from moving>forward.>>Not making any assumptions. Just considering all sentences in the question. The question is not whether a plane can take off from a treadmill. It is whether a plane can take off from a treadmill if...You are still conveniently ignoring certain parts of the question. The author of the question knows full well that the aircraft/thrust/airflow is separate from wheel/conveyor, which is why he added the stipulation of the recursive relationship between the treadmill and aircraft. Otherwise, the question would be simple. If the aircraft were to actually move across the treadmill, then its wheel would be moving at infinity+something while the treadmill spins at infinity. Which is disallowed in the question since they must rotate at the same speed. Of course, any question with an answer of infinity actually has no answer, since it means the answer is a big fat error. When we achieve an answer of infinity, anything can happen, the plane can takeoff, not takeoff or turn into a broccoli.

Infinity+Something...lol Reminds me of the Spinal Tap spoof documentary. Who can forget that 'infinity interview' and the amplifier that goes up to 11, not 10 :D

Why just 10 when you can have 11?

>>You are making an assumption. There is no corelation>between>>"wheel speed" and the movement of the aircraft relative to>the>>wind. Remember, as far as the question is concerned,>friction>>is not a factor. So effectively, the wheel/conveyor>>relationship is a SEPERATE SYSTEM from the>>Aircraft/thrust/airflow system. >>>>In physics each system has distinct boundaries- that is>avoid>>overcomplicating a problem, as well as to avoid outside>>influences. For example, when dealing with a thermodynamics>>system the boundaries of the system conduct no heat, so the>>system will have a well defined entropy- or overall>>temperature. If your thermos were 100% efficient your>coffee>>would never cool down- the hotter and cooler parts would>all>>mix together into equilibrium, and the system would remain>>that temperature indefinitely.>>>>So that is how you have to think of this question- with no>>defined relationship between wheel speed and aircraft (such>as>>mechanical friction on the plane from the wheel spinning, or>>friction from the wheel pushing the landing gear strut) then>>you can look at the wheel/conveyor as a seperate system>>entirely.>>>>There is no reason for the aircraft not to move forward>along>>the treadmill because there is nothing stopping it from>moving>>forward.>>>>>>Not making any assumptions. Just considering all sentences in>the question. The question is not whether a plane can take>off from a treadmill. It is whether a plane can take off from>a treadmill if...>You are still conveniently ignoring certain parts of the>question. The author of the question knows full well that the>aircraft/thrust/airflow is separate from wheel/conveyor, which>is why he added the stipulation of the recursive relationship>between the treadmill and aircraft. Otherwise, the question>would be simple. If the aircraft were to actually move across>the treadmill, then its wheel would be moving at>infinity+something while the treadmill spins at infinity. >Which is disallowed in the question since they must rotate at>the same speed. Of course, any question with an answer of>infinity actually has no answer, since it means the answer is>a big fat error. When we achieve an answer of infinity,>anything can happen, the plane can takeoff, not takeoff or>turn into a broccoli.I am ignoring nothing. I know what I'm talking about. I know it makes me look like a braggart, but the question IS simple.Motion is relative. The way people are interpreting this question, the wheel's motion relative to the airport is included.However, the treadmill has ZERO movement relative to the airport. You CANNOT have a relation between 3 different bodies that do not zero out (the airport, the treadmill, and the wheels). That's basic math.The wheels move at a rotational velocity of 40 fps relative to the treadmill. Then say they move at a velocity of 40 fps relative to the airport. That is 40 + 40 fps.The treadmill is moving opposite the wheels at 40 fps. But the treadmill is stationary- it CANNOT MOVE relative to the airport. Too many people are getting confused and assuming the the treadmill should be moving in the opposite direction of the wheels at the SUM of these numbers. Why would the treadmill need to factor in the motion of the wheels in relation to the airport?wheels 40+40=80conveyor -40 total 80-40=40 this is the wrong answer.So if you forget the speed of the wheels relative to the airport, it works.wheels 40conveyor -40total 40-40=0"The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction."Do we have that? Let's see- wheels rotation 40, conveyor opposite rotation at -40. so the question is PERFECTLY satisfied. Remember, the conveyor's movement is RELATIVE to the wheels, in the opposite direction.People are simply have difficulty accepting the fact that the question can be answered by saying the conveyour belt doesn't move (ie not turned on).That is the only way to answer it, unless you allow the wheels to skid along the conveyor belt.If not, the question becomes a simple physics question, and the answer is simply that the conveyor cannot match the speed of the wheels- it's not infinity- it's that they don't add up. It's a simple question of relationships answerable by any trig student.

Hmmm, yes I see what you mean.We have assumed that "moving in the opposite direction" means that the conveyer is moving relative to the airport, when in fact you have found a way of answering the question as it might be just as valid to say it is moving relative to the aeroplane's wheels only.However, it is quite clear to me that the question is mis-quoted and that it should be suggesting that the belt matches the speed of the aeroplane's ground speed and not the wheel speed. I think the intended interpretation of "moving in the opposite direction" is moving relative to the airport (as you put it).Nice bit of latteral thinking though!