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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?John

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>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?"Yes it was already posted a while ago. :)Basically the answer is that the situation described is physically impossible. As soon as the engine imparts a minumum speed to the aircraft, the treadmill and the wheels reach infinite velocity. And any sorts of thing happen when we introduce the infinity.Marco

>>Yes it was already posted a while ago. :)>>Basically the answer is that the situation described is>physically impossible. As soon as the engine imparts a minumum>speed to the aircraft, the treadmill and the wheels reach>infinite velocity. And any sorts of thing happen when we>introduce the infinity.>>Marco>>Actually, the rotational speed of the wheels would not reach infinite velocity. The rotational value would be the sum of the treadmill speed and the aircraft forward velocity. They would however reach a terminal rotational velocity and destroy themselves before the aircraft reached takeoff speed.Cheers,JohnBoeing 727/737 & Lockheed C-130/L-100 Mechanichttp://www.sstsim.com/images/team/JR.jpgwww.SSTSIM.com

>>"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?>>JohnThe reason it generated so much debate is the sentence "The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction." Some people read this sentence to mean that there can be no forward movement of the aircraft allowed. Other people don't put any weight in that sentence and say that it will of course takeoff. On an actual real life treadmill, like one of those used by OK-Go in their video of "Here it goes again"

the second group of people are right since the speed of the treadmill is fixed. But that is not the kind of treadmill hypothetically proposed in the question, since the wheel of the airplane will have to be greater than that of the treadmill in order to achieve forward movement along the treadmill surface, which is disallowed in the question. That is why it was such a long thread. This is just another one of those impossible answer questions.

Oh God, dear God. Noooo, not again!!

Who you going to call?MYTH BUSTERS!Sounds like a good project for them.

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.

>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.Except that the question postulates that the aircraft wheels' and the treadmill wheels' rotation have to match. 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, 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.

>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,JohnBoeing 727/737 & Lockheed C-130/L-100 Mechanichttp://www.sstsim.com/images/team/JR.jpgwww.SSTSIM.com

I don't get it? I keep reading about wheel speed. Wheel sheep does provide lift.I can see a plane setting still in a stong wind take off with a proper flow of wind.So if on a thread mill turning at a proper speed only provide speed of zero, because thrust becomes irrelevant since the speed of the wheels turning reduce the effective thrust forward or backward and gravity which pulls down becomes the force of dominance.Pretty interesting.

"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?"This is so imprecise that no answer is possible without making further assumptions. What is meant by wheel speed - linear (if so relative to what?) or angular velocity? What is meant by "match" - equal to the wheel speed or equal and opposite to the speed?Don't let's waste more time on this - see the original thread

I heard this one on the Neal Boortz radio show. Boortz holds a PPL and owns a Mooney, but even he seemed to be stumped by the question. I don't get it. The conveyor can move faster than the space shuttle, but it won't get you off the ground, unless you are facing into the wind and the wind is faster than V2. You need lift under the wings to get airborne, not speed in the wheels. The answer is "no".~EwingKATLMSI K8N Neo2 PlatinumAMD Athlon 64 3200+ 2.0 GHz2GB Corsair PC-3200 512x4 Dual Channel CL2.5 DDR DIMM eVGA nVIDIA GeForce 6800 GT 256MB DDR3Sound Blaster Audigy LSOCZ Powerstream 420WWinXPPro (SP1)

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.

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