Airplane on a Conveyor Belt

A riddle was proposed on the Neal Boortz show today:

If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?

Astoundingly, Neal and the rest of his crew took the position that the plane would sit there stationary! Good God… this man is a pilot and has a law degree! I could understand a random high school dropout being fooled by this, but a pilot?

Then I googled the riddle, and found a thread on that has been raging on, with the vast majority of people taking Neal’s position… that the plane would not be able to take off.

Their argument is this, to quote one poster:

Thrust acts accordingly to Newtons Third Law of Motion – every action has an equal and opposite reaction. In the case of an aircraft, the reaction of the engines is that of forward motion, against whatever medium it is stationary. But the ground the aircraft is sitting on in this case is NOT stationary, its providing an exactly CANCELLING force pushing the aircraft back.

The problem here, of course, is that the poster (and Neal) cannot disengage themselves from seeing the airplane as a car. The difference between a car and a grounded airplane is that a car uses its wheels to propel itself forward, and an airplane moves itself forward by moving air. They assume that the runway moving backwards would move the plane backwards. This is what would happen with a car (that is in gear), so why not for an airplane? Well, because an airplane’s wheels are free rolling. There is obviously some friction, so there would be some small backwards force, but it would be infinitely small as compared to the forward thrust of the airplane.

You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control.

So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object. Next, we’ll see what happens when the object is trying to move forward. Attach a string to the matchbox car. Place the car at one end of the paper, and use the string to start pulling the car forward with a steady force. As the car moves forward, start pulling the paper out from under the car, backwards. Do you feel increased resistance as you pull the string? Of course not. The wheels are free rolling! Spinning the wheels does not make the object move!

When an airplane takes off, there is one major forward force… the forward thrust. The main rearward force is air resistance. The turning of the wheels provides a small frictional force, but because the wheels are free-rolling, this friction is very small. Unless the wheels are locked, the friction is always going to be less than the thrust, which means that the overall force is still forward, and the plane will still move.

Gah… people are freakin’ stupid.

Update: There is a variation on this riddle that says that the conveyor belt matches the speed of the plane. It doesn’t matter… the plane still takes off. The conveyor belt could be going 5 times as fast as the plane, and the plane would still take off. You’d get into issues about tires blowing out, but assuming that the wheels can take the strain, the airplane would still take off.

Update: Well here we are more than two years later. The show “Mythbusters” attempted the experiment. And yes, the plane took off. The laws of physics still apply. Back to life as usual.

739 thoughts on “Airplane on a Conveyor Belt

  1. mattman2714 (subscribed)

    Yes Sttork you are 100% absolutely wrong.

    Because once the wheels are moving there is no point at whicch the aircraft will be at standstill.

    If the wheels are spinning rolloing resistance has been overcome and the aircraft is moving forward, as there is no longer any counter force to oppose the aircraft’s forward thrust.

    The only point where the conveyor belt and the wheels would be moving at the same speed would be when neither is moving. Yes that’s right when the aircraft is sitting on the runway not trying to take off. When it’s parked. And at this point it wouldn’t matter if the aircraft was on a conveyorbelt, tarmac, ice, or chocolate pudding.

    Now I will conceed that there is a brief period of time (very very brief as in less then a fraction of a second) when the aircraft will apply forward thrust and not move. This is because the force at that brief point in time is less than the rolling resistance on the wheels. This occurs in all vehicles, however, regardless of running surface and no aircraft will take off at that point. But if the question was seriously asking if an aircraft takes off at that point there would be no reason to mention a conveyor belt at all as this is just the natural delay caused by the vehicle tranferring power to it’s propulsion system from rest.

  2. mattman2714 (subscribed)

    Frankly sttork you just sound like another pathetic loser trying in vain to reword the question to make himself sound right because you can’t accept that you were incorrect in your evaluation of the question.

    If I were you I would read the posts and try to expand my understanding of things that I didn’t understand before. However if you wanna just keep posting like a whiny bitch be my guest.

  3. Harry

    Something seems to have a lot of you confused, and that is what makes an airplane capable of flight. The simple answer is lift produced by the wing and that is a function of relative wind over the wing and angle of attack (and a couple of hundred other more minor factors). Without the necessary relative wind and angle of attack the plane will not fly. That minimum wind speed (airspeed) is just a little less than the stall speed for the plane in a landing configuration due to ground effect. Gear speed has absolutely nothing to do with it.

    With that said, if you state the question so that engine thrust is only allowed to overcome the reverse speed of the conveyor, ie, the plane remains stationary with respect to the runway – it can’t fly. The wing sees no relative wind. If the engine is allowed to run normally, trust will easily overcome the reverse movement of the conveyor, airspeed (relative wind) will increase to takeoff speed and the plane will fly. The wheels will turn at airspeed plus conveyor speed and I don’t recommend doing that very often, but it will work.

    By the way – I’m a commercial pilot, CFI, CFII, MEI and Ground Instructor.

  4. stephen (subscribed)

    We get that. What has you confused is the question says nothing about the engine only overcoming the resistance of the conveyor.
    There is nothing in the question to stop the plane from moving forward unless you twist the question to make it say that.

    We get that the plane must move forward, you don’t get that the plane does move forward.

    If someone thinks that the plane moves forward the same way as the car then they will think the conveyor will stop it. But the original question has nothing to stop the plane from moving forward.

  5. sttork (subscribed)

    True – IF the belt is long enough. What bothers me, though, is that folks miss The Big Picture: the only purpose of the belt is to allow the plane to rev up at full throttle w/o initial forward movement (which is the point at which this puzzle peaks, so to speak). How about THIS thought: what if the plane was held by whatever means necessary to the ground so it could get to full throttle w/o forward movement and, at that instant, it was released AND the ground was removed (which would be even LESS friction than a treadmill). You think it would fly then? Nope. pretty much the same as the original premise as the ORIGINAL question as asked on the Boorts Show asks if it could fly AT THAT TIME…not eventually. Which is again a big NOPE.

  6. sttork (subscribed)

    To the person who says this thread started months before the Neil Boortz show – dumb statement. Why? Because the original QUESTION that started this thread REFERENCES the show as where the question was asked.

    Unless, I suppose, you heard a later rerun.

  7. stephen (subscribed)

    The purpose of the conveyor is to TRICK people into mistakenly thinking the plane does not move forward.
    Then some people would not admit to themselves they were tricked and pervert the question into one where the plane does not move forward.

    I didn’t say this THREAD started months before the show, the QUESTION started months before this show. And Boortz now says the plane moves forward and takes off.

    It is a nice simple question when the plane is allowed to move forward and turns into a stupid question if the point is the plane does not move forward.

  8. Trey

    thank god Mythbusters solved this. Basically, the prop provides thrust through the AIR. The ground means nothing. Let’s take for example hurricane force winds across the airport. If my takeoff speed in (indicated airspeed) is 70, and the wind is 70, the plane WILL take off. this will happen even if the plane is sitting still in reference to the ground. The prop is moving the plane through air not ground, and therefore, when the airspeed is sufficient to fly, it will fly.

  9. 5th Guy

    I was in an argument with the guys at work for over 3 hours regarding this theory.. and we finally came to one conclusion.. that there are 2 conclusions.

    The question is often worded leaving out 1 primary fact, if the plane itself moves or not. this is why there are litteraly thousands of comments all over the net on this.

    the question is most commonly posed
    “If you put a plane on a conveyor belt, and it matches the speed of the plane as it spins up its engine, would the plane take off?”

    sounds simple right? WRONG.
    Forget Newton, Forget aerodynamics.. forget that whole longwinded discussion…

    The question itself is the problem.. It is missing 1 simple piece of clarification, “the conveyor belt is moving to the rear the same speed as the plane MOVING forward.” thats it.. the PLANE is still moving forward, just it’s wheels are turning twice as fast and the pilot just needs to give a tick more throttle than normal because of the minor resistance on the wheels.. (as we all saw on Mythbusters)

    This became clear to me when someone said that the conveyor belt was the length of the runway.. which sounded obsurd for a plane that most thought wasnt moving.

    without that piece of info, one is to believe that the conveyor belt is moving at such a high rate of speed to produce enough friction on the wheel axels to match and push back the trust produced by the plane, therfore the plane does not move forward, and as if with its brakes on revving the engine, aint going nowhere…

    5th guy

  10. Stephen (subscribed)

    Except most of the original questions say “a plane is moving in one direction.”
    Plus there is nothing in the question to stop it from moving.

    People have to add all kinds of stuff to keep the plane from moving forward that isn’t in the question.
    Just because they can’t go “hey wait a minute I made a bad assumption.”

  11. Adam (subscribed)

    Coming back to this topic at over a year later, woohoo!

    Let’s think about the question in a different way: a real world example (wow, who’d have thunk?).

    Suppose the plane is on an aircraft carrier. Aircraft carriers have short runways, so they have to go full speed into a headwind just to launch the planes. Now let’s say, they were going full speed and the plane is attempting to take off in the opposite direction (ie, the conveyor belt is on and backwards). What happens?

    On an aircraft carrier, the plane cannot take off *because the runway is too short*. With a longer runway, it’ll still be able to take off at some point, provided that it can generate enough thrust propel the plane at the speed needed to create lift at that given wind speed.

    I think plane has to be moving backwards in order for the plane to not be able to take off. Like, if we had an infinitely long aircraft carrier that was already moving along at maximum thrust, the plane would only be able to generate enough thrust to stay in one spot while the carrier continued moving.

    The whole situation, regardless of how it is proposed, is completely preposterous. If belt speed matches plane speed, then the instant the plane moves, the wheels would blow up (Plane moving forward equals accelerating wheels equals accelerating belt ad infinitum). I’m kind of ashamed at myself for wasting so much time thinking about such a stupid hypothetical situation.

  12. T2

    Proof: put a car on some of those treadmill rollers and you had the speedometer redlining at 250mph… now try to fly a kite…

    That is the intent of the problem. The tricky thing and why in the real world the plane may take off is because the propeller blows a little air over the wings but not as much as normal.

    You don’t even need a treadmill, just two rollers per wheel and so for a front wheel drive car you only need the treadmill/rollers for the front wheels and the back wheels can be on the ground…. for a plane you don’t even need a treadmill and just use a steel cable because the wheels are free rolling and have no powertrain.

  13. Stephen (subscribed)

    Or you can simply take the problem at face value and realize that it tricks you into thinking the plane doesn’t move forward when in fact it does. And not go through all kinds of mental contortions to not admit the natural first assumption is wrong.

    The mythbusters method captures the original simple problem nicely. It’s only when you get into details like how do you measure the speed does the problem get stupid.

  14. Yes

    A plane will take off because the wheels aren’t pushing the plane forward, but the propellor.

  15. Stephen (subscribed)

    The plane moves forward. THAT is the point of the problem.

    The cable bit totally changes the problem.

  16. Aerodyne

    The plane will always fly, not matter how you word the question.
    It all comes down to the medium of operation.

    For the car the medium is the road the car sits on. It moves forward by exerting force on the road.

    For the plane it is air. It moves forward by exerting force on the air. It also flies by generating lift with the air.

    Let’s compare a plane with a takeoff speed of 40 MPH and a cruising speed of 60MPH

    As an added bonus instead of having the conveyor stationary at the beginning of the test, we will have it already running pulling the car and plane backwards at 30MPH in relation to a traffic cop on the side with a radar gun.

    They will both accelerate until the cop sees 30MPH on the radar and they both see 30MPH on their internal speed display. In this case, the car’s speedometer and the planes airspeed indicator (ASI). (for giggles we’ll also have a speedometer attached to the plane’s wheels and an ASI in the car)

    The car’s retrograde motion in relation to the ground slows until the car’s speedometer reads 30MPH but the ASi shows 0MPH. At this point it has stopped moving backwards and the cop sees 0MPH. The car applies more power and the cop finally sees 30MPH, but the car speedometer shows 60MPH with the ASI at 30MPH

    The plane applies power… It’s retrograde motion also slows until it reaches a point where the cop sees 0MPH the ASI shows 15MPH, but the speedometer reads 30MPH. BUT…since the aircraft thrust works on air, not the conveyor belt, it starts moving forward, realtive to the ground until it’s airspeed indicator reads 30MPH, the speedometer reads 60MPH, and the cop sees 30MPH
    The plane then accelerates to takeoff. At the point of takeoff(40MPH) the airspeed indicator would show 40MPH, the speedometer on the wheels would show 70MPH, and the cop would see 40MPH. …The plane would then lift gracefully off the conveyor belt, it’s wheels spinning furiously and climb out while accelerating to cruise speed.

    NOW if the stupid pilot got his gauges confused and looked at the speedometer instead of the ASI, then yes, he would not fly because when the speedo reads 40MPH, the ASI would only show 20 MPH forward motion.

    As an interesting sidenote, if we have the air moving in relation to the conveyor belt, then the cop would get to see the plane jump up into the air and hover in relation to himself. If the air then picked up a bit, he would see the plane fly backwards.

    But in the end, it’s a stupid, irrelevant question anyway.
    …Anybody who really knows anything about the theory of flight weeps, then laughs mockingly at the ignorance of anyone who says that a conveyor belt can keep an airplane from flying.

  17. Aerodyne

    As an addendum…
    If the Conveyor belt had a sensor that adjusted it’s speed to match the car or airplane, it could hold the car at 0MPH in the cop’s radar no matter how fast you drove, but all it would do is make the RPM of the planes wheels and the reading of the speedometer increase exponentially until the point where the plane tookoff and the wheels lifted off the conveyor. The plane’s ASI, however would show a normal, steady acceleration.

  18. Magnus

    This “myth” is just plain stupid. The only variable that is relevant to weather or not the plane will take off is wind speed over the wings. Neither thrust nor ground speed has anything to do with this.

  19. Stephen (subscribed)

    Magnus when you consider that there is nothing in the question that affects the wind speed over the wings then of course the plane takes off.

    hint; the conveyor has little to no effect. And to show that, people talk about thrust.

  20. Adam (subscribed)

    If belt speed always matches wheel speed exactly, then the wheels of the plane cannot move forward without breaking traction and skidding across the conveyor belt (similar to how a car’s wheels on a dyno always match the roller speed and the car does not go anywhere, even though the wheels are accelerating and decelerating). The plane might take off, but it has to break friction between the wheels and the conveyor belt. It will require more thrust than normal, since the wheels are normally free-wheeling.

    The wheels functionally turn into rubber blocks because they can never outrun the conveyor belt. Whether or not the plane takes off depends on what kind of plane it is, how much thrust it can generate, how heavy it is, etc. I realize the person who came up with this “riddle” was trying to come up with a simple test to see if people realized that air speed and not wheel speed is what makes planes fly (I’m not sure why anyone would think otherwise), but to answer the question correctly requires more thought than “duh, the plane will fly.”

  21. Stephen (subscribed)

    What is stopping the wheels of the plane from moving forward?
    As you say they are normally free wheeling.

    The person wanted to see if people would realize the plane moves forward unlike a car on a dyno. The plane is NOT like a car on a dyno. Put a JATO on that car and it will fly off the dyno. The thing is a lot of people can’t get past their first assumption that the plane does not move forward.

    How do you think a plane goes from take off speed to cruising speed without touching the ground?

  22. Charlie (subscribed)

    1. A plane on a moving conveyor belt is stationary.
    2. A stationary plane will not fly.
    3. That’s all you need to know.

  23. stephen (subscribed)

    But Charlie your number one is wrong!
    Everything after that does not matter because your number one is wrong.

    The plane moves forward.
    I ask you how do you think planes go from take off speed to cruising speed?

    They move forward on the conveyor belt the exact same way.

    Why do you think the conveyor has any effect let alone stops the plane from moving forward?

  24. Joe (subscribed)

    You are an idiot! A plane flies by generating lift… if AIR is not moving across the wings at 100 kts then the plane doesn’t have enought lift to take off. It doesn’t matter how fast the ground is moving if air isn’t moving across the wings.

    Good job, asshat.

  25. abc

    I believe some people do not completely understand the question. If the conveyor matches the speeds of the wheels, it is impossible for the plane to move forward. To move forward, the speed of the wheels has to be greater than the speed of the conveyor.

    Mythbusters did a show on this, where they dragged cloth the other way while the plane sped of the other way. The plane did manage to take off, but that’s because they weren’t matching the speed of the conveyor.

  26. DC

    Stephen is right. People are fooled in to thinking the plane will remain stationary and therefore no air will pass over the wings and therefore the plane will not take off.

    That’s not the case. The plane does take off because it does move forward and this causes the air to move over the wings.

    It doesn’t matter how fast or slow the conveyor belt moves (aside from a small amount of friction)…the plane will move forward at the same rate.

    ABC you’re missing the point. You think because the plane moved forward that the truck didn’t match the speed. Until you grasp what stephen has written you won’t get why the plane moves forward AND takes off regardless of the conveyor belt.

  27. WI_EE

    Interesting and spirited conversations going on here. Having not seen the exact wording of original question before seeing the responses its hard to say whether I would have answered the question “correctly”.

    But I agree that the plane will move forward and once its air speed is sufficient it will take off. The wheel “speed” is irrelevent and will always match the speed of the conveyor belt provided the wheel is not skidding.

    The “gotcha” is the misconception that by spinning the conveyor belt you will somehow prevent the plane from moving. You will not. No matter how fast you spin it.

    I think asking the following questions whose answers are more obvious cover the concepts wrapped up in the original question/scenerio:

    Q1: Can an airplane take off on a frictionless surface, for example ice?
    Answer: YES
    Q2: Can conveyor belts be used to reduce runway lenghts at airports?
    Answer: NO.

    Both of these point to the same concept that the wheels and wheel speed have nothing to do with creating and supporting flight.

    1. John Galt


      Q2: Can conveyor belts be used to reduce runway lenghts at airports?
      Answer: NO.

      Someone should call the navy on this one. They could save a lot of money on their carriers.

      1. James (subscribed)

        A steam catapult is very different to a conveyor belt contacting only the wheels. The catapult applies a force to the aircraft’s fuselage while the wheels spin freely as they travel along the flight deck.

        Place the aircraft on a conveyor belt with only the wheels contacting and it will plunge directly into the sea.

  28. Stephen (subscribed)

    Joe you can’t read.
    I said the plane moves forward.
    Nothing in the original question stops it from moving forward.
    The question even explicitly says it moves forward.

    ABC your second sentence is just plain wrong. Why do you think that the wheels make any difference? They don’t move the planes forward.

    If you understand the question you realize the setup would stop a car from moving forward but not a plane.

    People made a wrong assumption and can’t get past it. People like Joe and ABC

    And Joe you fell for the “IF” trap.
    For what you said to be relevent the part after the “if” must be true. It isn’t. Air is moving over the wings like normal.

  29. Scott Schroeder

    OK OK I HAVE IT 100% solved…..

    It’s clearly what the speed is relative to. if the plane is going 20mph right and the tarp 20mph left the plane won’t move, HOWEVER the planes speed is relative to the speed of the tarp… so simply said if you calculate from the starting point on the tarp the plane will be going 20mph…

    On the other hand if you calculate everything relative to the ground the plane will be going (truely) 40mph, therefore moveing 20mph compared to a point on the ground.

    So I believe the myth is true that the plane will not move in relation to the starting point on the ground.

    To explain why mythbusters found this busted… one their tarp wasn’t a great surface to pull the plane on (but in all respect what else could they have used) two they can’t have the plane 100% on the ground so the tarp wasn’t completely pulling the plane, and finally three event thought the plane and truck when 20mph in opposite dirrections if you weren’t exactly perfect with the increase of speed on both, the plane would have been skipping over parts of the tarp therefore giving them the result they had…. i 100% understand this myth and for those who say the plane is strictly 20mph from start, going right.. and the tarp is strictly 20mph from start, going left you are CORRECT… Please ask questions if you don’t understand

    the myth needs to be refined to make it more pure and therefore provable

    1. James (subscribed)

      Actually the plane is moving at 20mph relative to the stationary ground and 40mph relative to the tarp, while the tarp is moving at -20mph relative to the ground. Pretty basic physics and vector concepts really. Plug these numbers into [v_pg = v_pt + v_tg] and it all works nicely.

      Wheels spinning at 40mph are offering little resistance compared to the thrust of the plane’s propeller, so acceleration will be minimally affected. Once the plane reaches 20mph relative to the ground the wings are providing enough lift to fly. At this point the wheels are actually spinning at 40mph, despite the plane’s “true” speed of 20mph.

  30. stephen (subscribed)

    This version talks about the thrust of the plane. i.e. “exerting the thrust needed to move it forward at 100 knots,” That would be a lot
    The conveyor is going 100 knots in the other direction. That transmits very little force to the plane.
    The engines win big time.

    The earliest version I found was
    “A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

    The question is:

    Will the plane take off or not? Will it be able to run up and take off? ”

    notice the question includes “will it be able to run up”.
    That would not be part of the question and an assumption that it would not run up.

    all the “depends on what you measure relative to” argument is based on the assumption that plane stands still. But it is not a given in the question, it is the point of the question.

  31. James (subscribed)

    Think about it this way, you can spin a plane’s tyre by hand. It doesn’t take much to get it spinning. That is all the resistance the tyres are offering to the forward movement of the plane.

    The plane’s propeller, on the other hand, relies only on being surrounded by air. It doesn’t matter what the tyres are doing, that propeller will still be exerting the same forward force on the plane.

    So you can have your wheels spinning away at 800kph (500mph) on a conveyor belt and that propeller will still be exerting the same force and accelerating the plane in the same manner relative to the stationary ground (as long as the tyres and bearings can handle that speed).

    Lift one of a car’s drive tyres off the ground and see how little pedal depression it takes to have that wheel spinning at 200kph. That is how little resistance a spinning plane wheel is offering against the significant force applied by the propeller.

    The plane will take off. Jamie could have been driving that truck along at 100mph and the same result would have occurred.

  32. Jon Harris (subscribed)

    In order to solve this myth you must separate the concepts involved.

    1st concept(How does a plane achieve lift): An airplane achieves lift by moving enough air over the wings to achieve a thrust greater than the weight of the airplane.

    2nd concept(How does the plane accelerate): The airplane must accelerate with it’s engines and propell the plane forward in relation to the air, if there is no wind then the velocity of the air is, for all intents and purposes, equal to that of the ground.

    3rd concept(How does a conveyor belt affect acceleration):
    This is where the argument generally becomes confusing and is the basis for such a conflicted array of answers. There are variations to this riddle that affect the outcome so I will work through the two variations.

    Variation 1:
    The belt is moving at a fixed rate of speed that is independent of the planes movement. If this is the case the airplane will achieve a state of equilibrium with the forces acting upon it and will eventually begin moving in relation to the ground(air) and CAN take off. The wheels will begin to move at a faster pace than the belt because the belt remains at a static speed. Conclusion, the plane will take off in an ideal situation.

    Variation 2:
    The belt is moving at a speed equal to the wheels of the plane in the opposite direction. This variation gets tricky but bear with me. In an ideal situation where friction is not a factor. The plane will not take off. Here’s why; in order for the plane to move forward the wheels MUST move at a pace faster than the belt. If the belt is constantly speeding up. The force of the wheels will keep the plane from moving forward. In a less than ideal environment, the friction created by the wheels would most likely be overpowered by the engine and the the wheels would begin to skid on the belt, like pushing a car with the wheels locked up.

    The entire basis is that the wheels are indeed connected to the plane. In order for the plane to move forward with the wheels maintaining solid grip with the belt they have to move faster than the belt. The only other way to move it forward is to overcome the friction provided by the wheels and the ground.

    1. Fred Nurk (subscribed)

      Love this debate. Your argument is great.

      I really want to agree with you. I agree with 1st and 2nd concepts – yes the aircraft has to move forward relative to the ground in order to generate lift sufficient to fly.

      But, I think I can see a way to make it fly. Lets look at your variations:

      1. You agree in this case (fixed belt speed) the plane will take off, so lets go to 2
      2. Belt moving at same speed as the aircraft but opposite direction. Here’s some thoughts first:
      a. If the effect of a backward moving belt creates a frictionless (or at least very low friction) surface, then why can aircraft take off on ice? How do hovercraft move forward?
      b. If you put a car on ice with smooth plastic wheels(ie – no grip at all), would it move? No – movement relies on friction and is relative to the ground only. What about if you strapped a rocket to it? Would it move then? Yes – Rocket – like a prop – provides thrust relative to the air, not the ground.
      c. Is the belt matching the rotation speed of the wheels? or is the belt matching the forward speed of the aircraft relative to the ground? (The question seems to state the belt is matching aircraft’s forward speed to the ground).

      Let me explain why that is relevant. If the belt is matching the speed of the aircraft over the ground (or even say doubling it), the net effect is frictionless wheels – like a hovercraft. If it were a car, it would go nowhere, but like a hovercraft, aircraft use a prop for forward speed, and because the prop is pulling the aircraft forward relative to the AIR around it, the plane will still move forward, irrespective of what speed the wheels are spinning.

      Example: the aircraft moves forward 1mph. The belt moves backwards at 1mph, but then the wheel revolves at 2mph (1mph caused by the aircraft pulling it forward, and 1mph caused by the belt). Because the wheels are not driving the forward motion – the aircraft is still pulled by the prop – the wheels just turn twice their speed. Aircraft accelerates and wheels go twice their speed, but this hardly bothers the plane at all, and it takes off, wheels spinning twice the speed of takeoff. Making the wheels spin faster is NOT the same as locking the plane to the ground. Free spinning wheels (like a dynamo) would prevent a car (driven by wheels) from moving forward, but not an aircraft that is pulled by the prop. The wheels can do whatever they like (as long as they keep spinning and don’t lock up).

      Now, let me throw in what I first imagined when I read this puzzle (and said to myself it wouldn’t take off):

      Instead of the belt moving backwards at the same speed as the aircraft, rather the belt moving backwards at the same speed as the spinning wheels.

      OK. Aircraft going forward at 1mph. Belt goes backwards at 1mph. Wheels spin at 2mph. Belt then matches 2mph. Wheels then hit 3mph (1 from aircraft moving forward, 2 to counter belt). Belt then hits 3mph. As you can see, this will very quickly escalate to either wheels falling off or belt disintegrating. However, irrespective of what is happening to the belt or the wheels, the aircraft will still move forward. At 1mph aircraft forward speed the wheels might be doing 500, but that has no impact (other than marginal friction) on the prop pulling the aircraft forward.

      Here’s another example. Imagine you are standing on a treadmill wearing roller skates (I really don’t want to test this one). If there is no friction, there is no way you could move forward – right? But let’s say you had something you could pull on – like a rope. No matter how fast the treadmill goes, you can pull yourself forwards – infact, the speed of the treadmill will make almost no difference to the effort needed to pull yourself forwards. The aircraft has this piece of string – the prop – which is attached to something outside the conveyor belt (air in this case), which it can use to pull itself forward.

    2. Stephen (subscribed)

      @Jon you are wrong about your variation 2.
      The wheels on a plane are there to isolate the plane from the ground.
      On normal planes they do not move the plane forward.

      Who said anything about the tires maintaining a solid grip?

      Here is a translation of the oldest version
      “Russian to English translation
      “The aircraft (jet or screw) stands on the tarmac with a movable cover (type transporter). Dvigaetsya coating may be against the direction of take-off aircraft. It has a control system that monitors and adjusts the speed of cloth so that the wheel speed aircraft was equal to the speed blade motion. Question: Can the plane take a run on the track and take off?”

      I think the whole problem has been not the precise set up. The problem is with the question.
      The first English translation changed it to “can the plane take off”

      The stubborn “no” people later changed it to “can the plane take off without moving forward”.

      I think there would have been no major controversy if the question has always clearly been “can the plane move”.

  33. Bill

    Simple explanation…. Send them to the Mythbusters website and let them watch the results, or better yet, DO the experiment for themselves. They will see, no matter how much they argue with physics, the plane will always take off. Done deal. End of story. Bye-bye.

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