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 Airliners.net 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.

Comments

  1. Scott Schroeder says

    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

    • James says

      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.

  2. stephen says

    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.

  3. James says

    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.

  4. Jon Harris says

    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.

    • Fred Nurk says

      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.

    • Stephen says

      @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?

      BTW
      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”.

  5. Bill says

    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.

Trackbacks

  1. [...] Planet iCE Forums Author: Fresh Meat . <mymodem hotmail>    24.70.95.203 Date: 11/2/2007 5:30:06 PM Subject: RE: I’ll bet you a million dollars you dumb cu Argue this….WHAT FORCE ACTS AGAINST THE ENGINES!!!!!??? I like the Ice analogy. A plane on skates will take off. A car will spin in one place. At work I crush buildings into tiny little concrete pieces. Then we use a long uphill conveyor to stockpile the crush. Sometimes round rocks end up on the conveyor. The round rocks just roll forever at the bottom of the convayor. Sometimes the rocks come loose at the top of the conveyor, and they roll down to the bottom of the belt as if the convayor was standing still. OMG google works. First hit for conveyor airplane. Tones, read it, then admit stupidity. http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/ [...]

  2. [...] I guessed this might be a ‘classic’ type question, and googled for previous discussions.Huge number of opinions and arguments over all these threads.http://www.kottke.org/06/02/plane-conveyor-belt http://www.airliners.net/discussions/tech_ops/read.main/136068/http://forum.physorg.com/index.php?showtopic=2417&st=60http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/Having browsed that lot, I’ve decided I don’t care any more. [...]

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  4. [...] I am suprised at all the explanations of how the plane will take off and yet some will never get it…..    Brian you might as well come to the dark side and save the bashing after the show…..     The rope thing explains it purely…  The tires on the plane just keep the paint pretty.      Newtons Law of physics.   Look it up…   Now a taxi cab going up a elevator will it be closer or further from its destination when it hits the top floor….?That plane is gone…..     MORE Proof…..    http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/ [...]

  5. The internet has been abuzz for quite some time about the question of whether an airplane running on a conveyor belt can take off. There are countless websites and forums that haveattemptedto provide an answer to this question. The usual result, as with so many internet boards, is a lot of shouting and little definitive science. The world awaits expectantly, then, for tonight’s Mythbusters

  6. Airplane-Treadmill problem – Boing Boing “Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. … plane wouldn’t get off the ground even without a conveyor belt. …Airplane on a Conveyor Belt [ Tempus Fugit | TxFx.net ]The speed of the wheel is the planes speed forward + the belts speed backward. … Ok if the plane is on a conveyor belt, and that belt is spinning to match the … Being Airborne on A Conveyor Belt

  7. YouTube – Mythbusters – Plane on A Conveyor Belt – The only way for a plane to have a “treadmill effect” as you put it, is to put the plane in a wind … Conveyor belt cannot impose any forces on the plane. …Airplane on a Conveyor Belt [ Tempus Fugit | TxFx.net ]- If the treadmill matches the rotational speed of the wheels, the plane will …. Ok if the plane is on a conveyor belt, and that belt is spinning to match …