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Imagine an airplane is sitting on a conveyer belt, as wide and long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction… CAN THE PLANE TAKE OFF??
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Link to the Twitter Post: https://twitter.com/engineers_feed/status/1645313650100510720
By: Mehdi Sadaghdar

Hi There is this big Twitter account called World of Engineering that posts interesting engineering facts and questions. and they posted this thing that drove me nuts nuts. Let's read it together: Imagine a 747 is sitting on a conveyor belt as wide and 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 now? I Really want you to think about the answer? Take your time, Maybe leave a comment about it here.

Go ahead. don't let me speaking distract you. In fact, visiting my sponsor Brilliant could teach you how to deal with these physical problems. I Mean they have so many interactive courses on math Computing and science.

You can learn what you want easily. Are you done thinking? no? Then visit Brilliant.org Electro Boom to try Brilliant For free for 30 days and the first 200 of you will get 20 off Brillian's annual premium subscription. Okay, your time is up I Try to answer it myself. but the more I thought about it, the more annoyed I was.

And the replies to my answers were even more annoying. See, the question poses an imaginary situation. Reminds me of the electrical question Derek of Veritasium posted a while back that triggered a whole lot of discussions I Hate these questions with a mild passion because it's an imaginary situation. and in these situations, in order to arrive at the same answer, it must provide all the proper conditions.

but it never does. People fight about it and increase the interaction with the post, which is fine. I Guess at least in scientific cases it turns people into thinking. which is nice.

but I Hate it with a mild passion. What are the conditions? Is it happening on the moon with no air? Or the air is as thick as honey like those dreams where you can barely run away from a serial killer following you? Or maybe there are unicorns that can just lift the plane. see I Can only answer based on the conditions I pose on the question. Let's try to solve it.

Okay, let's assume we are on earth and there are no unicorns in our normal atmosphere. But what does it mean? The conveyor belt is designed to exactly match the speed of the wheels. Are we talking about the round per minute speed? because in one turn the wheel can go a couple of meters. but the conveyor belt a couple of kilometers for Simplicity.

Let's assume it means if the wheel wants to move forward at 1 meter per second, the belt would move backwards one meter per second. Now what causes the plane to fly? It must move with sufficient speed through air to create lift force on the wings. Which means that jet engines must be on pushing the plane forward. Now to simplify let's turn off the friction between the wheels and the belt.

The wheels simply slide over the belt and won't turn because there is no friction. The plane gains the speed and eventually flies Both wheels and the conveyor belt stay at zero speed. All conditions are mixed and that answers the question. Now the number of replies to my tweets saying if the wheel wants to move forward, the belt moves backward at the same speed and so the airplane is stationary is too damn.
High An airplane is not like a car that its engine. Powers The wheels to push the road to move forward. You would be right if that was the case. Like me walking on a treadmill, going nowhere.

but in an airplane, the jet engines push the air back at super high speeds creating trust and it has nothing to do with the wheels. Now, even if there was friction between the wheels and the runway, but the wheels bearings were frictionless, the plane would still take off. but there would be a problem if the plane moves forward at a speed V And so the wheels, the belt would have to move backward at the same speed re. Which means the wheels have to turn at 2v which means the belt has to go at 2v and so the wheels have to go at 3B and so on.

The belt and wheel speed would ramp up approaching infinity and beyond. Well, if the wheels bearings are frictionless, nobody cares. The plane speeds up through the air and eventually takes off. and if the wheels don't blow up going that fast, we can say the value of belt and wheel speed are equal at Infinity.

So we are still good. but now if we turn on the friction all over the place. as soon as the airplane moves forward, the same thing happens as the last case. the belt and wheel speeds would ramp up faster going towards Infinity.

But now the wheels bearings friction creates a growing Force as the wheels turn faster opposing the motion of the plane. At some high wheel speed, this force of friction becomes equal to the jet engine thrust and the plane stops moving forward. The airplane won't take off and the belt and Wheels speed match. And this satisfies the question too, although the belt would have to run at tens of thousands of kilometers for the friction to match the thrust.

We have three answers now, but I think the real answer could be super stupid. The question: States The airplane is sitting on the conveyor belt sitting as in doing nothing nowhere. It says that jet engines are on. It is like sitting on a regular.

Runway The airplane doesn't move and the belt and the Wheels speed are the same zero. The answer can be as boring as that, but now we have four answers. In two of them, the plane flies and in two of them it doesn't and we got nowhere. That's why I Hate these things with a mild passion.

One more note to add is MythBusters Did try to bust a similar myth in their case. the belt was designed to run at the same speed as the airplane in the opposite direction, not the wheels, which kind of was an obvious case. The airplane would fly with the wheel running at Double the speed of the airplane as long as it was touching the belt. Anyway, why don't you follow me on? Twitter with a mild passion and more importantly, what are you waiting for? Go, sign up for your 30 day free trial at Brilliant.org Electro Boom! My sponsor Brilliant is the best place to learn science, math and Computing through greatly interactive courses and quizzes, Brilliant is an educational platform.
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You can finish lots of courses already and if you choose to stay the first 200 of you can get 20 off Brilliance annual premium subscription. So go ahead and thank you for watching awkward.

14 thoughts on “Airplane question that drove me nuts!!!”
  1. Avataaar/Circle Created with python_avatars Ryan McCarthy says:

    U gotta be dumb if u think it would take off

  2. Avataaar/Circle Created with python_avatars Poly Morph says:

    Watching his video-which was released 5years ago- for the first time, made me wonder whether he's still alive. I am so happy that he is. Just subscribed.

  3. Avataaar/Circle Created with python_avatars CachoTognax says:

    Since the puzzle took me here's my honest answer before tackling the puzzle:

    The question is cursed: Ignoring the friction between the wheel and the plane no speed of the conveyor belt could prevent the wheels from going faster, since the plane is pushed forward and it can't push the plane back. If we have friction it'd have to be enough to push the plane back (finding a weird static equilibrium where the conveyor is pushing without moving), or I fall back to the previous case. Ready to see if I was wrong and how!

  4. Avataaar/Circle Created with python_avatars CorkBulb says:

    Yes it can take off. The thrust is coming from the engines, not the wheels. You don't need the wheels at all for the plane to take off. Don't need the ground either. If the plane was suspended off the ground somehow, it would still accelerate and reach takeoff speed. Actually, if there is a strong enough headwind, the plane could take off without moving forward at all. As long as nothing is actually pushing backwards on the plane itself, the engine trust will move the plane forwards. BTW, the Mythbusters tested this myth long ago. The conveyor did absolutely nothing to affect the takeoff of a small model plane on a treadmill. Or a full sized real lightweight plane on a giant treadmill.

  5. Avataaar/Circle Created with python_avatars Aces High Hobbies says:

    Simple answer. If the plane does not move forward, it will NOT take off. Period.

  6. Avataaar/Circle Created with python_avatars Marten says:

    Absolutely, as the mass is stationary, so it is possible, as long as the friction isn't too high.

  7. Avataaar/Circle Created with python_avatars سياسة says:

    Bro , You look like Louis from the serie "Suits"

  8. Avataaar/Circle Created with python_avatars Kurt Neumann says:

    The plane moves using air and the ground has no bearing on a planes ability to move

  9. Avataaar/Circle Created with python_avatars Jakob Rosenqvist says:

    Assuming he plane is in working order, attempts to take off and no other external factors stop it from doing so. There are 3 answers, the first one is the real world answer, and that is that the plane will take of no matter what the conveyor belt does.

    Then there are the theoretical answers, wich one we get depends on a small assumption. If we assume the conveyor belt will match the linear velocoty of the wheel then the plane will take of with the wheels spinning twice as fast.

    If we however assume the conveyor will match the wheels rotational velocity things get a bit of the wall. As soon as the plane attempts any movement forward the conveyor will accelerate to lights peed creating infinite energy and thus creating a black hole of infinite mass with a event horizon expanding outwards at the speed of light untill the whole universe is absorbed.

    So the answers are litterally either the plane takes of fine or the end of the universe.

  10. Avataaar/Circle Created with python_avatars Soham Shete says:

    because of aerodynamics.
    the wheels move but no interaction with the wind.

  11. Avataaar/Circle Created with python_avatars Protigy says:

    The plane needs the drag from the wind of the atmosphere to take off (you can check how the wings behave during takeoff), if it’s not moving there is no drag to lift off the ground

  12. Avataaar/Circle Created with python_avatars Padelos Tsoyhnikas says:


  13. Avataaar/Circle Created with python_avatars Suhrit Biswas says:

    Never will it fly…

  14. Avataaar/Circle Created with python_avatars Game-Editor2 says:

    The easiest thing would be to just ask Mr.Beast to build the world's largest conveyor belt and test all those theories in real life.

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