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conveyor belt plane

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I didn’t want to do it, honest, but I have really had enough of the “plane on a conveyor belt” myth, so I’m posting my take on the problem here. I’m using the kind of title that search engines will like, and I can point other people, on other forums, to this response.

The basic question goes something like this: if you could put a plane, of any size, on a conveyor belt, will it take off? The conveyor belt speeds up to match the plane’s exact speed, keeping it stationary, so it can’t move forward, right?

The question is framed badly – a bit like an “irresistible force vs. immovable object”. The first key point, which most people get, is that the engines are pushing against the air, not driving the wheels, which spin freely with a small amount of friction. This should make the answer easy, if you think in terms of Forces: the plane is trying to move forward, what would hold it back? Not friction – far too small a force. The plane moves forward, and eventually takes off, regardless of whatever the belt is doing.

Not enough? Well, what can the belt do, anyway? Another fundamental problem lies in the idea of the conveyor matching the plane’s speed. How would such a control system work?

  1. measure the plane’s speed
  2. speed up the belt to match the speed of the plane
  3. GOTO 1

Steps 1 and 2 both take time.

  1. All forms of speed measurement mechanism have an inherent time delay. If you doubt this, go back to the fundamental definition of what speed is: distance over time. This is even true of high-frequency speed measurement systems such as Doppler Radar or Lidar, as used by law enforcement.
    Another way of looking at it: if you could take a zero-time snapshot of any object at any speed, it would always appear to be standing still (velocity=0), making that useless for velocity measurement: you need time to measure the distance travelled.
  2. If the conveyor has any mass, it can not change speed instantaneously. That would require infinite acceleration of its mass, meaning an infinite force would be needed (since force = mass x acceleration). Anything less, there’s a time delay. Don’t believe me? Try putting the figures in to the basic Newtonian acceleration formula, A = ΔV / T , where A = acceleration, ΔV = the change in velocity, and T = time = 0. Oh, and before you invoke Einstein, be aware that his Relativity formulae do not contradict Newton’s at these non-relativistic velocities.
  3. With these inherent time delays in the control system: by the time the conveyor reaches its intended speed, the plane has accelerated to a new speed, so the conveyor is slower than the plane, which is thus moving forward! Repeat until V0, V1, and Vr (takeoff).

Other references:

Can I go now? 8)

Written by brian t

December 21, 2006 at 3:33 pm

Posted in aviation, internet, science

6 Responses

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  1. I have had this argument so many times with people of varying intellect and ego blockage. I am not going to be able to add anything that anybody else hasn’t already mentioned. Often times these threads fail to mention that a wheel and a treadmill always move at the same speed. There would be no “programming” required. A relationship exists between the wheel and the conveyer. Say the conveyer belt made a 1000 ft. (or just short of) runway making the belt 2000 ft. lets say your plane wheel travels 1 ft. per rotation. You have a solid unbreakable relation of 2000:1. That means no matter what the rate of the plane speed is in relationship to the ground speed, the wheels will (in this example) spin at a rate of 1 rotation of the conveyor belt to 2000 revelations of the plane wheels. If we are to believe that Newton’s third law is correct, then the conveyor belt will never actually have to move. The wheels will achieve flight 1000 ft down the runway, spinning 1000 times, with the ration remaining at .5 rotations of the conveyor belt to 1000 rotations of the wheel. The plane moved across ½ of the conveyor belt the full length of the runway. This is irrelevant to the speed in which the plane is moving across the ground. Wheels and conveyors move in terms of RPM not MPH.
    That said I have heard people try to argue that the questions was worded improperly and that it is sometimes stated that the conveyor belt matches the speed of the plane. Then the only required understanding is that once the planes thrust exceeds the friction coefficient then plan will move forward. You and your buds can prove this with a pair of roller blades, a treadmill, a water-ski rope, a fishing scale, and a 4 pack of really good Russian imperial stout. Attach the scale to the wall, the ski rope to the other end of the scale. Have your friend don the roller blades, climb on the treadmill, and power up the treadmill. The beer should be obvious. Note that only a small amount of pressure will be exerted on the fish weight scale. That will be true no matter what the setting is on the treadmill or even if he pulls himself forward.

    A plane moves through the air relative to the ground. Wheels are solely used to reduce friction at take off and increase friction upon landings.

    the_dude

    December 30, 2006 at 11:02 pm

  2. > That said I have heard people try to argue that the questions was worded improperly and that it is sometimes stated that the conveyor belt matches the speed of the plane. Then the only required understanding is that once the planes thrust exceeds the friction coefficient then plan will move forward.

    That’s the way I’ve always seen it worded. Of course the speed of the belt will match the speed of the WHEELS, but it’s always phrased as needing to keep the whole plane stationary, so that there’s no airflow over the wings and it can’t take off.

    See the videos I linked: the fact that the engines act on the air, and not on the wheels or ground (belt or not) is all you need to know. The belt’s technical inability to precisely match an object’s speed is just extra grist for the mill.

    > A plane moves through the air relative to the ground. Wheels are solely used to reduce friction at take off and increase friction upon landings.

    No. a plane, in flight (or aiming to be) moves relative to the AIR. If the air flowing over the wings provides enough lift, it can be stationary relative to the ground, or even going backwards. e.g. do we care about the ground speed of a “hurricane chaser” plane when it’s inside one? 8)

    brian t

    December 31, 2006 at 2:53 pm

  3. […] would require infinite acceleration of its mass, meaning an infinite force would be needed” (Source:conveyor belt plane) __________________ 420 Magazine Creating Cannabis Awareness Since 1993 […]

  4. Please!

    A plane with no movement relative to the air will not get lift upwards. The entire y-moment is because the wing’s shape that divides the air stream, generating turbulence under the wing, and then because of pressure difference (Bernoulli equation) an upwards force works under the wing.

    Forget the wheels, unless the movement of belt or the rotor makes enough wind to pass the wings the plane will not go up!

    Torstein

    May 21, 2009 at 9:34 pm

  5. And we were never to see the plane stationary to a camera on the side. the plane move forward! Accelerated!

    Torstein

    May 21, 2009 at 9:38 pm

  6. “A plane with no movement relative to the air will not get lift upwards.”

    So? The whole point of this piece was to explain why the plane WILL move forward: because a practical conveyor belt CANNOT hold the plane stationary. It moves, therefore it takes off. The plane’s engine is running, remember, why are you talking about the conveyor belt generating wind?

    If you ignore these practical considerations, this question becomes just a variation on “an irresistible force meeting an immovable object” i.e. a problem that has no resolution, because it describes an impossible situation.

    brian t

    May 21, 2009 at 10:20 pm


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