Airplane and Conveyor Belt Debate

[Pavel]

Airplane on the treadmill

A friend of mine told me about this mush discussed thought experiment (http://en.wikipedia.org/wiki/Airplane_treadmill_problem ). We immediately got into a debate, but we shortly reached an agreement. I wanted to run it by somebody who understands physics and tell me if we got it right.

Our consensus is that if we make an idealized and unrealistic assumption that the treadmill will instanteneously match the speed (or more appropriately force) of the airplane, the latter will NOT take off. The key word here is "instanteneously": the time between the increased jet force and the treadmill counterforce (mediated by the friction of the wheels) is absolute ZERO! However, since this is physically impossible, the plane will always take off.

Does this sound right? The only thing that bugs me is that there's an assumption in our agreement that the counterforce produced by the accelerating treadmill will increase without bound (I presume non-linearly). If this assumption is wrong, meaning there's a limit, then the force from the thrust (unlimited for the sake of the argument) will eventually overcome the counterforce from the wheels and the plane will take off even in the platonically idealized situation. What do you think? Thanks.

Pavel

 

[Phrak]

I can't follow your argument, but the Wikipedia article got it right.

You would be better understood stating the conditions, and leaving the argument out of it.

 

[atyy]

Wikipedia links to The Straight Dope, who provides two different answers, but without equations. I had a guess for the equations that roughly corresponds to each of the different answers: https://www.physicsforums.com/showthread.php?p=1864130

 

[Pavel]

I can't follow your argument, but the Wikipedia article got it right.

You would be better understood stating the conditions, and leaving the argument out of it.

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

 

[Vid]

http://blag.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

 

[Phrak]

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

no, no, no. I'm not getting suckered into this. There are explicitly three different problems, as given by Vids, link. Which one are you talking about?

 

[rcgldr]

Our consensus is that if we make an idealized and unrealistic assumption that the treadmill will instanteneously match the speed (or more appropriately force) of the airplane, the latter will NOT take off.

The only force is the rolling resistance of the wheels. The tires would either explode or simply start sliding, if the aircraft had enough power, and the aircraft would take off.

The wheels interact independently with the ground and only provide a relatively small amount of rolling resistance. The prop interacts independently with the air which isn't signifcantly affected by the treadmill speed except for shear effects near the surface of the treadmill.

 

[Hootenanny]

Please note: All threads involving aeroplanes, treadmills, conveyor belts and whether they will take off, have been merged into this thread. All further discussion on this topic should be confined exclusively to this thread. Any additional threads created on this topic may be deleted or merged into this thread at the complete discretion of the mentors.

It is highly likely that any questions you may have related to aeroplanes and treadmills has already been answered. Therefore, please read this thread in it's entirety before posting a related question.

 

[Danger]

Jeez, Hoot... couldn't you just make this a sticky and lock it so no other idiots can contribute?

 

[cabraham]

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

Sorry but even if the treadmill CAN instantaneously match the speed of the airplane, it WILL take off. This has been experimentally proven, but I don't have the link.

Let's take it one step further. Suppose the stall speed of a given plane is 80 mph (129 kph). If the conveyor is moving backwards at 90 mph steadily while the airplane is just sitting on the conveyor, the plane is moving 90 mph backwards, or -90. The airplane engine is then started. The thrust from the engine accelerates the plane *forward*. Since its speed is originally -90 mph, its speed increases to -80, -70, -60, etc. Eventually it reaches 0 mph where it is stationary wrt an observer on the ground. It continues to accelerate to +10, +20, +30, etc. until it reaches +80 mph. At this point the wheels are spinning as if the plane was going 170 mph on the ground. But, at 80 mph the plane takes off.

The key to this problem is understanding that the conveyor moving backwards exerts very little force on the plane. The wheels have a small friction so that the backwards conveyor presents a slight drag to the forward moving plane. The engine provides a thrust which is forward in direction, but the drag backwards by the conveyor is that of wheel friction, too small to prevent takeoff. The forward engine thrust is much much greater than the backwards conveyor drag. The plane takes off. It just takes a slight bit longer to reach stall speed due to the small drag incurred. Draw a free body diagram and you will see that the conveyor motion exerts a torque on the wheel in the reverse direction. This results in a little friction in the bearing and a slight backwards drag.

Now I remember, it was "mythbusters" that shot a video showing takeoff. A search should turn it up. BR.

Claude

 

[redargon]

Now I remember, it was "mythbusters" that shot a video showing takeoff. A search should turn it up. BR.

Claude

According to me, the plane will take off as has been discussed, the wheels are not powered, etc. As much as I like mythbusters, their experiment to prove this was not very good imo. It was a little rough,and ready I mean they drag a big sheet of material behind a pickup truck and have a prop plane running in the other direction. At no point do they take wind into account, they don't keep the "treadmill" going at exactly the same speed as the plane etc etc. I love their experiments, but this one for me was a little too far fetched to be conclusive. I definitely wouldn't call it experimentally proven. Proof busted