MHB Think about it - Airplane on a treadmill

[ineedhelpnow]

if an airplane is on a treadmill and both are at the same speed but the plane is going opposite the treadmill, so they remain at the same exact speed, will the plane take off? Apparently there are many answers to this.

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i was talking about it today and now i want to hear other inputs

 

[MarkFL]

There is only one correct answer, and it is easily found with a free body diagram. :D

 

[I like Serena]

if an airplane is on a treadmill and both are at the same speed but the plane is going opposite the treadmill, so they remain at the same exact speed, will the plane take off? Apparently there are many answers to this.

A plane needs a flow of air relative to the plane to take off.
On a treadmill in open air, there won't be any effect.
On a treadmill that brings air along (a kind of wind tunnel! :D), we can start to talk. (Nerd)

 

[Dethrone]

I guess it will take off. While the relative velocity is 0, the plane will not notice that and will take off as normal :D

 

[MarkFL]

Observe also, that unlike a car, an airplane is not wheel-driven. This I think is what confuses most people.

 

[Dethrone]

Haha, I always thought airplane had wheels. In that case, then the treadmill/conveyor belt would have no effect...(Dull)

EDIT: It uses wheels to take off, or does it not?

 

[I like Serena]

Observe also, that unlike a car, an airplane is not wheel-driven. This I think is what confuses most people.

If the airplane's propeller actually displaces air (and transfers energy), it will take off.
Otherwise it won't.
(Aka conservation of energy.)

 

[ineedhelpnow]

@Mark, people have different approaches so i think they can call maybe count so there's not necessarily only one answer

@ILS some may say "the plane is not directly related to the engine as it is in car. the plane gains its speed through the propeller. technically the wheels are only there so the plane doesn't slide against the ground or crash. don't you think if the plane gains the push it needs (assuming there's a good pilot flying the plane) it can fly. the propeller generates a wind and a force strong enough to lift the plane of the treadmill and to bring it up in the air in which there will then be enough wind that can then cause an effect on the wings."

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WHAT THE---- how did you guys have that much of a conversation already? did I really take that long to post?

 

[MarkFL]

Haha, I always thought airplane had wheels. In that case, then the treadmill/conveyor belt would have no effect...(Dull)

Airplanes have wheels, however these wheels are not driven by the engine to produce torque as they are in a car which propels it forward. :D

The plane is propelled forward by Newton's 3rd law of motion, where air is thrown backwards at great speed, resulting in the plane reacting by being propelled forward.

 

[I like Serena]

Haha, I always thought airplane had wheels. In that case, then the treadmill/conveyor belt would have no effect...(Dull)

EDIT: It uses wheels to take off, or does it not?

There is no engine accelerating the wheels (usually).
The wheels only serve to reduce the resistance of the ground while the propeller accelerates the plane.

 

[MarkFL]

@Mark, people have different approaches so i think they can call maybe count so there's not necessarily only one answer

Can they back these other answers up with science? Try the free-body diagram...you will be delighted and amazed! :D

 

[I like Serena]

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WHAT THE---- how did you guys have that much of a conversation already? did I really take that long to post?

It's about conservation of energy - not conversation. ;)
But yeah, you seem a bit slow today.
Are you feeling well? (Wondering)

 

[Dethrone]

My free-body diagram in text: (Giggle)

The forces pointing up is "lift" and "normal force". The forces downwards is the "force of gravity". Forces pointing in the direction of the airplane moving is the "thrust" and opposite that is "friction" experienced by the airplane wheels and "drag" due to air resistance. Adding the treadmill in, there's another force acting backwards? Am I missing anything (Nerd)

 

[ineedhelpnow]

It's about conservation of energy - not conversation. ;)
But yeah, you seem a bit slow today.
Are you feeling well? (Wondering)

:p haha ur hilarious dumbo ;)

 

[I like Serena]

My full-body diagram in text: (Giggle)

The forces pointing up is "lift" and "normal force". The forces downwards is the "force of gravity". Forces pointing in the direction of the airplane moving is the "thrust" and opposite that is "friction" experienced by the airplane wheels and "drag" due to air resistance. Adding the treadmill in, there's another force acting backwards? Am I missing anything (Nerd)

The normal force is only just as big as is needed to prevent the plane from falling down into the earth.
In other words, the only real force "up", is lift.
And you only have lift if you have an air flow relative to the plane. (Nerd)

 

[MarkFL]

My full-body diagram:

The forces pointing up is "lift" and "normal force". The forces downwards is the "force of gravity". Forces pointing in the direction of the airplane moving is the "thrust" and opposite that is "friction" experienced by the airplane wheels and "drag" due to air resistance. Adding the treadmill in, there's another force acting backwards? Am I missing anything (Nerd)

The additional friction introduced to the wheels caused by the treadmill attempting but failing to hold the airplane still relative to the surroundings would be negligible compared to the thrust, assuming the airplane is not only just barely able to take off under normal circumstances.

 

[ineedhelpnow]

actually now that i think about...
How is it possible for the plane to propel in the air if the there is no air acting under the wings in order to propel the plane because at the same time there is no air for the plane's engine to act against. Newton's Law of motion states that for every action there is an equal and opposite reaction. This means that for every force there is a reaction force that is equal in size, but opposite in direction. So whenever an object pushes another object it gets pushed back in the opposite direction equally hard.

so yeah i think you guys are right.

 

[Deveno]

There is no engine accelerating the wheels (usually).
The wheels only serve to reduce the resistance of the ground while the propeller accelerates the plane.

^ This.

The wheels on a airplane only serve to reduce the coefficient of friction between the airplane and the surface its on. Rolling friction < sliding friction. It wouldn't do for airplanes to heat up so violently on landing/take-off they burst into flames (although this does give me a nifty idea for a flying barbecue service).

What I think would "actually" happen, is that the plane would appear to an observer to be stationary until enough lift is generated to get it off the treadmill, at which point the observer would have their head chopped off by the propeller (or sucked into the jet turbines, resulting in a more finely distributed form of gore). I could be wrong about this, though.

 

[Dethrone]

That is what I thought first, but actually, the airplane does not appear stationary. While the wheels do spin, the airplane actually moves forward due to the propeller, because the wheels don't move the airplane forward. There's a youtube video on this.

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A good analogy: a toy car on a conveyor belt where you're pushing it forward with your hand. That external force is analogous to the propeller.

 

[Deveno]

That is what I thought first, but actually, the airplane does not appear stationary. While the wheels do spin, the airplane actually moves forward due to the propeller, because the wheels don't move the airplane forward. There's a youtube video on this.

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A good analogy: a toy car on a conveyor belt where you're pushing it forward with your hand. That external force is analogous to the propeller.

Well, it actually seems a bit more complicated: the airplane is accelerating, the treadmill is presumably moving at a constant speed. So it's initial velocity ought to be negative (for a short while), until the velocity produced by the thrust matches the speed of the treadmill. Of course, as it continues to accelerate, the velocity should over-take the treadmill, which may or may not happen before the airplane takes off.

Now, if as typical, the acceleration continues to rise (instead of being, say, constant) the airplane might start moving forward *very* quickly, so that any backwards motion due to the treadmill is imperceptible.

As I see it, we're almost mixing "apples and oranges" here, we're trying to resolve position by comparing a first derivative (the velocity of the treadmill) and a second derivative (the thrust of the engines, a force).

So a force-diagram seems to be a bit misleading, the net force is forward, but that doesn't mean the net MOVEMENT is forward (if you don't push on the toy car on the conveyor HARD enough, it will move back towards you-it's possible to push just enough to "keep it in place").

To underscore what I mean, suppose the treadmill surface is "rough" so that it takes more thrust to even get rolling (overcoming the frictive force). You would definitely see some backwards movement under those conditions. On the other hand, if the treadmill was super-smooth, and covered with a lubricating polymer, you should see forward movement almost immediately.

If the airplane was putting out enough thrust to taxi down the treadmill (when stationary) at a constant speed, I don't see how it would move at all when the treadmill was moving at that same taxi speed, until it went up. I assume the amount of thrust would be the same thrust required to balance the rolling friction horizontal component.

Of course, the stranger question is: how did this scenario come about, in the first place? What are the INITIAL conditions?

 

[mathbalarka]

^ This.

The wheels on a airplane only serve to reduce the coefficient of friction between the airplane and the surface its on. Rolling friction < sliding friction. It wouldn't do for airplanes to heat up so violently on landing/take-off they burst into flames (although this does give me a nifty idea for a flying barbecue service).

What I think would "actually" happen, is that the plane would appear to an observer to be stationary until enough lift is generated to get it off the treadmill, at which point the observer would have their head chopped off by the propeller (or sucked into the jet turbines, resulting in a more finely distributed form of gore). I could be wrong about this, though.

Perfect! You're not Randall Munroe, are you? (Wondering)

 

[Evgeny.Makarov]

This reminds me a Russian short science fiction story "http://www.oldsf.ru/zabytye-imena/vladimir-mikhanovskii/velosiped.html" by Vladimir Mikhanovskiy published in a journal for high school students interested in technology in 1983. It's a satire about the Soviet bureaucracy that made it difficult to register and develop inventions. The story takes place in the 17th century, after Galileo but before Newton. A guy invented a bicycle and took it to the patent office to register. However, the commission was highly critical of the new invention claiming that a stool on two legs cannot stand and that even horses with four legs stumble. The guy asked them to show how he rides the bicycle, and the chairman unexpectedly agreed. But instead of going outside and letting him ride, they stayed in the cabin and, using the recently discovered by Galileo principle of relativity, started walking single-file beside the guy who was trying to stay on the bicycle. Of course, after several seconds he crashed, and his invention was rejected. But before dismissing him the chairman suggested attaching a third wheel, thus giving the bicycle more stability and adding a co-author. Meanwhile, the bicycle had to be reinvented in the 18th century.