Going to settle the plane on a treadmill once and for all.

nbiggershaft · 01-22-2007, 11:41 AM

I emailed my system dynamics professor this:
(the guy has a phd in MAE and does nasa research)

Hey this is a student from your system dynamics class. I came across a physics problem that had a lot of debate online you may have heard before. I thought I would pass it along and see your take on it. It's the plane on a treadmill problem. Essentially you have a jet that is resting on a huge treadmill designed to oppose it's motion. The question is: will the plane take off?

There are two variations I've seen:
1. The treadmill moves at the same speed of the jet, relative to the ground.
2. The treadmill can be accelerated to whatever speed desired in order to stop the jet. (though there is the obvious limitation of the speed of light)

With 101 style physics it would appear the plane would take off, the engines would push the plane forward while the wheels would freely spin and you would get takeoff. A more complex view would consider non constant friction and angular acceleration of the wheels and possibly resist the motion of the plane, at least for variation #2 of the problem.

So, if I may consider you an expert of sorts, what do you think?

Hopefully he answers back

(edit: just realized my bad grammer in my email to my professor

)

ballz2wallz · 01-22-2007, 11:54 AM

Don't you need the air to pass over the wings to create the lift? If the treadmill is the only thing moving, why would the plane take off if there is no air moving over its wings? The treadmill will not make the air move...

nbiggershaft · 01-22-2007, 12:08 PM

Originally Posted by ballz2wallz

Don't you need the air to pass over the wings to create the lift? If the treadmill is the only thing moving, why would the plane take off if there is no air moving over its wings? The treadmill will not make the air move...

There is no drive train on the wheels of a plane, they are essentially free spinning. The arguement is that the plane would move forward on the thrust of it's jets.

ballz2wallz · 01-22-2007, 12:21 PM

Originally Posted by nbiggershaft

There is no drive train on the wheels of a plane, they are essentially free spinning. The arguement is that the plane would move forward on the thrust of it's jets.

Right, but the point of the jets is not to make the wheels turn, it's to make the plane go fast enough so that air can move over it's wings, creating the lift necessary to let the plane take off. The speed of which the plane move relative to its wheels or the ground is irrelevant; it's the speed at which it moves through the air.

If head-wind blowing against the plane, the speed of the plane needed to create lift is much lower than if a tail-wind were present. Amirite?

DosEquis · 01-22-2007, 12:55 PM

If you sprint really fast on a treadmill does it get windy? No. You have no forward motion. B2W is correct. No wind, no lift, no takeoff.

ballz2wallz · 01-22-2007, 01:35 PM

Originally Posted by DosEquis

If you sprint really fast on a treadmill does it get windy? No. You have no forward motion. B2W is correct. No wind, no lift, no takeoff.

Good analogy.

Although the other day I was lifting some heavy weight and I felt wind pass by my cheeks. I think the girl next to me heard me.

I have a feeling your prof might read this email and think 'uh, no wind, no takeoff'.

nbiggershaft · 01-22-2007, 03:10 PM

You guys aren't visualizing this right. Imagine you have a toy car on a treadmill. You push it with your finger(the planes jet engines) while the treadmill is running opposite to you. The wheels freely spin but the car moves forward because the force of your finger is much higher than the friction in the bearings of the toy cars wheels.

ballz2wallz · 01-22-2007, 03:17 PM

Originally Posted by nbiggershaft

You guys aren't visualizing this right. Imagine you have a toy car on a treadmill. You push it with your finger(the planes jet engines) while the treadmill is running opposite to you. The wheels freely spin but the car moves forward because the force of your finger is much higher than the friction in the bearings of the toy cars wheels.

Yes. In that case, the plane will not take off. The plane does not take off based on how fast the wheels are spinning; it takes off based on how fast air moves over its wings. If the ground is moving as the engines are pushing it, the wheels will only spin, and it will never go anywhere.

nbiggershaft · 01-22-2007, 03:37 PM

Originally Posted by ballz2wallz

Yes. In that case, the plane will not take off. The plane does not take off based on how fast the wheels are spinning; it takes off based on how fast air moves over its wings. If the ground is moving as the engines are pushing it, the wheels will only spin, and it will never go anywhere.

You still don't really get it, if I push the car, it moves relative to the air. Hence airspeed.

Lets take the reference of the ground outside the treadmill. This is the same reference as the sitting air. I can easily push the toy car so it has a forward velocity relative to this reference despite the wheels spinning very fast.

The idea is the plane is still supposed to move forward because it's jets are providing a force forward and the wheels are provided a much lesser force backwards in this outside reference frame.

There's a little man on a treadmill pulling himself forward on a rope(jet engines) who is wearing roller blades.

Now in more complicated mechanical terms friction of bearings is not a constant, it relates to angular velocity and viscosity, so the rate of the treadmill may be adjustable to a level that can oppose the motion, not sure though, thats why I am asking my prof.

ballz2wallz · 01-22-2007, 03:39 PM

Originally Posted by nbiggershaft

You still don't really get it, if I push the car, it moves relative to the air. Hence airspeed.

Only if the ground remains constant, so the friction between the tires and the still ground pushes the car through the air. If the ground moves with the tires, it has no 'air speed'.

Like dosequis said, if you run outside, you feel the wind in your face. If you run on a treadmill, you feel no wind; you have no 'air speed'.

nbiggershaft · 01-22-2007, 03:47 PM

Originally Posted by ballz2wallz

Only if the ground remains constant, so the friction between the tires and the still ground pushes the car through the air. If the ground moves with the tires, it has no 'air speed'.

Like dosequis said, if you run outside, you feel the wind in your face. If you run on a treadmill, you feel no wind; you have no 'air speed'.

The tires on a plane are NOT supposed to move a plane, they are supposed to be free spinning. Ideally, if the tires were massless the and the bearings were completely frictionless the plane could sit on the treadmill all day with it's wheels spinning and some infant could come and nudge it forward.

ballz2wallz · 01-22-2007, 03:50 PM

Originally Posted by nbiggershaft

The tires on a plane are NOT supposed to move a plane, they are supposed to be free spinning. Ideally, if the tires were massless the and the bearings were completely frictionless the plane could sit on the treadmill all day with it's wheels spinning and some infant could come and nudge it forward.

The tires provide friction between the jets and the ground, so it can gain enough 'air speed' to take off. If the ground moved as the plane moved, there would be no wind speed.

I feel as though this argument is spinning its wheels. I'm curious to see what the prof says.

nbiggershaft · 01-22-2007, 03:55 PM

Originally Posted by ballz2wallz

The tires provide friction between the jets and the ground, so it can gain enough 'air speed' to take off. If the ground moved as the plane moved, there would be no wind speed.

I feel as though this argument is spinning its wheels. I'm curious to see what the prof says.

Tires are not needed to gain speed. Take a boat that takes off from the water for example, The thrust is provided completely from the jet engines, all the surface it sits on does is oppose the motion with friction.

nbiggershaft · 01-22-2007, 04:10 PM

Plane Problem (explained by Moz) | Playing ignorant..

explains it pretty well.

ballz2wallz · 01-22-2007, 04:40 PM

Originally Posted by nbiggershaft

Tires are not needed to gain speed.

Uh, yes they are. Think the plane will gain speed if it's not moving over the ground?

all the surface it sits on does is oppose the motion with friction.

Exactly, and a treadmill doesn't provide that friction.

nbiggershaft · 01-22-2007, 04:44 PM

Originally Posted by ballz2wallz

Uh, yes they are. Think the plane will gain speed if it's not moving over the ground?

Exactly, and a treadmill doesn't provide that friction.

Yes the plain will gain speed if it is not moving over ground, that's what it does in the air. It gains speed with it's jet engines. It pushes air to move forward. Thats why planes can take off from water, ice, grass, ect. Friction doesn't move the plane forward Newton's third law does.

7960 · 01-22-2007, 04:46 PM

Originally Posted by nbiggershaft

....and the bearings were completely frictionless ....

tha'ts the problem, they're not

ballz2wallz · 01-22-2007, 04:47 PM

Originally Posted by nbiggershaft

Yes the plain will gain speed if it is not moving over ground, that's what it does in the air. It gains speed with it's jet engines. It pushes air to move forward. Thats why planes can take off from water, ice, grass, ect. Friction doesn't move the plane forward Newton's third law does.

Only after it gains enough speed to have lift! Before the wind provides lift, it needs a surface (and friction) to create the wind that creates the lift!

nbiggershaft · 01-22-2007, 04:49 PM

Originally Posted by 7960

tha'ts the problem, they're not

Right, and thats where the more complicated physics comes into play. Most likely though, the bearings will not create anything close in force to cancel the thrust of the plane.

nbiggershaft · 01-22-2007, 04:52 PM

Originally Posted by ballz2wallz

Only after it gains enough speed to have lift! Before the wind provides lift, it needs a surface (and friction) to create the wind that creates the lift!

NO IT DOESN'T. FRICTION HAS ABSOLUTELY NOTHING TO DO WITH ACCELERATING A PLANE. A car, which has a drive train attached to the wheels uses friction to accelerate, a person uses friction to accelerate. A PLANE PUSHES AIR TO ACCELERATE. It acts the same as a rocket. Push air one way, you move the other.