Stupid plane on a treadmill question

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Realms09 said:
Here's the problem. Somewhere along the way the following idea entered the picture:

"If the treadmill speed always exactly equals the wheel speed, . . .
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<SCREEEEEEEEEEEEEEEEEEECH>

You can stop right there and save a WHOLE lotta trouble. That's the detour that wastes time, energy, and brain cells.


The problem does NOT say the treadmill speed matches the WHEEL speed. The problem says the treadmill moves at the same speed as the -- get this -- AIRPLANE.


The problem also states that the airplane DOES move. Therefore, there's not a possibility that the airplane remains stationary. By definition, the airplane moves. It's not possible that the airplane moves, and the airplane does not move, both at the same time. Any line of reasoning that supports the view that the airplane does not move cannot be correct, for it contradicts the premise of the question: THE PLANE MOVES.






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SteveC said:
The plane will take off.

Picture yourself standing on a very long treadmill, wearing roller blades, hanging onto a rope that is tied to a tree at the far end of the treadmill. As the experiment begins, you are stationary, the belt is stationary, and all is well in the world. You, being the stud that you are, pull on the rope and you begin to roll forward. But hey, as you begin to move forward at the stately pace of one mile per hour, the treadmill starts running at the same speed, but in the opposite direction! The interesting thing, though, is that the roller blades that you are wearing are free wheeling, and they start to spin even faster - where they started spinning at an rpm that gives the surface of the wheel a speed of one mile per hour, now the ground moving underneath them causes the wheels to spin at two miles per hour! Amazing! Interestingly, your body is still moving forward in relation to the earth at one mile per hour, you have a one mile per hour "breeze" in your face, and your wheels are free wheeling underneath you at 2 MPH. You, feeling flush with success, begin to pull yourself forward on the rope at a faster and faster pace. Eventually you are hand-over-handing and pull yourself right off the end of the treadmill, while your wheels are spinning twice as fast as you were traveling over the ground, and the treadmill was futilely spinning in the opposite direction.

The key is in realizing that your roller blade wheels, just like an airplane's wheels, are free-wheeling. The wheels are not what drive an airplane forward, and the ground moving backwards underneath the wheels cannot stop the airplane from moving forward. Moving the ground (treadmill) underneath the plane will make the wheels spin faster and faster and faster, but they will not and cannot stop the plane from moving forward, unless you step on the brakes.


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Wow I finally get it. The other discriptions didn't make sense to me becuase I was too much in the mind set of it not working. However, this has got to be the best way to explain it (for me at least).

Now that I get it I can finally rest in peace tonight. :sarcasm:
 
I agree with Derek. I think the rollerblade scenario is the easiest way to explain the theory. The aeroplane represents you and the rollerblaes, and the thrust from the propellor represents the arm pulling on the rope attached to the tree.

Amen

I'm gonna go have a bear and watch Battle of Britain for the gazillionth time.
 
TonyC said:
<SCREEEEEEEEEEEEEEEEEEECH>

You can stop right there and save a WHOLE lotta trouble. That's the detour that wastes time, energy, and brain cells.


The problem does NOT say the treadmill speed matches the WHEEL speed. The problem says the treadmill moves at the same speed as the -- get this -- AIRPLANE.


The problem also states that the airplane DOES move. Therefore, there's not a possibility that the airplane remains stationary. By definition, the airplane moves. It's not possible that the airplane moves, and the airplane does not move, both at the same time. Any line of reasoning that supports the view that the airplane does not move cannot be correct, for it contradicts the premise of the question: THE PLANE MOVES.






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Hehe - didn't read much of my post, did you?
 
If this condition is maintained at all times, then the aircraft will never take off. That's a fact, and some stop there.

The catch is, this condition will not exist in reality.
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I began with a false premise to show how it is wrong. I explain the kinematic condition in which the aircraft is stationary, which is a perfectly fine concept, and then explain why it will never come about in the takeoff scenario. There are two possible problem definitions: either the treadmill is moving at some set speed which is controlled by a motor, or it is completely free to rotate. The first case is trivial. Therefore, I explained what happens and why in the second case using the principles of dynamics. I provided a point by point physical reasoning of why the aircraft takes off, how it moves, and how the treadmill moves in response. That's the whole of point of the question, right?
 
A proof that is based on a false premise is useless, even if it arrives at the correct conclusion.






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Beating a dead horse, but I'll add my 2 cents.

The force acting on the airplane which moves it forward is not connected to the wheels. One easy way of understanding why the airplane will indeed take off:

Visualize a small model airplane on a treadmill which does the whole "speed-matching" thing. Imagine connecting a string to the front of the model airplane and pulling the airplane towards you while the treadmill turns the wheels in the opposite direction (you're standing, of course, off the treadmill). You just pull the airplane with the string (instead of engines). Wheels might go faster, but you're pulling the string and the airplane will go. You don't even have to pull harder than normal.

Hope that was not as confusing as I think it might have been.

P&H
 
TonyC said:
<SCREEEEEEEEEEEEEEEEEEECH>

You can stop right there and save a WHOLE lotta trouble. That's the detour that wastes time, energy, and brain cells.


The problem does NOT say the treadmill speed matches the WHEEL speed. The problem says the treadmill moves at the same speed as the -- get this -- AIRPLANE.

.
Click to expand...
actually you missed the question....


as stated on the first page



A plane is standing on a runway that can move like a giant conveyor belt. The plane applys full forward power and attempts to take off. This conveyer has a control system that tracks the plane's wheel speed and tunes the speed of the conveyer to be exactly the same but in the opposite direction, similar to a treadmill. can the plane takeoff?

so........
 
Realms09 said:
The thing is, there is no means, idealized or otherwise, to implement such a control system.
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I disagree.

First off, I believe that there are two different ways to define "wheel speed", but in either case it is entirely possible to design and build a conveyor control system to run the conveyor at the exact same speed, in the opposite direction.

First off, the two ways to define wheel speed:

1. The average velocity of the wheel in relation to the stationary observer. In other words, if the plane is moving 10 miles per hour from left to right, then the wheel speed is also 10 miles per hour.

2. Rotational speed of the wheel. If the plane is moving 10 mph from left to right, the wheel speed is 186.7 RPM (revolutions per minute) in a clockwise direction.

Now, control system design:

1. This is easy. If the wheel is moving 10 mph from left to right, the conveyor simply needs to move 10 mph from right to left to match the wheel's "speed", but in the opposite direction. If the plane continues to accelerate from left to right, the conveyor will simply accelerate at the same linear rate from right to left. (Note that the wheel will *spin* at a rate exactly double that normally required based on the aircraft's speed over the ground, but the average velocity of the wheel will be exactly matched by the conveyor speed. Matched in , not negated.)

2. This one is also easy, but counterintuitive. If the wheel is rotating at 186.7 RPM clockwise (from the viewers position watching the plane travel from left to right), the conveyor simply needs to move at 10 miles per hour from left to right to exactly duplicate the wheel's rotational movement, but in the opposite direction (rotationally). The wheel will quit rotating. (The plane will still be moving at 10 MPH, but the wheel will be no longer turning.) If we look back at the original drawing in the first post you will see that this is the scenario that is depicted. The conveyor is moving in the same direction as the airplane. It is funny how few people responding in this thread noted that detail!



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Wait a minute, if the treadmill matches the WHEEL speed moving with the wheel, wouldn't the wheel speed become null and therefore the conveyor would stop? and if it goes against the rotation of the wheel, wouldn't it continually increase the speed of the wheel. I may be stating this opposite of what I am picturing in my head...
 
SteveC said:
I disagree.
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We're just using different definitions. I believe the most appropriate definition for wheel speed is rotations per minute times circumference, or frequency times radius, which is how a speedometer functions in a car. Assuming rolling without slipping, this gives the speed of the vehicle and wheel axle relative to the surface it is travelling on.

If the wheel is rotating clockwise at an angular frequency of 10 rad/s and has a radius of 1 meter, then the wheel is travelling at a speed of 10 m/s to the right relative to the surface it is on. If the converyor belt control system tries to match this speed in the opposite direction, the belt surface will start moving to the left. However, this will also cause the wheels to spin faster in the clockwise direction, increasing wheel speed to the right, and so the feedback loop goes on in an unstable fashion. Any attempt to match the wheel speed increases the wheel speed, so nothing is accomplished and the speed of the aircraft relative to the fixed ground is mostly unaffected. Based on this definition there is no succesful control system possible.

We really agree, it's just semantics :)
 
Texasspilot said:
actually you missed the question....
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Actually, you changed the question, or copied it from another forum that changed it. The question circulating around the internet states the treadmill matches the plane's speed, not the wheel speed.







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TonyC said:
Actually, you changed the question, or copied it from another forum that changed it. The question circulating around the internet states the treadmill matches the plane's speed, not the wheel speed.




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Click to expand...



noo.......my post my question.


and i guess, by definition, theres more than one circulating around the internet.
 
you guys do realize speed of relative wind creates the lift for the plane to get off the ground right?
 
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