plane on a conveyor belt?

[eskimo2]

Steve,

If the question were that the conveyor were matching the plane’s speed in the opposite direction, the conveyor would be traveling at the rate of 50 mph at take off and so would the plane. The plane would take off normally except its wheels would be rolling at twice their normal take off rpm. That consumes a tiny bit of energy that really can’t be felt by the pilot.

Conveyor matches the plane’s speed: plane will fly!

Our question, however, states that the conveyor must match the plane’s wheel’s speed.
In this case if the plane moves forward, its wheel has gone further, and therefore faster than the conveyor. The only thing that the conveyor can do about this is to speed up like mad!

Conveyor matches the plane’s wheel speed: plane will NOT fly!

Watch this 2 second movie to see the force that we arre talking about and just imagine it at a much greater rate:

AVI:
http://hallbuzz.com/movies/paper_treadmill.AVI

QuickTime
http://hallbuzz.com/movies/paper_treadmill.MOV

[Gunston]

I should have been more clear in the example of course the truck is not on or in any way affected by the conveyer, as thrust from the prop would not be. It is straight ahead on the far side of the contraption with a really long rope going back to the plane. Now tell me that the truck could not move the plane due to equal and opposite reaction of the conveyer

[Terror]

Does everyone agree that it takes energy to accelerate a wheel?  

If so, if I continually accelerate (spin faster) the wheel there will be a constant force in the the direction of acceleration.  So if I accelerate a wheel at a given rate, I can create a given force in the direction of acceleration.  If I have an unlimited rate of acceleration, I can create an unlimited amount force.  So if I accelerate the belt at a high enough rate to counter the thrust of the plane, then the plane will not move.  To keep the plane from moving, I will have to continually accelerate the belt, but the plane will not move.

So picture this:  Plane is sitting on conveyor idle.  I start to throttle up, the wheel starts to turn, the "sensor" realizes this and starts to accelerate the belt.  Now people think the belt will accelerate at the same rate as the wheel would on a normal take off, but it wont.  For the belt to equal the wheel, it will have to accelerate at an INCREDIBLE rate.  Magnitudes faster than the wheel would normally turn.  (The rate would be determined by the wheel mass and the radius of the wheel.)  For the belt to maintain "the same speed" it must literally stop the plane from moving forward down the conveyer.  Otherwise, if the plane moves forward doen the conveyor, the wheel would be turning faster than the conveyor.  And since that is not allowed by the original bounds of the question then the plane does not take off.

Real world terms:  the plane goes screaching doen the conveyer wheels smoking and takes off....  (wheel could never maintain enough friction to the conveyor to accelerated at the required rate...)

Terror

[Terror]

Darn double post   sorry

[Terror]

Originally posted by Gunston
I should have been more clear in the example of course the truck is not on or in any way affected by the conveyer, as thrust from the prop would not be. It is straight ahead on the far side of the contraption with a really long rope going back to the plane. Now tell me that the truck could not move the plane due to equal and opposite reaction of the conveyer

Doesnt matter where the "thrust" comes from.  If the original bounds of the question are maintained.  Then the plane CANNOT move.  The wheel and conveyor must maintain the same speed in opposite directions and if thats true, then the wheel cannot move down the conveyor.

Terror

[Terror]

Originally posted by SteveBailey
At this point, anyone who still thinks the plane will not fly should either take Physics 101 or maybe ground school, although if they are still convinced the plane will not fly I doubt they are teachable/ willing to learn.

It's funny cause I would say the same thing.  I was part of the "will flys" until I started understanding what the question stated.  It comes down to a simple idea.  For the plane to move forward on the conveyor, the wheel must move FASTER than the conveyor.  This is not allowed.  So essentially the simplest form of the equation is:

X = Wheel speed in distance travled
Y = Conveyor speed in distance traveled

X - Y = 0 (Conveyer equals wheel speed in the opposite direction)

So for the wheel to move down the conveyor:

X - Y != 0

So no matter WHAT you use to try to move the plane it wont move.  So for the  X - Y = 0 to balance the conveyor will accelerate at a rate to counter the extra X.  If X grows then so does Y to an infinite solution.

Terror

[2bighorn]

Originally posted by Terror
Doesnt matter where the "thrust" comes from.  If the original bounds of the question are maintained.  Then the plane CANNOT move.  The wheel and conveyor must maintain the same speed in opposite directions and if thats true, then the wheel cannot move down the conveyor.

I'm happy I do not live in your universe

[Terror]

Originally posted by 2bighorn
I'm happy I do not live in your universe

It's the universe of the question.  Alot of assumptions, perfect systems throughout.  But one overall definite.  Wheel speed and Converyor speed are equal.

Real world:  Plane takes off.  Thrust and acceleration would overcome the friction between the wheel and conveyor.  Would be a spectacular thing to observe.  Lots of smoke and probably fire....

Terror

[APDrone]

I think this has been settled as long as we stay in the terms of the original question.  It won't fly.  

Now, to promote the other questions that were inadvertantly addressed  in this thread, why don't we open up some new threads with the following questions.

1.  Can you build a device that can prevent the wheels of an airplane from acquiring a net acceleration, thus preventing sufficient airspeed to be attained for flight? What are the limitations?

1a.  While testing this device, if the airplane tires fail before the device fails, how far backwards from the device will the debris from the airplane be strewn?

1b. While testing this device, if the device fails before the wheels, how far backwards from the device will the debris from the airplane be whipped? ( envision a snapping rubber-band )

2.  Can such a device be built for older 'slow' aircraft? PT-13, for example.

3.  Is there an aircraft ( fixed wing )  that can achieve flight if all of its landing gear are locked and the runway is dry pavement?  This would be an aircraft that normally uses its landing gear for takeoffs and landings. No lubricants to be applied to the wheels, of course.. like vasaline or squirrel entrails.

That should keep y'all busy for a day or so.

[SteveBailey]

Terror, how do the wheels start turning?  What makes the wheels on the plane turn?

AP drone, feel free to answer this question as well.  

[APDrone]

Originally posted by SteveBailey
Terror, how do the wheels start turning?  What makes the wheels on the plane turn?

AP drone, feel free to answer this question as well.  

When the big blades of the propeller spin around, it makes the air go backward and pulls the plane foward.  

The wheels, whose task it is to stay under the plane and ensure that mother Terra doesn't merge with said propellers at a premature time, roll over and attempt to stay under or in front of  the center of gravity.. thus preventing the picture I posted 2 or 3 ( 4?? ) pages ago.

This, of course, is assuming the pilot isn't feeling naughty and is standing on the brake, thus preventing the wheels from fulfilling their mission and, potentially, jeapordizing the intergrity of the propeller by way of that picture I posted a few pages ago.

Now, remember the question.  Once the wheels begin to move, their motion is matched by this mystery device so the plane isn't moving anywhere in relation to any object that is not on the mystery device.

Your turn.

[SteveBailey]

so, the only way for the wheels to move is for the plane to move forward, we agree on that.

Based on what you are saying:

So the plane is now moving forward(wheels rolling), then it stops?  If it was moving forward a 1 mph and then stopped, the wheels would then slow down right?  By 1 mph?  Then the conveyer would slow down right?

[deSelys]

LOL....It will move. Because the conveyor belt is bringing energy into an 'energy tank' (the spinning wheels) which has next to zero influence upon the other energy tank feeded by the plane engines (cinetic energy= plane mass*(plane speed squared)/2).

The next to zero influence is the friction between wheels and axles. I've looked it up and friction is max when there is no relative movement. As soon as the two objects begin to 'slip' on each other, the friction lowers a bit and stays constant. The energy generated by the friction will be turned into heat. Will heat stop the plane?

You could consider the problem like this: a truck is filled with water. As soon as the truck engine tries to move it, heaters in the water tank kick in to try and stop the truck. Will it move?

[eskimo2]

Originally posted by eskimo2
Steve & deSelys,


Watch the Movie!

AVI:
http://hallbuzz.com/movies/paper_treadmill.AVI

QuickTime
http://hallbuzz.com/movies/paper_treadmill.MOV

[deSelys]

Sorry Eskimo, your demonstration is void. The items on the paper band don't have an engine pulling them in the opposite direction... You completely removed one force from the equation.