I don’t understand why people continue on posting erronous information. The correct answer is in post 255 with accompanying work in a pdf file. Only 19 people have downloaded this pdf file which is pretty disappointing. There is no reason for this thread to continue as it has already been answered. If you guys have any questions about the correct answer in post 255 I will be happpy to answer but I am no longer going to waste my time correcting erronous information multiple times. Read post 255 for it is the correct answer.
20 now.
I placed my answer in at post 206 or so, and have been responding to anyone who wanted clarfication of it, but I have no idea whether that answer jives with your results. From your PDF all I can tell is that you have various penish-shaped things, “Case 1” and various math that I am not sure what is trying to represent since there is no clear description of what the various penis shaped things are supposed to be doing, then “Case 2” followed by more penises and math.
The fourth page is coming up blank for me, though.
Imagine you are on the belt on roller skates. You are holding onto a rope that is attached to a winch on the wall in front of you. You are uncoupled from the bacward motion of the belt by the bearings in the skate wheels. You are coupled to the wall by the rope and winch. Will you move toward the wall when the winch pulls on the rope? Of course you will. The airplane is not coupled to the motion of the belt because of the bearings in the wheels and it is coupled to the air by the propellor or jet engine. It will take off if the wheel bearings hold out.
[QUOTE=Shagnasty]
You need to reassure me that the other people were joking or we are going to start taking away voting rights.
Airspeed is the only thing that matters to an airplane. The speed of the wheels has nothing to do with anything. You need air flowing very quickly over the wings and tail to generate lift…QUOTE] Right on. I just got through reading 7 pages of jibberish and the answer was in post #2 :smack:.
I am seeing spots now, and now fairies, strings, sub-atomic particles, faint thud.
Since this is GQ, I will try to add value [unless I missed the reference in these hundreds of posts] - try http://en.wikipedia.org/wiki/Aerodynamics
To some extent, but where it matters I am specifying turning as opposed to “physicaly moving.”
Yes. The OP requires that the speed of the outside edge of the wheel match the speed of the belt. If the wheel is turning at a rate where any point on the outside of the wheel will have turned around its perimeter a total of four miles at the end of an hour, then the conveyor belt needs to rotate at a rate where any point on the perimiter will travel 4 miles over the course of an hour.
Here’s another way I’m thinking about it, scratching some of the physics.
Assume the plane and the wheels move at the same speed - i.e. they’re attached. Asking if the plane can move forward relative to the ground is the same as asking if the wheel can move forward relative to the ground.
How can the wheel move relative to ground? It has to be moving faster - relative to the treadmill - than the treadmill - relative to the ground.
Can you do this? Sure. But then you’ve violated the condition of the question, because you’ve violated the magical property of the treadmill. Unrealistic, definitely.
This reduces the argument to:
What happens if you chain an aircraft down and apply full thrust to the engines.
The answer:
Nothing.
Well, if some people are going to interpret “the speed of the wheels” as “the forward speed of the airplane” then obviously the speed of the conveyor belt is also going in the opposite direction of the airplane.
Therefore, the conveyor belt slips out from underneath the plane like a rocket-powered banana peel, after which the plane begins to taxi forward to take off.
Now doesn’t it seem kinda silly to interpret “speed of the wheels” in that way? Nobody ever said that the conveyor belt would spin. 
I don’t understand why this question is so hard to grasp. Here’s the experiment to try:
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Put a plane on a conveyer belt. Tie a rope to the nose, with the rope attached to a strain guage. Start the conveyer.
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Measure the force that is being applied to the rope by the airplane. This force comes from the friction in the wheel bearings. If the force is less than the thrust available from the engine(s), the airplane will be able to move itself forward even though its wheels are spinning on the conveyer.
The result is going to show that the force is trivial compared to the thrust of the engines. For example, when an airplane lands, its wheels touch the pavement and start spinning immediately. Do you feel a surge of deceleration from the wheels? No. That tells you that the frictional losses in the wheels are very tiny. Likewise, when you leave the ground in an airplane, does it suddenly accelerate the moment the wheels leave the ground? Nope. Because the forces involved are so small.
Even small airplanes with low power can take off from water, and the friction of the water on the floats is orders of magnitude greater than the bearing friction from wheels turning at takeoff speed.
I suspect people are thinking that the conveyer is going to pull the airplane back at the speed of the belt. But that’s only true after a long time. If you start the conveyer immediately, the airplane will just sit there due to inertia. Eventually, the force on the plane from the bearing friction will cause it to slowly accelerate backwards. It doesn’t take much force to prevent that from happening, though. I’m guessing I could hold a medium sized airplane in place with a rope all by myself.
This is wrong. Friction between the wheel and the treadmill will accelerate the plane backwards.
The reason people like myself have indicated it would not take off has nothing whatsoever to do with physics, aerodynamics, etc.
Absolutely nothing.
Forget physics, forget friction, forget there is a plane, forget everything except for the single statement that implies no forward motion is possible under any conditions no matter what the objects are.
“The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation”
If, and that is clearly an “if” we don’t all agree on, but if you interpret “speed” to mean the linear speed of the circumference of the wheel at the point of contact with the belt (as opposed to the forward motion of the wheel, regardless of spinning or not), then mathematically the OP has created a situation where forward motion is impossible.
If you make different assumptions, you can get different correct answers.
The big assumption everybody seems to make is that the conveyor belt is firmly tacked down.
That’s what I just said. The frictiojn of the wheels causes a small force vector which *slowly accelerates the plane backwards. If you have enough thrust to overcome that force, you’ll just sit there with your wheels spinning. Add more thrust, and the plane will accelerate forwards.
The amount of thrust required to overcome wheel bearing friction in a typical airplane is trivial compared to the thrust required for flight. The conveyor belt is therefore almost irrelevant.
So what? This makes almost no difference. The way it works is that as the airplane speeds up, the speed of the conveyor belt will increase. But the airplane itself doesn’t care, other than that the force felt from bearing friction is eventually doubled at the point of takeoff over what it would be if there were no conveyer at all.
Maybe the confusion comes from thinking of the airplane like a car, with the wheels providing the driving force? In that case, the car wouldn’t move. With an airplane, this is irrelevant. The wheels are only there to keep the airplane from skidding on the ground. They have nothing to do with acceleration for flight. You can spin your conveyor 10X the forward speed of the airplane, and all that will happen is that the airplane will feel slighty more friction tugging it backwards as it accelerates. Spin the conveyor fast enough, and you’ll burn out the wheel bearings and bad stuff will happen. Until then, this whole exercise is almost meaningless to the airplane.
Right. The plane like any any object only reacts to forces upon it and the belt can only apply the force of the wheel bearing friction to the plane.
If the engine is idling and the belt start to move backwards the plane will move backwards because of bearing friction. You would need to rev the engine up just a little to overcome this friction with thrust in order to stop the plane relative to the ground and the air outside the belt.
Then if you revved up the engine more the plane would move forward. It would be the equivalent of taking off with slightly less than full throttle, some of the engine power being used to overcome wheel friction.
I’ll say it again, except for bearing friction, the treadmill is irrelevant.
It is not wheel bearing friction that would accelerate something on a treadmill it is the friction between the treadmill and the wheels. Sam you are making the same arguments that have been made pages back in this thread. They, quite simply, are wrong.
There are two possible interpetations to this problem. Case 1 is that the treadmill matches the linear forward speed of the wheel. In that case the airplane takes off but requires slightly more energy. Case 2 is that the velocity at the edge of the tire matches the velocity of the treadmill. In this case the plane goes nowhere and the tires simply spin faster and faster. To achieve this you need to accelerate the treadmill at a rate of 2*(Force from the Engines)/(Mass of tires). Note, the answer does not depend on velocity. It is soley dependant on the acceleration of the treadmill and the force from the engines.
These answers are correct and the math to prove it is linked in post 255.
And I will say it for probably the 10th time in this thread. There is a force due to friction between the wheels and the treadmill that is independent and irrelevent to wheel bearing friction.
No doubt about that. But the fucking wheels are decoupled from the fucking plane by the bearings and that force backwards on the wheels can’t be transmitted to the fucking plane.
Yes they can.
I don’t know what you mean by decoupled but the wheels can apply a force through the axel onto the rest of the plane.
Imagine that the plane has 25 foot high and 10 foot wide wheels that weigh 100 tons each. It has frictionless bearings and is sitting on a stopped belt. When the belt starts spinning, do you think the plane will just sit there in place relative to the ground? If not, do you think it would require more thrust to hold it in place than if it had normal wheels? How about if the belt got steadily faster and faster?
That should be: Yes it [the force] can [be transmitted].