I'm sorry I didn't include a diagram that represents the air flow that I am referring to
That's a big "if", when you can't name the force that would prevent it from moving.
If it is not moving through the air then there will be no lift. How many times must this be stated and an how many different ways, before you take that message on board. Whatever the wheels and the treadmill are doing will have no effect on the lift if the plane is not moving forward, relative to the air. There are no 'loopholes' to make your idea suddenly work.
PS the thrust from the engines that's required to keep the plane stationary relative to the Earth is very small - just enough to overcome the rolling friction of the wheels over the treadmill. Do not try to make your intuition govern your way of thinking here. Try to apply the laws of Physics, as have been stated in the other posts in this thread.
Alright, thank you
Well, ok. At this point whether the plane takes off or not and why is really up to you. You're making assumptions in order to correct the deficiencies in the problem statement. You don't necessarily need to correct all of them, I guess, so you are left with:
Q: A plane doesn't move. Does it take off?
A: No. (Obviously)
You've decided thats the answer you want and are filling in details to make it true. That's fine. These details of why (engine is at idle now apparently...) aren't important and don't necessarily need to be developed if you don't want to.
However, my personal preference is to fix it to be a more realistic and non trick question scenario, in which case the plane takes off.
[Edit] Also, I think you will find that except as a logical trick, the presence and behavior of the treadmill is irrelevant to whether the plane takes off. In your diagram, you included a force applied by the treadmill, but the treadmill isn't capable of providing that force on its own.
This is a complete non-sequitur. There can be as much thrust as you like when the plane happens to be stationary. You are totally confusing cause and effect. The thrust is not 'because of' airflow so your "therefore" is the wrong word.
You mean lift? "Thrust is conventionally taken to be the force that the engines produce. The only way you can get lift with aircraft not moving through the air is to use vectored thrust. VT has not been mentioned so far in the thread so it would be better not to move the goalposts by introducing it.
I think it's time for you to re-read this thread and to see how so many of your posts have not addressed the other comments. What do you actually want out of this exercise? You are not going to change the theory. Why not learn the theory and then you will be able to answer the questions yourself.
Going back to the original question.
The planes tires will spin twice as fast, which won't have much effect on the plane accelerating forwards due to thrust, and the plane will be able to take off, only using bit more distance to compensate for the relatively small increase in angular kinetic energy of the wheels.
The TV show myth busters did an actual demonstration, by pulling a "conveyor belt" backwards:
This is fine for your, my and Mythbusters' assumptions, but fails for the OP's assumptions, which define the plane to be at rest and include other necessary assumptions like an engine at idle.
If the aircraft has wheels there is very little or no friction between the aircraft and the conveyor belt. So the moving conveyor belt applies very little rearward force on the aircraft. This force is easily overcome by the thrust from the engine so the plane accelerates and takes of normally.
The only difference is that the wheels rotate faster.
If in doubt draw a free body diagram of the aircraft showing the force acting on it.
This again, really... all over, again... ?
To reduce this problem to its simplest terms, imagine that the velocity of the airplane and the velocity of the treadmill are equal, at zero. What happens?
The answer without all the nitpicking is no, the plane will not take off unless it is moving relative to the air it is in. If it is on a treadmill moving backwards at the same rate the plane is moving forward, it will not lift into the air.
Unless it is a Harrier jump jet., or AV8, with thrust vectoring. Or an Osprey. They can take off with thrust vectoring in still air.
That's the ambiguous condition this thread started with. Is the plane moving forward relative to the ground or relative to the treadmill?
Yeah, thread closed temporarily for Moderation...
The best way to visualize this problem is to imagine that you've taken your model airplane (with properly rotating wheels) into a grocery store, set it down on the conveyor belt, and are pushing it. Can you push it against the direction of the belt? Yes, whether the belt is moving or not. What do the wheels do when you push it against the direction of the belt? They turn. If the belt is moving while you're pushing they turn faster, but that's all.
The thrust from the engines is no different than the force of your hand pushing the toy airplane: the thrust is pushing the airplane forward relative to the air. Is there any force acting on the airplane in the opposite direction to resist the engine thrust? There is if the airplane is tethered to the treadmill or if the wheel brakes are locked so that the wheels cannot turn. In this case the airplane remains at rest relative to the treadmill and its wheels do not turn. There is if the airplane is tethered to the ground; in this case the airplane remains at rest relative to the ground while the treadmill moves and the wheels turn.
However, if the airplane is not tethered and the wheels are free to spin, then there is nothing to oppose the thrust of the engines so the plane accelerates forwards relative to the air, the ground, and the treadmill. The wheels turn faster because the airplane is moving relative to the belt, that exerts no force on the airplane.
I think we've beaten this to death. We'll keep it locked.
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