Eomer said:
Man you"re an idiot.
Show me a fucking airplane that gets it"s acceleration and speed by spinning it"s goddamn wheels, you moron.
I find this funny. The guy that"s wrong is calling the guy that"s right a moron.
The wheels don"t propel the plane. Salacious didn"t say that they do, I didn"t say that they do... What the wheels on an plane DO, in fact in the real world is prop the plane off the ground, and provide as low of a frictional impediment to acceleration as is practical.
The Wand states in his question that the conveyor not only counteracts the thrust of the plane, but even says that "However fast the plane moves, the conveyor moves just as fast." How can you interpret this to mean anything other than it"s going to keep the plane in place? TheWand didn"t say, "in the real world" or "would it be physically possible", he asked the question as it is stated in the first post, and as it was copied by me. Under the conditions he outlines he is simply saying, on an airplane that is kept from accelerating through the air (because ground speed only matters until it gains lift) will it take off.
In a normal situation, the thrust pushes the plane forward and the plane rolls on the wheels. The wheels are simply reacting to the force of the engines on the air behind the plane. It is the same as if you were standing behind the plane and pushing it. The physical mechanics are literally exactly the same. Pushing a plane with an engine or pushing it with a person, or another vehicle... all the same. As long as the external force of being pushed by another thing is related on the moving surface of the conveyor, you"ll get the same behavior.
Suppose you take the engine out of it.
Here"s this airframe sitting on a big ass conveyor and some really strong dude, like Superman is standing behind the plane (on the conveyor belt) and some other really fast guy (the flash for consistency) is adjusting the speed of this conveyor to match whatever speed the guy pushing the plane can muster. I"m not saying the belt is reacting to him pushing, I"m saying it"s counteracting his motion. In this case, the plane doesn"t take off. You can agree to that? Good.
It"s the same with the engine in the plane providing the thrust. Ground speed doesn"t "matter" except that it is a determination of how fast the plan is moving through the air (there is air around the plane and its wings), when the plane is sitting on the wheels, on the ground. It does"t matter at this point how much friction the belt produces or how much force is being applied to the wheels, it"s about whether or not the conveyor can go as fast as the jet can, in the opposite direction to the plane"s thrust. The question states that it can do that! I guess that"s what I"m asking you, Eomer, and consequentially TheWand... are you saying the question isn"t meant that way? If not, then the question needs to be changed. If you can counteract the forward motion of the plane with the conveyor, then it"s the same as if you nailed the plane in place.
(this could actually be shown IRL)
Let"s pretend we have a model plane. We attach a very fast processor computer to a laser camera and set it so that it controls the speed of a treadmill that the plane is sitting on. As the plane produces thrust, the computer adjusts the speed of the treadmill to counteract that thrust, so, in effect, the plane sits still in respect to a viewer standing on the ground; Which means there"s no airflow over the wings, which means no lift, which means no taking off. NOW let"s assume that I can provide enough thrust with my arm to make the model plane take off. I"m standing on the ground, and I have the plane in my hand. As I push the plane, the conveyor belt speeds up, and reaches its maximum speed as I"m pushing the plane faster and faster. The plane continues to accelerate with my arm, reaches its take off speed and well, takes off. The difference between these two scenarios, is that you mistakenly assume the thrust of the plane happens outside the system. It doesn"t. The directional force is being applied to the plane"s mass and the plane is on a surface that can move independantly of the surounding "ground" therefore it can counteract the force produced by the engine. When I"m pushing it while standing on the ground the force generates somewhere on my mass and is applied to the mass of the plane, consequently accelerating the plane regardless of the speed of the belt. It would be the same as if I were suspending the plane in the air with my arm.
I"m being serious about this at this point, because well... just because. If you"re just fucking around, then fine. If you don"t believe me, I"ll get force diagrams together, along with equations, with supposed values to prove out my point and post them here.