This thread is sooooo long I cant remember if I am repeating myself! but I have worked out a logical and physically "real" answer... The question says that the belt matches wheel speed, but it dosnt mention how this is achieved. So lets just decide that the belt MUST remain at the same speed as the wheels at all times by whatever means possible. Now it is possible to build a conveyor belt as big as a runway, but it would be impossible to get it to move (maybe slightly but certainly not as fast as the wheels at VERY low speed) and as soon as the belt began to move the wheels and belt would have to rapidly spin up to infinity which is physically impossible. So to get the belt to maintain wheel speed the pilot has to stop the wheels turning ie no thrust from the engines is allowed, hence wheels speed = 0 = belt speed = plane speed. Subsequently the plane dosnt move, hence no physical laws broken, rules laid out in the question followed and plane does not take off. Simple
This is way cool. Art as stated by many and by Shiggins note:- If the question asked was:- On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off? Then the plane will of course fly without breaking any of the statements constraints. You see the plane speed is linear without question here. Wheels can spin as friggin fast as the bearing friction allows, by which point it will be moving and flying period. However as Alan's question stated:- Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind. Can the plane take off? In the question asked by Alan he states that the wheel speed = conveyor speed. If (and I say if) we assume they mean the rotational speed as oppose to linear speed (Speed at tyre contact with belt, speed of wheel centre - axle respectively) then the plane can never actually move as the wheel will rotate and be turning faster than the conveyor for a split second and therefore breaking the problem constraints. Then he says opposite direction to rotation... now that really screws it up, as it suggests the conveyor move towards the same direction the plaine is intending to go (assuming rotational speed). Best advice is:- If you have been reading this problem as long as I have and causes you grief, the leave it well alone Me on the other had is enjoying the banter - keep it going
yes. i haven't contributed to the thread in about 20 pages now as it's just silly how this isn't the logical answer... as i provided in post #3 of the thread.
It's called a heavy dose of physics. As opposed to the junk science you guys count on to explain what you can't prove. Spoke to two engineers last night. Both said the same thing as me. For those who still don't agree, explain this. Since you think the plane will move forward and yet you agree that the wheels stay in place because their speed and acceleration is always matched by the treadmill going in the opposite direction, how does the plane move forward while the wheels stay in place? Do the two separate?
The guys that drive the big truck that picks up my garbage call themselves sanitation "engineers". Being an engineer in no-way guarantees common sense. I will say though, that I showed your bicycle post to my stepfather. He has been an engineer for decades and holds many patents, including aircraft component patents. His immediate response was this: "What was he thinking?" Seriously Art, what you have done with the bicycle scenario is described another conundrum that is basically a repeat of the plane conundrum. A physical impossibility, thus the scenario is invalid.
First of all, if two engineers agreed with you, they're either poor engineers, drunk after a long day at work, or you explained the question incorrectly. I would think the latter. Secondly, I think the plane will move but I do NOT think the wheels will stay in place. How could you think anyone would think that, it doesn't make any sense. The fact that you think that's what I, and others have been saying only strengthens my belief that you're not reading, and not trying to understand. Thirdly, I cannot think of junkier science than what you wrote below. This is not physics, and this is not right. You cannot say that the thrust of the engine magically causes rotational motion of the wheels. The only way that can happen is with forward motion of the bike. The only way. There is no physical connection between thrust and the wheels, unlike a normal bicycle that can make use of that device. It matters.
1. If you don't think the wheels will stay in place, how do you explain that they are moving forward on a moving treadmill that is exactly matching their speed in the opposite direction at all times? Do they jump forward when the treadmill is not looking? It just doesn't happen. They stay in place. And so does the plane that is attached to them. 2. It doesn't cause the rotation of the wheels by magic. It causes it by exerting a force on the axle, which "pushes" the wheels. Thrust is always thrust, whether it is transmitted by air (you can push paper with air, or an airplane), chain, shaft, long poles, wet noodles, whatever. It's about forces, not linkage. The type of linkage does not matter. What matters is that there is a linkage that allows the force to be transmitted. In this case, it's the engine mounts, plane body, landing gear assembly, axle, and bearings. Ultimately, it causes the wheels to rotate. You yourself said they are not powered. How else do they rotate? The treadmill is not powering them. It is merely matching their speed at all times. Which also implies it is matching their acceleration at all times. It's very simple. No drunk engineers, just some clear thinking.
1. They're FREEROLLING. 2. No. Under and external thrust, the bikes wheels will not turn unless the bike moves. Your "logic" suggests that I could take a hotwheels or any little model something with with wheels and face it against a wall. Place my finger on the top and push, and I would have wheel rotation, even though it's not moving. It's just not physically possible. It doesn't make any sense.
Force equals mass times acceleration (f=ma). From this, we can get a = f/m This means, for something with mass to experience acceleration, it will require a force to act on it. No force means zero acceleration. No mass means infinite acceleration with zero force. We have mass, and we have force (engine thrust), so we can ignore the extreme boundary cases of zero mass and zero force. OK, so we have the force or thrust acting on the plane. It tries to push it forward. It's a heavy plane. More force is required. It builds and builds. The plane trembles, the forces are really building up. If it was on a fixed stand, the stand would break...if it was on wooden blocks they would start sliding...if it was on a skis, they would start moving. Why do they give first? Because they are the weakest link and give in (shear, break, slide) due to the forces acting on them. If it's sitting on wheels, the wheels start to rotate before the plane breaks up, simply because it takes less force to rotate them than to break apart the plane's body. They are the "weakest link" and that is what acts like an outlet for the accumulating forces first. This is simply because the force acts on the entire rigid body uniformly, and the weakest link gives in to the force and experiences acceleration first. So now we understand why the wheels rotate despite the engine appearing to be "disconnected." Next, we just have to understand taht even though the wheels rotate, there is no forward motion. This is because the ground underneath the plane is moving backwards, since it is on a treadmill. If there was a difference in the forward speed of the plane and the backward speed of the treadmill, you would have relative motion of the two. But there isn't. The wheels can accelerate till the cows come home...the treadmill accelerates an equal amount in the opposite direction. The wheels go round and round, faster and faster, but the treadmill also goes round and round, faster and faster, in the opposite direction. It matches the speed of the wheels at all times. It goes no faster and no slower. Just the same. At all times. So the wheels spin, but don't go forward on the treadmill. Neither does the landing gear that they are attached to. Neither does the plane that is held up by the landing gear. If the plane doesn't move, it does not get air flowing past its wings. No air, no lift. No lift, no take off. It sits there, spinning its wheels faster and faster till the engine runs out of fuel and stops providing thrust.
1. So what if they are freerolling. Whatever the speed is that they roll at, the treadmill matches their speed in the opposite direction. How can they move forward? If they don't move forward, how does the plane? Does it separate from them? Is it by magic? Come on! 2. No, you are pushing the wall wiht your finger when you do this. The toy car is merely stuck in between, acting as a conduit for the forces. If it's a weak plastic toy, it will give before the wall though, and you will have a broken car. That's because the force of your finger was enough to overcome the rigidity of the car before the wall gave in. The wall exerts an equal and opposite force on the car and your finger. The weakest link gives in first, always. If it's a strong metal car, your skin will split and you will start bleeding, then, if you keep pushing, your finger bones will break. The bigger bones in your hand would be next, but hopefully you will learn your lesson about the weakest link and stop before this happens. There is no resulting component force vector that is going into the toy car's axle from one side. It's experiencing two equal and opposite forces, you pushing from behind adn the wall pushing back from the front. Is it possible to rotate a wheel by pushing it with two equal forces acting in opposite directions? Of course not! You rotate a wheel by exerting a force from one direction. To do this you need to push the axle from direction only. When the engine on the plane powers up, it creates thrust. The thrust forces push on the axle from one side. There is no opposing force on the other side of the axle. It tries to move forwards, exerts a force on the bearings, and the bearings in turn transmit the force to the wheel. The wheel turns because it is attached by a point about which it can pivot (and keep pivoting, hence the circular motion). So the wheel rotates. The airplane engine's thrust force acts on the axle from one direction only, from behind. If there was a wall in front of the airplane, touching its nose, then that would have to be over come before the wheels rotated. Either the wall would give, or the nose of the airplane. Try pushing on the back of a matchbox car without anything in front of it. Do the wheels rotate? How can that be? Now put it on a treadmill and push against it just enough to hold it in place. Do the wheels rotate? Now speed up the treadmill and push the car harder. Do the wheels rotate faster? Does it still sit there? How can that be?
The entire system "gives". The wheels, blocks, skiis, etc. are the means to the systems movement. The whole thing moves, the wheels rotation is the by product of the systems forward motion. They do not experience acceleration first, it happens all simultaneously. There rotational acceleration is caused by the axles longitudinal accleration which is caused by, and is the same as, the entire systems longitudinal accleration. The wheels will not rotate unless the airplane has a forward motion. You can't possibly think they can. Furthermore, the conveyer will not move unless the airplane has a forward motion. If the airplane has a forward motion, and the conveyer matches it in the opposite direction, the wheels will simply spin twice as fast. I defy you to show me how freerolling wheels can rotate without moving, as you suggest.
Which came first, the chicken or the egg? Which moves first, the wheel or the treadmill? In your scenario they would begin movement SIMULTANEOUSLY. They can't, because the wheels are not driving the treadmill (as in a car dyno). I channelled Isaac Newton and he said this: "Art is a man of convicition, thus I must admire him for that if nothing else. However, his convictions have clouded his logic. Or perhaps God has not endowed him with the logic necessary in this particular instance. Not that it makes him a bad man, for we all suffer our weaknesses. I must say, however, that even the ancient Egyptians, those who did not even possess the wheel! They would even understand that you can not accelerate the wheel of the plane (what is a plane, by the way?) without the plane acutally moving forward! Art doth protest the forward motion of the plane though. A preposterous thought, I swear on my chair at Cambridge."
They can do this on any surface moving in the opposite direction. Put on some rollerblades and go stand on a treadmill. You will not move forward. But the wheels will rotate. I defy you to show my how any wheel can move forward on a treadmill that is exactly matching its speed at all times and moving in the opposite direction
Art, you are saying that even though the wheels are not directly driven by the plane, and that the treadmill is NOT driving the wheels, the wheels will accelerate in rotation as the plane sits still when engine thrust is applied. THEREFORE: Given your understanding: If a crane attached to a hook at the top of the plane gently lifts the plane off the treadmill one inch, as soon as you applied thrust with the engines the wheels would begin rotating, yet the plane would not move forward!
This is a given condition in the question. Simple as that. I am sure it is technically feasible to build such a treadmill. It might cost more than a billion dollars, but it is possible. You just have to look at how quickly the segway reacts to angular acceleration with an equal and opposite angular acceleration. I am not 100% sure, but I am fairly confident it can be done. It would not need to be as long as a runway, just as long as a plane's wheelbase.
Art, I'm honestly beginning to think you're just ****ing with me. If the ground is moving, guess what, they're moving relative to the ground. Your example doesn't work. Try again. As for your question, for the upteenth billionth time, they're freerolling wheels. If the wheels are moving forward at a speed, and the conveyer backwards at the same speed, they still move forward, they just spin faster.
Read what I just posted and tell me if you agree: Art, you are saying that even though the wheels are not directly driven by the plane, and that the treadmill is NOT driving the wheels, the wheels will accelerate in rotation as the plane sits still when engine thrust is applied. THEREFORE: Given your understanding: If a crane attached to a hook at the top of the plane gently lifts the plane off the treadmill one inch, as soon as you applied thrust with the engines the wheels would begin rotating, yet the plane would not move forward!
You are getting close but this is not what would happen according to what I am saying. Now the weakest thing opposing the thrust of the plane is the air. The plane would move forward against the air which does not provide anywhere near the opposing force to cancel out the thrust of the engines. It would pull against the crane's cable. If the crane is off to the side, the plane would start going round and round, just like the toy planes on a string. Once the plane got enough angular velocity for the tilted wings to create lift, it would gain altitude. I suspect the cable would break at some point. Incidentally, a Piper cub owner did take off by going round and round after tying his plane to a tetherball pole in his backyard. He had a release mechanism for the tether.
You are just making this up as you go aren't you? Shiggins is right, you are just playing here, because you can't possibly be serious.
I honestly think you have a mental block. They are rotating. But they are not moving forward. Just like a car on a dyno has its wheels rotating but the wheels and the car attached to it is not moving forward. The wheels and the landing gear and the plane are not moving with respect to the air. That's what you need for lift. Since it ain't happening, there's no lift. No lift, no take off. Lol! You got yourself on that one. How can they spin at the same speed as the treadmill AND spin faster at the same time? This would imply that the treadmill is spinning at the same speed as the tires and yet somehow moving slower at the same time. Cannot happen. The question clearly states the speeds are matched at all times. If the treadmill and tire speeds are matched in opposite directions, the tire will not move forward on the belt. If the tire positioin does not change, how can the position of the attached landing gear and plane change?
Does it not happen with toy planes on strings? If you build it bigger and stronger, why would it not happen in real life? You are the one who came up with this example. Hang a plane off the ground and fire its engines and see if it moves forward until the cable stretches or not. What do you think will happen? What am I supposed to be making up? That a pilot took off like this? It was in Popular Mechanics a long time ago.
No mental block here. This is not like a car on a dyno. It will move with respect to the air. No Art, you got yourself not comprehending again. The wheels have 2 velocities. 1. Translational. The speed of a point on the wheel relative to the ground. (This, is the same as the airplanes forward speed, and is required for the conveyer to begin moving) 2. Rotational. The speed at which the wheel is rotating. So, lets look at what I said again. If the wheels are moving forward at a speed (TRANSLATIONAL), and the conveyer backwards at the same speed (TRANSLATIONAL), they still move forward (TRANSLATIONAL), they just spin faster (ROTATIONAL). Image Unavailable, Please Login
