I disagree... normal conveyor, normal airplane... it won't fly. The air is not attached to the conveyor, you have no relative montion through the air. The plane may be generating thrust with its engine against the air but it is not pushing the air over the wings in sufficient quanities to generation enough lift. Since the plane is in fact stationary when view from the perspective of the air it might as well be teathered, exactly why if you tie a plane down you can run it to full power and assuming your chain doesn't break it won't take off. Even a prop plane does not push air over the wings as much as it pulls the plane through the air. I'm sticking my position on this, let the discussion begin.
I say the plane would at least move. The engines produce a force which pushes the plane forward. For the plane to not accelerate there would have to be a force of the same magnitude pushing against the front of the plane. The friction of the wheels on the conveyor belt would be relatively small compared to the thrust of the engine, and the plane would accelerate foreward. Now someone could argue that the air resistance and wheel friction combined could equal the engine thrust and stop the acceleration before it has enough speed to take off, but then you just need a better engine.
OK I'll switch sides on this site. It should be easy since I really believe the plane will fly. The wheels only function to reduce the friction of the plane with the ground(or conveyor) not to propel it forward. The engine of the airplane is pushing against the air to provide forward motion. If it were a car that was using power through the wheels to propel it, of course it wouldn't go anywhere. The wheels will spin at a faster rate than the belt movement as the engine provides enough thrust to move the plane through the air and make the plane move forward relative to the surroundings. The problem is thinking wheel speed vs conveyor speed have to be equal. Wheel speed and plane speed can be different under this condition. Plane speed and conveyor speed have to be equal. When the plane hits air speed, the wheels will be rotating twice air speed.
Is the conveyor powered or unpowered? basically I'm ask is the conveyor an active or a passive part of this problem. If the conveyor is unpower then yes the plane will take off since it will accellorate, abeit more slowly than normal. If the conveyor is actively matched to the wheel speed then no it won't take off since the plane will never actually move.
I don't think it matters much even though it is supposed to be powered. I was looking around the internet for this riddle and found a real good analogy from another site. Since the landing gear on an aircraft are merely for support while on the ground then imagine you supported the plane on air like a hovercraft. In this situation the hovercraft would surely move forward.
let me put this in very simple terms conveyor matchs wheel speed, plane never physically moves plane never physically moves, no airspeed no airspeed, no lift no lift, no fly The plane pushes against the air to create thrust, agreed. However if the conveyor is matching the wheel speed all the engine is doing it acting like fan. The accelleration due to thrust is completely cancelled out by the conveyor. This leaves you with 0 force acting on the object as far as its motion is concerned. With 0 motion you are then relying on the air moving past the wings and a fan won't move enough. A fan will move air but only through it and like I said a tethered aircraft won't take off. Not to pull rank, but read my signature.
Careful fellas, this was posted on another forum I subscribe to and it turned into a 7 page sh*tfight. It was taken from another forum where it was a 10 page sh*tfight. I wont mention the result because I don't believe it!
I remembered your sig the first time you posted CTX. :laugh: I was going to point that out even, but didn't have the time. I figured if anyone would have the answer right, it would be you. EDIT: This link claims that the plane would take off. http://www.avweb.com/news/columns/191034-1.html However, I don't see the author has credentials like CTX. The main arguement he makes is that because the thrust doesn't come from the wheels the conveyor cannot stop the forward momentum of the plane. He also lists a theoretical situation involving a hovercraft and how someone used a rubberband plane and a treadmill. Too bad the latter doesn't acurately reflect the question. In fact, the hovercraft question doesn't seem to do so either. 2ND EDIT: The more I think about it, the more I think the plane would take off. I was reading too much into the contact the wheels have with the ground.
Let's put this another way: Airplane sits on conveyor which moves opposite to the direction of intended lift-off. Said conveyor is moving backwards at say 150 knots. The engines are providing exactly 150 knots forward thrust. These effects cancel each other out, plane just sits there is if it were sitting on the tarmac, parked. It boils down to simple arithmetic, and plus and minus numbers, ie -150 and +150. Add those two numbers together, you get 0, plane doesn't move. Have you ever seen an airplane levitate while sitting on the tarmac???? p
We have a winner.... yes it will take off. the wheel and conveyor have nothing to do with it. the conveyor is not driving the plane either way. the wheels are not driving the plane either way. It is a trick question. planes move on thrust from a jet or prop or other. the thrust will driv the plane down the aloted amount of runway until the plane reaches the suficient speed that it normally requires to take off, then do so. the wheels may be moving at differnt speed in a different way ...but it does not matter. At All. I thought it was funny they put down 13 pages of text(and counting) of the question :laugh:
What it boils down to is that the conveyor cannot overcome the thrust of the engines. As I was reminded, for every action there is an equal and opposite reaction. The mention of a rocket in space is why I rememberd the properties of thrust. The engines create thrust. Conveyor belt or not, the plane is going to move. The plane DRAGS the wheels. While not quite the same, think of it this way. Take a helicopter and add wheels to it. Now in this case, the "wings" are the propeller blades and they generate lift -and when tilted while spinning, thrust. The helicopter takes off vertically, say 20 feet from the ground. The conveyor belt is then raised to meet it. The blades are tilted which basically pulls or pushes it along. Now, the wheels on the helicopter will spin like mad, but the conveyor will not be able to stop the helicopter's forward motion. The plane really isn't any different. I hope that clears it up.
I revise my position after walking away from this problem for a bit. The plane would take off but it would take longer as it would have to overcome the drag of the wheels moving at a faster speed than normal. The wheels pinwheel under the plane so it is a trick question, the force is acting on the aircraft via the engine not the wheels so the wheels could almost care less if the ground is moving or stationary as they simply react to the forces applied. The wheel spins forward due to the force applied from the engine against the air, and moves backwards because of the conveyer. Thanks for the rocket analogy, I have a batchelors in Space Propulsion and it reminded me of this.
Drag of the wheels would be negligible. I think what makes this a riddle is a misunderstanding of what makes the plan move. If the wheels were what propelled a plane - if the wheels are what caused the forward motion - then the conveyor belt would keep the plane from moving forward, and without forward motion, no lift would be created. However, in this riddle, the wheels are merely along for the ride. They do not move the plane - it is the movement of the plane that moves the wheels. In the riddle, the conveyor moves at the speed of the wheels, but in the opposite direction. In reality, the belt speed is dependent on the wheel speed, and the wheel speed is dependent on forward motion.
The question doesn't state the limitations of the plane, so people may have a wide range of interpretation. This plane probably wouldn't fly off of the conveyor http://community.webshots.com/photo/339058906/339073040EoeyWf this one? http://www.knight-toolworks.com/graphics/highbackinfilll.jpg Debate is fun when people exchange thoughts and ideas respectfully No need to turn it into an argument :beer There are lots of ways to look at a problem, and just when you think you have the exact answer, you can find out that there is a side that you never thought about ou:
Interesting discussion here, yet one thing which has not been made clear. Is the conveyor belt powered or is it static??? Most every conveyor belt system I've ever observed has been powered so as to move items from point A to point B. Although I've never seen one capable of such high speeds as would be required to counteract an airplanes liftoff speed, in this theoretical discussion, I considered it as possible. :Comp: Thus if a the conveyor belt was powered by a separate source, and was capable of exactly matching the forward speed created by engine thrust, I still state that the plane would not be capable of lifting off. Friction between tires and conveyor belt would still exist, but there would not be any airflow over the wings to permit actual liftoff. Consider if you will, the example of an exrecise treadmill, which is little more than a small conveyor. These are powered, and allow you to "run in one place". Thus you get a nice jog/run, but never actually go anywhere. This is what I based my previous answer on. Now in rethinking the initial question, if the conveyor is not powered, but is static, and relying upon reverse thrust in order to move, such as the forward action from a powered wheel vehicle, then the vehicle would indeed move forward, albeit at a slower pace. As has already been demonstrated, an airplane on a static conveyor would indeed advance forward, and likely attain sufficient ground speed to allow for liftoff. Whew, that's enough thinking for this morning. :laugh:
The way I see it the conveyor would have very little effect on the motion of the plane, unless the plane was completly stopped, and even then depending on it's mass and the friction in the wheel bearings the conveyor could start moving, the wheels would turn and the plane would sit still. Beyond the friction in the bearings there is no way for the conveyor to impact the forward motion of the plane as the wheels are not what causes the motion in the first place.
From a Kinetic Energy standpoint... I'm thinking that the Conveyor would actually make it easier for the plane to start moving. As it would allow the plane to use less effort to start rolling (since it'll match exact speeds, it seems that the plane would only have to put up half the effort since the conveyor will put up the other half). ALthough, any benifit would be small and unnoticeable once the plane is actually moving. BTW.. I'm with the fly group.
the original question: 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? if this was framed as "The conveyer belt is designed to exactly match the speed of the plane at any given time, moving in the opposite direction" i would say that 73 Centurion had nailed the answer and that the speed of the wheels on liftoff would be twice that of the airplane ... although you'd still be getting altogether to close too or exceeding the destruction RPM of the tires/wheels (~300mph for the ~150mph takeoff speed of large jet aircraft). A1: Plane takes off however, that's not how this question is framed. this is framed as "The conveyer belt is designed to exactly match the speed of the wheels ... in the opposite direction of rotation". which doesn't make any sense at all. 1st - it doesn't matter how fast your vehicle is moving the contact patch of a tire has zero velocity in relation to the ground (or in this case, conveyor belt) excepting sliding or spinning when traction is broken. a plane has no means of applying torque to a tire except by the brakes so there's no reason for the tire to spin (in relation to the support surface) and the engines are aligned parallel to the axis of travel for the tires so there isn't any reason for them to slide in this example (no wind, therefore no crosswind. i'm taking it as given that the surface of the conveyor isn't tilted to one side). 2nd - if the question means as read, that the motion of the conveyor will be counter to the rotation of the tire, then the conveyor will maintain whatever speed necessary to keep the tire at zero rpm regardless of how fast the plane is moving. the motion at TDC of a tire is 2x the velocity of the vehicle and in the same direction/vector. the motion at BDC of a tire is 1x the velocity of the vehicle and in the opposite vector ... as long as the runway isn't moving. as stated, the conveyor will act counter to the "direction of rotation" which i can only take to mean as counter to the contact patch ( BDC ) ... or in the same direction as the motion of the aircraft. none of this has any impact on airspeed except possibly to shorten takeoff distance as energy losses to bearing friction and wheel inertia have been eliminated. A2: plane take off as though into a minor head wind (shortened field) 3rd - worst case scenario, the conveyor acts in opposition to the motion of the tire at TDC. for calculation purposes i'm going to do this at 1 sec intervals (it would happen instantly given the preconditions in the question). remember, the mph of the tire at TDC has to be twice the speed of the plane plus the speed of the belt (or contact patch at BDC). consider; the plane is at rest. tire speed is zero, belt speed is zero. the pilot receives clearance from the tower and initiates his take-off. T+1 sec = the plane reaches 3mph. rotation of the tire at TDC is 6 mph. belt has not yet responded, so 0 mph. T+2 sec = plane @ 6 mph. tire @ TDC would be 12 mph ... except that the belt has now engaged and is turning backwards @ 6 mph ... which accelerates the tire at TDC to 18 mph. T+3 sec = plane @ 9 mph. tire @ TDC would be 18 mph ... except that the belt is now turning backwards @ 18 mph ... which accelerates the tire at TDC to 36 mph. T+4 sec = plane @ 12 mph. tire @ TDC would be 24 mph ... except that the belt is now turning backwards @ 36 mph ... which accelerates the tire at TDC to 60 mph. T+5 sec = plane @ 15 mph. tire @ TDC would be 30 mph ... except that the belt is now turning backwards @ 60 mph ... which accelerates the tire at TDC to 90 mph. T+6 sec = plane @ 18 mph. tire @ TDC would be 36 mph ... except that the belt is now turning backwards @ 90 mph ... which accelerates the tire at TDC to 126 mph. T+7 sec = plane @ 21 mph. tire @ TDC would be 42 mph ... except that the belt is now turning backwards @ 126 mph ... which accelerates the tire at TDC to 168 mph. T+8 sec = noticing that something is out of the ordinary, the pilot kills the engines, plane @ 21 mph. tire @ TDC would be 42 mph ... except that the belt is now turning backwards @ 168 mph ... which accelerates the tire at TDC to 210 mph. T+9 sec = engines still shut down, plane @ 20 mph. tire @ TDC would be 40 mph ... except that the belt is now turning backwards @ 210 mph ... which accelerates the tire at TDC to 250 mph. T+10 sec = engines still shut down, plane @ 19 mph. tire @ TDC would be 38 mph ... except that the belt is now turning backwards @ 250 mph ... which accelerates the tire at TDC to 288 mph. once the time controls are removed and the belt response is set instantaneous to tire speed you see that this question creates an infinite runaway feedback loop which would destroy the tires almost immediately after the pilot initiated rolloff. A3: aircraft explodes on runway as disintegrating tires/wheels shred the wing tanks having read through the replies over at the Subaru forums i find that i agree with this answer the most: whenever you get to 12mph the turbo will spool and you'll go right into the nearest house. :Brow:
