I can't believe this thread is still going This explains it perfectly. If you go on a treadmill and run 5mph forward and the treadmill goes 5mph backwards, you stay still. Why? Because to move forward a person steps on the ground and pushes forward, if the ground is going backwards at the right speed, you don't actually travel anywhere. However, the mistake people are making is applying this to a plane and assuming it's correct. THINK about how a plane moves forward on a runway. Does the engine turn a shaft that turns the wheels to provide thrust like in a car? No, it doesn't. The wheels are not there to provide thrust for the plane, to make the plane go forward, simplifying it a bit; the propeller (or jet engine) pushes air backwards, which in turn pushes the plane forwards. Just like swimming. The wheels are just free to move, they have very little effect on the planes movement. So long as the planes forward thrust has overcome the initial friction of the bearing, the treadmill can be going a bazillion mph and it wouldn't effect the planes movement. The wheels would be going really, really fast, but the plane doesn't care because the forward thrust isn't in any way related to the wheels.
Of course it is friggin' possible! It is not a paradox! Wheels go forward at speed S; conveyor belt goes backwards at speed S; wheels rotate at speed 2*S.
There's no need to be quite so condescending. You have missed my point but perhaps I didn't explain well. Obviously in the original scenario (plane speed = conveyor speed), the plane takes off. I'm not that daft. My point pertains to an alternative scenario which you were talking about (speed of plane's wheels = conveyor speed). I will try and explain better: For a plane on a normal runway to go at 15mph, its wheels (the surface of the wheels) need to be rolling at 15mph - unless the wheels are skidding / spinning of course (And I'll assume they're not). This is regardless of where the power for the wheels comes from, right? If the same plane, doing 15mph as before, is on a conveyor which goes backwards at 15mph, its wheels must be spinning at 30mph, right? If the plane is to move forwards in real terms (at speed s), the speed of its wheels (w) must necessarily be greater than the speed of the conveyor (c). Since the speed of the conveyor (in the alternate scenario) is matched to the speed of the wheels, this cannot occur. s = w - c if w = c, s = 0 I hope I'm making more sense now?
While logically you seem correct however you are not looking at the system correctly. There are 2 situations you can take: 1) There is no retarding couple at the wheel axle 2) The is a retarding couple at the wheel axle Both cases require a non zero coefficient of friction between the wheel and the belt. Case 1: If you draw a diagram of a plane and draw the forces on the plane there is a force pushing it forward but no force pulling it back to it will accelerate. The wheels on the other hand due to the belt going at the same speed will spool up to infinite velocity instantaneously and so causes our maths to go wonky as infinity is not a number. But due to a lack of retarding force the plane MUST ACCELERATE. Case 2: With a retarding couple there is a retarding force. This means that the plane will not move until the friction at the axle overwhelms the friction between the wheel and the ground (this MUST happen assuming the plane has a sufficiently powerful engine) at which point the wheels will SKID along the belt and hence the plane will take off. I hope this clarifies the situation.
Sorry. I get carried away in my smart-assed geekness occasionally. Nope. You are still confused, I think. You are not distinguishing between wheel forward speed (as in wheels moving a certain distance, from A to B, per second), and wheel rotations per second. You are also not distinguishing between distance covered in space vs. distance covered on the moving conveyor belt (or perhaps I am thinking you are referring to one while you are referring to the other). When wheels move over a stationary surface, they rotate (as you know). The speed of rotation is the product of the distance covered in a certain time frame (i.e., the wheel forward speed) divided by wheel diameter. Now the conveyor belt can match wheel speed, but the wheels can still move forward. As the belt is moving backwards at the same speed as the wheels are moving forwards, for the wheels to move forward in space they now have to cover a distance on the belt twice as large, but they do that simply by rotating twice as fast. The speed of rotation is now the product of the (wheel forward speed + conveyor belt backward speed) divided by wheel diameter. Let's do the maths: Say the wheels move forward at 1 meter per second. Let's also say that the wheels have a diameter of 127cm (that of a Boeing 747). On a stationary surface, they will rotate at a speed of distance covered divided by circumference of wheel = 1m / 3.14 * 1.27m = 0.253 rotations per second. Now lets say that the wheels move forward at 1 meter per second, but the conveyor belt is moving backwards at 1 meter per second as well (matching the wheels' speed in the opposite direction). This means that effectively, for the wheels to move forward 1 meter per second in space, they have to roll twice that distance on the belt in the same timeframe: 2m / 3.14 * 1.27 = 0.502 rotations per second, i.e. they rotate twice as fast (logically). Changing the speeds involved does not change anything. The wheels simply have to spin twice as fast on a speed-matching conveyor belt as they'd have to do to move forward the same distance in the same time over a stationary surface. If you are referring to the speed of the belt matching the distence covered by the wheels on the belt in the same time frame, then you get into a recursive loop; the belt has to keep speeding up exponentially to keep up with the wheels moving over the belt until we hit light speed. However this only has consequences for the wheels spinning like crazy, not the forward movement of the plane which is independent from all this. It is not pushing off against the belt, after all.
The whole scenario is pointless and have nothing to do with the original myth, but anyway: Your formula is wrong. the correct is s= w - (-c) THEN the wheels spin at 30mph. That aside, why do people bother to discuss this any more? If someone still don't get it they: a: Doesn't WANT to understand b: Have a fear of loosing reputation and/or hate to be wrong, as in point a. c: Are stupid. Here is the summary: Planes move forward by air pressure, not via the wheels. And the air over the wings are unaffected by the engines AND the conveyor, hence, it takes off!
I do a little bit of surfing on coffee/muffin breaks, bit-tech is one of the popular stops, and it's funny to see a new post in the never ending plane on a conveyor thread It's just a play on words, where the conveyor isn't matching the plane's speed or wheelspeed, but trying to match the RESULTING wheelspeed of the conveyor matching the plane's speed, which is the conveyor = conveyor's speed + the plane speed! So how is the conveyor speed (C) supposed to = conveyor (C) + plane (P) speeds, or in short, C = C + P To those that simply do not understand the question/scenario here, have a look at the algebra here: C = C + P is not valid - this does not mean the plane won't take off, it means you have misunderstood the question. The conveyor only has to match the plane speed, or the speed of the wheels on a normal runway at take off, so it is simply: Resulting Wheelspeed = Conveyor speed + Plane speed Thats it, no more, speed of light is not required expect to see what you are reading And again, if the wheels locked, the plane will just skid along and the plane will still take off provided there is enough thrust from the plane
Depends on the plane, some don't like having their wheels locked up and nose into the runway, usually true of forward mounted prop planes.
What always amazed me - flying light aircraft the instructors whack the handbrake on, and put the engine to full power just before take off to make sure it 's ok. The plane shakes and twists around, but there is NO forwards movement! and that's with 3 small wheels vs relatively large engine + prop.
The engine of a light aircraft isn't really powerful enough to make the wheels skid right away from a standing position. the plane shakes because of the vortex of air created around the aircraft by the propeller. Put simply the vortex spins around the body of the plane. This vortex colliding with the wings will cause some shaking. If the surface is a bit wet or slippery the plane will move slowly forward.
I was. A recursive loop would only occur if there was some latency in the system - I.e. the plane moves and then there's some circuit to track the speed of the wheels, and adjust the conveyor accordingly a fraction of a second later. However, I was assuming a perfect, entirely hypothetical, scenario where the speed of the belt [is identical to] the (rotating) speed of the wheels (with zero latency). In which case there would be no recursive loop, but the plane itself could not move (following the logic in my previous post). Ergo it doesn't take off
You are thinking: conveyor belt speed = wheel speed over the belt, which is a sum of wheel speed in space + conveyor belt speed. Or as mvagusta says: C = W + C, which can only be valid if W = 0. However, you are looking at the wrong wheel speed. The plane's movement is entirely independent from the movement of the belt through the spinning of its wheels, as the inertia experiment demonstrates. The relationship between the belt and wheels is expressed in wheel rotation, not wheel movement through space.
Could somebody please explain to me why the rotational speed of the wheel is even considered in this problem? The wheels could be a bunch of ice cubes for **** sake! Rotational speed doesn't matter. It's the forward speed of the plane generated by the engines.
now that that myth has finally been busted, here's 2 new questions for the naysayers: 1. if a plane was chained to the ground and not able to move forward at all, will be able to take off? 2. if i was swimming, and someone placed a conveyor belt at the bottom of the pool that matched my swimming speed, will i go anywhere? 3. if a ski-plane tried to take off during an avalanche, will it fly?
