Baasha, OK, so I deserved that. Here's a more reasoned critique of your argument: If indeed aeroplanes used the engine power to drive the wheels to get forward speed, and no thrust at all came out of the engine in a rearward direction, you would be correct. I know of no plane that works in the manner you describe. Please answer this - when a plane (constructed according to your earlier description) takes off and the wheels are no longer in contact with the ground - how does it continue flying? Thanks, Rich.
Awesome plane, it delivers power to the wheels with no driveshaft or other drive mechanism. Cool. Now, in your plane, since the power is delivered through the wheels, how does it keep flying once it lifts off??? Uh Oh. Edit: sorry about repeating RichRowe's last post
An airplane takes off because of air moving over its wings. If the air is still, the plane has to move forwards to create this rush of air over the wings. If the air is moving forwards too (tailwind), the airplane has to move faster before the airflow over the wings is sufficient to allow takeoff. If the airflow is backwards (ie. there is a headwind), then the plane can take off at a lower speed. It's all about the wind speed over and under the wings. Even with ground effect, the lift occurs because of the mass of air being squeezed under wings. OK, so here we have an airplane that is not moving. Every time the engine thrusts it forward, the wheels roll forward. But the conveyor belt moves backward an equal amount. Net movement of the plane forwards is zero. Since the plane is not moving, the air is not moving relative to the plane. If you have an airplane sitting still, and push air back over the wings at 150 mph (or whatever the takeoff speed is) the plane will rise, engine or no engine. Even gliders fly. This is not the issue here. There is no wind except that made by the plane moving in relation to the air around it. Since the plane is not moving, there is no air rushing over and under the wings, creating lift either due to the Bernoulli effect or due to ground effect. So the plane will not take off.
OK hows this (again given the SIMPLE question)... 1) The question states that the belt speed matches the wheel speed, which suggests the wheel speed must always equal the belt speed (obviously), right? 2) So, if everything is stationary the belt speed = 0 = wheel speed. 3) Engines start (slight throttle), plane begins to move, wheels begin to move, belt moves instantaneously to match wheel speed. 4) Because of the friction involved the (slight) thrust from the jet is holding the plane in a fixed location relative to the earth (otherwise it would run off the back of the belt) - with wheels spinning at belt speed in a steady state with no acceleration, agreed? 5) OK, here is the crux where the discussion starts...throttle is applied 6) To move along the belt (ie gain airspeed) the plane has to thrust forward, this in turn causes the wheels to rotate at a higher speed than the belt is moving (because the wheel are now moving along the belt not matching its speed) - thus breaking the questions parameters so the pilot has to throttle back to maintain an equal belt / wheel speed, ergo the plane aint going anywhere. QED2
If the plane doesn't move, neither does the conveyor belt. The conveyor belt speed is the equal and opposite of the plane's speed forwards - plane 100mph forwards = conveyor 100mph backwards = wheels think they're doing 200mph, but so what? The wheels just get spun up to a faster speed by the conveyor belt than they would do if the plane was driving along a fixed runway. The rearward speed of the conveyor is equal to the forward speed of the plane (by the problem statement). The problem is designed to trip up two kinds of thinking: * the thinking that the plane drives forward because of its wheels. * the thinking that you can drag something backwards by its wheels when it is being propelled forwards by an external force. If you want to bring any real world stuff in, then what's appropriate is the wheel bearings will not be totally frictionless and so the conveyor can exert a TINY amount of drag on the forward motion of the plane. However, the plane has to be moving forward pretty darn quick for this drag to amount to a hill of beans. Going forward pretty quick means taking off. Still waiting to hear how the wheel-driven plane continues to fly once it's taken off. Regards, Rich
Ricard, that is pretty well resoned until you get to the bit where the pilot has to throttle back. Where does it say in the problem that the pilot is happy to sit in one place while the belt moves undrneath him? The problem says that the plane intends to take off. There are a few ways to look at the speed of the wheels - in relation to the belt and in relation to the Earth. Now, if the plane is able to move forwards (as you can concede it can unless the pilot purposefully throttles back) the wheels are 'gaining' on the belt but the belt speed can still be equal and exactly opposite to the wheels speed as long as the wheels don't break traction (which they have no cause or forces on them to do). A wheel doing 100mph down a road/runway 'sees' the road doing 100mph under it. The plane's wheels, doing enough rotations to appear to be doing 200mph while the plane is doing 100mph in relation to the Earth and the air 'see' the conveyor belt doing 200mph backwards in relation to the spinning speed of the wheels and all the constraints of the problem are intact. A simpler way to put it is someone walking backwards down a train - trains forward speed is (say) 100mph and the guy is doing 5mph backwards in relation to the train. The train is moving backwards in relation to him at 5mph and moving at 100mph in relation to the Earth. He is moving at 95mph in relation to the Earth. See how all these four speeds happily co-exist and no-one needs to call the Physics Police? I'm off to the pub, back later!! Regards, Rich.
Baasha wrote his explanation a bit ambiguously, but I don't think he meant that the forward motion was transmitted through the tires, but rather that the wheels are part of the drag when below flying speed and do matter. If the wheels are prevented from moving at all (wheel chocks), the plane goes nowhere because the thrust of the engines is less than the "drag" (the actual issue is that there's no vertical force in this situation and the wheel chocks require some vertical force to overcome) on the wheels.
Another view: I don't believe the original intent of this hypothetical situation was ever to do anything except pose this question: Does the the rotation of the wheels have anything to do with whether or not a plane can takeoff? The anwer to that simpler question is NO. Planes don't even need wheels, they can take off on skis or floats. You can even take all the landing gear off, grease up the belly of the plane and slide down the runway. In this thread the question was posed saying "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." Which simply doesn't work, the conveyor has to move with, not opposite, the direction of rotation or you have a tire skidding on the belt which clearly isn't the intent of this thought experiment. What I think the original poser of the question probably intended to say was that the conveyor moves WITH the direction of rotation, i.e; opposite the direction of motion of the plane, which almost everyone assumes it is doing anyway....and to plant the seed in peoples mind that this will keep the plane from moving. What happens in this case is that the moment the plane begins to move, the wheels and the conveyor instantly accelerate to an infinite speed. Not likely.
Thats the thing, read the problem statement again - its actually that "The rearward speed of the conveyor is equal to the wheel speed of the plane". This problem statement is different to all the others (about this kind of problem) that I have seen on the net and I think thats what is causing all the discussions as people are not appreciating the difference between the plane speed and wheel speed. In all the others the plane takes off but this problem statement is different as the wheels cant do 200mph whilst the belt is doing 100mph because that breaks the no.1 rule of the problem statement...
The gist of the problem as most people are taking it is: If a conveyer belt/wheel system tries to hold the horizontal-axis axle velocity at 0, via matching of the rotational speed of the wheel, then can a plane that is attached to that system take off? If it doesn't take off, the conveyer/wheel system successfully approximates the situation where the wheel is chocked (which also holds the horizontal-axis axle velocity at 0). If it does take off, there must be skidding going on somewhere - where is that going on? Picking one or the other is just a 50/50 proposition. A clear and convincing explanation of what goes on would be useful considering you've still got people convinced for each side.
An airplane just needs air to move, it does not need ground. The enignes suck air in and push air out thus creating thrust. This thrust is what pushes the plane. What happens beneath does not matter (unless the brakes are on).
Let me ask something: Let's say that the "treadmill" started rotating first and the plane started to be moved to the edge of the rear of the runway (almost falling off). As the pilot provided a little thrust the plane started to move backwards less because it was counter acting the energy with thrust. As the wheel rotation (through thrust) equaled the treadmill rotation the plane ceased moving backwards and was stationary in relation to the rotating runway. Now the pilot adds a bit more thrust and the wheels move a bit faster then the runway is moving backwards. As the plane starts to roll forward on the runway, the runway rearward speed is increased to counter act forward movement. The runway speed is increased rearward and the pilot maintains the planes position on the runway by counter acting with thrust. How is this plane going to take off with no relative wind? I think you need to think in very slow speeds to understand the physics. If you start thinking you can just add super amounts of thrust to solve the problem you have missed the point entirely.
ylshih, Hi - Baasha wrote these words: The thrust of the jet engines is NOT independent of the rotation of the wheels. and: the jet engines give thrust which is delivered to the ground (which is still--relative to us) through the wheels and: the engines by itself does not make a plane take off I think that's quite clear, but it is not the way a plane works. Also, regarding your later post, why must the wheels be skidding? They're freely rotating wheels - they are not in any way geared to the forward motion of the plane and simply spin at whatever speed the surface under them is moving in relation to the plane. In this case they just have to spin faster than normal because someone is pulling the runway backwards under them. Ricard: I have already explained the relative speeds part - if the wheels think they are doing 200mph in relation to the conveyor belt, they can be, because the conveyor belt is going backwards at 200mph in relation to the wheels and teh plane. This does not stop the plane moving forwards, or break the constraint of the problem - the plane can 'gain' on the conveyor belt at 100mph in relation to the ground, the conveyor goes backwards at 100mph (in relation to the ground). To directly address your point - about the wheel speed - the wheels are attached at a certain point on the plane and don't move backwards or forwards. The wheel speed IS the plane speed. How can a plane be doing take off speed down a runway and its wheels be doing any other/different speed in relation to the same reference point? Please, look back a few posts to the guy walking along the train - he's doing one speed in relation to the train, and the train is doing the equal and opposite speed in relation to him, and at the same time he is doing a vastly different speed in relation to the ground outside the train, and the ground outside the train is doing an exactly equal and opposite speed in relation to him. This is just the same as the plane driving down the conveyor. The constraints don't need to be broken, I have read and understood the problem statement. The conveyor belt can't drag the plane back with anything other than a tiny amount of friction due to the plane's wheel bearings not being perfect - so the plane travels down the conveyor and takes off. Cheers! Rich
Hi LetsJet, I understand your approach to the problem, and its a good one. However, do you acept that the conveyor belt can't 'grab' the plane because it is only working against wheels that are completely free-wheeling? The fact that the conveyor belt moves backwards faster as the plane with its attached wheels begin to move forwards simply, only, makes the wheels spin faster. The constraints are maintained (as per my post above) but the conveyor simply can't 'get hold' of the plane. What do you reckon? Regards! Rich.
I discussed this with two Engineer friends of mine as well as a Southwest Airlines Pilot adn we think we have the answer. The plane is going to move. We all agree on that. Think of a bike on a treadmill that has the same situation as far as the treadmill matching it's wheel speed. If you stand behind the bike and push it the bike will move forward. The treadmill will just be increasing in speed to match the wheels but since it is not the wheels driving the bike the bike can move forward due to it being an outside force pushing the bike. The plane will react the same way. My engineer buddies seem to think the wheels will always turn at double the speed they normally would. Were not to sure about that part though but we do know the plane will move but the wheels will just be moving faster than they normally would. Therein lies the problem for takeoff though. How much faster can airplane tires turn upon takeoff than they already do? Our pilot friend says that planes takeoff at about 140-180 mph depending on the plane. The wheels are really only rated to about 200mph hus we don't think the wheels would withstand double takeoff speeds so the plane could not take off but it could move.
Hi Alan, I'm with you all the way. I agree that if the tires are driven so fast that they explode, then the conveyor will be now acting against the rims of the wheels, the tires having departed to tyre-valhalla to ponder the argument. Even with this (extra constraint that wasn't in the problem, but is a possible result of it with some planes), the plane would still take off because to grab the undercarriage with any real backwards force the wheels themselves (being very much stronger than the tyres) would also have to disintegrate (what speed would that happen at?) and the conveyor would then be grinding away at the fixed, non-wheel parts of the undercarriage. The landing would be a bit of a problem though! Good, well reasoned post (as are they all for the most part) - thankyou! Best, Rich.
I didn't say the wheels skids, I said something in the system is skidding in order for forward motion to be occurring. As an example, of skidding in the system, the "freely rotating wheels" are skidding on the axle. I just realized the problem statement here is probably incorrect (as pointed out most people discussing it elsewhere on the net define the problem as the conveyer matching the plane speed, not wheel speed as here). Assume the tires are perfectly sticky (no skidding between tires and conveyer belt) and the wheel bearings are perfect frictionless (between wheel hub and axle). This just idealizes the problem (which we might as well assume if you're going to talk about a runway size conveyer belt that perfectly matches "wheel speed"). As the circumference of the tire rotates 1 full turn, the center of the wheel (also the center of the axle) moves forward 2 diameters. So the observation is that the tire surface speed and the axle center speed are not the same, i.e. the speed of the axle center is 0.64 of the speed of the tire surface. If "matching the wheel speed" means matching the axle center speed, this is equivalent to saying matching the speed of the plane (since the center of the wheel axle and the plane have a fixed relationship). If "matching the wheel speed" means matching the speed of the tire surface, then the plane actually moves net backward (tire rotates 1 foot forward, conveyer belt moves 1 foot backward to match, in the meantime the axle center moves 0.64 feet forward, not quite compensating for the conveyer belt motion (which is completely horizontal, while the tire surface is moving in the horizontal & vertical hence the difference). This means the axle/plane moves backward 0.36 feet in space external to the conveyer! So I'm now offering a third option - the plane falls off the back of the conveyer!
Some examples that might help you visualize this better: 1. Imagine a seaplane needs to be going to 50mph to take off. It is on pontoons on a fast flowing river. The water is flowing in the opposite direction to the direction that the plane is pointing in. There is no wind. Now, you can keep the airplane still by tethering it. Is it going to take off? Of course not. There is no airflow around the wings to create lift. The tethering rope would be stretched taut, but the plane is not going to go up or down, or forwards or backwards. What if you undid the tethering line? The plane would float backwards at the same speed as the water, just like you would float down a river on a raft if there was a current. Now what if you turned on the engines and ran them up a bit? If the river was flowing at 30mph and you ran the engines so your indicated speed was 10 mph, you would still go backwards, but not as fast as the water. You would essentially be going backwards at 20 mph. No takeoff. Now say you got the engines going so you were showing 30mph indicated speed. You would simply be standing still (relative to the riverbank) instead of floating backwards. No takeoff. If you got the engines to 50 mph, you would be going forwards, but only at 20mph. Still no takeoff. If you got the engines to 80mph, now you would be traveling forwards at 50mph in relation to the riverbank. Now we're talking! The plane would take off, because the airflow over the wings is 50mph, the magic speed needed to create enough lift to take off. It really is that simple. If there is no wind, it needs to go forwards relative to the still air in order to get lift. The conveyor belt going backwards prevents it from going forwards in relation to the air around it. Therefore it does not experience any lift, and does not rise. So, it's not going forwards and it's not going up. All this talk of wheel bearings and friction and infinite acceleration and earth's rotational speeds only confuses the issue further.
one problem here, the pontoon plane is fixed from the body to the pontoons. thus the plane is fixed into moving with the river. in the question of the 'treadmill' the wheels seperate the plane from the ground so indeed it would lift off and fly away. remove the wheels affix the plane to the 'treadmill' and watch it go backwords.
I'm enjoying this - but its midnight for me, so this'll be the last post of the day. Auraraptor - I like your argument - its a good one and well put. I do understand how an aeroplane's wings generate lift, and yes, in my explanations I have been intent on showing how the plane does in fact move forward on the conveyor belt, and how this is 'legal' within the constraints of the problem. It needs to move forwards in relation to the air to generate the lift and take off - that was never in doubt. I am mostly in agreement with you *until* you say: "The conveyor belt going backwards prevents it from going forwards in relation to the air around it." In your (very good) example of the seaplane being tethered with a taught rope against a current, or floating downstream untethered, there is pretty good 'purchase' of the water on the pontoons of the plane i.e. you have introduced an element of friction that you also state is confusing the problem. Let's stick to the original plane-with-wheels scenario but simplify the problem even further by dispensing with the conveyor belt (just for a moment). When the plane is doing, say 180mph forwards and about to lift off (according to Alan, who got that info from a Pilot), would you agree that in relation to the plane, the ground is departing away from under the wheels at 180mph. I hope so! Now, because the ground under the plane is doing 0mph in relation to the still wind, does the ground 'grab' the plane and hold it still? No, it doesn't. Yes, it exerts a small force backwards simply because the wheel bearings are not absolutely perfect, but that force is TINY. [That force on the hull or pontoons of a seaplane would be very much greater, but that's not the problem we're posed with here]. This problem is all about whether the conveyor belt can exert an equal and opposite *force* on the plane to stop it moving, such that the sum total of all the forces on the plane is zero. I know I've asked this question before, but how do you reckon the free-wheeling wheels be used to drag on the plane enough to counteract the dirty great massive jet engines/rocket engines? I really want you to answer that, and answer it in both the hypothetical sense (assuming perfect wheel bearings and NO friction) and also the real-world, little tiny bit of friction sense. Right - next, ylshih, Hi Yin, I was going to go into circumferences and the relationship with wheel sizes etc along your lines but decided not to - the size of the wheels is irrelevant and the 'speed' of the wheels can only be the same as the speed of the plane. To justify this, consider the following: My plane, having successfully taken off about a thousand times now D) is happily cruising at 36,000 feet, at, lets say, 560mph on its way with me and my buddies to the Caribbean. Lamour has disappeared off with a well-endowed hostess and a digital camera. The wheels are travelling at 560mph, agree? They're tucked up inside the landing gear bays and are going along with the plane, so they're doing 560mph. But wait! Are they turning? No! So what's the wheel speed? Gee, it's 560mph. If someone wants to spin the wheels while in flight, do you agree that they can spin them as fast or as slow as you like, and fundamentally, their own speed is still 560mph? This is how a wheel can spin at any speed whatsoever and also travel at a different speed in relation to the Earth (and crucially, the air that needs to flow over the wings of the plane for it to fly). All you need is something the decouple the wheel from the ground. When the plane is in flight the wheels aren't affected by the ground and when the wheels are on the conveyor belt they are just forced to spin to suit the speed of the conveyor belt. And your maths is wrong, too. Wheel circumference is 2 x pi x Radius (or pi x diameter, seeing as diameter is 2 x Radius) So if the wheel rotates one turn, the centre moves forward by 3.1415 (etc) times the diameter. Also, if you take into account that a wheel is circular, when the bottom of the wheel is in contact with the road, it is doing 0 speed whilst the top is doing twice the forward speed forwards. The wheel (in the rotational sense) is moving in every single direction in the plane (pun intended) of motion. The back is moving UP, the front is moving DOWN. If you sum all of these different velocities (and the correct word is velocity because it incorporates speed and direction), what you actually end up with is the speed of the wheel is the speed of the centre of the axle. To put it more simply - how can these two possibly be different if the wheel stays connected to the axle?? If they were going at different speeds they would move away from each other! OK - I'm done for now. Sleep tight, folks, I'm enjoying debating this you. Regards, Rich.
