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#51




You're All Wrong!
Airplanes don't stand on the runway, they sit on the runway. Try overcoming that friction.

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#52




Sorry about being late to this forum. I was going over the archives and found that Cecil's conclusion on the 'plane on a tredmill' question is in error. The plane if it remains stationary to the air surrounding it, will not not fly no matter how fast the prop spins and the wheels turn. Lift is provided by airspeed. The problem described only mentions groundspeed. Without sufficient air flow over the wings there is no lift.
Sorry folks, this turkey won't fly. 
#53




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You don't comprehend that the issue is what happens to the force created by the turning of the propellers or the igniting of the jet fuel. That force acts upon the plane. If you can explain how the plane can stay motionless relative to the air under those circumstances, then we will accept your answer. 
#54




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#55




I hate arguments semantics. Here's what is really going on here. The original question was badly phrased. This created two factions, one that took the question literally as is, and one that instead tried to assess the intention of the original question. Arguments over semantics are stupid, it's a lot of wasted energy to prove nothing except that you interpret something differently. Instead lets focus on what we do agree on.
You need relative motion of a plane to air to create lift. That's it, we're done, lets move on. 
#56




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__________________
Time travels in divers paces with divers persons. As You Like It, III:ii:328 Check out my dice in the Marketplace 
#57




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#58




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As for the version asked on the Internet, I've yet to see it asked in a way that allows the friction component to actually overcome the force of the engines. I suppose it might be buried in one of the many threads on the subject here on the board, but I've not bothered to find it. 
#59




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As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indycarquality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox...I've truncated it there because the rest of Cecil's argument is, to be charitable, not well thoughtout. Luckily, though, he did a bit better job of it in the second column on this subject. The point here is that you needn't rely on friction to balance thrust from the engine, but rather the inertia of the spinning wheel. 


#60




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Further, and this is VITAL, there simply is no way to reach the type of result in what Cecil calls BR2 without completely changing the wording of the problem. As long as the problem is worded to deal with the velocity of the aircraft, or the wheels, you cannot achieve the solution advocated and discussed in the second column. All of which means: As originally formulated, the problem was intended (CLEARLY) to make people stop and think that airplanes are not cars. Any other approach to the original question is simply an attempt to be a contrarian. 
#61




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#62




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I think I'll give this problem to high school classes as an interesting constructivist activity. I'm thinking water guns at fifty paces might be needed... 
#63




OMG, it's back.

#64




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If we are to assume that the treadmill can and will try to speed up to keep the plane stationary, friction does allow it to. Quote:



#65




I think I can offer some info for those looking at a realistic approach to this problem. Aircraft have max rated wheel speeds, on the ground obviously, above which the tires and bearings may overheat. So, even if it was at twice normal wheel speed, the tires and bearings will likely fail before the aircraft could reach take off airspeed, assuming a large aircraft. There is a surprising amount of friction on aircraft wheel assemblies even when not loaded. Even on jacks a wheel takes some effort to rotate. Just my 2c

#66




Now that this thread has been resurrected for a while, let me repost something that I've posted a few times before:
There are plenty of answers to this question, because the key to the question is the wording and your interpretation and what you assume from the beginning. And these answers can all be correct, but the assumptions are the key. Let's start off at the top: A. Suppose we actually built a treadmill and put a 747 on it, and had the treadmill match the speed of the plane. Would the 747 take off? If the treadmill matches the plane fuselage speed, then yes. The treadmill simply accelerates in the opposite direction that the plane does. The wheels wind up *rotating* twice as fast as they normally would, but the plane will take off, leaving a treadmill behind that's rotating in the opposite direction. B. Let's reword the question. Suppose we actually built a treadmill and put a 747 on it, and had the treadmill match the speed of the wheels. Would the 747 take off? Depends. If "exactly matching the speed of the wheels" means that the treadmill matches the *hub speed* of the wheels (the speed of the wheel center, which is the same as the fuselage speed), then yes. Just like in the last scenario, the treadmill accelerates in the opposite direction that the plane does, the wheels rotate twice as fast as they normally would, and the plane takes off. C. But that problem is trivial. Let's assume that "exactly matching the speed of the wheels" means "matching the outer diameter surface velocity"the velocity with respect to the hub, or the "speedometer" speed. Would the 747 take off? Almost certainly it would, but only because we can't build a treadmill capable of keeping up with the thrust transmitted to the plane by the enginesin other words, we violate the spirit of the question, because the treadmill isn't matching the wheel velocity. D. OK, that's stupid. It's a thought experiment. Posit a magic treadmill that can accelerate as fast as desired. And it doesn't break. I imagine the wheels will skid on the treadmill, because the friction won't be able to transmit the necessary force. In that case, we again violate the spirit of the question, and E. It's a thought experiment, smart guy. Assume there's enough friction to rotate the tires. All right. When the engine lights off, the treadmill will accelerate until the force transmitted through the wheel hub to the plane exactly balances the thrust. The plane would stay stationary as the thrust power was dissipated in the wheel bearings (as friction), tires (hysteresis), and in accelerating the wheel to everincreasing speeds. Since all the power is dissipated in the wheels, eventually either the bearings would overheat, the tires would blow, or the wheel would rip itself apart due to inertial forces. After that, the plane crashes and burns. Then you've destroyed a rather expensive magic treadmill. F. Thought experiment, I said! Let's posit ultrastrong and heat resistant tires. All right. It turns out the real world is rather complicated. If the treadmill is a long, runwaysized treadmill, it will eventually, running thousands of miles an hour, pull in air at high enough velocity that the plane will lift off at zero ground speed (but substantial air speed). However, now you're running into transsonic compressibility effects... G. No speed of sound effects! And assume magic air that doesn't become entrained with the treadmill motion. And don't throw in any other crazy stuff, either. In that case, the treadmill speeds up (still balancing the plane's thrust force) and the plane stays in place until the engines run out of fuel. I imagine the treadmill goes pretty fast at that point. The plane stays put until the fuel's gone, at which point the magic treadmill whips it backwards. H. Backwards, shmackwards. Now we're getting somewhere. What if we had infinite fuel? Then the wheels keep going until they're running near light speed, and relativistic effects take over. The wheels get smaller, I suppose... I. None of that! No relativity Hey, wait a minute. Back up. Suppose we have *zero friction* bearings and tires. That doesn't seem so unreasonable for a thought experiment. Well, zero friction tires would mean they just skid on the runway, since nothing turns them. So the plane will take off, tires motionless, and the treadmill won't move. J. Hey! Quit it! I already said the tires don't skid! Sorry. Just friction on the tire/treadmill interface, then, but none in the bearing or sidewall. With zero friction in the bearing, you lose the friction coupling between the treadmill and the jet. But you still have inertial coupling. The wheels *accelerate*, and that acceleration takes force. Now you have the same case as you do *with* friction. The jet stays stationary as the wheel accelerates; the wheel just accelerates faster. K. Well, how about the other way around? *Massless* wheels, but you still have friction? Here it starts to get complex. As you accelerate the wheels, the bearings will change shape and heat up and so forth, so it's reasonable to guess that the "friction coefficient" goes *up* with increasing speed. If that's the case, then when the engines start, the treadmill accelerates up to whatever speed will give *enough* friction to balance the thrust. The plane stays stationary, wheels rotating at some reasonably constant (but large) velocity, dissapating the engine power through friction. L. But I want massless wheels and a *constant* coefficient of friction. Indestructable wheels, remember? None of this handwaving "it's gonna get bigger" crap. OK. It *is* a thought experiment. With a limited "friction coefficient," only a limited amount of energy can be absorbed by the friction. When the engine lights off, the treadmill instantly accelerates to infinite speed. It's never able to counteract the thrust force, and thus plane takes off, leaving the infinitespeed treadmill behind. M. Ah. OK, one last step. What if we had no bearing friction *and* massless tires? What happens then? Pretty much the same thing. There's now *no* energy losses in the wheels and tires, *no* coupling between the treadmill and the planeno bearing friction, no inertial effects, no air resistance, and no way for the treadmill to affect the plane's motion. The same thing would happen as above, with the plane taking off, leaving the infinitespeed treadmill behind. However, there's one added interesting thing: This is now an unstable runaway system. There's no resistance to treadmill motion, and a positive feedback circuit. Imagine the poor mechanic who bumps a wheel, setting it in motion. A very slight roll by the tire is sensed, and the treadmill luches forward. The tire goes faster, the treadmill goes faster, the tire goes faster.... Since we've posited an instantlyaccelerating treadmill and no relativity and no air resistance and no wheel inertia, the treadmill goes from zero to infinity in no time flat. Try to keep your balance on that. Pick your scenariothey're all correct. 
#67




Excellent. There is one additional scenario. If the magic treadmill has zero friction in the direction opposite the plane's moement then it presumably has zero friction in the smae direction the plane is moving. In that case as the plane moves forward the whelels will not move (they have intertial resisitance) and the treadmill will move with the wheels. Since the wheels are not rotating they have no speed according to your scenario C, and the magic treadmill will not provide any force to resist them. In this case the airplane takes off and the wheels do not rotate.

#68




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#69




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Nonetheless, unless the treadmill is allowed to accelerate without limit, put me in the "plane takes off" camp. 


#70




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I don't understand why the wheels wind up rotating twice as fast as they normally would. Lets say the plane needed air traveling over the wing at 2 miles per hour in order to take off. Normal "real world" scenario. Plane's engine is pushing the plane forward at 1 mile per hour. Plane rolls onto a treadmill, and the treadmill comes up to a speed of 1 mile per hour. Plane stops moving forward. Plane's wheels are moving at the same 1 mile per hour. Plane accelerates to compensate.. such that were it not on a treadmill, it would be traveling at 2 miles per hour. Treadmill increases speed at the same rate to 2 miles per hour to compensate. Plane never moves forward. Plane's wheels now moving at the same 2 miles per hour that the treadmill is moving backward. No air is moving over the wing, plane remains stationary on the ground. I don't see where anything in the treadmill needs to be able to be capable of infinite acceleration (thus taking this out of the real world, into the realm of ideal physics) or the wheels move at twice as fast as they normally would. Can someone please explain to me the part of this mechanism that's like a rope, tied to a wall beyond the treadmill that the plane is pulling on to move forward? I don't think I'm moving from the real world (BR1) to the ideal/theoretical (BR2) unless you account for the treadmill's ability to compensate smoothly and perfectly matching the plane's acceleration . I am seeing where there might be an issue if we were talking about a prop driven plane where the engine is pushing air over the wing surfaces, but i am not even sure that these forces would have enough effect. (Yea, sorry folks, it got linked on BoingBoing to article to an article in the Times, which lead back here.. the discussion is coming back.. and the hamsters are gonna get a work out.) 
#71




What is the sound of one thread awakening?

#72




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So. How can the speed of the treadmill match the speed of the plane if the treadmill is moving and the plane isn't? It depends, of course, on the interpretation. In your scenario, the speed of the plane with respect to the treadmill matches the speed of the treadmill with respect to the ground. Nothing wrong with that. However, other people interpret the question as requiring the speed of the plane with respect to the ground to match the speed of the treadmill with respect to the ground. In that case, the plane's speed with respect to the treadmill is twice its speed with respect to the ground. Since (we assume) the plane needs to hit a certain speed with respect to the ground to take off, the wheels (which are running against the treadmill) must be going doublespeed. Quote:
In this case, ask yourself this: what limits how fast the plane is trying to go? You arbitrarily cut off your example when the treadmill goes two miles an hour. However, unlike a plane on a nonmoving runway, resistance to forward motion doesn't increase with increasing speed. So, with a particular amount of engine thrust, nothing prevents the plane from trying to go faster and faster and faster. Quote:
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#73




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If the plane has sufficient speed relative to the ground (or more accurately the speed of air over the wings), then it has to be able to take off period. If the plane's take off velocity is air moving over the wings at 2 miles per hour, it doesn't matter if the wheels are moving 2 miles an hour or 4 miles an hour, it's going to take off. The only way I can see the "problem" being any sort of a puzzle at all is if the plane is kept stationary relative to the ground by the speed of the treadmill. And I think that's the scenario you were explaining when we got to.. Quote:
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To elaborate, it seems like you're telling me that even without increasing the thrust, the plane will continue to accelerate and the treadmill will have to go faster and faster and that's not making sense to me. OK.. I just reread that last quote. I'm pretty sure you're discussing an element of fluid dynamics that comes into effect if the plane is actually moving relative to the ground, but can't then follow that to a point that supports any supposition we've mentioned. 
#74




zut is awesome. I hope, at this point, we all agree that when the belt matches the plane's air speed/relative ground speed, the plane takes off. But I think zut has made the "belt matches wheel speed" answer far too complex. And Cecil? Well he's just plain wrong.
Think of a toy airplane with freespinning wheels, just as a real airplane has free spinning wheels (like rollerblades, but unlike a car, a concept we all should agree on at this point). If I were to hold the plane in my hand and set it down on an actual treadmill traveling at 10 mph, the treadmill itself would push the wheels at 10 mph in the opposite direction, with zero thrust applied. And the plane, being pinched steady in my hand, would have an airspeed of 0 mph. Increase the speed of the treadmill to 20 mph, and the plane’s wheels would travel in the opposite direction at 20 mph, and the plane would still be held steady in my hand with an airspeed of 0 mph. Therefore, the paradox does not exist as Cecil suggests. There is no requirement whatsoever that the belt speed would force the wheel speed to double. Now, of course, I could simply move my hand forward independently of the wheels and overcome the speed of the treadmill — the way thrust would work, the way pulling the rope would work if I were wearing rollerblades on a treadmill — and the plane would move forward, attain lift and take off. And in the real world, that’s exactly what would happen, and the plane would fly. Aha? I got myself? No. The instant my thrust overcomes the friction and the speed of the treadmill, the wheels would be moving forward faster than the treadmill is moving backward, thus violating the spirit and rules of the question that the treadmill and wheels are always moving at identical, opposite speeds. In order to adhere to the rules of that question, thrust would never be allowed to overcome the friction, the wheels would never spin faster than the treadmill, and any actual forward motion is disallowed by the rules themselves. Therefore, so long as the treadmill can INSTANTLY adjust for any change in wheel speed and always match that wheel speed, the plane will continue to have an airspeed of 0 mph. 300 mph belt, 300 mph wheels, 0 mph airspeed. No airspeed, no lift, no flight. It may be overly strict, and I agree it’s a poorly worded, unintentional variation of the REAL question where the belt matches the plane’s speed. It's no longer about physics, it's about semantics. The question itself dictates that forward motion — any airspeed or relative ground speed greater than 0 mph — simply cannot occur, because that would require that the wheels move faster than the belt. Forget all the other complexities outside that simple argument. The plane cannot, and will not, take off under these rules. 


#75




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When the plane's engines light off, they produce thrust that pushes the plane forward. In order for the plane to remain stationary, the treadmill must do *something* to counter that thrust force. About the only thing the treadmill *can* do to counteract the thrust force is to accelerate the wheels, thereby transmitting a force. How else would the treadmill hold the plane stationary? Quote:
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(Note that there could be many different answers here, because it's possible friction increases with bearing speed, and tires will ultimately fail, and so forth and so on. But this is a thought experiment, and it's up to you to outline your assumptions.) 
#76




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Ok.. Let me back up and check my assumptions again. A place, given a certain level of thrust (x food pounds) will travel along a normal runway at speed (y miles per hour). If, instead of a normal runway, that plane is traveling along a treadmill that is moving in the opposite direction of the plane's travel also at speed y miles per hour, the whole thing will remain static, the plane will not move relative to the ground. At the same level of thrust, the plane will remain in the same place. As long as any change in thrust on the part of the plane is matched immediately by a corresponding change in speed of the treadmill, the plane will remain stationary relative to the ground. There is no speed at which this system breaks down if the maximum speed of the treadmill is greater than or equal to the maximum speed that the plane's maximum thrust can provide. 
#77




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foot pounds 
#78




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If a plane is moving down a runway at a particular speed (y miles per hour in your example), much of the thrust force is doing one of two things: either accelerating the airplane to go faster, or overcoming wind resistance. Since, in the treadmill example, you're assuming that the plane *doesn't* move with respect to the ground (or air), then it *doesn't* accelerate, and there's no wind resistance to overcome. A plane moving y miles per hour on a runway and a stationary plane on treadmill wich moves at y miles per hour are two different things. It's that difference that makes the problem more complex. 
#79




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Ok, yes there is a difference is the plane on the treadmill vs a plane that is moving relative to the ground because you will get wind resistance if the plane is moving relative to the ground. I can see that. But the only different I see there is at a lower level of thrust will be required to maintain the same "speed". The example still seems to hold that as long a the treadmill keeps the plane motionless relative to the ground, and thus no air moves over the plane's wing surfaces, that airplane will not leave the ground. The guy in the cube next to me likes the realistic view.. the plane rolls onto the treadmill, the treadmill is crushed by the weight of the plane, the plane takes off. 


#80




Let me paste in my email to BB.
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If the wheels have friction, then the friction from the belt on the wheels provides backward force to counteract any thrust, and the velocity changes so that these balance out, keeping the plane stationary. In the first case, the universe explodes in a puff of logic. In the second case, the plane cannot move. End of story. 
#81




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The problem is that (approximately) the level of thrust required to maintain a certain speed does not depend on the speed itself. So, for example, suppose you need 50 pounds of thrust to keep the plane stationary on a treadmill moving 2 mph. If the treadmill's moving 3 mph, the you need about 50 pounds of thrust to keep the plane stationary. If the treadmill's moving 10 mph, then you need about 50 pounds of thrust to keep the plane stationary. If the treadmill's moving 100 mph, then you need about 50 pounds of thrust to keep the plane stationary. And on and on and on. So. What happens when the engine produces 51 pounds of thrust? There's no speed where the additional 1 pound of thrust will be balanced. So the additional 1 pound of force goes into accelerating the wheels. And as long as you keep the engine lit at 51 pounds, the wheels (and the treadmill) keep accelerating and accelerating and accelerating until the tires blow or the engine runs out of fuel. 
#82




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__________________
John W. Kennedy "The blind rulers of Logres Nourished the land on a fallacy of rational virtue."  Charles Williams. Taliessin through Logres: Prelude 
#83




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This is one of the ways on interpreting the “the speed of the treadmill matches the speed of the plane”, and it’s perfectly valid. But you then make this assumption: Quote:
Consider a plane going down the runway at 5 mph. Lets say the wheels have to rotate once per second at this speed (I have no idea of the real speed). Now the plane drives up on a treadmill running backward at 5 mph. What happens? Does the plane stop relative to the ground? Almost certainly not. What happens is the plane continues to move forward at about 5 mph relative to the ground, but the wheels are now turning twice as fast (twice per second instead of only once). Now imagine a car going 5 mph drives up on that same treadmill. What happens? Does it continue forward like the plane? No, unlike the plane, it stops moving forward relative to the ground. Why the difference? With the car, the thrust of the engine is transmitted through the tires pushing back on the ground. By counteracting that movement with the treadmill, the car no longer moves forward relative to the ground. But the plane is pushed by the engines directly, not through the wheels. The thrust is not transmitted through the tires. They just freewheel. It’s as if the plane is pushing directly against the air. It’s not, it’s an action/reaction kind of thing, but in this case the effect is the same. So all that happens on the treadmill is that the wheels freewheel at a higher speed to make up for the fact that the treadmill is going backward, while the plane continues moving forward relative to the ground pretty much as if nothing had changed. So it takes off normally. Now if you make one of the other assumptions about “the speed of the treadmill matches the speed of the plane”, things can be different. But in your specific example, I think this is where you go wrong. 
#84




A different Problem with this...
Sorry if this has been explained elsewhere, but I haven't seen this covered...
This is a different look at why this seems to be highly problematic... Okay, a typical commercial jet needs to reach a speed of 150 to 180 miles/hour to lift off from the ground. If the plane achieves this speed on the treadmill (which is standing still relative to the earth), and it achieves takeoff speed, how does the plane suddenly go from 0 mph (again, relative to the earth) to 180 mph... This would be less of a takeoff and more of a launch. And even in scenarios where a rocket launches, the physics are much different. Someone please explain to me how the plane would make this seemingly miraculous jump from 0 to 180mph. cheers! 


#85




Please explain. Why would it be a sudden jump? The plane would gradually get up to speed, just like it would on a stationary runway.

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Well done. 
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I do understand a difference between the thrust being transmitted to the air by the engines of a plane vs the thrust being transmitted to the ground. I just don't see, when the airplane has less not reached takeoff levels of air moving over it's wing, how that matters. Whether the thrust is being transmitted through the wheels or the air doesn't seem to matter to me. I am still seeing this as "the ground is moving backward at x miles per hour, the thrust of the plane is moving it forward at x miles per hour, x from both sides cancel each other out." So is there some fact you are utilizing or step that you're not explaining? Is there something so implicit to your explanation that is just so very obvious (to those who do know it) that you're not explaining it (to those that don't get it)? 
#88




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However, I think Fzplus is interpreting the problem more as a thought experiment. In other words, he's ignoring the reallife effects on tires and bearings, and he's explicitly assuming a frictional torque that increases with speed. There's no need for infinite friction here, just wheel assemblies that will withstand the entire engine power being dumped into them as frictional heat. A tall order, yes, but a perfectly valid thought experiment. Quote:
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#89




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Okay, Assuming that plane is on a treadmill, and it is moving at a speed which progressively increases to 180 mph on that treadmill, but if you are not on the tredmill (say standing and watching from 50 ft away) the plane is moving at 0 mph relative to your position  when the plane "takes off" it suddendly should be moving at an airspeed of 180 mph relative to your position. There seems to be a basic problem with relativity here; or am I missing something? 


#90




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Perhaps the fact I'm not explaining is this: F=ma. Force equals mass times acceleration. If the forces aren't balanced, the object (plane, car, whatever) must accelerate. Let's back up to a more intuitive analogy. You're sitting in your car, cruising down the highway at a steady speed. Your foot's on the gas, the engine's delivering torque to the wheels, and the wheels are applying force to the road. With me so far? But you're not accelerating; you're staying at a steady speed. That's because the wheel force is exactly balanced by opposing forces: hysteresis force in the tires and air resistance forces being the two big ones. All forces add to zero, and you don't accelerate. If any of those forces change, your speed will change (because F=ma, or rather a =F/m). For example, you let off on the gas. The force pushing the car forward is now less than the force opposing the car, and you slow down (because F=ma, and negative total F means a negative total a). The nice thing here is that the air resistance force is a function of your velocity, So, as you slow, the air resistance force decreases, and eventually the forces are again equal, and you're travelling at a constant velocity. Likewise, if a tailwind suddenly springs up, the air resistance decreases, the forces are no longer equal, and (unless you let off the gas) your car accelerates (because F=ma).  Now, back to the airplane. Look at it from a force point of view, not a speed point of view. During a normal take off (on a runway, not a treadmill), the engines produce a force. That force is resisted by wheel friction, tire hysteresis, and air resistance. Normally the engine thrust is greater than the resisting forces and the plane accelerates (F=ma, right?). However, you could probably roughly match engine thrust force to some steady speed. If the engine produces just a little bit of force, the plane will accelerate to (say) 1 mph, at which time the air resistance force increases just enough to completely balance the thrust, and the plane stays at a constant 1 mph until it plows off the end of the runway. With a little more thrust force, the plane will accelerate to 2 mph, at which time the air resistance force increases just enough to completely balance the thrust, and the plane stays at a constant 2 mph until it plows off the end of the runway. And on and on and on. But once you put the plane on a treadmill, this force balance is no longer valid, because if the plane stays stationary, there is no air resistance. Suppose you fire the engine up to produce a little bit of forcethe same little bit of force that pushed the plane to go a constant 1 mph on the runway. What happens? The thrust force is the same, but the opposing forces are different: there's no air resistance. So the forces don't balance when the treadmill goes 1 mph. It's a different set of forces. So what does happen to the plane on the treadmill? Well, it depends on what you assume happens to the other forcesthe hysteresis and the bearing friction and so forth. Different assumptions lead to different answers...but one thing that's for sure is that in this case, the overall forces are different from the nontreadmill case, so the acceleration (and the velocity) must be different too. 
#91




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So, "If the plane achieves this speed on the treadmill (which is standing still relative to the earth)...", WHAT is standing still? The treadmill or the plane? And it is standing still relative to WHAT? The air? The ground? The treadmill? WHAT is achieving this speed? Relative to WHAT? The air? The ground? The treadmill? Using different assumptions will get you different answers. 
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#93




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*And even in those situations, the plane still takes off, though for different reasons. But let's not get into that right now. 
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Unless there is some force I'm not aware of acting here, it takes a pretty significant speed of air moving over the wings of the airplane before there's enough lift for air resistance to become one of the major factors. Until that lift is present, I don't care if the engine is attached to the wheels or not, it's still transmitting that force in part through those wheels, and the treadmill moving backward at the same rate as the plane is moving forward will prevent that lift from ever occurring. 


#95




Input from a newbie:
To all those who say the plane takes off with the wheels going twice as fast: You seem to be forgetting that it is the speed of the wheels we are measuring, not the speed of the plane. And by speed of the wheel, I am interpreting it as (distance around the circumference of the wheel that has rotated) / (time in which it has taken to do this). ie, if the circumference of the wheel was 3m, and it takes 3 seconds to perform a complete turn, the speed of the wheel as I interpret it is 1m/s. If the question had said that the belt matches the speed of the plane, then yes  it would take off with the wheels going twice as fast. But it matches the speed of the wheels, so with the wheels going twice as fast.. the belt goes twice as fast also, keeping the plane still. I'm very much in the 'plane does not take off' camp! 
#96




Oh.. and Mr. Emerson, your scenario is not my scenario. At least from my point of view it doesn't matter how quickly the wheels are rotating, it's a matter of whether the plane is moving forward or not. I'm still in the plane not taking off camp, but I'm also pretty sure that the place taking off camp knows something that they have not expressed in a way to enlighten me.
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Yet, I'm still not seeing the same thing happening if I make the mental switch back to the treadmill. Lets take the closest thing to a real world version of this scenario.. a pontoon plane vs. a pontoon boat. Both having the same weight, both having the same displacement in the water. The pontoon boat is acting against the water with a prop propeller in the water. the pontoon plane is acting against the air. Put both of these things in a fast moving river, point them upstream and start the engines. Prior to the point that the plane's speed decreases it's water displacement, what difference is there in the amount of force to move the pontoon plane upriver against the current compared to the pontoon boat. Similar to the treadmill exercise, the plane is not acting against the ground/water, it's acting against the air. A boat or car is acting against the ground/water. Are these similar enough for whatever the "something" is I don't get to become clear enough for someone to point out? 
#97




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The plane’s engines push directly on the plane. They push the same if the plane is on the ground or in the air, or on skis on the water. The wheels do nothing but spin, their only function is to reduce friction between the plane and the ground. Imagine it like this. The plane has no engine. Way down at the far end of the runway is a winch, with a twomile long cable that comes all the way back and attaches to the nose of the plane. The winch starts to pull the plan the plane forward at 5 mph relative to the ground. At the one mile mark, the plane rolls up onto a treadmill that is running at a constant 5 mph backwards. What happens? Does the plane stop relative to the ground? Of course not. The winch doesn’t care about the treadmill, it just keeps sucking that cable in at 5 mph relative to the ground. The only way the plane could stop is if the cable pulled the nose off. The only thing that changes is that the wheels on the plane have to spin twice as fast to account for the fact that the plane is moving forward at 5 mph relative to the ground, while the treadmill is moving backward at 5 mph relative to the ground. So the plane happily rolls right across and off the treadmill and on down the runway. So the thing to understand here is that the plane’s thrust comes from the action / reaction of pushing the air backward, and the “push” is directly on the part of the plane where the engines are attached, just as if there actually were a cable tied to plane and pulling it. The only way the plane could stop is if the engines break off, just as with the cable. The wheels are only along for the ride, and under anything like normal circumstances, you couldn’t possibly impart enough force to the plane by spinning them to slow the plane down much at all. 
#98




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Sorry, But I'm confused at what is being said here. If the plane is moving on a treadmill (I'm assuming that the treadmill is used so the plane will not move forward (off the treadmill) until it has reached takeoff speed). For example, lets say the "footprint" of the plane is 200 feet long, and the tredmill is 210 ft. (so the plane doesn't leave the treadmill, but the treadmill "spins" to accomodate the idea that the relative surface (and spin) of the treadmill allows the plane to move "forward" at 180 Mph without moving across the length of the runway. If this is the case, the plane is moving 0 mph relative to anyone (or anything) that is not on the treadmill (this is what relativity is all about). Please explain how the plane is progressively increasing to 180 mph relative to the position of someone not on the treadmill, because the increase in speed in the relative space of the tredmill doesn't apply to anything not on the treadmill. cheers! 
#99




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#100




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Is the force required (provided by the plane's engine, the winch pulling, the boat/s propeller) to move all three of these things 2 miles upstream the same? Because unless there is something that causes the boat to exert more force to move that distance than the other two options, then I'm still missing whatever factoid, point of view or advance physics formula you're using to say that the plane still moves independent of the ground before it gets lift. Personally, I can see where the winch might actually require less, but I think that the plane, at best, exerts a level of force between that of the winched boat and the propeller in the water driven boat. 
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