Good analysis. I think the real catch for most people -- it got me at first -- is that we think in terms of things that accelerate by pushing on the ground. Cars. Our feet. And, of course, if you put one of them on a treadmill like that, it doesn't go anywhere. Airplanes don't push on the ground to make 'em go, so that intuition is straight up your mom.

If the forward speed of the aircraft relative to the ground, or non-conveyor belt area is 0 (as described by the problem), then the amount of air flowing over the plane is 0. Since the plane must have enough airflow over the wings in order for laminar flow to occur, then the plane will not take off.

QED

I agree with your analysis except for the assertion that zero airspeed is described in the problem.
What the problem says is that the conveyor belt moves at the same rate (but opposite direction) as the plane, not that the conveyor moves such that the plane is stationary.

As an exercise, take a billiards ball and roll it very slowly across a piece of paper. Then try to get the billiards ball to stay in place by pulling the paper out from under it in the opposite direction. The friction is insufficient to overcome the inertia of the heavy ball.

In this example, the ball is not accelerating so at a sufficiently slow rolling speed you might be able to get it to work. For instance, if the ball was stationary and you pulled slow enough, you can get the ball to slide along with the paper. But if you pull faster the inertial force will overcome the rolling resistance and the ball will begin to roll in an attempt to stay in place (it will move slightly backwards as a result of the non-zero rolling friction).

In the case where the heavy object is driven by a constant force and the rolling friction is quite small in comparison, pulling the runway out from underneath it will not make it stop; it will just spin the wheels.

I seem to recall that the concorde crashed because the wheels rotated too fast and the tires decomposed. So you had best not push this too far.

The concorde crashed because of a tiny crack in the wheel, which set of a chain of events.

Glad to see your analysis. Finally a decent scientific analysis, which makes sense.

Most people I've talked to have a singular problem. They read the problem too quickly and assume that the plane is not moving relative to the fixed ground. Until you can convince them the plane actually moves forward regardless of the speed of the conveyor, they simply won't hear anything else.

There is a very easy way to do this for people who believe the plane is not moving. If the plane is not moving forward then the conveyor belt must not be spinning backwards. This gets them to think about it again.

Semantics, and unnecessary complication.

The question mentions nothing of wheels, or friction, or acceleration.

This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

Forward speed of plane equals 'x', backward speed of ground equals 'minus x' - no relative motion of plane, no lift, no takeoff.

the problem is about more than pure mechanics (read: aerodynamics).

the origin of lift during powered flight is directly related to airspeed, as you correctly point out.

however, lift is provided by the differential air pressure between the upper and lower wing surfaces, as generated by the differential air velocity (that is why the upper surface is always more convex).

because the plane is largely stationary with respect to the surrounding air, there is essentially no air flow over the wings, and consequently, almost no lift.

one can argue that the engine will generate some air flow, but that flow will be restricted to a relatively small area in the engine's vicinity, and will be turbulent (that is why turbines are placed more than a meter below the wing in modern aircraft).

the difficulty of arriving at the correct conclusion-- NO TAKEOFF!-- is precisely the reason why wings on airplanes need to be as large as they are.

BallJar: I'm not sure how you can say in the same sentence that plane has a forward speed and yet no force of lift. I guess you're talking about speed relative to something else that is moving, e.g. the conveyor. However, since the conveyor doesn't start until the plane starts moving, there is at least an initial precedent for forward motion. In order for the plane to stop moving forward relative to the Earth, the conveyor would have to overcome the sizeable inertia of a heavy aircraft.

If the engines are going full-bore and yet the plane is not moving (relative to the earth), then the conveyor must be cancelling out this force. So answer me this: How is this force asserted upon the aircraft?

I'd love to see you answer this without referring to the "wheels" or "friction," but of course this isn't possible. If there were no friction, then the wheels would spin freely and no movement of the conveyor could affect the acceleration of the aircraft. There is some friction, but you need to gain a sense of the relative magnitudes of force here. Wheels exist because they are low-friction devices. Aircraft engines are specially designed to provide a serious kick in the pants. Read up on Newton's Laws of Motion, specifically that an object in motion tends to stay in motion unless acted upon by an external force and that acceleration is force over mass, then try to convince yourself that the treadmill pushing against the wheel contact patches can account for an equal and opposite force to that of the aircraft engines.

Alex: You're still assuming that the aircraft can't get going very quickly. In a sense, you response is only slightly removed from those who assume the plane cannot move out-right. So I'll ask you the same question: What counteracts the force of the engines?

if this conveyer belt has a variable speed drive (implicit in having a control system), the belt necessarily has inertia. from this static perspective, this is conservation of momentum.

we can of course discuss the magnitude of this inertia, relative to the thrust generated by the engines and the mass of the plane, but we would be complicating the problem.

let's assume that the drive moving the belt can generate enough momentum to counteract that of the plane. what now?

Another way to think about it: imagine an airplane on a regular runway, but instead of it's usual landing gear, it has rods that slip into hollow tubes bolted to the ground (so that it is free to move up and down but cannot move along the ground plane). As long as the airplane cannot generate enough thrust to shear off the tubes, it obviously can't move air over its wings, and so cannot acquire any lift. (This is a shear force, not a frictional force, but the point is the same: if the plane cannot overcome the friction from the ground to achieve forward velocity, it can't take off).

Now imagine an airplane with teflon-coated skis sitting on a smooth-iced runway. In this situation, there's a miniscule friction force between the ground and the plane, and given enough runway, the plane can acquire sufficient velocity for takeoff with only enough thrust to overcome the drag from the air.

With regular wheels, the friction force the plane has to overcome is that associated with the wheel axles. If the runway is replaced with a conveyor belt that adjusted to try and keep the plane stationary, it would have to find the rotational speed of the wheels that created enough frictional force in the axles to counteract the thrust of the airplane.

Alex: The inertia of the conveyor belt itself is irrelevant. It could have an infinite amount of inertia, AND could have a perfectly "frictiony" connection to the aircraft tires. However, this just affects the slippage of the wheel on the conveyor. It does not change the fact that the wheel bearings are inherently low-friction. The friction in the wheel system is the only mechanism for force to be imparted from the conveyor to the aircraft. Unfortunately, tangential force applied to a freely-rotating wheel just isn't a good way to provide force on the center of mass of the wheel. In fact it's the worst non-zero way of doing so, hence the whole point of the wheel.

if the conveyer has unlimited inertia, and the frictional coefficient between the airplane wheels and the conveyer is infinite, won't the plane remain stationary with respect to the surrounding air?

am i misunderstanding something subtle or obvious?

The frictional coefficient is a value bounded between 0 and 1, 1 meaning that there's perfect friction between the two surfaces. If there were perfect friction between the wheel and the conveyor, that just means that the wheel won't slip at all. The important thing is the friction coefficient at the axle. If this is 1, then the wheel doesn't rotate, and you have a situation where the plane will move at the same velocity as the conveyor.

I don't know why the inertia of the conveyor belt would be relevant at all. Inertia is the tendency of a body to maintain it's current velocity. The only thing this would affect would be the difficulty of adjusting the conveyor's velocity.

Alex: Perhaps this is subtle... there is friction between the tires and the conveyor, which is what makes the different between the wheels skidding along the surface and actually spinning. But there is also friction at the interface between the rotating wheel/axel elements of the wheel and the non-rotating elements. THIS interface is the source of any affect the conveyor might have on the acceleration of the aircraft.

If the wheel/tarmac interface is infinitely frictiony, then the wheels won't slip. They will spin with a tangential velocity exactly matching that of the conveyor. However, if the axle bearing were friction-free, the wheel could spin as fast as it wants and have no affect at all on the aircraft velocity.

It's the friction of the axle that is key in this question. How much force is imparted on the non-rotating elements of the aircraft by the action of spinning the wheels? Is that force sufficient to completely counteract the aircraft engines? It will have to be if you expect the aircraft not to move relative to the Earth.

What I'm waiting to hear from anyone on the "stationary aircraft" side of this discussion is a description of how the axle bearing friction can possibly match up to the thrust of the engine(s).

Remember that the engine thrust can essentially be thought of as constant, whereas the wheel bearing friction is going to be a function of wheel rotation rate. If the airplane is to actually *NEVER* move at all, then the wheel friction would have to counteract the engine thrust even when the aircraft has only just started to move. If the wheels turning at 1 RPM cause sufficient frictional drag on the aircraft to counteract the engines, then obviously wheeled vehicles would never have gotten off the drawing board. I think we can discount the "totally stationary" case as preposterous.

So then, is there some non-linear effect that comes into play at higher speeds? I contend that there isn't. The wheel friction obviously doesn't cause any problems for planes taking off on normal runways, so at least up to the rotational speed necessary to allow the plane to take off, we can discount the wheel friction. The conveyor will never reach a speed faster than that of a plane at the moment of liftoff, so the wheel speed of a plane on the conveyor at the moment of takeoff would only be twice what is normal...

So to prevent takeoff we must make the assertion that somewhere between v(takeoff) and 2*v(takeoff) a hugely non-linear friction effect takes hold and prevents the aircraft from accelerating.

As far as I am aware no such effect exists.

I've given up trying to make all my friends understand why the plane takes off, but this explanation worked with a few people:

Imagine a plane flying three feet over a conveyor belt. The plane slowly extends its landing gear until a single, small wheel touches the belt. What happens to the plane? Does it come to a screeching halt? Or, does the plane continue in the air as the wheel spins really fast?

Of course, the plane continues in the air as the wheel spins. The conveyor belt exerts no significant force on the plane.

The "no takeoff" people must believe that my plane comes to a screeching halt as soon as the wheel touches the belt. But, that doesn't make intuitive sense to most of them.

Bonzo: That's a good example. For anyone out there who is handy with physics and still thinks the plane can't take off, consider the problem from the frame of reference of the conveyor. In this frame, the airplane accelerates away from the conveyor at some rate while the earth (and air) accelerate away from the conveyor at half that rate. It's exactly the same problem with the same forces and result, but from the frame where the conveyor isn't moving, it seems a lot less intuitive that the plane would somehow cease being able to accelerate. :)

Oh, man - you guys could all make great livings as bureaucrats.

Of course I'm talking about speed relative to the conveyor - this is a simple problem, and everyone is making it much too complex (I guess you've earned the PhD, might as well use it...) It's a frame of reference question - in order for the plane to lift off, it must move forward in relation to the 'static' air around it - however, as it moves forward, the conveyer moves in reverse - the plane stays motionless with respect to the 'static' air around it. Therefore, no lift.

All this discussion of friction and wheels, gravity, drag, etc. is irrelevant. It's a simple child's riddle, not a graduate thesis. The postulate is that the motion of the conveyor backwards keeps the plane stationary.

Sheesh.

There is a theoretical velocity for the conveyor belt that could prevent the plane from taking off. It would be determined by the amount of thrust the plane could put out as well as the frictional coefficients at the tire/runway interface and at the axle. If the wheels never slip, and the frictional coefficient at the axle is high enough, then that velocity doesn't even have to be very large. Of course, no real plane wheel would have a high enough frictional coefficient to actually let this happen... but we are talking about giant conveyor belts, so how is reality a part of the equation?

BallJar: Au contraire! I agree that the problem is simple; the governing equation is as simple as F=ma. If you're right, and the plane doesn't move, then somehow the conveyor must impart a force equal to and opposite that of the engine(s). Simply implying that the conveyor achieves this doesn't make it so. And, in this case, your intuition is letting you down.

It's the fact that you don't understand force balance and the mechanism by which a conveyor belt causes its "contents" to move that make the problem seem so obvious to you. That's what makes this question so popular; it seems obvious to everyone, despite some people coming to a conclusion based on physics and others based on intuition.

You said, "as [the plane] moves forward, the conveyor moves in reverse..." Correct; this is given in the problem statement. But your next phrase, that "the plane stays motionless with respect to the air" is where you've made an jump based on intuition that does not hold.

In order to make your argument hold water, you must describe why this is the case. We all agree that if the plane doesn't move it doesn't take off. But your argument is simply that the plane doesn't move, QED—and that's not compelling at all.

Part of the issue, to my way of thinking, is that the question is poorly formed. It doesn't specify whether the control mechanism causes the conveyor to move at a speed (relative to the ground) equal to the plane's speed relative to the ground, or to the plane's speed relative to the conveyor.

If it's the former (which seems the more sensible), then the plane takes off, no problem. If it's the latter, then we have a problem, because no upper bound is stated for the conveyor's speed (or its acceleration).

Assume for a moment that the plane's wheels are indestructible and have a non-zero coefficient of friction. As soon as the plane's jets overcome its inertia and the plane begins to creep forward, the conveyor will accelerate to whatever speed is necessary (5000 kph? 100000 kph? 10000000 kph?) to prevent the plane's speed relative to the conveyor from exceeding the conveyor's speed relative to the ground, by spinning the wheels fast enough for their friction to overcome the force from the jet engines.

In other words, it IS physically possible for the conveyor to stop the plane from moving... under certain insane assumptions.

Q: assuming tangential force due to friction on the bearing is sufficiently high, and the thrust on an engine maxes out at some value F, and thrust on the conveyor is infinite, and friction on the wheel to conveyor is not perfect (1); will the plane take off?

The correct answer to this problem has been posted by Alex, although it seems to have been largely ignored. THE necessary condition for lift is the relationship between the wings and the air. As far as whether the plane can take off, what's going on underneath can be safely ignored. If we isolate our system to the wings and the air you can see that neither is moving relative to the other and as such there is no aerodynamic activity going on, which would be necessary for lift. The plane cannot take off.

i am still trying to understand what is being missed (by me versus by the frictional dispersion theorists). can we simplify the problem?

what about a person standing on a treadmill, and then beginning to walk, with the treadmill matching the person's velocity (read: momentum)?

can the person attain any velocity relative to an observer?

Alex: Allow me to change you example to a car driving on a treadmill; it's the same result as a person walking on a treadmill. In this case, the vehicle's speed relative to the Earth can absolutely be kept at zero. The reason for this is that the car exerts its thrust via wheel friction on the treadmill. It applies its thrust and thus accelerates and decelerates in the treadmill frame of reference (I'm ignoring air resistance here). The treadmill can accelerate in the frame of the Earth such that the car's velocity in the Earth frame is zero.

An aircraft, however, does not exert thrust via the wheels. It exerts thrust via the engines which are pushing on the air (which is in the Earth frame of reference). Thus when the airplane accelerates, it does so relative to the Earth/air frame. The airplane is not constrained by the conveyor's motion or lack thereof, and this is exactly why it has low-friction wheels—to isolate itself from whatever drag the tarmac/conveyor might present.

Back to the car: Think of a car sitting on one of those roller things that they used for emission testing when they need to get the vehicle up to speed while in a lab. The car accelerates its wheels, but they only succeed in spinning the rollers. The car can't go anywhere because all of the force it exerts is just transformed into rotational motion in the rollers.

If the car had a jet engine on board (or a propeller, or a rocket, etc.) then it could generate some force that wasn't applied to the free-to-roll surface on which the wheels were sitting. The force would be applied to the air around the vehicle and the car would move forward off of the rollers.

The car wheel/roller example is actually a perfect analog to what is going on with the airplane wheel/conveyor problem. In this case it is the conveyor that is attempting to exert force on the wheel, but the result is the same. The airplane wheel is free to spin just like the roller and will absorb the frictional tangential force applied by the conveyor into wheel rotational energy. Meanwhile, the aircraft engines are still pushing on the air and accelerating the plane relative to the Earth.

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MVB: I believe you can set the numbers such that the force of friction is large enough to counteract the engines, but this doesn't represent any realistic aircraft.

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CHRIS: We're all in agreement that if the airplane doesn't move relative to the Earth (and air) then it doesn't generate lift. But you've made the a priori assumption that it can't move. Please describe WHY the plane cannot move relative to the Earth as a result of the action of the conveyor.

This is a simple mechanics problem and F=ma cannot be ignored here. If acceleration in the Earth frame is to be zero, then the net force on the aircraft in the Earth frame MUST BE ZERO. The aircraft engines exert a forward force in the Earth frame. Please show that the conveyor will impart such a force on the plane in the Earth frame, oriented backwards, and equal in magnitude to the force of the engine(s). If such a force does not exist, then the net force on the aircraft is non-zero and it will accelerate in the Earth frame.

mser, agreed! but, let's do some discrete kinematics.

the source of the thrust does not matter (engine on air versus engine on wheel). what matters is that in the problem we are assuming complete coupling between the motion of the plane and the motion of the conveyer belt. in some infinitely small time interval, the plane moves forward (by virtue of engine thrust on air), and simultaneously the conveyer moves backward. think in the limit as delta Time -> 0.

Balljar hit it. All this argument over problem domain -- frame of reference vs mechanics/vectors.

Let's say that the conveyor does not kick in til the plane reaches 1kph (relative to the ground/air). Then what? Nothing. As the conveyor kicks in, the plane, to a ground observer, slows down and comes to a halt.

Re the other weird analogy of a plane flying in extending its wheels onto a conveyor, man, the plane already has sufficient airspeed for lift. In THIS example, we're trying to achieve that sufficient airspeed. This isn't a mirror image experiment. Sheesh.

The plane does not take off. This is not rocket science (literally).

ALEX: OK, I think I see where your argument is coming from. For starters, I do not agree with the assumption that there is complete coupling between the motion of the plane and the motion of the conveyor belt. I can see complete coupling between the conveyor belt and the *wheels*, but as the wheels are free to spin, one must take into account the friction interface between the rotating wheels and the non-rotating aircraft. This interface is not a direct coupling, and thus there are losses. As the wheels are designed to be low-friction devices, the losses are enormous (nearly complete loss!).

In the discrete sense, I see it like this: the conveyor moves some infinitesimal amount, which turns the wheels by a corresponding amount. This causes some amount of drag force on the aircraft body, but in the same dt, the engines are exerting an instantaneous force in the opposite direction. The question is one of force balance and I'm failing to understand how the friction balances the thrust.

I feel that the source of the thrust does matter—I think it is the crux of the issue. The engine thrust is in the Earth frame and is thus independant of the motion of the conveyor. The thrust from a car is applied relative to the conveyor and thus its affect on the Earth-frame motion of the car is subject to the motion of the conveyor.

CHARLES: If the plane decelerates when the conveyor starts up, then the net force on the aircraft in the Earth frame points backwards. Therefore... the force due to the conveyor must be greater than the force due to the engines. Please help me understand how this can be so.

Caveat (my turn to overthink):

Think of running on a treadmill. Say I'm running near the back of it, chillin at 10kph, which is the set speed of the treadmill. Me is stationary, or running in place, relative to a bemused ground observer. Now, I can indeed (knees willing) outrun the set speed on the treadmill were i so moved to do so, and I would move from the back of the treadmill to the front (all relative to a fixed-ground observer). If the treadmill adjusts in real time to my increase in speed, well, i don't travel from front to back so easily. But I still *can* make it to the front, depending on the treadmill's reaction time.

The idea of a lag time, however tiny, between the increase in thrust and the reaction of the conveyor is important. If the plane had *limitless* thrust and the conveyor sufficiently long, that delta would mean that the plane would eventually achieve sufficient airspeed to lift off, assuming gradual uninterrupted application of that limitless thrust (and applied faster than the conveyor's reaction time).

But again, we're overclocking our brains on this. I doubt it was meant to be this complicated.

Mouser said: "Therefore... the force due to the conveyor must be greater than the force due to the engines"

Wrong. Or at least not at all necessary. I'm just saying it would decelerate relative to a ground observer. For him, it looks like the plane slows down (and then halts), irrespective of whatever forces are going whichaway.

CHARLES: The running on a treadmill example is a poor analog because in that case you exert your thrust on the treadmill and thus in the treadmill frame. If the treadmill can react instantly to your running speed, it can keep you stationary relative to the Earth. In a sense, this is because all of the force you exert (via friction in your shoes) goes to "spinning" the treadmill and does not result in forward motion.

Look at the force balance for the treadmill runner. You exert some force via friction on the treadmill surface, oriented forwards. This translates to forward motion of your body relative to the treadmill surface. However, the treadmill is free to move backwards and the two motions can cancel each other out in the Earth frame.

The airplane is not subject to this, as its force is not exerted in the conveyor frame. The engines produce thrust in the Earth frame, and thus cause acceleration in the Earth frame. Any force applied to the airplane in the Earth frame as a result of the conveyor must be conveyed through the wheels.

As for your second comment, I'm afraid you're disregarding F=ma. Nothing accelerates (forward or backward) unless the net force vector is non-zero. In the observer's frame, if the plane is slowing down, then there is a net force backwards on the plane. Force vectors are additive, so the existance of a known forward force (due to the engines) requires a greater backwards force (presumably from wheel friction) in order to slow the plane down.

MOUSER: at the outset, with all at rest, there is only one set of forces/friction/inertia to overcome. Now, even while the plane is in motion (say still ramping up to 1kph) there is still obviously some friction between the wheels and the conveyor, obviously, as without it (ie in a frictionfree setting), there would be no motion at all (the wheels would have no friction to act against and turn).

Thing is, when the conveyor does kick in, there is a *new* force added to the mix (the backwards vector) that was not there at the time of the initial time-zero environment.

If the thrust stays constant, as our host has assumed, the plane eventually comes to a halt (again, for the umpteenth time, relative to fixed-ground/air).

It surprises me how some people can walk up to a person with so much knowledge and background and still say: "You sir, are wrong, despite the fact that you hold a Ph.d in Physics from MIT. Despite the fact that there are so many decent explanations of why the plane takes off."

Toon, it takes all kinds. Some people never question authority, while others only respect their own. Thanks for the links, anyway. I'll try to understand those explanations before coming back.

p.s. the earth is totally flat and we never went to the moon.

Why do you guys think the conveyor belt has anything to do with the thrust coming from the propellor or jet engines?

Please explain to me your reasoning why the minimal friction force in the wheel bearings will counter a force from the jet engine or prop that is several orders of magnitude greater.

The direction or speed the wheels are turning really plays no part in this problem, nor does the conveyor. The engine pushes against the air (and the airplane -equal and opposite and all that) (oh, which could be summed up as being rocket science), the plane moves forward.

I would not like to land in an airplane that has its wheels directly coupled to the ground. It would mean an immediate stop upon touchdown which would probably be painful, although you might die before you actually felt any pain.

it is true that the source of airplane's forward motion is the thrust of plane's engines on the air. however, if you agree that there is sufficient friction between the plane's wheels and the conveyer, then the force of conveyer's backward motion is transmitted to the plane.

consider the case of a plane with its engines off on a conveyer that is moving backwards. if you agree that the plane will move backwards, then you have to conclude that the plane will remain stationary when its engined are powered.

conversely, if you believe that the plane with engines off will remain stationary on a moving conveyer, then there is nothing to discuss, as the basic premise of the problem, ie coupling between the plane and conveyer, does not hold.

TOON: For the record, my doctorate is in Nuclear Science & Engineering, not physics. But my bachelors is in physics, and Physics 101 is really all that is required for this problem. Having said that, I'd like to point out that having a fancy-sounding degree does not make me right and I am willing to entertain the notion that the plane stands still; but I will not ignore Newton's laws of motion to achieve that end. :)

CHARLES: I'm afraid you have a fundamental misconception about how thrust is conveyed from an airplane engine. If it's a propeller, then the airfoil shape of the propeller blades creates a pressure differential front-to-back and the plane is effectively "sucked" forwards. If the engine is a jet or rocket, then the exhaust is pushing against the engine nozzle for a net forward force. In either case, the wheels on the landing gear exist only to reduce friction between the ground and the aircraft. If the wheels were frictionless, the efficiency of the aircraft thrust during takeoff would be 100%!

Yes, I do agree with you alex, that if there is sufficient friction to counter the thrust of the engines that the airplane wouldn't move. That's a lot of friction. Designers have been using the wheel and bearings for a long time and have learned to reduce friction to very small amounts. So small that you can virtually ignore any friction in this particular problem.

Imagine running a long cable from the end of the runway (we'll assume the entire runway is a big treadmill) down to a spring scale, and the spring scale is attached to the airplane. Start your treadmill and read the force of friction directly on your spring scale. It will be measurable, but minimal. Now take the same spring scale and attach it to the rear of the airplane and the end of the runway behind the airplane. Start your airplane and throttle it up. Note the huge difference in force.

The treadmill will not play any significant role in the airplane takeoff other than spinning the wheels at twice normal speed. You can simulate this with no treadmill by changing the diameter of your airplane wheels to a smaller size. It's *exactly the same situation*

ALEX: The force from the conveyor is conveyed to the wheels as rotational motion. There is something called "rolling resistance" that must be overcome before the wheel will turn, but in a low-friction bearing this is generally quite small.

Try the pool-ball experiment. Place a pool ball on a piece of paper, then pull the paper out from under it. If you pull slow enough, then the friction force is less than the rolling resistance and the pool ball will slide along with the paper. If you pull faster, then the friction overcomes the rolling resistance and the pool ball starts rolling in place while the paper slides out from underneath it.

This is the same coupling as between the ground and the wheel—the rolling resistance is transmitted to the plane's center of gravity, while the remainder of the force (the vast majority unless the force is tiny) becomes rotational motion in the wheels and does not provide a force on the plane.

Mouser: Heh, kottke.org lied then, since that's where I got the idea that you had that Ph.d.

Also, I didn't mean to imply that you should never doubt authority, but come on, there has to be a line somewhere. Unless, of course, people plan to revolutionize physics.

TOON: Yeah, I'll have to scold Jason for that. But we all know that he's knee-deep in gin most of the time anyway...

final comment: to conclude this argument. think to the last time you were on a plane. the plane has taxied to the runway, waiting for permission to take off. the engines are on, but not fully powered. the plane is stationary. why?

because the energy required to deform the rubber wheels to turn them exceeds that provided by the engine.

then, the engines are fully powered. no discernable motion happens for at least one second. yet, the engines are exerting thrust. lots of it. when the engines achieve enough thrust to deliver sufficient energy to the deform the wheels, the wheels allow for rotation, and the thrust can translate into motion.

in the problem, this plane is on a conveyer belt with sufficient momentum (read: energy) and sufficient friction/traction to move the plane backwards. though the engines are acting on the air, because the conveyer is acting on the plane by way of the wheels, the plane remains stationary with respect to the air, the flow of which is required to generate lift, which in turn is required to reduce the energy needed to deform the wheels. in this problem, we are discussing planes, not rockets. planes need wings. rockets do not.

this is the origin of lift during powered flight, and this is why the plane _does not take off_.

Sigh.

Okay, being somebody who has actually flown an airplane before, I know that before you take off you perform what is known as an "engine runup" You take your airplane to full throttle. Then you release your brakes. You don't move before you release the brakes!

Bob et al, the reason why the wheels matter is because the plane hasn't actually achieved liftoff at the outset of the problem. Once the plane is airborne, you're right, it doesn't matter a whit what the treadmill is doing. It could spin at near lightspeed and the plane would still continue flying.

But the issue is that the plane's thrust is essentially acting on the wheels cuz them engines is connected to something that happens to be, at the outset on the earth.

So friction matters.

We're counting things at three stages tho: Time One (nobody moving), Time Two (plane moving forward, conveyor motionless) and Time Three (plane moving forward, conveyor moving backward). Like Mouser says, the forces are additive. Is the *additional* backward vector at Time Three enough to retard the plane.

Additonal vectors count. What if the plane were then to start rolling up 60 degree incline?

What if this were a hydroplane at first moving forward in calm waters, then suddenly having to deal with a current moving against its preferred direction? Will a person on a bank see the plane slow down (given no increase in thrust)?

....

Y'know what? I get it. The friction between the wheels and the conveyor ONLY AFFECT THE WHEEL. It's a *freewheel* so once the initial friction has been overcome, there is nothing that conveyor can do to stop the plane -- it will only make the wheel spin faster is all. Mouser's point about the efficiency of the aircraft thrust with frictionless wheels finally allowed the penny to fall.

I am converted. I was wrong. Many thanks.

I don't quite understand why some people aren't getting this. I have one question for you: What part of the airplane makes the airplane accelerate? Once you realize that the force being pushed on the plane is much more than the friction, you can see the plane taking off even if it is on the conveyer belt, no matter what the speed of the conveyer belt is.

The wheels absorb the force the conveyer belt is putting on the plane thus not pushing against the airplane with the exception of some minute friction which will be much less than the force of the jet engines pushing in the opposite direction.

What's the problem?

ALEX: I think Bob is right on this one. Aircraft have brakes and use them to hold position while running up the engines. That's why you hear the engines screaming before you move, and why your first movement is often rather jerky—the brakes have been released and suddenly all of that engine thrust is available to roll the wheels. The prime reason for doing this is that it takes time for the engines to come up to full throttle, and you don't want to waste precious runway accelerating under less-than-full thrust.

Now it's interesting to point out that the brakes effectively prevent the wheels from rotating, which means that any friction from the wheel/tarmac interface is transmitted directly to the center of mass of the aircraft. If the brakes were on, then the conveyor would drag the aircraft backwards with it. But without the brakes, the wheels just spin and the plane accelerates happily on its way to flight.

btr and mser: you are missing the moral of the story. the wheels on planes are not merely ball bearings. they effectively transmit force-- to and from the plane-- under the weight of the plane.

ALEX: It's true, they do transmit force. And the weight of the plane is what makes the friction non-zero and therefore the transmitted force non-zero. But the key point is that the wheels are there to MINIMIZE the force transferred.

I think I have an easy-to-grasp way of looking at this:

Let's pretend you have a little toy airplane with wheels extended. Let's also pretend you have a treadmill handy. Hold the plane on the treadmill. Can you move it up and down the running surface? Sure. But what if the treadmill started moving? Would it be any more difficult to run the plane along the running surface. Nope. The wheels just spin faster is all.

CHARLES: That's exactly it. As long as you can see the external force of pushing the toy airplane along as equivalent to the internal force created by an aircraft's engines, it's the same problem.

Please see:

http://www.straightdope.com/columns/060203.html

The issue boils down to one thing: are the friction coefficients at the wheel axle and at the tire/conveyor interface great enough to allow the conveyor belt to counteract the thrust of the engines?

If the answer is yes, then the plane doesn't take off. If the answer is no, then the plane does. Done.

In the real world, the answer is most certainly no: the whole point of the wheel is to provide lots of friction between the tire and runway so that the plane doesn't get blown off course, and very little friction at the axle so that the runway doesn't counteract the plane's thruster too much. It's kind of dubious to claim the high ground by latching on to "the real world" when discussing giant conveyor belts, though.

In the math world, the answer is: if the friction coefficients are high enough, then it doesn't matter how much thrust the engines put out. In fact, if there's "perfect friction" at both the tire/conveyor interface and at the wheel axle, the plane will move at exactly the velocity of the conveyor (and the conveyor will move at exactly the velocity of the plane).

This argument has essentially devolved to:

A: x is greater than 4!
B: no, x is less than 4!

when nobody ever bothered to specify x.

CALAMBRAC: I think I covered this when I said, "I believe you can set the numbers such that the force of friction is large enough to counteract the engines, but this doesn't represent any realistic aircraft." See above.

MOUSER: I know you understand the issue, and yes, you touched on it. I thought I could clarify things a bit by taking the part about "realistic aircraft" and making it an incidental detail of the actual underlying question, which is:

How does the conveyor belt convey its force to the plane, and how do the engines convey their force to the plane, and how do these forces interact?

Here's another example that's effectively the same: An airplane has skiis instead of wheels and is trying to take off from an iced-over lake. The lake is so icy that a person can't walk on it. Can the plane take off?

Of course it can, for the same reason.

I am not smart and I have no scientific background so this may stink but it seems to me that if the military could simply build a conveyor system to lauch aircraft without runways, then they would. The cost of Harriers and similar aircraft that are developed to be a short or vertical take off and landing craft would surely be dismissed in favor of a simple and elegant conveyor system. No need to launch with a catapult from an aircraft carrier either!

Wow. A couple of remarkable things I noted here.

To Charles: a big shout-out! I was skimming through, shaking my head and saying to myself, "The real shame is that nobody is actually going to change their thinking..." and then you proved me totally, utterly, pessimistically wrong. You quite literally renewed some of my faith in the world.

(Yes, I have a PhD in physics. And yes, I like to teach.)

The other remarkable thing, to me, is how not-really-simple all this stuff is. It's really hard! You want an example? As far as I can tell, nobody in this discussion really got friction right. Check out the early discussion of "coefficient of friction". The frictional coeff doesn't actually tell you anything about the frictional force directly -- it tells you the ratio of the frictional force to the NORMAL (e.g., gravity) force.

I'm not picking on anybody here, merely pointing out that this stuff is objectively hard to intuit, and having a lot of practice with it is a huge advantage. I've spent a few dozen hours working on problems like this while TAing at Berkeley. Practice makes perfect.

Another thing that strikes me is that everybody noted that the plane's speed (V) appears twice -- once as the plane's velocity, and once as minus the conveyor belt's velocity. The remarkable thing is that I think all of us (at least me) initially assumed that the correct way to combine V and V was to subtract them (hey, why do F=MA if you can guess the answer?). That gives the idea that "Zero velocity is important here... must be the plane's forward velocity." Actually, you add them. Zero doesn't appear anywhere in the solution, but 2V does -- as the conveyor belt's final backward velocity. So it is kind of a trick question, because it violates our intuition that "Zero" is a much more likely way of combining V and V than "Twice V".

Finally, a note to Dave: a carrier's catapult is identical in function to a conveyor belt. So in one circumstance, they've done what you propose. However, (a) if you have room for a runway, then a runway is cheaper and easier than a catapult; (b) Harriers can take off and land in places that don't have either a catapult/arrestor system or a runway. So there's room for all three solutions. But a functional catapult/conveyor isn't actually all that simple or elegant.

Thanks, Robin. I do like a good argument, but I respect Truth more than my own ego. You're just talking past each other if you don't try hard to understand what your 'enemy' is saying -- and what's the point of that?

I agree that this isn't so easy. Even when I was on the wrong side, thinking i had the correct, simple answer, I only thought the others were overthinking the problem not that they were stupid. Not sure what was blocking that 'aha!' moment for me tho. It's like that classic vase/face thing; once you see the other image, it's hard to imagine how you missed it before.

Skeptic, that's a great analogy, too (if only cuz that one occurred to me as well ;-). Mouser, we really appreciate your patience in trying to explain it.

I have not yet read all the comments on here. So excuse me if this has been mentioned.

This problem requires an understanding of physics (which, admittedly, I´m not too great at) and an understanding of aircraft mechanics (I know a bit more about that).

Comparing cars or people on a treadmill to this airplane on a conveyor belt is the proverbial apple and orange comparison.

For a car or human the means of propelling itself forward (I´m Dutch and not good at the semantics of physics, sorry) is friction. Make a walking motion while wearing skates, you're not going to go anywhere like that.

Not true for an aircraft. Its engines push and pull the fuselage through the air with the wings creating lift. The wheels are there to eliminate friction as much as possible. Unlike a car, the axle of the wheels on an airplane is not connected to any sort of driveshaft going from engine to wheels. Such a driveshaft exists on propellor planes, but it doesn't go to the wheels, it goes to the propellor.
Imagine an aircraft without wheels on a regular runway. Suddenly the engines would have to overcome all the friction of the craft scraping against the runway. And considering the immense power of jet engines, I´m not entirely convinced that THAT would stop the plane from taking off.

If a plane were to take off from a runway made entirely of ice, it would have no problem doing so the wheels wouldn't turn as much because there is no friction to make them turn. Imagine the plane hitting a big patch of asphalt in the middle of that icy runway. Suddenly there's more friction to contend with. Result: the wheels start spinning, the plane will not noticably slow down. And then, a bit further on, the plane hits the conveyor belt already up to the same speed as the plane. Yet more friction to contend with. Result: The wheels start spinning twice as fast, but again, the plane will not noticably slow down.

So an aircraft will start moving. It may, at worst, take a little bit longer to reach the required airspeed for take-off.

Even in the case of a rocket engine (which does not have quite the same critical requirement for wing lift), take-off requires lifting the nose of the aircraft off the ground. Unless you can explain how this is done while there is no air flowing over the wings and ailerons, there is no lift and therefore there can be no takeoff. The speed of the wheels and the amount of thrust being generated are not the key to this problem.

I personally kept being able to see both sides of the argument and wasn't completely convinced until recently one way or another ("the plane's not moving foward, so there's no air going across the wing, so there's no lift... but the conveyor belt cannot keep the plane stationary no matter how fast it spins... but if the plane moves forward faster than the conveyor is turning, the premise of the question says the conveyor belt will just turn faster to match, so it keeps the plane stationary, after all, while the wheel's on the belt, the plane can't move faster than the wheel... etc...").

But I think I've come up with an analogy that's made it clear to me at least, and hopefully to others.

Imagine a skateboard on a conveyor belt that behaves according to the original premise. The board's been hacked with a motor. No matter how fast the board tries to move foward, the conveyor keeps it stationary relative to a reference point not on the conveyor.

Now imagine there is no motor on the board. Instead, the board's connected to a car (that's off the conveyor belt) by a chain. Those who believe the plane won't take off should then believe that a skateboard on a conveyor belt will be able to prevent a car from moving forward by chaining it in place.

While I haven't done real world experiments, I'm pretty sure the car will be able to move forward, and drag the skateboard off the conveyor, spinning wheels and all.

This is exactly the same situation as the plane. The wheels on the plane is unpowered, like a skateboard. The car off the conveyor belt is the jet engine. The jet will move forward and take off.

To Lionheart:
Raising or lowering the nose is done by using the flaps on the wings to create a pressure difference above and below the wing which will make you go up or down.

The speed of the wheels as you say, does not enter the equation. When the plane is going 300mph, the conveyor belt could be running at 1200mph in the opposite direction. Not taking wheel breakage into account, the plane will still take off.

Everyone needs to understand that an airplane is fundamentally different from a car or bicycle.
As said before, the wheels on an airplane are not motorised. They are not what makes a plane move. The engines are. Jet engines can only provide thrust in one direction, which is why airplanes can't reverse out of terminals.

The engines on a plane act on the air. What the ground does is completely irrelevant.
You know those 2 story bridges they(/you) have in America right? Imagine driving your car over the upper level. Think if this as the jet engines acting on air. Now imagine the lower level being such a conveyor belt that is matching your speed in the opposite direction. Think of that as all the effect the conveyor has on the airplane.
The two are completely seperate.

The wheels of the plane will spin as fast as they need to to pretty much negate all friction. Whether that is at half speed, full speed or ten times the speed, it simply does not matter.

The body of the plane WILL move forward, the wheels will be moving twice as fast. There will be airflow and there will be takeoff.

What people need to realize is that the forward movement of the plane is not bound to the ground...while the conveyor speed will be the inverse of the wheel speed, the plane will still be moving forward - in other words, even if the runway is conveying... the plane will still roll all the way down it and take off.

My initial reaction was that the plane will not takeoff because I was picturing a treadmill. Instead, imagine a conveyor the length of a runway, giving the plane the same space to roll down the 'runway'.

This analysis seems right to me now - the plane will still take off, but the wheels will be spinning twice as fast.

If I drive a car at 88mph and another car wooshes past in the opposite direction at 88mph the combined speed is 176mph, not 0mph and my speed is still 88mph - I still get to achieve time travel.

Plane goes forward at 100 mph.
Conveyer belt goes the other way at 100mph
Plane wheels whizz their little hearts out.
Plane takes off.

...or if I'm in a sailing boat, and the tide is going the other way, I still get to go sailing, because my hull is streamlined.

fun puzzle. I got it wrong at first.

I am by no means any more educated in physics than high school physics but let me toss this idea out:

For the longest time I couldn't wrap my head around how the plane in the question could generate forward movement. The plane must move in relation to the air (not the ground or the conveyor) to take off, correct? I couldn't figure it out until this notion came to mind:

I kept imagining a Cessna (or any prop aircraft) on a runway. Its engine powers up and eventually the plane rolls forward. The plane's engines are propelling the fuselage forward by moving the air around it. It's the same as a submarine. It pushes the water so therefore it moves. The wheels are really not a factor in the equation, they'll just spin faster on a conveyor, is all.

All the conveyor can do is counteract motion relative to the ground, not relative to air.

Think of it like this: would the plane ,or the conveyor, move at ALL if the experiment were in a vacuum? Nope. It's because the plane would never be able to generate forward movement. How's that plane generate that movement? Air.

ur right and wrong
im wrong and right

if the conveyor accelerates to the speed of the aircraft it will not fly

if the conveyor does not accelerate and remains the speed of the tires it will fly only with frictionless wheels.

but in reality it would never fly. there is no conveyor belt that goes a 100 mph backwards and is runway sized. There are no tires that would last or withstand the friction.

in reality its a bogus idea. like standing on the sun or jumping in a black hole

First off, the plane will move forward and take off normally. No problem there.

However, you imply that friction will increase continuously as the wheel speed increases, and that this continual increase in friction imparts a continuously increasing force (however small and insignificant) on the plane body. (Your sentence "before a wheel could provide enough friction ... to completely counteract an aircraft engine ... the wheel would be spinning so fast that it would come apart." implies that as wheel speed continuously increases, the force on the plane's body also continuously increases.)

Given the force equation for rolling friction: F = Fr * R * W, how does the wheel rotation affect F? (Fr = coefficient of rolling friction, R = wheel radius, W = weight)

Does the coefficient of rolling friction change with the speed of rotation? If not, what part of the equation is changing, so as to impart a force on the plane's body?

It is my belief that the once the plane's thrust exceeds the maximum force of rolling friction given by the equation above, the wheels impart literally zero additional force on the plane's body, regardless of their increasing speed of rotation.

Thanks for your time and effort. The only reason I ask for clarification of this tiny detail is because the "will not fly" crowd will latch onto any little detail to support their erroneous beliefs. P.S. the plane takes off normally :)

Drew: Actually I think you are completely correct. I was playing a bit fast and loose with the friction physics. Your treatment is correct in an ideal case; I was speaking slightly more generally to include things like thermal effects on bearing size, lubricants, etc. Nothing specific, just a general catch-all for real life engineering where chaotic and non-linear effects might creep in. These sorts of "engineering effects" would most likely manifest themselves as changes in the friction coefficient (Fr). But again, any effect these sorts of things might have on the acceleration of the plane would be negligible at a take-off wheel rotation rate that is only twice normal.

Nice write up, Mouser.

I'm certainly not well versed in physics, but I kind of like to think of this sort of problem in simpler terms.

A comparable example in my mind would be a car on a treadmill. If the car is being pulled along by a winch and the wheels are turning freely then the car is going to be pulled at an identical rate whether or not the treadmill is there or not (assuming as you did that the treadmill's speed is inverse to that of the car).

Sorry, but I have to ask...

If instead of a conveyor belt, as stated in the original problem we had a "jet propeled very very long board of some alien super-light material", floating on water, going in the oposite direction on the same velocity and aceleration of the airplane.

Would the darn airplane take off then?!

:)

Sorry to break the model originaly stated, but I just have to know if some kind of a jet-conveyor-belt would sufice to keep this stupid airplane stationary and stop it from flying!

Best regards...
Bruno Accioly

Bruno: Yes, with a jet propelled board of alien material acting on the wheels, the plane will still take off. What the ground (or whatever surface it is) does is largely inconsequential.

To all people who think the plane can't take off because a conveyor belt is acting against the wheels, let me ask you this: How does a plane stay airborne? The wings only make it go up and down, they don't provide any thrust.

The wheels aren't turning in the air. Heck, they're retracted to make for a more streamlined body of the plane. So how come a plane doesn't start slowing down once its wheels are off the ground? Right, because it's the jet engines/propellors that provide the forward movement.

This fact does not change according to the position of the plane.

You know that REALLY large Russian cargo plane? It has disposable wheels under the tip of each wing to keep the wings from touching the ground. Once the plane gets to the speed required for the wings to generate lift, the wheels just break off and the plane takes off.

So the wheels are just there to keep the plane from scraping the ground (thus reducing friction). They do nothing more.

this is quite a tricky one - the plane will be generating forward movement due to the fact that the conveyor belt won't be able to match the acceleration of the plane exactly due to friction etc the plane will move forwards but the question then is whether the plane will be able to generate enough thrust to generate the required airflow over the top of the wing for the plane to reach V1 and generate sufficient lift to take off - the will basically come down to the excess thrust the aircraft will have - if there is insufficient excess thrust then the plane will not have sufficient airflow to take off. In my opinion this could depend entirely on the type of plane used - if you were to use a jet aircraft i would say this could be possible to do - with a piston engine i wouldn;t think so as it will not have the excess thrust needed to generate the required forward momentum for take off
i don;t think this can simply be answered yes or no
would be interesting to see what people think of this view

regards

Apart from wearing-out the conveyor belt, the aeroplane will NOT take-off. Dynamic pressure is required to generate lift and there is no more flow of air over the wing than if it were stationary on the ground.

I think this discussion is awesome. It was in the opposite position at first, but I now see why TAKEOFF DOES HAPPEN. No matter how fast the conveyor belt moves, the engines will cause a forward motion relative to the earth (and conveyor). Eventually, there would be enough forward motion for takeoff. The wheel would be spinning wicked fast. Good Chat, we'll see you at the front porch. Mojoe

You can't think of it in the same manner as a car. Cars work by turning the wheel, while an aircraft works by accelerating air. An aircraft's wheels are independent from its propulsive mechanism. Therefore the tires will spin extremely fast because of the conveyor belt, the the forward motion of the aircraft will be unchanged and enough lift will be generated to get the plane off the ground.

This problem can be understood quite simply by considering the example of a plane with frictionless bearings in the wheels. Examine the case when no thrust is applied and the conveyer moves at any speed. The plane will remain motionless with respect to the ground while the wheels spin at the conveyer speed. Now apply some thrust and the plane will start to move forward relative to the ground because in this case the speed of the conveyer (with frictionless bearings) can have no effect on the plane motion. As you increase thrust the plane will take off just like a normal plane. In fact from an observer on the ground the take-off will look perfectly normal. Now add some friction to the bearings and the only thing you will have to do is add a little more thrust to overcome this friction. Again from an observer on the ground the take-off looks exactly the same with the exception that the wheels seem to be spinning too fast. This is different from a car because the car must have locked (not frictionless) bearings (at least in one axcel) in order to move.

Thrust of the plane is constant, weight of the plane is constant. Rolling resistance is measureable. Rolling resistance force is a linear function of velocity. The force of rolling resistance acts at a right angle to the bearing's thrust surface. It is applied to the center of rotation, not the bearings. A rolling ball with no bearings still has rolling resitance, otherwise it would never slow down when rolled across a level floor. Rolling resistance results because of deformation at the radius of any rolling object.

The answer to the airplane/conveyor question is "it depends". Why, because there is more than one way to measure the airplane's "speed".

If we measure groundspeed relative to the conveyor by attaching a speedometer to the wheel then at the instant the plane starts to accelerate (t>0), the the conveyor accelerates. The conveyor is the drive source for the wheels because they are the only point of contact with the airplane. The tires and conveyor accelerate at a 1:1 ratio because they are not slipping. This increase in velocity increases rolling resistance. Since F=ma both wheels and conveyor continue to accelerate until thrust= force of rolling resistance. At that point all acceleration ceases.

Does that work for anyone?

Semantic argument: The question states the airplane is "standing" on the runway. This implies it is not accelerating. How can it move without accelerating.

Semantic argument: The question states the airplane is "standing" on the runway. This implies it is not accelerating. How can it move without accelerating?

get a model plane
take it to K-Mart
put it on the checkout conveyor belt
and see if it will take off
you don't need a PHD to work this one out
just a big boys toy and some retail therapy

remember this is all just theory,
you can use as many analogies as you want but they have no ref. on the question as they have different variables,
and anyone who has any scientific knowledge should know this,
nobody has tried the math behind this issue, to theorectically prove their idea
(yes this would take a little more than 5 minutes)
your making an educated guess at this point

and also until someone does the perfect world practical,
then we will still never 100% answer this question

More scientists are proven wrong compaired to those who are proven right
even things that seem straight forward can be proven wrong in practice

My answer is
It is possibble for the plane to take off
but it is also possible that it might not

Never discount any answer, as nobody here has proved a thing, they have simply made educated theoretical judgements
I hear alot of scientist say "we never expected that to happen"
when they do their first practical, after years of theory

The plane will take off. Forward motion is created by thrust which doesn't have the first thing to do with the wheels. The wheels just hold the up plane off the ground. The thrust is created by the differential pressure between the inside of the nozzle and atmospheric. Imagine that the plane held up by a string. If you fire the engine, the plane will rotate about the end of the string.

You could not STOP the plane on a conveyor, however.

I am with the no fly party. If I had a prop/jet driven car (with free-spinning wheels) on this conveyor belt runway, It would not move foward wrt the non-conveyor ground around it. Therefore, winged or not - net ground speed=0, net air speed=0 (assuming a windless day). prop car no go - plane no fly.

HERE'S THE PROBLEM- i thought at first it wouldn't fly, because i missunderstaood the concept. i thought they were setting up a situation where the plane was staying stationary to the world, to the air- as many who say no fly - are assuming when they say the conveyor is moving in the opposite direction at same speed, assumed you meant 'speed as determined by what the wheels think they are going- - but when you see the video, the plane is moving forward, so its wheels are spinning twice as fast as usual, so of course it flies- the speed of the wheels has nothing to do with lift... the conveyor is just making the wheels spin fast, as plane's engine is still pulling it forward.. now that i see the situation of course it flies!

At first I thought "If a plane is unable to achieve sufficient air movement across its wings to induce lift, isn't it just a car? It shouldn't matter about 'thrust' or 'bearings'. If the lift from moving air isn't present, it aint going up."

I hate to admit it, but I'm wrong.

Put a rocket on a launchpad and tilt it sideways, it still launches given sufficient thrust. The trick is, no one ever said that they were only going to take the engines up to standard take-off speed! At full thrust, the plane would likely fly. Maybe even without wings. The wings shorten the time and space needed to achieve takeoff, and give you STABLE flight, adding to the time one stays aloft...

Just my 2¢...
Mark

I think I can help here. Let's start by forgetting all about friction, lift, wheels, delta-ts, even airplanes. Let's forget about our physics classes and pretend we're 12 years old and our grandpa tells us the riddle and he knows that we're old enough to get it.

Major point one: This is a riddle not a physics problem.

(Well, I'm a physicist and its a fun physics problem too, but seeming as everyone has exhausted that way of looking at let, I'll move on.)

Now, if you've made it this far down the comments, you'll have forgotten the precise statement, so I'll post it here:

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

Major point two: Any movement is in relation to an observer standing on the ground.

THE MAJOR POINT: "The plane moves" implies that the plane moves relative to the observer.

It's said right in the problem. "The plane moves." Forget trying to saying that the plane is motionless because the conveyor cancels out the planes motion. The riddle states that the plane moves! End of story. Plane moves, therefore can take off.

Still don't believe? Let's examine how this riddle riddles you step by step. Here is the initial logical thought process:

1. "The plane moves in one direction..." (forward and relative to the observer.)

2. "...the conveyer moves in the opposite direction." (backward and relative to the observer.)

3. Therefore they cancel each other out and the plane doesn't move and can't take off.

Here is the part that points out why this is a riddle:

4. Wait a minute, if the plane doesn't move because of the canceling from the conveyor, then the "plane speed" is 0.

5. Wait a minute, if the "plane speed" is 0, then the conveyor speed is also 0.

6. Wait a minute, I said in steps one and two that the plane and conveyor moved. The observer even saw it with his own eyes!

The result: a paradox where we start our argument with the conveyor moving and end up with the same conveyor not moving—exactly why this is riddle!

When we reach this point of a riddle, we re-read it and try again. Here's the final logical thought process:

1. "The plane moves in one direction..." (forward and relative to the observer.)

2. "...the conveyer moves in the opposite direction." (backward and relative to the observer.)

3. Hey, the plane is moving forward, it's speeding up.

4. What's this, the conveyor is speeding up too.

5. Forget about the conveyor, I can't even see the plane anymore.

6. Hey, there it goes, off into the air!

The point: This is like one of those word problems with extra information that you try and try to fit into the answer to the problem, when all you have to do is read the question, "Can the plane take off?" and then the second line, "The plane moves in one direction..." and then write your answer down: YES.

I think BALLJAR's comments early on exemplify how riddles work:

BALLJAR says, "The postulate is that the motion of the conveyor backwards keeps the plane stationary."

The riddle says, "The plane moves in one direction, while the conveyer moves in the opposite direction."

Obviously BALLJAR's statement contradicts the riddle, and that's the point.

I don't think I can say it any more ways. I was introduced to the riddle yesterday and was gotten by it at first just like everyone else. I tried using my technical knowledge of physics and aerodynamics to explain what the plane did just like everyone else. In the end the simplest way to explain it is to go back and re-read the problem and re-work the logic of your answer.

- Aaron