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Will it take off?


Coytee

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a plane is standing on a movable runway( something like a conveyor).as the plane moves the conveyor moves but in the opposite direction.the conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction.

the question is

will the plane take off or not?

There is the original question.

Let's now get back to a still day with a treadmill. The wind is NOT blowing. We get on a treadmill and stand still. If the treadmill is moving us backwards 20 mph, we have.... a 20 mph wind. It would be a tail wind. If we want to get back to having no tail wind, we need to start running on that treadmill and achive a running speed of 20 mph. Then, we will offset the tail wind, and experience a resultant zero wind.

Now, let's say we do not want to run. Let's put on roller skates. Will it make any difference? No, we need to skate 20 mph to offset the 20 mph treadmill and have zero resultant wind.

Let's say we don't want to have to exert effort by skating, so we keep the skates on and we attach a mini jet engine backpack. We crank the thrust to achieve the 20 mph speed. Still, the resultant wind is the same - zero. It does not matter what type of propulsion we use, the result is the same.

Somewhere between the original post and your replies, the fact that the treadmill moves in response to movement of the plane got turned into the treadmill moving the plane backwards.

Also, in your above examples, you change the application of force from you to the treadmill by your feet, then by roller skates, both of which are acting directly on the treadmill. Then you lose it and go off into jet pack land, the jet pack does NOT apply force to the treadmill, it applies force to you.

Lets put you on a treadmill, on rollerskates with perfect bearings, so that regardless of how fast you skate or how fast the treadmill spins, you still remain stationary. Now, according to your example, if an outside force is applied to the object on the treadmill, be it you or a plane, it still will not move forward. What if the outside force were a Warn 1 ton winch mounted to the wall with the cable attached to your belt? Or maybe, ohhhhh a jet engine!

It's not really all about vectors, it's about force and the application of it.

THIS is why I said "Oh my Goodness"; I knew where things were headed. Again.

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Jeff,

Oldtimer and CTBB are making good points. In the time you've spent supporting an erroneous conclusion, you could have read the whole thread. I gathered up a few previous posts that I hope will steer you to places in this thread where your arguments have been addressed. Go back and read around these posts.

From Page 1

Interestingly enough, here's a guys response, I've deleted his name but otherwise, a direct copy of his comments. Seems he's one of them smart ones and his answer is the plane WILL take off. [:$]

This is a very simple dynamics problem. Draw a free-body or force diagram of the airplane and you will see that the only horizontal force applied to the airplane by the conveyor is through the almost freely spinning wheels. That force resolves itself into a force applied to the a/c via the rolling resistance of the wheels. The only other horizontal force (neglecting aerodynamic drag) felt by the airplane is thrust from the engine.

Now, the engine thrust must greatly exceed the rolling resistance of the wheels or the airplane couldn't move even if the conveyor were dead still. Since the engine thrust pulling the airplane is much greater than the force of the wheels retarding the airplane, the airplane must accelerate in response to those unbalanced forces. Sir Isaac Newton taught us that back in the 1600's. F=MA where F is the unbalanced forces acting on the object, M is the Mass (or in very loose terms, the weight) of the object, and A is the acceleration of the object.

Don't confuse displacement with force. The conveyor can be "displacing" at a phenomenal rate, but the only force it can exert on the airplane is through those freely spinning wheels. It is FORCE which accelerates and moves unrestrained objects.

Said it before, and I'll say it again. The airplane doesn't care one iota what that conveyor is doing, anymore than if the airplane were flying with the wheels .001 inch above the conveyor.

If the engine is producing, say, 1000 lb of thrust, the airplane would act just like a stationary winch was attached to the airplane and pulling with a constant 1000 lb force. That 1000 lb force, reduced by the drag of the wheels, will accelerate the airplane forward regardless of what the conveyor is doing. Neither the a/c engine nor that imaginary winch cares about, or is even aware, of the existence of the conveyor, they just continue to apply that 1000 lbs of motivating force - and that a/c motivates!

But, since the wheels spin as if the a/c is moving at twice its actual speed (relative to a stationary observer) and a/c tires are rated for a specific maximum speed (RPM) you may ruin your tires or wear out the wheel bearings, but you will fly the a/c- if the tires/wheels last long enough.

I was an aeronautical engineer in the aviation industry for going on 40 years (MSAE), and a rated a/c pilot (Private, ASEL, Instrument) longer than that. I can categorically state that this is one of those logic problems in which your intuition leads you to a dead wrong conclusion. The key is to identify the forces acting on the a/c. Everything else is totally irrelevant.

If anyone cares to read that thread it's here:

http://www.tractorbynet.com/forums/owning-operating/90325-will-take-off.html

From Page 5

No problem Phil. I like these discussions. The challenge is to cut through what doesn't matter and evaluate what does matter and then try to explain it clearly. To answer this problem, there is really no need to get into aerodynamics, or Bernoulli's equation or any of that stuff - we know it's a plane and it's capable of flight. We know that a plane needs airflow over it's wings to achieve lift. In still air, the plane must move forward to fly. So, the question boils down to whether or not the conveyor affects the forward motion of the plane.

The plane will accelerate when there is an unopposed force applied to it. It will move in reponse to the force according to Newtons second law of motion where Force = Mass times Acceleration. Force is a vector quantity, having both direction and magnitude, so the direction of the force will be the direction of the acceleration of the mass. For a plane, this force is applied by the action of the engine (propellor or jet thrust).

The crux of the question is: Can the conveyor impart a horizontal force on the plane to oppose the engine thrust? It really just boils down to that.

We know that the conveyor and plane's tires move in response to each other, but is that motion and associated force transffered to the rigid body of the plane? The mechanical connection between the tire and the plane is the wheel bearing. In a way it acts like a hinge. If you hang a door hinge to swing vertically and push on the lower end, it just swings up and the top part above the hinge doesn't move. If it were a solid bar (no hinge point), the force would be transferred to the top. The plane's landing gear wheel bearing sort of acts like a hinge and does not allow transverse forces to be transmitted to the plane from the tire. Think of the wheel on a rollerskate - you can turn the skate upside down and run your finger over the wheel and spin it without really applying any force to the skate itself. So, the conveyor doesn't really impart any horizontal force to the body of the plane because such a force cannot be transmitted to the plane through the wheel bearing. Common sense and experience tells us that there will be some resistance in the wheel bearing (friction) but this is a very small force compared to the engine thrust and it can be ignored in order to visualize the problem better. At any rate, there is no horizontal force transferred from the conveyor to the body of the plane that can significantly oppose the engine thrust, so the plane accelerates and takes off. The conveyor can be moving at any speed and still not really affect the plane's acceleration - that speed matching thing just gets people confused.

Someone asked if the plane would remain stationary if the conveyor were moving but the plane's engines were shut down - no force acting on the plane. Under the ideal frictionless scenario, yes, the plane would remain stationary while the conveyor just spun the plane's wheels. Did you ever see an orange or an onion that falls onto a moving supermarket conveyor just sort of roll in place. It's the same as that.

I'll stop for now. I hope that helps.

From Page 12

Although a couple of the analogies that have been given don't really apply, the plane will take off. The aircraft carrier is not the same as the conveyor problem - the carrier is actually more of a slingshot. The rotating earth example is also not really the same as the conveyor problem since everything is in the same inertial frame - the earths rotation is not really felt as an external force to an observer on the earths surface.

Again, the problem is not aerodynamics but simple mechanics. Bernoulli's equation, laminar flow, boundry layer effects, etc., etc., are just not relevant to solving the question. The pilots, admirals, and aeronautical engineers can take a break for a while. It's about forces, moments, and how wheel bearings transmit certain forces but not others.

I drew up a diagram that I hope helps and I'm going to try to put concepts into terms for non-engineers. We have an aircraft landing gear wheel on a yellow conveyor. The gray part of the wheel is the rubber tire, the blue part is the pin, or axle, of the wheel and the red ring is the wheel bearing.

I've shown the horizontal forces acting on the wheel. F(t) is the thrust from the plane's engine that is transmitted to the axle of the wheel. F© is the force from the conveyor that acts tangentially on the surface of the tire - so it creates a shear force on the surface of the tire perpendicular to the contact patch between the tire and the conveyor. As you might expect, the shear force results in tire rotation (as shown). The tire contact patch is shown as line A-A' on the figure (to make things easy we'll assume there is no tire deformation so the contact patch will be a line and not a rectangle). Remember, this is the only point of contact between the tire and the conveyor and so it is the only place a force from the conveyor can act on the wheel assembly. Also for simplicity, I've not shown the vertical forces acting on the wheel, consisting of the plane's weight on the axle or the resultant, or normal, force counteracting it from the conveyor to the tire - they will cancel each other out. We only need to focus on the horizontal forces (engine thrust and shear force from the conveyor).

The function of a wheel bearing (shown in red on the diagram) is to eliminate frictional forces between a wheel and an axle. Let's say this wheel bearing is truely frictionless (again for simplicity). As a frictionless ring, it is not affected at all by shear forces. The spinning tire does not twist (apply a torque) to the axle - again, the bearing prevents that by not transferring the shear force from the tire surface. If the red ring is a rigid connection such as a weld, brake, or drive gear instead of a wheel bearing, then the force, F©, from the conveyor will apply a moment (or torque) to the axle and affect the planes forward motion.

The only horizontal force acting on the axle is the result of the thrust of the plane's engine, F(t), so the tire (and the rest of the plane) accelerates in response to that force. The force, F©, from the conveyor does not oppose this force - it only spins the tire.

To convince yourself, try the following experiement. Take one of your kid's skateboards, turn it upside down (wheels up) and lay it on the floor of your garage. Fire up your belt sander and run the sanding belt on the wheels of the skateboard. I've never done this, but I know that the skateboard will not go shooting across your garage but will just sit there while your sander spins the wheels. There might be some movement since the skateboard wheel bearings are not truely frictionless, but you'll get the idea. Just as the plane's forward motion is not affected by the conveyor, the skateboard is not affected by the shear force you are applying to the wheels (unless you slip and drop the sander on the board).

Frm Page 15

Can anyone from the "will not fly" brain trust explain how any horizontal force from the conveyor is transferred to the structure of the aircraft?

If you can't answer that, you can't support your conclusion.

Added: I found this video. It was simply done, but it just might be enough for some disbelievers to see the light.

Amateur Home Video Demonstration

From Page 16

There is nothing in the problem that constrains the wheels to spin at the same rate as the conveyor. The wheels aren't mentioned at all. The problem just boils down the the question: Does the conveyor inhibit and/or prevent the plane from taking off? Or in the simplest terms: Does the conveyor make any difference?

If there is no thrust from the aircraft, the wheels will spin at a rate to maintain the same tangential velocity as the conveyor. In a frictionless system the plane will remain stationary as the conveyor moves under it when there is no thrust. If we want to account for rolling friction and bearing resistance, it would take very little force to overcome the small frictional components that would comprise a force in the direction of the conveyor motion. You could counter this force with your pinky finger (only a slight exaggeration) and maintain the plane's position. Once the plane applies any thrust, it moves forward regardless of the motion of the conveyor. Thrust or no thrust, the plane is not really affected by the conveyor's motion.

If you want the plane to remain in place once thrust is applied, you must impose an external force to oppose the plane's motion (you correctly mentioned the need for a drive motor or a wire) and this force must be equal to the thrust of the aircraft. There is no mention of such a mechanism in the problem and so no "Option B".

Someone said that gravity somehow pins the plane to the conveyor and it will travel backwards. I can understand how someone might think this. If the conveyor starts up very slowly, there may not be enough force to overcome the static coefficient of the minor frictional forces I mentioned earlier. In a frictionless system, the plane remains in place as the conveyor moves under it (as long as there is no engine thrust). In the real world, it just takes a bit more initial force to overcome the static frictional force and allow the wheels to roll. Think of a magician that swiftly pulls a tablecloth from a table without disturbing the place settings. They must pull quickly and with enough force to overcome the static friction between the plates and the table cloth. If someone tries that slowly, they just drag the dishes off of the table. It's an easier trick with the plane since it's on wheels.

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(I cannot believe I am posting here. Yes my first post in this thread).

The conveyer belt has no bearing on whether or not the plane takes off. The belt will just be causing the jet's tires to just spin like crazy as the jet engines thrust the plane foward. The jet engine is pushing against the air, it does not care how the plane is coupled to the earth as long as it is fairly frictionless. Planes even take off from water using pontoons. You can spin the tires as fast or slow as you want to, the jet engine is still going to push the plane foward. This is NOT a wheel driven car with wings that depends on ground traction to get going. I agree, the conveyer belt vector will cancel out the wheel vector, but NOT the thrust of the jet engine. To cancel the jet engine vector, one could use a super strong wall of some sort, but not a conveyer belt.

With the foward motion of the plane, air will move over the surface of the wings creating lift per Bernoulli's equation (yes, I've taken plenty of physics) and the plane will take off and fly.

To further illustrate, think about a shopping cart on an airport's pedestrian transporting conveyer belt. You are standing beside the conveyer belt (feet on firm ground) holding the shopping cart with your hand - the wheels are spinning, but the cart is stationary (even if the conveyer belt is speeding up and slowing down). Now you break out into a full run still holding the shopping cart. The shopping cart will move foward regardless of how fast or slow the conveyer belt is running - it only affects the speed the little wheels are spinning. The conveyer belt can match your foward speed, but it will not slow you down (except for a little extra friction). You could grab that cart and mow down the proverbial little old lady riding the conveyer belt if you wanted to.

Now take that same shopping cart on the conveyer belt and replace your holding hand with a 100,000 lb thrust jet engine on it. That engine will thrust the cart foward much more efficiently than your arm, regardless of the speed of the conveyer belt. Now put a set of wings on the cart...you get the idea.

Now, picture a 150 pound guy riding a unicyle against the flow of a conveyer belt so he is stationary. The belt will speed up or slow down to match the speed of his tire. Now we hire Hulk Hogan to break out into a full sprint parallel to the conveyer belt and proceed to "clothesline" the dude under the chin. What will happen?

Now take that same fellow and attach a Lear Jet engine with a Pratt & Whittney afterburner to his helmet. The conveyer belt will always speed up to match his speed of his unicycle tire. Now by remote button we give the jet engine/afterburner full thrust against the direction of the conveyer belt. Will this guy just be sitting still with the afterburner shooting a 40 foot flame (the conveyer belt is helping him in his unusual circumstance), or will that tire just spin about a bazillion miles an hour as he goes on a serious joy ride?

To sum: the conveyer belt does not, I repeat does not prevent foward motion of the plane whether prop or jet propelled. Would a conveyer belt prevent the foward motion of a typical car...yes. A plane....no.

I can't believe this went on for 20+ pages (now I am part of the problem...LOL)

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In physics, the problem is one of vectors. A vector is a combination of magnitude (i.e. speed) and direction. It's solved like this:

Let's say you have a wind speed of 40 mph. That is NOT a vector. It is only a magnitude. When you say a wind speed of 40 mph east, then, you have a vector.

40 mph east would be represented by an arrow, like this: -------------------->

80 mph east would be represented by an arrow, like this: --------------------------------------->

If you had 2 separate winds blowing, one 40 mph east, and the other 80 mph east, the resultant vector is a 120 mph wind blowing east (all you do is add them).

Now, say you have an 80 mph wind blowing east, and a 20 mph blowing west. The resultant is a 60 mph wind blowing east. So, these two winds have the same effect as a single 60 mph wind blowing east.

There's Vectors 101 for you.

Now, we need a certain magnitude AND DIRECTION of wind in order to lift a jet. Let's say 100 mph headwind.

Using that example, let's assume it is a still day. So, if you move that jet 100 mph in ANY DIRECTION, it will lift.

Let's now assume, the wind is aimed in the same direction of the plane and is blowing 40 mph. Now, the plane needs to go 140 mph to lift. That is because we need a 100 mph headwind, but we are needing to first offset a 40 mph tailwind. uhhh..... now it would only need 60 mph as 40 mph is given by the wind...... remember the tailwind helps a bit while in air but the air going from front to back is crucial to get it in the air as the air needs to travel over the wings from front to back to create lift

Let's assume the wind is blowing opposite the plane's direction by 20 mph. Now, we need only 80 mph of speed from the plane to get our 100 mph headwind.

Let's now get back to a still day with a treadmill. The wind is NOT blowing. We get on a treadmill and stand still. If the treadmill is moving us backwards 20 mph, we have.... a 20 mph wind. It would be a tail wind. If we want to get back to having no tail wind, we need to start running on that treadmill and achive a running speed of 20 mph. Then, we will offset the tail wind, and experience a resultant zero wind.

Now, let's say we do not want to run. Let's put on roller skates. Will it make any difference? No, we need to skate 20 mph to offset the 20 mph treadmill and have zero resultant wind.

Let's say we don't want to have to exert effort by skating, so we keep the skates on and we attach a mini jet engine backpack. We crank the thrust to achieve the 20 mph speed. Still, the resultant wind is the same - zero. It does not matter what type of propulsion we use, the result is the same.

If we crank the backpack up to achieve 30 mph on our 20 mph treadmill, we have a resultant headwind of 10 mph. To fly a plane, the example I used above requires a 100 mph headwind to achieve lift. So, if the treadmill is moving us backward at 20 mph., if we use enough thrust to achieve 120 mph, then, we will begin to rise because the resultant vector is a 100 mph headwind.

But what if as we keep adding thrust to outpace the treadmill and gain this headwind, the treadmill keeps speeding up against us. The tail wind created by the treadmill offsets any of our gain, and we never achieve the amount of headwind we need. In fact, in the example, there will never be any headwind or tailwind because the opposing movement of the treadmill is always EQUAL to the thrust of the jet engine. Therefore, the resultant is always ZERO - a perfect calm.

Try Googling on vectors, and you will see.

But, Hey! If I'm wrong, I'm wrong. Somebody just show me. It has nothing to do with pride.

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Okay, the video of the kid unscientifically pulling a sheet of paper under a skateboard with a fan on it is hardly a controlled environment. I can't buy the theory based on that video.

What has been said in the accumulation of posts by CTBB is intriguing, but I can't buy it.

Here's why. The plane will not - WILL NOT - rise without forward motion. It has to have forward motion into a headwind to lift. That is why the wing has the shape it does.

Now, for there to be forward motion on this treadmill, the wheels must - BY DEFINITION - move FASTER than the treadmill. The problem stated that the treadmill speed adjusts to the wheel speed. Therefore, there can be no forward motion. Did you catch that? The wheel must spin faster than the treadmill for there to be forward motion.

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Okay, the video of the kid unscientifically pulling a sheet of paper under a skateboard with a fan on it is hardly a controlled environment. I can't buy the theory based on that video.

What has been said in the accumulation of posts by CTBB is intriguing, but I can't buy it.

Here's why. The plane will not - WILL NOT - rise without forward motion. It has to have forward motion into a headwind to lift. That is why the wing has the shape it does.

Now, for there to be forward motion on this treadmill, the wheels must - BY DEFINITION - move FASTER than the treadmill. The problem stated that the treadmill speed adjusts to the wheel speed. Therefore, there can be no forward motion. Did you catch that? The wheel must spin faster than the treadmill for there to be forward motion.

jeff..... get a piece of paper, a clean one, put it on your bottom lip (the edge) and blow on top side of the paper but not on the bottom. What happens? The paper did not need forward motion to get lift

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Not a convert, yet. But guys, I gotta tell you, you are messing up my law practice. The rest of the office is now in debate.

Jay, the paper lifted BECAUSE you blew against it. In the problem, we had to get wind in the first place. I took it that to achieve the required wind, you'd have to have some forward movement. If you want to assume the plane is in an artifical, make-believe super wind tunnel, I'm a convert. But, there is no wind tunnel.

Now, we must get this plane moving forward at enough speed to generate sufficient headwind.

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The conveyer belt matches the speed of the plane (as stated in the very first post) and will no way impede the aircraft from moving foward. The engines will push against the air to thrust the plane foward independent of what is spinning the little wheels prior to this plane leaving the ground. The belt is completely irrevlevant as clearly explained about a million times by a bunch of people here. This problem is absurd once one is able to understand the easy trap layed in this rather clever mind teaser.

People just hate to admit when they are wrong.

It takes a big man to admit when he is wrong, but it takes an even bigger man to make that man admit he is wrong.

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Jeff,

Forget about all of the nonsense about lift and drag and blowing on a sheet paper. There have been some fine points made by several people throughout this thread about why the plane can take off. Did you read the posts I looked up for you? I think that the burden of proof is up to you. You haven't explained your conclusion. Explain how the conveyor keeps the plane from taking off. Explain how the conveyor is at all relevant. Use vector resolution or whatever you want.

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Jeff,

Forget about all of the nonsense about lift and drag and blowing on a sheet paper. There have been some fine points made by several people throughout this thread about why the plane can take off. Did you read the posts I looked up for you? I think that the burden of proof is up to you. You haven't explained your conclusion. Explain how the conveyor keeps the plane from taking off. Explain how the conveyor is at all relevant. Use vector resolution or whatever you want.

I'll bet he can explain it using tort law.

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No, folks. You are wrong. I am surprised there is not an easy-to-find final word on this through a Google search. But here's an example my law partner came up with - and he is right on the money!

You are on a treadmill with roller skates - the same example many of you have used. Also, to keep you from going backwards (i.e. to get past the initial friction), somebody puts a little force behind your back - just enough to get the wheels spinning.

Now, you're in a state of equilibrium - going as fast on the skates as the treadmill spins. Then, somebody comes up from behind you and pushes you real hard in the back to speed you up. Instantaneously, the treadmill speeds up to compensate. Are you going to move forward and gain any ground? NOT!

Perfect logic. It prevails. There is no difference between a jet backpack and someone pushing you in the back. Just keep it simple.

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I'd look for another law partner. Ok, you're wearing roller skates on a flat treadmill. Instead of someone pushing you, suppose you are pulling (hand over hand) on a rope attached to the wall in front you. The pulling force is similar to the aircraft thrust. With each pull on the rope you're moving toward the wall regardless of the treadmill speed.

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I can't believe this woke up again. This is such a simple question and it gets over-analyzed to death here. Here is the simplest analogy I can come up with.

The plane's engines exert a force on the plane. They push it forward. Let's replace the engines force with another force. Say, uh, how about the force of gravity. Instead of igniting jet fuel and oxygen to generate a "longitudinal force vector" (aka "push"), tilt the ground so the plane is rolling downhill. If we tilt the ground steep enough, and the plane gains enough speed, it will generate lift and begin to fly. Of course, eventually we come to the bottom of the hill and smash into the ground, but let's leave that aside for the moment.

Now, while we're rolling merrily down the hill, before our wheels leave the ground, start up our conveyor belt, moving in the opposite (uphill) direction. Will the plane stop rolling downhill and come to a stop (relative to the ground under the conveyor belt)? Will it begin rolling backwards, up the hill? No, unless our wheel bearings cease up or something. No matter how fast the conveyor belt moves under our plane, we're going to continue rolling downhill faster and faster. Eventually we'll lift off. The belt could be moving at any arbitrary speed under us, it's not gonna matter. All it does is make the wheels spin faster. That is, if our downhill velocity is 50 mph and the belt is going uphill at 50 mhp, our wheels are turning at the equivalent of a 100 mph taxi. Likewise, if we're going downhill at 50 mph and the belt is moving uphill at 1,000 mph, our wheels are revolving at the equivalent of a 1,050 mph speed. Doesn't matter, we still roll downhill.

Now, put our plane on a level surface and replace the force of gravity with the force of the engines. Same exact thing.

Duh.

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Sputnik wrote:

Can anyone from the "will not fly" brain trust explain how any horizontal force from the conveyor is transferred to the structure of the aircraft?

If you can't answer that, you can't support your conclusion.

Here is why the above proposition is wrong. The conveyor is in contact with the plane, and thus, PART of the plane. So, the force countering the jet engine IS IN FACT the conveyor.

Maybe planes are too intriguing. Try a car. What if the car is on a treadmill, and however much the driver speeds up, the treadmill speeds up in the opposite direction. Will the car fly? Hell no. It will stay in one place - AND THERE WILL BE NO WIND - ABSOLUTELY, POSITIVELY NO WIND. So, feel free to use a convertible for this experiment (your hair won't be windblown).

Now, put some wings on the car. Will it all the sudden fly in the absence of this wind? I win!

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