The plane gets its lift via the bernoulli effect. This has to do with wing shape and its interaction with air moving rapidly past. If the plane has no motion relative to the wind, there will bo no lift to force the plane up. That plane is going nowhere fast. Kind of.

The force that makes the plane move forward is air pushing on air, not rubber rolling on asphalt (or conveyor belts). Like Cecil says, the stuff going on at ground level is largely irrelevant.

So, the plane takes off.

Exactly what I was thinking. I wasnt even thinking about the wheels... just the fact the plane isn't really moving, therefore no lift force provided to make the plane actually go... up!

An example would be like sitting on those gym bikes with no wheels. You can peddle as fast as you want, but you wont feel the fresh breeze of that speed. No breeze, no wind... no lift!

The only purpose the wheels serve here is to hold the plane up, and to eliminate most of the friction between the plane and the ground. When the engines fire up, the plane will still start moving forward. The only difference will be that the wheels are turning twice as fast as normal.

I don't know how many of your are pilots, but that plane isn't gonna lift off unless it has a very unusual aspect ratio (wing shape) and an unusually large prop.

The prop produces thrust which helps drag the plane through the air. That air, flowing over the wings, produces lift. The prop is not simply a fan that blows air over the wings.

Please?!,
I Have been following your page for about a year, from when you first made it known that you were going Pro. And up until this I have had a pretty good feeling about your ability to reason. I have agreed and made movie choices after reading your reviews. But this is a very difficult thing for me to read. If the plane while still on the ground can not make forward progress it can not create the lift necessary to leave the ground. It uses the wheels roll in this way on take off. No matter how much force it can generate it can not leave the ground. Now if there is a major wind blowing at say 150 plus and depending on the size and weight of the plane, but this would have to be a air mass and consistency that would allow the plane to get far enough into the air, and then use the lift generated by the wing and engine. But hey if you pointed the plane stright up (Rocket) or say had the lift generating wing move(helecopter) you could solve the roll to forward speed thing that runways provide for. Because no matter how fast the air is moving through the engines the wind fmoving over and under the wing is the lift.

If prop thrust were enough to lift the plane up, then the wings would be no larger than the area behind the prop. Clearly, however, wings extend out much further than the props of plans. Consider also jets, which do not thrust any air at all on the wing, the thrust of a jet goes behind the wing.

Planes fly because there is more surface area on the top of the wing than on the bottom (the bottom is flat the top is curved). Because the air has to travel a greater distance over the top than on the bottom, the air gets spread out, as it were, and the air-pressure on the top of the wing is less than on the bottom. Because the air pressure is less, it generates upward lift.

It takes a whole lot of air moving at a rapid speed over a wing to generate lift. The props or jets aren't going to move the plane forward because the plane is on a belt. If the plane is not moving forward, then there is no motion of air over the wings (and remember, the prop blast won't cover the entire wing, so it is not enough). No air moving over the wings? No lift.

That dog won't hunt.

I smell some scientific testing needing to be carried out.

Just remember that the propulsion is relative to the air, and not the ground. Unless that conveyor belt can move the air above it at the same speed as the plane (but in the opposite direction), it's not going to be stopping any takeoffs.

The question is broken, it seems to me. It says the speed of the belt matches that of the plane, whatever that means, but also implies that the plane is kept in its starting position.

When the plane starts rolling forward at 1 MPH, how fast does the conveyor belt move? 1 MPH the opposite direction? That means the wheels of the place are rolling at 2 MPH but the plane's overall speed is not affected, except perhaps marginally by the added friction in the wheel bearings. The plane accelerates, and assuming the wheels can withstand moving at twice their normal maximum rate of rotation, it takes off.

But if you interpret the question as saying that the plane is somehow kept stationary by the conveyor, then of course there is no way the plane can take off, or move at all. However, if this is your assumption, then you had better be able to think of a mechanism by which the plane is kept stationary. I can't imagine it.

The assumption that the plane never moves seems doubly flawed. Reading the question again, it would seem that while the plane is kept stationary, then the belt is also stationary (it moves at the same speed as the plane but in the opposite direction). So what is the purpose of the conveyor belt anyway?

Now,
After reading Cecil's responce I now have a better understanding of the math problem. He states that if the plane is moving at 5 forward the wheels also move forward. ??? if the plane is mooving the belt is not keeping up the wheels hould only move in a backwards direction. If the belt is set to mach forward thrust. the wheels mach the belt' speed. it is not twice the speed as stated in the 100 plus 100 = 200 example. It is 100 thrust matched by 100 belt = 100 wheels. which is still zero forward and zero lift.

Max, the first poster, is dead on right. No forward motion relative to the air = no lift.

Relative links would be Science of Wings and Bernoulli's Principal.

Anyone who liked this problem would probably like these two as well: the three-cylinders problem and the tether-ball problem.

The prop produces thrust which helps drag the plane through the air. That air, flowing over the wings, produces lift. The prop is not simply a fan that blows air over the wings.

Cecil certainly isn't arguing that. The lift is created by the plane moving relative to the air around it (like you said). Prop or jet, the plane will fly.

Well, that didn't work.

The three-cylinders problem: http://biocurious.com/the-three-cylinders-problem

The tether-ball problem: http://scienceblogs.com/principles/2006/02/pop_quiz_hotshot.php

The fallacy of your logic (as I see it at least), is that you're forgetting something. The wheels of the airplane are connected to the plane, and friction exists between the runway (conveyor belt) and the wheels.

For the plane to take off, it has to reach a certain airspeed - the speed at which the air passing over the wing is enough to create lift. In order for the plane, which is on the ground, to reach a forward speed, its wheels would need to be travelling in a net forward direction. In order for this to happen, their speed would have to be GREATER than that of the belt running beneath them.

If, as the above indicates, the speeds are ALWAYS equal, then the plane will not move.

So what is the purpose of the conveyor belt anyway?

Exactly. The belt and its speed, if any, are red herrings. The belt could be moving at any speed relative to the airplane (forward or backward) and the plane would still take off.

thank you Bryan

Good explanation here.

The point of the riddle is that the motion of the wheels exerts only a minor frictional force opposing the forward movement of the plane. The major force being supplied is from the plane engine, and that force is a forward force. The net force is equal to the forward force minus the negligible frictional force. This obviously produces a net forward force. Therefore, the plane moves forward, regardless of how much the wheels are spinning. The plane is not remaining stationary on the conveyor belt becasue there is a force acting on the plane that is not dependent on the motion of the conveyor belt.

This is really a fairly simple problem for anybody who has taken an introductory physics course, and I can't believe that so many people are having such a difficult time with it.

The trick in Cecil's question is that you read this sentence: "[t]his 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)" and assumed that this meant that the plane is stationary with respect to a ground observer.

This is not the case.

The conveyor would have _no effect_ on the plane with respect to the ground observer. The wheels would spin madly, but no matter how fast the conveyor moved it would not slow the plane or send it backwards: the rotational velocity of the plane's wheels only tell you what its speed is relative to the ground, not to the air around it. The jet engines are acting upon the air around the plane, not pushing against the ground.

In fact, since the conveyor belt would drag along a bit of air due to simple friction the plane would actually get into the air _quicker_ than if it was taking off from a normal runway. The conveyor moving in the opposite direction would drag a bit of air backwards with it, increasing the relative airspeed of the wing and increasing its lift (there may be some additional ground effect in play here that assists the takeoff as well...)

I have to agree with the people who are saying the the question is misleading. The plane will not in fact remain stationary.

Also, just for the record, the Bernoulli effect isn't what makes planes fly! From the wikipedia article:

One common and incorrect way of understanding how an airfoil develops lift relies upon the pressure differential above and below a wing. In this model the pressures can be calculated by finding the velocities around the wing and using Bernoulli's equation. However, this explanation often uses false information, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge, and the assumption that it is the difference in air speed that causes the changes in pressure.

Bryan, you're neglecting the fact that the wheels (through the axle) are exerting only a minimal force on the plane itself. This friction is going to produce a small backward force, but not enough to cancel out the forward motion being created by the engine of the plane. Of course, we're supposing that the system is near-ideal and that there is little friction between the axle and the plane. In a real case, the friction could be much greater, but theoretically the plane's engines could still produce enough force to move the plane forward.

Okay, here's a different way to think about it:

Let's say for the sake of argument, that the engines on a jet propel it forward at 800 miles per hour (I have no idea how fast they really go, but bear with me here). Now imagine that the plane is sitting on a really long conveyor belt. Both the belt and the plane are stationary, and the jet engines are off. Now, imagine that the conveyor belt starts moving at 800 mph. Seeing that the plane's engines are off, the plane gets dragged backward at 800 mph by the belt.

Now, if the pilot fires up those engines, that 800 mph of force is only going to counteract the backwards-moving conveyor belt, right? 800 mph in one direction less 800 mph in the other direction equals 0 mph. So, the plane sits stationary as the conveyor belt goes by beneath it.

If the plane isn't moving, then the air isn't moving above and beneath the wing at the required 800 mph, thus creating no lift. And that's that.

On the other hand, if the conveyor belt could somehow drag the air along with it at 800 mph in the opposite direction of the plane, the jet propulsion would counteract the conveyor belt and the movement of the air itself would lift the plane off the ground... But that's another story entirely.

The last of the idea of forward moving planes. If you look to the aircraft carrier. Would the navy have to use a catapult to get the planes into the air, no they could just hold them waiting for them to gain "forward thrust". Planes don't produce forward thrust they produce back thrust. if the belt was matching speeds the plane would not move.

The lift is created by the plane moving relative to the air around it (like you said)

But the conveyor is not moving the air around the plane. The plane is not moving in respect to the ground, the air (for simplicitys sake) is not moving irt the ground. The plane is moving irt the conveyor belt, but that doesn't matter at all for the purposes of getting off the ground.

There is a serious problem with the wording of the question (and it's discussed on the SD site). The terms "moving" and "speed" are not well-defined in the statement of the problem, and disagreement over the outcome can probably be traced back to differing interpretations of these terms.

If the plane is "moving" relative to stationary objects in the immediate environment (the ground, trees, buildings) then it is "moving" in a sense identical to any other plane during takeoff, and the outcome will be identical as well. If the plane is "moving" only relative to the conveyor belt (which requires a definition of "speed" that is questionable, in my view), then it's behavior is identical to that of a stationary plane parked on the tarmac, and it will not take off.

Just remember that the propulsion is relative to the air, and not the ground. Unless that conveyor belt can move the air above it at the same speed as the plane (but in the opposite direction), it's not going to be stopping any takeoffs.

I have to correct myself quickly, what I meant was:

Unless that conveyor belt can move the air above it at the same speed as the plane (and in the same direction), it's not going to be stopping any takeoffs.

I hate these kind of problems. And yet, my first reaction was "of course the plane takes off. Its speed is the only thing that matters. If it reaches takeoff speed, it takes off."

But it's hard to wrap one's head around - like when I was little and someone asked me "which weighs more, a pound of feathers or a pound of bricks?"

The idea that the bricks didn't weigh more was very hard to deal with.

thank you grey

An observer standing stationary on the ground nearby would see this plane moving forward, at almost normal speed. The rolling conveyor is just 'the rug being pulled out from under it', and is barely slowing it down, right? If that's the case, then this is a poorly worded question, giving the impression that the airplane is sitting still relative to a stationary observer.

I am trying to imagine this:

I am on a moving sidewalk. I am wearing roller skates. I am wearing a jetpack. I am facing backwards, that is, towards the sidewalk's motion instead of with it.

When I fire up my jetpack...I move forward. Against the grain of the moving sidewalk.

Right?

Isn't the plane example the same thing?

Grey, you wrote "Now, imagine that the conveyor belt starts moving at 800 mph. Seeing that the plane's engines are off, the plane gets dragged backward at 800 mph by the belt." That's not the case. This would in fact happen if we replaced the plane with a car that is "in gear" because the movement of the wheels is then able to produce a force on the car. However, an airplane's wheels are nothing but free-spinning discs on axles. The backwards movement of the treadmill is going to spin the wheels, but these wheels will only exert a minor frictional force on the plane itself. Therefore, the plane will move backwards, but at a very small speed nowhere near the 800 MPH that the treadmill is moving. The case would be different if the brakes were engaged. Now the wheels would be supplying much more force to the plane, and it would move backwards at nearly the same speed as the treadmill.

If you don't believe me, go try this out. Put a pair of rollerblades on and go stand on a running treadmill (you can hold on to the sides if you want). Your feet will move backwards due to some frictional force of the rollerblades' axles, but they won't move backwards at anywhere near the velocity of the treadmill. You'll even find that you can pull yourself forwards with your arms (kind of like an airplane's engine, huh?) Now, take the rollerblades off and stand on the treadmill in bare feet. I guarantee you that you're going to be moving backwards a whole lot more quickly because now the force of the treadmill is acting on your body much more efficiently than it was when you were wearing the rollerblades.

You could almost imagine the wheels as casters and the conveyor belt running sideways relative to the plane - the result would be a tiny bit of sideways motion, but the plane would still take off.

Assuming ideal wheels, (infinite friction between the ground and the wheel surface, and no rotational friction between the wheel and its axle) if a conveyer belt started moving backwards, the planes inertia would keep it stationary. There is no force from the belt being put into the plane. If you add in the engine's thrust, the plane would move forward at the same speed if the ground was stationary. Of course wheels are not ideal, but at real world speeds, its close enough to ignore the minimal friction.

I do what I can.

and then we move on

Seth, Alan, and Justin- good explanations. It's nice to see that there are still some people left in the world who have a basic understanding of physics.

I don't think this is a really tough question, but as Kottke points out, having some beginning physics helps. Imagine the plane is on a completely frictionless surface (oil so slick, friction between the tires and the ground is absolutely zero). A car on that surface couldn't budge. A plane, however, will move, since the force that propels it is independent of the ground. As a matter of fact, the wheels on the plane are acting just like a frictionless surface, allowing the planes propulsion (prop, jet, rubber bands, etc.) to create forward force. (where the lift comes from seems to be common knowledge amongst all the commentors here)

Same principle applies with the belt that equals the speed of the plane. The belt moves faster as the plane speeds up, resulting in the wheels spinning twice as fast (as compared to not have the belt/runway). Since the forward force (thrust, push, pull... it doesn't matter in a force diagram) is independent of the ground, the plane takes off.

It's nice to see that there are still some people left in the world who have a basic understanding of physics.

It's nice to see that condescension remains an abundant commodity.

I agree the whole wheels thing is a red herring. A plane can take off from a frictionless surface. A plane can take off with those pontoons on a roaring river.

I think the wording of the question is what throws people off, not a misunderstanding of physics: Interpreted strictly it creates a paradox of wheels and conveyor belts that spin at infinite speed.

"That's not the case. This would in fact happen if we replaced the plane with a car that is 'in gear' because the movement of the wheels is then able to produce a force on the car. However, an airplane's wheels are nothing but free-spinning discs on axles."

Okay, that's fair, and I didn't know that.

-- Wait, before I go on: is that really true? On a jet? How does a jet taxi then? Isn't there some sort of drive system involving the wheels? They don't fire up the engines until they're on the runway and cleared for takeoff, right? --

Okay, but, assuming that's true of all planes, then it seems that that fact screws up the point of the question more than anything else. Suddenly it's a question about planes and not a question about physics (which is a whole lot less interesting, if you ask me). I understand it to mean that the conveyor belt moves at whatever speed is required to counteract the forward motion of the plane. If that's true, the plane doesn't move at all relative to the ground and the air (even though it's moving along at 1600 mph relative to the conveyor belt), and no lift is created.

Yeah grey, the wording of the question makes it a little awkward. I've seen it worded better in other versions. It is possible to read this version so that the backward movement of the treadmill is producing enough frictional force to counteract the foreward force of the engines.

As for your question about the wheels, I believe that most planes use their turbines or propellers for taxiing. That's why you see those little cars pushing planes back from the gates. So the wheels aren't connected to any kind of drive train.

Also, if you read the article originally linked by Kottke, there is a description of the paradox that this wording creates (at the bottom of the page).

Similar strangeness. Nearly Weightless Car in neutral on the same conveyor. You are standing next to the conveyor on stationary ground. You stretch out your hand and push the car forward a centimeter and stop moving. As you do, the conveyor goes backward. As it does, you keep your hand out, holding the car in place (1 cm from its original position), with just enough force to counter the reverse movement of the conveyor. If friction between the wheel and axle is 0, will the rpm of the wheels spin up to infinity if you keep holding the car in place?

Or what about: how fast are the plane's wheels moving relative to the ground at takeoff if the takeoff speed is 60 knots and it takes 11 seconds to reach takeoff speed?

60, and you are funny

"It's nice to see that there are still some people left in the world who have a basic understanding of physics."

Wow. That is nice, there, Einstein. Thanks for honoring me with your presence.

"I agree the whole wheels thing is a red herring. A plane can take off from a frictionless surface."

Okay, that's fair, but the way I'm reading the question, it's much worse than a frictionless surface. It's a surface which is dragging the plane backwards at a speed equal to the force that's pushing (or pulling, depending on the sort of plane) it forward.

"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)."

The conveyor moves at the same speed as the plane, regardless of what the wheels are doing. The wheels truly are a red herring, I think, because they aren't meant to be part of the equation.

ok how about this one?

imagine you are running on a track strapped to a hangglider. whats gonna happen? the hanglider will generate resistance and a little bit of lift until you momentarily lose contact with the ground.

now imagine you are on a conveyor. you're running, but you're not generating any resistance or lift cuz you aren't going anywhere.

does this make sense?

Einstein, da Vinci, the Wright bros, throw them all out we have a basic understanding of physics.

yes

Right, John, that's how I'm seeing it.

"Thanks for honoring me with your presence."

(I just quoted myself right there. What a loser.) Does it just blow your mind that a physics riddle could drive an internet conversation to this sort of snippiness? As much as I feel like I was right in reacting that way to that sort of condescension, I apologize to you guys for letting a conversation about something as inocuous as this bring that sort of snottiness out of me, no matter what anyone else said.

Having said that, if anyone brings up Hitler or the Nazis during this conversation, I'm throwing my monitor out the window. You have my word.

The conveyor is moving backwards at exactly the same speed of the plane, but that doesn't mean that the backwards force is being transmitted to the plane. Again, the wheels have very little friction on the plane and therefore the plane can still move forwards with respect to the treadmill, even if the treadmill is moving backwards at the same speed. Because the wheels are freely spinning and have a minimal impact on the plane, you can essentially pretend that the plane is already floating in the air.

I just ran the question by a friend who is in grad school for Physics and he agreed that the plane would definitely take off.

The plane can not take off. To take off, the plane's wings must reach a minimum speed relative to the surrounding air to generate the sufficient lift. Regardless of what's happening on the ground, the wings are simply not generating lift (unless there happens to be a 180mph headwind on the ground).

The tricky part is that the limiting factor to a plane's speed is usually the equalization of air resistance to engine thrust. If there's no air resistance (because the plane is standing still) then the wheel resistance is the limiting factor. Since the rolling resistance of an airplane wheel is much less than the friction of wind on the body, the conveyor belt would likely have to be running at several times the speed of sound in order to generate rolling friction sufficient to match a jet under full engine thrust. Under those conditions the landing gear would likely melt or otherwise disintegrate.

Looked at another way, the energy being used by the jet engines should be equal to the energy that is being generated by the wheels, namely in the form of heat. Given that a commercial jet expends several gallons of fuel per minute those wheels would not be able to take the heat.

Of course, when the wheels break the jet will get pushed backwards at high speed when the body of the jet hits the conveyor belt. Too bad that the wind over the wings will be travelling in the wrong direction.

Also, as for my statement about people having a basic understanding of physics, I apologize for its negativity. It wasn't really directed at anybody here, but rather was the product of some of the lame explanations that I've been reading around the internet these past few weeks. Again, I apologize if it offended anybody.

Now, let's get back to discussing physics.

I don't want to engage in snippiness, but better student than teacher. If the engine thrust and belt movement are zeroed there is now movement relative to the air and wing relationship. Credentials ( full thrust stall training at 5,000 feet) and planes do not float on air.

thank you Kenvin Fox, sorry grad student for my negativity.

Derek, the wheels can freely spin as much as they want to along the treadmill. They're exerting negligible force on the plane itself, so there can be a net forward movement if the plane's engines produce enough thrust to overcome the backwards force.

jason,
if the wheels are "freely" spining to stay up with the thrust you can not move forward. It is only when the wheels can not keep up that you could move forward.

"The conveyor is moving backwards at exactly the same speed of the plane, but that doesn't mean that the backwards force is being transmitted to the plane. Again, the wheels have very little friction on the plane and therefore the plane can still move forwards with respect to the treadmill, even if the treadmill is moving backwards at the same speed. Because the wheels are freely spinning and have a minimal impact on the plane, you can essentially pretend that the plane is already floating in the air."

See, that makes this a riddle about how the wheels on a plane work, not about physics.

"If the engine thrust and belt movement are zeroed there is [no] movement relative to the air and wing relationship."

(I'm assuming you meant no 'cause I thought you agreed with me here.) That's what I mean. The belt is moving at whatever speed counteracts the movement of the plane, is the way I'm reading the question.

"See, that makes this a riddle about how the wheels on a plane work, not about physics."

The brilliance of the riddle is that it combines the two. If you tried the same experiment on a car, there is no way that the car could move forward because a car relies on the contact of the wheels with the ground in order to gain its propulsion. A plane, on the other hand, can move forward without its wheels touching the ground. Therefore, if we assume that the wheels on the axle have minimum friction, they don't effect how the plane moves forward.

"That's what I mean. The belt is moving at whatever speed counteracts the movement of the plane, is the way I'm reading the question."

The riddle doesn't say that the speed of the conveyor counteracts the speed of the plane. Rather, it says that the speed of the conveyor equals the speed of the plane. In order for it to counteract the forward movement of the plane, the belt would have to transfer all of its backwards force into the body of the plane. However, because the wheels can spin freely, only a small fraction of the force is actually transferred, and therefore the plane can move forward.

yes [no]

Kevin, the wings are generating lift because the engines are pushing against the airmass in which the plane is located, not against the ground (no matter which direction it happens to be moving.)

A plane's wheels can spin very quickly. When a plan lands those wheels go from zero mph to several hundred miles an hour of equivalent rotational velocity in an instant (which is why you see the puff of smoke on a landing as some rubber gets vaporized when the heat caused by the sort of friction necessary to spin up the wheels takes effect.)

Let's imagine that the plane is taking off on a calm day. It turns on its engines and in a few seconds it is exterting the thrust that would normally move the plane forwards at 10mph. At this point the plane _is_ moving forwards at 10 mph (because it is pushing against a stationary airmass) and the wheels are spinning at a rotational speed that would measure 20 mph if you attached your car's speedometer to these wheels; 10mph for the planes forward speed and 10mph due to backwards movement by the conveyor belt.

Please re-read the first paragraph of the problem and explain to me how this is not going to happen. The plane's speed is 10 mph and the conveyor (which "tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)") speed is 10mph.

The plane still moves forward because it is not pushing against the ground and the wheels spin freely.

to kevin fox, and the folks who posted earlier and were also thinking that the original problem implies that the conveyor belt turns so fast that it's keeping the plane stationary: no, it does not! absolutely no mention of that in the problem description.

to john: ni, in this context, your otherwise nice illustration does not make any sense, because the plane is not running on the ground in any way. that treadmill isn't impacting its ability to move forward and generate uplift in any significant way.

if i may shoot down one more point: "In order for the plane, which is on the ground, to reach a forward speed, its wheels would need to be travelling in a net forward direction." -- Wrong!

"I don't know how many of your are pilots, but that plane isn't gonna lift off" -- Jeremy, are you implying you're a pilot? If so, I think your licence should be revoked at once. I'd be scared shitless if I found out I was on a plane piloted by you.

I'm convinced that the plane will fly...

unless the wheels explode since they spin much faster than they are manufactured to do (atleast 2 times faster), the landing gear diggs into the conveyorbelt that breaks apart, pieces flying are sucked into the engines that fail, thrust is no longer generated and the massive increase of friction from the conveyorbelt against the broken landing gear starts affecting the airplanes speed...

And suddenly the conveyorbelt stops and the passengers can exit the aircraft...

And if the conveyorbelt reacts to the passengers I wish that all move either in opposite directions at equal speed or that they head for the side.

I may be misunderstanding this question, but the point of the conveyor belt is to maintain the plane in a single location relative to a stationary bystander? So I'm standing there watching the plane, and thanks to the conveyor belt it moves not an inch, relative to me. Right? If that is the case, then:

(a) the length of the conveyor belt is 100% irrelevant. If the wheels are stationary but spinning very quickly, the thing making them do that could be like two spinning rods like in a factory.

(b) the plane is not moving -- the wheels are spinning madly but the plane itself is stationary. Therefore it can't fly. If this scenario would work then they would forget the conveyor belt and just take off from a standing position in real airports. But they can't do that, because a plane is not a helicopter.

Cecil says that planes fly by pulling themselves through the air. But if it's standing still, how is it doing this exactly? Then why wouldn't this work (to repeat myself) if the plane were turned on and standing on the runway? It wouldn't, because a plane has to be moving through the air and letting air pass through and over it in some specific way.

I would also point out that the answers given thus far seem to be missing the element of time. If a conveyor belt plane (so to speak) will work, then would it work if the speed were very low and/or the time spent ramping up speed were very low? If not, why not? I submit that the process of working up to a "real," from-the-plane's-perspective speed of 800 mph or whatever is the same thing that ensures that the plane must be moving through the air from-the-plane's-perspective to work.

Either I'm misunderstanding this, or the "fly" camp is just wrong.

The question does NOT state that the conveyor belt moves fast enough to negate any forward motion. It matches the forward speed of the plane, but in the opposite direction. That is, if the plane starts at X=0 and moves forward to X=100 feet, the portion of the conveyor belt that was originally at X=0 is now at X=-100 feet. The plane has gone 100 feet forward, the runway has gone 100 feet backwards, and the wheels have traveled over 200 feet of conveyor belt.

That's the setup. The question is merely: can the plane move forward?

Ponder this:

1. The conveyor belt does not move backwards unless the plane moves forward. (You CANNOT dispute that... it's in the definition of the problem.)
2. If the belt is moving backwards, the plane is moving forward. (Logically follows from #1.)
3. If the plane is moving forward, it has air moving over its wings and can take off. (From a rudimentary understanding of how flight works.)

Q.E.D.

I just solved it without using physics at all. The definition of the problem states that the plane can take off, because the only force that (in a small way) would counteract it only happens if the plane moves forward. If the plane can move forward, it can take off.

The way the wheels of a plane work _is_ physics. :)

The reason a plane has wheels is to create what amounts to a frictionless take off surface. It merely needs to remain upright until it reaches a velocity where it can be supported by the air.

It's true that _if_ the conveyor belt can zero the forward motion of the plane then the plane will not take off. However this would take a stupendously fast moving conveyor belt as it's force is only being applied to the plane in negligible quantities due to the low friction between the wheels and the plane. This is a hard concept to grasp, but no less true.

The entire point of the question is to trick you into assuming the plane will be stationary. It wont be.

:)

"I may be misunderstanding this question, but the point of the conveyor belt is to maintain the plane in a single location relative to a stationary bystander?" -- Martin

Yes, you misunderstood. No, the plane is not kept stationary. If it was, your explanation would be entirely right, and it's entirely reasonable to entertain that notion after reading through all the confusion above, but the original problem clearly says otherwise.

Also, ponder this: Lets imagine the conveyor was in fact moving extremely quickly because it tried to keep the plane stationary. I think it would move quite an amount of air along with it, throwing said air right at the plane. Now, this would make the plane take off even quicker.

lets take the big peed part of this out of the problem and think of the Alaskan bush pilot. If my Cessna needs 90 miles an hour to lift off, and I happen to be in a river at high melt that is traveling at 40 miles an hour, but I can only generate 120 miles an hour thrust, and I can only attempt a take off into the current can I get up. By the way there is no wind. It could be worse the wind could be blowing up the river, but that is a question for another time because I have to rush this liver to Anchorage. By the way the doner was mauled by a bear that can run at twenty miles and hour while he could only hop at two in his sleeping bag.

Inreresting perspective. So, if you were on a still lake, you could go 120 mph on it. But the water is moving at the unrealistic speed of 40 mph. How much does that slow you down? Surely not by a whole 40 mph. As you become faster, you'll start rising out of the water and it'll impact you even less. I'd say there's no way it could prevent you from taking off. But if it did, at some point you'd have traveled several miles upstream; then you could just turn around and try in the opposite direction.

These things are usually easier with numbers.

Plane's engines propel it with a force that would normally cause it to go 300mph.

Thus, the plane's wheels start to spin at the speed they would at 300mph.

Thus, the treadmill goes backward at 300mph.

Thus, the wheels spin at the speed they would at 600mph.

The plane doesn't care how fast its wheels are spinning, since it's basically just dragging them along frictionless. Instead, imagine the plane is simply magically hovering one spinning wheel's height above the ground.

A plane's jets or props are perfectly happy propelling it when it's flying at 35,000 feet, and they're perfectly happy propelling it when it's flying one spinning wheel's height above the ground.

The plane takes off.

And if you don't believe me, the treadmill/rollerblades example above is the next best explanation.

As I taxi away from the dock live on Ice. the river pushes on me at an unrealistic 40 I turn up river I push my throttle forward. I come up to the dock generating enough thrust on the still lake to generate 40 mph but I am just staying equal to the dock the woman from the cafe hands me the coffee I forgot still with throttle generating 40 I now push it and get the engine to the max rpms which on the still lake would have given me a cool 120 but I am still not generating lift because the air relative to the wing not the engine is still only traveling at 120 minus the backward force of 40 which only gives me an air speed of 80 which is ten below my needs. the guy in Anchorage dies the guy in the sleeping bag died, and I tie my plane up and grab a burger because no matter how much I want my plane to fly physics will not let me into the air. and the jet at 30,000 feet is not on the ground an has attained enough forward speed to get where it is.

the 300 600 relationship I still don't get

If you care to read my work , you will soon understand that the plane will not get off the ground. No matter how fast the wheels and propeller, and jet engine are going, the plane is not moving. And a stationary plane will not take off. Ever.
Unless, it is the plane that Arnold was flying around at the end of True Lies. Or if there are tornado speed winds.

Derek, as to the lack of those 40 mph: It's wrong to assume that the stream pushes everything submerged in it along at its full speed. The water flows around the pontons/floaters (what are they called? I'm not a native English speaker), they're *designed* to let it flow around them with as little resistance as possible.

As to the 300--600 relationship: If the plane, compared to the stationary ground the conveyor is mounted on, goes 300 mph in one direction, and the surface below it (the moving conveyor belt) goes 300 mph in exactly the opposite direction, then from the point of view of the plane, the conveyor belt is moving at 600 mph. Thus, its wheels spin as quickly as if ... etc. Simple, right?

"I just solved it without using physics at all. The definition of the problem states that the plane can take off, because the only force that (in a small way) would counteract it only happens if the plane moves forward. If the plane can move forward, it can take off."

The thing that people are interpreting differently is relative to what the plane is moving forward. If it's moving forward relative to the air, then you're right. If it's moving forward relative to the conveyor belt, then you aren't (unless it's moving forward relative to the air as well).

"The way the wheels of a plane work _is_ physics. :)"

No, it's mechanics (and trivia, if you ask me).

"The entire point of the question is to trick you into assuming the plane will be stationary."

"No, the plane is not kept stationary ... the original problem clearly says otherwise."

First, I think it's pretty clear at this point that it certainly doesn't clearly say otherwise.

And I don't think it's tricking us into assuming anything. I think we're assuming it because what the hell's the point of the question otherwise? If the plane can move forward, then of course it can take off. If the "trick" to knowing the answer here is knowing whether or not the wheels on a plane spin freely, then it's a terribly uninteresting riddle, no?

o.k.
if the plane generates enough force to move at 300 and the conveyor belt matches that 300 the wheels need only 300 to keep up. the wheels themselves are not driven. so they can only be acted on by ether force generated by plane or belt. Each of which is 300.

If the plane can move forward, then of course it can take off. If the "trick" to knowing the answer here is knowing whether or not the wheels on a plane spin freely, then it's a terribly uninteresting riddle, no?

Exactly, yes it is, yes they do and yes it is once you get it.

Jason, I'm sorry for spamming your wonderful blog with so many comments, but ... I can't resist ... I simply must point out to Bernoulli once again that the plane is not stationary. If it was, the conveyor belt would also be at rest and thus act like any other runway. Also -- again this is redundant, others have pointed it out already -- it's wrong to credit the uplift that makes planes work solely to the Bernoulli effect. If a Concorde, for example, redlied only on the Bernoulli effect to take off, it wouldn't be much more than an extraordinarily big paper-weight.

Um, I'm running on a treadmill. I don't feel any breeze on my face no matter how fast I run. No breeze = No lift. Am I missing something here?

If it were possible for planes to take off on conveyors. Many countries would be using this technology. Short runways are particularly valuable in wartime (easier to hide or build carriers).

ok, so maybe my numbers were weird. here's another set:

Time = n; Plane speed = 0; Conveyor speed = 0; Wheel speed = 0.

Time = n+1; Plane speed = 1 (from jets pushing it forward); Conveyor speed = 1; Wheel speed = 2.

Time = n+2; Plane speed = 2; Conveyor speed = 2; Wheel speed = 4.

Since the wheels just spin faster, the conveyor speed doesn't ever get to affect the plane speed. The wheels are the grease between the plane and the conveyor--both can move freely.

Isn't getting a plane flying a two stage process?

In the first stage, the jet engines are exactly equivalent to the motor of a car - they propel the vehicle forwards. But the diffrence is that a plane has wings which create lift and the plane takes off.

If the car had wings, or indeed was capable of getting airbourne it would only do so once it had achieved enough foward motion for the air passing over the wings to create lift.

In a simlar way, if the plane had a gigantic internal motor that drove the wheels (much like a car), and could reach a fast enough speed, it too would take off.

Of course once this plane was in the air (or the car with wings for that matter) it would fall back to the ground as it's method of propulsion effectively ceases.

With the second stage of flight - the propulsion from the engines pushes the air backwards and the plane forwards, creates enough foward motion for the wings to maintain their lift affect.

The pupose of wheels on a plane is to create a frictionless environment BUT only so that it can move forward.

Think of a dragster, as it spins on grease and remains stationary - at this point there is no danger of it taking off. But as it propels down the track and reaches a significant speed, a malfunction may sometimes cause it to lift off.

The plane will not fly. I think.

nex,
the numbers were round. the point was that if a force conveyor( I could even spell conveyor before this talk) or river works against a grounded plane. it has to over come that force to get enough air speed for flight. I am also aware that a bear does not have to run after a guy in a sleeping bag. fish in a barrel, or their term campers in a tent.

I guess my point is that if planes could lift off from conveyors. Everyone would be doing it. The Advantages of a short runway are enormous. In the most critical cases, carriers at sea, a catapault is used to move the plane faster relative to the air (the ground is not relevant) in order to get it airborne. If the plane is stationary in relation to the air, I don't think it will take off.

To look at it yet another way...

If a particular plane needed 40,000lb of thrust to travel at 300mph and somebody put it on a conveyor belt running backwards at 300mph, how much thrust would you need to keep the plane stationary? In reality I could probably hold it still with my pinky finger*

Sure, the wheels would be spinning at 300mph, but I'd be holding the plane still with very little effort. If somebody then turned on the engines and applied 40,000lb of forward thrust, the plane would obviously start moving forward and ultimately reach something very close to 300mph.

Hence, YES the plane would clearly take off in the given example.

* Okay so the pinky finger example might be a slight exaggeration, but you get the point ;)

beautiful,
Heliconia Summer photo. Yes pfong you are right the capault is used to generate forward force to get a plane into the air. and yes Hongknog and many other places would have conveyors if it were that simple.

Derek, imagine an aircraft carrier moving through the ocean at 10 mph (8.7 knots). Imagine you are on the flight deck of said carrier, jogging 10 mph in exactly the same direction. Assuming you use the full length of the deck, you half a little over half a minute, before you fall off the end, to think about this: How fast are you moving with respect to the ocean? Yes, you are only running at 10 mph as far as your feet are concerned. Yes, the carrier only moves 10 mph, too. However, this is where we introduce the mysterious concept of *addition*.

And might I add, defensively, to grey: "The plane moves in one direction [...] tunes the speed of the conveyer to be exactly the same (but in the opposite direction)." -- original problem. It's clear that the speed of the plane is not measured with respect to the conveyor, because if it was, the speed of the conveyor would *always* be the same as the plane, but in the opposite direction. (It would be impossible to find out which speed to *tune* it to.) Thus, it's clear that the plane isn't stationary.

The plane will take off, because there is no way the conveyor could make it remain stationary.

The question is posed in a way that leads one to assume that the plane would somehow remain stationary by means of the conveyer moving in the opposite direction. This assumption is wrong. The plane will move forward and take off regardless of how fast its wheels are turning (which is the only effect the conveyor has).

jj,
your point is correct until you didn' let the belt mach the 40,000lb. If matched your pinky wouldn't even bend

Nex - I understand your point. The plane is not stationary relative to an oberver, it is moving forward until it reaches takeoff speed.

Derek - thanks for the compliment. I think I shall stick to photography and not dabble in things I wot not of :-)

not mysterious at all. If I am running a ten and the boat is at ten in the "same" direction then relative to the water I am traveling at ten plus ten and over a given time say one half minute I would have traveled ten plus ten at time rate of on half minute which would put me at the end of the boat or wet in your example. the distance traveled relative to the water would be more as two forces propelling me forward. But if I travel ten in the opposite direction than the boat my time to end is decreased, beause the boat moves under my feet when I am in the air, my strides then can be longer, but my relation to the water is equal. That is the theory of relativity.

Sorry by Nex, I meant Jon.

Derek... The conveyor belt could be running at 2000mph, it's still only going to take 40,000lb of thrust to get my plane to 300mph. I could also still (theoretically) hold the plane stationary with my pinky finger - no matter what speed the conveyor belt was moving. Sure the wheels would be spinning faster, but there would be very little extra backwards force to counteract.

pfong - Nobody is saying the take-off distance will be any shorter. This conveyor belt would have to be the length of a normal runway.

JJ, yes I understand your point now. The plane is moving forward.

nex, ya know, I read the passage you quoted and see it exactly the opposite way. To me, it seems that the speed of the plane has to be measured relative to the conveyor. Otherwise, like I said, the whole thing quickly degenerates into something much less interesting.

But, my point was that it clearly isn't clear because all of these people are arguing, basically, about that one point of fact.

Derek, I only meant to say, if you have to equal speeds, they can still add up to twice that speed. This was just in reference to your question regarding the 300 + 300 == 600 example. If you are moving at 10 mph with respect to the ocean (soil) and the flight deck (conveyor) moves at 10 mph with respect to the ocean, but in the opposite direction, then your shoes (wheels) would move over the deck (conveyor) at 20 mph. 10 mph in opposite direction == -10 mph in the same direction, and difference between -10 and 10 is 20. I just simplified the problem to only involve addition :-) Also, it only involves demonstrative speed comparisons: Ship vs. water, runner vs. ship. In our new example, which is more analog to the original problem, however, you're running 10 mph with respect to the ocean, but really 20 mph with respect to the deck. So yes, you'll fall off sooner, BUT: If you just ran 10 mph, according to your pedometer, in one direction, turned around at the end, and then ran back at the same 10 mph, both durations would be the same. Here, the velocity of the ship is of no consequence.

The boat moves under your feet while you are in the air? No. Because: Before you jumped up into the air, you were standing at the boat. It imparted its velocity on you. If we ignore the effects of air friction (they aren't so great anyway), you can jump up all you want, you're still moving as fast as the boat, it won't move under your feet. If that was true, you could travel around the earth just by jumping straight up and down, because, you see, the earth rotates beneath your feet[*].

________
[*] Offer void at North Pole and South Pole.

PS: Yes, I'm aware we're basically of the same opinion, are both right, and just exploring the weirdness of relativity. But heck, it's amusing.

Thank you for flying Kottke Air, we hope you enjoyed your journey and hope to see you again in the near future.

(The plane takes off.)

grey, I think that's exactly the point: Once you phrase the problem in a simple, understandable way, it's so trivial, it's not worth any amount of conversation. So if you define 'clear' to mean 'instantaneously obvious to every reader' ... yes, you're right, absolutely. I was thinking more along the lines of 'it arguably means this-and-that, there isn't so much ambiguity that the other position might also be valid'.

This reminds me of the problem with the bell boy and the three hotel guests who initially paid too much. The punch line being something like "but where did the other two dollars go?" Now, this question is actively misleading many people so much that they no longer are able to see the problem in an objective light, thus they don't realize how trivial it is and will argue about it ad infinitum. However, what we're dealing with here is just phrased a little awkwardly, it lacks this sinister quality ;-)

it is funny what happens when the plane on conveyor belt finallly DOES lift off - poof, it disappears suddenly at 300 mph or whatever speed they are flying :)))

now,
I am confused and I said 100 would be my comment limit before sleep. I will have to get this straight or I will not sleep. the difference of ten miles per hour in one direction and ten in the opposite is 20. So in the gym when I am running on a treadmill and the speed indicator reads 3 miles per hour I am really putting out enough energy to be doing twice that. If I had ten apples and gave away ten apples I really gave away twenty. Or my real example while on rollers on my bike I am peddling and my speed reads twenty and the rollers are friction free and keeping up, they have to be traveling at forty to keep up with me. I'm still not there but I may be getting closer. If I am walking on a treadmill on an aircraft carrier facing towards the stern, and a guy is on a bike next to me on rollers but facing towards the bow we are not moving relative to each other, although he is riding at twenty and I am running at three. But if a dolphin swims by the boat from bow to stern and is traveling at three and the boat is traveling at eleven( because that is better than ten) the relative to each other their speed is 14. in fact relative to me and my biking buddy the dolphin is moving at 14, but if the dolphin is moving at three in the same direction then relative to the boat he is swimming at 8 in the opposite direction and the boat is moving at 8 relative to the dolphin.

Yes, that's exactly it, with one exception: On a treadmill (simplifying just a bit), you can only be stationary with respect to the gym floor, because it's too short to allow for movement forwards or backwards. So if the top half of the conveyor moves at 3 mph, the difference between 0 and 3 is 3, and the speed indicator reading is correct. You're just keeping up with the belt, no need to put in twice the effort. If you removed the supporting structure, so the bottom half of the conveyor would land on the floor, the whole treadmill would move at 3 mph. Including its axles around which the belt spins. Now, the top half of the belt would suddenly move at 6 mph. After a while, this force would have been pretty much transferred to you, so now you'd really have to run at 6 mph to stay on the darned thing. But realistically, treadmills face a wall or a window, so long before that could happen, it would crash into said obstacle and cause blowenfuse with spitzensparken. Fun!

The plane can take off. Force exerted by the engine(s) pushes/pulls the air to make the plane go forward. The wheels simply roll. If the plane has a forward wind-speed of 100 mph and the belt is moving at 200 mph, the wheels may be spinning backwards at 100 mph but they are free-wheeling and don't affect the forward movement of the plane.

Force exerted by the engine(s) only pushes the air, it doesn't pull. If the plane has a forward wind-speed of 100 mph and you'd want its wheels to spin backwards at 100 mph, the belt would indeed have to move at 200 mph, but in the *same* direction as the plane. In the example at hand, it moves in the opposite direction.

grey said: "Having said that, if anyone brings up Hitler or the Nazis during this conversation, I'm throwing my monitor out the window. You have my word."

haha, Grey, you gave a nice funny twist to Godwin's law. Sort of :)

Coming to that damn plane -- it will take off. Since there is some confusion in the question and I must admit after reading some comments, for a brief moment even I JohnKerry-ied, but then I JKied again to my original position, that the plane will take off. The conveyor belt could be moving at 10 times the speed of the plane backward if it wanted(assuming that speed paradox is taken care of), the plane will still take off.

Think of it this way: if conveyor belt is stationary(your local airport), say, the plane moves at 300mph. It takes off. Good pilot. If conveyor belt is moving backwards in such a way that the plane appears stationary to a bystander, but the plane is still moving at a speed of 600mph relative to the belt (and it's surrounding air). Infact, it might even be helped by such a conveyor belt due to whatever little extra air-current pushed back against its wings and hence will take off a second sooner than it would normally. I agree with others here, the treadmill-rollerblades example is the closest approximation.

I would like to see Jeremy Zawodny respond back, since he _IS_ a pilot, and he is disagreeing. I am surprised!

I've never seen so many people with such obvious lack of logic.

"Toon Van Acker says:
Just remember that the propulsion is relative to the air, and not the ground."

That's all you need to know. The end.

"I've never seen so many people with such obvious lack of logic."

You're not a regular churchgoer, I take it.

The plane takes off because of wind acting on the wings, not on the specific turbine part. You can do this experiment in any flight simulator. Have a Cesna parked and change the environment to very strong winds (80 mph if I am not mistaken... the stall speed for the Cesna). Let the parking breaks go and the plane simply lifts up, like a kite.

So I say the conveyor-plane would NOT take off for the reason Ricardo said in the 3rd comment: there would be no wind acting on the wings.

for god sake Derek Demarco, from the comment u had put into this discusion, i guest u're not a mechanical engineer. So i'll help you with some basic knowledge how an airplane and car can move forward:

1. plane can go forward, because the engine is pushing the air behind it.
2. Car can move forward, because the wheel "push" the ground.

please understand these simple principle first
-----------------------------------
now, to make matter simple, let us imagine a swimming problem,

fictional fact:
Derek is a cyborg who had a wheel leg, he can swim but very affraid of drowning, so he went into children pool, in this pool derek's wheel touch the bottom of the pool but his head is still above the water, so he can breath freely, the owner of the pool change the floor of the pool into some kind of waterproof conveyor belt (with the same speed control with the above topic).

assumption:
the conveyor only move the the floor but the water is not moving at all.
derek's wheel can be changed into 'freewheel" mode with no friction whatsoever

now:
if derek had to go from one side of the pool to other side, what will he do?this what derek will do:(s=second)

1s.
Derek: derek is still standing at the edge of the pool. and his wheel (remember that he is a cyborg with wheel legs) is always thouching the floor. also remember that derek now in "freewheel" mode, meaning that his wheel can rotate freely
conveyor: detected that derek's body is not moving (0km/h)

1,5 s.
Derek: derek start using his hand to propel himself forward, his speed now 0.5 km/h
conveyor: detected that derek's body is moving and now moving to other direction (0.5km/h)

2s.
derek: derek body start to have steady speed of 5km/h because he had a cyborg power hand to
conveyor: have the same speed with derek but with reverse direction (5km/h)

20s.
derek: derek now reach the other side
conveyor: stop moving


why derek can reach the destination even though the conveyor moving the other direction? because to move in water, we actually gain speed by our hand, so it doesnt matter if the floor is move.
by putting this principle into above topic, now we know that the plane can move just like usual.

now derek, can now u understand why the conveyor belt had nothing to with the plane movement?i hope u can now.

very sorry for my english

The plane won't take off because the plain isn't moving through the air.

If the plane is stationary, no air will be moving over the wings. Without air moving over the wings there is no lift.

Think about a flying a kite. The kite stays in a position relative to the ground (at the end of its string), its the air (wind) moving past that gives it lift.

Without the wind, the kite drops like a stone. So you have to run to drag the kite through the air.

Maybe this needs to be thought of as a riddle, rather than a physics question...

The wording of the riddle is designed to trip you up, lead you down the garden path, and come back with the wrong answer.

The plane will take off, because the conveyer belt can't keep it stationary, no matter how fast it moves.

christiano, please explain how the conveyor would cause the plane to remain stationary. bonus points are awared for fictional facts involving cyborgs.

Someone just pointed me at this discussion and I thought I'd put my oar in...

Forget about speeds.

A object will move if a force is applied to it.

If the aircraft moves relative to the air (in a forward direction) and continues to accelerate (i.e. the force continues to act upon it), it will eventually reach its take off velocity and take off.

If the plane's engines are generating x pounds of force on the plane, the conveyor belt has to exert an equal force to the plane, in the opposite direction to stop it accerelating.

The force that the conveyor belt can apply to the plane is due to friction in the bearings of the axles of the plane and between the tyres and the surface of the conveyor belt.

If the bearings and tyres are very very very inefficient, or the plane has its brakes on or is glued to the belt, i.e. coefficient of friction approaching 100%, then the conveyor belt has to be capable of counteracting the thrust of the plane's engines to keep it stationary.
If it can do that, the plane remains stationary (and so does the belt).

Assuming the tyres and bearings are normally efficient i.e. CoF approaching 0%, then the force that the conveyor belt can exert on the plane will be much less than the force being applied to the plane and therefore the plane will accelerate and eventually take off.

Just a thought: for the plane to take off, we have to assume that the wheel is frictionless, yes?

With a real world wheel with friction, could it still take off?

Not frictionless, just that the force due to friction is less than the thrust of the engines.... as long as there is a positive force on the plane it will accelerate (ignoring friction due to air resistance)

Cross post. I think Martyn just answered my question. Thanks.

I think this question would be better stated as: How much friction would there have to be so the plane could be prevented from taking off? Any real world wheel would cause so little friction that yes, the plane could still take off. But let's say the friction is 90% (where 0% is no friction and 100% means plane glued to conveyor). What happens now? What exactly? Boggle, the mind doth.

It _is_ true that the engines push against the air and not the ground. However, while the wheels are on the ground, the conveyor belt _does_ have a "pulling back" effect on the plane.

Think about these perspectives:

(1) Imagine that the plane and the conveyor belt were both stationary, and the conveyor belt started moving backwards at a fixed speed. The plane would move backwards as well. If the engines were fired, the plane could accelerate to the point where it was no longer moving backwards. Right? The plane and the belt are at a balance under which the forward force of the plane (by pushing air back) perfectly counters the effect of the conveyor belt pulling back on the plane (by contacting the tires). There is some proportional relationship between the plane's force and the belt's speed. The belt doesn't exert that much force on the plane because it only contacts it through the tires, which can spin. So the belt speed is probably some large multiple of the plane's force: B=kP. So as long as B/P always equals k, I think, the plane can't take off.

(2) Imagine the opposite. The plane is landing on the same conveyor belt. There is a speed at which the belt can move such (assuming that the plane can somehow get all of its wheels on the belt at the same time) that plane will appear to be stationary to an outside observer. Again, some relationship exists between the amount of force being put out by the plane's engines and the speed at which the belt is spinning. If the plane reduces engine power and the belt reduces its speed -- keeping this engine power:belt speed ratio intact -- the plane and the belt can make adjustments in lock step so that the plane can eventually shut of its engines and the belt can stop moving at just the right time so that the plane will have never moved after both of its wheels were on the belt. Since it's possible for this to happen without the plane taking back off, it stands to reason that the take-off scenario should be reciprocally _impossible_.

==> The real problem is this: The question supposes that there is _speed_ tracking in place, which isn't right. The conveyor belt can be adjusted so that the plane never has _any_ speed. The real relationship that needs to be tracked is the relationship between the force exerted on the plane by the conveyor belt through its contact with the wheels and the force exerted by the engines by blowing air.

...right?

I think you're right, pfong, Martyn answered that one succinctly and eloquently. However the conveyor would have to be sufficiently long, and of course the plane would have to carry enough fuel to keep it going for however long it takes to reach take-off speed. Just imagine a regular runway, a regular plane, but with the brakes applied. It would taxi very, very slowly to the end of the runway.

But if the wheels were frictionless, then none of the above would be true. The plane, engines off, would remain stationary, even if the conveyor belt started moving backwards. Then the plane could take off because no amount of convery belt speed could exert any force on the plane, and the wheels would just spin faster. Also, the plane wouldn't be stationary if it landed on the conveyor belt, because the contact between the wheels and the plane wouldn't have any slowing effect. However, as soon as the brakes were applied, the plane would slow much normally than it would on a stationary landing strip, because applying the breaks would interfere with the no friction assumption.

But the physical reality is that the conveyor belt would have some pull on the plane, though not much. It would have to move back _extremely_ fast in order to prevent the plane from taking off / keep it stationary when landing.

"So the belt speed is probably some large multiple of the plane's force: B=kP." -- John

On one hand, you state that k is a simple multiplying factor. On the other hand, B is supposed to be a speed, and P is supposed to be a force. Thus, you don't have an equation there, and there's no straightforward way to resolve this.

Your other approach (hah!) is quite ingenious, but the conclusion doesn't convince me. It's supposed to be the same problem run backwards, right? So if the plane can successfully land and come to a stand still, the reverse would be a successful take-off. The fact that the plane wouldn't take back off just reinforces this view.

Am I right that your last paragraph should be interpreted as: "The problem would have to be different in order to keep the plane stationary, but at it isn't different, the plane will move and take off." ?

"The plane will take off, because the conveyer belt can't keep it stationary, no matter how fast it moves."

Kottke should add this to his original post as it's the most succinct and accurate explanation in this thread.

As has been stated several times, eventually the question isn't one about airspeed, it's about friction. Imagine the wheel is completely frictionless. In that situation you should be able to understand why the plane will take off. (Even if the belt moves at 100 Mph, it has no effect on the plane). In the real world, the wheels aren't frictionless, but they are much closer to that than the other end of the spectrum. No matter what the speed of the plane, the effect of the conveyor belt is very small.

Really don't understand why this is being debated. With no movement in the aircraft (as the belt keeps it stationary) then no air moves over or under the wings. Therefor no upwards air pressure or lift. The wheels of the aircraft serve no purpose other than to allow it to move AGAINST the air fast enough to achieve airspeed. If you had a steep, long enough incline you could slide a plane to airspeed. Wheels on a belt mean nothing, if the wheels were travelling at twice the speed of the belt it would mean the plane would be travelling at only half it's required airspeed.

Why do you think the belt keeps the plain stationary? Please explain. I've asked for this too often already, but since no one every replied, I'm asking once again.

he thinks it stays stationary because he thinks it is a car. it is not a car - it's a plane, the wheels will free spin. the belt cannot keep it stationary.

My typo rate is increasing dangerously. Maybe I should go to bed. But then, over here it's 13:20. Will doesn't think it's a car, he stated that the wheels only serve the purpose of allowing the plane to move, which excludes the possibility of using them for propulsion. Well, that's a start :-)

"You're not a regular churchgoer, I take it."

Zing!

You're standing at the start of a long treadmill wearing rollerblades, and I'm at the other end - but on the ground beyond the treadmill.

The treadmill is moving at 10mph backwards, but you're holding on to the side, your wheels spinning at the same 10mph. That's pretty easy right? Because you're only having to overcome the friction in the wheel-bearings of the blades.

Now, we tie a long piece of rope around your waist, and the other end around mine and I start running away from you at a constant pace.

Of COURSE you'll move forward. Because the force I'm exerting is stronger than the friction of the wheels on the rollerblades.

Doesn't matter how fast the treadmill moves in the other direction, the only force I have to overcome is the friction inherent in your rollerblade wheel bearings.

And the propeller, or jet engine on the plane is pushing the plane's mass not against the conveyor belt, but against the surrounding air.

The plane takes off. The wheels are passive, not active.

Now a road-car, where the force is applied directly through the wheels to the road, well that's a different proposition entirely.

IT WILL TAKE OFF, if the plane in question is a Sea Harrier. Otherwise it's obvious that it will not. : )

It does not take off. Imagine that it did take off. The second the plane left the ground, it would no longer be touching the conveyor belt. Now remove the conveyor belt from the scene since it is no longer interacting with our plane. You have a giant heavy plane, stationary, above the ground, with it's engines going gangbusters. It's like it's taking off like a Hawker Harrier jet which it can't do. It would hit the ground.

dino, once again I'm inclined to asked, why in the world would you assume that the plane is stationary? Why? Are you just pretending to assume this, without giving any explanation whatsoever, in order to make me go insane?

Sea Harrier does take off !!!

It wouldn't take off. Lift is generated by air passing over the winds, even if the engine configuration was once that pushed air over the wings it would not be sufficient. The plane is remaining in a stationary spot, even if the engine is on 100% power.

Additionally, the conveyor belt is unlikely to keep up. I've seen comments suggesting this is why it would take off. Again, it won't take off. Once the engine hits 100% and very little lift is being generated over the wings the aircraft will become unstable on the conveyor belt, hopping on and off the belt. Which will lead to at some point one wheel touching down before the other wheel(s) thus leading to a crash.

That plane isn't taking off. The basics of aerodynamics make the possibility impossible if the aircraft is not moving forward at an adequate speed.

Oh, I just figured it out in my head. If the conveyor belt is going the opposite way to the move of the aircraft then it obviously will take off, and it will do so at ease.

The problem is trying to think outside the mindset of a human moving on a conveyor belt. Unlike humans, who can only move against the conveyor belt by moving one foot after the other, the aircraft's wheels are constantly in contact with the belt, and the belt is moving in the same direction as if the plane was actually moving. So once the engine perks up and starts providing enough pull then I can imagine the aircraft will be able to gain sufficient speed.

I think!

The propellers are the propulsion, not the wheels. Seriously, people.
The conveyor belt can push as hard as it wants, and it won't slow the plane down except a tiny bit for the friction in the wheels. The propellers will pull the plane through the air and it will gain enough speed to take off. Using the logic of you "no-fly" people, no plane should ever be able to fly, because as soon as it leaves the ground its wheels no longer have anything to push against. So it'll fall out of the sky, right? In fact, we have just such a giant conveyor belt. It's called the Earth. And it goes at 1669.79 K/h (at the equator) -- using your (flawed) logic, a plane would have to have propellers powerful enough to shoot the plane at that speed (plus 200+ for the actual speed required to take off) in order to take off on a runway facing west. Since no engines can do that, you'd only be able to travel east (or at least, take off going east and turn around).

There's no question that the plane would take off... It's not that confusing, is it?

For the sake of a genuine discussion, will *anyone* claiming that the conveyor is holding the plane back by any significant amount care to explain *how* this is possible at all? Are all of those people just trolls? Or sock puppets of one and the same person?

Personally, I like to think that they are different persons and not trolling, but once they realize their mistake, which is inevitable if you try to explain the impossible and make any progress, they don't dare to come back and admit their mistake. Cowards. But that's just what I'd *like* to believe.

The plane is remaining in a stationary spot, even if the engine is on 100% power.

There is little to no correlation between the free spinning wheels of a plane and a plane's speed. By the last few commentor logic, a plane should not be moving when it is in the air because its wheels aren't moving. Think about the instant directly before and after a plane touches down. The wheels go from no rotation to many thousand RPMs within a second...what's the difference in speed of the plane before and after that same second? very little. If there's no connection between wheel speed and plane speed then, why do you guys think there is one when it is taking off (or any other time)?

This is absolutely ridiculous. I'm terrified that those of you that say the plane will fly are in positions of serious responsibility. FFS, look up the principles of flight. Under your logic we don't need runways for takeoff, we could just hold on to the plane, wind up the engines and then let go. Ridiculous.

I was totally gonna tell the MythBusters on you guys, but they're already inundated with the imbecility of this concept. Apparently this one's been making the rounds.

The plane will take off because it is *not* a car with wings. The wheels are there to keep it up, not make it go. The prop/jet/rocket makes it go. The conveyor will just make the wheels spin faster.

Ugh, another one claiming that if a plane could take off from a conveyor, that runways would be miraculously shorter.

I get it now. Thanks for the thought trip. I enjoy thinking about stuff like this.

Another one I thought about recently - and couldn't stop thinking about for days - is why Astronauts are weightless. I, stupidly, thought astronauts were weightless because they were in space and were somehow outside of the influence of Earth's gravity. Duh... they're weightless because they're constantly falling to the earth and it's their forward motion that causes them to keep missing the planet. I can't believe that I wasn't taught this - and how space objects orbit - at school. Or maybe I just wasn't listening.

HM says:
"This is absolutely ridiculous. I'm terrified that those of you that say the plane will fly are in positions of serious responsibility. FFS, look up the principles of flight. Under your logic we don't need runways for takeoff, we could just hold on to the plane, wind up the engines and then let go. Ridiculous."
You are absolutely ridiculous. I'm terrified that so many of you that say the plane won't fly are silently assuming that it's stationary. FFS, look up what the other side is saying. Under our logic, the plane is NOT stationary, but you just assume so and don't every give any explanation whatsoever why this would happen. Ridiculous.

Okay, whether or not the plane can take off is a function of the conveyor belt.

If we assume a magic conveyor belt that can move at arbitrary speed to try and control the position of the plane it will *always* win and here is why:

Consider a 747 sitting at rest on this conveyor belt. It's landing gear is supporting the mass and at rest on the still belt.

At time t = 0, the pilot fires the engines and releases the brakes to begin his take off rool.

At time t = 0+epsilon (where epsilon is a very small amount of time) the conveyor belt controller notices that the plane has started to move, and applies back travel to prevent the plane from moving. Of course the engines are applying tons of thrust against the air and the wheels are low drag so the conveyor belt can't apply much force to prevent the plane from moving.

So the conveyor belt speeds up. Two things happen: 1) the bearings in the landing gear get hot. 2) the skin drag of the belt blows more air resisting the motion of the plane. At some conveyor velocity, probably around 1500mph, the bearings in the 747 landing gear will fail; the wheels will lock and the whole thing will be thrown of the back of the conveyor assembly.

Of course assuming an reasonable conveyor belt that human civilization can build; the plane won't care and will just take of, suffering only a little extra bearing wear in the process.