the plane on the conveyer belt - a different question

[R. U. Serious]

I have a question on the explanation of the original

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

The question is: Will the plane take off or not?

You've probably heard of this one. It basically comes down to how you interpret "speed of the plane". If you equate it with how fast tires are spinning, then by definition the plane is not allowed to move forward an inch (thus air and wing do not move relative to each other, hence no lift).
If however you equate the speed of the belt with the speed of the plane relative to the (unmoving) earth/airport, then the belt will obviously not be able to apply enough force to the plane so stop it from moving forward.

Now my question is, whether the amount of force which the belt can apply to the plane is physically limited? Isn't it connected to the weight of the plane? Does the answer change depending on whether the turbines are applying an equal force in the opposite direction, or whether the plane "just sits there" (with no other forces pulling it in the opposite direction)?

[Ok, given the question I have, it doesn't really matter that it's a plane. Just some object with "free spinning" wheels.]

[Darth Wong]

You've probably heard of this one. It basically comes down to how you interpret "speed of the plane". If you equate it with how fast tires are spinning, then by definition the plane is not allowed to move forward an inch (thus air and wing do not move relative to each other, hence no lift).

If however you equate the speed of the belt with the speed of the plane relative to the (unmoving) earth/airport, then the belt will obviously not be able to apply enough force to the plane so stop it from moving forward.

If the conveyor belt has an assumed unlimited speed, then it could prevent takeoff despite the fact that the plane is using jet engines rather than wheeled propulsion, by spinning so quickly that the plane's landing gear is superheated from friction and disintegrates. But this is not a practical solution to the problem; obviously, the practical solution is that the wheel rotation is totally irrelevant since the jet propels itself forward through means that have nothing to do with ground velocity, so the conveyor would immediately go to maximum speed and still be unable to do anything about the movement of the plane.

[Spoonist]

The question doesn't supply enough information.

To answer the question you need to also know the plane type and the wind speed and direction in relation to the plane.

If it is a plane like the Harrier then it doesn't need a runway for instance.
If it is a glider it just needs enough wind-lift to get airborn, regardless of engine.

If we do equate it with having no runway and no wheels on its landing gear, and instead is launched from a "rocket pad" then most commercial planes would get propulsion for a short stretch and then crash because they don't have enough lift under their wings.
But something like a fully loaded 747 wouldn't even create enough propulsion to crash.

[Darth Wong]

If the plane had no wheels, it would be a matter of applying force to hold the plane in place against its thrust, rather than a question of the conveyor belt's speed.

This strikes me as a trick question for high school kids, who might be tempted to treat the question as if it's a car rather than a plane.

[Sriad]

An arbitrarily powerful conveyor belt would be able to produce high winds along with its motion relative to the plane; this would keep the plane stationary on the X axis, but it would still have lift. Whether these winds would be created before or after the plane's wheels have disintigrated as in Wong Reply #1 is obviously the true goal of this question.

[lPeregrine]

*sigh*

Not this question again... there's an insanely long thread on diabloii.net debating this one, and it's a bit disturbing how many people don't understand the physics behind it.

And yes, Darth Wong, that's exactly what it is. And apparently an effective one, as half the forum made that assumption and debated it to the death.

Now my question is, whether the amount of force which the belt can apply to the plane is physically limited?

It's only limited by structural failure of the plane and/or belt. If the belt can somehow spin at up to infinite speed without any failures, then it can apply limitless force.

Isn't it connected to the weight of the plane?

Yes, friction is based on the mass of the object. A heavier plane will have more friction in the wheels (and therefore can transfer more force), but not enough difference to change the outcome.

[AMX]

Uh, guys...

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

Since |v(belt)| = |v(plane)|, and the plane lifts off before reaching infinite speed, the top speed of the belt is a nonissue.

The only thing that matters here is whether the plane's landing gear can take twice it's designed take-off speed.

[Darth Wong]

At very high speeds, pneumatic tires will separate from the rims due to centrifugal forces, and then they will disintegrate. But as noted above, this is obviously not what the question was intended to examine; it was meant as a trick question.

[R. U. Serious]

@lPeregrine: Thanks for clearing that up. I somehow had something else mixed up in my head. All cleared up now.

@Darth Wong:

This strikes me as a trick question for high school kids

Well, you don't have to be a high school kid, just have the physics-knowledge of (or even less than) a high school kid. There's a lot more of the latter than the former I think.


When I initially was confronted with the plane-belt question, the person stating it, made specific reference to the tires of the plane, asking what would happen, if the belt would always spin exactly as as fast as the tires of the plane - implying that the plane would not gain any speed against the airport/surrounding air - which messed it up...

[Broomstick]

I have a question on the explanation of the original

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

The question is: Will the plane take off or not?

I feel like I'm coming into the conversation mid-stream here, but what the hell.

Airplanes (fixed-wing non-harrier) fly because of air moving past the wings. Keeping it simple - when the air moving past the wing reaches a certain velocity then the lift generated is sufficient to pull the airplane off the ground.

Note: what counts is the SPEED OF THE AIR RELATIVE TO THE WING.

Thus, if the "conveyor belt" is moving in the direction opposite to the airplane's propulsive force (jet, prop, whatever) at exactly the same speed as the airplane landing gear is attempting to move it then relative to the air the wing is motionless and the airplane does not fly.

Now, continue discussing tire blow-outs and such like to your heart's content.

[Ninja of the North]

I have a question on the explanation of the original

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

The question is: Will the plane take off or not?

I feel like I'm coming into the conversation mid-stream here, but what the hell.

Airplanes (fixed-wing non-harrier) fly because of air moving past the wings. Keeping it simple - when the air moving past the wing reaches a certain velocity then the lift generated is sufficient to pull the airplane off the ground.

Note: what counts is the SPEED OF THE AIR RELATIVE TO THE WING.

Thus, if the "conveyor belt" is moving in the direction opposite to the airplane's propulsive force (jet, prop, whatever) at exactly the same speed as the airplane landing gear is attempting to move it then relative to the air the wing is motionless and the airplane does not fly.

Now, continue discussing tire blow-outs and such like to your heart's content.

From what I understand, it is not the landing gear that is providing the propulsion, but the engines on the aircraft, which the conveyer belt has no effect on. Imagine an airplane with repulsorlifts on it instead of wheels.

[lPeregrine]

I feel like I'm coming into the conversation mid-stream here, but what the hell.

Airplanes (fixed-wing non-harrier) fly because of air moving past the wings. Keeping it simple - when the air moving past the wing reaches a certain velocity then the lift generated is sufficient to pull the airplane off the ground.

Note: what counts is the SPEED OF THE AIR RELATIVE TO THE WING.

Thus, if the "conveyor belt" is moving in the direction opposite to the airplane's propulsive force (jet, prop, whatever) at exactly the same speed as the airplane landing gear is attempting to move it then relative to the air the wing is motionless and the airplane does not fly.

Now, continue discussing tire blow-outs and such like to your heart's content.

And that's the assumption the question expects you to make (and the one I thought of when I saw it the first time), that it's testing whether you realize that a motionless plane has no lift regardless of tire speed. But what the question doesn't bother mentioning is that the belt will not be able to slow the plane (at least to any significant amount). The idea that the plane does not move relative to the air is an assumption on your part, that isn't supported by a careful look at the question.

Notice it just says "it moves the same speed backwards", not "it moves the same speed backwards, which cancels the plane's attempts at forward motion." All it says is that when the plane is moving 100mph forward, the belt is moving at 100mph backward. In other words, the plane is moving 100mph through the air, while the wheels are spinning at the equivalent of 200mph. Assuming the wheels can handle the extra stress, the plane takes off.

[Broomstick]

From what I understand, it is not the landing gear that is providing the propulsion, but the engines on the aircraft

That is true (barring some weird-ass case - but I assume the question is discussing somethine like the typical/average airplane)

Imagine an airplane with repulsorlifts on it instead of wheels.

That would be easier to imagine if I knew what the hell a "repulsorlift" is, and how it induces motion.

[Edi]

Imagine an airplane with repulsorlifts on it instead of wheels.

That would be easier to imagine if I knew what the hell a "repulsorlift" is, and how it induces motion.

Basically it's an antigravity device that presumably provides propulsion by pushing off from objects via a force field system. Most of those flying little thingamajigs in Star Wars are repulsorlift vehicles.

Edi

[Broomstick]

I've got an idea.

Someone call Mythbusters - there's no reason this can't be tested in real life. (Other than time, money, obtaining aircraft, large conveyor belt...)

I could see them trying this first with an RC model (advantages are light weight and small size, enabling them to use a fairly convential conveyor belt)

No doubt they would want to move up to a "real plane". Use something like a Cessna 150 or 152. You'll need a belt that can support 1600 lbs. One advantage is that you won't need to get up to 100 mph, which will simplify matters. (I'll even voluteer to "fly" the plane)

No doubt some wanker will maintain there's a difference between jets and props - there's a guy in Ohio who brought a jet-powered ultralight to Oshkosh a few years back, if you could locate him maybe we could use his aircraft to see if the situation is different for jets. Again, the lower weight and speed will make empirical testing easier.

I still say there's a confusion here between groundspeed and airspeed, but I'll need to think it over to see if I can better express my thinking on the matter.

[AniThyng]

AVWeb link

Scroll down the article, there's a section that addresses this issue there...

[Molyneux]

I was having a little trouble with this, 'til I thought of thinking about a plane with runners instead of wheels...

[Broomstick]

I still say the key thing here is airspeed.

So the question is (rephrased) would a conveyor belt running in the opposite direction of the landing gear wheels somehow prevent the airplane from gaining airspeed?

The answer is... not necessarially, or even often, but it could.

It depends partly on friction, and partly on the thrust available.

An RC model may, aerodynamically, be a decent scale representation of a full size airplane, but from the perspective of thrust it's wildly different - RC models have MUCH more thrust per unit of weight/mass than full size airplanes, much less mass, much smaller moment arms, and so forth.

An example of the difference this can have on performance can be seen on take-offs in grass/vegetation reaching over the tops of the wheel of an RC model vs. a Cessna 172. The RC model will take a slightly greater length to get off the ground in such relatively deep grass than on a surface such as pavement, but the full-size C172 will take much longer, 30-40% more distance, or perhaps will never leave the ground at all under such conditions. It just doesn't have the surplus of thrust that would allow it to overcome the resistance presented by deep grass. An RC model can power through grass up to its belly - with the possible exception of the Stearman, none of the other airplanes I've flown could do that. The plane would move forward, but it would never be able to achieve sufficient forward motion to get enough airspeed to get airborne. Again, there's just not enough thrust available to overcome the resistance in that situation.

(And yes, I have experienced the frustration of finding myself in a $150,000 three-wheeled ground vehicle in real life. That's not just theory talking, I have some practical experience with this.)

The same situation is faced with an airplane on skis - on snow or ice the friction of the landing gear is low enough that the available thrust can overcome it and produce sufficient acceleration to gain flying airspeed. Land one of those on grass or sand, though, you'll never get off the ground when it's take-off time.

And again, on the water - I'm not entirely conversant with seaplane operations, however, most descriptions I've seen of take-off's involve getting enough groundspeed to partially hydroplane the pontoons or boat hull and, again, reduce friction to allow greater acceleration.

So - IF there is sufficient thrust available to overcome the friction/resistance posed by the conveyor belt the airplane will take off. Whether or not there is sufficient thrust for a given airplane is going to depend on a number of factors, such as engine power and what the conveyor is made of. For some low powered aircraft the resistance to motion imposed by such an arrangement may be enough to keep the airplane grounded. For others, there could very well be sufficient thrust to get airborne.

Which is yet another reason I'd like to see this tested emprically, preferably with several different airplanes.

[Darth Wong]

I find it highly doubtful that the rolling resistance of a plane's landing gear wheels could possibly approach its engine thrust on full power, especially since they are, in fact, designed to roll with as little friction as possible. Are you assuming that the wheels are fixed or braked so that they don't roll?

[Broomstick]

What airplane wheels are we talking about? Those on a 747? An F-16? A Piper Cub?

Some of the smaller airplanes really don't have very much power available and there isn't much available to overcome friction.

I can see where someone used to the effects of ground surface on take-off performance might react to the conveyor belt idea with the notion that it might impede acceleration enough to prevent flight. Hard surface vs. grass vs. slush/snow/ice all have a noticable effect on the acceleration and take-off distance required of any airplane.

Friction is a factor when the wheels on are the ground. That's why on rough fields - nonpaved, grass, etc. - you pull the airplane up off the ground before you achieve normal flying speed (actually, as soon as you can get it and keep it off the surface) and finish the acceleration and take-off in ground effect. Because you accelerate so much better in the air vs. on the ground (any ground).

So the key becomes the friction between the wheels and the belt. If it's closer to that of wheels on pavement yeah, the airplane will fly. If it's closer to that of tall, wet grass or sand then it's possible the airplane won't fly.

As for rolling resistance vs. full thrust - again, that varies with the airplane. There are airplanes where, at full thrust, you can't rely on the brakes to hold it in place. On a slick surface - such as slush - you can lock the wheels with the brakes and the airplane just ignores it and will happily wear a flat spot into the wheel as the engine drags the machine along the ground. On the other hand, deep grass can impede forward motion sufficiently to prevent take-off even without a conveyor belt involved.

Airplanes are different than cars because the car relies on contact with the ground to move, but the airplane relies on contact with the air. But contact with the ground still counts. Friction is friction. The only question is how much friction and what effect does it have on acceleration.

So, Wong, I'm just a pilot - you're the engineer. Assuming normal tire rubber for the airplane, what's the conveyor belt made of and what's the friction between it and the wheels?

(If I wanted to be a real bastard I could also drag temperature and altitude into the argument since that also has a significant impact on performance, but let's avoid that and just assume the standard reference atmosphere.)

[Admiral Valdemar]

I thought this question was simply aimed at whether the plane would achieve flight if it was at military thrust but not moving anywhere (in which case Broomstick posted what I was going to say). This issue about wheels and friction sounds like overanalysing an otherwise simply hypothetical, but then the question is somewhat vague.

[Dooey Jo]

I thought this question was simply aimed at whether the plane would achieve flight if it was at military thrust but not moving anywhere (in which case Broomstick posted what I was going to say). This issue about wheels and friction sounds like overanalysing an otherwise simply hypothetical, but then the question is somewhat vague.

But then it wouldn't really be a trick question. Who thinks airplanes fly because of their speed relative to the ground, anyway? It depends on what the question is supposed to show and how idealised the conditions are...


About friction and stuff:
If I remember correctly (it is rather late here, after all), the friction does not, once overcome, increase with the relative velocity (under normal conditions, excluding the heat produced melting the wheels or something), because the wheels' contact surface does not move relative to the ground. Thus, once the plane starts rolling (and it will, otherwise the belt wouldn't start), it shouldn't be much different from starting on a non-moving conveyor belt.

Except if you're turning. Then it will be bad, as there will be a sliding friction force applied, and that one is going to be a lot bigger than the rolling friction from the wheels.

Now, if the plane had gotten all its thrust from the wheels, and thus depended on the relative speed to the ground, it obviously would have been different. But if that had been the case the plane wouldn't be able to fly once off the ground anyway so...

[tharkûn]

the friction does not, once overcome, increase with the relative velocity (under normal conditions, excluding the heat produced melting the wheels or something), because the wheels' contact surface does not move relative to the ground. Thus, once the plane starts rolling (and it will, otherwise the belt wouldn't start), it shouldn't be much different from starting on a non-moving conveyor belt.

At high velocities the standard friction model is not applicable. You will eventually encounter viscious resistance and air friction. These are proportional (or worse) to velocity as well as surface area. Even if we ignore those at sufficiently high RPMs the tire simply cannot hold togethor.

Before any of that occurs we will see the temperature of the tire going up. The energy of friction is proportional to the distance travelled. As the wheel rotates faster it heats up and that changes the surface of the tires; this is why drag racers intentionally use friction to heat the tires to get better performance.

[Darth Wong]

What airplane wheels are we talking about? Those on a 747? An F-16? A Piper Cub?

Some of the smaller airplanes really don't have very much power available and there isn't much available to overcome friction.

I can see where someone used to the effects of ground surface on take-off performance might react to the conveyor belt idea with the notion that it might impede acceleration enough to prevent flight. Hard surface vs. grass vs. slush/snow/ice all have a noticable effect on the acceleration and take-off distance required of any airplane.

That's because you're no longer dealing with normal rolling friction on a surface like snow-covered grass; you have to actually push through material. On a conveyor belt, this would not apply; the belt would not have to rotate too many times to shake off whatever junk is on it.

Friction is a factor when the wheels on are the ground. That's why on rough fields - nonpaved, grass, etc. - you pull the airplane up off the ground before you achieve normal flying speed (actually, as soon as you can get it and keep it off the surface) and finish the acceleration and take-off in ground effect. Because you accelerate so much better in the air vs. on the ground (any ground).

Friction is only a factor if the wheels are locked. Otherwise you have bearings in the wheels which are designed to reduce friction. And in this hypothetical scenario, the plane is attempting to take off, so there is no reason why the wheels would be locked.

So the key becomes the friction between the wheels and the belt. If it's closer to that of wheels on pavement yeah, the airplane will fly. If it's closer to that of tall, wet grass or sand then it's possible the airplane won't fly.

I don't see how a conveyor belt is going to approximate the consistency of sand or a muddy grass field.

As for rolling resistance vs. full thrust - again, that varies with the airplane. There are airplanes where, at full thrust, you can't rely on the brakes to hold it in place. On a slick surface - such as slush - you can lock the wheels with the brakes and the airplane just ignores it and will happily wear a flat spot into the wheel as the engine drags the machine along the ground. On the other hand, deep grass can impede forward motion sufficiently to prevent take-off even without a conveyor belt involved.

Sorry, by "rolling resistance" I meant the friction of the free-rolling wheel bearing, not the friction between a locked wheel and the ground.

Airplanes are different than cars because the car relies on contact with the ground to move, but the airplane relies on contact with the air. But contact with the ground still counts. Friction is friction. The only question is how much friction and what effect does it have on acceleration.

So, Wong, I'm just a pilot - you're the engineer. Assuming normal tire rubber for the airplane, what's the conveyor belt made of and what's the friction between it and the wheels?

The friction coefficient between the conveyor belt and the wheels could be as high as you like and it wouldn't matter if the brakes aren't on.

[Broomstick]

Who thinks airplanes fly because of their speed relative to the ground, anyway?

A lot more people than you'd suspect.