Principles of flight?

[AirNZ]

I think the best analogies given here were that of the matchbox car on a piece of paper that you push forward with one hand while pulling the paper backwards with the other hand, and the saktes ona treadmill with a rail.

Somehow the car still moves forward on the piece of paper right? Even though the paper moving bckwards is causing the wheels to spin, the of force of the paper on the car itself (even though it exerts force on the wheels) is absolutely minimal.

The skates and rail example is great too. If the conveyer belt is moving backwards at 10km/h, it's still pretty easy to hold yourself in place with a rail or rope. Only minimal extra effort (thrust in the case of the plane) is required to move forward.

The hovercraft explanation is valid too. Most people will have no problem understanding that a hovercraft floating on a cushion of air can move forward on the belt right? A plane with wheels is just the same, only with just a little bit more friction, which is negligible anyway.


The whole thing though is a bit like that old problem of an arrow always having to cover half the distance between it's head and the target. Even though there really should always be at least half the distance between to objects to cover, in the real world and arrow can make contact with a target.

Seeing as we all like cars, just think of that one as two cars heading towards each other. There is always at least half the distance between two cars to be covered by each car, no matter how infinitessimally small, yet we know that car crashes do happen.

The conveyerbelt is a red herring.

And anyway, if the conveyer belt is always turning at the exact same speed as the wheels and we talk about the plane going 5km/h forwards and the belt going 5km/h backwards, then the wheels spin at 10km/h.

How is it possible for the belt to be moving at 5km/h and 10km/h at the same time? I mean it's supposed to match the actual speed of the wheels right? Not the speed of the wheels relative to the ground?????

Is the conveyer belt always accellerating to infinity, never quite catching up?

Like the arrow meets the target (and pierces it), even though it must travel half the distance, the plane will take off, because the belt is a red herring and would be impossible (as above) anyway (belt can't move at two speeds at once).

At 0km/h the belt is possible, but once the plane moves forward, the belt moving at the same speed as the wheel is impossible.

Other things to consider...

If the belt is a reactionary belt, there must always be a delay in it's reaction, which would allow forward movement.

If it is a preemptive acting belt, then it's cheating isn't it, as it changes speed preemptively, regardless of how fast the plane is moving forward.

It never can be moving at the same speed as the wheels, except when the plane isn't moving to start with.

[AirNZ]

Crazy imaginative belts. What'll they think of next?

[RedMist]

AirNZ, there is no disparity between the wheelspeed and conveyor belt speed.
If the wheelspeed is 10kph the conveyor belt speed is 10kph.

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. "

Its a theroretical question that is impossible to model in real life, as you are correct a reactionary time is required, and a slight forward movement will always be experienced before the conveyor reacts. However the question states "exactly match, at any given time"

So if we apply thrust in our plane, the only thing that is there to slow it down is the frictional forces of the wheel to conveyor surface and any bearing surfaces in the wheel. So you apply a moderate amount of thrust, the wheelspeed is accelerated till the point where these two frictional forces counteract the thrust, perhaps 10,000 kph or more? and at the same time the conveyor is accelerated at exactly the same speed to match the wheelrate. IE the vehicle does not move.

The only way for the plane to move forwards is for the wheelspeed to match the conveyor speed but still make groundspeed. IE the wheels need to slip. Obviously with the theroretical frictional forces involved, slip is certainly probable However I see it like attempting to take off with the brakes on, lack of thrust, no directional stability.

My view is much that of fivebobs, however I doubt very much that this plane will take to the air.

In regards to the conveyor developing enough airspeed to lift the plane. Interesting proposition, I don't know enough about aerodynamics to know if a belt as long and wide as a runway would develop a smooth fast enough airflow to create the lift necessary. My vote is the airflow would be so disturbed our plane would be destroyed on the ground.

[pidge]

*SIGH*

Things to keep in mind:
The thrust used to maintain airspeed (i.e. overcome airdrag) is a fraction of the thrust used for take off.
Jet Planes have to use brakes AND reverse thrust to stop short of the end of a runway. (i.e. the wheel bearing friction is "bugger all")

[RedMist]

*DOUBLE SIGH*

Whats so hard to understand? The concept is really really simple. You need to accelerate in order to move. You need a change in speed in order to accelerate. If I spin the wheels to achieve 10kph - the reverse conveyor at 10kph what speed relitive to ground am I doing? ZERO. If I add thrust which attempts to propell the plane forward, I indirectly attempt to accelerate th wheels. Which in turn accelerates the conveyor. So if I'm now approximating 10000 kph at the wheels - travelator speed of 10000kph what speed am I doing ? ZERO! Whatever movement you attempt to put forward, is instantly reversed by the conveyor. Do 10,000kph the conveyor is doing 10,000kph in reverse. In doing so its also accelerating the wheels, which in turn accelerate the conveyor, which in turn accelerate the wheels, which in turn.... UNTIL the frictional forces are so great that the thrust is counteracted by another equal and opposite force (ever heard that one before?)... SIGH.
In this case the only force I can think of is friction.

How much friction do you think there would be in a plane wheel bearing doing 100,000 kph? or 1,000,000 kph??

Amount of thrust DOES NOT matter. Other than the more thrust the higher the speed of the wheels spinning, as the frictional forces need to be greater.

Think of it this way. If the brakes are on, and we have thrust, wheelspeed = 0, groundspeed = 0, conveyor = 0, airspeed =0.

Brakes are off wheelspeed = 100000 kph at circumferance, conveyor = 100000 kph, groundspeed =0, airspeed = 0

Fivebob has the theroy right, I just don't believe in his outcome.
There are only two possible exceptions, create airspeed by passing air over the wing or slip, where wheelspeed - travelator speed =0 but you are still getting some groundspeed.

[malc]

THANKYOU!

I cannot understand how anyone can believe that something can move forward on a surface that is matching that motion, in the opposite direction.

All of those analogies are impossible to create exactly.
pulling a car along a piece of paper, your cars went forward on the paper because you could not match the speed that the wheels were turning.
It would be simply impossible for someone to believe that their hand eye coordination is so fine tuned that they are pushing their car and pulling their piece of paper at exactly the same speeds, no matter how hard they push or pull

The ONLY way for a rolling plane to make forward movement is to have its wheels rolling faster than the surface below.
The entire weight of the plane at rest is on its wheels, which is obviously on the ground, or belt in this case.
Until a plane can get to the required speed for lift off, all it has is weight, when it is stationary it has no lift.
When you push something faster, its wheels speed up, the conveyor counteracts this, I cant see how the plane is somehow getting a headstart over the conveyor.

aaaand if the plane was stationary, the wheels would not spin at all

and, if the plane tried to move forwards, the conveyor would move backwards.

[pidge]

*DOUBLE SIGH*

Whats so hard to understand? The concept is really really simple. You need to accelerate in order to move.

With you so far...

You need a change in speed in order to accelerate.

A change in speed is acceleration (a=dv/dt), acceleration causes a change in speed (dv=a.dt). Neither of the two statements (or equations) tell you what causes the acceleration, they just provide the relationship between speed, acceleration and time. To accelerate, a net external force needs to be applied (2nd Law of motion).

If I spin the wheels to achieve 10kph - the reverse conveyor at 10kph what speed relitive to ground am I doing? ZERO.

If you move the plane, the wheels move with the plane, causing them to rotate. The wheels are free to rotate (the are not driven directly, nor are the brakes on). Note that there is difference between the and rotational motion.

If the plane is moving forwards at 10kmph, the wheels move 10kmph forwards, so the conveyor belt moves at 10kmph backwards, causing the wheels to rotate with an rotational speed such that the outside edge of the wheel has a speed of 20kmph (the difference in speed between the wheel and the conveyor belt).

<"stuff">

redmist, by what mechanism is the converyor belt going to provide the force through the wheels to match the thurst of the engine? Friction?

On the ground, landing gear wheels with the brakes on have trouble stopping a (jet) plane whose engine is running at full thrust from moving forwards.

It's the forces that matter, not speed. You've not demonstrated an understanding of Netwon's Laws of Motion...

btw, as an aside, what's your highest educational qualification in Physics?

For that matter, how about anyone who's provided an answer?

[pidge]

THANKYOU!

I cannot understand how anyone can believe that something can move forward on a surface that is matching that motion, in the opposite direction.

That's simple. You don't understand the Laws of motion. Therefore you cannot understand the question to answer it, nor understand the correct answer.

What's your highest educational Qualification in physics?


Here's a "simple" physics question. No maths required.

You are floating in space. No net force is being applied to you. Floating immediately above you is your twin (for this question scenario, you have a twin. At least a person identical in mass), at a distance such that you can easily push them away. You are "at rest" (not moving) relative to the fixed point halfway between you and your twin. What happens when you push them away, relative to that fixed point?
a) Only you move away from the fixed point, your twin remains at rest.
b) You both move away from the fixed point at the same speed.
c) Only your twin moves away from the fixed point, you remain at rest.

(hint: Third law)

[RomanV]

Ive been thinking about this a bit more, and (as much as I hate to admit it) Ive sort of changed my mind.

I think the intent of the original question has been lost in the wording, and the wording in its current state is an ambiguous impossibility.
I think the original intent of the question was probably "Could the plane take off, if the conveyor moved at the same speed as the *plane* in the opposite direction"...
As I am quite sure that the intent of the original question was a simple question about relative speed, more than anything else.

In which case the question and answer are very simple.
Yes, the plane takes off, and the wheel speed is double the plane speed.

However, the problem with this question, is that the conveyor doubles the WHEEL speed, what ever it is.

Ignoring everything else, the problem boils down to "wheel speed = wheel speed x 2."
As opposed to "Wheel speed = plane speed x 2"

If the plane is stationary, and wheel speed = 0, then nothing happens.
But if the wheel moves even 0.00001mm, (eg, an ant farts on the wheel) then the wheel speed increases and increases towards infinity.......

It wouldnt keep on increasing until the force is equal to the thrust of the jet engines....
As this would imply, that at a certain wheel RPM, the wheel speed would stop increasing by 2.
The wheel speed would keep on increasing, until it surpassed even the forces generated by the engines.
So the plane would be spat off the back of the runway, as the wheel speed and conveyor speed would increase and increase.

Either way, we are forced to make assumptions about the complexity of the question.
Do we assume that they really meant to say "plane speed" instead of "wheel speed"?
Do we assume that the plane is invincible, and can widthstand all of these forces?
Do we assume that the tires wont slip?
Do we assume that the conveyor and wheels can spin to infinity?

Since the conveyor and the wheels are spinning at an infinite speed, do we assume that they turn into pure energy?

If we are assuming that the friction of the wheels holds the plane back, part of the friction is heat. infinite speed = infinite friction = infinite heat. What are we to assume about this? Does the conveyor melt the universe?

I think that all of these questions cant be answered, and I think that none of this was intended in the original question....
It is probably the chinese whisper rewriting of the question that has caused the dispute, as a simple change of 'wheel speed' to 'plane speed' changes things completely.

It seems like a simple question that someone would ask, similar to "If I am travelling at 5,000kph, and fire a bullet at 5000kph behind me, does the bullet drop to the ground?"

The problem being that in this case, a slight change in wording completely changes the scope of the question from simple and plausable, to horribly overcomplicated, and impossible to answer without some very crucial assumptions being made.

EDIT:

Thinking about it some more, it depends totally again on the wording of, and how they define "matches the wheel speed" for the conveyor.

If you think about it, if a wheel is rotating to move at 10kph on flat ground, then relative to the wheel, the ground is moving backwards at 10kph already.
If this is the interpretation of "matches the wheel speed" you take, then the plane will take off, as the conveyor belt wont move at all.

[RedMist]

Pidge, you need to re-read the original post. It clearly states...
"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. "

I gather because you can't read you attempt to insult others intelligence.

When it is you that is clearly wrong.

You state a blatant contridiction in your own post.

"If the plane is moving forwards at 10kmph, the wheels move 10kmph forwards, so the conveyor belt moves at 10kmph backwards, causing the wheels to rotate with an rotational speed such that the outside edge of the wheel has a speed of 20kmph (the difference in speed between the wheel and the conveyor belt). "

If the outside of the wheel has an instantaneous speed of 20kph how fast is the conveyor going?
Given "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. "

So it is impossible to accelerate unless, wheelspeed <> groundspeed.

[RedMist]

RomanV, I think thats the entire point in the question. Its to pose the partially impossible and think of a plausable answer to the remaining constraints.
Much like Schrodingers Cat.

[AirNZ]

So if the plane is moving forward at all, the belt is not doing it's job. Which according to the question can't happen, because the speed always matches.

That's a problem right there, because we're working off a falsehood. The belt can no more always match the speed of the wheels than an object can reach absolute zero in temperature because to do so would require the presence of an even colder body.

The only thrust necessary for the plane to move forward is whatever thrust is necessary to overvcome the friction of the wheels, which is pretty small.

The trick in the question is this, once the plane starts applying thrust, the belt can move as fast as it wants, but still won't move the plane backwards (or keep it stationary in this case). The thrust from the engines will overcoming the inertia that held the plane still to start with.

Another example how the belt moving backwards doesn't affect the speed of the plane on top (when done right) is the pulling of a table cloth from under the dishes spread on top of it. Pull the cloth fast enough and you still have the dishes on top right? The slipping of the cloth under the dishes is the same as the belt moving under the plane.

It really can move as fast as it wants without having an effect on the plane above it, because moving the belt under frictionless wheels (I mean if we're talking about a belt that can "always" match wheel speed then surely we can have some frictionless wheels) has no effect on the inertia of the plane once sufficient thrust is applied by the engines to overcome it's initial inertia.

So once the planes engines develop enough thrust to overcome the inertia of the stationary plane, the speed of the belt becomes irrelevant.

However because the question does say the belt always matches the speed of the wheels, we are expected to believe the plane will no move forward.

Things to consider...

We all know a plane's wheels can't turn unless it's moving forward, and that if the plane is not moving, its wheels aren't spinning.


For the belt to be moving in the opposite direction to the plane (wheels), the plane must itself be moving

i.e.
The belt cannot move in the opposite direction unless the plane is moving

Therefore..

If the belt is moving at all, the plane cannot be stationary.


As an example of how the belt speed is irrelevant to the plane moving forward (relative to the ground for sure) and taking off, think about this...

Once the plane's engines have created enough thrust to overcome the plane's initial inertia (of being stationary) the belt could literally spin a million miles an hour (cos it's a perfect belt that won't break and we have perfect tyres that won't pop and perfect bearings that disspate heat and wont disintegrate) in the opposite direction to the tyres, but the plane would still move forward.

That's how irrelevant the belt speed is.

Even if it did spin that fast, the wheels would always be going faster, because the plane IS moving forward.

The equal and opposite reaction of the belt spinning backwards, which supposedly is the cancellation of forward movement of the plane, is actually the wheels on the plane spinning forward twice as fast as normal, not the plane being pushed backwards.

The wheels can spin independantly of the plane moving.

Short answer, question sets impossible rules for itself. Perhaps in theory the plane won't take off, but I am yet to be convinced of this or that the backwards spinning belt has any effect on the inertia of the plane over and above the small amoun of friction on the wheels.

[RomanV]

Alright, here's my official revised theory.

The conveyor wont move at ALL.

When the wheel moves fowards, it is effectively the same as the ground moving backwards underneath it at the same speed.
by staying still, the ground has already acheived the criteria of matching the wheel speed, and in the opposite direction.
(The only way that the ground speed relative to the wheel, couldnt match the wheel speed (but in the opposite direction) relative to the ground, was if the tire was slipping)



Imagine if the ground was another wheel, sitting underneath the planes wheel.



When the planes wheel moves foward and spins, the wheel underneath spins at the same speed, in the opposite direction.
It also matches the speed of the wheel, by rolling fowards with it.

This is effectively the same as the wheel rolling over flat ground.

[Ako]

I feel like I just lost a full hour of my life reading all this. Not to mention confused the f%$k out of myself and my workmates.

Makes total sense it can take off.. Until you mentally try to view it - then it all goes pear shaped.





*sits quietly rocking in the corner*

[AirNZ]

The wording with the "wheels" bit in the original question is almost evil, lol. If the wheel speed is always matched by the belt, it sounds like the plane isn't going to move anywhere at all.

It should be noted though, that unless contact is broken in any way between the wheel and the belt, that the wheel and the belt are at any given moment always going the same speed, whether the plane is moving forward or not.

If you had a perfect camera that could take photos of a single instant in time, and you used it to take photos of the wheel on the belt, then at any give moment you choose to take the photo, you will see that the wheel is always in contact with the belt until it takes off, and in that sense it is always matching the belt for speed. At any given moment if you were to freeze frame, within the freeze frame, the wheel and the belt are both spinning at zero speed. If both are spinning at zero speed, then clearly they are both spinning at the same speed in opposite directions.

Thus the condition of the belt and wheel always spinning at the same speed has not been broken even though the plane itself is at that present moment moving forward, relative to the ground and wind.

So as long as the wheel is in contact with the belt, it is moving at the same speed as the belt. The speeds of the wheel and the belt are only different if you measure them independently of one another.

Strangely enough, this line of reasoning works whether the conveyer belt ever actually spins at all, or is a solid runway.

Same deal as a car accellerating away from a start line, even though we all know the car itself is the only object in motion, the start line can be said to be accellerating away from the car in the opposite direction at the exact same speed as the car is accellerating away from the start line. At any given moment!

[/b]

[AirNZ]

Nice pictures romanV


In regards to the...

pulling a car along a piece of paper, your cars went forward on the paper because you could not match the speed that the wheels were turning.
It would be simply impossible for someone to believe that their hand eye coordination is so fine tuned that they are pushing their car and pulling their piece of paper at exactly the same speeds, no matter how hard they push or pull

The wheels on the car are always exacttly matching at any given moment the speed of the paper. For the wheels to not match the speed of the paper they were travelling over they would have to be doing the matchbox equivalent of a burnout, with the wheels actually spinning faster than the paper is moving (or slower for that matter).

[pidge]

Pidge, you need to re-read the original post. It clearly states...
"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. "

Does the question mean by the speed of conveyor belt, the linear speed of the surface of the conveyor belt that the plane is resting on? Or does it mean the conveyor belt itself is moving (not rotating) relative to the ground? I'll assume it means the linear speed of the surface support the plane.

What do they mean by "speed of the wheels" ?

Speed of the wheel could be the linear speed of the wheels centre of rotation, (the wheel hub) or it could mean the tangential speed of the wheel (speed of rotation). Since they don't say "speed of rotation", I've assumed it is the speed that the wheel (and plane) is moving along the converyor belt, with respect to the ground (not the conveyor belt!) (e.g. car on a rolling road. What's the speed of the car? the wheels? what's the rotation speed of the wheels? Three different speeds, only two of them equal.)

What does "moving in the opposite direction of rotation" mean?

Treat the conveyor belt as one gear, the wheel as the other.

Meshed gears rotate in opposite directions, correct? If the wheel rotates anti-clockwise, the converyor belt will "rotate" clockwise, staying in mesh.

Note that no relationship is provided between speed or direction of rotation of the wheel and the wheel hub's speed - as it should be since wheel is free to rotate on its hub.

If the wheel hub is moving to the left, the wheel will be rotating anti-clockwise as rolls along the converyor belt.

The surface of the converyor belt supporting the plane will be moving to the right, which means the converyor belt will be rotating clockwise... the opposite direction of rotation of the wheel.

Note that no relationship is given between the speed of rotation of the wheel and the speed of the conveyor belt, only the direction in which the wheel and conveyor belt rotate with respect to each other.

----->---->---->
O------------------O (bah! ASCII art...)
<----<----<---<

This question highlights assumptions people make. For this question, people seem to keep assuming that the landing gear wheels are not free to rotate.

Here's another one:

You have a set containing the numbers 1 to 9 {1,2,3,4,5,6,7,8,9)}
Which numbers in that set are divisible by 3?
Why?

[UTERUS]

Of course the plane wil take off!

Maybe its because im so simple minded that i got it in a few minutes, you lot are thinking too much











(Giving the pot of shit a good stir!)

[malc]

The wording with the "wheels" bit in the original question is almost evil, lol. If the wheel speed is always matched by the belt, it sounds like the plane isn't going to move anywhere at all.

You said it!

[Adamal]

*Skips 9 pages of stuff he can't be bothered reading*

Too many concerning factors if you ask me.

One of the biggest is the size of the leading edge of the wing. The larger the curve of the leading edge effects the amount of 'lift' that can be created by the wing. The down side is that this will reduce the planes top speed, but we're not concerned about this here.

One thing is that in this situation, the runway is only as long as it is wide. If we're assuming that the width of the runway in question is the same as say, Auckland International, then you're probably not going to be able to take off in ANY plane (Except my dad's Zennith Air STOL701 Microlite ) unless the rate of acceleration is increadible. (When you consider that a 747-400 is about as long as a runway is wide!)