plane on a conveyor belt?

[eskimo2]

Originally posted by 2bighorn
I believe somebody already told you that your analogies don't hold the scrutiny of reasoning.  

Would you please explain in what way does the conveyor brakes the airplane's wheels? And please, no more movies of belt sander and flying shoes. Just words if possible.

It takes energy to accelerate a wheel’s rpm. A treadmill accelerating at thousands of g’s can load a force equal to or even greater than an aircraft engine’s thrust into the aircrafts wheels.  The wheels are acting like flywheels in this case, constantly gaining energy and revolutions per minutes.  Since the rotational inertia load is being transferred at the bottom of the wheel/tire and toward the back of the plane, the wheel will also want to move in the direction of the treadmill (just like the wheel on the sander or hollow cylinder and balls on the paper treadmill.).  This linear non-rotational force will push the axel, gear and plane in the direction of the treadmill.  Assuming that the theoretical super treadmill has no strength or power limits and the aircraft tire/wheel and bearing also have unlimited strength, it power delivery capabilities would only be limited by the traction available between the treadmill and the tire.  Any aircraft that could break free from the super treadmill and take off would also be able to take off on a regular runway with its wheels locked.  Most planes could easily be held in place by the super treadmill.  At any given time, the total energy expended by the engine would be equal to the rotational inertia energy stored in the wheels/flywheels.

If we change the wheels to be mass-less, however, the conveyor and wheels would go to an infinite speed instantly (and absorb no energy) and the plane would take off better than normal since it has mass less wheels.

[Rash]

If the the conveyor was made out of "super teflon" and the wheels where actually super teflon bricks with no friction, then the plane would fly.

[Golfer]

Eskimo your pictures, movies, drawings, stories and ideas all make sense for something the question doesn't ask.

If the airplane were on the treadmill standing still and you turn the treadmill up to uberfastlightspeed as quickly as possible then the things you're saying are plausible.

In the context of the question the conveyor is reactive to the airplanes wheels...not proactive.  It can't just start movign as quickly as possible like your belt sander examples, your falling shoe or your toy cars with heavy wheels that actually have built up intertia to propel it forward.

Because an airplane is not propelled through its wheels, but instead by an engine to say the airplane has wheel speed it must have airspeed to cause the wheels to turn.

Now that the wheels have begun to turn, instantly the conveyor matches equally and oppositely the speed...effectively doubling the wheelspeed in relation to the airspeed of the airplane.  If the airplane flys at 100kts then the wheels will be spinning at the equiviliant RPM of 200.

I submit if there were a car (which derives its power through actually turning the wheels) on the conveyor...it wouldn't move.

Because its an airplane and not driven by the wheels contacting the ground...the airplane in relation to a fixed point not on the conveyor moves normally, the only difference being a doubling of wheel speed.

Again Eskimo...you're not wrong for what you're saying (having the treadmill being the active and overpowering force it is) you're just off base for this particular question.

[eskimo2]

Golfer,

How would you answer this question (and simply, why?):

“A plane is standing on 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? Will it be able to run up and take off?”

Note: “Wheel” has been removed.

[Golfer]

The plane takes off.  The conveyor has no zero none nary nil effect on the thrust being produced by the aircrafts method of propulsion.

Provided the aircraft is a "normal" aircraft taking off on a normal runway that just happens to be a conveyor system..

[vorticon]

bowling balls roll backwards while moving forwards all the time.

and i just checked with a bike and rollers, pushing the bike off with the wheels not moving, the wheels at a steady pace, the wheels accelerating, and the wheels de-celerating, and i tried pushing off in both directions.

there was no noticable effect.


IIRC
a gear is sitting on a geared track, the gear wont move if you just spin the gear.

if you push the gear forwards it will move forward, and turns the track at the same rate that it rotates.


im probably completely wrong with this to but:

"A treadmill accelerating at thousands of g’s can load a force equal to or even greater than an aircraft engine’s thrust into the aircrafts wheels."


FR = μR*W

μR = v/(t*g)

i see absolutly no sign of acceleration on a level surface having any affect whatsoever on friction...

also

the treadmill is rotating in sync with the wheels. the wheels are rotating in relation to forward movement by the plane....

therefore the treadmill is rotating in relation to the forward movement (velocity) of the plane?

however

can a floatplane take off going up a fast moving river? and why is this different?


and will someone please put a treadmill on its fastest setting, and see what  effect it has on a RC plane?

[lukster]

Take a real Cessna 172. Does anyone doubt that a conveyor capable of maintaining a high acceleration could prevent it from taking off?

[eskimo2]

Originally posted by 2bighorn
Seriously, after running those toys forward and flywheel has enough energy stored and you put them back on the ground, will they suddenly move backwards?

I thought your answer might be something like that.  You need to play with toys a bit more; you missed out.

[eskimo2]

Golfer,

In the wheel speed question, why does your conveyor move at 100 knots if the plane is also moving at 100 knots?  Many people assume that the instant the plane moves the conveyor has failed at matching the wheel speed and therefore will be satisfied matching the plane’s speed.  That’s changing the description on how the conveyor control works.  Why choose the plane’s speed?  It might as well not turn at all.  Why not twice the plane’s speed?  Why wouldn’t the conveyor try to do its job and catch up?

Reconsider the question where the conveyor matches the plane’s speed.  Why don’t we have a problem with how exactly or accurately the conveyor matches the plane’s speed?  Isn’t the conveyor control issue really the same?  The plane must move first!  Not only must the conveyor match the initial acceleration of the plane, it must constantly lower the acceleration rate as the airplane has less power to devote to acceleration due to the ever increasing air resistance, in a way that is more complex!  For some reason, no one has a problem accepting that its control works.  The answer is that it does not matter how the control works, what is important is to understand that the plane can take off because the aircraft motor grabs air, not the ground (or treadmill).  The fact that the wheels consume a bit more energy is irrelevant.  This question is all about identifying forces and physics.

In our question where the conveyor matches the wheel speed: it accelerates at such a rate to keep the plane in place because it must!  The question says it does; therefore if there is an explainable way and/or speed that will hold the plane still, it has to be the answer!  Our question forces this answer.  Why was our question phrased this way?  Because it is a much harder and much more interesting question!   The answer is not obvious; at first we all thought it was an impossible question.  I honestly thought that rabbidrabbit asked an honest question that showed a poor understanding of physics and was poorly worded.  Once someone pointed out that there was a thread on a physics board that was 458 pages long, I Googled the question and found that the plane speed question has been all over the Internet for a couple of years.  Our question, however, is new (I think).  At least in my brief searching I have not found it.  Someone either put a very clever twist on it or unknowingly added a word that changes everything!  This question also is all about identifying forces and physics, it just has another level.  Most people have no comprehension of the effects of rotational inertia.  It is easy to dismiss.  When I posted the wheel video on the physics board they pointed towards everything but rotational inertia; it was right in front of them and they didn’t get it (I think that the AH BBS posters are a brighter bunch BTW).  

I’m waiting for rabbidrabbit to chime in and tell us where he got the question from.  If he intentionally rephrased it himself, he may very well be the smartest one on this board.  I know that he must be following this thread, but he has not posted since he asked the original question.

I think that most people will never see or understand the difference between the two questions.  I also think that most people cannot comprehend the answer to this one no matter how it is explained.

[Golfer]

I understand where you're coming from eskimo with the exponential increase in speed of the conveyor.  The plane moves, conveyor tries to match, in turn speeds up wheel even more...which it must accelerate more.


Point is if the conveyor doesn't change things matching the planes speed...why's it change the wheels speed.

Even if you match the wheels speed you still have the fact the airplane is producing thrust to deal with.  If the wheels are free spinning to do what they please independent of the airframe (assuming they hold together) how are you stopping the airframe from saying byebye as it claws itself through the air.

[mietla]

Originally posted by vorticon

can a floatplane take off going up a fast moving river? and why is this different?

A float plane and a plane on wheels are not the same.

Plane on wheels.

The force exerted on the bottom of the wheel is caused by rolling friction which DOES NOT depend on velocity. The force of rolling friction is ...

T = C * W

T - force of friction
W - the weight of the plane
C - constant coefficient dependent only on materials of the wheel and the surface on which the wheel is rolling

There are two sources of rolling friction. The rolling friction between the bottom of the wheel and the ground (or the conveyor), and the other is the rolling friction of the wheel bearing . The former is designed to be large. You do not want wheels to lose traction and slip, so you make the tire out of soft rubber. The later source of friction is designed to be as small as possible (thus you use hard and polished steel balls rolling on the hard and polished steel surface). Both friction points are subject to the same equation (F = C * W), but they have significantly different coefficients C. One purposely large the other one purposely small.

Now, imagine the wheel (forget the plane for a moment) weighing W sitting on the ground. The rolling friction is as we said T = C * W, but remember this is not a force yet.

Now, this is very important to understand. Friction is a tricky thing. It is not a force in itself. It is "an ability" of the coupling between two surfaces to resist the tangential force P. When P is zero, T will be zero as well. As P slowly increases, T will match it exactly and as a result the there is no movement between the surfaces. This continues until P reaches C * W. This is the MAXIMUM resistance to movement coupled surfaces can produce. As soon as P exceeds C * W, the wheel starts rolling (or in a case of static friction the surfaces start slipping).

Until now, we had equilibrium. For all values of force P between 0 and C * W, P was always matched by equal and opposite T, and therefore no movement.

As P increases even more, the equilibrium is no more. The coupling can only produce a maximum of C * W, the rest of the force P becomes unbalanced, so the movement must result. The wheel starts rolling and if P > C * W the wheel rotation will accelerate. If P = C * W, the wheel will not accelerate but it will maintain its state. If it was stationary, it will remain so, but if it was rolling with the velocity of V it will remain doing so.

This is why if you want to start taxiing, you must apply more thrust to get the plane rolling, but then you can lower the power to sustain a constant roll.



The moral from this story is that there is a limit to how much force the ground (or conveyor) can exert on the plane. There are two friction couplings between them, and the amount of force transfer is determined by the weaker of the two. Normally the wheel/ground coupling is stronger (it was designed to be so) and the wheel/axle coupling is weaker. The wheel will not slip on the ground, the wheel will roll. When the engines push the plane, the plane moves forward because the wheel/axle friction is too small to stop it.

The situation changes when you apply brakes. Now you just made C of the wheel/axle coupling very large. Now, since the wheel/ground coupling is weaker of the two, the outcome depends only on its coefficient C. If this coupling is strong enough to transfer a force equal to engines thrust, the plane remains stationary (this is what we want), but if the coupling gives, the wheels slip (no rotation) and the plane moves forward. Put the plane on ice and even with brakes applied the full thrust most likely will move it forward.


Unless the brakes are applied, you can tug the bottom of the wheel forward or backward all you want. You can use any value of the force you want. Only a small fraction of this force (defined by C of the wheel/axle friction) will be transferred to the plane. The rest will produce an accelerated angular velocity of the wheel.

The angular momentum of the wheel does not affect plane's movement forward even if it is very large. It will only affect the plane if it turns left or right (gyroscopic effect), which we don’t care about in this case.

Float plane.


The force exerted on the pontoons by the flowing stream is NOT friction. It is a force produced by the pressure of water (drag) which is proportional to the square of the velocity of the stream.

A simple case, a torpedo. To simplify the case let’s assume that instead of the domed bow, its bow is flat. In other words, our torpedo is a cylinder.

What kind of forces act on the torpedo. The thrust pushes it forward, and two forces push back (let’s ignore cavitation, turbulance and other gunk). The first is the pressure of water in front of the torpedo being compressed by its movement. Let’s call this force P. The other one is a viscotic friction acting on the sides of the torpedo as it moves forward. Let’s call it Q.

Q depends on the velocity V, but unless the torpedo is moving extremely fast in molassas, it will be negligible in comparison with P.



Let’s start with the Newton’s law. A familiar form is …

F = m * a
or
F = m * V / t

F * t = m * V


… but this is a static case where neither of the components changes.

Let’s consider an infinitely small interval of time dt and virtual movement. The torpedo wants to move forward a distance dx which with the constant velocity V will be equal to V * dt. The mass of water displaced by this movement dm is equal to the volume of water displaced W times water’s density R.

So, we star with …

F * t = m * V

… for a virtual movement

F * dt = dm * V

Both F and V are constant (do not depend on time). The mass of water displaced does depend on time. More time elapsed more water is displaced.

The volume of water displaced in time dt is equal to the surface of the torpedo’s cross section S times the distance traveled dx

dm = S * dx * R

since

dx = V * dt

and
S = pi * D^2 / 4


dm = pi * D^2 / 4 * V * dt * R


so

F * dt = pi * D^2 / 4 * V * dt * R * V

F = (pi * D^2/4 * R) * V^2

F = const * V^2


This was a simple solution for a flat surface. If the torpedo’s bow is conical or semi spherical, the solution is the same but the const will change.

The point is that for the sea plane moving against the current, the force resiting the movement IS NOT FRICTION. It is a water pressure which not only depends on the velocity, but the dependency is pretty strong (V squared).

There is no friction coupling between the pontoon and the plane. The connection is rigid, so the entire force applied to the pontoon by the water will be transfered to the plane.


For the plane moving on wheels, the force resisting the movement is friction and it DOES NOT depend on velocity.

There is a friction coupling between the wheel and the plane, therefore only a portion of the force applied to the wheel by the ground/conveyor will be transfered to the plane.

[2bighorn]

Originally posted by eskimo2
You need to play with toys a bit more; you missed out.

Maybe,
but
you missed that rotating body has angular moment which always works in the same direction as a rotation. You can not have two of those working in the opposite direction in a single wheel.

If you apply linear force to the rotating body everywhere but through its center of mass it'll be translated into rotational motion.

If you apply two opposite linear forces (plane, conveyor) to it everywhere but its center of mass it'll be again translated into rotational motion.

No single body can rotate into two directions at the same time.

Hitech statement "if force sum = 0 plane does not move" is false when it comes to rotational motion since opposing forces contribute to the same rotation (otherwise things such a bearings, pulleys and conveyors wouldn't work).

The statement that "Basicly a force is a force is a force no mater where you exert it on an object" is false. (otherwise things such a length of moment arm wouldn't matter, also torque is rotational analogue of the force and he claims: thing that changes when you push on a different spot is you add a torque".)

Flywheel releases energy during the same rotation it has received the energy. During the process you can not reverse the rotation.


No matter ad hominem attacks by Hitech and you, it still want change the physics and until such time the physics laws are actually changed in a way that would make your theory plausible, I'm done with this thread.

[JCLerch]

Originally posted by lukster
Take a real Cessna 172. Does anyone doubt that a conveyor capable of maintaining a high acceleration could prevent it from taking off?

This is the crux of the problem.  Your question, and the original thought experiment, mix "real world" physical items with intellectual constructs.  (Non-existent hardware).

For instance, You put a "real Cessna 172" on a intellectually constructed, artificially constrained, treadmill.  Aka a "Super Treadmill"  Then to answer your question to the finish, we have to add some additional constraints.

• Are the Cessna wheel assemblies indestructible? Yes/No
• Are the Cessna wheel bearings and axles indestructible? Yes/no
• Is the super tread mill indestructible? yes/no
• Is the super tread mill capable of continually accelerating at 910ft/sec/sec? Yes/no
• shall we ignore the effects of Relativistic Quantum Field theory? Yes/no

IF you answer yes to all the above, then the airplane will not move forward (with respect to the ground the treadmill is attached to) while producing thrust.  Of course, this will be an interesting experiment to an outside observer, as the surface of the treadmill will go from 0 to 700mph in about 1 second. 11 seconds later (12 seconds after opening the throttle on the airplane engine) the treadmill surface speed will be traveling at Mach 10 and still accelerating. In a little over 2 years, the linear surface speed of the super tread mill will exceed the speed light.  As I said, answering YES to all the thought constraints will be very interesting to observe from a distance!

IF you decide to answer yes to everything except the last question, and  include Einesten's theory of relativity, then the end result is sufficient energy in the system to be equivalent to enough mass to create a Black Hole.

IF you answer yes to everything except the last two questions, then the treadmill will eventually stop accelerating, and the airplane WILL take off.

IF you answer no to ANY of the first three questions, you will roll the Cessna up into a little metal ball.

IF we constrain the experiment to things that CAN BE FABRICATED, then  I predict it is impossible to build a treadmill assembly that can accelerate at 910ft/sec/sec for anything longer than a few fractions of a second.  Once the treadmill stops accelerating, the airplane will move forward relative to the ground the treadmill is attached to, eventually gain enough airspeed and takeoff.  How unusual the takeoff appears depends on the rate of acceleration and  the top speed the treadmill is capable of.

[hitech]

If you apply linear force to the rotating body everywhere but through its center of mass it'll be translated into rotational motion.

No it will be translated to a torque and a force. Depending on all other torques and forces sums the object will move in the direction of the force sum. And rotate in the direction of the torque sum.

Also if this was not the case, AH's model would not be even close to correct because it is the way the Physics engine really works, just keep adding force vectors at given points, calculate the 3 dim torques at that point (cross product of force and point) . and keep track of torque sums and force vector sums.

After all is added, use the F = M * A to calculate new speeds (note there is an integration that occurs based on the time sample)

BTW assume when I use the word force vector I am assuming direction and magnitude.


HiTech

[2bighorn]

Originally posted by hitech
No it will be translated to a torque and a force. Depending on all other torques and forces sums the object will move in the direction of the force sum. And rotate in the direction of the torque sum.

Here, two identical conveyors, same power, same speed. Two equal and opposing forces work on the wheel.
According to you, wheel in the middle shouldn't rotate since NET FORCE SUM = 0.