plane on a conveyor belt?

[nexus69]

My Question is. Where is the plane going?

[2bighorn]

Originally posted by eskimo2
Guys, the main force at work here is NOT friction!  The plane is held in place by rotational acceleration.  It need friction/traction to work, but that is not the only work.

Flow: belt -> friction1 -> rotation -> friction2 -> airframe

[takeda]

Ok, I have recovered my confidence in HT, so much I might even resub to AH after a long long hiatus

Mechanics with things spinning are hard and mechanics with friction are hard. Mix them and you are in a minefield. And my college level physics are 15 years old and rusty for lack of usage.

So yes, some uber-conveyor that could fling stuff into space would keep hitech's wimpy plane from taking off

I finally undestood it by reading this:

http://www.straightdope.com/columns/060303.html

[john9001]

clip from your link<>



it talks about the belt counteracting the speed of the plane, if the plane is  not moving because of the movement of the belt then the belt can't move because the plane is not moving. but if the plane moves the belt has to move so then the plane will not move and the belt will not move.

it is a paradox, there is no answer

[takeda]

He, and hitech are talking about different problems from the initial one. There are three problems/solutions:

1. Treadmill conunteract plane forward speed: Plane flies, wheels spin faster.
2. Treadmill matches "wheel speed": Problem is flawed, can't give a definitive answer because of that.
3. Treadmill accelerates continuously at a rate enough to counteract the plane thrust: Although the numbers end up being a bit silly, the plane won't fly. This situation is the one explained in the link I posted.

[Kuhn]

I gather by reading Cecil's column that the conveyer could possibly make the plane not move but it would have to go faster than just matching the wheel speed.

[mietla]

Originally posted by john9001

it talks about the belt counteracting the speed of the plane,

No, it says match not counteract. Match means it moves with the same speed (same direction or opposite depending on your interpretation). A cop chasing you matches your speed, he does not counteract it. A passing cop driving with the same speed as you are is not not "counteracting" your speed either)


It is impossible for the belt to counteract (negate) the movement of the plane. To do that, the belt would have to be able to exert a force (on the plane) equal to the thrust. This is not possible because of two friction couplings. No matter how much force the best applies to the wheel only a portion of it (defined by the weakest friction link) it transfered to the plane.

With the brakes applied, the wheel/belt friction defines the force on the plane. With no brakes, the wheel/axle friction is the deciding factor.

Even if the belt's "logic" is to drive the belt not "to match", but "to negate" the airplane's speed, it can't accomplish that. A small portion of the force will transfer to the plane (insufficient to counteract the thrust), the rest will start spinning the wheels, but no inherent infinities here. The belt is defining the speed, and the belt (not the plane) provides the energy necessary to accelerate the rotation of the wheel. There is no "race" between the wheel and the belt which according to Eskimo and Hitech will generate infinite speeds in infinitely short time. The belt is active, the wheel is passive.

From the plane's perspective it does not matter. Spinning wheel does not affect translation. As long as the rotation axis does not rotate itself (as it would if the plane would try to turn, or if you apply ailerons titling the plane), the plane moves forward just fine. As a matter of fact the wheels act as gyroscopes steading plane's movement forward.

[Kuhn]

Originally posted by Kuhn
The wheels wont roll if an airplane does not move forward. Being that the wheel movement is is controlled by the prop moving through the air ,the plane will move forward nomatter what the wheels are doing. The conveyer can try all it wants to keep the wheels spinning fast enough to keep up with the rotation but in no way is it possible even in theory for it to keep up with the wheel speed. It will keep accelerating as the plane moves forward and the plane will lift off. So actually the original question is flawed and cannot be answered the way it was asked. It is not possible for the plane not to move forward when the prop is pulling it through the air. It is not possible for the plane to move forward if the wheels dont rotate when in contact with the ground.

I could go on but I wont

Remember this?  

[2bighorn]

Originally posted by takeda
I finally undestood it by reading this:
http://www.straightdope.com/columns/060303.html

I'd respectfully disagree with Cecil. Not so much about the end effect but in principle of cause and the futility of creating such system which would be paradox by itself.

Rotating body is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object.
In our little system we have two, both are directly result of the friction.

In order to achieve the hypothetical angular velocity (close to light speed) we would have to ignore torque caused by friction of the bearings at some time.

At that time our model becomes flawed since we lose the only linkage between angular momentum and the airframe, therefore no matter how fast wheel would rotate it would not counter plane movement since now we have two completely separate systems instead of one.

[hitech]

takeda: Thanks.

And I agree with your link, the question as stated is meanless, note my very early conclusion on this.

2bighorn:

n order to achieve the hypothetical angular velocity (close to light speed) we would have to ignore torque caused by friction of the bearings at some time.

Increase in the bearing friction would just help hold the plane more.

Also the angular vel is not what holds the airplane. It is angular acceleration. And I just like Cecil I am almost to the point of swearing on having to repeat physics.

At that time our model becomes flawed since we lose the only linkage between angular momentum and the airframe, therefore no matter how fast wheel would rotate it would not counter plane movement since now we have two completely separate systems instead of one.

Are you saying the wheels departs the airplane?Limits like those are not really part of the question. Infact I belive I could build a flyable plane that would only have to have the belt accelerate the wheels at about 1/4 FPS per sec or less. At those rates you could build a system that would acctualy demonstrate the principle.

But to fly the thing off a runway you would also need some motors on the wheels to get them up to speed land the bloody thing. And a very long runway to take off and land.


HiTech

[2bighorn]

Also the angular vel is not what holds the airplane. It is angular acceleration. And I just like Cecil I am almost to the point of swearing on having to repeat physics.

angular acceleration -> increase in angular velocity -> bigger angular momentum

Are you saying the wheels departs the airplane?Limits like those are not really part of the question. Infact I belive I could build a flyable plane that would only have to have the belt accelerate the wheels at about 1/4 FPS per sec or less. At those rates you could build a system that would acctualy demonstrate the principle.

That sounds awful small number.

Calculate wheel torque acting on plane via bearings.

For comparison GE90-115B fan rotates at about 2500rpm at full thrust and core at over 10.000rpm and it did create 127,000lb of thrust in test run and there's not much of a torque acting on frame via bearings.

[eskimo2]

Originally posted by hitech
Eskimo: I think it is really just a perspective thing, weather you view it as friction  or rotational acceleration. The force outside the plane is based on static friction tire to the ground. What creates that friction is the rotational acceleration.

Hitech,  

I think the big problem is that so many people do not understand what happens with rotational acceleration.  People are still stating that when a wheel is accelerated it has absolutely no impact on the axel or plane.  They keep pointing at bearing and rolling friction.  People need to understand that a wheel being accelerated by a force at one point is not balanced.

[eskimo2]

Originally posted by mietla
Eskimo, hitech

The problem as stated is illdefined and ambiguous. I dont want to go back and read this entire thread again, so can you please state how do you understand the problem setup, and where do you guys get your infinities.

Case 1.
To me, "the belt matches the wheel's speed" simply means that the wheel does not skid on the belt. The belt is not powered, it simply moves along dragged freely by the wheel. The wheel is the driving element. The wheel can translate left or right, and/or it can rotate clock, or counterclockwise. The belt does not care. The belt is a passive element and just follows.


Case 2.
"the belt matches the wheel's speed but in the opposite direction" is only possible if the wheel's rotational speed is 0. The wheel can not rotate clockwise while the belt is moving to the right (or counterclockwise while the belt is moving to the left. The friction prevents that. If the forces exceed the friction, the wheel simply separates and both the belt and the wheel move independently.

The plane moving to the left is pushing the bottom of the wheel to the right. Just because the wheel is pushed does not mean that it starts to rotate. The belt senses the force pushing it to the right (by the wheel), and compensates by applying an equal force ( the belt can not apply "a movement", it can only apply a force which may or may not result in movemnet) to the left. Both forces cancel each other and the result is that the wheel does not rotate at all. It translates to the left along with the plane. An outside observer sees the plane taking off to the left with wheels that do no spin. You could get an analog situation if you put a plane on teflon. The friction between the teflon tarmac and the wheel is miniscule in comparison with a friction in the axle bearing so the wheel does not spin and the wheels skid on teflon.

What is your understanding of the problem statement?

Why does "your" belt need to be powered is case 1.

Where do the infinities come from?

Mietla,

Many folks assume that in the wheel speed question the plane will take off with the conveyor matching the plane’s speed.  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. The question says it matches the wheel speed.  If the plane moves forward its wheel cannot be traveling at the same speed as the treadmill because it has traveled further in the same amount of time.  The only place that the wheel speed will match the conveyor speed is when the plane remains at the same spot.  So, 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?  

Consider the question where the different 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(s) 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 as an original question starting a discussion.  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).

[kamilyun]

Check your PMs eskimo

[hitech]

For comparison GE90-115B fan rotates at about 2500rpm at full thrust and core at over 10.000rpm and it did create 127,000lb of thrust in test run and there's not much of a torque acting on frame via bearings.

Because bearing friction is not the cause of the force in my drawings. Bearing friction will add more drag, but that just means we have to accelerate slower than the estimation.

Just had a thought, can you draw a diagram of how bearing friction turns into drag?

My sample plane would have just enough power to fly, very big wings for as much lift as possible, as big as wheels as I could fit, with as much weight as I can put on the outside of the wheel.

HiTech