Airplane physics question

Sit on a skateboard on a treadmill. Start the treadmill very slowly, with almost no jerk, if possible. You move backwards. So, wheel speed is not matching belt speed.

Now just lightly arrest your backward motion putting your hand against a wall, railing, etc. anything that is not moving relative to the treadmill. Ok, your wheels' rotational inertia has been overcome and now you are sitting there, wheels happily turning, wheel speed matching the belt speed and no forward or backward motion.

Now accelerate the belt to twice or thrice the speed. You won't move. This is because:
1. wheels are accelerating to match belt speed, as there is friction between the surfaces,
2. angular acceleration of the wheels is not resulting in any linear force being imparted to the axles, and therefore, to the skateboard, or you sitting on top of the skateboard.

This proves that the belt's backward acceleration cannot impart any force to the skateboard beyond angularly accelerating the wheels to have faster and faster or slower and slower rotational motion.

Therefore, when the plane's engine fires up, the belt will not be able to oppose the linear thrust force. No matter how much it accelerates or decelerates. Unopposed force leads to acceleration in the direction of the resultant vector. You know the rest.

You are confusing rotational inertia with linear acceleration.

 

You are understanding the forces correctly, but you are misapplying them. Add mass to the can. Add friction at the surface of the can (tire grip). Now add a LOT more mass above the can, pressing down on it via an axle in the center about which it can rotate. Now do your experiment. The can will happily sit there and spin about the axis of the axle as you pull the paper/any grippy surface underneath.

That would be a much closer approximation to the situation with the plane. The plane will not move linearly once the rotational inertia of the wheels is overcome. It will sit there, wheels spinning away, because the belt cannot and does not impart a linear force to it. No linear force means no opposing force to any thrust. Resultant vector is forward and the plane will move and experience airflow and lift and take off.

 

Please note : you can have two wheels connected by an axle, with perfectly frictionless bearings. I promise you, if you lift up both wheels ... the axle will rise off the ground too

My point being : it's easy to get confused because the friction force of the accelerating conveyor is not applied to the "center" of the wheels ... instead, it's applied to the perimeter. I think we'd all immediately agree that a force applied at the center of the wheels would move the plane.

But alas, kinematics tells us that off-center forces cause a lateral translation just as if all the forces are applied to the center of mass. But since they're off-center, they also impart a rotational torque.

-- The easiest way to imagine that this must be so, is to compare two situations : One where a tire experiences a single perimeter force of F at its bottom. Another, where a tire experiences two forces : F/2 at the bottom and -F/2 at the top. Will these two situations result in identical translational and rotational movement of the tire?

-- The easiest way to prove that this is so, is to perform my little 5 minute experiment

 

My can already has mass. There is already friction between the can & paper. Can moves LATERALLY, even time you accelerate the paper underneath. Just like kinematics tells us that it must. And there's zero friction to the can's axle, because there's zero axle.

From kinematics : an off-center force acting on a mass can be resolved into TWO forces :

1. translational force acting on center of mass
2. rotational torque

I understand these forces well. I understand their application. And my experiment proves it all to be true.

 

If you could get a tricycle (no bicycle, as you would need to hold something for balance and that could prevent/enable forward and backward motion) with nice bearings in the wheels, and if you could find a treadmill wide enough to accommodate it, you could put yourself on the tricycle to simulate the relatively large mass of the airplane and then get the treadmill going and accelerate and decelerate it to see if the tricycle falls off the treadmill. I am betting it won't. If it doesn't, then obviously any forward or rearward thrust on the tricycle cannot be opposed through accelerating or decelerating the belt surface.

 

NOW we are getting somewhere. The torque you are referring to, unfortunately, results in zero linear force, because the frictionless bearings do not provide any opposition/friction/linkage to the torque. It spins them, they spin, absorbing 100% of the torque as angular acceleration, leaving zero for linear acceleration. You are on the right track, but you are applying your knowledge incorrectly.

 

Please ponder this question, if you will. The answer, of course, is no ... these two scenarios do NOT result in identical translational & rotational movement of the tire. One causes a lateral, or translational, movement of the mass (as well as rotation), the other does not.

 

OK, I am going to draw you something. Give me a few minutes. This will allow you to prove whether or not there is linear thrust imparted to an axle on frictionless bearings if you spin the wheel at the circumference.

 

If the center of mass of the tire is experiencing a net lateral, or translational force, it will move laterally ... along with its axle. Zero-friction bearings will not change this simple conclusion.

Kinematics, once again : a single, off-center force can be resolved into TWO components:

1. A lateral or translational force acting on the center of mass. This is not somehow "nullified" by zero-friction bearings at the mass center.

2. A rotational torque, forcing the body to rotate about it's center of mass.

 

going to bed ... it's 1:30 AM. But i will return.

Meantime, anyone interested please perform my little paper experiment. See if the rolling can ALSO moves laterally, with an accelerating piece of paper beneath it. What FORCE must be acting on the can's CENTER OF MASS to impart this motion? Is that force somehow "nullified" with zero friction bearings at the center? If I pick up two wheels connected by a zero-friction axle ... only touching the wheels ... why does the axle rise off the ground too?

 

Right, here's the experiment. Mount a bicycle wheel on an axle and then mount that on a skateboard. Put heavy weights on the skateboard. Dangle a ribbon or string or something from the skateboard and mark the point where it touches the ground. Now bring a spinning object like a belt sander to the top of the bicycle wheel and gently touch it to the tyre to get it to spin up. If it results in linear motion, the skateboard should scoot away from you, and the ribbon should move from the spot where it was originally touching the ground (the spot you marked).
Image Unavailable, Please Login

 

Again, you are on the right track, but completely misapplying the principles involved and ignoring a few key factors.

First, to answer your question about lifting of the axle, it's because it's connected to the wheel. Any force other than a rotational force about the axis will result in the axle experiencing the same acceleration as the rest of the connected mass. Move the wheels sideways, the axle will move sides. Up, axle moves up. Down, axle moves down. Forward and backward? Ditto axle. But, spin the wheels about the center, and magic happens. Axle stays put. Except it's not magic, is it?

Now, move a surface with friction against the tyre/circumference of the wheel. Wheel again spins/rotates. Axle again stays put. Attach anything heavy to the axle. It will also stay put. Let's call the surface a conveyor belt. Let's call the heavy thing an airplane. Oh look, it's the exact same thing.

Your experiment is flawed. On several levels. Do mine. It simulates a belt surface. With friction. It has a heavy mass (airplane). Heavy mass is attached by long mount (landing gear). Landing gear is attached to wheel with frictionless bearings. Except it's all upside down and the belt sander (conveyor belt) is on top and the plane is on the bottom, to make it easy to spot linear movement relative to the ground (a marked point).

And because right now we are focusing on the first half of the situation: debating whether the conveyor belt's friction on the tires, resulting in the wheels spinning, will impart a linear force on the landing gear.
If it does, great, plane's thrust can be resisted and plane will not take off.
If it does not, plane's thrust will not be opposed and plane will move and experience lift and take off.

 

You are STILL missing something VERY fundamental. I will respond to each of your points, as clearly as I can, to clear things up for you.

The bolded sentence is correct. But this is what kinematics tells us: Any single force acting off-center on a mass actually has TWO components : A rotational torque, which attempts to spin the mass, AND a linear, translation force acting on the center of mass. This second component of the off-center force EXACTLY satisfies your bolded sentence above.

In a more complex scenario, EACH of any combination of forces acting off-center on a mass can be resolved (or decomposed) as described. If, in this more complex scenario, there is a NET translational force acting on the center of mass, the mass will experience translational acceleration ... even though NONE of the forces may in fact be directly applied to the center.

Just because a force is causing the mass to spin, does NOT mean that the same force can not also cause the mass to translate, laterally. Spinning does not "exclude" translation. The SAME force may indeed cause BOTH motions to happen. This is what you fail to understand.

If a SINGLE surface with friction is brought against something that can rotate, the wheel will indeed rotate, and it will ALSO experience a lateral translation. YES, a single force can cause BOTH movements : rotation and lateral translation. This is because that single force has two components : a rotational torque, AND a translational force acting on the center of mass of the wheel.

If TWO surfaces with friction are brought against a wheel that can rotate, one on top and one on bottom, the translational components of these two forces acting on the center of mass cancel, and there will be no translation.

LOL

My experiment is NOT flawed. It CLEARLY shows that a single, friction force acting on the perimeter of mass that can rotate causes TWO motions: rotational AND translational. If you agree to this, our "debate" is over And anyone can do it in five minutes!

Surely, you're not suggesting that I need "more mass" in my experiment to demonstrate a fundamental principle? If so, our "debate" never even started

Why do you have so much difficulty understanding that an off-center force has TWO components, and can actually cause TWO motions of the mass : rotational AND translational?

Another simple thought experiment for you:

A mass floating in free space.

Case one : another object hits that mass, dead center. I think we would both agree that the mass moves in translation, with zero rotation.

Case two : another object hits that mass, off center, near its perimeter. The mass now rotates. Does the center of mass of ALSO experience translation ... from this single collision?

Anyone who understands kinematics, or has performed my simple 5-minute experiment will immediately know the correct answer

 

Thank you for taking the time to draw the picture.

I will answer your question with one of my own:

Case 1 : a SINGLE belt sander is brought into contact with the TOP of your rotating wheel.

Case 2 : TWO belt sanders are brought into contact with your wheel, one on top and one on bottom (in opposite directions).

Are all net motions the SAME in both these cases?

You say "yes". I say "no".

My answer (to my question lol) : One of these cases will cause BOTH rotation AND lateral translation

 

The translational motion you refer to WILL NOT happen. Your experiment is flawed. Approximate the scenario more closely, as my experiment does, and perform it. See for yourself. We can argue till the end of time. Facts will be facts.

 

I've done everything humanly possible in this thread.

I've presented kinematics theory. I've answered every question asked of me. I've presented arguments from various points of view. I've offered simple experiments that anyone can do in 5 minutes on their kitchen table.

All pointing to the exact same conclusion : a single force acting on the perimeter of a mass will cause BOTH rotation AND lateral translation. This is the very force that will accelerate a plane backwards, with engines off, when the plane is placed on a rearward-accelerating conveyor. This is the very force that can balance the forward thrust of the planes engines, ultimately & simultaneously satisfying all conditions of the original question.

Many of my questions have gone unanswered. Nobody even attempted my simple, 5 minute experiment ... which CLEARLY demonstrates that a single friction force at the perimeter of a rotating body will cause BOTH rotation AND lateral translation.

All i get in return is "it won't happen like that" ... ????

LOL

I'm out!

 

Your experiment is flawed. That's why I am not bothering with it. You claim to have an understanding of kinematics, but you keep repeated omitting basic facts and neglecting basic principles.

If what you are claiming is true, then every airplane would end up on its nose or tail and broken in half when the same foces would act on the second set of wheels that were to touch down.

If what you are claiming is true, then every time we turn a doorknob, it would shift horizontally.

As for your two forces versus one force argument, that is complete and utter nonsense. All force vectors can be summed into one resultant vector. That vector, when it acts tangentially on the circumference of a circle pinned at the center with a heavy mass and able to rotate without resistance, results in ONLY circular motion of the wheel. The rotational inertia of the wheel is overcome LONG before the linear inertia of the mass resting on the axle. Mankind has been harnessing this for centuries.

 

You apparently haven't spent much time in the "real World". The "question" is irrelevant, the plane flies every time.

 

Why should this force be able to balance the thrust?

Sure, there is a small amount of friction, but you can neglect this force.

 

What part of "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation", do you not understand?

"Exactly match the speed"... Where is the mention of friction? If there are lateral and translational forces then the rules set by the question are negated.

 

I didn't imagine my first post here would be in a topic like this, but anyways, why does friction on the wheels have anything to do with the plane taking off? It needs lift from the wings, and is propelled by thrust, not it's wheels. Lots of planes have enough power to just drag the wheels with brakes on at or below full power, so why would a conveyor belt pulling wheels that aren't driven by anything have any effect?

 

Mythbusters - Plane on conveyor belt
[ame]http://www.youtube.com/watch?v=S377HwOthjo[/ame]

[ame]http://www.youtube.com/watch?v=KSBFQOfas60[/ame]

[ame]http://www.youtube.com/watch?v=YORCk1BN7QY[/ame]

 

See Post 1


via iPhone / Tapatalk

 

Ok, let's try it this way

1. A plane is not a helicopter ( it cannot hover)
2. Air MUST be moving above and under wings to generate lift ( fly), thus forward motion
3. Read post 1...
4. Read Zack's post

If you take the question itself as PURELY written ( wheel speed=conveyor belt speed) there can be no forward motion of the plane.Read statement 2 above.

Solved.

 

Is this a " how to write a question " question....or a " what makes an airplane fly " question.