Will it take off?

[Jay481985]

Maybe planes are too intriguing. Try a car. What if the car is on a treadmill, and however much the driver speeds up, the treadmill speeds up in the opposite direction. Will the car fly? Hell no. It will stay in one place - AND THERE WILL BE NO WIND - ABSOLUTELY, POSITIVELY NO WIND. So, feel free to use a convertible for this experiment (your hair won't be windblown).

Now, put some wings on the car. Will it all the sudden fly in the absence of this wind? I win!

Somebody prove this statement wrong. It is complete absurdity to think all you have to do is add wings to a car in a windless environment and it will fly.

cars and panes are different. Put it this way thing of the car as fixed object as the engine is fixed to the wheels. The plane think of a pin wheel, as much as you blow the pinwheel it will not effect your arm from moving as the force vectors are not pushing against each other but is dissapated by the bearing.

[Jay481985]

I can't believe this woke up again. This is such a simple question and it gets over-analyzed to death here. Here is the simplest analogy I can come up with.

The plane's engines exert a force on the plane. They push it forward. Let's replace the engines force with another force. Say, uh, how about the force of gravity. Instead of igniting jet fuel and oxygen to generate a "longitudinal force vector" (aka "push"), tilt the ground so the plane is rolling downhill. If we tilt the ground steep enough, and the plane gains enough speed, it will generate lift and begin to fly. Of course, eventually we come to the bottom of the hill and smash into the ground, but let's leave that aside for the moment.

Now, while we're rolling merrily down the hill, before our wheels leave the ground, start up our conveyor belt, moving in the opposite (uphill) direction. Will the plane stop rolling downhill and come to a stop (relative to the ground under the conveyor belt)? Will it begin rolling backwards, up the hill? No, unless our wheel bearings cease up or something. No matter how fast the conveyor belt moves under our plane, we're going to continue rolling downhill faster and faster. Eventually we'll lift off. The belt could be moving at any arbitrary speed under us, it's not gonna matter. All it does is make the wheels spin faster. That is, if our downhill velocity is 50 mph and the belt is going uphill at 50 mhp, our wheels are turning at the equivalent of a 100 mph taxi. Likewise, if we're going downhill at 50 mph and the belt is moving uphill at 1,000 mph, our wheels are revolving at the equivalent of a 1,050 mph speed. Doesn't matter, we still roll downhill.

Now, put our plane on a level surface and replace the force of gravity with the force of the engines. Same exact thing.

Duh.

Ray, double DUH back at you! Gravity = 9.8 meters/second squared. It is a force of ACCELERATION. Now, let's match your force of ACCELERATIONa with another force of acceleration. For example, all masses generate a certain degree of gravitational force. That's why the Sun keeps the earth in orbit.

Now, if you took a mass that generated a gravitation force in equal magnitude as that of the earth BUT IN THE OPPOSITE DIRECTION, you would in fact stop falling down that hill. Remeber, the forces are completely offsetting. In your example, Ray, you are countering a non-accelerating force with an accelerating force. It will not work.

If you were to drill a hole in the earth and mind you neglect the lave/magma and made a "well" to the other side of the earth, if you were to go down it you would fall until gravity slowed you down enough from terminal velocity and then you would start falling back.

[Jeff Matthews]

I re-read the guy's reasoning again, and he is right. So, how are we to have a meaningful discussion???? Eh? []

Danged lawyers! []

Now, as I, and I think most people read the question, a pure friction-less environment was not assumed. (But if you assumed it, and came up with a different answer, you did it based on the wrong assumptions). In a frictionless environment, a fly could bump into the plane and send it off at the speed of light - never to stop again.

Now, introduce a little friction (the more normal case), and the treadmill (which magically does not burn up, just like the magic tires that don't burn up) keeps pace with the plane. And the two cancel each other out, with no forward movement to the plane. Then, you get into extreme thinking about how the friction of air at the surface of the fast spinning treadmill can cause lift at some theoretical speed. Doubtfully, this friction-based airflow at the surface of the treadmill was intended to be a factor, and you get left with a motionless plane - of course, under the more ordinary reading of the problem.

I feel I should win on this one, despite being a lawyer. []

[sputnik]

Sput, here's your answer. The guy lays out all the physics formulas. The force to spin the wheel is transmitted to the plane.

All right, then. Apropos of a number of posts in this thread (no *single* post, but the cumulation of multiple posts), let's talk about forces and force transfer. Let's talk about forces in the context of, say, a wheel:

Code:

*******

** **

** **

* *

* *

* *

* O *

* *

* *

* *

** **

** **

*******

The wheel is round, and it has some mass, m, with a center of mass in the center of the wheel at "O". It's also got rotational inertia, I. One way to think of mass is as the resistance of the wheel to motion when a force is applied. In the same way, rotational inertia can be thought of as the resistance of the wheel to rotation when a torque is applied. With me so far?

In addition, let's assume that the wheel has a bearing in the center, at the "O". The other side of the bearing is connected to Something. We haven't defined what Something is, yet, but we will. Be patient. Let's make this simple and assume the bearing is frictionless. We can add friction in later if we want, but let's keep it simple for now. Now, the bearing is a pin joint--it allows both horizontal and vertical forces between the wheel and the Something that it's connected to, but does not allow torques to be transferred.

One last thing. Let's make this wheel and the associated forces as simple as possible. So let's ignore gravity and everything else. No gravity, no treadmill, no Earth, no nothing. This is, right now, just a wheel in space connected to Something through the bearing. OK. Got it?

Now let's change the story.

Code:

*******

** **

** **

* *

* *

* *

* O *<----F

* *

* *

* *

** **

** **

*******

I've added a force F on the wheel; this force F passes through the center of mass. This force is, as drawn, unbalanced, and it isn't yet the whole story. From here on out, a few different things could happen.

Suppose the wheel isn't connected to anything at the bearing (the Something is Nothing, in other words). In this case, there's no way the force F can be resisted, and the entire wheel will accelerate to the left. The acceleration, in fact, will obey Newton's law, F = ma.

OK, but what if the wheel is actually connected to Something? What if that Something was the ground, and the wheel is prevented from actually moving to the left? In that case, there will be a reaction force at the bearing. The wheel will push on the ground, through the bearing, and the ground will push back:

Code:

*******

** **

** **

* *

* *

* *

* R---->O *<----F

* *

* *

* *

** **

** **

*******

The ground will push back, in fact, so that R exactly equals F. This is the key: because the wheel does not move, the forces must be add to zero. If they didn't add to zero, the wheel would accelerate to the left or right. But it doesn't. So the forces must be balanced, and the force F is transmitted to the ground.

Another possible thing that could happen would be that the Something that the wheel is connected to is something very massive, but moveable, which has a mass M. In that case, as soon as the force F is applied, everything accelerates--both the wheel and the Something--at an acceleration of F = (M+m)a. In this case, there will still be a reaction R on the bearing, but the reaction R will be less than F. How much less is left as an exercise to the reader.

All right, got all that? Now let's do something a little different. Let's move the force:

Code:

*******

** **

** **

* *

* *

* *

* O *

* *

* *

* *

** **

** **

*******<----F

Now the force F is no longer a the center of mass. How does that change things?

First or all, let's go back to the assumption that the wheel is just free in space--nothing is connected to the bearing. In this case, the wheel will still accelerate to the left in accordance with F = Ma. The force F is still unbalanced, and the unbalanced force must result in an acceleration. However, the wheel will also rotationally accelerate. The force F is not through the center of mass, and that creates a torque T = Fr. This torque rotationally accelerates the wheel through the rotational equivalent of Newton's law: T = Ia (a being rotational acceleration). So the wheel will begin to move to the left, and spin clockwise.

Now let's assume, instead, that the wheel is connected to the ground at the bearing--the Something is the ground again. This gives a case like so:

Code:

*******

** **

** **

* *

* *

* *

* R---->O *

* *

* *

* *

** **

** **

*******<----F

Here's the key question: does the center of mass of the wheel accelerate to the left? No! it's connected to the ground! It can't move to the left. And because it can't move to the left, the forces must add to zero, and the force R equals the force F.

Of course, the difference between this case and the one above where the force F was pointed toward the center of mass is that now the wheel will spin. And we can calculate exactly how much it will spin: the two forces set up a torque T = Fr, which rotationally accelerates the wheel through the rotational equivalent of Newton's law: T = Ia.

So all that leads to the real question: how does this apply to an airplane? The point is, to keep an airplane from moving, you need to apply a force F to the plane that is equal and opposite the engine thrust. Assuming the plane won't flip end-for-end or anything silly like that (adding back gravity and so forth), it doesn't matter if that force is applied to the nose of the airplane, or the tail, or the landing gear.

It doesn't even matter if the force is applied at the bottom of the tires. That force will still be transmitted to the plane and oppose the engine force. Given that this is a thought experiment, it is possible to apply an opposing force to keep the plane in place via the tires. However, this will come at the cost of rotationally accelerating the wheels. And that acceleration is apt to be very large.

This looks to be the work of some high school student (probably a C student at that). He is saying the the hub is fixed to the ground (where I bolded the text). This in no way explains the problem. I'll grant you that the plane won't move if you anchor it to the ground. Try again.

[Jeff Matthews]

Maybe planes are too intriguing. Try a car. What if the car is on a treadmill, and however much the driver speeds up, the treadmill speeds up in the opposite direction. Will the car fly? Hell no. It will stay in one place - AND THERE WILL BE NO WIND - ABSOLUTELY, POSITIVELY NO WIND. So, feel free to use a convertible for this experiment (your hair won't be windblown).

Now, put some wings on the car. Will it all the sudden fly in the absence of this wind? I win!

Somebody prove this statement wrong. It is complete absurdity to think all you have to do is add wings to a car in a windless environment and it will fly.

cars and panes are different. Put it this way thing of the car as fixed object as the engine is fixed to the wheels. The plane think of a pin wheel, as much as you blow the pinwheel it will not effect your arm from moving as the force vectors are not pushing against each other but is dissapated by the bearing.

The pinwheel example. That's where your wrong. If the pinwheel could endure enough wind, your arm will move. Read how this occurs in the previous post containing the wheel diagrams.

[Jay481985]

You were onto something about wheel speed versus plane speed. Now you are going backwards. Could it be that you are confusing an accelerating force (plane's engine acting against air) with a non-accelerating force (spinning conveyor belt)? What part of freely spinning wheels don't you get? Dr.Who had it on the very first page by saying that the wheels would simply spin twice as fast.

Dr. Who did not get it right. If you run on the normal ground at 15 miles an hour, you move forward at 15 miles an hour. If you suddenly jump onto the treadmill (which is going 15 miles an hour contraflow) and you keep running at 15 miles an hour, you go nowhere. That does not mean your feet are now moving 30 mph.

Ah! But you'll say wheels are different than feet. Not at all. Here's why. Put the wheel on the conveyor and run it at 100 mph. The wheel spins at 100 mph. But does it? No, it will not - not unless you apply some force to the axle to keep the wheel stationary. So, let's say you run the conveyor belt with the plane on it. The plane WILL go backwards with the belt UNLESS there is a counter-force. This counter-force can be a rope attached to an imaginary ceiling. In this case, this new force will allow the wheel to spin and have no movement of the plane - forward or backward - IF AND ONLY IF the force equals the opposing force. So, when the rope tied to the ceiling stops the plane from going backward at 100 mph, it is actually pulling the plane forward at 100 mph. Thus, the wheel spins and the plane does not move. Substitute the rope for an equal force of jet propulsion, and you get THE EXACT SAME RESULT.

and if you measured the force that is required to hold the plane in stationary position it will be a lot less force then the energy required to move the belt 100 mph. the bearing dissapates the energy back to the conveyor belt. That is why it is easier to move something on wheels as opposed to something like a big brick.

[Jay481985]

jeff check your pm I will send you my cellphone number and we can talk

[Jeff Matthews]

No, Sput. His "high school" example is right on. It is a simple variant to give explanation. If a bearing could not transfer force to the load carried by the wheel, movement would not be achieved. That is how cars are propelled. The bearing must transfer energy to the frame.

The same holds true with planes. Your challenge to the nay-sayers was how to show that the force from the treadmill was transferred to the body of the plane. You suggested it was all disippated in the wheel. Not true, and there's your proof.

[Jeff Matthews]

jeff check your pm I will send you my cellphone number and we can talk

Cool. How about I call you tomorrow?

[Jay481985]

you can call me now, i have free nights and weekends and im fine.

[Jay481985]

I think you are getting confused with speed and force. Remember just because the conveyor belt is spinning at the speed of the plane does not mean all the energy would be transfered from the conveyor belt to the wheels.

I understand where you are getting the vector idea from but the fact that the conveyor belt spinning the speed of the plane does not mean the full force of the conveyor belt will be transfered into the wheel. Remember the wheel reduces alot of friction as it is easier to move 1000 pounds of sand on a wheel thing as opposed to 1000 pounds of sand on a pallet that needs to be nudged.

[Jay481985]

btw jeff are you a patent lawyer cause i have been looking for one, seriously

[Jay481985]

seriously call me I'm a college student I will be up till 2 am EST

[oldtimer]

I know a patent agent Jay. He still needs to pass the bar to be a lawyer but has the agent credentials now.

[Klipschguy]

Well, I guess we are all in agreement now? The plane takes off. Cuz...(after 30+ pages of discourse)

The energy required to overcome the rolling resistance of the tires + the friction of the wheel bearings on a variable conveyor belt is quite easily overcome (with incredible room to spare) by a good ole modern day jet engine. The accelerating jet will encounter a little resistance with the conveyor belt spinning its tires, but is almost negligible compared to the thrust capability of the jet engine.

Newton would agree that objects at rest tend to stay at rest unless acted on by an outside force. A jet engine is a serious outside force.

BTW, do you guys like Cornwalls or La Scalas better?

[Jeff Matthews]

seriously call me I'm a college student I will be up till 2 am EST

Hey, college student. I am sleepy. I'll call you tomorrow. It will show a (281) area code, and you'll know it's me.

Now, before I go, here's another post I found by some fellow named Cecil. He supports you guys, and I remain intrigued - but not embarrassed. Embarrasment is reserved for those who don't care to learn. Anyway, here it is:

Dear Cecil:

Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. Here's the original problem essentially as it was posed to us: "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 the opposite direction). Can the plane take off?"

There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail

Cecil replies:

Excuse me--did I hear somebody say Monty Hall?

On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.

First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.

A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

--CECIL ADAMS

[sputnik]

No, Sput. His "high school" example is right on. It is a simple variant to give explanation. If a bearing could not transfer force to the load carried by the wheel, movement would not be achieved. That is how cars are propelled. The bearing must transfer energy to the frame.

The same holds true with planes. Your challenge to the nay-sayers was how to show that the force from the treadmill was transferred to the body of the plane. You suggested it was all disippated in the wheel. Not true, and there's your proof.

This is exactly where you and the C-average high school student fall into an erroneous conclusion by thinking that a car's propulsion system is the same as a plane's. The car's wheel is coupled to the frame of the car via the axle, differential, drive shaft, transfer case, transmission, engine, and engine mounts. The aircraft landing gear is like a roller skate - basically, a free rotating or dead axle for load bearing purposes only. There is no torque-bearing coupling between the wheel and the frame of the plane. The wheel spins indepedently of the frame and engine of the aircraft and does not transfer any non-orthogonal force component.

Edit: Did I miss something while I was posting? Jeff, it looks like you've seen the light. But what's this, you'll believe some stranger you meet on the internet named Cecil and yet argue with your friend Sputnik?

[Klipschguy]

Well Cecil is just simply restating what many here have been saying over and over for 30 pages. Excellent explanations here too. I especially enjoyed the hyperbolic illustrations that certainly entered the realm of the absurd. I loved ChampagneTaste's example of a 30 foot hammer with a head the size of a 55 gallon drum hitting the poor fella on the treadmill. Some of the other examples were just as priceless and left me cracking up. Using absurdity to shine light on the obvious is a great method for helping others understand the truth.

[Klipschguy]

Jeff said: "He supports you guys, and I remain intrigued - but not embarrassed. Embarrasment is reserved for those who don't care to learn."

I disagree, embarassment, especially healthy shame is reserved for those who DO care to learn and change.

To each his own.

[Speedball]

This reminds me of the red tape involved with being an employee of the State of Indiana......

example:

1. Must have quotes from three vendors for any amount of $......even a $2.00 item!

2. Two weeks orientation for new employees.......10 whole paid days of doing nothing!

3. Two day's training on how to properly use a walkie talkie.......silly?

..................and the list goes on and on................lol.

Oh, please continue......