Flight and the Conveyor Belt

Cecil's Columns/Staff Reports
41

I couldn’t believe it when this question prompted such a long thread in the other forum, and I’m further surprised that Cece deighned to answer it. It seems to me that the issue is all in the poor wording of the problem - if it were stated clearly, there would be no disagreement.

Cecil of course answered the problem correctly for the interpretation he assumed. Plane moves through the air at 160 mph, conveyor turns backwards at 160 mph, wings generate lift and it takes off. I can’t imagine anyone disagreeing with this.

However, in his last few sentences he dismisses what I think is the interpretation most people are using - the one where the treadmill turns however fast it must to keep the plane stationary. Instead of leading to a paradox, it’s more a matter of practical difficulty. The wheels will have a moment of inertia and friction, so that it would be theoretically possible to perfectly balance the engine thrust by greatly increasing the speed of the belt. After a few seconds equilibrium would be reached, the engines would spool up to full thrust, the belt would be going thousands of mph, enough to create friction on the wheels equal to that thrust. Cecil’s explanation treats it as a paradox only because he starts with the case where the plane hits 5 mph, but in this scenario, the whole assumption is that it can never hit 5 mph because it’s held at zero by the moment of inertia and friction of its wheels!

42

The conveyor belt is supposed to move so that a point on its circumference moves at the same speed as a point on the surface of the wheels (sorry, I can’t get the maths to come out of my head and onto the screen :smack: ) There are supposed to be all sorts of rationalisations where the belt moves automatically at whatever speed the wheels move at, the wheels have frictionless bearings to move around the axles on etc.

And I’m starting to see now what’s the issue at hand, all the wheels are doing is providing as friction free a surface for the plane to move over, so the engines move the plane forward and the wheels stop it from sinking into the ground. So they should have no bearing on the forward motion of the plane, as long as there is little friction in the axles right?

43

This is an uncorrect analogy. For this analogy to be correct, the car towing the glider is not on the conveyor, but the glider is. Can the car pull the glider forward if it is on a road beside the runway/conveyor? Yes it can. The glider moves forward relative to the wind and takes off. Cecil was right.

44

You understand better than you think you do. The entire point of this thought experiment is to determine how much a plane relies on its wheels. You got stuck on exactly the same thing that got me: namely how ludicrous the question is, if phrased correctly. If the plane is prevented from moving foward, of course it will not take off. However, if the treadmill runs such that it has equal and opposite velocity to the plane, the plane still takes off (assuming it has good enough tires/axles/bearings).

45

After reading over the posts here, and elsewhere, regarding this question I have concluded that most of the confusion stems from a lack of clarity in stating the key detail of this scenario. That is whether or not the plane can achieve any forward motion relative to an observer off to the side (not on the treadmill runway). This is absolutely the key to this question.

If the plane can move forward then, as others have pointed out, air can flow over the wings to provide lift and the plane can eventually take off. If it cannot move forward at all, relative to a stationary observer off to the side then there will be no airflow over the wings and no lift.

So, it all comes down to your answer to one basic question that somenone asked earlier - If I were to stand to the side off of the treadmill runway and grabbed hold of the wingtip, does the plane stay put??

46

**BINGO. **

Ding-ding-ding, we have a winnah!

47

I’m still not seeing it. It’s been over 20 years since I studied math. If the conveyor belt turns at such a speed that it exactly matches the rotation of the wheels (assuming a ‘perfect system’) then it seems to me that the aircraft would not move forward in the airmass.

(As a helicopter pilot, I move my wings through the air without moving the rest of the aircraft through the air. :wink: )

48

I agree–this could be wrong. It sounds like a delicate issue, but the thing that really illustrates it to me is the “pusher biplane”, an early form of aircraft that had propellers behind the wings. For these airplanes, Cecil’s explanation is clearly wrong. Now, what if the propellers were pointed downward, so the wash didn’t go over the wings? Isn’t it true that the propeller really is for… propulsion, and once the wings are moving relative to the local air (because the plane is traveling forward) we get true lift? What about jets with engines under the wing? Clearly the major use is for propulsion. It may be that it also contributes some to lift… but?

–Chi

49

OK, try this…Get in your plane or jet and get up to speed moving down the runway and stick your hand out the window and see if you get lift(careful you don’t rip your hand off). Now put your jet on the conveyor belt, get up to speed and stick your hand out. NO LIFT. The conveyor belt doesn’t move the surounding air needed to cause lift, just the ground.

50

Let’s say I’m standing next to the runway, eyes boggling at the sight of an enormous conveyer belt with Sisyphus Airline Flight 100 on top of it.

Sisyphus Air revs the jet engines, conveyor belt starts spinning.

Relative to me, the non-conveyor-belt-riding observer, is the plane moving?

a) If the plane is still making positive headway down the runway, then I agree with the “plane takes off” crowd.

b) If the plane is standing still relative to the ground (more importantly, relative to the air - we are assuming a wind-less day), then I don’t buy it.

But if the answer is (a), then I don’t understand the question. I thought the wording of the question was that the conveyor belt spins such that the aircraft doesn’t move forward.

51

This is exactly my thinking. The key is whether or not the plane moves relative to a stationary point off to the side, a point no on the magical runway. Everything else seems to me to be irrelevant.

52

Ok, there’s a paper airplane on the runway, it has tiny wooden wheels afixed to it. Attached to the paper airplane is a Saturn 5 moon rocket. The rocket it aimed so that it can keep a horizontal course above the runway. Can the conveyor exert a force great enough on the wooden wheels to prevent the Saturn 5 moon rocket from pulling the paper airplane forward?

53

Dern helicopter pilots. Those things don’t fly by aeronautics, they fly by magick :wink:
I think, though, from your last post, you get the idea. So long as the wheels can spin freely, the plane takes off. If the conveyor system is suped up enough to spin at such a great velocity that it can actually force the plane to stand still, the plane doesn’t take off. For our puprposes, we can assume that the conveyor would need to spin at a really fast rate to prevent the plane from taking off.

54

The problem is that we’re assuming that the plane is not moving relative to the Earth. It is.

Look it’s a badly worded question (no offense). The assumption everyone makes when hearing this is that we have a conveyer belt roughly the length of the plane. Hence the treadmill example, where the person stays stationary relative to the ground, and if they move forward they hit a wall. People think “oh, the plane is staying in one place relative to the Earth - it has to be to stay on that little conveyer belt.” (It doesn’t help that the drawing shows almost exactly that).

But that’s not it. It’s a treadmill the length of the runway. The plane isn’t staying in one place, it’s moving down the runway (which just happens to be a conveyer belt) the same as if there were no conveyer belt.

So to clarify -

What everyone seems to think the question is: “Does a plane which is forced by a conveyer belt to stay in place relative to the Earth nonetheless generate lift and take off?”

The actual question: “Does increasing the speed at which the wheels turn have any effect on the ability of a plane to generate lift as it moves down a runway?”

The answer to the actual question is obvious - increasing wheel speed won’t affect the plane.

(The answer to the other question is no - no lift, no flight.)

But here’s where it gets complicated. Assume that as the plane starts, the conveyer belt goes fast enough to create enough friction to prevent the plane from going forward relative to the earth (and assume that the tires don’t melt).

The friction of the tires is miniscule compared to the force of the engines, I’d think - but it exists. If the conveyer belt is fast enough, and there is enough friction from the desperately turning wheels, the plane wouldn’t move - right? Or think of it another way - the plane, instead of wheels, has skids. Can the engines overcome the friction?

Or am I wrong in thinking that the speed of the conveyer belt would create added friction?

55

I still don’t understand why the plane does not move forward friction from the wheels?

56

:smiley: bwah! We have a name for the airline!

No. The conveyor belt is described as running backwards as fast as the plane is moving forwards. The plane is MOVING. It says so, right there in the question. The only thing slowing the plane down is the minimal friction of the wheels, and although the wheels are turning as if the plane were moving twice as fast, that still isn’t enough force to counteract the force of the engines.

57

The only reason for the plane not to move is if there is some counteracting force pushing back on the body of the plane as hard as the engines are trying to push the plane forward. If there were a strong enough headwind to generate as much backwards pressure on the plane body as the engines did, the plane wouldn’t move. If it was facing up a hill and the force of gravity was strong enough to keep it from going straight up, it wouldn’t move. If the conveyor belt was made of velcro, with the other half on the wheels, and the conveyor belt went fast enough to generate enough friction to slow the wheels down enough to push the axles back against the thrust of the engines, the plane wouldn’t move. None of these scenarios fit into the question, however. Given a normal jet, a normal set of wheels, and a conveyor belt the length of a runway capable of going backwards as fast as a jet goes forwards, the jet will still move forward because that system can’t counteract the force of the engines with force against the body of the plane.

58

How bout if we turn the problem around and think of it another way…
Since we are assuming frictionless wheels, it would not matter which direction the wheels turn. If the conveyor belt were turning in the forward direction, the wheels of the plane would actually turn backward (assume no axle friction) and the plane would stay stationary. The plane is a large mass and remembers Newtons laws say that an object at rest stays at rest unless acted upon by an outside force. There is no outside force (no axle friction) so in this case the plane (with no engine running) would sit still on the treadmill.
Now if we were to start the engine, the plane would move forward thru the air because the air provides a force equal to and in the opposite direction of the engines thrust. The plane has no choice but to move forward THRU THE AIR!
Now lets assume that we are doing this experiment in a vacuum, does the airplane move? Nothing to push against.
My best guess is that the little drawing of a plane on a treadmill the same length as the plane is that the plane would very quickly run off the front of the treadmill. On a treadmill the length of the runway and again assuming no wheel axle friction, the plane would takeoff in the same distance as it would on a standard asphault runway.

59

Look at the diagram. It’s fairly simple, the plane will NOT fly no matter how fast the engines are going or how fast the conveyer belt is. No airflow, no flight.

<img src=“http://www.vinsin.com/shared/airflow.jpg”>

This is incorrect. The airplanes engines do not provide lift, they strictly provide forward movement. This forward movement is counteracting the “conveyor belt” meaning the plane stays in the exact same location. There is no air passing over the wings yet, as the plane has not moved through the air, rather the engines have continued to push through a form of “fake drag”.

Newton’s first law states a body at rest will remain at rest or a body in motion will continue in straight-line motion unless subjected to an external applied force. That means, if one sees a bend in the flow of air, or if air originally at rest is accelerated into motion, a force is acting on it. Newton’s third law states that for every action there is an equal and opposite reaction.

According to that, all that has occurred is the air passing through the engines are now equally matched to the movement of the “conveyor belt”, all the while no air has moved over the wings. In order to generate lift a wing must do something to the air. Again, the wings have not done anything other than sit in one location while the rest of the plane is struggling to remain in one fixed point on the “conveyer belt”.

The major problem here is the wings have nothing to push downward because the wings themselves have not moved through the air. The power needed to lift the airplane is proportional to the load (or weight) times the vertical velocity of the air. Again, there is no air movement here.

To put it simply, the engines are only holding the plane from flying backwards. The power associated with lift is often called the “induced” power. Power is also needed to overcome what is called “parasitic” drag, which is the drag associated with moving the wheels, struts, antenna, etc. through the air. What you are doing here is overcoming “parasitic” drag while having no “induced” power. Induced power is the power required to maintain enough lift to overcome the force of gravity.

The energy the airplane imparts to an air molecule on impact is proportional to the speed2 (form ½mv2). The number of molecules struck per time is proportional to the speed. The faster one goes the higher the rate of impacts. Thus the parasitic power required to overcome parasitic drag increases as the speed3. As you can see, the air is not impacting the wings. The engines are the only ones feeding off the air and pushing it back out counteracting the “conveyer belt” but generating no forward motion relative to the air.

I think there is much confusion here as to what engines are doing. The engines do not provide lift; they provide forward motion through the air itself in order to generate lift. If you do not get the wings to move through the air, then you can not generate lift.

Air movement = Lift

No air movement + speed = Lift

I don’t think the second equation makes much sense, now does?

60

I am so glad I avoided reading the GQ thread, now that I read the Cecil summary of what all the fuss is about.