Will it take off?

DizRotus · November 18, 2006

You need CO2 cartridges for your home soda fountain so you go to the local grocery/party store to buy them. You place a CO2 cartridge on the check-out conveyor belt with the bottom facing you and the top facing in the direction of the belt's motion. While the belt is moving away from you (moving the cartridge with it), you accidentally puncture the top of the cartridge (don't worry about how) and the cartridge instantly rockets in the direction opposite the belt's motion. The thrust produced by the escaping gas cares not what the conveyor belt is doing. The motion of the belt will have no discernable effect upon the cartridge as it shoots in the opposite direction.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

The plane flies.

mas · November 18, 2006

Just a quick thought as to what might be 'behind' the two camps perceptual differences...although I have no personal issue with the problem...<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

One camp seems to focus on the wheels and the conveyor.

If we see the wheels as being the source of propulsion - the forward force for the plane, then their frictional coefficient becomes significant...their potential to skid, slip, etc. relative to the conveyor is important.

And if we simply focus on this 'subsystem, if the forward velocity remains equal (by definition) with the conveyors diametrically opposed velocity, they will remain equal and the net displacement will remain zero. If this continues, and as we are not provided with any information regarding air movement (therefore assuming the air is stationary), the plane will remain with zero net physical displacement for as long as the above conditions hold.

Perhaps I have missed something, but I think that this just may summarize the "it won't fly" group's position...

But let's stop for a second and stand back. Let's refocus OUR perspective. Rather than simply focus on the relationship of the forces applied by the wheels and the conveyor, let's look at the rest of the system.

We are still free to apply force via air pressure. Nothing in the initial conditions precludes the application of additional force in a 'new' manner. And this force may be delivered by many potential means. If we apply force via the fluid known as air, we can move the plane relative to the ambient air that we might assume to be standing still. We can accelerate the plane, not via the wheels, but by the air - just like a jet or rocket of even a prop does. In this case we are looking at the net forces within the frame of reference of the air. And a significant force applied to the plane via air pressure can accelerate the plane relative to the standing 'ambient' air.

In doing so, the fundamental coupled relationship between wheel velocity and conveyor velocity ceases to be a limiting factor. We can provide an additional net force to the plane via the air pressure, and thus the net sum of the forces moving the plane becomes greater than the net sum of the forces opposing its movement, and their is a net positive physical displacement. And if we apply enough force in such a manner, we can achieve sufficient lift to fly the plane - regardless of how fast the conveyor or wheels are turning.

Thus we can achieve flight if we understand that our frame of reference has shifted to one other than that of the wheels and the conveyor. We can apply other forces in other 'places', yet still have an effect on the total system known as the plane. And I think that this captures the general gist of the "it will fly" group's perspective.

Maybe this helps a bit and maybe it doesn't...but this is simply intended to try to reframe the issue a bit and present a perspective for the two groups to step back and look at their assumptions a bit. As I think the real problem is that each group is tending to redefine the initial question into a form with which they are more comfortable, rather than looking at the problem in its strict sense - and it is, at best, a very poorly framed question!

Personally I am amazed that some of you are still at this! []

Especially as everyone knows that the color of the interconnects' insulation has a critical bearing on the quality of the conducted signal within! []

klipschaholik · November 18, 2006

Da#@ Ray you had me worried. Welcome back. Now if we could just get them to understand the difference between acceleration with respect to the treadmill and acceeleration with respect to the ground/earth. Big difference!

sputnik · November 18, 2006

...........and it is, at best, a very poorly framed question! .........

Nice recap, all in all, there mas, but I think the open wording of the question is the beauty of the problem. The red herring of the conveyor speed matching the plane's speed creates a distracting paradox for people until the light bulb finally goes on and they realize that understanding the conveyor action, whatever it is, just doesn't matter in order to answer the question correctly.

Ray Garrison · November 18, 2006

Here's another way of looking at this that might maybe possibly convince some people that the damn plane will fly away.

Let's say you have a plane with a maximum level flight velocity of, uh, 450 mph. A nice P-51 or something. You put it on a conveyor belt, with wheel chocks in place and the engine off, and accelerate the belt (with the plane going backwards) to, uh, 500 mph. The belt is whizzing along with the plane sitting on it, going backwards at 500 mph. Now, remove the wheel chocks, climb in, and fire the plane up. Begin moving forward (relative to the belt) and attempt to take off. Can you?

Answer (A). No, stupid, of course you can't. The belt is going backwards at 500 mph, and the plane's maximum velocity is 450 mph. Even if you reached this maximum velocity while running with your wheels on the belt, which I doubt you could do, you'd still be going *BACKWARDS* at 50 mph when you reached your maximum velocity. Obviously you can't fly.

Answer (. Look, let's try one more time. The plane's maximum velocity of 450 mph is a maximum *AIRSPEED*, not a maximum *GROUNDSPEED*. The first thing that's gonna happen when you remove the wheel chocks is that the air rushing past the plane at 500 mph is going to begin pushing the plane forward (relative to the belt.) When you climb in and fire up the engine, you will begin moving forward along the belt, or reducing your rearward velocity, however you want to look at it, and doing so at quite a rapid pace. As you apply engine thrust you will reach a point where the plane is not moving at all relative to the surroundings (zero airspeed), and is wheeling along at 500 mph relative to the belt. At this point the engine is hardly working at all, because all it's doing is fighting the "pull" of the belt passing beneath its wheels. As you continue to throttle up, the plane begins to move forward relative to the air. You reach the Vlof speed, and take off. Granted, at that point the wheels are travelling at a rotational speed equal to moving at 500 mph + Vlof, but we shod the thing with really, really good tires.

Answer ©. The belt produces a thrust vector that imparts a transient kinentic moment equal in magnitude to, but opposite in gradient scale, to the forward lift component of the rotating prop, or the expulsed compustion products. As is clearly stated in the original suppopreposition, the vector magnitude of the scale of the velocity of the belt is diametrically opposing and offset to the velocity component of this vector. This being the case, no amount of force application will circumtranslate into the derivation of forward velocity sufficient to exceed the amount required to negate the rearward component. The system is in a statis equilibrium that cannot be violated without ignoring the 2nd law of thermodynamics. This should be clear to anyone who has half a brain and spends any time at all thinking about this.