will it take off?

[Egon]

Egon, I don't have a clue of what you're talking about

Hey Me's Bye, that makes two of us!!

Remember the Avro Arrow

http://http://www.airforce.forces.gc.ca/equip/historical/arrowlst_e.asp

 

[Tom_Veatch]

The original details were

"a plane is standing on a movable runway( something like a conveyor).as the plane moves (relative to what, the conveyor or the ground?) the conveyor moves (relative to the ground? Presumably so, but not stated.) but in the opposite direction.the conveyor has a system that tracks the speed of the plane (relative to the ground? or relative to the conveyor?) and matches it exactly in the opposite direction (relative to the ground? or relative to the plane?)"

The only fixed point I see in this scenario is the ground on both sides of the conveyor? (That is all that I can see, also. But nowhere does the original problem state that the speeds are measured relative to that fixed point.) Are/can you read something else into it?

Let's restate the problem with the assumptions explicit.

"a plane is standing on a movable runway( something like a conveyor).as the plane moves forward, relative to the ground, the conveyor moves relative to the ground, but in the opposite direction.the conveyor has a system that tracks the speed of the plane relative to the ground and matches it exactly in the opposite direction, also relative to the ground. In other words, at any point in time, the conveyor moves aft relative to the ground at the same speed the plane moves forward relative to the ground. The air is stationary relative to the ground."

With the added stipulations, it becomes obvious that a person standing beside and facing the moving runway with the plane pointed to the right will see the plane moving to the right at some speed, say 10 mph, and the conveyor moving to the left at 10 mph. The plane is moving at 20 mph relative to a point on the conveyer. This is identical to a person standing beside a road seeing a car moving to the right at 10 mph and another car moving to the left at 10 mph. The occupants of each car see the other car moving closer (or farther away) at a rate of 20 mph.

A person riding on the conveyor will see the ground moving at 10 mph. That is exactly like the occupant of a car moving at 10 mph seeing the road moving past at 10 mph. That observer on the conveyor will also see the plane moving at 20 mph. That is identical to a person standing on the highway watching a car move away from him/her at 20 mph.

So, is the plane's movement measured relative to a tree growing beside the conveyor, or is it relative to the surface of the conveyor belt? If it's relative to the tree, then the plane moves forward relative to the air and will fly. If it's movement is measured relative to a point on the conveyor, then the plane stands still relative to the tree and the plane doesn't fly.

Of course, in the latter case, the pilot has to be very precise with power settings so that only enough thrust is generated to overcome the rotary inertia of the wheels and the friction in the wheel bearings. In other words, to apply only that power needed to taxi forward at a speed relative to the conveyer that's equal to the speed of the conveyor relative to the tree.

In an inertial coordinate system, net forward thrust on the a/c will cause the a/c to accelerate, gain speed, and move forward, as viewed in that coordinate system.

So, define your terms and explicitly state your assumptions, and the "problem" becomes a non-problem.

 

[BillyP]

Egon, I don't have a clue of what you're talking about

Hey Me's Bye, that makes two of us!!

Remember the Avro Arrow
http://http://www.airforce.forces.gc.ca/equip/historical/arrowlst_e.asp

Ah, the day Sputnik 1 hit the news

 

[BillyP]

So, is the plane's movement measured relative to a tree growing beside the conveyor, or is it relative to the surface of the conveyor belt?

From what I read into it, the plane is moving forward or will. In order for me to see the plane move forward. imagine me as a tree, innocent bystander, news reporter, Janusz Zurakowski or whatever but I'm standing still beside (not on) the conveyor.

 

[RayH]

So, is the plane's movement measured relative to a tree growing beside the conveyor, or is it relative to the surface of the conveyor belt? If it's relative to the tree, then the plane moves forward relative to the air and will fly. If it's movement is measured relative to a point on the conveyor, then the plane stands still relative to the tree and the plane doesn't fly.

Of course, in the latter case, the pilot has to be very precise with power settings so that only enough thrust is generated to overcome the rotary inertia of the wheels and the friction in the wheel bearings. In other words, to apply only that power needed to taxi forward at a speed relative to the conveyer that's equal to the speed of the conveyor relative to the tree.

.

The problem with the scenario of the plane moving forward relative to the conveyor but not the surrounding ground is that its impossible to initiate. Meaning, that the conveyor, by definition, instantly matches the planes speed. The plane starts out not moving at all, so the conveyor isnt moving either. Some force has to be applied to the plane for it to move, so you start the engine and run up the power.
The thrust is either going to make it move forward or its not, those are the only two choices.
If it does move forward, then the scenario above is void becuae the plane is moving and will take off..
If the plane does not move forward, the wheels can not be turning at all so the conveyor will not move at all because it only matches what the plane is doing, which is absolutely nothing, so the plane just sits still with its engine running full throttle and not moving anywhere. Does that make sense?
If the plane does not move forward, the conveyor does not move backward. If the plane does move forward, the conveyor does move backward.

 

[Tom_Veatch]

The problem with the scenario of the plane moving forward relative to the conveyor but not the surrounding ground is that its impossible to initiate.
...

Oh, Ray, there you go getting practical! I agree, as a practical matter, it would be extremely difficult to initiate and maintain that scenario. However, a mathmatical argument might be made supporting a "conveyor-centric" view of the situation. But I'm not going to do it.

First, I'm sure it would be deadly boring to anyone not fascinated with things mathmatical, and second, I'm not sure my proficiency in calculus has survived the years since I last exercised it. But, for the mathmatically inclined, if you allow stepwise changes in the state vector while the system remains in equilibrium and then take the limit as the step size approaches zero, you may find the velocity of the plane relative to the conveyor can increase while it's velocity relative to the ground remains zero. Or you may find a singularity that renders the scenario impossible.

In either case, the proof is left as an exercise for the student. I'm quite content with a "ground-centric" view of the system in which the airplane accelerates to liftoff speed, the tires self-destruct, the wheel bearings melt, and the plane flies merrily away into the sunset as the pilot wonders whether or not to use synthetic oil at the next oil-change.

 

[greenedeere]

Since you settled that!!!Real good. What about the landing? If the pilot tries to land on the conveyor will it move as soon as and be at the same speed as the plane on touch down.HEEHEE.

 

[Tom_Veatch]

Since you settled that!!!Real good. What about the landing? If the pilot tries to land on the conveyor will it move as soon as and be at the same speed as the plane on touch down.HEEHEE.

If so, I sure hope the no-fly boys can come up with a way to keep the pilot from flying through the windshield when the plane comes to an instantaneous stop. Seat belts and shoulder harnesses are good, but they aren't designed for g-loads that high.

And if we assume the standard, single engine, tractor (Hey, back on topic!) propeller configuration, they need to figure out how to keep that pilot projectile from going through the propeller disk too.

 

[RayH]

Oh, Ray, there you go getting practical! I agree, as a practical matter, it would be extremely difficult to initiate and maintain that scenario. However, a mathmatical argument might be made supporting a "conveyor-centric" view of the situation. But I'm not going to do it.

First, I'm sure it would be deadly boring to anyone not fascinated with things mathmatical, and second, I'm not sure my proficiency in calculus has survived the years since I last exercised it. But, for the mathmatically inclined, if you allow stepwise changes in the state vector while the system remains in equilibrium and then take the limit as the step size approaches zero, you may find the velocity of the plane relative to the conveyor can increase while it's velocity relative to the ground remains zero. Or you may find a singularity that renders the scenario impossible.

In either case, the proof is left as an exercise for the student. I'm quite content with a "ground-centric" view of the system in which the airplane accelerates to liftoff speed, the tires self-destruct, the wheel bearings melt, and the plane flies merrily away into the sunset as the pilot wonders whether or not to use synthetic oil at the next oil-change.

At least we agree that the plane would take off.
Im not with you on the runaway conveyor thing though.
What I see is a conveyor that is limited to what the plane is doing and a plane that needs some sort of force to continue moving, it wants to stop moving because of friction and drag. Remove or limit the trust acting on the plane and it stops.
It would seem you are on the verge of inventing a machine that creats its own source of power. It should be a real money maker for you.

 

[Egon]

We seem to be a bit hung up on relatives.

Air flow over airfoils; is this the crux of the debate ??