will it take off?

[MossRoad]

Lets keep it tractor related...

Welcome to Air Tractor in Olney, Texas

 

[Egon]

Those tires spinning at infinite speed blew when the bearing grease coked heating up the hub. This would surely reult in airframe damage and fire. Now all that is left is a puddle of melted metals on a burning conveyor. Surely this residual will be placed inside another aircraft and flown to the lab for analysis. This is definet indication the plane can fly.

 

[MossRoad]

And that's the problem with everyone's logic - and I mean both sides!

If the conveyor is capable of infinite speed, it can also produce infinite DRAG at the wheels. Since acceleration occurs only if Thrust is greater than Drag, then it follows that the plane will NOT fly IF the conveyor is capable of creating enough drag (by turning the wheels at well-above-takeoff speed - maybe 10X to 20X that speed?). All you pilots, engineers, and mathematicians out there should remember that formula - it's part of basic ground school If Thrust = Drag, acceleration is ZERO.

On the other hand, if the conveyor is NOT able to turn that fast, and cannot change it's speed instantaneously to counteract the thrust provided by the propeller, the plane will eventually fly, becuse thrust will exceed drag for at least brief moments. When Thrust is greater than Drag, acceleration occurs.

Real world? The plane can (and will) take off, because the "perfect" conveyor doesn't exist.

Theoretical world described in the problem as stated? The plane will not move (it's so stated in the problem definition), and therefore won't take off.

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[MossRoad]

Taking the theoretical even further...

The moving conveyor has friction with the air in contact with it. This will cause the air to move (boundary layer theory). As the conveyor speed increases so does the air speed and thickness of this layer of moving air. Eventually, the moving air will be thick (tall) enough to flow over the airplane wings. Even if this does not create flight, it will reduce the normal force on the landing gear which will provide a proportionate reduction in the drag force of the wheels on the conveyor. The reduction in drag will want to make the plane move faster but then there's that pesky infinite speed conveyor. It will move faster yet, creating even more airflow due to the boundary conditions. More airflow equals more lift. Eventually, the airflow will produce enough lift to balance the airplane just above the rapidly moving conveyor.

Thus we have flight at zero ground speed... theoretically.

Now right after I thank that guy you go and make my head hurt again!

 

[RayH]

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I dont get why the conveyor is capable of infinate speed. The only way that can be true is if the plane travels infinately fast. In the original question it was stated that the conveyor "MATCHES" the planes speed. If the plane reaches takeoff speed at around 80kts, the plane is going 80 forward and the conveyor is going 80 backward to match it. How are you getting infinate out of that?
Can someone please explain to me how this could occure? One more thing, how can the wheels spin without the whole plane moving? What is motivating them to do that?

 

[daTeacha]

You could tie a real plane in place on a real moving conveyor belt, run the belt up to any speed, and the wheels would match it without the plane going anywhere. The wheels are not driven by the engine in any airplane I know of.

Our plane could be sitting on our conveyor facing into a headwind. If the engine runs fast enough, the plane can sit still while the wind blows. The conveyor will not move, but if the wind gets to blowing fast enough the plane will lift off the conveyor while not moving forward or rearward. If the engine quits, the plane settles back down and is then blown rearward by the wind. This would cause the conveyor to run forward and the plane's wheels would then be spinning backwards.

 

[BillyP]

The problem doesn't state the plane has wheels. Since everything has gotten theoretical, what if it had very slippery skis, like a bush plane? Then the boundary layer over the conveyor would tend to lift the skis as conveyor speed increased.

Wheels? It never even said the plane had an engine

 

[NewToy]

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You are sure looking for the answer you want to hear. That plane is long gone
John

 

[Paddy]

You could tie a real plane in place on a real moving conveyor belt, run the belt up to any speed, and the wheels would match it without the plane going anywhere. The wheels are not driven by the engine in any airplane I know of.

On stationary pavement the engine does drive the wheels. What else drives the wheels? Engine creats thrust and moves the plane forward driving the wheels. What you likely ment to state is the wheels don't drive the plane.

 

[rback33]

Well crap....I guess I can have paper...or plastic. But I can't have both at the same time!!!

Sure you can.. how much beer did you buy to read the rest of this?