would a plane take off if..

[RTHolmes]

indeed it does, however the wheel speed is 0, so the speed of the conveyor relative to the wheels, and hence also relative to the plane is also 0.

[sluggish]

indeed it does, however the wheel speed is 0, so the speed of the conveyor relative to the wheels, and hence also relative to the plane is also 0.

Wrong.  The wheel speed is not zero;  the difference is zero in the opposite direction.  It is a mathematical impossibility whereas the instant the wheel begins to move the conveyor belt counters by ramping up to infinity.

[RTHolmes]

nope, from earlier:

as the plane starts to move forwards, the wheels start to rotate. the conveyor belt instantaniously matches their speed in the opposite direction of rotation counteracting the rotation of the wheels.

edit: starting from rest, the wheel speed would indeed tend to infinity if the conveyor belt matched the wheel speed in the same direction of rotation, however it matches it in the opposite direction of rotation so it tends to 0.

[sluggish]

I can't help you.

[DREDger]

There is still debate on this?

The plane takes off, as a professional engineer I am certain of this.

Lets look at it a different way.  Suppose the conveyor belt is made of snow or ice, and instead of wheels, the plane has skids on the bottom of it.  Would the plane take off then?  

Of course it would, because no matter how fast the conveyor belt is moving, the plane's skids simply skate over the top of it no matter what the speed.

[sluggish]

There is still debate on this?

The plane takes off, as a professional engineer I am certain of this.

Lets look at it a different way.  Suppose the conveyor belt is made of snow or ice, and instead of wheels, the plane has skids on the bottom of it.  Would the plane take off then?  

Of course it would, because no matter how fast the conveyor belt is moving, the plane's skids simply skate over the top of it no matter what the speed.

So... You're an engineer and you don't know about Newton's law and rotational inertia....  Scary.

[lengro]

So... You're an engineer and you don't know about Newton's law and rotational inertia....  Scary.

the conveyor belt counters by ramping up to infinity.

How much energy does it take to ramp a conveyor belt up to infinity, and what happens with time at light speed?
Can there only be one answer to a paradox - is their an answer at all?
 

[sluggish]

Did you know you can measure how much acceleration energy was absorbed by an airplane's wheels by how long they spin after the plane takes off?

[RTHolmes]

I can't help you.

you might be able to if you can supply a formal proof for:

"starting from rest, the wheel speed would tend to 0 as the conveyor belt matches the wheel speed in the opposite direction of rotation."

my calculus is a bit rusty

[sluggish]

you might be able to if you can supply a formal proof for:

"starting from rest, the wheel speed would tend to 0 as the conveyor belt matches the wheel speed in the opposite direction of rotation."

my calculus is a bit rusty

If the wheel is turning clockwise the conveyor belt is most definitely turning counter-clockwise...

[lengro]

Did you know you can measure how much acceleration energy was absorbed by an airplane's wheels by how long they spin after the plane takes off?

Really, I was pretty sure I also would need to know something about the friction in the wheel bearings, and the mass of the wheel?

[sluggish]

Really, I was pretty sure I also would need to know something about the friction in the wheel bearings, and the mass of the wheel?

What does mass of the wheel have to do with it?  you say the plane on the conveyor belt will fly, right?

[DREDger]

So... You're an engineer and you don't know about Newton's law and rotational inertia....  Scary.

In point of fact, Newton has three laws of motion, not one.  Also, when you describe rotational inertia, I'm going to assume you mean 'angular impulse and momentum'.

The 'intertia' of the wheels as you put it however, is not applicable in this situation, and only acts as a resistance to the thrust of the airplane while spinning, similar to how air friction (drag) would.

This hypothetical scenario can be mathematically described with a free body diagram.  The reason I used the sled example was to try to show it in laymans terms so it can be understood more easily.  The wheel and sled both serve to highlight the frictionless interaction between plane and undercarriage.

Of course in a real world situation, the sled and snow conveyor belt would generate 'some' friction which the planes thrust would have to overcome.  Same goes for the wheels, the planes thrust would have to overcome the inertial resistance you mention.

There is no debate, the plane flies.  It is a mathematical certainty.

[RTHolmes]

in fact for this example the wheel bearing friction and inertia of the wheel are irrelevant, because the rotational speed of the wheels is 0.


just in case anyone hasnt got it yet:



 

[lengro]

What does mass of the wheel have to do with it?

I think mass would be handy if I was given some friction coefficients in the wheel bearings - but so far you stated that spin time after take off was all I needed?

you say the plane on the conveyor belt will fly, right?

Hey - it's your turn to answer one of my questions