Wouldn't the conveyor and therefore the wheel speed accelerate to infinity. Each time the plane moved forward relative to the ground (not the conveyor), the conveyor would sense an increase in speed and then match that speed.
No. The speed of the hypothetical conveyor would always equal twice the groundspeed of the aircraft. This is established as one of the initially stated conditions in your first post:
When the runway senses the wheels moving, the runway will match the speed of the airplane's wheels, but in the opposite direction.
The speed of the conveyor would only approach infinity if the ground speed of the aircraft did.
Your new question confuses movement with acceleration.
mystic_1
Then I guess what I'm saying is forget the 'old version' and consider the new. It's more interesting. The old version is solved - the plane will fly. The fun is gone. Now tackle the infinite problem.
Seriously, moment of inertia...
Moment of inertia does not increase until relativistic speeds. In this situation the power the engine must provide to accelerate the wheels to twice rotary speed will make the net take off distance a little longer. Twice as much energy is required to accelerate the wheel leaving less net thrust to accelerate the plane, but this is still a fairly small number. Not relevant to the thought experiment.
Something as important as causing the wheels to spin at a radial velocity equal to 99% C is too important to leave out.
Unless,
Methinks you might be obfuscating for entertainment.
First thing to note is that I'm suggesting we no longer consider the conveyor that goes to twice the plane speed. That problem is indeed trivial.
Considering a conveyor that goes to infinity:
Not sure if the moment of inertia
needs to increase... the wheels have a moment of inertia that's
non-zero, compounded with something that goes to infinity.
That alone is an interesting challenge.
Another challenge is if we consider relativity. Nothing can travel faster than light. If we have a conveyor that's moving at (or near) the speed of light, then it's interesting to consider the possibilities of
a. the motion of the bottom of the wheel,
b. the motion of the top of the wheel,
c. the motion of the center of the wheel,
d. all the above in relation to each-other, the ground, and the conveyor.
Compound all that with this little paradox:
Imagine we are sitting still on the conveyor waiting to test this experiment (if it were possible). Everything is still - the plane relative to the ground is still, the wheels are not rotating, and the conveyor is motionless. Then the pilot releases the brake...
This is the paradox: How do the wheels
start to rotate?
Do I claim that this plane will fly? No.
Do I claim that this plane will not fly? No.
I claim that this problem is, at the very least, not trivial.
Again, all the above is in the context of the
infinite conveyor. If anyone's still thinking in terms of a conveyor that goes to twice the speed of the plane, then the above does not apply. And the 2-times the wheel speed conveyor problem is solved.
That plane
will fly.
You should all stick to motorcycles if you don't know sh*t about the principles of flight!
I'm so over this! It's just so much fluff and mirrors and crap and it doesn't make any sense. And the original poster getting all superior and using red text when even a 14 year old can see that the physics is all wrong.
To whom it may concern, this riddle is a difficult problem and is not for everyone.
Poll