cjcampbell wrote:
"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward. Does the airplane take off?" (Assuming the tires hold out, of
course.)

Cecil Adams (world's smartest human being) says that it will take off
normally.

Here's my read...

The propeller or jet provides thrust to move the plane forward through
the air mass. The prop wash on a propeller aircraft will not itself
generate sufficient airflow over the wings to lift the plane. Nor will
a jet engine. The purpose of these devices is to accelerate the whole
aircraft into the air mass. Once the plane is moving forward through
the air the wings will begin to generate lift... but you need positive
airspeed, not just propeller wash.

So, IF the plane is stationary in the air mass it WILL NOT take off.


The complete problem description states that the treadmil's control
system tries to counteract forward movement of the plane by speeding up
the treadmil. It's a flawed idea as the plane's thrust is mostly
decoupled from its wheels. Unless the wheel bearings are superheating
with friction and actually providing a braking force the plane is going
to move forward into the air mass... regardless of the rolling ground.

So the plane will trivially overcome the treadmill, accelerate away and
WILL take off.

.... unless the wheels melt.


Finally...

If, as the plane's prop runs up, a headwind is encountered which
perfectly cancels out the thrust then the plane will be accelerating
into an oppositely accelerating air mass all the way up to take-off
speed. Neither the plane not the treadmill will never have moved
relative to the ground, but the wings are getting all the airflow they
need. The plane WILL take off (like an elevator until equilibrium is
lost).


Regards,
Paul.