Plane on a treadmill poll...

[speedminded]

*sigh*

Forget about the damn wheels.
If the conveyer belt offsets the plane's speed, then the plane is
stationary to the ground and will achieve no more lift than if it was
just sitting still on the ground without a conveyor belt.

So unless there is a very strong headwind, it will not be able to
generate the lift necessary to take off.

Read the question again. The treadmill plays a crucial roll in the
plane's acquistion of speed as long as the plane is not airborne. If
it is still on the ground and the wheels are rolling forward at a rate
to move the plane at, say 150 mph, the conveyor belt is pulling it
backwards at the same 150 mph. So relative to the stationary earth,
the plane is going exactly nowhere. This is like going up the steps
of the down escalator at the same rate of speed the steps are going
down - you get nowhere. And if you are going nowhere and the wind is
not blowing, you will not generate any lift at all and therefore will
not be able to take off.

It DOES NOT offset the speed, it has NO effect on the speed of the plane, if the planes isn't going anywhere then the conveyor isn't either. If the planes engines are propelling it 50mph and the treadmill is spinning towards it 50mph then the plane is still going forward at 50mph....still going forward at 50mph...still going forward at 50mph...still going forward at 50mph...do you get it? The conveyor has no effect on the planes engines and it's ability to propel it forward, it can only make the wheels spin faster. If the plane is going forward at 50 mph and the treadmills is going backwards at 50 mph then the wheels are spinning at 100mph but the plane is still going forward at 50 mph.