upon further consideration..
Turok is WRONG.. the plane CANNOT take off
why?...
start the treadmill,
place the plane on it engines off.
the plane is moving relative to the air, but not the treadmill, it's wheels are not turning.
there is now a condition of "negative lift", ie air is now flowing in opposite direction moving from posterior wing to anterior. because plane is moving thru space, backward!
start plane's engines. progressively increase thrust.
the plane begins to move "LESS backward", but never forward.
the lift remains "negative".
until sufficient thrust pulls/pushes the plane's movement, and wheels, EQUAL to treadmill's speed.
at THIS point in time, after gradually diminishing "negative lift, there is NO air flow over the wing,
ZERO, NADA, ZILTCH!
and still NO POSITIVE LIFT.
the plane CANNOT take off!
the plane is FIXED IN SPACE!
unfortunately, it remains grounded.
the treadmill is moving CLOCKWISE at a certain speed, the plan'es wheels are moving at a speed EQUAL to treadmill but counterclockwise.
Only FURTHER increase in planes thrust and speed above and beyond that of the treadmill would permit the plane to reach sufficient POSITIVE air FLOW over the wing to liftoff eventually.
at this point the plane would be ADVANCING along the treadmill's belt, ie relative to the treadmill but its wheels FASTER than the treadmill/s backward speed (and the air, which are one and the same for the intent of this problem), but NOT necessarily the PLANE relative to the AIR
only when the plane is advancing relative to the treadmill and air can the plane have any hope to take off.
A: the plane CANNOT take off under the initial conditions set in this physical problem!!
ps turok, wrong again, what else is new
psps post edited numerous times to enhance clarity of argument