[quote]I think that the one thing you are not understanding is that airplane speed is not measured by how fast the wheels are moving, it is measured by how fast the airplane is moving with respect to the air around it...
therefore, if the airplane has a takeoff speed of 50knotts then the airplane would have a forward speed of 50 knotts and the treadmill would have a reverse speed of 50 knotts... therefore the wheels on the airplane would be rolling at 100 knotts... which wheels on airplanes are free rolling anyway[/quote]
Where is the air speed?

"Where is the air speed?"
the airplane would be moving forward to create airspeed... the wheels would be moving twice as fast as the treadmill is moving, because the treadmill is moving the speed of the airplane(measured in airspeed or even GPS ground speed.... not measured in speed that the wheels are moving).