From the OP:
"The conveyor belt is designed to exactly match the speed of the wheels"
Case 1: the reference for the speed of the wheel is the tire contact patch. The treadmill top surface is stationary with respect to the airport lounge. I'll call the stationary treadmill "the runway." This is a normal takeoff.
The contact patch of the tire's speed matches the (stationary) treadmill as the plane accelerates away due to thrust from its propeller, fan or reaction motor (jet or rocket) and lifts off normally. The wheel rotates at airframe speed/wheel circumference (in radians/2pi sec).
Case 2: the reference for the speed of the wheel is the axle of the wheel which translates at the same speed as the airframe as the plane accelerates away and lifts off normally. The top of the treadmill also translates at airframe speed. The wheel does not rotate.
Case 3: the reference frame for the speed of the wheel & treadmill is the topmost point on the wheel circumference. For this point to be stationary with respect to the treadmill contact patch, the wheel cannot rotate. This case must be identical to case 2 where the treadmill runs at airframe speed. The aircraft accelerates away and lifts off normally.
Other cases involving rotated reference frames are too silly and will not be considered. I'm also ignoring the difference between velocity and speed for case 3.
In each case the treadmill has to be long enough for the plane to reach liftoff speed, v2min or greater.
"The conveyor belt is designed to exactly match the speed of the wheels"
Case 1: the reference for the speed of the wheel is the tire contact patch. The treadmill top surface is stationary with respect to the airport lounge. I'll call the stationary treadmill "the runway." This is a normal takeoff.
The contact patch of the tire's speed matches the (stationary) treadmill as the plane accelerates away due to thrust from its propeller, fan or reaction motor (jet or rocket) and lifts off normally. The wheel rotates at airframe speed/wheel circumference (in radians/2pi sec).
Case 2: the reference for the speed of the wheel is the axle of the wheel which translates at the same speed as the airframe as the plane accelerates away and lifts off normally. The top of the treadmill also translates at airframe speed. The wheel does not rotate.
Case 3: the reference frame for the speed of the wheel & treadmill is the topmost point on the wheel circumference. For this point to be stationary with respect to the treadmill contact patch, the wheel cannot rotate. This case must be identical to case 2 where the treadmill runs at airframe speed. The aircraft accelerates away and lifts off normally.
Other cases involving rotated reference frames are too silly and will not be considered. I'm also ignoring the difference between velocity and speed for case 3.
In each case the treadmill has to be long enough for the plane to reach liftoff speed, v2min or greater.
So how, exactly, does God know that She's NOT a brain in a vat?
