The "Plane on a Treadmill" Question

[skysidhe]

The answer to the original question is no.

I took aerodynamics in high school and even though I squeeked by with a D due to a terrific Huey camofluage model I made I did learn something and that is a plane needs lift to fly.

Since ditching my flying career I have forgoten the little I did learn so
I went and made sure so I found proof.



Straight and Level Flight
In order for an airplane to fly straight and level, the following relationships must be true:
Thrust = Drag
Lift = Weight
If, for any reason, the amount of drag becomes larger than the amount of thrust, the plane will slow down. If the thrust is increased so that it is greater than the drag, the plane will speed up.

Similarly, if the amount of lift drops below the weight of the airplane, the plane will descend. By increasing the lift, the pilot can make the airplane climb.
http://travel.howstuffworks.com/airplane1.htm

[tw]

A plane is standing on a runway that can move, like a giant treadmill. When the plane's engines throttle up, it begins to move forward, but the treadmill is made to match the forward speed of the plane, only in the opposite direction. So, as the plane moves forward, [treadmill] moves backwards beneath the aircraft.

First - what is the purpose of wheels (landing gear)? So that velocity of a plane is totally irrelevant to ground. Wheels will spin as slow or as fast as necessary so that velocity of the runway and velocity of plane stay totally independent.

Second - plane's velocity is determined by a force applied between plane and air. As engine force increases, then airplane acceleration (and therefore velocity) is according to the well known F=ma equation. Engine force determines airspeed - a relationship between plane and air.

Meanwhile, what do wheels do? See point first. They spin as fast as necessary so that plane's velocity is irrelevant to (independent of) earth.

Since air and runway remain at same location, then plane's velocity to air is same as plane's velocity relative to runway. Therefore wheels spin at plane's airspeed which is same as runway speed.

In this problem, we have added something unique. Runway is replaced by a treadmill. As plane moves forward 1 MPH (relative to air as in point second) then treadmill moves 1 MPH in reverse. Again, wheel's job is to keep airplane and runway completely separate (point first). Therefore wheels must now spin at 2 MPH to keep treadmill and plane independent of each other.

If wheels applied the "F=ma" between plane and runway (as in a car or bicycle), then wheels and ground would not be independent. But wheels do not move this plane. Motion is created completely by a relationship between air and plane - its jet engine. No matter how fast ground moves, plane's velocity (and acceleration) is only based upon F=ma between plane and air. No matter how fast ground moves, wheels will spin as necessary to keep treadmill and plane completely independent of each other.

Now we address other possible (and unstated) references.

Since treadmill will always move backwards (relative to air) at the same speed that plane moves forward (relative to air), then wheels will spin at twice the airspeed.

Treadmill is set to match forward airspeed. Relative to what? If treadmill's speed is relative to air and plane's speed is relative to air, then wheels spin at twice airspeed. But if treadmill's speed is relative to plane, then treadmill never moves relative to air. Now we have wheels only moving at one times airspeed.

One fact we do know. Airplane's speed is always relative to air because those engines create a relationship only between air and the plane. Treadmill's speed (in this problem) could be relative to air or relative to plane. But again, point first - those wheels always make ground independent of the plane. Wheels will always spin as slow or fast as necessary so that plane and earth velocities do not affect each other.

[hideouse]

The initial premise is flawed, implying that moving the surface the plane rests on can keep the plane from moving forward or have some kind of influence over the lift achieved by the lifting surface of the plane.
As we have seen ad nauseum, the resting surface has no effect on the forward motion of the plane. Rather, the moving treadmill will make the wheels turn faster while the plane will move forward as it would normally at any given engine setting. If the forward motion of the plane where to be inhibitted (sp?) or restrained somehow so as to prevent adequate airflow over the lifting surfaces then the plane will not fly. If the plane is stationary, yet somehow adequate airflow is achieved over the lifting surfaces then the plane will fly.
Both sides of the discussion so far seem to me to have made these points but without noting the flaw in the initial premise.