Quote Originally Posted by Alpha_One View Post
Ah, your FBD is incomplete and your analysis is completely wrong.
Let's see your FBD then.
Major flaw: The runway friction and engine thrust spin the wheels in the SAME direction, not in opposite directions. Try mo pa sa matchbox on a tablecloth. The only opposing force acting on the wheels is the friction of the wheelbearings, which is constant (unlike engine thrust) as well as negligible.
The forces shown on the FBD are accurately depicting their directions and where they are applied.

Obviuosly, Fb, being off-center, produces torque which tends to rotate the wheel. Friction force is always against motion, if the wheel tends to move forward with Ff, then Fb will try to oppose it.

The friction on the wheel bearing is basically negligible and because of this, the wheel is allowed to rotate. When the wheel rotates, it will move forward (and the plane flies) IF the runway is not moving. With a moving runway, the forward motion of the wheel is exactly opposed, hence the wheel, although rotating, stays in place.

In the FBD, a moving runway is depicted as Fb being significant to oppose Ff. If Fb is made greater than Ff, then the wheel/plane would be moving backward! (meaning, the conveyor/runway was adjusted too fast!)

The wheel bearing, with almost zero friction, actually plays an important role of the wheel. It is its frictionless property that allows the wheel to move along the road. But with a moving runway, it is also its frictionless property that allows the wheel to stay in place while rotating.
We're not concerned about forces acting on the wheels, we consider the forces acting on the plane itself. The big force acting against the plane is wind resistance, not friction from the ground. Remember, the wheels are designed to freewheel.
The wheel is attached to the plane. If it moves, the plane moves. Sure you can have an FBD of the plane, and it will show the same forces. There will be Fb that will oppose Ff. There is no wind resistance when the plane is stationary or just starting to move.
It's not the runway that's frictionless, it's the wheel bearings as far as this problem is concerned.
Yes, its the wheel bearing that is frictionless. It does simulate a frictionless runway in the case of non-moving runway. If the runway is frictionless, the plane can take off with a ski, instead of wheels, and it would not matter if the runway is moving or not.

If the wheel bearings got stuck, the plane will not move if the runway does not move; the plane will move backwards with a moving runway (even if the engines are at full thrust).
Again, runway speed = plane speed (for the nth bloody time) does NOT imply runway force ACTING ON THE PLANE = engine thrust.
Then let's see your FBD so you could clarify what "runway speed = plane speed" would imply.