Can a Plane on a Treadmill Take Off?

Let's do the old Einstein thought experiment. Let's presume a motorized
conveyor belt that is being rotated towards the departure end of the runway.
Let's also presume frictionless wheel bearings in an aircraft sitting at the
departure end of the runway on the conveyor belt.

What happens to the aircraft? Nothing. THe airplane remains motionless
because the aircraft wheels, which are rotating, do not impart any force to
the aircraft to make it move in any direction (F=ma). To a bystander
sitting on the taxi light at the end of the runway, the conveyor belt is
moving left to right, the wheels are spinning in a counterclockwise
direction, and the aircraft itself is motionless.

Now introduce wheel bearing friction. The aircraft will begin to slowly
move left to right as a function of how much friction there is. Fire up the
propeller and give it just enough throttle to overcome wheel bearing
friction. Again, the observer on the taxi light sees the aircraft
motionless.

Now give it full throttle. Not only do we now have enough thrust to
overcome wheel bearing friction, we have more than enough to launch the
aircraft successfully into the air.

If ya can't see this, I give up.

Jim




"BDS" wrote in message
t...

"Greg Copeland" wrote
Nitpicking aside, I suspect that everyone agrees that in order for the
plane to take off it must move
forward along the conveyor.

RST Engineering wrote:
Let's do the old Einstein thought experiment. Let's presume a motorized
conveyor belt that is being rotated towards the departure end of the runway.
Let's also presume frictionless wheel bearings in an aircraft sitting at the
departure end of the runway on the conveyor belt.

What happens to the aircraft? Nothing. THe airplane remains motionless
because the aircraft wheels, which are rotating, do not impart any force to
the aircraft to make it move in any direction (F=ma). To a bystander
sitting on the taxi light at the end of the runway, the conveyor belt is
moving left to right, the wheels are spinning in a counterclockwise
direction, and the aircraft itself is motionless.

Actually, that isn't true. You don't need wheel bearing friction to
apply a horizontal force to the wheel at the contact point. The wheel
has inertia and accelerating the wheel will cause a reaction at the
contact point with the belt and the aircraft will begin to move along
the direction of the conveyor. This force will go to zero once the belt
reaches a steady-state speed, but the aircraft will continue to move
along with the belt.

Now if the wheels have no mass as well as no bearing friction... :-)


Matt