Peter Duniho wrote:
"Ray" wrote in message
...
Looks like airplane treadmill problem, regularly a spark for flame wars on
R.A.P., has made it into the mainstream.

http://pogue.blogs.nytimes.com/

And handled with every bit as much intelligence and consideration as we've
seen here. Which is to say, there's no shortage of people convinced that
the airplane won't take off, even though it will.


The problem is that as it is stated, the scenario is not one that could
ever be created with a real treadmill subject to normal engineering
constraints.

Let's imagine that the plane gets started in a slow roll down the
runway at a steady 10 mph relative to the calm air & earth. Now the
treadmill has to speed up to 10 mph, but that makes the plane's tires
start spinning at 20 mph. Therefore the treadmill has to speed up to
20 mph which makes the tires spin at 30 mph, which makes the treadmill
speed up to 40 mph, etc.
Even though the plane is only moving slowly relative to the earth, the
tires and treadmill speeds are in an infinite loop to ever higher
speeds.

As soon as the plane starts moving at all relative to the earth, the
tires and treadmill will start their endless positive feedback loop to
try and reach an infinite speed. If the treadmill has a fast enough
response mechanism to keep up with the increasing tire speed the system
will reach some kind of physical limit before the plane can get any
appreciable speed relative to the air. The tires might explode, the
wheel bearings may fail, the treadmill propulsion system may run out of
power, but you can't satisfy the conditions as stated and have the
plane get up to takeoff speed.

Of course the above is based on a particular interpretation of "speed
of the wheels" i.e. that it is measured based on the speed of rotation
and therefore measures show fast they are rolling on the treadmill
surface. If instead the "speed of the wheels" is measured by seeing
how fast the wheel hub is moving forward relative to the earth then the
above infinite feedback loop doesn't arise and the plane can take off
fairly normally although the wheels will be spinning twice as fast as
normal at takeoff.

But that second interpretation of wheel speed doesn't strike me as
consistent with normal usage - i.e. when a bicyclist is on a stationary
trainer we would normally measure the speed of his rear wheel based on
rotation rate, not say that it's zero since the hub is just spinning
but not moving forward.