Vic Smith wrote:
Wayne.B wrote:
I've become convinced that this thing does what they say.

Never doubted it worked [...] An explanation is here at 3:00 in.
http://www.youtube.com/watch?v=LjLPPInzSzI

I think perhaps the best intuitive explanation is at
http://www.youtube.com/watch?v=1pSYALWQ-nI
(and similar videos) showing a model wheeled vehicle on
a running treadmill, making forward progress against the treadmill.

Now, this situation is identical to the full-sized vehicle
moving downwind exactly at windspeed. That is, in both cases,
there's zero apparent wind on the vehicle, and in both cases
the wheels are spinning. The treadmill under the stationary model
is just like the "moving ground" under the full-scale vehicle
travelling downwind at wind speed. You see that???
And now, those spinning wheels are used to power a propeller.
And since there's no apparent wind on the vehicle, any little push
from that propeller will start moving the vehicle forward. In the
treadmill case, the model begins making forward progress.
On the ground, the full-scale vehicle begins moving faster
than wind speed.
There's one potential little glitch -- the spinning wheels
do have some rolling friction with the ground. So the propeller's
forward push must be greater than the wheels' retarding frictional
force. Is that possible? That's a calculation you simply have
to do -- you can't just sit here and argue the outcome with words.
But it's not physically impossible, and clever engineering might
be able to accomplish it. And since we see the results in the videos,
I assume the calculations back that up.
How fast can the vehicles eventually move? To start with -- i.e.,
either on the treadmill or at downwind speed -- there's no apparent wind,
so there's nothing (besides rolling friction from the wheels) retarding
their additional forward acceleration. So any little forward push from
the propeller gets them started. But then they immediately begin to feel
an apparent headwind, and at some speed that headwind balances the
propeller's push, and that's the steady-state speed.
Finally, note that the propeller spins faster and thus pushes harder
as the vehicle speeds up, so you might be tempted to wonder if that
harder push continues defeating the headwind, letting the vehicle
continue to speed up, and up, etc. Common sense says "no", and
physics backs that up. If you double the groundspeed, you double
the wheels' rate of spin and, so, the propeller's rate of spin, which
more or less doubles the forward push.**[see footnote] That is,
propeller push is roughly linear with ground speed. But air resistance
goes roughly as the square of speed, and it therefore quadruples
as the propeller push doubles. So resistance eventually overtakes push,
which is the final speed the vehicle winds up travelling.
Again, you need detailed calculations to work out all these numbers,
but that's the overall picture of how it goes.

**[footnote] You might hope you could just change the wheel/propeller
gear ratio to increase propeller speed more and more. The problem here
is that extra torque comes from wheel/ground friction which would have
to increase, and which would be an additional retarding force defeating
any additional push from the faster propeller.
--
John Forkosh ( mailto: where j=john and f=forkosh )