Alrighty -- following is a simple energy/force analysis for a small
propeller equipped DDWFTTW vehicle. In this analysis, we show that
in a 27.5ftsec wind, and with the vehicle traveling over the ground at
55ft/sec, the retardant force on the wheels needed to drive the
propeller is less than the propeller needs to keep the vehicle at that
speed.

A:
1.0 HP = 550 foot-pounds per second
(http://en.wikipedia.org/wiki/Horsepower)
This means that @55ft/sec, 10lbs of force exerted on our chassis will
allow us to harvest 1.0hp from our wheels with a lossless generator
(we'll deal with losses below)

B:
1/2HP = 275 foot-pounds per second
This means that at 27.5ft/sec, 10lbs of force can be produced by a
lossless propeller consuming 1/2hp. (we'll deal with losses below)

C:
If the wind is blowing at 27.5ft/sec and our vehicle is traveling DDW
at 2x the speed of the wind, the vehicle is traveling over the ground
at 55ft/sec and through the air at only 27.5ft/sec.

D:
Through the establishment of "A", we know we can pull 1.0 HP from the
wheels of the vehicle if it's propelled by 10lbs of force, and through
the establishement of "B" we can see that the propeller in the
relative tailwind only needs 1/2HP input to produce that same 10lbs of
force.

E:
We subtract the 1/2hp that the prop needs to produce its 10lbs of
thrust from the 1.0hp that the wheels can produce from that same 10lbs
and you have 0.5hp left over for the system losses.(told you we would
get to losses).

In the real world we don't have lossless components of course. If you
consider an 85% efficient propeller (easy to achieve) and an 85% drive
train (even easier to achieve) we've still got nearly 1/4 HP left over
for the Crr of the tires (very low for high pressure bike tires) and
aero drag (which is also very low as our relative headwind is slight).

Do the same calcs on a no wind day and it's easy to see that the
wheels still produce 1.0HP at 55ft/sec, but now the propeller is force
to do work at 55ft/sec rather than 27.5ft/sec and it now takes a full
1.0HP at the prop to produce the 10lbs of force. This of course means
that there is nothing left for losses and since there are *always*
losses, the vehicle simply can’t motivate itself when there is no
wind.