faster than wind

Update: It looks like Mark has changed his mind. So it seems, that faster-than-wind travel is indeed possible. I'm awaiting Mark's detailed analysis of the problem.

On Word Munger, I saw this really tough physics problem (below is my rephrasing):

Is it possible for a machine to harvest energy from only wind, yet capable of travelling faster than wind, yet in the same direction as the wind?

So far I haven't figure out if it's possible. Over at Word Munger, there is an argument going on between Dave and Mark, and I haven't been able to tell who is right yet.

Under "normal" conditions, a cart with a sail can't move faster than the wind speed; Dave argues that with the correct setup, it is possible to move faster than wind.

The counterintuitive part is that if the cart moves faster than the wind, the relative velocity of the wind becomes negative, resulting in a drag instead of a push. Yet somehow Dave is able to mitigate this by allowing the wheels to thrust the cart with a propeller. I'm not sure if the latter part is possible, since it feels like a "pull oneself out of a swamp with one's own hair" kind of problem. How can a wheel thrust itself? This is one thing I don't understand.

I wanted to come up with a mathematical model/equation that describes the cart's motion (in a simple way), but so far I haven't been able to do so because I don't know how propulsion thrust depends on rotational speed, nor do I know how wind thrust depends on relative wind speed. I might make some linear assumptions, but those are only assumptions.

If anyone has any idea about this, let me know.