Gone with the wind (or something like that)
 

I came across a video about an astonishing wind powered vehicle that travels faster that the wind going straight downwind.
So it moves forward faster than the wind and even accelerates while encountering a virtual headwind. There is even a vane on the tip of the craft that goes backwards, indicating virtual headwind.

Impossible, a trick? I could not work it out until well into the video:

https://www.youtube.com/watch?v=jyQwgBAaBag
I can explain how it works more clearly than the video does, if anyone is interested.

The same car could well be used to drive straight into the wind, it just needs different gearing then (more propeller rotations per distance traveled).

This reminds me of when people were claiming rockets can't move in space because there is nothing to push against.

Watching the whole tower sway with the turbine revolution was scary.

There's an interesting paradox going on here: The car can be either wind- or ground powered depending on which inertial frame of reference we choose, but if we look at the mechanisms inside the car, then energy is always transferred from the wheels to the propeller.

Now the question is: How can that be? Shouldn't we see energy flowing in the other direction while we are standing on the ground and observing the car be wind powered?

Transferring energy to the prop only results in a drag moment aka brakes.

They can't because there isn't anything for the rocket engine to push against as there is no athmosphere.

/sarcsm

The thing to keep in mind is that the wind is not pushing the car body but rather the propeller.

Obviously the wind could not push the car if it is moving faster than the wind, but the propeller is turning slowly against the wind, powered by the wheels.
Its blades form a surface that moves forward more slowly than the car does, and slightly slower than the wind. So the wind is still pushing against the blades.

The force acting on the blades can be split in a forward vector and a counterrotating vector.
If the blades are angled at 45 degrees, they would be equal in force.

When the blades rotate more slowly than the car moves forward, the forward force transfers to a greater force (at a lower speed) through the gearing that powers the propeller. If the difference exceeds all sources of friction the vehicle will accelerate and move past the wind speed.
We have a theory to match the results :)

Now let's check what happens if the setup or gearing changes.
If the propeller does not move the car will sail forward with the wind, but never as fast.

If the propeller moves with the wind rather than against it then the gearing would help power it forward, but of course the wind would not be able to power the blades well before the vehicle nears wind speed. You'd have great pulling power at low speed though.

If the propeller moves as fast as the vehicle (e.g. the surface of the vanes does not move compared to a fixed point on the ground, as it moves just as fast backwards compared to the car as the car moves forward) then the forward and counterrotating forces are in balance; it won't move the vehicle no matter what.

If the propeller moves faster than the vehicle then the vehicle will run backwards against the wind.