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PhilGoetz comments on The Correct Contrarian Cluster - Less Wrong
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I don't believe it.
Contrary to what the article says, sailboats can't travel downwind faster than the wind (except briefly, when the wind changes). If this were possible, I would have experienced it.
When the vehicle is moving as fast as the wind, in order to go faster, the energy output from the propeller must be more than the energy input through the wheels. The energy output of the propeller comes entirely from the energy input through the wheels, so this is impossible.
Right?
I'm feeling uncertain, because dozens of people reviewed the article and all agreed that the thing works.
Here's where I am now:
Sailboats can move with a downwind component faster than the wind.
The first (windsock) video shows no evidence that the cart moves downwind faster than the wind.
The string video is more convincing, but I'm not convinced that this particular cart works as advertised. The rational offered for how it works is that when it moves at a velocity v, this causes the propeller to turn at a rate that thrusts air backwards with a velocity greater than v. Hmm... okay, maybe. The propeller blades moving perpendicular to the wind are a lot like the sails of a boat moving perpendicular to the wind.
This ignores mass. Thrust is (mass flow rate) * v_air, so it can get enough thrust by moving enough air at a velocity less than v_car. As for energy, power = 1/2 * F * v for air or car, so again, you can get enough thrust if v_air < v_car.
There's no perpetual motion, because as the originally linked solution says, eventually the apparent headwind becomes too strong. (The above assumes apparent wind is zero.)
That's what I just said. But what's the energy flow?
I concede that it works, and in basically the same way as the sailboat going downwind that I also said couldn't work.
Oops, sorry, I wrote an incorrect explanation, having relied on confabulation of fading memories too much. Here is a reworked one:
In the simplest case, air pushes the propeller forwards, but it doesn't significantly rotate it. The propeller is a sail. If it were a normal cart moving faster than wind with propeller not attached to anything, it would be the same direction of the rotation (but our propeller rotates faster). At the same time, the propeller is rigidly connected to the wheels, which allows it to rotate faster than the headwind would make it. As a result, it is pushed by the wind from behind rather than resisted, which accelerates the cart, which lends power to the propeller to keep on rotating faster than it otherwise would.
It is a bad intuition to see propeller as throwing the air backwards at speed higher than the difference of cart's speed and the speed of the wind, as the cart is essentially fueled by the resulting hind-wind, not the other way around. Also, the propeller only needs to go a little bit faster than it would because of the headwind.
That's a pretty good explanation. Another way to look at it is to think what would happen if the propeller was not connected to the wheels. In that situation, the cart would travel as fast as the wind, but the propeller would spin at high speed. If you connect the propeller to the wheels that energy is used to further increase velocity.
In fact, it would work if you place a radio controlled clutch between the propeller and the wheels. First wait for the cart to accelerate to wind speed, and the propeller to rotate faster than the wheels (if it's 1:1 ratio without gears), then engage the clutch. The end result would be that the wheels would rotate at a higher speed and thus the cart would travel faster than the wind.