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wedrifid comments on The Correct Contrarian Cluster - Less Wrong
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The movement of the wind backwards is coupled to the movement of the vehicle forward; but that's the effect of the energy, not the source of the energy.
If your intuitions don't think it will work then two options available are building the device or doing the actual math.
My intuition tells me that the source of the energy is the wind and some of that energy is removed from the wind and ends up on the cart.
Think push not twist. The energy taken from the wind is not in the form of increased rotation of the blade. Rather, it is being pushed along like a sail. It just happens to put some of the energy back into increased rotational energy of the blade by means of gears connected to the ground.
For the gears connected to the ground to take energy out of the ground, it has to slow the vehicle down. You are then trying to speed the vehicle up, through the propeller, using only energy derived from the contact with the ground, which is necessarily less than or equal to the energy loss that the vehicle sustained in order to convert its forward momentum into the rotational energy to turn the propeller.
No, I'm not trying to do that because that wouldn't work. Energy taken from the ground/vehicle difference is not being used to accelerate the vehicle.