Ubergeekian
Well-Known Member
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I can't see the cart would accelerate to even reach the constant wind speed as the relevent velocity of the wind over the blades reduces as the cart accelerates, then the force on the blades driving it reduces, until at some point where equilibrium is reached and the cart is travelling at a velocity lower than wind speed. Any extra energy derived from the wheels would then need to be converted to thrust at the propellor which would counteract the thrust already at the propeller! That would only be achievable if the blades could be turned to provide thrust in the opposite direction to which the cart is moving, so that the cart is being pulled along by the propellor
You're on the right lines, but there is no need ever to have the propeller driving the wheels. It's always the other way round.
Imagine the cart arranged so that as it moves forward the fan blows backwards. Put it at a standstill in the wind. Windage will start moving it forward. As it accelerates, the back draught from the fan increases, effectively increasing the windage, so the net force increases, and so on.
Why doesn't it increase for every? Two reasons.
First of all, there is the windage of the the rest of the structure to take account of. Without the benefit of a fan blowing backwards the force on the rest decreases as the cart speed approaches wind speed and at wind speed it reverses.
Secondly there are drag losses in rotating the propeller and these increase with the square of the speed.
For any setup of this sort, therefore, there is an equilibrium point where the the work done by the wind pushing against the fan exactly balances the work needed to turn the fan and overcome other losses. The big question is whether this occurs above or below windspeed, and that depends entirely on the setup in question.
Once final point. Loads of people think that if the car/boat exceeds the windspeed, the propeller must be doing work on the wind. That's not true! Since the cart/boat is moving downwind, the fan is blowing the air back upwind: reducing its velocity and extracting energy from it. The mechanism for extracting the power is force in the direction of the wind: some of this power is then used to overcome drag losses in the propeller.
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