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But this isn't the case. What Atom man needs to know is the power output versus power input for a propeller, and the minimal amount of thrust required to overcome the aerodynamic drag from a small apparent headwind on the cart and the rolling resistance from larger apparent head speed from the ground (rolling resistance) to obtain a specific maximum speed. Chances are that the prop chosen will generate more thrust than is minimally needed, but this will be opposed by the wheels that drive the prop, and the ratio of opposing force / thrust is < 1 if the prop and related gearing are efficient enough. So the ratio of opposing force / thrust remains about the same, but since the drag related factors remain about the same, the ratio (thrust - opposing force) / (drag factors) increases with prop thrust.uart said:Now Atom Man knows that if his strategy is to be successful he must be sure that the drag from his generator is less than this amount, so he decides to use only half of this extra thrust in powering the generator.
The speed of the molecules thrown back doesn't need to be 10 m/s. 4 m / sec would probably be sufficient. The cart is only attempting to go DDWFTTW, not twice as fast as the wind. So restated:schroder said:Let’s use those heavy air molecules you mentioned that weigh 1 kg each and let’s start out at wind velocity of 10 m/s and we need to throw 10 of those molecules back every second, so n = 10. That will be (1kg) (10m/s) (10 molecules/s) = 100 Newtons of Force.
(1kg) (4m/s) (10 molecules/s) = 40 Newtons.
KE = 1/2 mv^2 so at 4 m/s the KE is 8 Joules.
power output = Energy/time or Energy x n = 8 J x 10 = 80 watts.
Assume the cart is moving at 12 m/s down wind.
Assume prop and gearing efficiency to total about 69.4%.
So power input needs to be (1/.694) = 1.44 times power output = 144 watts.
At 12 m / s, the required driving force = (144 / 12) = 12 Newtons.
So we have 40 Newtons of thrust opposed by 12 Newtons of force related to driving the prop, leaving 28 Newtons of force to compenstate for the opposing aerodynamic drag of the apparent 2 m/s headwind, and the rolling resistance from the 12 m / sec forward speed of the cart.
