schroder said:
It is where Silly Atom Man “DECIDES” to extract energy from the force of the propeller, to drive the propeller!
The energy is not "extracted from the propeller to drive the propeller", but is extracted from the WHEELS to drive the propeller (in the cart frame).
It is amazing that you stopped your correct calculation (namely, the kinetic energy of the thrown balls = 500 W to throw out 10 times a 1 kg mass per second with a velocity of 10 m/s, with which everybody here agrees, and the correct thrust that this gives, namely 100 N) when you had to calculate the drag force that a generator driven by the WHEELS will induce to produce 500 W when it is going 10 m/s. It is amazing that you were capable of such a feat while at the same time maintaining the blatant elementary errors (the famous 10 m/s left and 2 m/s right gives you 8 m/s relative - that's a real gem, but also the fact that the wheel slows down when the arm starts to get out of sync with the turntable, and other very elementary mistakes which you defended here). So some part of your brain seems to know some mechanics. Some part of your brain seems to know how to calculate the necessary power to throw 10 1kg balls out at 10 m/s per second. Some part of your brain is capable of calculating the thrust that this will give.
Having a generator produce 500 W when you go 10 m/s gives you a drag of 50 N. Having brakes which give you a drag of 50 N when you go 10 m/s will dissipate 500 W.
I'm pretty sure that the same part of your brain is capable of calculating the drag force that a generator, extracting 500 W, at 10 m/s, will cause. But suddenly, that part of your brain is shut off from the fingers that type posts here on PF, and another part of your brain, the one in denial, takes over to write just about any blatant nonsense in order to avoid the over-evident conclusion: *you are dead wrong on this*.
Because you're only two lines away from that evident conclusion. The first line is:
extracting 500 W (you know, the 500 W that will be FED INTO the propeller which the propeller will USE to get its thrust of 100 N) on a wheel running at 10 m/s induces a drag of:
500 W / 10m/s = 50 N
The second line of this embarrassing reasoning (that that shut-off part of your brain must be trying to yell in there) is that 100 N of thrust, and 50 N of drag, result in a net trust of 50 N.
But here, the emergency shutters have locked up and you seem to be incapable of admitting this.
Now, I understand where your difficulty comes from (apart from psychological factors such as an over-inflated ego). It comes from the "obvious" fact that we "drive the propeller from the wheels" but that if there is any "source of energy" it must be the "wind". This is an elementary although understandable error for a beginning student in mechanics (although for an established engineer, especially a "rocket scientist" it is rather embarrassing), and it is the point I've illustrated several times:
energy balances are not the same in different reference frames. It is a known, elementary error of students.
In the cart frame, where it is easy to do the FORCE calculation, the energies are not the same than in the ground frame. In the cart frame, the ground is moving, and can deliver power but the air receives power. In the ground frame, the ground is not moving, and the air is delivering power. The whole "intuitive reason" why one thinks that one cannot go "faster than the wind" is that one looks upon two different energy balances at the same time and mixes up the terms. It is as if one were doing a bookkeeping in US dollar and in pound sterling, mixing up different entries.
In the ground frame, the air is just loosing speed through an interaction with the cart, and that will give it a forward thrust, which is partly offset by a drag of the wheels. In the cart frame, the air is gaining speed, and will result in exactly the same forward thrust which will just as well be partly offset by the drag of the wheels, only in this frame it is easy to calculate this drag force by using conservation of energy internally to the cart.
In the ground frame, the air is loosing energy. That's the ultimate "energy source" (in the ground frame). Going into the cart frame is only done to study the inner workings of the cart (from which we can derive the drag force).
Perhaps a clarification of terms? All we're really talking about here is the work done by an airfoil, in this case a sail based airfoil. The sail will generate lift above any angle that does not 'back' the sail, typically from 20 degrees off the wind all the way up to the stall angle. The sail airfoil will generate lift from a vessel dead stop from a wind stream at any angle above the backing angle, do work and accelerate the craft over the surface. As the craft accelerates the apparent wind speed does indeed increase and the apparent wind direction moves toward the bow. 
