I will make this problem as a reply to all of you and even do the calculation for you just let me know if I'm wrong.
Start conditions:
Wind speed 0m/s
Vehicle speed 0m/s
Vehicle mass 1kg
Available energy 10Ws
Wheel efficiency 90%
Propeller efficiency 70%
So vehicle will end up with 9Ws of Kinetic energy if energy is used to power the wheel and 7Ws if propeller is used.
Thus you probably agree that using wheel for propulsion is best option thus 9Ws is kinetic energy and vehicle is at 4.24m/s
Now at this point with vehicle at 4.24m/s will there be any logic in taking energy from the wheel and putting in to propeller ?
I hope you agree it will make no sense.
Now let say same conditions with vehicle at 4.24m/s but now there is a wind speed of 2m/s in same direction as the vehicle.
Will this change anything ? Will it make sense to take energy from the wheel and power the propeller ?
If your answer is yes please provide the calculation showing that vehicle can increase the current 9Ws kinetic energy using that 2m/s wind.
OK, that is easy enough. Assuming your wheel generator has the same 90% efficiency and the propeller 70%, load the generator so that there is a 1N force (backwards) on the car. I can't be more detailed because I don't know the radius of the wheel, but that won't matter. ( 1N * 4.24m/s * 0.9 efficiency ) = 3.816W. Now if you take the 3.816W and use the propeller to generate a force, you will get a larger force because...power is force * speed and you don't have to generate that force at 4.24m/s, but rather
2.422.24m/s, the airspeed that the propeller sees. So the force generated will be (3.816W * 0.7 efficiency /
2.422.24m/s) =
1.1041.1925N. The net force (propeller force minus wheel force) will then be 0.1925N and the vehicle will accelerate at 0.1925m/s
2. Thus the vehicle will continue to accelerate even though it is already travelling at over twice the wind speed. In this example, the propeller is providing 2.6712W of power, which is obviously less than is taken out at the wheels, but the wind provides (1.1925 * 2m/s) =
2.028 2.385W of additional power for a total of
4.6992 5.0562W, which is
more than is being taken out at the wheels, so a net gain of (
4.69925.0562- 4.24) = 0.8162W. And then you can check the math to make sure that the net power I just gave you results in the acceleration stated--which is why I had to go back and fix my numerical transpositions.
But I think I've made an additional error, so wait a bit.Edit: Should be all good now. If not, someone point out the errors.