swerdna said:
Can the thrust if the propeller ever exceed the rolling resistance caused to create that thrust?
Yes, I already explained this in earlier posts. Effective gearing between the driving wheels and the propeller muliptly the force and divide the speed. The reducion in speed works because the propeller is interacting with the slower (relative to the cart) moving air, while the wheels interact with the faster (relative to the cart) ground.
Vw = speed of wind
Vc = speed of cart
Vp = speed of induced wash from prop
Fp = force from prop
Fc = force from cart wheels
Fd = overall losses (drag) related to forward speed of cart
Speed of air through the prop = induced wash + relative air speed = Vp + (Vc-Vw)
The power input = Fc x Vc
The power output = Fp x (Vp + Vc - Vw)
The power loss = Fd x Vc
The net force on the cart = Fp - (Fc + Fd)
Vc can be > Vw, Fp can be > Fc, with power output still well below power input as long as Vw is greater than zero (a tailwind). The gearing factor (diameter ratios between wheels and prop, gearing at the differential, prop pitch), multiplies the force and divides the speed. The reduction in speed is relative to the ground though, but the prop is interacting with the air, so although its speed is a fraction of it's ground speed, if the gearing ratio is not excessive, the prop speed is still positive relative to the air it interacts with, Vp + (Vc-Vw) > 0.
A conservative setup might only try to achieve DDWFTTW by a ratio of 1.2. In a 10mph wind, the cart would move at 12mph, resulting in a 2 mph working air speed for the propeller. If the effective gearing for wheel speed to prop speed was 2:1, then the prop speed would be 6mph, and the induced wash speed, Vp - (Vc-Vw) = 4mph. If the gearing was 1.5:1, the prop speed would be 8mph, induced wash speed: = 6mph. The actual force from the prop depends on the change in air speed due to the prop times the mass flow, and this force propels the cart forwards. The force at the driving wheels (Fc) is the prop force minus all the losses in the system (rolling friction, aerodyanic drag of the cart, prop inefficiencies).
If someone gets some actual numbers for the mini-cart, and prop, here's a link for some prop math:
http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html