> Direct downwind faster than wind is impossible with a windmill(turbine).

Incorrect.

> Your words, they make no sense.

Only to someone lacking the understanding of basic physics.

> A propeller is powered. It cannot be used to extract power.

It can, and it is.

> you cannot have wheels powered by a propeller.

Your say-so, no matter how vigorous, does not make it correct.

It's great to see comments form people who really understand what's going on, like beelsebob.

> It's unclear whether this is merely a language quibble, or you don't yet understand how it works.

Well, no. I understand "how it works" just fine, wheras you don't.

> The propeller is exerting a rearward force on the air.

No, it doesn't, as simple as that.

> The propeller is exerting a rearward force on the air.

Again, nope.

> Newtons Laws: for every action there is an equal and opposite reaction. If a force exists from the prop towards the air, there also
> exists and equal and opposite force from the air towards the prop.

Yes, so far so good.

> The air *is* exerting a forwards force on the cart, even when the cart is going above windspeed.

No, it does not, even if you put a few more asterisks around "is". The correct statement is, "wind is exerting rotating force on the propeller, even when the cart is going above windspeed. "

> the wind" is indeed pushing forwards on the propeller.

No, the net force on the propeller from the wind is directed backwards (plus rotating momentum, which, being transmitted to the wheels, is pushing the craft forward)

> So the net force on the craft, from the wind, is a forwards acceleration.

Nope, you are still wrong. The original approach to the analysis - sideways motion of the blades with respect to the wind - is the correct one.

> You'll have to break out the differential equations if you want to calculate what's going on.

No, you don't (though I have no trouble doing so, when needed). This is high-school level problem

> The movement of the ground in the opposite direction is what powers the propeller

Incorrect - what powers the propeller is the relative speed between the ground and the wind.

> The problem that people are having is that they don't see how the wind can still be pushing the cart when the cart is moving faster than the wind.

That's not a problem, that's a solution. The wind can not be pushing the cart when it is moving faster than the wind. The problem are the people who insist on incorrect solution.

Again, no. The net force from wind on the craft is pushing it backwards. It's the wheels that propel the craft forward. And the wheels are powered by the propeller, not the other way around

That's completely incorrect. The wind can't push the craft forward - the craft goes faster than the wind, so the net force on the craft from the wind is braking it.

"Hot", "smart", "female" - pick any two

I'm an AI researcher, and I think that once the computing power becomes available, we'll have the kinds of AI advances that you're talking about very quickly.

You have been thinking that for the last 50 years. Meanwhile, the AI "scientists" have not reproduced an "intelligence" of a common household cockroach.

But you get no upvotes unless it's "Raspberry PI" and "3D-printed"

That's kill the goose that laid the golden gate logic.

Bad idea, clearly. Talented engineer geese must be encouraged, not killed.