First of all, show me a frame of reference where the air is at rest, outside in the real world. Winds don’t move over the ground in response to the motion of the earth’s surface as happens on a treadmill. If you think they do, how would you explain the tornados that just tore through much of the South? Was the surface of the earth spinning wildly around in many different places, causing those wind funnels? You see, you can take these batty reference frame transformations too far, and arrive at all sorts of incorrect conclusions. You may as well stand on your head and call the floor the ceiling, and now your head is touching it. Little kiddies do that sort of thing and we think it’s cute. When grown men do that sort of thing, we call them crackpots.
As I said in response to another poster, you can say a sail cart or a wind turbine is powered by the ground, if it makes you feel somehow superior to say such a thing. But the reality is the planet earth is a large rock with a mass of about 6 x 10^24 kg, more than one million times the mass of the entire atmosphere. Due to gravitational attraction, the atmosphere moves with the planet, with the exception of local disturbances mostly due to temperature differentials and these are what we call winds. The winds are for the most part unpredictable, changing velocity and direction pretty much with a mind of their own, while this big rock we call the earth stays rock solid under our feet, regardless of how it moves through space. Objects sit still on the surface of this big rock due to gravitational attraction and friction with the surface, and it requires energy to move them. It is ridiculous to say that the energy to move them against the friction and gravitational attraction comes from the earth itself, the very thing that is holding things in place! It is ridiculous to say that a road, fixed on the earth’s surface, is going to power something to move along that road, because it most certainly does not do that!
Once again, if you want to act that that little boy, standing on his head and saying his head is now on the ceiling, go right ahead and do so. But you will probably find more than a few people laughing at you.
The kinematic energy for the sail cart is coming from that thing that is filling those sails, the wind and not from the ground. Changing the reference frame does not change reality, only your perception of reality. If your claim for DDWFTTW rests on a change in perception, as it appears it does, then it rests on nothing but nonsense and is probably not even worth discussing.
If you want to continue, then show me some mathematics to support this claim.
Why? Your own math has already shown to anyone who looks at it that the cart must work.