Hi Momos. I think it's getting confusing with all the different systems. I know you won't want to read all the history, but me and Paul have discussed various configurations, including doing it underwater, and come to one he described clearly in message #34053.
I noted that it required more height than the atmosphere had. But this is where my thoughts are at this stage:
a) Convert a liter of water to HHO, let it float up (throw away that energy), burn it back to water (throw away that energy), then drop the water back to the ground (recover that energy).
b) We know how much energy you can get from a liter of water falling through a height of 978 miles (4212 W-hr)
c) We know how much energy it takes to convert a liter of water into HHO at atmospheric pressure (4212 W-hr)
d) If you had an atmosphere that was >978 miles high, but had a pressure at ground level the same as our atmosphere, then it looks like you come out better than even. This atmosphere would have to be made of a gas less dense than air, and a tiny bit denser than HHO.
e) You don't even need such an extreme because you can recover more from the "throw away that energy" stages in a).
f) There's another option of pumping out a vacuum to generate the HHO in.
Maybe my requirement in d) is impossible. I have to work that out, but I'd rather wait for Paul to present a new complete system.
A big stumbling block is not knowing how much extra energy is needed to produce HHO at higher pressures.