Excellent calculation! That really does cut through all the talk and get the point.
However! :P I spot a serious fault. HHO is only bouyant in air, not in vacuum. So it can't float up past the atmosphere.
Assume optimistically that the top of the atmosphere is at the ISS (200 miles, there are some air atoms at the ISS). Your machine can recover 51kW compared to 252kW used generating the HHO. That's 20% of the energy recovered.
Hmm. That's a curious coincidence. Do you suppose the commercial HHO plants have about 20% loss because they're operating under a column of air that could recover 20% using bouyancy? That suggests this machine is pushing us right close to 100% HHO generation efficiency.
To show that it goes over 100% I think you need to find an existing HHO generator with more than 80% efficiency at 1atm. And also find out how high HHO will really float. I imagine it can't reach the ISS without somehow losing its usefulness.
the important thing about this is that it shows that the current usage of thermodynamics is a load of CR@P.
So you've said several times, but still haven't shown it.
I understand that you don't trust conservation of energy. So you'll notice that I only referred to it tentatively for things I wasn't sure of. None of my reasoning depends on it, because doing so would be circular. If I depended on it I would simply say "E_out > E_in, violates 1st law, goodbye".
Well of course we all do assume the 1st law holds sometimes. But those cases are a bit too trivial and obvious to mention.
By the way, mixing imperial with metric, and miles with feet is the opposite of keeping things simple!!! Hehe that's why I don't check your calculations thoroughly. Too complicated :P