How Rosch probably faked their 5 KWatt KPP AuKW

[lumen]

1: the air at the bottom needs to be at a higher pressure than at the top, so the air at the top cannot be used to partially pressurise the bottom float.
2: if the system is optimally configured, the air in the top float will be near atmospheric pressure; remember that water has to replace that air.

That is wrong.
You are viewing it as the float is open to the water. If you purge the water at the bottom and close the float then the float still has the pressure used to purge it and it's no longer needed. If you simply connect it to the next float, it will partially purge another float at no extra cost.
Then if you pumped the remainder to the second float you could fully purge it also and never need any new air to continue the process.

Would it be more efficient to simply pump the water from a sealed float while letting atmospheric air flow in? Water pumping is much more efficient.

[MarkE]

When I see a device that someone claims works I don't usually look for the reasons it cannot work because they a fully understood, I look first to what they could possibly do to make it work as claimed.

So in view of that I was simply examining a method (possibly the only method) this device could overcome all it's losses, and I agree there are many.

If a tank is under 20 feet of water and you fill it with air to purge the water, then the energy extracted by floating to the surface would be the same as the energy you put into purging the tank minus some losses.

However, if I use the air in the tank to run an air motor and generator, I have recovered some energy + that of the tank floating to the surface.
If I use the compressed air in the tank even more wisely by filling the next tank, then the losses are further reduced and the gain is even greater.
Time will tell if they have reached that goal.

No, if you use the air in the tank to run an air motor, then you consume energy doing so and the air pressure is less and will displace a lower head of water.  If your ending air pressure is not higher than the water head at depth, then the machine stops.  If the ending pressure is greater than the water head, then your overall efficiency is better than without the air motor.  Any excess pressure above the water head results in loss.  Which leads to the corollary:  Efficiency only approaches 100% as the machine velocity approaches zero.

[MarkE]

That is wrong.
You are viewing it as the float is open to the water. If you purge the water at the bottom and close the float then the float still has the pressure used to purge it and it's no longer needed. If you simply connect it to the next float, it will partially purge another float at no extra cost.
Then if you pumped the remainder to the second float you could fully purge it also and never need any new air to continue the process.

At the top you have to flood each float.  Excess air pressure will keep the water from flooding.  In the best case you could return the air at the top to the compressor input supply.  If you had perfect check valves that consume no energy, and exhibit no leaks, then you have a closed air loop submerged in water.  IOW, an overbalanced wheel that gets its overbalance condition from the compressor.  Take whatever practical compressor efficiency you can manage and you will find the thing is very inefficient.

[lumen]

At the top you have to flood each float.  Excess air pressure will keep the water from flooding.  In the best case you could return the air at the top to the compressor input supply.  If you had perfect check valves that consume no energy, and exhibit no leaks, then you have a closed air loop submerged in water.  IOW, an overbalanced wheel that gets its overbalance condition from the compressor.  Take whatever practical compressor efficiency you can manage and you will find the thing is very inefficient.

When I say pump the air from the closed float that means it will have 0 psi at the bottom and still 0 psi when it reaches the top.
If the float has a solid shell and does not compress then the float is just as buoyant with 10 psi or -10 psi air inside.
It's only the displacement of water with something lighter that makes it float.

If you look back I thought it may be better to pump out the water and let air flow in since pumping water is much more efficient.

[memoryman]

There is no -10 psi; the best vacuum is 0 psi.
"If you look back I thought it may be better to pump out the water and let air flow in since pumping water is much more efficient." how so? either way you have to displace the same volume of water.