Here's the idea: A large spherical LH2 tank is placed inside a spherical LOX tank.
The reason I thought of this is so the inner tank doesn't need to be insulated. It doesn't need to be a double-walled, or "dewar-flask" tank. The outer tank full of LOX keeps it insulated. Therefore, the LH2 tank would reduce its weight by 50%.
Or at least, that's the idea. Would this actually be good insulation for the inner tank? If so, would it actually cut the LH2 tank weight in half? And even then, are there insurmountable complications with this?
In other words, is the tank within a tank a sound engineering concept for rocket stages?
Some possible complications I can think:
Both tanks might have to be filled at the same time.
Plumbing from the LH2 tank to the engine would have to go through the LOX tank too, at first.
The LOX might be cooled even more than normal, changing its density and maybe other properties important in the pumps that feed it to the engine.
AFAIK these are not bad/expensive enough to be impossible. But I want to hear what you think.
EDIT: Yes I'm talking about large cryo tanks for large rocket stages that carry payloads to orbit. It could be any stage, although I'm not aware of any sole first stage that uses LH2/LOX (with no other parallel boosters), so probably it would be the 2nd or 3rd stage. These can still be pretty large for, say, Saturn 1B or Saturn V.
EDIT: It looks like LOX would not be a great insulator, because the temperature difference between LOX and LH2 is very great. I thought that, with both of them exchanging heat through conduction, the LOX would also go down or near to LH2's temperature.