“I still think using electrolysis, to split H2O into hydrogen and oxygen, and then feeding those gases into the air intake, has some potential.”
Tap water is mostly hydrogen that has already been burned... (it’s energy removed) Your going to remove it again?
You can split hydrogen and oxygen and burn the hydrogen again.
YES, that is absolutely possible.
It is entirely possible to “recycle” atoms and molecules and burn them again. It is called “life” -—
The only question is: can this be done efficiently?