I can't see how adding hydrogen could aid in the economy of the engine.

If you are forming H2 and 02 on board, then you have to put energy in the form of e- to break the O-H bond, and then some of the potential energy from O- and H+ floating around is lost when H2 and O2 is formed. Its like perpetual motion, you can't get more energy out then you put in.

If you were taking just the O2 and putting into the engine then you should be able to achieve a more efficient burn but still not close to enough to make up for the electrolysis. With both the H2 and the O2 all you are getting is the energy you put in to make them from water in the form of heat. This heat may aid in the combustion of the diesel, but I can't imagine its much.

So the extra energy you get out will be lost in the production of e- at about 50% efficiency (thats a high estimate) from the alternator, then another 5-10% as heat/resistance in the wires to the electrolysis machine, then I have no idea how much is lost in that process.

If there was a way to make H2 and O2 efficiently using the engine as a power source, then we all would be driving around with H2/O2 internal combustion engine and a tank of water, instead of hydrocarbons.

Just my thoughts on the subject.