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That's incorrect. If you're reducing combustion temperatures (which must be happening if the engine is running cooler due to HHO), it's a tenet of physics that you're losing thermodynamic efficiency.
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In that video, the engine runs cooler due to very lean mixures or late timing. That is not due to the hydrogen, the use of hydrogen just allows that to be done. They seem to be saying that if you time the engine for later firing, the hot gas stays in contact with the engine walls for less time, thus less heat is transfered to the body of the engine, thus efficiency rises as less heat is wasted heating up parts of the engine.
Also, for this to really be optimized, an engine would get rid of the oxygen sensor and the throttle body to reduce pumping loss and allow really lean mixtures. In an unmodified engine I think the only gain would be from late timing.
The improvements that are happening here are because parasitic losses of the engine are being reduced. I don't think the theoretical engine cycle is being changed.
JamesLaugesen, Thanks for the link!