I've been trying to think about mechanisms by which this hydrogen generation system could actually improve gas mileage. These are just ideas, and some of them conflict; I'm just throwing them out there.
My basic premise is that the energy available in the chemicals coming out of the electrolysis process is less than the electrical energy that goes in.
My strong hunch is that any apparent fuel savings is actually caused by the placebo effect, where the driver unintentionally drives differently, in a more fuel efficient fashion, and that the fuel savings is not directly caused by the device.
But I decided to brainstorm some actual physical processes that might improve gas mileage.
1) The hydrogen/oxygen mixture is 33% oxygen by volume; air is only 21% oxygen by volume. You get more oxygen in the cylinder for a given amount of pumping losses, perhaps actually improving the efficiency of consuming the gasoline.
2) The H2/O2 input is essentially _water injection_, which increases the amount of mass flowing through the engine for a given amount of fuel burned. The increased mass flow means more 'thrust' on the cylinder head for a given amount of energy input, perhaps improving the efficiency of consuming gasoline. Of course, direct water injection might be even better.
3) The H2/O2 input somehow _reduced_ the performance of the engine, making an 8 cylinder engine act more like a 4 cylinder engine, thus giving less maximum power output, but in general operating at a greater fraction of full power. As is well known with 'economy cars', if you put a smaller engine in, you will get better gas mileage, but have worse acceleration and worse performance.
4) The H2/O2 input somehow makes the engine act differently (by its sound, peak output, torque profile, etc), in a way that essentially forces the driver to use the car in a more efficient fashion.
I think that the suggestion of validating these results on a dyno is a good one. I suspect that the objective efficiency change at any given fixed output level will be small and probably negative. But a car driven in the real world is not a car on a dyno; if this system makes you drive differently, or the system changes the performance of the car, or any savings results solely from the 'placebo effect', then so what? You are getting better mileage. _Understanding why_ is only important if you want to sell this to someone else.
-Jon