'chargers themselves don't actually produce energy.
air+gas+ignition(spark) = energy released from the air+gas
pumping more gas into the engine is easy, just install a bigger pump...
normally aspirated engines suck in the air on their own. 'chargers are nothing more than an air pump so we can cram more air in the engine so that we can pump more gas in the engine and get more energy in the end.
bigger engine make more power because they have more air and gas going into them... 'charged vehicles make more power for the same reason.
No joke, you could strap a leaf blower to your intake and your car will make more power, and this actually works, because it acts like an air pump the same way a turbo or supercharger does.
chargers take energy to run, but so does any pump... but you're still getting your energy from gas+air though... the energy lost running your "air pump" is much much smaller than the energy you get from the air your sucking in and the additional gas that lets you burn.
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The concept of HHO generation is that the energy comes from the water, the problem is that when burned the same way we burn gas and air, it produces less energy, not only that the process of electrolysis is like having a mini-refinery in your car to convert the energy in the water into a more usable form.
The reason, from a scientific stand point, that this concept is bankrupt is that water in it's natural form... doesn't contain any energy. by performing electrolysis you're putting energy into it, and then you're taking that energy back out once it hits your engine... The problem is that when you put energy into it only about 70% makes it into hydrogen (the rest is lost to heat and other natual losses that come from any energy conversion), and when you burn it in your engine only about 40% of THAT gets turned into energy at the crank (again the rest lost to heat, friction, etc.).
It's analogous to installing a 2nd empty gas tank in your car that only gets gas in it by stealing gas from your normal tank... except it spills most of the gas it's stealing in the process. The only difference is that it's stealing in the form of electrical energy, giving it back to you in the form of air energy and spilling it in the form of heat energy.
The idea that your "alternator produces unused energy" is foolish as well. Most of the accessories are designed to only produce the energy they need, when they need it. Do a test for me the next time you start your car while your parked. Pull the wheel quickly in one direction and watch the RPMs... you'll see them blip up, this is because the power steering pump is only drawing energy from your motor when it needs it. Turn on your AC while you're parked and idling and you'll see the RPMs rise too... Your alternator is no different, if you were to flip on all your lights, crank your stereo and run some power hungry device from the cigarette lighter while you rolled down all your windows at the same time you'd see the RPMs increase slightly as well while it adapts to the load and strains the engine harder.
Even if the theory of the over productive alternator were true, don't you think a better method for recycling that energy would be to hook up an electric helper motor, since electric motors are the most efficient way to convert electrical energy into mechanical energy... or even just simply installing a smaller alternator that's not as wasteful... or if either of those were viable solutions to an existing problem that auto makers would be using them...
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All in all I'm very interested in seeing the results of this test... I'd really like to see pictures of the install and if possible engine data as well particularly air/fuel and O2 sensor readings.