The question is where does the extra energy to improve the gas mileage come from?
It can't come from the hydrogen... to split water and get hydrogen requires energy, lets say 1 unit of energy.
First, If you burn that hydrogen, you will get less than 1 unit of energy back. This is easily testable and has been done so; it's a fundamental aspect of our universe.
Second, the act of splitting is inefficient. Let's be optimistic and say that 75% of the electricity being used generates hydrogen. That means that we've already lost 25% of the energy we're drawing from the engine. So not only is this not gaining us anything, right off the bat we're at a net loss.
Finally, the energy to split the water has to come from somewhere. It comes from the alternator, which produces electricity from the engine's rotation. The alternator is very inefficient as well. And drawing electricity from the alternator increases the load it puts on the engine, so more gas is burned.
The end result is that to generate 1 unit of energy in the engine from burning hydrogen, you have to burn much more than 1 unit of energy's worth of gas.
People have tried these things.. the problem is there are too many variables in an anecdotal test. Was it colder the next day? Was there a wind? Most people who put fuel efficiency devices on their car actually drive differently, which can have a HUGE impact on how much gas you use.
It's very easy.. put an engine on a dynamo, have this on it, and do the measurements. Proponents who sell these things have never done that, and never will though, because they know that in a controlled environment they won't get a positive result. So they rely on anecdotal evidence, they can filter out the people who have no gain, and focus on the people who report a gain (for any number of reasons, none of which have anything to do with their device).
This is the problem when one doesn't have any critical thinking skills; they get taken in by anything.
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Uncertainty is an uncomfortable position.
But certainty is an absurd one.
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