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It would appear that the efficiency gains come NOT from the actual BTU's of hydrogen that you are adding, but from the effect that the hydrogen has on how the main fuel charge burns.

From http://www.hydrofuelsolutions.com/Go..._releases.html

...a Hydrogen Generating System (HGS) for trucks or cars has been on the market for some time. Mounted on a vehicle, it feeds small amounts of hydrogen and oxygen into the engine's air intake. Its makers claim savings in fuel, reduced noxious and greenhouse gases and increased power. The auto industry is not devoid of hoaxes and as engineers are sceptics by training, it is no surprise that a few of them say the idea won't work. Such opinions, from engineers can't be dismissed without explaining why I think these Hydrogen Generating Systems do work and are not just another hoax. The 2nd law of thermodynamics is a likely source of those doubts. Meaning ...the law -would lead you to believe that it will certainly take more power to produce this hydrogen than can be regained by burning it in the engine. i.e. the resulting energy balance should be negative. If the aim is to create hydrogen by electrolysis to be burned as a fuel, the concept is ridiculous. On the other hand, if hydrogen, shortens the burn time of the main fuel-air mix, putting more pressure on the piston through a longer effective power stroke, and in doing so takes more work out, then this system does make sense. Does it work? Independent studies, at different universities, using various fuels, have shown that flame speeds increase when small amounts of hydrogen are added to air-fuel mixes.

The results of tests at Corrections Canada's, Bowden Alberta Institution and other independent tests reinforce the belief that combustion is significantly accelerated. They found with the HGS on, unburned hydrocarbons, CO and NO, in the exhaust were either eliminated or drastically reduced and at the same R.P.M. the engine produced more torque from less fuel.

Recently I took part in the highway test of a vehicle driven twice over the same 200-kilometre course, on cruise control, at the same speed, once with the system off and once with it on. A temperature sensor from an accurate pyrometer kit had been inserted directly into the exhaust manifold, to eliminate thermal distortion from the catalytic converter. On average, the exhaust manifold temperature was 65°F lower during the second trip when the Hydrogen Generating System was switched on. The fuel consumption with the unit off was 5.13253 km/li. and 7.2481 km/li. with it on, giving a mileage increase of 41.2% and a fuel savings attributable to the unit of 29.18%

>From the forgoing, the near absence of carbon monoxide and unburnt hydrocarbons confirms a very complete and much faster burn. Cooler exhaust temperatures show that more work is taken out during the power stroke. More torque from less fuel at the same R.P.M. verifies that higher pressure from a faster burn, acting through a longer effective power stroke, produces more torque and thus more work from less fuel. The considerable reduction in nitrous oxides (NOx} was a surprise. I had assumed that the extreme temperatures from such a rapid intense burn would produce more NO.,. Time plus high temperature are both essential for nitrous oxides to form. As the extreme burn temperatures are of such short duration and temperature through the remainder of the power stroke and the entire exhaust stroke, will, on average, be much cooler. With this in mind, it is not so surprising that less NOx is produced when the HGS is operating.

An engineering classmate suggested a grass fire as a useful analogy to understand combustion within an engine. The flame front of a grass fire is distinct and its speed depends in part on the closeness of the individual blades. If grass is first sprayed with a small amount of gasoline to initiate combustion, then all blades will ignite almost in unison. In much the same way, small amounts of nascent oxygen and hydrogen present in the fuel-air mix will cause a chain reaction that ignites all the primary fuel molecules simultaneously. Faster more complete burns are the keys to improving efficiency in internal combustion engines. Power gained from increased thermal efficiency, less the power to the electrolysis unit, is the measure of real gain or loss. It follows from the foregoing paragraph that even a modest gain in thermal efficiency will be greater than the power used by an electrolysis unit. The net result should therefore be positive. Thus onboard electrolysis systems supplying hydrogen and oxygen to internal combustion engines, fuelled by diesel, gasoline or propane, should substantially increase efficiencies.

Mixing hydrogen with hydrocarbon fuels provides combustion stimulation by increasing the rate of molecular-cracking processes in which large hydrocarbons are broken into smaller fragments. Expediting production of smaller molecular fragments is beneficial in increasing the surface-to-volume ratio and consequent exposure to oxygen for completion of the combustion process. Relatively small amount of hydrogen can dramatically increase horsepower and reduce emissions of atmospheric pollutants.

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