Hydrogen does indeed have a faster burn rate than gasoline. Blending even a little bit of it with gasoline will indeed increase the burn rate of the mixture. The idea that was put forward in at least one of the comments is that this would faster burn would trigger knocking in the engine that would be detected by the engine management system resulting in retarding of the spark and more of the explosive force pushing the piston down during the power stroke. This is nominally true, but it only applies to newer engines that have knock sensors. There are however a number of problems with this. Read on after the jump for the rest of this discussion.
[Source: Fuel Cell Insider, Popular Mechanics]
As I said, only newer engines equipped with knock sensors will be able to automatically compensate for the knocking that can generated by hydrogen injection. Those hoping to benefit from hydrogen injection on older engines will be out of luck unless they go in and start manually adjusting spark management calibrations. For those with older carburated engines even more manual adjustments will be required. There is another problem with this whole theory however, Hydrogen increases the effective octane rating of the fuel mixture, increasing knock resistance. Therefore knocking may not even be detected and thus no automatic adjustment.
Another potential benefit of injecting hydrogen is the ability to lean out the air fuel mixture. Again here there are limitations on how much can be achieved here. The engine management systems are calibrated in order to minimize fuel consumption while still meeting all emissions standards. Again, an engine with a carburetor would not be able to adjust itself and would have to be manually adjusted. Other engines may not have enough compensation range in their controls to make a measurable difference. Regardless, recalibration of the engine management system will be required to allow the system to run lean enough to get any benefit.
If the spark can be sufficiently retarded with hydrogen injection, one way that efficiency can be improved is by increasing the use of late intake valve closing, essentially creating an Atkinson cycle as used on hybrid vehicles.
All of these potential benefits are unlikely to be realized on any retrofitted engine without significant recalibration and potential mechanical changes. If H2 injection is designed in, the increased knock resistance and faster burn rate could be utilized to achieve some benefits through higher compression ratios, optimized spark and valve timing and fuel management. All of this requires system level changes that are not a part of any of the kits being sold.
The combination of running lean and the higher temperatures resulting from the hydrogen burn rate on retrofitted engines can increase production of NOx which means that the engine might not pass a smog test. Tampering with the emissions control systems actually poses a problem in states like California. Such a system may have to be removed or disabled before a smog test. It's also not clear that even with an engine designed for hydrogen injection, that the benefits would be significant to overcome the thermodynamic losses inherent in generating hydrogen on the fly. Also note that hydrogen has no magical catalytic effect on burning the gasoline. Modern engines, especially direct injected units have relatively little unburned fuel that will be influenced by the hydrogen.
While we haven't actually tried out a hydrogen injection system ourselves, Popular Mechanics has. Mike Allen at PM installed a hydrogen generating and injection system in a test vehicle and used a data logging system to record the fuel flow. The hydrogen system had a switch to enable and disable the system. By monitoring the fuel injection pulses, the most direct measure of how much fuel was being delivered to the engine, he found absolutely no change in fuel consumption. The one change Allen did see was a drop of a couple of tenths of a volt in the vehicle system voltage when the electrolyzer was turned on indicating the load it was putting on the electrical system.
We've also learned about about a column at Fuel Cell Insider pointing out that some of the electrolyzer systems being sold are labeled as fuel cells. This is a misnomer, since a fuel cell consumes hydrogen and oxygen to produce electricity. An electrolyzer is essentially the opposite of a fuel cell, consuming electricity to produce the hydrogen and oxygen.