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Numerous independent studies have shown that hydrogen-enhanced diesel combustion has the potential to improve fuel economy and reduce emissions.   
 

Early Studies:

NASA Study of hydrogen-enhanced combustion (1977)
nasa_hydro_gas_study_1977.pdf
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California Institute of Technology, Jet Propulsion Lab - 1975
jet_propulsion_lab_1975.pdf
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The Cal Tech JPL study is particularly pertinent because it focused on the viability of on-board electrolysis.  The conclusion, presented in the final sentence:

“Overall, increases in engine efficiency are more dominant than the energy loss incurred in generating hydrogen, resulting in improved fuel economy for the system as a whole”

In other words, JPL demonstrated a net increase in fuel economy, even taking into account the energy required to drive the electrolysis process.   Over 35 years later, technology improvements have enabled far more efficient (and “clean”) hydrogen generation, which increases the overall efficiency gains possible using hydrogen-enhancement.  The PEM electrolysis process used by the Marz Electrolyzer is more efficient than any other hydrogen generators on the market today, and for more efficient that what JPL was able to produce, given the technology limitations of that era.

Contemporary Studies:

University of Idaho
univ_of_idaho_hydrogen_diesel_study.pdf
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University of South Australia, 2008
univ_of_south_australia_2008.pdf
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