## Equations relating engine friction and fuel consumption

When a portion of the horsepower lost to friction is recaptured for useful work it reduces the fuel consumed for a given power output. The equation that shows the relationship between reduced friction and the improvement in the fuel consumed for a given horsepower output is: R2= R1(hp2-hpfg)/hp2; where R1 and R2 are initial and reduced friction fuel rates; hp1 and hp2 are the respective horsepower’s produced, and hpfg is the horsepower gain from reducing friction. Since hp2 = hp1+ hpfg , it can be substituted so that R2/R1 = 1- (hpfg/hp1+ hpfg). Also, since some desired gain z can be introduced, where R2/R1 = 1 – (z/100), the two equations can be set equal to each other and a series of curves plotted for any particular set of desired gains. Here are the resulting curves relating BMEP and rpm for fuel consumption improvement of the Brickley engine over a current conventional in-line four cylinder. Note that the curves have a positive slope as compared to changes that address pumping losses which have a negative slope (less improvement with an increase in rpm).