Two mathematic methods are presented to prove that 2-parameter hyperbolic model and exponential model are the superior limit and lower limit of the corresponding new 3-parameter model respectively.

It is meanwhile good practice to limit performance metrics to as few as possible, and the carbon footprint does not belong on the list when far superior techniques are available.

If the diesel engine has a superior economic performance, a dependable work, and if the noise and the vibration can be controlled in a lower limit, which usually depends upon its valve train system.