Fuel consumption is determined by the following relationship:
where I is for indicated, F is for friction, P is for pumping, and MEP is the mean effective pressure in each category. The fuel consumption model is derived from a methodology to estimate an engine map using a semiempirical model developed by researchers at Ford and the University of Nottingham (Shayler et al., 1999). In this formulation, fuel consumption is proportional to IMEP divided by indicated thermal efficiency (sometimes called the Willans line), friction is determined empirically from engine layout and is a function of RPM only, and PMEP is simply intake manifold pressure (atmospheric pressure). Intake manifold pressure is solved for any given BMEP, since IMEP is also proportional to intake pressure. This model explicitly derives thermal efficiency, friction loss, and pumping loss for the baseline vehicle. Fuel consumption at idle and closed throttle braking are modeled as functions of engine displacement only. The baseline engine is always modeled with fixed valve lift and timing, and the pumping loss is adjusted for the presence of variable valve timing if applicable. The model can be construed as a two-point approximation of a complete engine map and is a very reasonable representation of fuel consumption at light and moderate loads where there is no fuel enrichment.
The technologies are characterized by their effect on each of the losses explicitly accounted for in the model, and the representation is similar in concept to the representation in the EPA model. In the EEA-ICF analysis, the committee collected information on the effect of each engine technology on peak engine efficiency, pumping loss, and friction loss as a cycle average from technical papers that describe measured changes in these attributes from prototype or production systems. When these losses are not explicitly measured, they are computed from other published values such as the change in compression ratio, the change in torque, or the measured change in fuel consumption.
Both EEA-ICF and EPA have compared the lumped parameter results with new full-scale simulation modeling results on several vehicle classes with different combinations of planned technological improvements. The simulations were done by the consulting firm Ricardo, Inc., and documented in a separate report (Ricardo, 2008). The Ricardo work modeled five baseline vehicles (standard car, large car, small MPV, large MPV, and large truck) and 26 technology combinations, covering gasoline and diesel power trains used in the EPA model, but there was no simulation of hybrids.
In a majority of the comparisons done by EPA, the lumped parameter model estimates were close to the Ricardo estimates, and the EPA concluded the results of their model were plausible, although a few technology packages required additional investigation. The EPA has indicated that it will continue to use the lumped parameter approach as an analytical tool, perhaps adjusting it to improve its fidelity as more simulation results become available.
EEA-ICF also performed analysis for the NRC Committee on Assessment of Technologies for Improving LightDuty Vehicle Fuel Economy (Duleep, 2008a, 2008b). Based on the committee’s experience, when a number of engine, transmission, and other technology improvements are simultaneously added to a baseline vehicle, the net fuel economy benefit can be approximated by taking 90 percent of the additive sum of the individual technology benefits, as developed by EEA-ICF. The committee used this technique to develop a quick approximation of the level of agreement likely between the Ricardo simulations and the EEA-ICF lumped parameter model. It was able to perform a quick analysis of only 23 of 26 packages developed by Ricardo, since there were no data on HCCI engines, which were used in three of the Ricardo technology packages.
Ricardo included one technology for which the committee had no specific data. It called this “fast warm-up” technology because it involved the control of coolant flow to the engine immediately after cold start. Based on the data presented by Ricardo, the benefit of the technology was estimated at 1 percent, including the benefit of the electric water pump. All other technology benefits were based on the data from ICF-EEA previous reports to DOE on fuel economy technology. These benefit estimates were adjusted for the presence or absence of technologies on the baseline vehicle, since all benefits in the DOE reports have been typically defined relative to an engine with fixed valve timing and a four-speed automatic transmission. The results are illustrated in Figure K.1, and the plot shows the difference between the Ricardo results and the quick approximation method.
In 16 of the 23 cases, the Ricardo estimate is within +5 percent of the quick estimate. In two cases, the Ricardo estimates were more than 10 percent lower than the quick estimates, as shown in Figure K.1. In five cases, the Ricardo estimates were 10 percent (or more) higher than the quick estimate. The difference implies that the benefits are larger than the simple sum of individual technology benefits and that technology synergies are positive. The committee also examined the technology packages in the two “low” and five “high” outliers. Both low outliers had technology packages with a continuously variable transmission (CVT) as one of the technologies. The five high outliers had no major technology improvement in common.
More detailed analysis was also done with the EEA-ICF lumped parameter model. Constraints on resources and time allowed the committee to analyze only 9 of the 23 cases with the lumped parameter model, but the 9 cases included both high and low outliers from the previous analysis. Three technology packages were analyzed for a standard car, which used a Toyota Camry baseline; three for a compact