MEMORANDUM

FROM: Aron Butler, Assessment and Standards Division

David Good, Compliance Division

Arvon Mitcham, Assessment and Standards Division

Office of Transportation and Air Quality

Office of Air and Radiation

United States Environmental Protection Agency

TO: Tier 3 Docket #EPA-HQ-OAR-2011-0135

DATE: February 28, 2013

SUBJECT: Analysis of the Effects of Changing Fuel Properties on the EPA Fuel

Economy Equation and R-Factor

Fuel economy is one important measure of a vehicle’s efficiency. Under federal regulations, it is 

EPA’s responsibility to set specific methods used to measure and calculate fuel economy to be 

used in determining automobile manufacturers’ compliance with the Corporate Average Fuel 

Economy (CAFE) program, as well as the window stickers on new vehicles that inform 

consumers of a variety of fuel economy related factors. 

The proposed change in test fuel, if finalized, could have implications for the CAFE emissions 

compliance program and the fuel economy labeling program. Therefore, it is important to 

characterize the potential change in fuel economy as a result of the changes in certification fuels 

proposed in this rule. As outlined in the preamble to the 2017 and Later Model Year Greenhouse 

Gas Emissions and Corporate Average Fuel Economy final rule, if the EPA test fuel used for 

certification and fuel economy vehicles changes to include ethanol, EPA is committed to address 

whether the fuel change has a potential to affect the stringency of the standards.1 As a result, we 

reviewed the parameters and inputs for the fuel economy equation to explore whether changing 

fuel properties have any affect the equation in its current form.

Historically, there was no simple, non-invasive method to accurately measure the amount of 

liquid fuel consumed over the course of a fuel economy and emissions test. Therefore, the 

standard method of calculating fuel economy has been to determine the miles per gallon based 

on the sum of the amount of carbon-containing compounds emitted from the tailpipe (primarily 

CO2 which can be measured with great accuracy) during a standard emissions test, and then 

combined with the measured properties of the test fuel (density (specific gravity) and carbon 

weight fraction which determine the amount of carbon-containing compounds in the fuel), miles 

per gallon metric can be determined. This calculation is known as the “volumetric fuel 

economy” calculation and has also been referred to as the “carbon balance” equation in the 

literature2as shown in Equation 1 below, where “T.fuel” subscript indicates properties of the test 

fuel and “exh” indicates properties of exhaust hydrocarbons. 

 

1

77 FR 62777-62778, October 15, 2012.

2 The volumetric (carbon balance) fuel economy equation is documented in various technical sources and EPA 

technical reports, including 59 FR 39638, August 3, 1994.
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0 749 4 0 429 0 273 2

3781 8

CWF NMHC . * CH . CO . CO

CWF SG .

FE

exh

T . fuel T . fuel

volumetric Eq.1

The Energy Policy and Conservation Act (Pub. Law 94-163 December 22, 1975) requires EPA 

to:

“...measure fuel economy for each model and calculate average fuel economy for a 

manufacturer under testing and calculation procedures prescribed by the Administrator. 

However, except under section 32908 [Fuel economy labeling (new vehicle window 

sticker) requirements] of this title, the Administrator shall use the same procedures for 

passenger automobiles the Administrator used for model year 1975 (weighted 55 percent 

urban cycle and 45 percent highway cycle), or procedures for passenger automobiles the 

Administrator used for model year 1975(weighted 55 percent urban cycle and 45 percent 

highway cycle), or procedures that give comparable results.”3 

In the 1970’s, EPA promulgated regulations to calculate fuel economy (mpg) based on the 

carbon balance (volumetric) fuel economy equation, combined with a specific set of fuel 

properties which were representative of 1975 gasoline. A carbon wieght fraction of 0.866 and 

specific gravity of 0.739 were determined to be representative of 1975 gasoline test fuel and 

incorporated into the carbon balance fuel economy equation, as shown in Equation 2 below (note 

that NMHC and CH4 are combined into the HC term here).

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2

1975 0 866 0 429 0 273

2421

. HC . CO . CO

FE ( city / highway ) Eq.2

4

As outlined above, EPCA also mandated that the fuel economy equation used for passenger cars 

should account for any future change in test fuel properties such that the test procedure would 

give comparable results compared to the 1975 test procedures. 

In January, 1982, the U.S. Court of Appeals for the Sixth Circuit remanded a case to EPA 

concerning the need for CAFE adjustments based on test procedure changes since 1975, so that

EPA could initiate rulemaking proceedings concerning any appropriate adjustments for the then 

current test procedures. From 1983 to 1986, EPA made various regulatory changes to account 

for test procedure changes since 1975 which were determined to have an effect on CAFE.5 This 

included revisions to the 1975 fuel economy equation. Beginning with model year 1988 

vehicles, the fuel economy equation was revised from an equation which assumed the test fuel 

had average 1975 fuel properties to an equation which was based on the measured fuel properties 

of the test fuel which was used to perform the actual test. The fuel economy equation corrected

the fuel economy results to account for the differences in the actual fuel properties of the test fuel 

compared to the properties of the 1975 baseline test fuel. 

 

3

49 USC 32904(c).

4

Federal regulations at 40 CFR 600.113-78(d)

5

48 FR 56526, December 21, 1983; 49 FR 48024, December 7, 1984; 50 FR 27172, July 1, 1985; 50 FR 27188, 

July 1, 1985; and 51 FR 37844, October 24, 1986.
Beginning with model year 1988 vehicles, EPA modified the calculation method so that the fuel 

economy calculation accounted for difference between the test fuel and the 1975 baseline fuel by

accounting for differences in carbon weight fraction (CWF) and net heating value (NHV or 

volumetric energy content) between the actual test fuel and the 1975 baseline fuel.

6

 

Accompanying the NHV adjustment was a sensitivity factor, called “R”, which represents the 

response of a typical vehicle’s fuel economy to small changes in the fuel’s energy content. 

Accordingly, the R-factor can be determined using the general formula shown in Equation 3, 

where “B.fuel” indicates baseline fuel:

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1

1

B. fuel

T . fuel

volumetric ,B. fuel

volumetric ,T . fuel

NHV

NHV

FE

FE

R Eq.3

Studies of fuel economy data done in 1985 by General Motors and others suggested an R-factor 

of 0.6 would be appropriate. 7 Based on this information, EPA regulations currently account for 

changes in test fuel properties compared to the 1975 baseline fuel by calculating fuel economy as 

shown in Equation 4.8

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exh T .fuel T .fuel

T .fuel T .fuel

EPA CWF HC . CO . CO . NHV SG

CWF SG FE

0 429 0 273 5471 0 6

5174 10

2

4

Eq.4

The constants in Equation 4 (i.e. 5,174 x 104and 5,471) contain values for the baseline fuel’s 

NHV (Btu/gal), CWF, and specific gravity. The R-factor of 0.6 is also visible in the 

denominator.

A theoretical analyses done by EPA in 1987 described how only a small fraction of the fuel’s 

chemical energy is used to propel the vehicle, and that the many losses to heat and friction are 

nonlinear and do not depend on fuel properties. It concluded that while a maximum R-factor of 

0.95 was possible, a value of 0.82 was more plausible.9 

Other studies examining the R-factor have been published since then. For instance, in a 1993 

study conducted jointly by members of the automobile and oil industries (known as the Auto/Oil 

program), the authors suggested that “[f]or the current fleet, R had a value of 0.93 ± 0.05 and for 

the older fleet, the value of R was 0.92 ± 0.21.” 10

 

6

Ibid

7 Letter to Docket #A-83-44 from T.M. Fisher, Director of Automotive Emission Control at General Motors 

Corporation (Letter #FE 3419) to the U.S. EPA in response to the Notice of Proposed Rule Making on “Fuel 

Economy Test Procedures; Proposed Procedures for Adjustment to Test Results to Compensate for Changes in 1975 

Test Procedure,” 48 FR 56526, December 21, 1983.

8

See the Code of Federal Regulations at 40 CFR 600.113-12(h)

9

”Draft Regulatory Impact Analysis, Control of Gasoline Volatility and Evaporative Hydrocarbon Emissions from 

New Motor Vehicles,” Section V, July 1987. 

10 Hochhauser, A., et al., "Fuel Composition Effects on Automotive Fuel Economy - Auto/Oil Air Quality 

Improvement Research Program," SAE Technical Paper 930138, 1993.
More recently, EPA staff assessed the R-factor based on the EPAct/V2/E-89 dataset. The 

EPAct/V2/E-89 test program was sponsored by EPA, DOE/NREL, and CRC to assess the fuel 

effects of various fuel parameters on exhaust emissions of Tier-2-compliant passenger cars and 

light trucks. This resulting dataset contains 956 emission tests conducted on 15 high-sales 

vehicles of 2008 model year conducted by Southwest Research Institute between March 2009 

and June 2010. More details on the vehicles, fuels, and test procedures can be found in the 

program report.11 

While the focus of the EPAct/V2/E-89 test program was not to evaluate R-factor, the resulting 

dataset included volumetric fuel economy results for all emission tests (using Equation 1) as well 

as NHV measurements for all test fuels. Since R-factor is defined as sensitivity of fuel economy 

to NHV, it could be empirically determined from the test program results. Ethanol content has a 

significant effect on NHV, an issue of special relevance given the proposed increase in ethanol 

content in certification fuel used during emissions and fuel economy testing. Figure 1 shows 

NHV for all test fuels used in the EPAct/V2/E-89 test program.

Figure 1. Net heating value versus oxygen content for EPAct/V2/E-89 fuels.

For the remainder of this analysis we divide the dataset based on whether the test fuel was E0,

E10, or E20. R-factor was calculated using Equation 5, where the averages were taken for all 

tests on that fuel type.

12

 

11 See technical report “EPAct/V2/E-89: Assessing the Effect of Five Gasoline Properties on Exhaust Emissions 

from Light-Duty Vehicles Certified to Tier 2 Standards, Final Report on Program Design and Data Collection”, 

Report Number EPA-420-R-13-004, March 2013; also available in this docket (Tier 3 Docket #EPA-HQ-OAR2011-0135).

12 This equation follows the form of Equation (2) in footnote reference 10. A similar equation was used when 

comparing the E20 tot eh E0 test results for the vehicles. The BTU/gal for the E0 fuels in this test program is 

similar to the BTU/gal used for the 1975 baseline fuel. 
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1

1

0

10

0

10

E

E

E

E

NHV

NHV

FE

FE

R Eq.5

Since the fuel economy values vary significantly by test vehicle, it was useful to calculate an Rvalue for each test vehicle individually. Figure 2 shows the results for composite-cycle weighted 

values (combined results of cold and hot portions of the emission test) by test vehicle for both 

E10 and E20 groups compared to E0. Also shown on Figure 2 are simple averages computed 

across the test fleet, with both values falling between 0.8 and 0.9. Though not shown, the 

average R-factors determined from the cold start portions of the test were very similar to the hot 

running results. 

Figure 2. Empirical R-factor results for EPAct/V2/E-89 dataset by vehicle.

An important consideration in doing empirical analyses for R-factor is the sensitivity of the result 

to measurement variability. Since the differences in fuel economy and fuel NHV being 

examined are typically small relative to their values, Equation 5 can produce widely varying 

quotients from test to test as evidenced by the variability in results between vehicles for the same 

fuel comparison and fuel comparisons for the same vehicle. This makes it difficult to reply on 

data of limited sample size or studies where other confounding changes may be occurring. The 

EPAct/V2/E-89 dataset is large, with at least 16 tests behind the averages for each ethanol level 

in Equation 5 when producing each vehicle result on Figure 2.

These results pointing to an R-factor between 0.8 and 0.9 are generally consistent with findings 

of the Auto/Oil program and EPA’s 1987 theoretical analysis.

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

CCOB CIMP CSIL DCAL F150 FEXP FFOC HCIV HODY JLIB NALT SOUT TCAM TCOR TSIE

EPAct Phase 3 Fuel Economy R-values by vehicle

wtd E10 vs E0

wtd E20 vs E0

E10 avg = 0.86

E20 avg = 0.82