EPA-AA-SDSB-80-05
Technical Report
Carbon Balance and Volumetric
Measurements of Fuel Consumption
by
Terry Newell
April 1980
NOTICE
Technical Reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis of
issues using data which are currently available. The purpose in
the release of such reports is to facilitate the exchange of
technical information and to inform the public of technical deve-
lopments which may form the basis for a final EPA decision, posi-
tion or regulatory action.
Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Source Air Pollution Control
Office of Air, Noise and Radiation
U.S. Environmental Protection Agency
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I. Introduct ion/Background
A recently completed EPA test program investigated the effects
on emissions and fuel consumption of different types and brands of
tires. In that program, fuel consumption was measured using both
the carbon balance and volumetric methods. The number of tests
conducted provided adequate data for a comparison of the results
obtained by these different methods.
A previously conducted investigation into the differences
between carbon balance and volumetric measurements of fuel con-
sumption concluded that a consistent difference exists between
them. Fuel consumption measured volumetrical1y was found to
average three percent higher than when measured by the carbon
balance method .J_/ This report presents another analysis of this
question. Further background information on carbon balance vs
volumetric fuel consumption measurements can be found in the
earlier report, which is attached as Appendix A.
II. Discussion
This test program consisted of repeated cold-start FTP and
hot-start HFET cycles. Fuel consumption was measured by both
methods during each of the cycles.
A. Test Program
A total of 47 paired measurements of fuel consumption were
acquired in the course of this test program. The test vehicle was
a 1979 Chevrolet Nova with a 250 CID engine. The standard EPA
emissions and fuel economy tests were conducted with four different
sets of tires mounted on the vehicle, three sets of radials and one
of bias-plys. Use of both test cycles resulted in fuel consumption
being measured over a range of approximately 90 to 160 cm-Vkm.
A more detailed description of the test program is given in
the technical report on t ire effects on emissions and fuel econ-
omy .2]
B. Data Reduction
The basic data reduction was use of the standard EPA computer
analyses of the FTP and HFET data. This data reduction is the same
as that used in the previous investigation, and is discussed in
greater detail in the corresponding section of that report, Ap-
pendix A.
C. Data Analysis
A scatter plot of the paired fuel consumption data appears as
Figure 1, with carbon balance measurements on the vertical axis and
volumetric on the horizontal. The cluster of points at upper right
represents the FTP test results, while those at lower left repre-
sent the HFET test results.
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v Figjire I
x \
Carbon Balance vs. Volumetric Fuel Consumption
SCATTER PLOT
N= 47 OUT OF 47 2. CARBON VS. 3. VOLUME
CARBON
157.00 +
150.00 +
*
*2
+ * 2** *
« *
* *
143.00 + ** *
**
*
+ *
FTP
Tests
136.00 +
129.00 -f
§
CO
O
U
.00
115.00
108.00 +
+ * *
2 *
101.00 + *2 HFET
Tests
2**
+ **23
**
2 '
94.000 -+ .
+ + + + + + + + + + + + + 1 + + + + +
94.000 108.00 122.00 136.00 150.00 VOLUME
101.00 115.00 129.00 143.00 157.00
VOLUMETRIC
CFUEL CONSUMPTION
cm /km
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Analysis of the data showed no evidence of nonlinearity in the
relation between volumetric and carbon balance measurements; thus
only linear regressions of these data were fitted.
Application of the linear model:
Fc = a + bFv (1)
where:
Fc = fuel consumption (carbon balance);
Fv = fuel consumption (volumetric);
a,b = constants,
requires use of the method of least-squares to determine the
appropriate values of the constants a and b. The equation that
results from using this model to describe the relationship between
the two methods of measuring fuel consumption is:
Fc = 4.315 + 0.9552 Fv (2)
The nonzero value of the constant a in the righthand side of
equation (2) implies that a positive constant offset exists between
these methods. The correlation coefficient r of equation (2),
which is a measure of how well the linear model describes the
relationship between the fuel consumption measurements, is greater
than 0.99, indicating that this equation fits the data very
closely.
n
However, a constant positive offset of 4.32 cmj between the
results of the two methods is difficult to satisfactorily explain.
Evaporative losses from the carburetor of the test vehicle, after
the fuel has passed through the flow meter but before it is burned
and converted to exhaust gases, would logically lead to a constant
offset, but such an offset would be negative, as would any constant
offsets due to exhaust system leakage. Also, equation (2) predicts
that the carbon balance measurements will be greater than volumet-
ric for fuel consumption rates below approximately 96 cm^/km, while
this relationship would be reversed when fuel consumption exceeded
96 cm-Vkm. Very few of the data points obtained in this program
were at fuel consumption levels below 97 cnH/km, thus such a
reversal it not evident from these data.
It is interesting to note that in twelve of the 47 paired
measurements of fuel consumption taken in this program, the carbon
balance measurement of fuel consumption was actually slightly
greater than the corresponding volumetric measurement. These cases
all occurred in the HFET cycles, at fuel consumption rates between
96 and 105 cm^/km, and were interspersed among other pairs in which
volumetric measurements were greater. Thus, these instances do not
provide support for the reversal in the relationship between the
results of the two methods predicted by equation (2). The differ-
ence between the two consumption rates, when the carbon balance
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measurement was greater, averaged 0.5 percent, and never exceeded
0.8 percent. ;
Due to the theoretical problems with the results and inter-
pretation of the linear model regression, a simple proportional
model was investigated. The proportional model is a linear model
similar to equation (1), except without the constant term a. The
closest proportional relation of the results of the two methods of
measurement is given by:
Fc = (0.9893) Fv (3)
Equation (3) states that carbon balance measurements of fuel
consumption will be about 1.1 percent higher than will corres-
ponding volumetric measurements. The coefficient of correlation
of this equation is very nearly as high as that of equation (2),
r > 0.99.
A relative comparison of equations (2) and (3) to each other,
and to the line representing equality in the measurement methods,
appears as Figure II. The mean of the data points from each of the
driving cycles is also shown.
The previous analysis of this question was conducted using
fuel consumption measurements taken during steady-state testing.
As noted earlier, the data analyzed in this discussion were col-
lected during repeated FTP and HFET driving cycles. The HFET cycle
bears more resemblance, in its speed-vs-time characteristics, to
steady-state operation than does the FTP cycle. If the observed
differences in fuel consumption measurements are in some manner
dependent on the type of driving done in the test, then the dif-
ferences in the HFET paired measurements should correspond to those
observed during steady-state testing more closely than would those
based on FTP measurements.
In this program, the carbon balance method yielded fuel
consumption rates averaging 0.2 percent lower than the volumetric
method during HFET cycles. In the FTP cycles, carbon balance
averaged 1.6 percent lower than volumetric. The steady-state tests
resulted in carbon balance figures averaging 3.1 percent below
volumetric figures. The fact that the FTP results from this
analysis are closer to the earlier steady-state results than are
those from the HFETs suggests that the driving cycle over which
fuel consumption is measured is not an important parameter in
determining the extent of the difference between the two methods of
measurement.
The ranges over which fuel consumption was measured were
(approximately) 90-110 cm3/km for the HFET tests, 100-135 cm3/km
for the earlier steady-state tests, and 140-155 cnr/km for the FTP
tests. Taken together, these points provide additional support
for stating that the difference between results obtained by the two
methods is proportional. In both analyses, this difference is seen
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QJ
O
cd
"td
§ §
0)
O
c
(0
•-i
CO
CO
Fijure II
110 __
100
90
80 .
100
Volumetric cm /km
110
165 .ITT:
155
145
135
HFET
Mean of HFET
pairs
Vol =99.6 cm /km
CBal =99.4 cm3/km
FTP
• Mean of FTP pairs
' Vol = 147.5
CBal = 145.2
Volumetric cm /km
KEY
F = F
c v
= (0.9893)
(EON 3)
Fc =4.315+ (0.9552) Fv (EON 2)
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to be greater as the rate of fuel consumption increases.
There are reasons to accept the results of volumetric mea-
surements, which are direct measurements of fuel flow rate,
as being less susceptible to error than the indirect carbon
balance measurements. Flow meters used in this testing, and in
the earlier steady-state testing, were calibrated to within their
rated accuracy of 0.5 percent. The carbon balance method, which
measures fuel consumption indirectly, relies on calibration of the
instruments used to measure each of the components of the vehicle
exhaust that contain carbon: CO, C(>2, and hydrocarbons. The
potential exists for error tolerances to accumulate in the same
direction.
The difference in the results of the two methods is small and
relatively consistent, and it was less in this program than was
observed in the earlier steady-state testing. Measurements taken
during both programs were characterized by high degree of preci-
sion; and since the difference has changed over time, it appears
likely that the cause lies with instrument calibrations. It would
appear that slight alterations in the calibration of instruments
used in the carbon balance method could eliminate the difference in
the results of these methods.
III. Conclusions
1. It is concluded that direct volumetric measurements of
fuel consumption show greater rates of consumption than do carbon
balance measurements taken in the same tests. As a result, fuel
economy estimates are higher when based on carbon balance measur-
ements than they would be if based on volumetric data. In this
investigation the observed difference ranged from 0.2 percent at
the lower fuel consumption rates, to about 1.6 percent at the
higher rates.
2. The difference in the results of these two methods
appears to be proportional. Available data show the difference in
carbon balance and volumetric measurements increasing with in-
creases in the rate of consumption.
3. The most likely source of the difference between the
results of these methods is the laboratory calibration of instru-
mentation. This is indicated by the proportional nature of the
offset, and the fact that different investigations have shown
evidence that the proportionality differs over time.
IV. Recommendat ions
1. In future test programs involving a fairly large number
of repeated tests, fuel consumption should be measured by all three
available methods: carbon balance, volumetric, and gravimetric.
This would provide a basis to determine which measurement method is
the more accurate.
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2. Fuel consumption data should be collected under condi-
tions of lower fuel flow rates, under 90 cm^/km. Analysis of
paired measurements of fuel consumption at these lower levels
should allow a final determination of whether the difference is
strictly proportional, or proportional with a small constant
offset.
3. If the volumetric method is determined to be more ac-
curate than the carbon balance method, then the effect of lab
calibrations of the instruments used should be investigated more
thoroughly. It should be possible to bring the carbon balance
measurements of fuel consumption into agreement with the volumetric
measurements, resulting in more accuracy in the EPA fuel economy
estimates.
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Reference
I/ Turton, Dale "Fuel Consumption Measurements—Carbon Balance vs
~ Flow Meter," EPA Technical Report, SDSB 79-28, July 1979.
2J Jones, Randy and Terry Newell, "The Effects of Tire Rolling
Resistance on Automotive Emissions and Fuel Economy," EPA
Technical Report, SDSB 80, Draft: May 1980.
» VS. GOVERNMENT PRINTING OFFICE: 1980- 651-112/0252
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