Technical  Report
                  Carbon Balance  and  Volumetric
                Measurements  of Fuel  Consumption

                           Terry Newell

                            April 1980

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

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.

                                          v  Figjire I
                                            x    \
                          Carbon Balance vs.  Volumetric Fuel  Consumption
            N=  47  OUT OF 47  2. CARBON VS. 3. VOLUME
  157.00    +
  150.00   +
           +                                                                         * 2** *
                                                                                    «   *
                                                                                  *  *
  143.00   +                                                                     ** *
           +                                                                  *
  136.00   +
  129.00   -f
   108.00   +

           +              *  *
                         2 *

   101.00   +         *2        HFET
           +   **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


                                          CFUEL  CONSUMPTION

                                               cm /km

     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)


     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
     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

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

     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



§   §

                                 Fijure II
            110 __
             80 .
                         Volumetric cm /km
            165  .ITT:

                                                      Mean of HFET


                                                      Vol =99.6  cm /km

                                                     CBal =99.4  cm3/km

•  Mean of FTP pairs

 ' Vol = 147.5

 CBal = 145.2
                           Volumetric cm /km
                     F   =  F
                      c     v
                         = (0.9893)
                                  (EON 3)
  	  Fc  =4.315+  (0.9552) Fv   (EON  2)

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

     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.

     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

     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


       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