Report No. SR92-10-06
Development of Vehicle
Emissions Computer Simulation
Model
prepared for:
U.S. Environmental Protection Agency
October 16, 1992
prepared by:
Sierra Research, Inc.
1801 J Street
Sacramento, California 95814
(916) 444-6666
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DEVELOPMENT OF VEHICLE EMISSIONS
COMPUTER SIMULATION MODEL
EPA Contract No. 68-C1-0079
Work Assignment No. 06
prepared for:
U.S. Environmental Protection Agency
October 16, 1992
principal author:
Larry Caretto
Sierra Research, Inc.
1521 I Street
Sacramento, CA 95814
(916) 444-6666
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DEVELOPMENT OF VEHICLE EMISSIONS
COMPUTER SIMULATION MODEL
Table of Contents
page
1. Summary 1
2. Evalutaion and Development of an Alternative Emission
Mapping Procedure 3
Introduction 3
Review of An Dissertation 3
Correlations for Filling Holes in Engine Emission Maps 11
Computer Graphics Techniques for Generating Engine Maps 23
Conclusions from this Task 26
3. Protocols for Interpolation and Extrapolation in Engine
Mapping Data 27
Introduction 27
Preliminary Protocol for Filling Emission Maps 27
Sample Application of Preliminary Protocol 31
Final Procedure for Determining Results at Zero and
Negative Torques 34
Analysis of Improved Methods for Interpolating Sharp
Emissions Changes 37
Tentative Proposal for Interpolation of Enrichment Point 40
Conclusions on Mapping Protocol 45
4. Correlation Between Inlet Manifold Pressure and Brake—Mean
Effective Pressure 46
Introduction 46
Examination of Engine Mapping Data 46
Analysis of the Theoretical Relationship Between BMEP and
Intake Manifold Pressure 51
Conclusions from this Task 60
5. List of Symbols 61
6. References 63
Appendix A - Engine Emission Maps
Appendix B - Regression Analysis Tables and Charts
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DEVELOPMENT OF VEHICLE EMISSIONS
COMPUTER SIMULATION MODEL
1. SUMMARY
EPA is currently developing a new motor vehicle emissions simulation
model called VEMISS (for Vehicle EMISSions). This study was intended to
provide critical evaluation of concepts and methods to be used in
supporting EPA's development of VEMISS. The model requires input engine
maps giving fuel consumption and emission at several engine operating
points. The independent variables for these operating points are engine
speed and engine load. This study examined methods for taking data
obtained at a smaller number of speed and load points and constructing
an engine map for a wider range of speed and load points.
The first task was an examination of the approach in the dissertation by
Feng An which showed that fuel consumption at low speeds and loads could
be correlated for a wide variety of engines by the simple equation
pfud - a' Vd N + b Pragine [1.1]
In this equaion are P^, is the fuel energy rate, Vd is the engine
displacement, N is the engine speed, and P,^^ is the brake power output
of the engine; a' and b are empirical constants.
This equation has produced good results for low speed and power outputs,
but is not applicable for off-cycle operations at high engine speeds.
In addition, the data used to fit the constants a' and b did not
consider the normal engine idle point. The equation had an average
error of -42% in predicting the idle fuel flow rates for the EPA engine
data.
The relation between emissions rates and engine operating parameters was
studied. No simple quantitative relation was found that could be used
as a "magic bullet" to fill in missing data point in the engine maps.
Two significant problems were noted for missing data points. The first
was a need to determine the fuel flow rates and emissions at zero and
negative loads to obtain a complete engine map. The second problem was
for the interpolation of missing data. The observed engine maps showed
sharp transitions, particularly in hydrocarbon (HC) and carbon monoxide
(CO) emissions. An important step in the development of good engine
maps is the accurate determination of these transition points for
conditions where the exact location cound not be found from the
experimental data.
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Several procedures were evaluated for providing answers to these missing
data points. A final procedure was developed to provide fuel and
emissions rates at zero and negative loads which could be used in a
straightforward manner. This procedure examined two analytical
approaches and used the best combination of the two that was consistent
with the experimental data.
A protocol was developed to estimate the location of the transition
points in the emissions map. This was based on the observation that
these transitions were typically associated with enrichment of the
fuel/air mixture. Some analysis of the behavior of these transition
points was done, but no automated system could be developed for filling
in these data points as was done for the fuel and emissions rates at
zero and negative loads.
A second task was the investigation of a possible correlation between
manifold vacuum and engine load expressed as brake-mean effective
pressure. This task consisted of two parts: (1) an examination of the
mapping data for these parameters and (2) a theoretical analysis of
their relationship. The experimental data showed a linear behavior with
extremely high correlation coefficients. This experimental relationship
was supported by the theoretical analysis which showed that the BMEP
should be related to the manifold intake pressure, pm, at a given engine
speed, by a linear equation,
BMEP - a(N) + /?(N) PlD [1.2]
From the theoretical analysis an estimate could be made of typical
values for a and f)\ these estimates agreed with the values found in the
empirical correlations of BMEP and p^.
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2. EVALUATION AND DEVELOPMENT OF
AN ALTERNATIVE EMISSION MAPPING PROCEDURE
Introduction
This task was intended to provide EPA with a way to fill holes in the
engine mapping data that EPA obtained for use in their VEMISS program.
The initial subtask was a critical review of the dissertation by Feng An
on vehicle fuel economy. The results of this work were evaluated for
potential application to filling fuel flow rates in the EPA engine
mapping data and for extending this work to filling in emisions data.
Based on this work and a literature review Sierra was to develop a
technique for interpolating and/or extrapolating data in the EPA engine
maps. The goal was the development of a procedure for determining fuel
consumption and emissions as a function of engine speed and load
(expressed as brake mean effective pressure, BMEP). EPA provided Sierra
with preliminary copies of their engine mapping data for use in this
task.
Review of An Dissertation
The work reviewed for this subtask was the doctoral dissertation of Feng
An1 and a related paper by An and his dissertation chair, Marc Ross.2
In addition to reviewing these documents we contacted Dr. An and Prof.
Ross to clarify some points of their work.
Description of An's Results - The dissertation appears to provide a good
engineering analysis of vehicle fuel economy for use in transportation
studies. It results in a simple analytical expression for the fuel
economy of various vehicles in various driving cycles. This analysis
consists of two parts. The first part defines a relationship for engine
fuel consumption as a function of engine speed, and load; the second
part determines the engine power required for various driving cycles in
terms of a few basic driving cycle parameters.
In the first step, An has determined regression coefficients that relate
engine fuel energy rate, P,^,, which is simply the the mass flow rate of
fuel times its heat of combustion, engine speed, N, engine
displacement, Vd, and engine power, P^^ by the following equation:
Pfce. - a' Vd N + b P^ [2.1]
The engine displacement, Vd, is the only parameter that characterizes a
particular engine. The values of the constants a' and b that An
recommends for "1990 vehicle models" are:3
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a' = .271 kJ/rev-liter* b = 2.5 (dimensionless)
An used values of a' = 0.286 kJ/rev-liter and b = 2.5 for the data
examined in his dissertation. The actual regression fits for fuel
economy data were for an equation of the form
- a N + b PCTglM [2.2]
After the regression coefficients a and b were determined the simple
dependence of a on engine displacement, a ¦=¦ a' Vd, was found.
Ross and An note a wider range for a' values in newer engines and state
that it is "premature to draw detailled conclusions about the values of
a for modern engines."4
Equation [2.1] or [2.2] is intended to apply in the low speed and load
regions in which the engine spends almost all of its time during typical
driving cycles.5 The specific regions that were used in a regression
analysis to determine the coefficients a and b are given below.6
1500-2500 RPM for four cylinder engines
1300—2100 RPM for six cylinder engines
1200-2000 RPM for eight cylinder engines
This speed range starts above the normal idle range for most engines;
all the engines considered by An in his dissertation have idle speeds
between 600 and 800 RPM.7
In addition to a limited speed range, the data used at each engine speed
were limited to the points for which the engine power was less than some
fraction of the wide-open-throttle power at that speed. (I.e. only
points for which < f PengmeiwoT) were considered. Three different
methods were used to select the value of f; these were shown to provide
consistent results. For the final regression analysis the fraction, f,
was chosen to produce the best fit. The restriction to the low speed-
load points was justified by an examination of typical emissions test
and fuel economy driving cycles which have a majority of their operation
in the low speed—load region used for the regression analysis.
The second step is based on the conventional equation for the vehicle
power required to overcome rolling friction and aerodynamic friction and
the power required for acceleration that is ultimately absorbed in
braking losses.8 The major thrust of the dissertation is the
combination of the equation for fuel energy rate and the equation for
the vehicle power requirements, along with some models for the resulting
terms, to arrive at a single equation which gives a general equation for
the energy consumption of a vehicle over a driving cycle. This final
The units of kJ/rev-liter are equivalent MPa/rev. Thus the
fuel equation could be written in terms of the brake mean
effective pressure (BMEP) as follows (for four-stroke engines)
Pfue. = [ a' + (b/2) (BMEP) ] N Vd
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equation uses only a few simple parameters for the vehicle and the
driving cycle.9 These are:
vr The average running speed ~ cycle distance/(total time - idle
time)
vp The mean square peak speed. Most cycles consist of subcycles.
The peak speed in each cycle is noted and averaged in an root mean
square manner to obtain this quantity.
tc The proportion of the time that the brakes are applied.
t^,. The proportion of time that the engine is powering the vehicle (as
opposed to braking and idling).
n The average number of stops per unit distance.
In addition to these driving cycle parameters, An's analysis requires
the following vehicle parameters to compute the fuel consumption for a
cycle:
N/v
The
engine speed/vehicle velocity ratio at the highest gear.
N^e
The
idle speed of the engine.
M
The
vehicle mass.
vd
The
engine displacement used in the
equation for P,^,.
cr
The
coefficient of rolling friction,
cd
The
aerodynamic drag coefficient.
A
The
frontal area of the vehicle for
aerodynamic drag.
The
fuel
economy from the model equation
was compared with actual data
on the fuel economy of nine cars For the composite Urban/Highway EPA
cycle; the agreement was within 5%.10
The fuel economy model was further refined to consider variables more
appropriate to transportation analysis. In this refinement the cycle
speed parameters given above are replaced by the average speed, vavg, the
"free-flow" speed (defined as vff = (vp)2/v«vg). and the average time per
stop, T„.
The use of these results in conjunction with the EPA engine mapping data
is discussed below.
Implications of Ross/An Work for Fuel Consumption Calculations in Engine
Simulation Programs - The most significant part of the An disseration
for the application to the EPA mapping data is the basic relation
between fuel rate, engine speed, and engine power given by equation
[2.1] or [2.2]. There are two aspects to this equation. The first is
the qualitative notation that there is a linear relation between these
variables over a limited range of engine operating conditions. The
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second is the use of specific empirical constants a' and b which could
be applied to estimate the fuel energy rate for an engine at a given
speed and brake power output knowing only its displacement.
The qualitative results provide important support to the bilinear
interpolation process typically used in engine simulation programs such
as VEHSIM. The equation of the form = a N + b is consistent
with bilinear interpolation. The discussion on interpolation below
shows that this is true even if torque or BMEP is used in place of brake
power to represent the load on the engine. The quantitative results can
be used to provide a check on interpolated data, but they should not be
used blindly because of the limited range over which the empirical
constants were derived.
This limited range for quantitative applicability is perhaps the most
important aspect of this work for application to engine mapping.
Although excellent agreement has been demonstrated for some cycle data
the authors point out that the empirical constants used previous may not
be applicable to modern engines.
Some of the reasons for the limitations of this equation can be seen by
examining the physics of engine friction. Setting the engine brake
power to zero in equation [2.1] gives the fuel energy rate as
*>fiiei(pengine°,0) ~ a N. This fuel rate is that required to overcome engine
friction at the given engine speed. One reason for the limitation of
the An equation to lower speeds is that this linear representation of
engine friction is only valid at such speeds. This is discussed further
below.
Heywood11 divides engine friction forces into three components:
Boundary friction between two solid surfaces without sufficient
lubricant. This is independent of engine speed.
Hydrodynamic friction force between surfaces separated by a
sufficiently thick lubricant film. This force is proportional to
the engine speed.
Fluid friction. This is proportional to the fluid velocity
squared which is roughly proportional to the engine speed squared.
Thus, the friction force (or the friction mean effective pressure) is
expected to follow an equation of the form
(mep)fnc^0n - Cj + C2 N + C3 N2 [2.3]
For example, friction mep data for six engines at wide open throttle
have been correlated by this equation with the following constants:
Ct ~ 0.97 bar C2 = 0.00015 bar/RPM C3 - 5xl0*8 bar/(RPM)2
The increasing importance of the non-linear terms at higher engine
speeds is shown in the table below:
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RPM
c,
C2 N
C3 N2
Total
Increment
0
.97
0
0
0.97
1000
.97
.15
.05
1.17
0.20
2000
.97
.30
.20
1.47
0.30
3000
.97
.45
.45
1.87
0.40
4000
.97
.60
.80
2.37
0.50
Because these data were obtained at wide open throttle they will not
include throttling friction.
From the usual relation between power and mean effective pressure, the
friction power will proportional to the friction mep (or force) times
the engine speed. Thus the friction power is expected to follow an
equation of the form
Pfncuon - ( C, N + C2 N2 + C, N3 ) (Vd/2) [2.4]
This represents the actual energy required to overcome mechanical
friction. The fuel rate required for this friction power will equal the
friction power divided by the "efficiency" for converting fuel energy
into the mechanical power required to overcome this friction. This
"efficinecy" is not commonly reported, but it would be expected to be
low because low power operation is the least efficient engine operating
condition.
This efficiency can be be roughly compared with the An equation at low
speeds where the quadratic and higher terms can be neglected. The value
of a' = 0.271 MPa/rev. The fuel energy rate for zero brake power, P^, ~
a' N Vd. The friction power (neglecting quadratic and higher terms) is
pfncuon = ci/2. The "efficiency" of coverting fuel into mechanical motion
required to overcome engine friction is then [ C,/2 ] / [ a' N Vd ] -
Cj/(2a'). Cj = 0.97 bar = 0.097 MPa and a' = 0.271 MPa giving a value
of 16% for the conversion of fuel energy into mechanical power to
overcome friction. This seems like a reasonable value confirming the
magnitude of the a' factor in the An equation.
Interpolation of Fuel Flow in Vehicle Simulation Codes - An is critical
of the process of using brake specific fuel consumption (bsfc) data from
an engine map and interpolating to find the actual fuel consumption.12
He points out that a linear interpolation on an engine map, particularly
at low engine power, is not accurate. This has already been recognized
by the original authors of the VEHSIM program13 who required the basic
engine map data to be entered as mass per unit time of fuel. It is not
given in terms of brake specific fuel consumption (bsfc). This avoids
the errors created by interpolating brake specific quantities in low
load regions where the brake-specific quantities approach infinity.
The analysis below shows how the double interpolation in VEHSIM, which
is used to find the fuel flow rate as a function of engine speed and
engine load is entirely consistent with the equations in An's
dissertation. The fuel data in VEHSIM as in terms of fuel rate (mass
per unit time) which is simply P^, divided by the heat of combustion of
the fuel. Thus the same procedure would be used to interpolate the fuel
mass flow rate, mftlcl, or P^, - m^, C^. The basic relation between fuel
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energy rate, P,^,, engine speed, N, and engine power output, that
An uses as the starting point in his analysis'4 is a mathematical
representation of a chart in the Bosch handbook:
Pfcel - f(N) + g(N) P^ [2.5]
In this equation f(N) and g(N) represent arbitrary functions of engine
speed. Equation [2.2] is obtained by assuming that f(N) = a N, and g(N)
= b. The more general f(N) and g(N) notation can be used to describe
the VEHSIM interpolation used to find P,^ at a given engine speed, N,
and engine power, Pa,^, between tabulated data such that
N, < N < N1+1 and P^j < P^ < P^^,
At any (speed, power) point in the engine map, (N,,P^^j), the value of
the fuel rate is P^^. The double interpolation starts with an
interpolation over engine power points which is equivalent to computing
the following terms:
g(N,) = [Pfuclij+l "
Pfucl i j 1 / t P engine j+1 ^cagmcjl
[2.6]
f(N.) - PfacWj - g(N,) P^,
[2.7]
g(N,+ I) = [Pfue|,+ lj+l
Pfueli+ljl / [Paigmej+l — P engine j ]
[2.8]
f(N1+1) = Pfi,di+lj ~ g(N1+1) Peoginej
[2.9]
Thus the first steps of the usual linear interpolation in the VEHSIM
program may be regarded as an evaluation of f(N) and g(N) in An's basic
equation. From these values we can compute the fuel rate at the two
tabulated engine speeds in the map data and the given engine load. This
computation gives:
^.(N.-P^e) ~ f(N.) + g(N.) P^ [2.10]
- f(N1+1) + g(N1+1) Pragme [2.11]
The desired fuel rate is given by a final linear interpolation between
these two fuel rate values:
Pfucl - f(N.) + g(N,) P^ + [ Pfije^^i+l , Pengine) "
^.(N.-Pcng™)] [ N - N, ]/ [ N1+, - N, ] [2.12]
Combining equations [2.10], [2.11], and [2.12] gives
Pfce, " f(N.) + g(N.) P^ + [f(N1+1) + g(Ni+1) ?mgax -
f(Ni) - g(N,) P^J [ N - N, ]/ [ N1+I - N, ] [2.13]
In order for this to be consistent with the basic result of equation
[2.5] that P^, ~ f(N) + g(N) P^^ the values of f(N) and g(N) implied by
equation [2.13] are:
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f(N) - f(N,) + [ f(NI+1) - f(N,)] * [ N - N, ] / [ N1+1 - N, ]
[2.14]
and
g(N) - g(N.) + [g(N1+I) - g(N,)] * [ N - N, ] / [ N1+1 - N, ] [2.15]
Substitution of An's assumptions that f(N) = a N and g(N) - b is
consistent with equations [2.14] and [2.15]. Torque is often used,
instead of power is used as the interpolation variable for engine load.
Since = 2 it N T, equation [2.5] may be writtten as
Pfiid - f(N) + h(N) T [2.16]
where
h(N) = 2 w N g(N) [2.17]
It the above derivation were repeated using this interpolation equation,
equation [2.14] would be unchanged and equation [2.15] would be replaced
by a similar equation in h(N) instead of g(N):
h(N) - h(N,) + [h(N1+1) - h(N,)] * [ N - N; ] / [ N1+1 - N, ] [2.18]
Under the assumption that g(N) - b equation [2.17] gives h(N) = 2 ir N b.
Equation [2.17] is consistent with this expression for h(N).
Thus, the linear interpolation for the fuel rate as a function of engine
speed is consistent with An's results that g(N) can be regarded as a
constant and f(N) is proportional to N. This is true if engine power or
if engine torque is used as the load variable. Since the interpolation
process is consistent if torque is used as the interpolation variable it
will also be consistent if BMEP is used as the interpolation variable to
represent load.
Extension of An Model to Emissions - An states that additional
applications can be made "to supplement transportation and highway
planning models with simple but accurate modeling of fuel consumption
and N0Xemissions."1S He further states that it should be possible to
"analyze the dependance of N0X emissions on engine and vehicle
parameters and driving characteristics."
We contacted both Professor Ross and Dr. An to discuss their ideas for
modelling emissions. Both of them told us that they intended their
remarks to be limited to N0X emissions and expected that the results of
applying a similar model to N0X emission would yield less accurate
results than they obtained for fuel economy. The expected that the
initial approximation would be to assume that the N0X emissions were
directly proportional to the engine power, over the range that they
expected their model to be valid. This would be equivalent to assuming
that the brake-specific N0X emissions are constant over the region in
which the approximate model is to be applied.
An is interested in exploring models of CO and HC emissions which he
believes are linked mainly to cold starts. He believes that a model
which uses the number of starts and stops as the main parameter can be
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used to obtain results for CO and HC emissions that will be useful in
transportation analysis.
Literature Search - The literature search for this part of the project
started with presonal references of Sierra personnel. Additional
literature searches were made using a) Sierra's in-house computerized
SAE literature data base, b) a computerized literature search of the
National Technical Information Service (NTIS) data base, c) a
computerized literature search of the Engineering Index, and d) follow-
up on references found by these preliminary searches.
There is a wide range of spark-ignition engine models available.
Heywood,16 Ramos,17 and various Society of Automotive Engineers (SAE)
publications18 provide overviews of the range of available engine
models. The use of detailled computational fluid dynamic models (e.g.
KIVA-II)19 is a current research topic, but these models are not ready
for direct application of these models to the determination of emissions
data for engine maps.
A key classification of fuel economy/emission models is their need for
input data. Most of the models discussed below have significant
requirements for input engine mapping data. These data represent both
emissions and vehicle performance. An alternative to such data-
intensive models are those which attempt to compute the emissions from
some model of the in-cylinder combustion process. Such models typically
require other assumptions or data (e.g. a model for the heat release
rate or data on cylinder pressure rise) and are not capable of treating
the behavior of multicylinder engines. The most frutiful path for
improved emissions modeling, in the short term, is with data-intensive
models.
Most of the recent work on engine modeling that had applicability to the
engine mapping data dealt with emissions. The previous work on fuel
economy modeling was reviewed by An in his disseratation. Much of that
work was done in the 1970s and 1980s in reponse to concerns over energy
shortages. The papers by Watson and his co-workers,20,21 cited in An's
dissertation, provide a good background to the modeling of emissions and
fuel economy. These papers look at emissions and fuel economy for
various driving cycles in use throughout the world and point out the
need for consideration of transient, warm-up operation to obtain better
agreement between theory and experiment.
The work that is most applicable to EPA's engine mapping work has been
published by Nissan. Hori, et ai.22 discuss the Total Automotive
Performance (TAP) program which models fuel economy, emissions,
performance, acceleration, and exterior noise. This model is similar to
the VEHSIM code in that it requires a large amount of input data about
the vehicle being modeled. In a later work Matsumoto et ai.,23
developed a similar model that was able to account for transient
behavior in the intake system. This is potentially an important source
of emissions. This model also required extensive data inputs for each
engine and vehicle. The road load was translated into an engine speed
and load in a manner similar to that used in the VEHSIM program. In
addition to having a data base for engine speed, engine load, throttle
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opening, and intake raainfold pressure, additional data was available on
the air volume entering the cylinders and the volumetric efficiency.
The feedback behavior of the oxygen sensor and the response of the
air/fuel ratio to this sensor was modeled to compute the fuel flow rate
and the air/fuel ratio. The engine-out exhaust emissions were
determined from engine maps which determined the composition at various
air/fuel ratios for a given speed/load combination. The tail pipe
emissions were computed from a model for the three-way catalytic
converter which included a term for adsorption of pollutant species on
the catalyst. Again, the specific empirical constants were required for
use in this catalyst model. The authors developed the model to evaluate
the effects of changes in the feedback control system on emissions from
the vehicle. For the one data comparison shown the discrpeancy between
experimental data and the model was as large as 25% for engine out
emissions and 20% for tail pipe emissions. This model appears to have
the greatest promise in terms of its ability to handle engine
trasnients, however, it requires a large amount of data on a specific
vehicle/engine/catalyst combination in order to work.
Previous work by Sierra Research for EPA has examined the use of
simulation programs for cold start.24,25 This work used the VEHSIM
code and an emissions simulation model which required engine mapping
data for performance and emissions. The cold start was handled by using
an adjustment factor for engine out emissions and for catalysts light-
off time. The authors considered these adjustment factors to be a
"first-order approximation" requiring additional work prior to any
widespread application. However, their use of a light-off time for
catalyst warm-up is consistent with the work of Chen et ai.,25 who
developed a detailled model of catalyst performance. Their detailled
model showed a shart rise in converter efficiency over a very brief
time. It appears that the concept of a catalyst light-off time is a
good starting point for extension of models to transient operation.
The current status of engine modeling can be divided into two groups.
The first is a research area, which does a fundamental analysis of
engine combustion using computational fluid dynamics approaches and
supercomputers. Simplifications of these models, which require some
empirical input on a fundamental level such as a correlation equation
for the flame speed, are available, but are mostly useful for predicting
trends. The second group, discussed here, are data-intensive models
which require certain data for various engine operating conditions and
use various analysis tools to determine how combinations of vehicle and
engine operations will affect emissions and vehicle performance. This
second class of models requires a large amount of data input, but can
provide the most accurate results in the short term.
Correlations for Filling Holes in Engine Emission Maps
An initial exploration of the fundamental relationships between
emissions rates and engine operating variables was done to determine the
basic relatiionships between these variables that should be reflected in
any interpolation or extrapolation procedure. With this basic
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understanding in mind the EPA mapping data was examined to determine
possible correlations.
Theoretical Background - The exhaust emissions rate can be related to
engine variables through the exhaust flow rate. To do this, the mass
flow rate (mass/time) of the i4 pollutant species, m,, is written as its
mass fraction, w,, times the mass flow rate of exhaust. The latter is
given by the mass of air plus the mass of fuel which equals the mass
flow rate of fuel, m^,, times one plus the air fuel ratio. We thus
have,
®. ~ w, "fad ( 1 + A/F ) [2.19]
The pollutant mass fraction is used here as a measure of "concentration"
because it provides a simpler analysis of the mass rate data on
emissions and fuel consumption that are used in the engine mapping data.
The mass fraction is related to the usual parts per million measurement-
—on a mole fraction (volume) basis—as follows:
w, = 106 (ppm), M, / Mexhuut [2.20]
where M, is the molecular weight of the pollutant species and M,,, is
the molecular weight of the exhaust. Although equation [2.19] gives a
basic relationship between emissions rate and other engine parameters it
reatains the unknown mass fraction as a variable.
Sierra was asked to investigate the use of emissions per engine
revolution as a possible fitting variable. This can be done by writing
the fuel mass rate, m^^, in equation [2.19] as P^^O,. and using equation
[2.2] for P^, to give
m. - w. [a N + b ] ( 1 + A/F ) [2.21]
Dividing by N and using the usual relation between engine power, speed
and torque, P^^ = 2 n N T, gives
m/N = w, [a + 2 ir b T ] ( 1 + A/F ) [2.22]
This shows that the relation between emissions per revolution and torque
is not a simple one, but depends on the pollutant mass fraction.
For a catalyst-equipped engine the pollutant concentrations, w,, depend
on the engine-out emissions and the catalyst efficiency. The engine-out
concentrations are a function of engine parameters. The catalyst
efficiency depends on the catalyst temperature, exhaust flow rate, and
air/fuel ratio over the catalyst.
The behavior of engine-out emissions has been studied for many years.27
Engine-out concentrations of CO concentration depend only on the
air/fuel ratio. The NO concentration is governed by the peak
temperatures in the engine. Hydrocarbons in the fuel may be trapped in
engine crevices or absorbed in the oil layer on the cylinder wall and
remain unburned during the combustion process. During the power and
exhuast strokes these unburned hydrocarbons may be entrained in the hot
combustion products and undergo some oxidation. Increased turbulent
-12-
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mixing, usually produced by higher engine speeds, can enhance this
oxidation and reduce unburned hydrocarbons; a rich air/fuel ratio will
reduce this oxidation rate and increased exhaust hydrocarbons. These
qualitative observations have been established by many quantitative
studies, but there is no simple mathematical relationship between engine
variables and emissions.
Although there is no simple relationship for the concentration of
pollutant species in the exhaust, equation [2.19] can be used to
interpolate or extrapolate emissions data over small regions if no data
are available. If the pollutant concentration and the air/fuel ratio
are assumed to be constant constant over this small region, equation
[2.19] states that m/m^, will be a constant. Thus pollutant emissions
rates at an unknown point, 2, can be found by knowing the fuel rate at
that point and the emissions and fuel rates at some known point, 1, by
the simple ratio:
®i2 - "Viz (m, i / ""tan) [2.23]
This would be expected to apply only over a very narrow range and only
at lower loads. At higher loads where enrichment occurs the air fuel
ratio is expected to change and pollutant concentrations will also show
sharp changes.
Empirical Approaches - Another possible approach is the direct
interpolation or extrapolation of emissions from two load points (0 and
1) at a given engine speed. This would result in the following equation
for the emissions rate at point 2 if torque, T, is used as the
extrapolation variable.
m, , - itii „ r
®i,a = mx,i + ^ lTa - rj
1 0 [2.24]
If the exhaust mass flow rate is significantly different between these
interpolation points, equation [2.21] can be used to compute the mass
fraction and the intrepolation of equation [2.24] can be replaced by the
following interpolation on mass fractions:
",.2 = + "V " I1'0 lTa - rj
•*1 "*0
[2.25]
This would require an interpolation/extrapolation procedure for fuel
rate and air/fuel ratio to compute the emissions rate at point 2. It
could account for differences in these variables beween different
interpolation points. This procedure is expected to produe more
accurate results provided that a satisfactory interpolation/—
extrapolation for the fuel rate and the air/fuel ratio can be found.
The interpolation/extrapolation equation for the fuel flow rate at point
2 is similar to the previous equations:
m - m j. 111 fuel, 1 ~ mfUOl, 0 { T _ 1
"'fuel.2 "'fuel, 1 + Tf. ~ lr2 T\i
¦*i Jo
[2.26]
-13-
-------
It is possible to use the interpolation/extrapolation of equation [2.26]
to find the fuel rate and the scaling of equation [2.23] to find the
emissions. Combining these two equations gives:
m ~ mfuel, o
l.i mi.i
mi.2 = + =—T tuel>1 [r, - rj
•*1 *0
[2.27]
The choice of which extrapolation procedure to use will be determined by
an examination of the actual mapping data.
Examination of Initial EPA Mapping Data — Engine mapping data were
provided to Sierra by EPA in the form of Lotus spreadsheets. Sample
copies of the spreadsheets for two test vehicles were delivered to
Sierra at the start of the projet. These were used to learn the basic
structure of the mapping data and to determine subsequent analysis
procedures. Subsequently Sierra obtained preliminary data for twenty-
nine vehicles; these data were used for the main part of the analysis on
this project. A final set of corrected data were used in the later
stages of the work.
The initial analysis used a spreadsheet template which could be combined
with the EPA spreadsheets to perform the following computations for all
data points:
Carbon balance across the catalyst
Computation of mass fractions and emission per revolution for both
engine out and tail pipe gas streams.
Computation of fuel rate by An equation and comparison with
measured data.
Linear regression of all data points to obtain the best straight
line fit of fuel consumption per revolution to torque.
A check on the reported air/fuel ratio as described below.
The mapping data were given in terms of mass emissions, not
concentration. The check of the air/fuel ratio started with the
computation of the exhaust mole fractions from the equation:
y. - / [ M, m^, (1 + A/F) ] [2.28]
where the exhaust molecular weight was assumed to be that of air. The
use of this assumed molecular weight and the reported air/fuel ratio in
a procedure to check the air/fuel ratio are obvious weak points in this
check, but it was the only alternative for computing mole fractions from
the available data. Once the mole fractions for HC, CO, C02, and N0X
were known the air/fuel ratio was computed by simple element balance
equations.
The fuel energy rate predicted by the equation P^, = a' Vd N + b P^^
was computed for each data point. As expected, the agreement was much
better for lower engine speeds and loads than it was at higher ones. An
-14-
-------
attempt to do a correlation of fuel rate per revolution versus torque
using all data points did not produce a good result. This was not
considered a serious problem since the fuel rate data in the engine maps
is well behaved and closely spaced so that linear interpolation should
provide an effective tool for filling any missing data. The correlation
could have been improved by using a limited data set, but this did not
seem to be an important task for this study.
The equation underpredicted the idle fuel rate for all vehicles. The
errors ranged from -18% to -72% with an average value of -42% for the 29
vehicles in the EPA mapping study. This was not unexpected since idle
points were not used in determining the empirical coefficients.
However, it did point out concerns with using this approach for
estimating fuel rates at zero torque.
Except for the idle point, the errors in the predicted fuel rates
usually ranged from 5% at low speeds and loads to 50% at higher speeds
and loads. Points with larger errors usually had some error in the fuel
rate. Thus, the An equation provided a useful tool for flagging
potential errors in fuel rate measurements.
All data were reviewed for probable errors. A partial, but not
exclusive, list of problems found is shown below:
a. Brake-specific fuel consumption below 0.4 lb/HP-hr.
b. Fuel rates that do not increase with load at constant RPM.
c. Air-fuel ratios greater than 16.
d. Negative catalyst efficiencies or catalyst efficiencies greater
than 100%.
e. Inconsistent emissions results (e.g., C0/C02 ratios greater than
one at stoichiometric or lean air/fuel ratios).
These points wre eliminated the points identified above from further
consideration unless there was some independent confirmation of their
validity. Points with "irregular" behavior were not eliminated unless
there was some reason to suspect an error. These points were assumed to
be valid data points representing irregular behavior in the emissions
map.
The problems identified were communicated to EPA during the performance
of this project. At the same time EPA was reviewing the correctness of
their data. Following the completion of this initial task EPA delivered
a revised set of mapping data which was used for the second part of this
work assignment.
Computer graphics of the emissions data were produced to provide a
visual evaluation of potential data relations. These were done as
surface plots and topographical plots. Emissions data were examined on
four bases: (1) emissions rates (grams/second), (2) brake-specific
emissions (grams/HP-hr), (3) mass fractions, and (4) emissions rate
-15-
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divided by engine speed (grams/revolution). Figure 2.1 shows surface
plots of the emissions data on a brake-specific basis for the Mercedes
300E. Although there is variation in the emissions maps for various
vehicles, the samples shown here are typical of all the engines
observed. Additional surface plots of emissions are shown in Appendix
A.
The most significant observation from the surface plots is the division
of each emissions map into two regions: the first has very low emisions;
the second has very high emissions and the transition between the two
regions is fairly sharp. This is especially true for HC and CO where
the transition is associated with enrichment. The effect is less
noticeable, but still substantial for NOx emissions.
The same data are shown as a contour plot in Figure 2.2. These plots
use logarithmatic contour lines with values of 1x10°, 2x10" and 5x10"
with values of the exponent n chosen to cover the entire range of data.
(Some plots also include a contour for 7.5x10°.) These contour plots do
not provide the clear picture of the overall emissions behavior shown in
the surface plots. They do show large relative changes in emissions,
even in regions where the surface plots show nearly constant emissions
near zero. Of course, the absolute level of these emission changes is
small compared to the maximum level.
Thus, the combined use of surface plots and contour plots gives the
following picture of the emission maps.
o There are two distinct regions with sharp separation; one is a low
emissions region, the other is a high emissions region.
• The low emissions region has changes which are large compared to
the levels present.
These same observations hold regardless of the basis for the emissions
maps. Figures 2.3 to 2.5 are contour plots of emissions maps for
emission rates, mass fractions and emissions per revolution,
respectively.
A clear feature of these maps is the lack of any regular behavior that
can be used to determine simple relationships between emissions and
engine operating conditions. Contour plots for throttle setting,
manifold vacuum, and fuel consumption are shown in Figure 2.6. The
regular behavior noted here is a marked contrast to that observed for
emissions. These data confirm the results of the theoretical analysis
that there is no simple relation between emissions and engine operating
varibles that can apply to the entire range of engine operating
conditions.
-16-
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M© rcedes 300E
BSHC ( gm/HP-hn)
risrcedes 300E BSNOx ( gm/HP-hr)
Rgure 2.1
Surface Plots of Brake-Emissions for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
Mercedes 300E BSHC (grams/HP — hr)
1510 1910 2310 2710 3110 3510 3910 <310 4710
¦Qe= k
0 5 —
"O
a
O
o
71
cr
31
11
1
1510 1910 2310 2710 3110 3510 3910 4310 4710
Engine Speed ( RPM )
Mercedes 300E BSNOx (grams/HP-hr)
1510 1910 2310 2710 3110 3510 3910 4310 4710
—m 1——v—i—.—i v—T7—i—i—r—y il^
5510 5910
11
131
111
"O
OS
91
o 0*
'O 02
CL
71
51
cr
h-
=r
' ) o
31
1
11
3510 3910 4310 4710 5110 5bl0 bdIO
Engine Speed ( RPM )
1910
Mercedes 300E BSCO (grams/HP-hr)
1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
1510
1110
131
.*0-
111
91
CL
71
51
cr
| ' ' I I \ I I I I I lillt IS ^ I . I .
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
Figure 2.2
Contour Plots of Brake Specific Emissions for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
Mercedes 300E HC (grams/sec)
1110 1S10 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
0 002
1110 f *>10 1910 ^310 2/10 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
3
Mercedes 300E NOx (grams/sec)
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
cwj
<3.
0
1110 1510 1910 2310 2710 3110 3510 3910 .4310 4710 5110 5SI0 5910
Engine Speed ( RPM )
Mercedes 300E CO (grams/sec)
1910 2310 2710 3110 3510 3910 4310
1110
1510
131
111
91
Q_
001
71
51
CT
31
11 1 1—
1110 1510
2310 2710 3110 3510 3910 4310 4710 5110 5510 S'JIO
Engine Speed ( RPM )
Figure 2.3
Contour Plots of Emission Rates for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
Merc ,s 300E Tail Pipe HC Mass Fraction
1510 1910 2310 2710 3110 3510 3910 4310 4710
1 ) V 1^! \ ¦ J~r
11
5510 5910
0 00025
131
11 1
1E-004
Q>
91
2 5E-005
CL
71
St
cr
31
n
ii
1510
Engine Speed ( RPM )
Mercedes 300E Tail Pipe NOx Mass Fraction
1110 >510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5810
131
O
CD
a>
D
cr
O
11
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
Mercedes 300E Tail Pipe CO Mass Fractior,
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
131
^02!
£0
91
a.
O
1E-004'
cr
1510 1910 2310 2710 3110 3510 3910 <310 471(1 VI0 5S10 5910
Engine Speed ( RPM )
Figure 2.4
Contour Plots of Mass Fractions for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
vlercede- jOOE Tail Pipe HC (grams/revolution)
1910 2310 2710 3110 3510 3910 4310 4710 3110 5510 5010
11
U1
91
2 5E-003
a_
71
o
51
5E-005
O"
O
11 1—
1110
1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 59)0
Engine Speed ( RPM )
Mercedes 300E Tail Pipe NOx (grams/revolution)
IIIO 1510 1910 2310 2710 3110 3310 3910 4310 4710 5110 5510 5910
%
10 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
Mercedes 300E Tail Pipe CO (grams/revolut
1 j
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
Figure 2.5
Contour Plots of Emissions Per Revolution for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
cedes 300E Throttle (sg of WOT)
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
J
Mercedes 300E Fuel Rate (lb/sec)
1110 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
%
10 1510 1910 2310 2710 3110 3510 3910 4310 4710 5110 5510 5910
Engine Speed ( RPM )
Mercedes 300E Manifold Vacuum
11
1510
4710
131
111
*o
9
a.
71
51
cr
31
i
11
2310 2710
3510 3910 4310 4710 5110 5510
Engine Speed ( KPM )
Figure 2.6
Contour Plots of Engine Performance Parameters for
1992 Mercedes Benz 300E
3.0L A4 4-Door Sedan
-------
Computer Graphics Techniques for Generating Engine Maps
The algorithm that is used for gridding irregularly spaced data for
computer graphics was investigated for possible use as an engine mapping
tool. This algorithm proceeds by taking a set of input data points,
e.g., a series of pollutant concentration data points, Ck, at measured
speed, Nk, and torque, Tk. These data are used to construct a set of
regularly spaced data points representing the initial data. If the grid
values of speed and torque are denoted as Ngndl and Tgr)djI then the
problem is to find the values of the variable at these grid points,
C(Ngndil ,Tgndj) • There are a variety of ways for doing this. The most
common uses an inverse distance weighting of the nearest neighbor
points. The distance between the measured data points and the
desired grid point is defined as follows:
A set of n measured data points in the neighborhood of the desired grid
point is selected and the value of C on the grid is computed by the
following formula:
There are many alternatives for choosing which n data points to use in
this equation. The simplest choice is to take the n nearest neighbors.
Alternative choices limit the points used to those within a certain
radius of the grid point. Another selection method requires that points
come from each quadrant (or octant) surrounding the grid point. It is
also possible to use alternative equations for fitting the experimental
data to the regular grid. A technique known as kerning is based on
fitting gradients at the boundaries of the region.
The methods for developing plotting techniques are taken from drafting
and mapping where there is no difference in scale for the two
independent variables. In cases where the physical variables are not
the distance in a coordinate direction, it is important to define the
distance to account for the difference in scale as is done in equation
[2.29], Actually, it is only necessary to use the single parameter, K,
defined as the ratio of Speed to Torque ranges. This is defined by the
following equation.
This definition of K can be used to obtain a modified distance, Dk,
defined as
d2 = - -*Wi)2 + (Tk - Tgridij)2
" (^max-^in)2 < ^ ~ rnln) 2
[2.29]
[2.30]
(N - N ¦ ) 2
X} = mi n'
/ 7» - T )2
v max
[2.31]
D\ = (JW-Nmin)2 4 = - Ngrld.l)2 + & < I* - TgridJ)2
[2.32]
-23-
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Equation [2.32] can be used to substitute Dk for in equation [2.30],
When this is done the (N^ - Nm.n)2 terms cancel leaving
It was necessary to consider many of these ideas in order to obtain
satisfactory plots of the EPA engine mapping data. The Surfer software
package28 used for generating surface and topographical plots allowed
various user options for selecting the method used to distribute
experimental data over the regular grid used in the plots. One of the
poor features of this system was the use of a default value of K = 1.
Since the difference in speed range was typically about 4000 RPM while
the difference in torque was about 125 ft-lbf, the typical K value was
about 30. Plots obtained with a K value of 1 displayed an irregular
pattern which was not observed when the actual K value based on the
minimum and maximum torque and speed values was used.
The observation of several surface and contour plots of the mapping data
suggested the use of this technique for the formation of a final engine
map. This had the particular appeal of being able to handle the slight
variation in the engine speed data and the ability of treating the
occasional point which was available at only one engine speed. A
Fortran program was written to take the intermediate file from the
graphics program and use it to generate an engine map. This provided
the values of engine speed, torque, intake manifold vacuum, throttle
position, fuel flow rate, and emissions rates (both engine out and tail
pipe) for HC, CO and NOx. These were obtained on a 50 by 50 grid of
speed and load points.
In order to verify the utility of this procedure, a second Fortran
program was written which used the engine map generated by the first
program to compute the values corresponding to the speed and load points
in the initial mapping data. Although good agreement was obtained for
most points, some points had relative errors of 1000% or more in CO and
HC emissions. This was due to the nature of equation [2.30] or [2.33]
which tend to smooth the experimental data. The actual data does have
sharp increases in emissions over a narrow region of engine load. The
process used in generating the graph tends to smooth these out resulting
in enormous errors for points where the sharp increase is occurring.
This effect was studied by varying the number of nearest neighbor
points, n, used in equation [2.30], The agreement improved as the value
of n was decreased. However the resulting engine maps were very jagged.
Figure 2.7 shows the hydrocarbon emissions rates as the number of points
used in constructing the graph was decreased from the five poins used to
generate the usual surface plots to two and one point. Although the map
generated by equation [2.30] for one data point is very jagged, it
provided the best agreement between the engine map and the experimental
data. For this map, at a given location on the regularly spaced grid,
the "interpolated" value was simply set equal to that of the nearest
i' ^gri d, j
n
[2.33]
-24-
-------
Mercedes 300E To LI Pipe HC Cgm/sec)
Mercedes 300E Toll Pipe HC (gm/sec)
Plot generotad using only
two nearest ne Ighbore
to compute grid values.
*5^
Figure 2.7
Effect of Number of Fitting Points
on Emissions Map
-------
experimental data point. This one—point scheme can be reduced to the
following rules:
1. For a given grid point (Ngnd ,,Tgndj) use equation [2.29] to compute
the "distance" to the nearest neighbors. Find the smallest value
of djj.
2. Set the value of C at Ngrjdl,Tgndj equal to the value, Ck at the
minimum distance c^.
Although this approach gave a gridded engine map which matched the
experimental points well in most cases, the result was essentially a
step function which did not seem to provide a good representation of a
real engine map. In addition, this approach did not provide any
relation to the underlying engine operating parameters. Consequently,
no further application of this method was explored. Although the
results of this study were not used in the final procedure for preparing
engine maps, the work in obtaining these results did point out the need
to resolve properly the sharp increases in emissions that did occur in
the actual engine maps.
Conclusions from this Task
The use of the equation Pfad = a' Vd N + b is limited to low speed
and load points. It does represent a bilinear representation and is
consistent with the usual interpolation procedures used in engine map
codes such as VEHSIM.
The data used to determine the empirical coefficients a' and b did not
include the normal idle points. Its use for estimating the fuel rate at
zero torque is uncertain.
There is no simple relation between emissions rates and engine operating
conditions which is valid over the entire range of engine operating
conditions.
The emissions maps can be divided into low—emission and high—emission
regions with a fairly sharp transition between them. An analyticla
representation of these maps must have a careful definition of these
regions.
-26-
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3. PROTOCOLS FOR INTERPOLATION AND EXTRAPOLATION
IN ENGINE MAPPING DATA
Introduction
As noted in the previous section, there is no simple correlation between
emissions and engine operating parameters that can be applied in a
simple fashion to all data to produce the desired predictions of
emissions (and fuel rate) where such data are missing in the EPA mapping
data. The theoretical background and the data analysis of the previous
section can be used to develop a protocol for filling in the missing
values to allow the mapping data to be used in a vehicle emissions
simulation code.
Preliminary Protocol for Filling Emission Maps
This protocol was developed and submitted to EPA about midway through
the work assignment. Following their comments, additional work was done
to improve this protocol. An improved method was developed for filling
fuel and emission rates at zero and negative torques, but the
examination of improved methods for filling in transition points in the
engine map did not yield a significant improvement.
Background and Rationale - The most significant feature of the emissions
engine maps is the dramatic increase in CO and HC emissions in operating
modes that have fuel—rich operation. This can increase these emissions
rates by factors of 10 to 1,000 over very small changes in engine speed
and/or load. This is the key feature that will need to be considered in
any interpolation process. For all pollutant species, there are regions
of the engine map where the emissions rates are dramatically higher than
in all other regions. Any small time spent in these regions would
probably result in failing an emissions test.
Emissions data show irregular trends. In some cases, there may be
reason to suspect experimental error. In most cases, however, these
"irregular" points are mutually consistent. For example, at a single
engine speed the emissions of HC and CO may generally increase with
torque, but there may be one torque point where there is a dip. If this
occurred only in HC and not in CO, it might indicate a measurement
error. Generally, such dips occur in both HC and CO indicating a
consistent improvement in emissions reduction for that point. Such
"irregular" data should be included in any final engine unless there is
some other indication of experimental error.
-27-
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There is no "magic bullet" that will automate the correlation of
emissions with the usual engine mapping variables—engine speed and
load, the latter usually expressed in terms of torque or brake mean
effective pressure (BMEP). Instead, the holes on each engine map must
be filled using good engineering judgement. The following procedure is
recommended to provide the final vehicle simulation engine maps from the
experimental data.
Rules for Preliminary Protocol -
1. Review all data for probable errors. A partial, but not
exclusive, list of problems found is shown below:
a. Brake—specific fuel consumption below 0.4 lb/HP—hr.
b. Fuel rates that do not increase with load at constant RPM.
c. Air—fuel ratios greater than 16.
d. Negative catalyst efficiencies or catalyst efficiencies greater
than 100%.
e. Inconsistent emissions results (e.g., C0/C02 ratios greater than
one at stoichiometric or lean air/fuel ratios).
2. Eliminate the points identified above from further consideration
unless there is independent confirmation of their validity.
3. Do not eliminate "irregular" behavior data points unless there is
some reason to suspect an error. Assume that these points are
valid data points representing irregular behavior in the emissions
map.
4. Form the engine map for a VEHSIM type code; this requires data at
fixed speed points, but the load points can change from speed to
speed. A procedure for filling in missing points is given below.
This discussion assumes that the emissions map will be described
in terms of a mass emissions rate (e.g., grams per second - g/s)
rather than using brake-specific emissions rates to avoid problems
as the load goes to zero.
a. Use an average engine speed for all points in a series of runs
with different torques provided that the measures engine speed
is within ±70 RPM of the average speed.
b. Examine the various runs at each average speed and determine
the region where any sharp increases (or decreases) in
emissions occur. Depending on the engine speed, there may or
may not be such a point.
c. Define a "sharp change" in emissions levels as 50% of the
maximum emissions rate. Where the sharp change in emissions is
contained in a torque interval which is less than 20% of the
maximum measured torque, use the experimental data only.
-28-
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d. Where the sharp change is found in a wider torque interval, use
data at adjacent engine speeds to estimate the point at which a
dramatic increase in emissions would occur. Place an
interpolated point in the engine map that defines this
transition more sharply.
Determine the torque value for this point from those at
neighboring speed runs. Use linear interpolation to obtain the
fuel rate, throttle setting and manifold vacuum for this point.
Set the emissions rates at this point to a value determined
from adjacent regions of the engine map. This determination
should be based not only on the observed emission rates, but
also on the corresponding operating conditions such as air/fuel
ratios, operation as open or closed loop, and anticipated EGR
operation.
This procedure is illustrated in the following hypothetical
example.
Speed Torque Emissions
(RPM) (ft-lb) (grams/second)
Assume the experimental data shown above were for an engine
whose maximum measured torque was 120 ft—lb and whose maximum
emissions rate for the species shown was .2 g/s. The emissions
increase shown is greater than the defined sharp change (50% of
the maximum rate). This rise should be contained in a torque
interval of (.2)(120 ft-lb) = 24 ft-lb. In order to sharpen
the definition of the increase in emissions, a torque point
would be "interpolated" between these two points.
Examine the data at neighboring speed points. If the data
showed that the sharp increase in emissions rate took place
closer to the higher (90 ft-lb) torque point—and if the
expected operations in terms of air/fuel ratio were expected to
be similar for this speed range—an interpolation point would
be created with a low emissions rate. If a mean value of 70
ft-lb were picked for the interpolation point, the emissions
increase between the observed value at 50 ft-lb and the
interpolation point would be estimated from the change in
emissions for a similar increase in torque in neighboring
regions. For example, if such data showed a 25% increase in
emissions might be expected between 50 and 70 ft-lb, the
interpolated point at 70 ft-lb would be assigned an emissions
value of .0015 g/s.
If data at neighboring speed points indicated that the
transition took place closer to 50 ft-lb torque point, then a
high emissions rate would be used for the interpolation point.
If the mean value of 70 ft-lb is chosen for the interpolation
point and data from nearby regions indicate a 10% decrease in
emissions might be expected between 90 and 70 ft-lb, the
4500
4500
50
90
.0012
.12
-29-
-------
interpolated point at 70 ft—lb would be assigned an emissions
value of .11 g/s.
In either case, the value used should be consistent with the
engine operating conditions expected at the interpolation
point. Note that this approach produces dramatically different
results for the emissions at this interpolated point (.0015 vs.
.11 g/s); if simple linear interpolation were used with the
experimental data, this point would have an interpolated
emissions rate of .06 g/s for both cases.
The approach above has been constructed as a first-order
approximation using emission rates. An improved approximation
technique would interpolate emission concentrations and obtain
the emissions rate by multiplying the concentrations by the
exhaust flow rate. This should provide a better approximation
because the emission species concentrations are more nearly
constant than the emission rates as the engine speed varies.
e. Vehicle emission simulation codes usually require a point at
wide-open throttle (WOT) for each engine speed. The emissions
at this point can usually be set to those of the highest
measured torque at the same speed. If the highest load value
is significantly below WOT operation, the WOT emissions rates
can be determined from those at neighboring speed points.
f. Interpolations of fuel rate, engine vacuum, and throttle
setting are generally regular and can be done by linear
interpolation.
g. To get data at zero and negative torques, try the various
estimation procedures outlined below. Choose the most
"reasonable" results to provide physical reality and overall
consistency in the engine map. (Negative fuel and/or emission
rates and fuel rates at zero torque that are higher than fuel
rates at the lowest measured torque point are examples of
"unreal" results that may be obtained by these procedures.)
The differences in these procedures should be checked by some
preliminary runs with a VEHSIM-like code. Because the fuel
rates and emissions rates are low at these conditions, the
procedures used should not have a significant difference on the
overall cycle results. The procedures to be used for fuel rate
are the following:
i. Assume that fuel rate at zero torque, at a given
engine speed, is found by multiplying the fuel rate at
idle by the ratio of the given engine speed to the
idle speed. This may produce an zero-torque fuel rate
which is greater than the fuel rate at the first
measured torque point.
ii. Extrapolate the fuel rate from the lowest two torque
points. This may produce negative fuel rates.
-30-
-------
iii. Extrapolate the computer-generated engine mapping data
from the lowest torque points to zero torque.
iv. Use the Ross-An regression procedure to get an
intercept which gives the fuel per revolution at zero
torque. Multiply this value by a given engine speed
to get the fuel rate at that speed.
The following procedures will be tried for estimating emissions
rate at zero torque:
i. Use the value at the lowest torque point.
ii. Extrapolate from the two lowest torque points; this
may produce a negative emissions rate.
iii. Multiply the emissions rate at the lowest torque point
by the ratio of the fuel rate at zero torque divided
by the fuel rate at the lowest torque point. This is
equivalent to assuming that the mass fraction of the
pollutant species and the air/fuel ratio do not change
between these points.
iv. Multiply the emissions at the idle point by the ratio
of the given engine speed to the idle speed.
For both the fuel rate and the emissions rate of the various
species, engineering judgement will be used to reconcile the
values obtained by these different approaches and select the
most reasonable value.
h. Assume that the lowest possible operating RPM is the normal
engine idle speed and that the emissions and fuel rate at this
speed are the same, at each torque point, as those at the
lowest measured engine speed. This is not a significant
assumption as the lowest measured engine speed is usually the
speed that would be encountered in normal engine operation.
i. Assume that the highest measured engine speed is the maximum
speed so that no extrapolation is needed at this point.
j. Assume that emissions and fuel rate values for negative torque
points (i.e., deceleration) will be the same as those for zero
torque. This will not be correct if there is significant
enrichment of the mixture for deceleration. However, this may
not be a significant problem because the exhaust flow rates are
low under these conditions.
k. The above discussion has focussed on emissions. As noted
above, codes such as VEHSIM expect a wide open throttle load
point at each speed. Values for the torque and fuel rate at
these WOT points would be based on the observed relationship
between these variables for similar engines.
-31-
-------
Sample Application of Preliminary Protocol
Table 3.1 is an engine map for the Chrysler New Yorker which illustrates
how this protocol would be applied to one engine. The points excluded
from the original data and the added points are noted. The maximum
measured torque is 176.8 ft—lb. Any sharp increase and/or decrease in
emissions should be contained in a torque interval which is 20% of this
maximum or 35.76 ft-lb. For this engine, the maximum measured HC, CO,
and NOx emissions rates are .099, 9.8, and .11 g/s, respectively. Half
of these emissions levels (.05, 4.8, and .055 g/s for HC, CO, and NOx)
define a sharp change in emissions.
Examination of the data shows that it is necessary to add three
interpolation points to the data in order to improve the definition of
the sharp changes in the map.
(1) at 2765.85 RPM between 83.2 and 133.2 ft-lb to better define the
increase in NOx a point is added at 100 ft-lb with an NOx
emissions rate similar to the one at 3313.29 RPM and 96.8 ft-lb.
All other data found by linear interpolation.
(2) at 4182.22 RPM between 56.1 and 96.9 ft-lb to better define the
increase in HC and CO a point is added at 80 ft-lb. Emissions
data are estimated based on data at neighboring speed points.
(3) at 4508.75 RPM between 89.3 and 134.4 ft-lb to better define the
increase in HC and CO and the decrease in NOx. Emissions data are
estimated based on data at the lower RPM.
Extrapolation points for zero and negative torque and for WOT operation
are also added. The method used for obtaining these points is given in
the "Description of Point" column.
Final Procedure for Determining Results at Zero and Negative Torques
The various methods for determining the emissions at zero and negative
torques outlined in step 4.g of the preliminary protocol were examined
for each engine in the data set. There was no one procedure that was
most effective.
The best estimation of the emissions and fuel rates for negative torque
was to set these equal to their values at zero torque, for each engine
speed. The justification for this approach was that the fuel energy
required to overcome engine friction would depend mainly on the engine
speed. Although the air flow, and hence the fuel flow, would be
expected to increase as the manifold pressure increased from the most
negative torque to the zero torque value, these differences could be
ignored for lack of any more reasonable approximation to use.
Similarly, the emissions rates would be expected to be the same at both
zero and negative torque. The problem that remained was the estimation
of the values of emissions and fuel flow at zero torque.
-32-
-------
1991 CHh. .^EW YORK
4 OR SEDAN 3 8 L L4
VIN: 1C3X466R9MD260
Table 3.-
SAMPLE EXPANDED ENGINE MAP
July 14, 1992
RPM
Torque
BMEP
Man Vac Throttle
Fuel
TP HC
TP CO
TP NOx
ft-#
psi
In hg %WOT
lbs/sec
gms/sec
gms/sec
gms/sec
743 97 <
—Average
Speed
for Data below
693
00
00
299
0
0 000899
0 000306
0.000620
0.000151
795
162
10.5
17.6
0.7
0.000937
0 001984
0 004560
0 000165
0 001964
0 004560
0 000165
1115 85 <
—Average
Speed for Data below
-50
-32 5
299
0
0 001031
0 000562
0 000231
0 000231
0
00
299
0
0.001031
0.000562
0 000231
0 000231
1114
11.2
7.3
188
30
0 001191
0 000649
0 000266
0 000267
1118
26 5
17.2
17.3
42
0 001409
0 003398
0 011484
0.002358
0 003398
0 011484
0 002358
1666 57 <
—Average Speed for Data below
-50
-32.5
29 9
0
0 001500
0 000229
0 000968
0 000000
0
00
29 9
0
0.001500
0 000229
0 000968
0.000000
1661
36 2
23 5
16 4
66
0 002252
0.000344
0 001453
0.000000
1672
82 8
53 9
11 0
139
0 003864
0 002482
0 020203
0 001021
0 002482
0 020203
0 001021
2331.54 <-
—Average Speed for Data below
-50
-32 5
29 9
0
0 003303
0.001097
0011012
0.000674
0
00
299
O
0 003303
0 001097
0011012
0.000674
2229
25 1
163
160
129
0 003700
0 001229
0 012335
0.000755
2222
ao o
52 0
11 6
172
0 005140
0 003632
0 008320
0 001159
2221
1383
89 9
54
25 6
0 007011
0 001085
0 000871
0 061383
2220
1502
97.7
1.9
39 2
0 007975
0 000957
0 000959
0,075298
1503
97.7
0
100
0 007975
0 000957
0 000959
0 075298
2765.85 <-
--Average Speed for Data below
-50
-32 5
299
0
0.003600
0.001225
0 009890
0 000139
2801
0
00
299
0
0 003600
0.001225
0 009890
0 000139
42 3
27.5
16 1
15.4
0 004607
0 001568
0 012656
0 000178
2773
832
54 1
11 1
203
0 006418
0 002758
0018919
0 001091
100
65 0
9 1
23 6
0 007991
0 002098
0013584
0 001300
2772
133 2
866
53
302
0 011096
0 000796
0 003057
0106257
2766
155 9
101 4
1.9
46 0
0 012792
0.000946
0 002404
0 083582
2717
165 1
107 4
04
96 8
0 019398
0 078899
6 507581
0 001571
165 2
107.4
0
100
0 019398
0 078899
6 507581
0.001571
3313.29 <-
- -Average I
Speed for Data below
-50
-32 5
299
0
0 003800
0.000162
0 000288
0.013110
0
00
29.9
0
0.003800
0 000162
0 000288
0013110
3313
14 9
97
193
140
0 004095
0 000175
0.000310
0014126
3324
33 8
22 0
175
15.9
0 004990
0 000304
0 001525
0 000148
3309
43 0
27.9
163
17.8
0 005521
0 001462
0 022420
0 000311
3306
536
34 9
15.1
24 2
0.006141
0 001922
0 035396
0 000326
3297
85 3
55 5
11 1
29 3
0 007791
0 001074
0 016686
0 000421
3328
96 0
63 0
80
34 9
0 011970
0 001433
0 024995
0 001252
3323
134 3
87 3
56
36 8
0 013524
0000612
0 001927
0 090989
3319
147 3
95 8
34
42 6
0 017264
0 036821
1 958976
0 008560
3288
173 9
113 1
20
54 2
0 017778
0 054263
2 498950
0014817
3311
178 8
1163
1 0
73 4
0 019020
0048818
2 926357
0 008537
3328
177 6
1155
07
97 9
0 024251
0 087890
8 669626
0 001792
179
116 4
0
100
0 024251
0 087890
0 669626
0 001792
Description of Point
Original Data In Final Map
Original Data In Final Map
Extrapolation point; last-torque emissions
Extrapolation Point; Use zero torque entry.
Extrapolation Point, Extrapolate Fuel; Scale Emissions by Fuel Rate
Original Data In Final Map
Original Data In Final Map
Extrapolation point; last-torque emissions
Extrapolation Point, Use zero torque entry.
Extrapolation Point; fuel rate by concensus; emissions scaled by fuel rate
Original Data In Final Map
Original Data In Final Map
Extrapolation point, last-torque emissions
Extrapolation Point; Use zero torque entry.
Extrapolation Point, fuel rate extrapolated, emissions scaled by fuel rate
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Use previous data for extrapolation point
Extrapolation Point; Use zero torque entry.
Extrapolation Point, Idle—scaled fuel rate; emissions scaled by fuel rate
Original Data In Final Map
Onginal Data In Final Map
Interpolation pokit to localize NOx emissions rise
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Extrapolation point to give highest measured values
Extrapolation Point, Use zero torque entry.
Extrapolation Point, fuel rate by concensus; emissions scaled by fuel rate
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Onginal Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data In Final Map
Original Data Eliminated From Final Map Because of Torque Decrease
Extrapolation Polnl
-------
Table 3,1 Ccpnt^-nued)
3812.15 <—Average Speed for Data below
-50
-32 5
299
0
0 006011
0 001173
0 035823
0 000476
Extrapolation Point, Use zero torque entry.
0
00
29 9
0
0 006011
0 001173
0 035823
0.000476
Extrapolation Point; fuel rate extrapolated, emissions scaled by fuel rate
3844
44 6
290
16.1
20 1
0 003020
0 001760
0 053757
0 000714
Original Data In Final Map
3835
93 1
605
10 9
28 1
0 012287
0 003708
0 058764
0 003636
Original Data In Final Map
3853
142.4
92 6
54
41.1
0.016006
0 001550
0.008150
0.075068
Original Data In Final Map
3716
1530
99 5
4 3
63 5
0 018680
0 013577
1.037994
0 065016
Original Data In Final Map
179
1164
0
100
0 027902
0 070000
8.500000
0.010000
Extrapolation Point Based on Neighboring Speed Data
3982
171 0
111.2
1 9
51.1
0 024760
0 070236
5 299946
0 010832
Excluded Data - Out of RPM Range
4182.22 <-
—Average
Speed
for Data below
-50
-32 5
29 9
0
0 006500
0 001294
0 036402
0 001243
Extrapolation Point; Use zero torque entry.
0
00
299
0
0 006500
0 001294
0 036402
0.001243
Extrapolation; fuel from neighboring speeds; fuel-scaled emissions
4159
44 2
28.7
164
20 2
0 009441
0 001880
0 052875
0 001806
Original Data In Final Map
4182
56 1
365
14 8
23 0
0 010492
0 001085
0 042622
0 000607
Original Data In Final Map
80
52 0
125
27 1
0.015356
0 002000
0.100000
0.003600
Interpolation pohtto localize CO/HC emissions rise
4190
969
630
108
30 0
0 018794
0 075311
6 028088
0.005716
Original Data In Final Map
4198
145 0
94 3
5.4
43 2
0 025795
0 099146
8.873959
0.005692
Original Data In Final Map
179
1164
0
100
0 030611
0 099146
8.873959
0.005692
Extrapolation; fuel/torque from previous speed; last-torque emissions
4508.75 <-
—Average
Speed
(or Data below
-50
-32 5
29 9
0
0 007036
0 001241
0 030116
0.000834
Extrapolation Point; Use zero torque entry.
0
00
29.9
0
0 007036
0 001241
0.030116
0 000834
Extrapolation Point, fuel rate extrapolated; emissions scaled by fuel rate
4520
38.7
25 2
163
21 7
0 009968
0 001758
0 042665
0001181
Original Data In Final Map
4505
53 1
34 5
14 8
24 2
0 011055
0 002115
0 054925
0 001902
Original Data In Final Map
4506
89 3
58.1
10.8
31.5
0 015038
0 010494
0 654554
0 010692
Original Data In Final Map
100
65.0
95
348
0 018042
0 070000
8.000000
0.005000
Interpolation point to localize CO/HC emissions rise
4504
134.4
87.4
54
45.7
0.027718
0 088631
9.765052
0.004418
Original Data In Final Map
179
116.4
0
100
0.034665
0.088631
9.765052
0.004416
Extrapolation: fuel/torque from previous speed, last-torque emissions
-------
The preliminary protocol recommended making estimates by all the various
methods and to use "engineering judgement" to determine the best values
of the fuel and emissions rates at each engine speed. Further
examination of the various methods led to the development of the
procedure outlined below. This procedure works in all cases studied and
is capable of automation by a Lotus 1-2-3 macro for the data on the
spreadsheets provided by EPA.
The first step was to use the scaling equation for emissions. This was
done because extrapolation could lead to negative emissions rates
whereas the scaling procedure would not. This provided a
straightforward procedure for determining emissions rates with an
understanding of its limitations. I.e. this procedure rests on the
assumption that the pollutant species mass fraction and the air/fuel
ratio are essentially constant over the region that this scaling is
being done.
This reduces the problem of determining emissions and fuel flow at zero
and negative torque to the single problem of finding, for each engine
speed, the fuel flow at zero torque, m^^N.T-O) . The two possible
values considered are the value found by extrapolation from the two
lowest torque points and the values found by scaling the fuel rate by
the engine speed. For convenience these are called the "extrapolated"
and "scaled" value in the discussion below. The exact definition of
these values are:
m IN T=M = m IM T \ - T JJjfuel^^i ^2^ ~ ^fual
fuel, excrap' ' ' mZue2 ^1' "Tl
T2 - T,
mfuel. scaled^' ® ^ mfuel, idle
[3.1]
[3.2]
N.
Idle
The automated procedure for doing this uses the following set of
decision rules.
I. Determine the "best" value of the zero-torque fuel rate at each
engine speed as follows:
1. If the extrapolated value is positive and the scaled value is
less than the value at the lowest torque point use the average
of the extrapolated and scaled value.
2. If the first condition is not satisfied and if the extrapolated
value is positive, use the extrapolated value.
3. If the first two conditions are not satisfied and if the scaled
zero-torque fuel rate at the given engine speed is less than
the fuel rate at the first load point, use the scaled value.
-35-
-------
4. If none of the first three conditions are satisfied set the
zero-torque fuel rate to 90% of the value at the lowest load
point.*
II. Once the best value at each speed has been determined based on
data for that engine speed alone, adjust the zero-torque values to
ensure that the fuel rate increases as engine speed increases
according to the procedure below. Start with the first engine
speed above idle. Assume that the idle fuel rate is correct
unless there is some indication that there is an error in this
value. Repeat this process for each engine speed.
1. If the zero-torque fuel rate at a given engine speed is greater
than the value at the next lower engine speed, accept the given
value for fuel rate.
2. If the first condition is not satisfied adjust the zero-torque
fuel rate at this engine speed as follows:
a. If this is the last speed point compute the zero-torque fuel
rate at this speed as the engine speed ratio
times the zero-torque fuel rate at the previous engine
speed.
b. If this is not the last speed point compute the average of
the zero—torque fuel rate at the previous engine speed and
the next highest engine speed. If this is greater than the
zero-torque fuel rate at the previous engine speed use this
average value.
c. If conditions a and b are not true compute the zero—torque
fuel rate at this speed as the engine speed ratio
(Nemrent/NprevKm.) times the zero-torque fuel rate at the
previous engine speed.
III. Steps I and II will provide zero-torque fuel rates at each engine
speed that are positive, lower than the value at the first load
point, and increasing with engine speed. The final behavior may
be irregular, however. Use the values determined in steps I and
II as the input to a regression analysis. Since engine friction
power depends on engine speed as a cubic function, the starting
point for the regression analysis should be a cubic equation with
a zero intercept.
IV. Step III will usually produce the desired final result. Some
further judgement may be used to fine-tune the final results. In
particular, the regression analysis may produce a zero-torque fuel
rate that is greater than the fuel rate at the first load point.
Such values should be adjusted downward. This is usually done by
replacing only the zero—torque fuel rates which are physically
unrealistic by the values obtained from step II for the given
The 90% number is arbitrary. Any other value (e.g. 80% or 95%)
might be used.
-36-
-------
engine speed. For some vehicles the extrapolated fuel rate at a
given engine speed was very high. Under the "bootstrap" approach
of step II such values would triger increases in the fuel rates at
all higher engine speeds. These increased zero-troque fuel values
could exceed those of the first torque point. In such cases it
was necessary to reasign the best value for that engine speed
(i.e. to return to step II) and redo the analysis. It is also
possible to try to redo the regression analysis using a linear or
quadratic fit with or without an intercept.
The decision rules outlined above in steps I to III have be automated in
a Lotus 1-2-3 macro which constructs the zero and negative torque values
for fuel rate and emissions from the most recent spread sheets supplied
to Sierra by EPA. The results are displayed graphically to help the
fine—tuning in step IV. This macro has not been used by anyone except
its author and has only minimal documentation. It can be delivered to
EPA with the understanding that it is somewhat less than a beta version
of software.
Analysis of Improved Methods for Interpolating Sharp Emissions Changes
This additional study started from the preise that the major sharp
changes in emissions are the increases in HC and CO emissions associated
with enrichment of the fuel/air mixture. Improvements to the
preliminary protocol must find ways to model this process.
Fuel enrichment is done mainly to increase engine power when the maximum
engine flow is present at a given engine speed. By definition of the
overall efficiency, rj, the engine power can be expressed as follows:
^engine = "W (F/A) tj [3.3]
As engine speed starts to increase the air flow increases, the fuel/air
ratio remains constant and the efficiency increases due to reduced
throttling losses. Near wide open throttle, when the air flow is near a
maximum, the engine power can be increased by increasing the fuel/air
ratio. Although this will decrease the efficiency, small increases in
fuel/air ratio will increase the (F/A)?; product increasing the power
output of the engine. Enrichment is also used to provide lower
temperature operation at high loads. The actual enrichment pattern is
dependent on the design decision about the need for such enrichment at
various operations loads.
As a simplified approach assume that enrichment behavior is governed
only by the only need to provide additional power when air flow is near
a maximum and further assume that some characteristic air flow variable
at which enrichment begins and/or ends can be determined. This approach
starts with an examination of some model of enrichment behavior to
determine an appropriate variable then examined the mapping data to see
if such an approach would be fruitful.
-37-
-------
The relation of the air flow rate to other engine variables is discussed
in Chapter 4. Rearrangement of equation [4.4], gives the air flow rate
as follows, where tyv is the volumetric efficiency.
"W - 1v Vd N Pin / 2 tm [3.4]
Equation [4.27] gives an empirical correlation of volumetric efficiency
with the ratio of intake to exhaust pressures as,
r?v - C, — C2 p„ / pm [3.5]
In general, Ct and C2 may depend on engine speed. However, for an ideal
cycle these constants are independent of engine speed and their speed
dependence may be neglected for this analysis. Combining these two
equations gives
*W " vd N C, p„ / 2 tB - Vd N C2 pB / 2 tm [3.6]
Assuming the dependence of inlet temperature, t,,,, and exhaust pressure,
Pej, on engine speed can be neglected in this simple analysis. Dividing
equation [3.6] by the engine speed gives the following result.
iW/N = C3 — C4 pm [3.7]
where
Cj - Vd C, / 2 tB and C4 = Vd C2 / 2 R„ t,, [3.8]
Equation [3.8] suggested the following approach:
• Examine the mapping data to determine regions where enrichment can
be well defined; call the air flow and manifold inlet pressure at
this point nv.«nCh and Pm.ennch. respectively.
• Find the air flow rates at these points from the mapping data on
fuel flow rates and air/fuel ratio and compute mair.elinch/N.
• See if any correlation exists between the value of mairennch/N for
enrichment and the measured inlet manifold vacuum or pressure, pm.
• Use this correlation to determine the enrichment points for engine
speeds where this point is not clearly defined.
• Determine a relationship between emissions concentration and other
characteristics of the enrichment point. Air/fuel ratio should be
the main variable governing these concentrations for HC and CO.
(For example it may be possible to find a relationship between
pollutant mass fraction and air/fuel ratio.)
• Use the relation bewteen emissions concentration and engine
variables to determine the emissions at the interpolated
enrichment point. (For example if pollutant mass fraction were
known as a function of air/fuel ratio, the correlated mass
fraction could be scaled by the exhaust flow rate to get the mass
emissions of the pollutant at the interpolation point.)
-38-
-------
This was tried for three engines, particularly the Geo metro, for which
a large data set is available. Two approaches were utilized. The first
approach tried to develop a correlation for lean points just before
enrichment and the first "rich" point to develop two correlation
equations—one for the start, the other for the end of enrichment. This
was not successful. The second approach defined the the enrichment
point was arbitrarily defined as a boundary air/fuel ratio.
Various values were tried for this boundary air/fuel ratio. The most
successful correlation was obtained by using linear interpolation, in
each speed range where enrichment occurred, to find the values of fuel
flow and intake vacuum for an air/fuel ratio of 13.5. The linear
regression of m^^^/N with manifold vacuum for the three engines
studied is shown in Figure 3.1. For two of the three engines there was
a good correlation matching the predictions of equation [3.7]. the air
flow per revolution, m^^^/N at a 13.5:1 air/fuel ratio, and intake
vacuum at the same air/fuel ratio, it was not possible to develop a
relation to determine how each of these quantities varied across speed
ranges. Figure 3.2 shows that both of these variables generally
increase with engine speed, but not in a predictable fashion.
Furthermore an examination of the pollutant mass fractions as a function
of air/fuel ratio for these three engines did not show a good
correlations. Figures 3.3 to 3.5 show that there is a reasonable
correlation for CO, less of a correlation for HC and no correlation for
NOx. These figures indicate that a simple process in which one
interpolates to a certain air/fuel ratio to determine the enricument
transition point should be possible for CO, may be done with some error
for HC and cannot be done for NOx. However, the values of NOx in rich
regions are low so that direct linear interpolation of the mapping data
could be used.
Tentative Proposal for Interpolation of Enrichment Point
The results of the previous section are not conclusive and require
additional confrimatory work. However, based on the results obtained so
far the following procedure may be used to determine the enrichment
point.
1. Use all data for the engine to deterine the best fit between HC
and CO concentrations (mass fractions are the perferred approach,
but parts per million can be used) and air/fuel ratio.
2. Determine the value of the air/fuel ratio for engine speeds where
the enrichment transition is considered to be well defined.
3. Use the correlation found in step 1 to find the HC and CO mass
fractions at this air fuel ratio.
4. For engine speeds where the transition is not well defined use
linear interpolation in air/fuel ratios to determine the engine
load and fuel flow rate at which the air/fuel ratio determined in
step 2 occurs.
-39-
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Interpolated Points for A/F = 13.5
Geo Metro
I I I I L
Manifold Vacuum6(in Hg)7
a Data Regression Line
Interpolated Points for A/F = 13.5
Chrysler New Yorker
3
4
5
Manifold Vacuum (iH°Hg)11
12
i)
i4
a Data Regression Line
Interpolated Points for A/F = 13.5
Saturn SL2
Manifold Vacuum (iri°Hg)11
Data Regression Line
12 1)
Figure 3.1
Correlation of Air Row Per Revolution
With Manifold Vacuum at Interpolated Point of
13.5:1 Air/Fuel Ratio
-------
Interspeed Interpolation Test
Geo Metro
1 2 Tfaoulandi A 5
Engine Speed (RPM)
Air Flow ^.Mainfold Vacuum
Interspeed Interpolation Test
Chrysler New Yorker
3000 3200
^nirneSJec^crfPl^J
.400 4600 4800
Interspeed Interpolation
Saturn SL2
Test
1SD0 .4000 _ 4500 . iQpJ)^,5SCl0
Engine Speed (RPM)
Air Flow Mainfold Vacuum
Figure 3.2
Variation in Air Row Per Revolution and
Manifold Vacuum at Interpolated Point with
13.5:1 Air/Fuel Ratio
-------
HC Mass Fractions
Geo Metro
uAir/Fuel'katio 14
NOx Mass Fractions
Geo Metro
"Air/Fuel'katio 14
CO Mass Fractions
Geo Metro
"Air/Fuel'katio
Figure 3.3
Pollutant Mass Fractions as a
Function of Air/Fuel Ratio for Geo Metro
-------
„ HC Mass Fractions fnr 1991 Chrysler Nrw Yorker
11 113 12 12.5 a . /i» « H 14 5 IS 15 5
Air/Fuel R'Mio M
VJQ Mass Fractions fnr 1991 Chrysler Nrw Ynrkftr
11 11J 12 12J . - nW , t->U5- 1* 14 5 IS 15 5
Air/fuel Ralio 14
HO Mass Frantinns fnr 1991 Chrysler Npw Ynrkpr
Air/fuel R&iio
Figure 3.4
Pollutant Mass Fractions as a
Function of Air/Fuel Ratio for Chrysler New Yorker
-------
HC Mass Fractions
Saturn SL2
105 11 111 12 Ajf/Fuef Rat/65 M "5 15 ,u
DO HC
NOx Mass Fractions
Saturn SL2
10$ 11 IIS 12
-jgsWflta a i—a i nW n ' n ' ii.
Xif/Fuef Ratio5
CO Mass Fractions
Saturn SL2
103 II US 12 >^n H 14} IS 1)]
Xlf/Fuef Ratii5
Rgure 3.5
Pollutant Mass Fractions as a
Function of Air/Fuel Ratio for Saturn SL2
-------
Although there was a reasonably successful correlation between
5. Create an interpolated point using the air/fuel ratio found in
step 2, and the fuel flow rate found in step 4. Compute the mass
rates of CO and HC at this point as m^, (1 + A/F) w,, where w, is
the mass fraction of CO or HC found in step 3.
6. Use linear interpolation to find the NOx mass rate at the
interpolation point.
7. Check the resulting pollutant emission rates to see that they are
not out of line with neighboring points.
This procedure may be regarded as a formal way to implement the
interpolation suggested in the perliminary procedure. More extensive
study of this approach should be done to determine the limits of its
applicability. For example, the use of all engine data to obtain the
relation between air/fuel ratio and HC and CO emissions may be replaced
by an examination of neighboring speed ranges only, if sufficient data
are available.
Conclusions on Mapping Protocol
A preliminary protocol for determining a complete engine map from the
data obtained by EPA in their engine mapping studies has been proposed.
The two main problems addressed are the determination of fuel and
emissions rates at zero and negative torques and the refinement of the
location of sharp increases in emissions.
Further study led to an improved procedure, which could be automated,
for the determination of the emissions and fuel rates at zero and
negative torques.
Further investigation of the sharp emissions change led to a tentative
proposal for better defining this change.
-45-
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4. CORRELATION BETWEEN INLET MANIFOLD PRESSURE
AND BRAKE-MEAN EFFECTIVE PRESSURE
Introduction
This task involved two different subtasks. One was an examination of
the (revised) engine mapping data obtained by EPA to determine the
empirical relationships between brake mean effective pressure (BMEP) and
intake manifold vacuum for these data; the other was an analytical study
of the basic relationship between these two variables. Although each of
these tasks is discussed separately below, these subtasks were done in
parallel and the fairly consistent observation of a linear relationship
between these variables motivated the analytical work to determine the
fundamental basis for this empirical observation.
Examination of Engine Mapping Data
The data analysis for this task was done on the revised set of engine
mapping data provided to Sierra by EPA. The operations on this revised
engine mapping data are described below, followed by a discussion of the
results of the analysis.
Analysis Procedures for Revised Data - The first step was to obtain a
correspondence between the initial mapping data and the revised data
set. The initial mapping data were provided to Sierra as a three-layer
Lotus 1-2-3 spreadsheet. The revised data were a modified version of
the third sheet of the original data set. Although this had the same
format as the original data set, there was not a direct correspondence
between the rows of the original and revised data sets because points
had been removed or added in generating the revised data set.
The engine torques used in the EPA mapping data were found from
measurements of dynamometer torque and calculations of the equivalent
load on the engine. This was done by using a calculation procedure
similar to the one used in the VEHSIM vehicle simulation program. In
some cases where load measurement problems occurred, such as during
excessive tire slip on the dynamometer, the torque was estimated by
linear interpolation or extrapolation of BMEP and manifold pressure
data. Part of EPA's interest in this task was to have Sierra determine
the validity of this interpolation/extrapolation for the mapping data.
In order to do this, we generated a data set which included only points
for which the torque was found by measurement (and appropriate
calculation of the engine torque equivalent to the measured dynamometer
-46-
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torque.) The following tasks were done by a series of Lotus macros and
a spreadsheet template.
1. Copy the final three columns of the torque calculations from the
initial engine mapping spreadsheet to allow a comparison between
old and new data sets.
2. Copy the air/fuel ratio from the old data set to the revised data
spreadsheet for use in subsequent calculations.
3. Compute the volumetric efficiencies for the engine mapping data to
observe the behavior of this quantity which was shown to play a
role in the relationship between BMEP and manifold pressure.
4. Create a series of named ranges for use in generating graphs and
linear regression calculations of BMEP and manifold pressure.
5. Generate graphs, linear regression coefficients, and output for
BMEP and manifold pressure at each engine speed.
The torque columns on the original data set were used to determine the
data points for which the torque values were actually obtained from
dynamometer measurements and VEHSIM-like calculations. The previous
torque data had three final columns that showed the torque determined
from the dynamometer measurements and the VEHSIM-like calculations,
notations if any problems were observed with the measurements, and the
value of torque actually used for the final results. Data points for
which EPA's calculated torque value were not the same as the one used in
EPA's final results were ignored in our analysis of the relation between
BMEP and manifold pressure. These data points were already established
by assuming a linear relationship between BMEP and manifold pressure and
their use in any analysis of the relationship between these two
variables would bias the analysis.
The air/fuel ratio was copied from the original data set so that the
mass fraction of the exhaust emissions could be computed for our
presentation of emissions data in the final report. It was also used to
compute the volumetric efficiency as discussed in the next paragraph.
After copying the air/fuel ratios and the final torque columns from the
initial data set to the revised data set, it was necessary to edit these
data to obtain the correct values for the revised data set.
The analysis in the next section shows that the volumetric efficiency is
a key parameter in the relationship between manifold inlet pressure, Pm,
and BMEP. Equation [4.7] provides the relationship between these
variables as:
BMEP ~ rjv (F/A) P„ / (BSFC) R„ T,.
where qv is the volumetric efficiency, F/A is the fuel/air ratio, BSFC
is the brake specific fuel consumption, R^,. is the gas constant for air
and Tm is the inlet manifold temperature. This equation was rearranged
as follows to compute the volumetric efficiency from the mapping data.
rjv - BMEP (A/F) BSFC Tm / Pm
-47-
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All data in this equation, except for the inlet manifold temperature,
are available in the mapping data. The inlet manifold temperature was
assumed to be 500 R for computing the volumetric efficiency. The
volumetric efficiency increased with manifold pressure as expected. The
only concern was that some data points have a volumetric efficiency
greater than 100%. This might have been due to the assumption of a
constant value of 500 R for the manifold inlet temperature. Although
the computed engine torque is used to determine the BMEP and BSFC, it
cancels when these two quantities are multiplied. Thus, any errors in
the engine torque measurement/calculations would not affect this
calculation. There may have been some errors in the other experimental
quantities that are used to find the terms in this equation (fuel rate,
air/fuel ratio, manifold inlet pressure, inlet speed). Absent such
errors, the volumetric efficiencies that were greater than 100% would
presumably be caused by the supercharging effect of pressure waves in
the intake manifold runners.
The final set of BMEP and inlet manifold pressure used for this analysis
was set up as named ranges in the spreadsheet. These named ranges were
then used in plots and regression analyses of the data. This process
retained all the data on the spreadsheet while using the appropriate
subset for the analysis here.
Experimental Variation of BMEP with Inlet Manifold Pressure — A linear
regression analysis of BMEP versus manifold pressure, at a given engine
speed, was done for all engine mapping data. The full regression
procedure, including the computation of the standard error, requires at
least three data points for the regression. The data were fitted to the
following equation:
BMEP = a + b p„
The results for each vehicle and each engine speed are presented in the
tables attached to this memo. The values in the tables include the
number of data points available at the particular engine speed, the
slope, b, and the intercept a. In addition, the standard error of the
estimated BMEP values, ay|x, and the R2, the square of the correlation
coefficient, are listed. The values for R2 show an almost perfect
correlation for most of the engine speeds as summarized in the table
below:
Total Number of Speed Correlations 214
Speed Correlations with R2 > .980 182
Speed Correlations with R2 > .950 207
Speed Correlations with R2 > .900 212
The standard error for the predicted BMEP is correspondingly small. In
only ten cases is this standard error greater than 7.0 psi. Two typical
plots of experimental data points and the corresponding least squares
line are shown in Figure 4.1. The data at 3200 RPM have an R2 value of
0.9987 and a standard error of 1.3 psi in BMEP. This is an example of
the best linear agreement. The data at 4060 RPM have an R2 value of
0.95 and a standard error of 7.2 psi in BMEP. This is an example of the
poorer agreement in some correlations.
-48-
-------
Figure 4.1
Example of Linear Regression Fits
1990 Ford Ranger XLT Truck 2.3L L40D
Data and Regression Line at 3200 RPM
100
0
K
"Manifold Absolute Pressure (IcPa)
100
90
1990 Ford Ranger XLT Truck 2.3L L40D
Data and Regression Line at 4060 RPM
^100 -
w
Cu
N-/
cu
W
2
30 ^Manifold Absolute Pressure (IcPa) 50 icn
Although the observed correlations are very good, there is a need for
caution in using data for extrapolation. Data for the Chrysler New
Yorker at two different engine speeds were fitted using the full data
set and a partial data set. The fitted line for the partial data set
was then extrapolated to higher manifold pressures and the predicted
results were compared to the experimental ones. These results, shown
graphically in Figure 4.2, are an example of potential problems that can
arise in extrapolation.
The regression lines for the full data set at the two engine speeds
shown on these charts are as follows:
RPM ~ 2222 R2 = 0.97 ay|x ~ 8.8 psi N = 4
RPM = 3320 R2 = 0.98 ay|x = 6.4 psi N = 10
The partial fits, using the lower manifold pressure points only, have
the following regression statistics.
RPM ~ 2222 R2 = 0.99 ay[x = 4.3 psi N ~ 3
RPM = 3320 R2 = 0.98 ay|x = 3.7 psi N ¦=• 6
-49-
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Figure 4.2
Example of Extrapolation Error
1991 Chrysler New Yorker 3.3L L4
Data and~Regression Line at 2222 RPM
1991 Chrysler New Yorker 3.3L L4
Error in Extrapolauon at 2222 RPM
ftfamfoTd Absolute Pressure ^kPa)
ftlanifoTd Absolute Pressure ^kPa)
1991 Chrysler New Yorker 3.3L L4
Data andRegression Line at 3320 RPM
1991 Chrysler New Yorker 3.3L L4
Error in Extrapolation at 3320 RPM
N?anifofd Absolute Pressure"OcPa)"
Ivfanifofd Absolute Pressure"QcPa)"
When the regression lines formed from a partial set of data at lower
engine loads are extrapolated to find the BMEP values at high manifold
pressures, the following errors occur: (1) at 2222 RPM, the BMEP is
overpredicted by 15%; (2) at 3320 RPM, the four extrapolated points are
underpredicted by 8%, 18%, 16%, and 15% as manifold pressure increases.
The lines fitted to the partial data sets have a smaller standard error
than those fitted to the complete data sets. The direction of the error
is not consistent—the BMEP is overpredicted at one engine speed,
underpredicted at another.
A review of the data for the empirical correlations of BMEP with
manifold pressure shows a remarkable consistency. For almost all the
engines and all engine speeds, the slope lies between 1.3 and 2.2
psi/kPa and the intercept lies between -20 and -80 psi. This range of
values is consistent with the theoretical analysis in the next section
-50-
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and the order of magnitude values computed there of 1.9 kPa/psi and -33
psi for the slope and intercept, respectively. Some exceptions to these
observed ranges are noted below.
• The Volvo 740 at 2000 RPM has the poorest correlation (R2 = 0.497)
and standard error (23.4 psi). This is probably due to a bad data
point that has a decrease in BMEP at the highest inlet manifold
pressure.
• The Ford Escort at 4700 RPM, with only three data points, has a
small slope.
• The Ford F250 has generally smaller slopes for all speed ranges.
This truck has a 5.8 liter engine, the largest displacement in all
of the engines tested.
• The Ford Ranger at 1630 RPM has a small slope. This line has only
three data points.
• The GMC Sierra pickup, with a 5.0 liter displacement, has a small
slope at all engine speeds.
• The Saab 9000 has slopes similar to other engines at the first
four engine speeds, but the slopes are much higher at the five
highest engine speeds.
EPA certification data for the four European cars (Saab, Volkswagen,
Volvo and Mercedes) were reviewed to determine that only the Mercedes
had exhaust gas recycle (EGR). EGR would be expected to increase the
manifold pressure required per psi of BMEP; howeer, no difference in the
relationship of BMEP to manifold pressure that could be attributed to
EGR was observed for these vehicles.
Plots of all the data of BMEP versus inlet manifold pressure are
included in Appendix B.
Analysis of The Theoretical Relationship Between BMEP and Intake
Manifold Pressure
The starting point for this analysis was the use of the volumetric
efficiency of the engine which can be related to the inlet manifold
pressure, pm. (For this study, the absolute pressure is a more
convenient variable than the manifold vacuum.) The volumetric
efficiency can be defined as follows:29
rjv - 2 m^, / pBirin Vd N [4.1]
where
r)v = Volumetric Efficiency
m,,, ~ Mass flow rate of air into the engine
-51-
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Pna.m " Density of air in the intake manifold
Vd = Displacement volume
N - Engine speed
This definition of volumetric efficiency, which uses the air density in
the intake manifold, is a measure of the pumping performance of the
inlet port and valve only. It is also possible to define the volumetric
efficiency in terms of the intake (ambient) air density; in this case,
the volumetric efficiency measures the efficiency of the entire intake
system, including elements of the system (e.g., mass air flow sensor and
air cleaner) that are upstream of the manifold.30 The air density can
be related to the pressure through the ideal gas law:
Pair.in ™ Pair,in / ^atr ^in [ ^ • 2 ]
where
Poir.in = Partial pressure of air in the intake manifold
R,,,. ~ Gas constant for air
tm ~ Intake manifold temperature
Ignoring EGR, the mole fraction of air in the intake manifold is nearly
one for typical gasolines and we can assume that the partial pressure of
air in the intake manifold is essentially the same as the intake
manifold pressure, pm:
[4.3;
With this substitution in the ideal gas equation, the volumetric
efficiency equation becomes:
r/v - 2 nv tm / Pm Vd N [4.4]
The brake mean effective pressure (BMEP) is defined (for a four—stroke
engine) as
BMEP ~ 2 P^ / Vd N [4.5]
The engine power, P^g^, can be replaced by the brake specific fuel
consumption, (BSFC) , and the fuel flow rate, m^,, giving
BMEP - 2 m^, / (BSFC) Vd N [4.6]
If this equation is divided by equation [4.4] for volumetric efficiency,
the relation between BMEP and intake pressure is obtained:
BMEP - r,v (m^AO / (BSFC) R^ tB [4.7]
The basic relation between engine load, expressed as BMEP, and intake
manifold pressure is thus related via the engine variables of volumetric
efficiency, fuel/air ratio, BSFC, and inlet manifold temperature. Over
-------
a range of speeds, the intake manifold temperature—expressed as an
absolute temperature—will be essentially constant. Thus, it is the
combination, rjv (F/A) / BSFC, that governs the relationship between the
BMEP and the intake manifold pressure. The changes in each of these
variables, for a given engine speed, is considered further below.
Studies of volumetric efficiency are usually directed at wide open
throttle behavior where the air flow rate limits the engine performance.
The behavior of volumetric efficiency under throttled conditions can be
found, for an ideal cycle, from the equation31
where pex is the exhaust pressure, rc is the compression ratio, and 7 is
the specific heat ratio. This ideal equation shows that the volumetric
efficiency is one when the exhaust and intake pressures are equal; for
throttled operation where pm/pex is less than one, the volumetric
efficiency decreases.
In actual engine operation, the volumetric efficiency depends on engine
speed, inlet and exhaust temperatures, as well as the ratio of exhaust
to inlet pressure. (It also depends on engine design variables such as
compression ratio and valve sizes.) However, the main variable that
represents the effect of part-throttle operation on volumetric
efficiency is the exhaust/inlet pressure ratio.32
The volumetric efficiency will also be affected by the operation of
exhaust gas recirculation (EGR). The exhaust gases that are
recirculated at a given engine operating condition will reduce the
amount of air flow available into the cylinder. However, Servati and De
Losh33 developed a correlation equation for volumetric efficiency for
one Ford 4.9 liter engine which gave good agreement between predicted
and measured results with no parameters to account for EGR operation.
The effect of EGR probably entered their correlation through other
parameters such as the intake/exhaust pressure ratio. Their correlation
showed a linear dependence on this p„/pm ratio.
It is also possible to make a slight revision to the above analysis to
explicitly consider the effect of EGR on the volumetric efficiency. At
wide open throttle operation, where there is no EGR, the only gases in
the cylinder result from intake air/fuel and from residual gas. The
volumetric efficiency should measure the pumping capacity of the engine
for bringing in new cylinder gas. Thus, when EGR is present the
definition of volumetric efficiency should be modified to be34
The difference between this equation and equation [4.1] depends on the
definition of volumetric efficiency. With the original definition, two
engines with the same intake system design would show different
volumetric efficiencies, for the same mass flowing into the cylinder, if
one engine used EGR and the other one didn't. With the modified
definition, the two engines should show the same volumetric efficiency.
r>v - (7 - l)/7 + (rc - pex/pj / 7(rc - 1)
[4.8]
= 2 ("W + ^gr) / Pw.m Vd N
[4.9]
-53-
-------
If the relative EGR rate, fegr, is defined as
^egr " megr/m»ir [4.10]
the modified volumetric efficiency equation can be written as
I*' " 2 iv (1 + fegr) / Paum Vd N [4.11]
This is simply related to the previous definition of volumetric
efficiency,
r?v' - (1 + f^) r/v or rjv - ' / (1 + fegr) [4.12]
For engines without EGR, fegr is always zero and both definitions of
volumetric efficiency are the same. For engines with EGR, the EGR
fraction will decrease as load is increased until some point where the
EGR is discontinued giving fejr = 0. Thus, we expect that fegr will
decrease as load is increased.
If the modified volumetric efficiency relation in equation [4.12] is
introduced into the BMEP/Pm relation in equation [4.7], the following
result is obtained:
(BMEP) = ,v'
-------
written as the gross (or indicated) engine power, P^,, less the power
due to rubbing friction, Prft and due to pump work,* | Pp,,mr 1 :
Pbrake "* P|nd — Prf — I Ppump I [4.16]
The reciprocal brake-specific fuel consumption then becomes:
(BSFC)'1 - (P^ - Prf - IPp^l) / m^, [4.17]
The air/fuel ratio can be introduced into this equation giving
(BSFC)"1 - (A/F) (P^ - Prf - IP^I) / nw [4.18]
This expression can be substituted into equation [4.14] for r to
eliminate the BSFC term. Doing this and simplifying gives:
rp - < «l, (F/A) / Rmt tm ) * ( (A/F) (P^
- Prf - IPpumpI) / ®sir [4.19]
rp - [ r?v (P^ - Prf - IPpun.pl) 1 / [ Kr nu ] [4.20]
The terms (P^ - Prf) / m^ represent the gross and friction power per
unit mass of air charged. These quantities should be relatively
independent of inlet pressure." It will, however, depend on the
engine speed. We can define a new quantity, C3(N), as follows.
C3(N) - (P^ - Prf) / ( nv tB ) [4.21]
This quantity should be only a weak function of intake pressure and, for
this analysis, is assumed to be a function of engine speed only.
Substituting this into equation [4.20] gives:
rp ~ »»v C,(N) - ( r?v|Ppuinp| ) / ( t. ^ ) [4.22]
The pumping power that appears in these equations will have a strong
dependence on the inlet pressure. For an ideal cycle, the pumping work
is given by the equation:
I Ppump,ideal I — (Pex — Pin) ^d ^ / 2 [4.23]
This ideal cycle result will be substituted for |Ppump| in the analysis
here. This will be more nearly correct when the pumping work is small,
*The pumping power is written in absolute value signs to indicate
that it is the positive value of this term that is intended here.
Thermodynamic convention in cycle analysis would make the pump work a
negative quantity.
"This statement is true for a fixed air/fuel ratio. For high
output power, with richer fuel mixtures, the net power per mass of air
will increase. Thus, any empirical results that are compared with this
analysis would not be expected to agree for points where the engine has
rich operation.
-55-
-------
i.e., at high manifold pressure. When the manifold pressure is low and
the pumping work is high, the error from introducing this ideal equation
will increase. Substituting the ideal pump work for the pump work term
in equation [4.22] gives the following result:
rp - »jv Cj(N) - [ «;v (P„ ~ Pb) vd N ] / [ 2 tm ] [4.24]
Rewriting the definition of volumetric efficiency from equation [4.11]
as ijv Vd N / (2 m^) = 1 / and substituting this result into
equation [4.24] gives:
rP - 1V Cj(N) - (p„ - pj / ( Kr ) [4.25]
Applying the ideal gas law, Ptum = pm / tm, gives the following
equation for rp
rP = Cj(N) - (pex/Pin - 1) [4.26]
The discussion of volumetric efficiency given above noted that this
efficiency depended linearly on the ratio of exhaust to intake pressure
in both the ideal cycle analysis and in observed experimental data.
This general result can be summarized by the following equation:
Vv ™ C,(N) — C2(N) Pex/Pin [4.27]
Here C,(N) and C2(N) are regarded as empirical "constants", depending
only on the engine speed. These empirical terms account for changes in
volumetric efficiency caused by engine speed. Equation [4.27] is also
consistent with equation [4.8] for the ideal cycle volumetric efficiency
if we define:
Ci- (7 - l)/7 + rc / 7(rc - 1) and C2 - 1 / 7(re - 1) [4.28]
Substituting equation [4.27] for the volumetric efficiency into equation
[4.26] and rearranging gives
rp - [ C,(N) - C2(N) p„/Pin ] Cj(N) - (Pejt/Pin - 1) [4.29]
rp = [ C,(N) Cj(N) + 1 ]
- [ C2(N) C3(N) + 1 ] p„/pm [4.30]
The dependence of rp on pm given in this equation has the simple form,
rp(N) = «(N)/Pin + ^(N) [4.31]
if the following definitions are made,
/?(N) = [ C,(N) Cj(N) / tm + 1 ] [4.32]
and
q(N) - - [ C2(N) Cj(N) / tm + 1 ] Pex [4.33]
-56-
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Substituting the definition of rp = BMEP/pm into equation [4.31] gives
the result that BMEP should have a linear dependence on p,,, for the
conditions assumed in this derivation.
BMEP - a(N) + /3(N) pm [4.34]
There are three important conditions that limit the applicability of
this equation:
• The engine pumping work is taken to be the pumping work for the
ideal cycle. This will make equation [4.34] less accurate at
lower manifold pressures where the pumping work becomes
significant.
• The gross work per unit mass of air is assumed to depend only on
the engine speed. This will make the equation less valid at
higher manifold pressures when the air/fuel mixture is fuel-rich
giving more power per mass of air.
• a(N) will depend on manifold pressure because it is proportional
to the exhaust pressure. The exhaust pressure increases with
inlet manifold pressure at a given engine speed. This variation
increases at higher engine speeds. In one example, there was
about a 25% increase in exhaust pressure at the highest engine
speed as the intake pressure increased from 40 kPa to 100 kPa.35
Thus, the linear dependence of BMEP on manifold inlet pressure given in
equation [4.33] can be expected to hold for moderate inlet pressures,
but should be extrapolated to very high or very low inlet pressures with
caution. Also, this derivation started from equation [4.14] which did
not take explicit account of EGR in the definition of volumetric
efficiency.
In order to account explicitly for EGR, equation [4.15] is used for the
definition of rp. Substituting equation [4.18] for (BSFC)"1 into [4.15]
and rearranging gives:
rp - { nv' (F/A) / [ (1 + fcgr ) R^ tj ) • { (A/F) (P^
" - |PpumpD / "W [4.35]
rP - 1v' - Prf - IPpompI) / Id + f„r) Kr tB n,J [4.36]
In this case define C3'(N), analogous to the definition of C}(N) in
equation [4.21],
Cj'(N) = (P^ - Prf) / [in.,, (1 + fegr) R.,, tu ] [4.37]
Here C3'(N) represents the gross power minus the rubbing friction power
per unit mass of air plus recycled exhaust into the cylinder. This will
change if the EGR fraction changes. Substituting this definition of
Cj'(N) and the definition of the ideal pumping power from equation
[4.23] into equation [4.36] gives
-57-
-------
rp - «?v' Cj'(N)
- [ fv' (Pcx - Pm) Vd N ] / [ 2 (1 + f^) th n^] [4.38]
Rewriting the modified definition of volumetric efficiency from equation
[A. 11] as tjw' Vd N / [2 (1 + f^) m^] - 1 / and substituting this
result into equation [4.38] gives:
rp - 1y' Cj'(N) - (p„ - pm) / ( Ptaa R^ tm ) [4.39]
Applying the ideal gas law, PtaM - Pin / R^ tm, gives the following
equation for rp
rP - »?v' Cj'(N) - (pex / pm - 1) [4.40]
This equation is exactly the same as equation [4.26], except that the
modified volumetric efficiency is used here. We assume that the
dependence of this modified volumetric efficiency can be represented by
an equation of the same form as equation [4.27], i.e.,
- C,»(N) - Cj'(N) pex/Pin [4.41]
The substitution of equation [4.41] into equation [4.40] proceeds in
exactly the same way as the previous derivation where equation [4.27]
was substituted into equation [4.26].
rp - [ C,'(N) - Cj'(N) p„/PlI1 ] C}'(N) - (Vex/Vm - 1) [4.42]
rp - [ Cj'(N) Cj'(N) + 1 ]
- [ Cj'(N) C,'(N) + 1 ] pex/pm [4.43]
The dependence of rp on pm given in this case has the simple form, as in
the case where EGR was not considered:
rp(N) - a'(N)/Pin + 0'(N) [4.44]
Here the following definitions are made,
P'(N) - [ C,' (N) Cj'(N) + 1 ] [4.45]
and
a'(N) - - [ C2'(N) C,'(N) + 1 ] P„ [4.46]
Substituting the definition of rp = BMEP/p,,, into equation [4.44] gives
the result that BMEP should have a linear dependence on pm for the
conditions assumed in this derivation.
BMEP = o'(N) + j9'(N) pm [4.47]
-58-
-------
There are four important conditions that limit the applicability of this
equation:
• The EGR fraction is constant. If this is not the case, the
collection of terms which involve C3' will change and both a'(N)
and fi' (N) will depend on the manifold pressure.
• The engine pumping work is taken to be the pumping work for the
ideal cycle. This will make equation [4.34] less accurate at
lower manifold pressures where the pumping work becomes
significant.
• The gross work per unit mass of air is assumed to depend only on
the engine speed. This will make the equation less valid at
higher manifold pressures when the air/fuel mixture is fuel-rich
giving more power per mass of air.
• q'(N) will depend on manifold pressure because it is proportional
to the exhaust pressure. The exhaust pressure increases with
inlet manifold pressure at a given engine speed. This variation
increases at higher engine speeds.
Equations [4.34] and [4.47] for the case of no EGR and EGR,
respectively, show that under given conditions we can expect a linear
dependence of BMEP on intake manifold pressure. This has also been
observed experimentally in the EPA engine mapping data discussed
earlier. Although this analysis provides support for the use of linear
interpolation, extrapolation to engine operation at high manifold
pressures where enrichment takes place or to low manifold pressures
where the pumping work is significant, are not justified by the results
here. In addition, the use of linear interpolation in regions where EGR
operation is taking place and the EGR fraction is changing is not
justified by these results.
In order to compare the analysis of this section with the results of the
previous section, an order of magnitude estimate of a(N) and /J(N) was
carried out for the case of no EGR. The values of C,(N) and C2(N) were
estimated from the ideal cycle values given in equation [4.28]. The
effective value of the specific heat ratio, 7, was assumed to be 1.3 and
the compression ratio, rc, was assumed to be 9. This gives the
following values for these dimensionless quantities:
Cj = 1 and C2 = 0.1
Equation [4.21] is used to compute C3(N) = (P^, - Prf) / (j^ tm ) .
This was estimated by using the gas constant for air as 0.06655 BTU/lb-R
and assuming the inlet temperature was 500 R. The term (P^ - Prf) / m^
was estimated by assuming (1) a 15:1 ratio for m^/m^, (2) that (P^, -
Prf) is about 30% of the fuel energy m^ Q,., and (3) the heat of
combustion of the fuel is 20,000 BTU/lb. This gives the dimensionless
value of C3 as
C3 - 12
-59-
-------
When the values of C,, C2, and C3 are substituted into equations [4.32]
and [4.33] for /?(N) and a(N), with an assumed exhaust pressure of 15 psi
(absolute), the following values are obtained:
a -33 psi and /3 « 13 [dimensionless]
or p =» 1.9 psi/kPa
These values are the same order of magnitude as the linear regression
constants obtained when the BMEP was fit to the manifold pressure.
Conclusions from this Task
The measured correlation between BMEP and inlet manifold pressure is
quite good for almost all of the engines and speed ranges considered.
An analysis of the expected behavior of BMEP and inlet manifold
pressure, at a given engine speed, shows that a linear relationship
between these two variables can be expected under certain conditions.
The experimentally observed regression coefficients in the equation BMEP
- a + b Pm have the same order of magnitude as predicted from the
analysis in all cases except one.
Extrapolation of an experimental linear relationship between BMEP and
inlet manifold pressure has been shown to produce errors in experimental
data and violated the conditions used to derive an analytical linear
relationship between these two variables.
The analytical results do not provide any useful guidance on a non-
linear extrapolation approach. Although linear extrapolation should be
used with caution, it is the most reasonable approach to use in the
absence of any data.
-60-
-------
5. LIST OF SYMBOLS
a
Empirical constant in equation for fuel energy
rate (kJ/rev)
a'
Empirical constant (~ a/Vd — kJ/liter-revolution)
b
A/F
Empirical constant in equation for fuel energy
(dimensionless).
Air/Fuel ratio
rate
BMEP
Brake-mean effective pressure (psi)
BSFC
Brake—specific fuel consumption (lbuj/HP—hr)
fc8r
Ratio of EGR flow to total of air plus EGR flows
m
Mass flow rate (lb/sec or kg/sec)
Mass flow rate of air.
Mass flow rate of fuel.
m.
Mass flow rate of i"1 pollutant species.
^exhaust
Molecular weight of exhaust.
M.
Molecular weight of i"1 pollutant species.
N
Engine speed (RPM)
P
Pressure (psi or kPa)
P
engine
Engine brake power output (HP or kW)
Pfud
Fuel energy rate (~ m^, Q,. — HP or kW)
p
fncttoa
Power required to overcome all friction (HP or
kW)
P.nd
Indicated or gross power (HP or kW)
P
ptimp
Pump work (HP or kW)
Prf
Total friction power minus pump work (HP or kW)
ppm,
Parts per million (by volume) for species i.
Kr
Gas constant for air
-61-
-------
rc Compression ratio
rp Ratio of BEMP to manifold inlet pressure
T Torque (ft-lbf)
tm Temperature of intake manifold (R)
Vd Engine displacement volume (in5 or liters)
Wj Weight fraction of i"1 pollutant species
q(N) Constant in linear equation between BMEP and pm (psi)
/?(N) Coefficient of pm in equation for BMEP (dimensionless or
psi/kPa)
7 Ideal gas specific heat ratio (dimensionless)
ri Overall engine efficiency
fjv Volumetric efficiency
»7V' Modified volumetric efficiency for explicit consideration of
EGR
Air density (lb/ft3 or kg/m3)
-62-
-------
6. REFERENCES
1. Feng An, Automobile Fuel Economy and Traffic Congestion, Phd
Dissertation, University of Michigan, 1991. (Subsequently
referred do as An, Dissertation.)
2. Marc Ross and Feng An, "The Use of Fuel by Spark Ignition
EnginesDraft for Review from Applied Physics Department,
University of Michigan, May 18, 1992.
3. An, Dissertation, p. 47.
4. Ross and An, op. cit., p. 7.
5. An, Dissertation, p. 38.
6. Ross and An, op. cit., p. 5.
7. An, Dissertation, p. 84.
8. Bosch, Automotive Handbook (1st English edition), 1976, pp.218-
223.
9. An, Dissertation, p. 75.
10. An, Dissertation, p. 83.
11. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill
1988, p. 719
12. An, Dissertation, p. 32.
13. Russell W. Zub, "A Computer Porgram (VEHSIM) for Vehicle Fuel
Economy and Performance Simulation (Automobiles and Light
Trucks)," Report DOT-HS-806-037, U. S. Department of
Transportation, Transportation Systems Center, Cambridge, MA,
October, 1981.
14. An, Dissertation, p. 36.
15. An, Dissertation, p. 116.
16. Heywood, op. cit., Chapter 14.
17. J. I. Ramos, Internal Combustion Modeling, Hemisphere, 1989.
-63-
-------
18. Engine Combustion Analysis: New Approaches, P—156, Society of
Automotive Engineers, February, 1985. This is somewhat dated, but
provides a good introduction to the field.
19. A. A. Amsden, P. J. O'Rourke, and T. D. Butler, "KIVA-II: A
Computer Program for Chemically Reactive Flows with Sprays," Los
Alamos National Laboratory, Report LA-11560-MS, May 1989.
20. H. C. Watson, et al., "Predicting Fuel Consumption and Emissions—
Transferring Chassis Dynamometer Results to Real Driving
Conditions, SAE Paper 830435, Detroit, February 28, March 4, 1983.
21. H. C. Watson, et al., "In-use Vehicle Survey of Fuel Consumption
and Emissions on Dynamometer and Road," SAE Paper 850524, 1985.
22. Yoshihary Hori, Mizuho Fukada, and Yoichi Kobayashi, "Computer
Simulation of Vehicle Fuel Economy and Performance," SAE
Transactions, v. 95, pp. 2.652-2.665, 1986. (Paper Number 860364)
23. Mikio Matsumoto, et al., "Improvement of Lambda Control Based on
an Exhaust Emission Simulation Model that Takes into Account Fuel
Transportation in the Intake Manifold," SAE PAper 900612, Detroit
Michigan, February 26-March 2, 1990.
24. Thomas C. Austin, Thomas R. Carlson, and John M. Lee, "Estimating
the Effect of Driving Pattern on Exhuast Emissions Using a Vehicle
Simulation Model," Prepared for EPA, Certification Division,
Office of Mobile Source Air Pollution Control, October 1990.
25. Thomas C. Austin, Thomas R. Carlson, and John M. Lee, "Development
of an Improved Computer Simulation of Vehicle Emissions During
Cold Start and Warm-Up Operation," Sierra Research, Inc. report
for EPA Certification Division, Work Assignment 1-02 under
Contract 68-C9-0053, September 30, 1991.
26. David S. K. Chen, Edward J. Bissett, Se H. Oh, and David L. Van
Ostrom, "A Three-Dimensional Model for the Analysis of Transient
Thermal and Conversion Characteristics of Monolithic Converters,"
SAE Paper 880282, Detroit, February 29-March 4, 1988.
27. Heywood, op. cit., Chapter 11.
28. Golden Software, Inc.,'SURFER* Reference Manual, P. 0. Box 111,
Golden, CO 80402.
29. 29.
30. ibid.
31. C. F. Taylor and E. S. Taylor, The Internal Combustion Engine,
International Textbook Company, 1961, p. 238.
32. Taylor and Taylor, op. cit., pp. 243-244 provide a dimensional
analysis to show that the effect of inlet and exhaust pressure
-64-
-------
enter the functional equation for volumetric efficiency only
through the p^/p,,, ratio.
33. H. B. Servati and R. G. DeLosh, "A Regression Model for Volumetric
Efficiency," Paper 860328 at SAE International Congress, Detroit,
MI, February 24-28, 1986.
34. This is similar to a definition of volumetric efficiency which
accounts for both the intake charge and the residual gases given
in the text, Internal Combustion Engines, by Benson and Porter
(Cited in Kimon Roussopoulos, "A Convenient Technique for
Determining Comparative Volumetric Efficiency," SAE Paper 900352
at International Congress, Detroit, February 26-March 2, 1990.)
35. Heywood, op. cit., p. 214.
-65-
-------
APPENDIX A
ENGINE EMISSION MAPS
-------
i&WsM
Bu l ck LeSabre Ta LI Pipe NOx ( gm/sec)
-v ,t£*
Surface Plots of Emissions for
1990 Buick LeSabre 3.0L L40D
-------
Ce ma ro ITe LI Pipe CO ( g m/s e c)
Surface Plots of Emissions for
1991 Chevrolet Camaro 5.7L L40D
-------
Ceval ler Tell Pipe HC (gm/sec)
Ca v a I Ler Tall Pipe NOx ( g m/s e c)
Ceval ler Tell Pipe CO (gm/sec)
Surface Plots of Emissions for
1990 Chevrolet Cavalier 2.2L L3
-------
Ne w Yorker T
m/s e c)
' "«#•
-------
r o ui n
-------
Surface Plots of Emissions for
1991 Ford Probe 2.2L L4AEOD
-------
Ford Re n g e r
CO ( g m/s e c)
y
o
Surface Plots of Emissions for
1990 Ford Ranger 2.3L L40D
-------
Ge o riatro Tall Pipe NOx C g m/s e c )
Surface Plots of Emissions for
1992 Geo Metro 1,0L M50D
-------
Tall Pipe CO ( g m/s e c )
i
vO
i
Surface Plots of Emissions for
1990 GMC Sierra 5.0L L40D
-------
Me r c 0 d e s 300E
HC ( g m/s e c )
Mercedes 300E
CO ( g m/s e c)
Surface Plots of Emissions for
1992 Mercedes Benz 300E 3.0L A4
-------
Surface Plots of Emissions for
1991 Volkswagen Jetta 1.8L A3
-------
APPENDIX B
REGRESSION ANALYSIS TABLES AND CHARTS:
CORRELATION BETWEEN BRAKE-MEAN EFFECTIVE PRESSURE
AND INLET MANIFOLD PRESSURE
The following set of tables shows the linear regression coefficients
(slope and intercept) as well as the correlation coefficient squared
(R2) and the standard error in the estimated BMEP (ffy|x). The data are
shown for each engine at each speed for which three or more data points
are available to obtain the correlation.
Following the tables, a plot of the experimental variation of BMEP with
inlet manifold pressure is shown for each engine.
-------
1990 PONTIAC 6000
4 DR SEDAN 3.1 L L40D
VIN: 1G2AF54T2L6211503
RPM Slope Intercept
psi / kPa
psi
1370
1.468
-43.20
2030
1.682
-44.08
2680
1.757
-50.85
3325
1.860
-53.53
3950
1.718
-41.27
4600
1.337
-33.45
5000
1.367
-38.63
5420
1.348
-42.54
R2 ay|x No of Data
Points
0.9983 0.3281 3
0.9725 7.5744 4
0.9977 1.6765 5
0.9807 6.5840 5
0.9844 5.4083 9
0.9979 1.2071 4
0.9999 0.4177 3
0.9983 1.4944 3
1991 VOLVO 740
4 DR SEDAN 2.3 L L40D
VIN: YV1FA8845M2514833
RPM Slope Intercept
psi / kPa
psi
1360
2.924
-96.80
2000
0.952
-4.86
2630
1.717
-41.70
3260
1.717
-54.24
3950
1.495
-41.42
4540
1.471
-49.45
4900
1.670
-70.65
5350
1.546
-65.71
R2 av,x No of Data
y\x
Points
0.9755 2.9552 4
0.4974 23.4387 4
0.9960 2.7103 5
0.9507 9.9048 5
0.9840 3.5075 6
0.9769 4.9086 4
0.9925 2.8170 4
0.9949 1.7535 4
1990 CHEV CAVALIER
4 DR WAGON 2.2 L L3
VIN: 1G1JC84G91J187781
RPM Slope Intercept R2 cry(x No of Data
psi / kPa
psi
Points
1240
2.303
-80.05
0.9983
0.6287
3
1810
1.790
-61.60
0.9869
5.5093
4
2400
1.821
-62.46
0.9982
2.1389
4
2975
1.687
-51.65
0.9982
1.6402
5
3550
1.912
-67.96
0.9976
1.8470
9
4140
1.692
-56.01
0.9888
3.9043
7
4500
1.770
-62.52
0.9968
2.3156
6
4880
1.828
-69.18
0.9980
1.7814
5
-1-
-------
1991 FORD F150
4x2 PCKUP 4.9 L L4AE0D
VIN: 1FTEF15Y4MLA82098
RPM
Slope Intercept
R2
yl*
No of Data
psi / kPa
psi
Points
1190
1.537
-55.93
0.9497
9.2199
4
1760
1.624
-56.69
0.9828
5.6242
3
2325
1.655
-56.10
0.9932
3.3850
11
2930
1.289
-43.30
0.9910
3.2246
3
3180
1.691
-67.63
0.9813
5.6080
5
1991 FORD ESCORT LX
2 DR HTCHBCK 1.9 L L4AE0D
VIN: 1FAPP14J7MW137707
RPM
Slope Intercept
R2
yl*
No of Data
psi / kPa
psi
Points
1270
1.535
-35.82
0.9748
5.6275
4
1870
1.371
-21.30
0.9819
4.0176
5
2475
1.395
-27.25
0.9726
6.1244
4
3093
1.828
-47.83
0.9980
2.1162
4
3700
1.741
-37.48
0.9905
4.2203
7
4320
1.717
-43.63
0.9367
11.7374
4
4700
0.951
-8.87
0.9826
3.3514
3
5100
1.320
-29.60
0.9471
6.5325
3
1990 FORD F250
4x2 PCKUP 5.8 L L4AE0D
VIN: 1FTEF25H9LLA85776
RPM Slope Intercept
psi / kPa psi
'yl*
No of Data
Points
1110
1.267
-44.22
0.9745 3.8692
5
1560
1.118
-32.97
0.9091 9.3799
3
2070
1.073
-31.19
0.9999 0.2522
5
2550
0.989
-24.34
0.9978 1.2008
3
3060
1.273
-35.80
0.9968 1.3965
7
3570
Only two
data points at this
RPM
3860
Only two
data points at this
RPM
4180
Only two
data points at this
RPM
-2-
-------
1991 FORD PROBE GL
2 DR HATCH 2.2 L L4AE0D
VIN: 1ZVPT20C2M5163427
RPM Slope Intercept R2 ay)x No of Data
psi / kPa
psi
Points
1325
1.118
-26.05
0.9470
3.0065
4
1950
1.609
-49.02
0.9951
2.9665
3
2580
2.186
-84.00
0.9904
4.9519
6
3215
2.266
-88.94
0.9860
6.0707
6
3840
2.438
-103.68
0.9855
3.7762
9
4500
2.089
-73.53
0.9951
4.0959
4
4875
2.182
-84.50
0.9981
2.3745
4
1990 FORD RANGER XLT
4x2 REG CAB 2.3 L L40D
VIN: 1FTCR10A9LUA34064
RPM
Slope
Intercept
R2
°y|x NO Of
Data
psi / kPa
psi
Points
1125
1.475
-41.92
0.9697
2.1258
4
1630
0.551
0.27
0.9753
1.4098
3
2150
1.331
-36.73
0.9969
1.9450
3
2675
1.508
-45.97
0.9826
4.5010
6
3200
1.466
-44.09
0.9987
1.2997
12
3750
1.467
-46.59
0.9650
6.2710
6
4060
1.461
-46.87
0.9519
7.2385
6
4395
1.503
-50.76
0.9997
0.6547
5
1991 NISSAN SENTRA
2 DR SEDAN 1.6 L M50D
VIN: 1N4EB32A9MC727980
RPM Slope Intercept
psi / kPa
psi
2210
1.809
-50.98
2930
1.902
-55.43
3640
1.934
-48.87
4340
1.772
-34.86
5080
1.480
-18.31
5520
1.706
-32.31
5980
1.935
-50.11
R2 ay|x No of Data
Points
0.9977 2.2714 5
0.9974 2.2287 6
0.9990 1.4243 6
0.9897 4.5973 11
0.9534 8.1272 6
0.9815 5.8557 6
0.9920 4.3450 6
-3-
-------
1990 NISSAN PICKUP
KING CAB 2.4 L M50D
VIN: 1N4EB32A9MC727980
RPM Slope Intercept
psi / kPa
psi
920
1.532
-40.08
1300
1.644
-39.67
1915
1.769
-45.79
2530
1.894
-54.38
3150
1.760
-43.44
3775
1.760
-40.64
4400
1.855
-44.59
4780
1.759
-42.10
5175
1.649
-35.91
R2 (7^ No of Data
Points
0.9925
3.9713
6
0.9979
1.8780
10
0.9986
1.6934
5
0.9973
2.3034
6
0.9969
2.1935
6
0.9957
2.9413
11
0.9966
2.8161
4
0.9938
3.4846
5
0.9821
4.8551
6
1992 GEO METRO
3 DR HATCH 1.0 L M50D
VIN: 2C1MR24C4N6704201
RPM Slope Intercept R2 ay|x No of Data
psi / kPa
psi
Points
998
1.721
-51.62
0.9929
3.7926
5
1425
1.837
-55.99
0.9932
3.7934
11
2109
2.054
-64.75
0.9924
4.1925
6
2793
2.390
-88.71
0.9942
4.2127
6
3477
2.379
-85.39
0.9969
3.0603
6
4161
2.223
-72.56
0.9995
1.1713
10
4845
2.243
-77.50
0.9998
0.6594
6
5273
2.233
-80.99
0.9996
1.1838
6
5700
2.224
-87.30
0.9991
1.9639
4
1991 TOYOTA MR2 TURBO
3 DR LFTBK 2.0 L M5
VIN: JT25W22NXM0015597
RPM Slope Intercept R2 ay|x No of Data
psi / kPa
psi
Points
1040
1.497
-39.12
0.9918
3.6765
6
1500
1.561
-43.96
0.9944
4.0131
9
2200
1.355
-16.74
0.9919
3.0831
4
2950
1.415
-21.72
0.9637
7.0640
4
3675
1.516
-34.90
0.9947
3.7655
8
4350
1.500
-32.52
0.9965
2.9419
17
5090
1.559
-35.59
0.9992
1.6817
3
5550
Only two
data points
i at this
RPM
6000
1.369
-35.08
0.9896
3.6185
4
-4-
-------
1991 CHRY NEW YORK
4 DR SEDAN 3.3 L L4
VIN: 1C3X466R9MD260
RPM Slope Intercept R2 <7y|x No of Data
psi / kPa psi Points
1116
Only two
data points at this
RPM
1665
Only two data points at this
RPM
2222
1.982
-64.08
0.9722 8.8408
4
2775
1.759
-46.23
0.9973 2.3446
5
3320
1.980
-56.98
0.9845 6.3687
10
3850
1.958
-52.32
0.9958 4.3713
3
4180
2.141
-61.48
0.9961 1.8408
3
4510
1.944
-55.66
0.9993 1.0263
4
1991 DODGE SHADOW
4 DR HATCH 2.5 L L3
VIN: 1B3XP48D8MN638550
RPM Slope Intercept R2 ay|x No of Data
psi / kPa
psi
Points
1425
1.593
—44.64
0.9970
1.0160
5
2110
1.468
-38.10
0.9961
2.4126
4
2770
1.431
-36.88
0.9983
1.3315
6
3450
1.484
-40.95
0.9985
1.3288
6
4130
1.562
-47.58
0.9995
0.7723
10
4850
1.553
-51.72
0.9984
1.3190
5
5230
1.497
-51.63
0.9989
1.0564
5
5700
1.380
-51.23
0.9981
1.4116
4
1991 SATURN SL2
4 DR SEDAN 1.9 L L4AE0D
VIN: 1G8ZK5471MZ102666
RPM Slope Intercept R2 ayU No of Data
psi / kPa
psi
Points
1610
1.263
-26.34
0.9770
1.9119
4
2350
1.576
-38.90
0.8317
16.7249
5
3120
1.860
-51.31
0.9843
5.5225
5
3880
1.925
-56.41
0.9962
3.1070
5
4650
2.075
-59.39
0.9899
4.9678
10
5400
2.084
-60.34
0.9898
5.3358
5
5850
2.154
-70.17
0.9944
4.0372
5
6250
2.111
-76.66
0.9900
5.2961
5
-5-
-------
1990 GMC SIERRA
2 DR PKUP 5.0 L L40D
VIN: 1GTDC14H9LE506190
RPM Slope Intercept R2 <7y|X No of Data
psi / kPa
psi
Points
1135
0.286
-8.10
0.9767
0.9566
8
1550
0.444
-11.44
0.9113
3.6949
3
2050
0.521
-13.38
0.9855
1.6500
4
2550
0.618
-14.67
0.9840
2.0322
4
3050
0.713
-16.73
0.9901
1.7521
10
3550
0.871
-25.38
0.9784
3.1084
7
3880
1.166
-41.09
0.9873
3.2288
5
4200
1.220
-45.05
0.9658
6.0115
4
1991 GMC SONOMA
4x2 PKUP 2.8 L M50D
VIN: 1GTCS14R7M0534382
RPM Slope Intercept R2 cry(x No of Data
psi / kPa
psi
Points
825
1.513
-60.47
0.9997
0.6805
5
1200
1.770
-78.63
0.9354
8.8373
8
1750
1.559
-57.49
0.9931
3.4145
5
2350
1.645
-61.93
0.9954
2.7203
6
2900
1.706
-66.13
0.9992
1.2391
5
3520
1.698
-67.00
0.9957
2.5584
8
4050
1.648
-64.00
0.9696
7.4549
5
4440
1.728
-71.45
0.9866
4.5258
6
4800
1.636
-64.71
0.9847
4.4507
6
1991 GMC SONOMA
EXT CAB PICKUP 4.3 L L40D
VIN: 1GTCS19Z3M0517197
RPM Slope Intercept
psi / kPa
psi
1120
1.271
-34.59
1620
1.255
-23.59
2150
1.670
-44.29
2670
1.485
-36.20
3200
1.556
-40.88
3740
1.533
-41.76
4050
1.329
-37.17
4400
1.050
-32.42
R2 oy|X No of Data
Points
0.9884 2.8669 4
0.9718 5.7191 3
0.9987 1.6226 3
0.9986 1.4456 3
0.9966 1.9423 8
0.9930 3.4380 4
0.9799 5.0412 4
0.9660 5.1522 3
-6-
-------
1990 TOYOTA 4RUNNER
4x4 5 DR 3.0 L L4AE0D
VIN: JT3VN39W5L0017546
RPM Slope Intercept
psi / kPa psi
R2
1373 1.5782 -42.45 0.9638
1900 1.4674 -39.45 0.9964
2750 2.0727 -80.73 0.9975
3531 2.5664 -104.17 0.9888
3811 2.5293 -96.27 0.9952
4488 Not enough data
5042 1.7127 -57.83 0.9973
5246 1.6153 -54.93 0.9668
<7y|x No of Data
Points
2.0135
2.2949
2.6542
6.9969
4.0659
1.8199
5.0528
4
3
5
4
6
4
5
1992 MERCEDES-BENZ 300E
4 DR SEDAN 2.6 L A4
VIN: WDBEA26D61B235485
RPM Slope
psi / k
1124
1570
1.4917
2316
1.8152
3049
1.8337
3800
1.9816
4549
2.0011
5306
2.0776
5747
2.1152
6209
2.0723
Intercept R2
l psi
Not enoug
-42.82 0.9959
-55.54 0.9960
-51.71 0.9980
-59.65 1.0000
-56.20 0.9997
-62.77 0.9996
-68.98 0.9994
-72.83 0.9998
ay|x No of Data
Points
1.9910 6
3.0047 4
2.1544 4
0.2629 4
0.9325 4
1.1114 4
1.3488 5
0.7304 4
1991 SAAB 9000
5 DR HTBK 2.3 L M5
VIN: Y53CK55B2M1001898
RPM Slope Intercept
psi / kPa
psi
945
1.6862
-58.74
1245
1.7343
-55.27
1633
1.8737
-54.12
2283
1.8303
-54.40
2848
2.6397
-120.63
3684
2.7514
-120.97
4318
2.7967
-126.86
4634
2.7595
-128.22
5230
2.4666
-114.52
R2 ffy|X No of Data
Points
0.9970 2.3406 5
0.9839 5.4520 11
0.9962 3.0022 5
0.9880 5.1884 5
0.9971 3.6163 4
0.9889 6.1903 6
0.9973 3.3598 6
0.9963 3.6155 5
0.9954 3.1623 5
-7-
-------
1991 HONDA ACCORD
4 DR SEDAN 2.2 L L40D
VIN: 1HGCB7654MAI36491
RPM Slope Intercept R2 ay!x No of Data
psi / kPa psi Points
1298
1.0333
-25.73
0.9990
0.2471
4
1924
Not enough
data
2535
1.9755
-63.06
0.9921
4.4093
5
3153
1.9668
-54.19
0.9934
3.5966
6
3774
2.0026
-49.36
0.9983
2.1712
10
4384
2.2204
-57.93
0.9994
1.3205
4
4762
2.1692
-55.46
1.0000
0.0346
3
5200
1.7502
-40.67
0.9894
4.7829
4
1991 CHEV CAMARO
2 DR LIFT 5.7 L L40D
VIN: 1G1FP2381ML190343
RPM Slope Intercept R2 oy,x No of Data
psi / kPa psi Points
1214 1.7879 -58.73 0.9997 0.1995 4
1690 Not enough data
2328 1.3404 -28.49 0.9921 3.1110 3
2938 Not enough data
3524 2.0270 -56.14 0.9972 0.8375 4
4099 2.1565 -69.25 1.0000 0.0994 3
4454 2.2258 -77.76 1.0000 0.0162 3
4814 1.9590 -70.17 0.9979 0.9979 3
1991 DODGE CRVN
MINIVAN 3.0 L L3
VIN: 2B4GK4530MR273404
RPM Slope Intercept R2 ay|x No of Data
psi / kPa psi Points
1234
Not enough
data
1822
Not enough
data
2401
1.5682
-26.76
0.9935
3.2571
3
2961
1.8760
-47.07
0.9987
1.6699
5
3498
1.9380
-49.15
0.9982
1.8538
9
4136
1.9435
-47.97
0.9999
0.3774
3
4517
1.7642
-42.11
0.9904
3.4674
4
4868
1.9602
-59.18
0.9989
1.3830
5
-8-
-------
1992 FORD CRWN VIC
4 DR SEDAN 4.6 L L4AE0D
VIN: 2FACP74W4NX113934
RPM Slope Intercept
psi / kPa psi
R2
1172 1.1529 -31.85 0.9213
1734 1.5579 -57.53 0.9970
2297 1.4955 -52.76 0.9999
2822 1.5146 -53.76 0.9510
3408 Not enough data
3971 1.5597 -62.21 0.9914
4313 1.3511 -53.61 0.9984
4675 1.1065 -42.53 0.9603
ay|X No of Data
Points
7.3386
1.6976
0.4429
7.7331
3.5891
1.2045
4.9154
3
4
4
4
4
3
4
1991 PONTIAC GRAN PRIX
4 DR SEDAN 2.3 L Q4 L3
VIN: 1G2WH54D8MF271439
RPM Slope Intercept R2
psi / kPa psi
1486
2224
2921
3629
4349
5067
5517
5928
2.2641
1.6392
1.7096
1.8697
1.8050
2.1261
2.0666
1.9196
-81.21
-50.28
-50.41
-61.34
-53.16
-66.75
-65.54
-62.25
0.9744
0.9970
0.9981
0.9990
0.9924
0.9936
0.9994
0.9906
ay|X No of Data
Points
3.1371
2.3677
1.9610
1.4007
3.2701
3.4897
1.0034
4.8184
3
3
4
4
9
4
4
4
1992 DODGE DAKOTA
4x2 PKUP 5,2 L L40D
VIN: 1B7GL23Y5NS502694
RPM Slope Intercept
psi / kPa psi
R2
1096 1.6109 -57.55 0.9904
1629 1.2771 -39.58 0.9632
2157 Not enough data
2698 1.2587 -37.96 0.9907
3204 1.6185 -52.81 0.9986
3735 1.5731 -39.25 0.9997
4066 Not enough data
4409 1.6141 -44.47 0.9819
<7y|x No of Data
Points
0.9042
6.0561
3.7830
0.7117
0.7216
5.6106
3
3
3
5
3
-9-
-------
1991 VW JETTA
4 DR CUSTOM 1.8 L A3
VIN: 3VWRA21G3MM027141
RPM Slope Intercept
psi / kPa
psi
1399
1.9135
-61.09
2127
1.5077
-38.80
2811
1.7588
-51.83
3495
1.7518
-52.18
4173
1.7073
-49.42
4861
1.7403
-56.42
5290
1.7503
-62.79
5687
1.6182
-67.80
R2 ay|X No of Data
Points
0.9959 0.7015 3
0.9865 4.6277 3
0.9991 1.4060 4
0.9977 2.2361 4
0.9955 2.8140 11
0.9997 0.7431 5
1.0000 0.2008 3
0.9995 0.7498 3
1990 BUICK LESABRE
4 DR SEDAN 3.8 L L40D
VIN: 1G4HP54C2LH473366
RPM Slope Intercept R2 ay^ No of Data
psi / kPa psi Points
1094
1.2508
-31.83
0.9862
0.9632
3
1645
Not enough
data
2175
1.3963
-39.18
0.9930
2.8663
4
2734
1.3510
-35.80
0.9975
1.8686
3
3232
1.3777
-36.35
0.9968
1.5018
3
3745
1.7514
-58.49
0.9948
3.8782
4
4098
1.7598
-62.11
0.9910
3.5505
6
4401
Not enough
data
-10-
-------
1990 Buick Le Sabre 4-Door Sedan 3.8L L4C 1990 Buick Le Sabre 4-Door Sedan 3.8L L4C 1990 Buick Le Sabre 4-Door Sedan 3.8L L4C
Data at 1150 RPM Data at 1645 RPM ... Data at 2175 RPM
a.
03
a.
m
' Manifold Absolute Pressure (£Pa)
"Manifold Absolute Pressure (£Pa)
" Manifold Absolute Pressure (fcPa)
1990 Buick Le Sabre 4-Door Sedan 3.8L L4C 1990 Buick Le Sabre 4-Door Sedan 3.8L L4C 1990 Buick Le Sabre 4-Door Sedan 3.8L L4C
Data at 2730 RPM
Data at 3250 RPM
Data at 3750 RPM
&
m
a.
pq
" Manifold Absolute Pressure (ItPa)
1990 Buick Le Sabre 4-Door Sedan 3.8L L4C
Daiaal 4100 RPM
"Manifold Absolute Pressure (fcPa)
Manifold Absolute Pressure (IcPa)
>• «•- » ^
-------
Cu
tQ
s
CO
1991 Chevrolet Camaro 5.7L L40D
Data at 1200 RPM
1991 Chevrolet Camaro 5.7L L40D
Data at 1690 RPM
1991 Chevrolet Camaro 5.7L L40D
Data at 2300 RPM
"Manifold Absolute Pressure $Pa)
1991 Chevrolet Camaro 5.7L L40D
Data at 2940 RPM
"Manifold Absolute Pressure (HcPa)
1991 Chevrolet Camaro 5.7L L40D
Data at 3525 RPM
"Manifold Absolute Pressure (IcPa) "
1991 Chevrolet Camaro 5.7L L40D
Data at 4100 RPM
• >• 44 ?• JUt ft
Manifold Absolute Pressure (*Pa)
1991 Chevrolet Camaro 5.7L L40D
Data at 4450 RPM
|| f| y ^|
Manifold Absolute Pressure (lcPa)
1991 Chevrolet Camaro 5.7L L40D
Data at 4800 RPM
|| )| || )| Jb|
Manifold Absolute Pressure (kPa)
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure $Pa)
-------
199Chevrolet Cavalier 4-Door Wagon 2.2L L 199Chevrolet Cavalier 4-Door Wagon 2.2L L 199Chevrolet Cavalier 4-Door Wagon 2.2L L
Data at 1240 RPM ... Data at 1810 RPM Data at 2400 RPM
flu
ia
2
CQ
'Manifold Absolute Pressure (VPa) » » "Manifold Absolute Pressure (Vpa) ** #Manifold Absolute Pressure (tPa) "
199Chevrolet Cavalier 4-Door Wagon 2.2L L 199Chevrolet Cavalier 4-DoorWagon 2.2L L 199Chevrolet Cavalier 4-Door Wagon 2.2L L
Dala at 2975 RPM 3 Data at 3550 RPM * Dala at 4140 RPM a
u>
l
M <• J* M M f# |M M M M If M M 1M
Manifold Absolute Pressure (i(Pa) Manifold Absolute Pressure (kPa)
199ChevroletCavalier 4-DoorWagon 2.2L L 199ChevroletCavalier 4-DoorWagon 2.2L L
Data at 4500 RPM s Data at 4880 RPM a
44 M 44 It u
Manifold Absolute Pressure (*Pa)
cu
LL)
s
CQ
it
Manifold Absolute Pressure (kPa)
Manifold Absolute Pressure Pa)
-------
1991 Chrysler New Yorker 4-Door Sedan 3.3L 1991 Chrysler New Yorker 4-Door Sedan 3.3L 1991 Chrysler New Yorker 4-Door Sedan 3.3L
Dala al 1116 RPM Data al 1665 RPM Dala al 2222 RPM
cu
UJ
s
CQ
Cu
W
2
m
" "Manifold Absolute Pressure $Pa) " "Manifold Absolute Pressure (KcPa) ** "Manifold Absolute Pressure $Pa)
1991 Chrysler Nev^Yorke^-Door Sedan 3.3L 1991 Chrysler Nev^Yorke^-^oor Sedan 3.3L 1991 Chrysler Nev^Yorke^-^oor Sedan 3.3L
a*
UJ
2
CQ
Qm
UJ
2
CQ
" "Manifold Absolute Pressure (*£Pa) "Manifold Absolute Pressure $Pa)
1991 Chrysler New Yorker 4-Door Sedan 3.3L 1991 Chrysler New Yorker, 4-Door Sedan 3.3L
1 Data at 4180 RPM 7 Data al 4510 RPM
Manifold Absolute Pressure $Pa)
"Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure ^(Pa)
-------
1991 Dodge Caravan Minivan 3.0L L3
3 Data at 1234 RPM
1991 Dodge Caravan Minivan 3.0L L3
a Data at 1822 RPM
1991 Dodge Caravan Minivan 3.0L L3
Data at 2400 RPM
4# 34 if
Manifold Absolute Pressure (lcPa)
1991 Dodge Caravan Minivan 3.0L L3
a Data at 2960 RPM
"Manifold Absolute Pressure (\cPa)
1991 Dodge Caravan Minivan 3.0L L3
a Data at 3550 RPM
• )• •• ?• M
Manifold Absolute Pressure (KPa)
1991 Dodge Caravan Minivan 3.0L L3
a Data at 4515 RPM
II f| ||
Manifold Absolute Pressure (KPa)
1991 Dodge Caravan Minivan 3.0L L3
3 Data at 4900 RPM
II || II ^1 U II
Manifold Absolute Pressure (kPa)
1991 Dodge Caravan Minivan 3.0L L3
a Data at 4135 RPM
o-.
UJ
2
m
"Manifold Absolute Pressure (lcPa) "
I >1 II 71 n
Manifold Absolute Pressure (kPa)
Manifold Absolute Pressure $Pa)
-------
1992 Dodge Dakota 4x2 Pick Up 5.2L L40D 1992 Dodge Dakota 4x2 Pick Up 5.2L L40D 1992 Dodge Dakota 4x2 Pick Up 5.2L L40D
Data al 1100 RPM Data al 1630 RPM ... Daia al 2155 RPM
a.
W
2
CQ
" "Manifold Absolute Pressure $Pa) " " "Manifold Absolute Pressure $Pa) '** Manifold Absolute Pressure (T£Pa)
1992 Dodge Dakota 4x2 Pick Up 5.2L L40D 1992 Dodge Dakota 4x2 Pick Up 5.2L L40D 1992 Dodge Dakota 4x2 Pick Up 5.2L L40D
3 Data at 2700 RPM a Data at 3200 Rl'M Data al 3735 RPM
V
I a.
a,
W
2
CQ
&.
a,
LU
2
CD
Manifold Absolute Pressure (^Pa)
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure (^Pa)
1992 Dodge Dakota 4x2 Pick Up 5.2L L40D 1992 Dodge Dakota 4x2 Pick Up 5.2L L40D
a Data al 4065 Rl'M a Data at 4410 RPM
"Manifold Absolute Pressure (IcPa)
"Manifold Absolute Pressure (IcPa)
-------
1991 Dodge Shadow 4-Door Hatchback 2.5L 1991 Dodge Shadow 4-Door Hatchback 2.5L 1991 Dodge Shadow 4-Door Hatchback 2.5L
s Data al 1425 RPM a Data at 2110 RPM ... Data at 2770 RPM
'Manifold Absolute Pressure $Pa)
"Manifold Absolute Pressure $Pa)
'Manifold Absolute Pressure (^Pa)
1991 Dodge Shadow 4-goor^Hatchback 2.5L 1991 Dodge Shadow A^Doo^Hatchback 2.5L 1991 Dodge Shadgw^goo^Hatchback 2.5L
S.
Oh
u
2
m
Manifold Absolute Pressure (IcPa)
'Manifold Absolute Pressure (IcPa)
"Manifold Absolute Pressure (tPa)
1991 Dodge Shadow 4-Door Hatchback 2.5L 1991 Dodge Shadow 4-Door Hatchback 2.5L
3 Data at 5230 RPM a Data al 5700 RPM
'Manifold Absolute Pressure (HcPa)
Manifold Absolute Pressure (tcPa)
-------
1992 Ford Crown Victoria 4.6L L4AEOD
Data al 1170 RPM
1992 Ford Crown Victoria 4.6L L4AEOD
Data al 1730 RPM
1992 Ford Crown Victoria 4.6L L4AEOD
Data at 2300 RPM
y* *• it u h
Manifold Absolute Pressure (Kra)
1992 Ford Crown Victona 4.6L L4AEOD
Data at 2350 RPM
4* , M H ?l M M
Manifold Absolute Pressure (kra)
1992 Ford Crown Victoria 4.6L L4AEOD
Data al 3400 RPM
'Manifold Absolute Pressure (tPa)
I Crown Victoria 4.I
Data at 4000 RPM
1992 Ford Crown Victoria 4.6L L4AEOD
'Manifold Absolute Pressure (£Pj)
1992 Ford Crown Victoria 4.6L L4AEOD
Data at 4300 RPM
'Manifold Absolute Pressure ^(Pa)
. .I
)ata at 70 RPM
1992 Ford C^own Victoria 4.6L L4AEOD
Manifold Absolute Pressure (V.Pa)
Corrected engine mapping data.
Only points whose BMEP values
are calculated from measured dyno
torques are included
Manifold Absolule Pressure
Manifold Absolute Pressure |
-------
991 Ford Escort LX 2-Door Hatchback 1.9L L4/991 Ford Escort LX 2-Door Hatchback 1.9L L4/991 Ford Escort LX 2-Door Hatchback 1.9L L4/
Data at 1270 RPM Data at 1870 UI'M Data at 2475 UPM
0L,
UJ
Manifold Absolute Pressure (1
1V* — — 1 >>~ I - * ^ ¦ i im . . Data al 4 20
I _ ik
vo
l
Dm
UJ
2
a-
w
2
CQ
Manifold Absolute Pressure ^Pa) Manifold Absolute PnUsurc (fcPa) "
991 Ford Escort U< ,f-aDaOO{0HatcJiback 1.9L L4&91 £-p°<$[H^c^ack 1.9L L4>
M M M T9 M
Manifold Absolute Pressure (&Pa)
Manifold Absolute Pressure (ItPa) "
"Manifold Absolute Pressure ^(Pa)
-------
I
N>
O
1991 Ford F150 Pickup 4.9L L4AEOD
Data at 1190 RPM
1991 Ford F150 Pickup 4.9L L4AEOD
Data at 1760 RPM
1991 Ford F150 Pickup 4.9L L4AEOD
Data at 2325RPM
a.
UJ
2
co
II II ||
Manifold Absolute Pressure (kPa)
1991 Ford F150 Pickup 4.9L L4AEOD
Data at 2930 RPM
jl || j| ^|
Manifold Absolute Pressure (kPa)
1991 Ford F150 Pickup 4.9L L4AEOD
Data at 3180 R"
I RPM
|| )| || f| Uf
Manifold Absolute Pressure (KPa)
'Manifold Absolute Pressure (lcPa)
"Manifold Absolute Pressure $Pa)
-------
1990 Ford F250 4x2 Pickup Truck 5.8L L4AEOD
Data at 1100 RPM
1990 Ford F250 4x2 Pickup Truck 5 8L L4AEOD
Data at 1560 RPM
1990 Ford F250 4x2 Pickup Truck 5.8L L4AEOD
Dalaal207DRFM
Manifold Absolute PrSsure (kPa)
1990 Ford F250 4x2 Pickup Truck 5.8L L4AEOD
Data at 2550 RPM
Manifold Absolute Pressure (ItPa)
1990 Ford F250 4x2 Pickup Truck 5 8L L4AEOD
Data at 3060 RPM
" Manifold Absolute Pressure (kPa) * "
1990 Ford F250 4x2 Pickup Truck 5 8L L4AEOD
Data at 3570 RPM
Manifold Absolute Pressure (kPa)
1990 Ford F250 4x2 Pickup Truck 5 8L L4AEOD
Data at 3860 RPM
* Manifold Absolute Pressure (kPa)
1990 Ford F250 4x2 Pickup Truck 5 8L L4AEOD
Data at 4180 RPM
Manifold Absolute Pressure (kPa)
Manifold Absolute Pressure (kPa)
Manltold Absolute Pressure (kPa)
-------
991 Ford Probe GL 2-Door Hatchback 2.2L L4/991 Ford Probe GL 2-Door Hatchback 2.2L L4/991 Ford Probe GL 2-Door Hatchback 2.2L L4/
Data at 1325 RPM ... Data at 1950 RPM ... Data at 2580 RPM
Cm
UJ
2
0Q
" "Manifold Absolute Pressure (HcPa) ** ' * Manifold Absolute Pressure $Pa) Manifold Absolute Pressure (ItPa)
991 Ford Probe GL 2-Doo| Hatchback 2.2L L4/991 Ford Probe GL ^-Do^H^tcJiiback 2.2L L4/991 Ford Probe GL Door Hatchback 2.2L L4/
II Jl 44 71 u n m
Manifold Absolute Pressure (KPa)
991 Ford Probe GL 2-Door Hatchback 2.2L L4/
Data at 4875 RPM
II H II 71 u
Manifold Absolute Pressure (liPa)
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure $Pa)
-------
1990 Ford Ranger XLT Truck 2.3L L40D
Data at 1125 RPM
1990 Ford Ranger XLT Truck 2.3L L40D
Data at 1630 RPM
1990 Ford Ranger XLT Truck 2.3L L40D
Data at 2150 RPM
"Manifold Absolute Pressure (IcPa) " "* * "Manifold Absolute Pressure (IcPa) " "Manifold Absolute Pressure (tPa)
1990 Ford Ran^er^XL^J^JC^ 2.3L L40D 1990 Ford Rag^er^XLTT^JC^ 2.3L L40D 1990 Ford Ra^erXj^T^c^ 2.3L L40D
sj o"
V 2.
I N-/
X.
UJ
S
00
Ou
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s
CQ
I ^ 49 79 u
Manifold Absolute Pressure (KPa)
1990 Ford Ranger XLT Truck 2.3L L40D
Data at 4060 RPM
|| || j0 ^|
Manifold Absolute Pressure (KPa)
1990 Ford Ranger XLT Truck 2.3L L40D
Data at 4395 RPM
'Manifold Absolute Pressure $cPa)
II j| II 71 u
Manifold Absolute Pressure (KPa)
Manifold Absolute Pressure (IcPa)
-------
1990 GMC Sierra 2-Door Pickup 5.0L L40C 1990 GMC Sierra 2-Door Pickup 5.0L L40C 1990 GMC Sierra 2-Door Pickup 5.0L L40C
Data at 1135 RPM M Data at 1550 RPM r ... Data at 2050 RPM
O.
U
2
CQ
'Manifold Absolute Pressure (^Pa)
i 2-Door
)ata at ^550
Bu
tu
S
CQ
'Manifold Absolute Pressure (tPa)
"Manifold Absolute Pressure $Pa)
1990 GMC Sierra 2-Door Pickup 5.0L L40C 1990 GMC Sierra 2-Door Pickup 5.0L L40C 1990 GMC Sierra 2-Door Pickup 5.0L L40C
Data at 2550 RPM r Data at 3050 RPM K Data at 3550 RPM r
a.
UJ
* "Manifold Absolute Pressure $Pa)
1990 GMC Sierra 2-Door Pickup 5.0L L40C
Data at 3880 RPM K
l| 44 94 j|4 94
Manifold Absolute Pressure (KPa)
1990 GMC Sierra 2-Door Pickup 5.0L L40C
Data at 4200 RPM r
"Manifold Absolute Pressure (£Pa)
O.
UJ
S
oa
8.
CL,
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2
BQ
"Manifold Absolute Pressure (IcPa) "
'Manifold Absolute Pressure (tcPa)
-------
1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D
Data at 825 RPM ... Data at 1200 RPM w Data at 1750 RPNf
cu
UJ
2
QQ
Dm
UJ
2
CO
M 4# M M 7# jU 199 )| 44 4# ?# i| ^ n j0 ||
Manifold Absolute Pressure (lcPa) Manifold Absolute Pressure (lcPa) Manifold Absolute Pressure (lcPa)
1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D
Data at 2350 RPM Data at 29&0 RPM Data at 3516 RPM
cu
UJ
5
CD
Qm
UJ
2
CO
Manifold Absolute Pressure ^cPa)
I II H U
Manifold Absolute Pressure (lcPa)
41 ft 44 f| u
Manifold Absolute Pressure (kPa)
1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D 1992 GMC Sonoma 4x2 Pickup 2.8L M50D
Data at 4050 RPM Dala at 4440 RPMr Data at 4800 RPM
Manifold Absolute Pressure (^Pa)
)l (I n u
Manifold Absolute Pressure (IPa)
'Manifold Absolute Pressure ^&Pa)
-------
1991 GMC Sonoma Ext Cab Pickup 4.3L L40 1991 GMC Sonoma Ext Cab Pickup 4.3L L40
Data at 1620 RPM „ Data at 2150 RPM
1991 GMC Sonoma Ext Cab Pickup 4.3L L40
Data at 1120 RPM
Q.
Ou
>•
Manifold Absolute Pressure ^cPa)
Manifold Absolute Pressure (IkPa)
Manifold Absolute Pressure
1991 GMC Sonoma E«£abB£|Ckup 4.3L LAO 1991 GMC Sonoma Ex^fjgkup 4.3L L40 1991 GMC Sonoma Ext Ca^gkup 4.3L L40
... IZ 1 u - IM ¦¦ ' I
IM
¦ ' ' I 1 i_
4# M 7# H
Manifold Absolute Pressure (lcPa)
"Manifold Absolute Pressure (fcPa)
N
X
Manifold Absolute Pressure (jfcPa)
1991 GMC Sonoma Ext Cab Pickup 4.3L L40 1991 GMC Sonoma Ext Cab Pickup 4.3L L40
r\^i» /
-------
1992 Geo Metro 3-Door Hatchback 1.0L M5C 1992 Geo Metro 3-Door Hatchback 1.0L M5C 1992 Geo Metro 3-Door Hatchback 1.0L M5C
Data a( 998 RPM ... Dala at 1425 RPM ... Data at 2109 RPM
s.
0*
UJ
2
«
** "Manifold Absolute Pressure (ItPa) ** Manifold Absolute Pressure (\cPa) Manifold Absolute Pressure ^£Pa)
1992 Geo Metro 3-Door ^Hatchback 1.0L M5C 1992 Geo Metro 3-^oorJ^atcpback 1.0L M5C 1992 Geo Metro 3-aDoor j^atgpback 1.0L M5C
B.
w
cu
U)
s
ffl
D-.
11]
s
m
* "Manifold Absolute Pressure (l&Pa) " " "Manifold Absolute Pressure (UPa) " ' " Manifold Absolute Pressure (IcPa)
1992 Geo Metro 3-Door Hatchback 1.0L M5C 1992 Geo Metro 3-Door Hatchback 1.0L M5C 1992 Geo Metro 3-Door,Hatchback 1.0L M5C
Data at 4845 RPM Data al 5273 RPM Dala at 5700 RPM
Oh
U]
2
m
Manifold Absolute Pressure (^tPa)
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure (tPa)
-------
1991 Honda Accord 2.2L L4CI991 Honda Accord 2.2L L4C1991 Honda Accord 2.2L L4C
Data at 1300 RPM Data at 1925 RPM ... Data at 2530 RPM
o,
iu
2
CO
'Manifold Absolute Pressure (ItPa)
Manifold Absolute Pressure $Pa)
'Manifold Absolute Pressure (£Pa)
1991 Honda Accord 2.2L L4CI991 Honda Accord 2.2L L4CI991 Honda„Accord 2.2L L4C
Data at 3150 RPM
Data at 3775 RPM
Data at 4400 RPM
I
N3
00
1 8.
Manifold Absolute Pressure (l
-------
1992 Mercedes-Benz 300E 4-door Sedan 2.6L1992 Mercedes-Benz 300E 4-door Sedan 2.6L 1992 Mercedes-Benz 300E 4-door Sedan 2.i
Data at 1125 RPM Data at 1575 RPM Data at 2315 RPM
a.
U
2
CQ
On,
uj
2
CQ
|| 0 n || ^ iii || || j| || fi i| || m || || ji || fi
Manifold Absolute Pressure O*''3) Manifold Absolute Pressure O'Pa) Manifold Absolute Pressure (K^a)
1992 Mercedes-Benz 300E 4—door Sedan 2.6L 1992 Mercedes-Benz 300E 4—door Sedan 2.6L 1992 Mercedes-Benz 300E 4-door Sedan 2.6L
Data at 3050 RPM Data at 4550 RPM Data at 5300 RPM
a.
UJ
2
CQ
'Manifold Absolute Pressure $Pa)
enz 300E 4-do
D.ita at 5750 RPM
"Manifold Absolute Pressure Pa)
1992 Mercedes-Benz 300E 4-door Sedan 2.6L 1992 Mercedes-Benz 300E 4-door Sedan 2.6L
Data at 6200 RPM
"Manifold Absolute Pressure (tPa)
Corrected engine mapping data
Only points whose BMEP values
are calculated from measured dyno
torques are Included
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure (HcPa) "
-------
1990 Nissan Pickup Kinq Cab 2.4 L M50D 1990 Nissan Pickup King Cab 2.4LM50D 1990 Nissan Pickup King Cab 2.4 L M50D
Data at 92
-------
1991 Nissan Sentra 2-Door Sedan 1.6L M5C 1991 Nissan Sentra 2-Door Sedan 1.6L M5C 1991 Nissan Sentra 2-Door Sedan 1.6L M5C
Data at 2210 RPM Data at 2930 RPM Data at 3640 RPM
" "Manifold Absolute Pressure (KcPa) "Manifold Absolute Pressure (TcPa) " ' Manifold Absolute Pressure (tcPa)
1991 Nissan Sentra 2-Door Sedan 1.6L M5C 1991 Nissan Sentra 2-Door Sedan 1 6L M5C 1991 Nissan Sentra 2-Door Sedan 1.6L M5C
Data at 4340 RPM Data at 5080 RPM Data at 5520 RPM
I
OJ
Ou,
UJ
2
CO
II jl 70 M H | m
Manifold Absolute Pressure (kPa)
1991 Nissan Sentra 2-Door Sedan 1.6L M5C
Data at 5980 RPM
'Manifold Absolute Pressure (IcPa)
Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure (IcPa)
-------
1990 Pontial 6000 4-Door Sedan 3.1L L40C 1990 Pontial 6000 4-Door Sedan 3.1L L40C 1990 Pontial 6000 4-Door Sedan 3.1L L40C
Daia ai 1370 RPM Data at 2030 RPM Data at 2680 RPM
S.
m
' Manifold Absolute Pressure (fcPa)
"Manifold Absolute Pressure (IcPa) "
" Manifold Absolute Pressure (£Pa) "
1990 Pontial 6000 4-Door Sedan 3.1L L40C 1990 Pontial 6000 4-Door Sedan 3.1L L40[ 1990 Pontial 6000 4-Door Sedan 3.1L L40C
Data at 3325 RPM .. Data at 3950 RPM ... Data at 4600 RPM
8.
CQ
' Manifold Absolute Pressure (£Pa)
"Manifold Absolute Pressure (EPa)
Manifold Absolute Pressure (1cPa)
1990 Pontial 6000 4-Door Sedan 3.1L L40C 1990 Pontial 6000 4-Door Sedan 3.1L L40C
Daiaat 5000 RPM Data at 5420 RPM
—-
a.
&
-------
1991 Pontiac Grand Prix 4-Door Sedan 2.3L-Q41991 Pontiac Grand Prix 4-Door Sedan 2.3L-Q4991 Pontiac Grand Prix 4-Door Sedan 2.3L-Q4
Data at 1490 RPM Data at 2222 RPM ... Data at 2910 RPM
d.
ID
2
CQ
8.
Va/
Cu
UJ
2
«
" "Manifold Absolute Pressure (\
U)
I
8.
w
Oh
UJ
S
a*
UJ
2
CQ
4# M Tl u 4# 3# 4# t# If |n
Manifold Absolute Pressure (kPa) Manifold Absolute Pressure (kP®)
1991 Pontiac Grand Prix 4-DoorSedan 2.3L-Q41991 Pontiac Grand Prix 4-DoorSedan 2.3L-Q4
Data at 5500 RPM Data at 5910 RPM
"Manifold Absolute Pressure $Pa) "
LU
2
m
"Manifold Absolute Pressure ^cPa)
'Manifold Absolute Pressure (HcPa)
-------
1991 Saab 9000 5-Door Hatchback 2.3LM5 1991 Saab 9000 5-Door Hatchback 2.3LM5 1991 Saab 9000 5-Door Hatchback 2.3LM5
Data ai 940 RPM Data at 1360 RPM Data at 2020 RPM
'Manifold Absolute Pressure (litPa) " "Manifold Absolute Pressure (liPa) " ' Manifold Absolute Pressure (t;Pa)
1991 Saab 9000 5-Door Hatchback 2.3L M5 1991 Saab 9000 5-Dgor Hatchback 2.3LM5 1991 Saab 9000 5-Door Hatchback 2.3LM5
Data at 2675 RPM Data at 3350 RPM Data at 4000 RPM
0*
U)
s
CO
Manifold Absolute Pressure $Pa) "Manifold Absolute Pressure (VPa) " "Manifold Absolute Pressure (TcPa)
1991 Saab 9000 5-Door Hatchback 2.3LM5 1991 Saab 9000 5-Door Hatchback 2.3LM5 1991 Saab 9000 5-Door Hatchback 2.3LM5
Data at 4650 RPM Data at 5050 RPM Data at 5450 RPM
"Manifold Absolute Pressure $Pa)
"Manifold Absolute Pressure $Pa)
"Manifold Absolute Pressure (tPa)
-------
1991 Saturn SL2 4-DoorSedan 1.9L L4AEC 199lSatumSL2 4-DoorSedan 1 9L L4AEC 1991 Saturn SL£ 4-Door Sedan 1.9L L4AEC
Data at 1610 RI'M Data al 2350 UI'M ... Data at 3120 RPM
S.
o_
UJ
2
m
CL
tu
2
CQ
"Manifold Absolute Pressure $Pa) "
"Manifold Absolute Pressure (ItPa)
"Manifold Absolute Pressure (ttPa)
1991 Saturn SL2 4-DoorSedan 1.9L L4AEC 1991SatumSL2 4-DoorSedan 1.9L L4AEC 1991 Saturn SL2 4-Door Sedan 1.9L L4AEC
Data at 3880 RPM Data at 4650 RPM Data at 5400 RPM
a.
UJ
2
CD
Manifold Absolute Pressure $Pa) **
1991 Saturn SL2 4-DoorSedan 1.9L L4AEC
Data at 5850 RPM
" "Manifold Absolute Pressure (tPa) "
1991 Saturn SL2 4-DoorSedan 1.9L L4AEC
Data at 6250 RPM
"Manifold Absolute Pressure (t;Pa)
"Manifold Absolute Pressure (IcPa)
"Manifold Absolute Pressure (liPa)
-------
1990 Toyota 4-Runner Five-door 3.0 Liter L4AE« 1990 Toyota 4-Runner Five-door 3.0 Liter L4AE' 1990 Toyota 4-Runner Five-door 3.0 Liter L4AE
J n.. . otr\ J r\-.- ' r>ni« iccn
Dala al 1370 rpm
Data at 2020 rom
Dala at 2550 rpm
"Manifold Absolute Pressure (tiPa) »>•«>• "Manifold Absolute Pressure (ItPa) " ' " Manifold Absolute Pressure (tcPa)
1990 Toyota 4-Runner Five-door 3.0 Liter L4AE< 1990 Toyota 4-Runner Five-door 3.0 Liter L4AB 1990 Toyota 4-Runner Five-door 3.0 Liter L4AE
Data at 3200 rpm Data al 3800 rpm Data at 4472 rpm
b.
UJ
2
m
Manifold Absolute Pressure (tPa) Manifold Absolute Pressure (KPa)
1990 Toyota 4-Runner Five-door 3.0 Liter L4AE' 1990 Toyota 4-Runner Five-door 3.0 Liter L4AE'
Data at 4850 rpm Data at 5200 rpm
it W M Tt M
Manifold Absolute Pressure (kPa)
ii ii ii ^i j>i ^|
Manifold Absolute Pressure (kPa)
"Manifold Absolute Pressure (\cPa)
-------
1991 Toyota MR2Turbo 3-Door Liftback 20L I 1991 Toyota MR2Turbo 3-Door Liftback 2.0L 1991 ToyotaMR2Turbo 3-Door Liftback 2.0L
3 ~ 11\an i3vkj * Data at 1500 RPM n»i» at 9?nn rpm
Data al 1040 RPM
Data al 2200 RPM
1W 1M
" "Manifold Absolute Pressure ([KPa) "" "* " "Manifold Absolute Pressure (icPa) "* ' * Manifold Absolute Pressure ^KPa)
1991 Toyota MR2 Turbo 3-Door Liftback 2.0L 1991 Toyota MR2 Turbo 3-Door Liftback 2.0L 1991 Toyota MR2 Turbo 3-Door Liftback 2.0L
1 Data at 2950 RPM bata at 3675 RPM bata at 4350 RPM
I
LJ
I
4ft H u |M 17#
Manifold Absolute Pressure (kPa)
ii« i
44 4ft 44 im ||4
Manifold Absolute Pressure (kPa)
44 44 4ft |m IM
Manifold Absolute Pressure (kPa)
14* IM
1991 Toyota MR2 Turbo 3-Door Liftback 2.0L 1991 Toyota MR2 Turbo 3-Door Liftback 2.0L 1991 Toyota MR2 Turbo 3-Door Liftback 2.0L
Data at 5090 RPM 3 Data at 5550 RPM Data at 6000 RPM
# 4# 4ft |M |H 11^
Manifold Absolute Pressure (kPa)
Manifold Absolute Pressure (JtcPa)
144 144
44 4ft 44 Jftft IM
Manifold Absolute Pressure (kPa)
i4« m
-------
1991 Volkswagen Jetta 4-Door 1.8L M3
Data at 1400 RPM
1991 Volkswagen Jetta 4-Door 1.8LM3
Data at 2120 RPM
1991 Volkswagen Jetta 4-Door 1.8LM3
Data at 2800 RPM
"Manifold Absolute Pressure $Pa) "
1991 Volkswagen Jetta 4—Door 1.8LM3
Data at 3500 RPM
4# yt to w i
Manifold Absolute Pressure (kPa)
1991 Volksw^cjer^Jett^ 4-^oor 1.8L M3
«• M *4 T# . H
Manifold Absolute Pressure (kPa)
1991 Volksw^^n Jeg^ 4-^oor 1.8LM5
"Manifold Absolute Pressure (IcPa) "
1991 Volkswagen Jetta 4-Door 1.8LM3
Data at 5280 RPM
"Manifold Absolute Pressure (KcPa) " '
1991 Volkswagen Jetta 4-Door 1.8LM3
Data at 5710 RPM
"Manifold Absolute Pressure (tPa)
'Manifold Absolute Pressure (^Pa) "
"Manifold Absolute Pressure ^tPa)
-------
1991 Volvo 740 4-Door Sedan 2.3L L40D 1991 Volvo 740 4-DoorSedan 2.3L L40D 1991 Volvo 740 4-Door Sedan 2.3L L40D
Data at 1360 RPM ... Data al 2000 RPM Data at 2630 RPM
I 14 4# || || pQ
Manifold Absolute Pressure (lcPa)
"Manifold Absolute Pressure (ttFa)
"Manifold Absolute Pressure (tPa)
1991 Volvo 740 4-DoorSedan 2.3L L40D 1991 Volvo740 4-DoorSedan 2.3L L40D 1991 Volvo 740 4-
Data al 3260 RPM
Data at 5950 RPM
Data at 4540 RF
2.3L L40D
Manifold Absolute Pressure (VPa) " "Manifold Absolute Pressure (tcPa) "
1991 Volvo 740 4-DoorSedan 2.3L L40D 1991 Volvo 740 4-Door Sedan 2.3L L40D
Data al 4900 RPM Data at 5350 RPM
Manifold Absolute Pressure (tPa)
'Manifold Absolute Pressure $Pa)
Manifold Absolute Pressure Pa)
------- |