EPA-AA-SDSB-81-2
Technical Report
An Energy Demand Model for Light-Duty Vehicles,
with Concepts for Estimating Fuel Consumption
by
Terry Newell
April 1981
NOTICE
Technical Reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis of
issues using data which are currently available. The purpose in
the release of such reports is to facilitate the exchange of tech-
nical information and to inform the public of technical develop-
ments which may form the basis for a final EPA decision, position
or regulatory action.
Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Source Air Pollution Control
Office of Air, Noise and Radiaton
U.S. Environmental Protection Agency
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EPA-AA-SDSB-81-2
An Energy Demand Model for Light-Duty Vehicles,
with Concepts for Estimating Fuel Consumption
by
Terry Newell
April 1981
NOTICE
Technical Reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis of
issues using data which are currently available. The purpose in
the release of such reports is to facilitate the exchange of tech-
nical information and to inform the public of technical develop-
ments which may form the basis for a final EPA decision, position
or regulatory action.
Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Source Air Pollution Control
Office of Air, Noise and Radiaton
U.S. Environmental Protection Agency
-------
I. Introduct ion
This report presents and discusses a computer program that
models the energy demand at the drive wheels of a light-duty
vehicle operated over a specified driving cycle. The model is
based on direct interpretation of the physical forces that act on a
vehicle in motion. In this manner, the model deterministically
calculates the energy required to operate the vehicle.
The energy model is also used to estimate vehicle fuel con-
sumption. In this application of the model, the underlying concept
is that fuel consumption can be related to energy demand if the
characteristics of the drivetrain are known. It is because of the
importance of this link that this approach is described as a
conceptual means of estimating fuel economy.
There are several advantages inherent in estimating vehicle
fuel consumption by this type of approach. The most significant is
cost. If a direct empirical approach is taken to observe small
changes in parameters affecting vehicle fuel economy, the resulting
effects are easily obscured by other factors, and multiple tests
are required to isolate and quantify these effects. The "noise" in
a computer simulation is limited and predictable; thus a single
inexpensive computer modeling provides the desired information.
In his book on computing for scientific and engineering
applications, Richard Hamming emphasizes the philosophy that "the
purpose of computing is insight, not numbers."[1] The primary
intent of this model is to provide the user with added insight into
the effects on vehicular energy demand that occur, as vehicle and
driving cycle parameters are varied.
The following sections of this report describe the development
of the energy demand modeling program, the use of the program, and
the verification of using the energy demand concept to estimate
vehicle fuel consumption. In addition, several applications of the
model are presented and other potential applications are discussed.
II. Development of the Energy Demand Model
A. General
The guiding principle in the development of this model was the
efficient determination of energy demand, which then can be used to
estimate fuel consumption. Energy demand is computed by maintain-
ing a cumulative total of the vehicle power requirements at each
time interval. These powers are computed from knowledge of the
forces acting on the vehicle. Therefore, these forces are the
fundamental parameters required by the model. This program con-
siders the three primary forces that act on a vehicle that is in
motion on a level surface:
F = F + F + F (1)
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where:
F = component of total force due to rolling resistance;
F = component of total force due to aerodynamic resistance;
and ,
F = component of total force necessary to overcome inertia.
The rolling resistance component of the total acting force is
primarily a function of the tires used on the vehicle. Tire
rolling resistance is nearly constant at velocities up to approxi-
mately 60 mi/hr. [21 Since the EPA urban (modified LA4) and Highway
Fuel Economy Test (HFET) cycles do not specify driving in excess of
60 mi/hr (the top speeds are 56.7 mi/hr and 59.8 mi/hr, respec-
tively), modeling rolling resistance as velocity-independent is
reasonable.
Aerodynamic drag increases proportionally with the square of
velocity, and the force due to inertia is the product of the mass
of the vehicle and its instantaneous rate of acceleration. Thus,
the total force acting on the moving vehicle can be expressed[3]
by:
which is a reformulation of equation (l). This is the basic
equation of the model. Energy demand can be computed from equation
(2) after the force coefficients f and f and the mass of the
vehicle, along with a driving schedule, have been supplied.
B. The force coefficients
The values of fn and f for use in equation (2) are typically
not available in this direct form. Values of these force coeffi-
cients can be obtained from three other, more readily available
forms of vehicle data. Each of these is particularly well-suited
for a given type of simulation by the model, and are briefly
outlined below.
1. Road/track coastdown data. If road coastdown data have
been collected and analyzed for the vehicles of interest, the
resulting coefficients of the acceleration equation can be used to
obtain values of f and f . This method of determining the
force equation coefficients is the best for modeling vehicle energy
demand for on-the-road operation.
Analysis of the speed versus time data collected during
coastdown testing gives an equation describing the deceleration of
the vehicle: [3]
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A = an + a2 V2. (3)
Applying Newton's Second Law of Motion and distributing yields:
f0 - tna0 (4)
f2 = ma2 (5)
(Since there is no conventional assignment of units for a and
a_, care in applying unit conversion factors to the right-hand
side of equations (4) and (5) is necessary). From these numbers,
the energy demand of the vehicle operated on the road according to
a given driving cycle can be modeled.
2. Dynamometer coastdown data. If a vehicle-dynamometer
coastdown has been conducted for the vehicle in question, the
results of that test can be used to determine values for fn and
f „. This method of obtaining values for the force coefficients is
tfie best for use in modeling energy demand of the vehicle operated
on the dynamometer. The information required is the 55 to 45 mi/hr
coastdown time At, and the actual (total) horsepower absorbed by
the dynamometer, AHP.
The total force acting on the vehicle at the road-dynamometer
match point speed of 50 mi/hr is approximated by:
(6)
F(50) = m(-^)
At
Of the total power absorbed by the dynamometer (AHP), the
power absorber unit (PAU) accounts for the greatest portion. The
power absorbed by the PAU is proportional to the cube of the
velocity. Therefore, converting dynamometer AHP from horsepower to
watts and factoring out the velocity yields an estimate of the
component of total force that is proportional to the square of the
velocity:
745.7 - x AHP ,..v
F = h£ (7)
A sn El 1609.3 m-hr
5 hr X 3600 mi-s
The use of dynamometer AHP in equation (7) results in a slight
overestimation of the V force term of equation (2), since it
includes some minor effects (e.g. dynamometer bearing friction)
that may not be proportional to V . The PAU setting can be
substituted for the AHP in equation ,17) if desired; however, this
would tend to underestimate the V component. The AHP .value
appears to be more readily available, and the error in the V term
associated with its use is relatively small.
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Equations (6) and (7) can then be used to obtain values of
f0 and f2:
fQ = F(50) - FA (8)
_ ^A, V = 50 mi/hr = 22.35 m/s (9)
2 = V2
and vehicle energy demand over the driving cycle, on the dyna-
mometer, can then be modeled.
3. Vehicle design parameters. Modeling energy requirements
using force coefficients derived from vehicle design parameters,
such as aerodynamic drag coefficient, allows certain analyses to be
performed concerning design goals and future possibilities. Using
this type of input to the model, the drag coefficient (or mass
reduction, etc.) required for a targeted fuel economy increase can
be estimated. Conversely, the impact on energy demand and fuel
economy of intended changes in design parameters can be approxi-
mated. In this case, the force coefficients are:
fQ = (mg)(RRC) (10)
where:
m = vehicle mass (kg)
2
g = acceleration due to gravity (9.81 m/s )
RRC = rolling resistance coefficient of tires; and
f =1
2 2 p V
where:
p = air density (kg/m )
C = coefficient of aerodynamic drag
A = vehicle frontal area.
Equation (2), which forms the basis of the energy demand
calculations, can then be reformulated as:
2 A (12)
F = (mg)(RRC) + ( p CA)V
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From equations (10) and (11) it is apparent that the force co-
efficients can be computed given the mass of the vehicle, the
rolling resistance of the tires, and the aerodynamic parameters
of the vehicle. Note that the important information for cal-
culation of f is the product of the frontal area and drag co-
efficient.
Equations (10) and (11) also provide a means of estimating
values of the vehicle design parameters from road or dynamometer
coastdown data:
RRC = fQ/mg (lOa)
CDA = 2f2/p (lla)
The rolling resistance coefficient obtained from (lOa) will
include wheel bearing and other losses, and as such will be
slightly higher than the measured value for the tires only. If the
vehicle frontal area is known, then an estimate of C can also be
derived from equation (lla).
C. The Energy Demand
After all of the information necessary for solving the force
equation,
has been assembled, the vehicle energy demand can be modeled. This
basic equation of the forces acting on the vehicle is solved at
each second for the duration of the specified driving cycle.
The physical interpretation of this solution depends upon
the signs of the total force at velocity V, F(V), and the inertial
term of the right-hand side, m dv/dt. There are three combinations
of the signs of these terms that can occur, each representing a
different physical situation.
If the vehicle is accelerating or is maintaining a constant
nonzero velocity, then m dv/dt _> 0 and F(V) > 0. In this case,
all of the forces acting on the vehicle result in power being
demanded of the engine. The current (instantaneous) power demand
is obtained by multiplying total acting force by current velocity:
P = FV.
When the acceleration is negative (i.e., the vehicle is
decelerating), the inertia component of total force is also nega-
tive. The situation has a different physical meaning dependent on
whether the total acting force is positive or negative.
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If the acceleration is negative but the magnitude of the
rolling resistance and aerodynamic terms is sufficient to result in
a net positive acting force, then power is still being demanded
from the engine. Physically the vehicle is operating under powered
deceleration: the rate of deceleration is slower than that of a
"free" coastdown, and power from the engine is required to main-
tain the prescribed driving schedule.
During rapid decelerations, especially at low speeds, the
magnitude of the negative inertia term can equal or exceed the sum
of the (positive) rolling resistance and aerodynamic components,
resulting in a zero or negative total force F. The vehicle is
either freely coasting or braking, and no energy is being demanded
from the engine to keep the vehicle moving in the prescribed
fashion.
III. Computer Operation of the Model
This section of the report describes the Fortran computer
program used to model LDV energy demand, the required input, and
the program output. A listing of the program is provided as
Appendix A for reference. The statements having line numbers
enclosed in boxes are used only to estimate fuel economy from
modeled energy demand (See Section IV), and are deleted if only
energy demand is desired as output.
A. Input
Two sets of data are necessary for running the basic energy
demand modeling: vehicle parameters and a driving cycle. The
driving cycles that have been used in the development and testing
of the model are the modified (1371 second) version of the LA-4
cycle, which forms the basis of the EPA urban driving cycle
(FTP),[4] and the 765 second highway fuel economy test (HFET)
cycle.[5] Any driving cycle that is defined by a time versus
velocity history can be used.
The driving cycle should be listed as a time-vs-velocity
table, with time intervals of one second and velocity given in
miles per hour. Conversion of mi/hr to m/s is built into the
program; if the velocities are given in units other than mi/hr,
one line of the program must be modified or deleted.
The required vehicle information consists of the coefficients
of the force equation (2). These can be supplied to or calculated
by the program, as described in the previous section. All of the
calculations in the program are performed using SI (metric) units;
the appropriate units for each program variable are given as part
of the program listing in Appendix A.
One other short data file must be attached to the program,
containing the number of cases to be run, the length of the
driving cycle in seconds, and an indication of the type of vehicle
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tire-wheel-brake assembly is known, an appropriate adjustment can
be made to the vehicle mass and entered as part of the vehicle
data. When this information is not known, as is generally the
case, standard (default) estimates are used.[3] These estimates
are built into the program:
M = 1.035 m (road) (16)
M = m + 0.018 m (dyno) (17)
where:
M = total effective mass of vehicle (road simulation) or of
vehicle-dynamometer system (dynamometer simulation)
m = gravitational mass of vehicle
m = equivalent mass simulated by the dynamometer flywheels.
The contribution of the rotating wheels to the total effective mass
is, of course, less on the dynamometer than on the road, since only
the two driving wheels are rotating during dynamometer operation.
Since the acceleration dv/dt is negative if V(i) < V(i-l), the
inertia component of total force is frequently negative. After
calculating the force acting on the vehicle by equation (15), the
model tests the signs of the total force and the inertia component.
As was discussed in the previous section, there are three possible
outcomes of this dual check: 1) both are nonnegative, 2) the
inertia term is negative but the total force remains positive, and
3) both are negative. These three cases are treated seperately in
the model, as described below.
B. Three Modes of Operation
In the first case, where both the total force and its inertia
component are positive, all of the acting forces result in power
being demanded of the engine. This condition is identified in the
program as "A"-mode, and can be physically interpreted as accelera-
tion or steady-speed cruise.
A cumulative total of all "instantaneous" power demands
represents the total energy demand. When all of the terms of
equation (15) are nonnegative, the maintenance of individual suras
representing rolling resistance, aerodynamic, and inertia demands
corresponds to the actual physical breakdown of energy demand.
The second case, where the inertia component is negative but
of insufficient magnitude to provide for all of the demand of the
rolling resistance and aerodynamic components, is identified in the
program as "B"-mode. Vehicle operation in "B"-mode can be
physically interpreted as deceleration without braking. Stored
kinetic energy resulting from the motion of the vehicle is used to
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data to be used and the type of operation (dynamometer or road) to
be simulated. The number of cases refers to the number of dis-
tinct sets of vehicle data to be modeled over the same driving
schedule, and is limited only by time and cost to the user.
The length of the cycle in seconds is used to control the num-
ber of loop iterations per vehicle. The EPA and SAE standard
driving schedules are all under 2000 sec; if a cycle of longer
duration is to be used, the dimensioning of the velocity vec-
tor V must be increased. The third entry in this file is "1," "2,"
or "3," corresponding to the use of dynamometer coastdown data,
road coastdown data, or vehicle design parameters respectively.
Simulation of dynamometer operation is assumed if dynamometer
coastdown data is input, and road operation is simulated if the
other two types of input data are used. The distinction between
road and dynamometer simulation is detailed in the subsection on
calculations, below.
B. Calculations
After f and f have been read into or calculated by the
model, there is a loop of instructions that is executed once for
each second of the specified driving cycle. One pass through this
loop is described here.
The driving cycle has been input to a vector V, where V(i) is
the velocity at time t = i, 1 _<_ i _<_ number of seconds in cycle.
The mean velocity for the i second and the acceleration during
that second are calculated as:
V(i) = [V(O + V(i-l
dv/dt(i) = V(i) - V(i-l)
(13)
(14)
The total force acting on the vehicle during the time segment t = i
is then the sum of the rolling resistance, aerodynamic, and inertia
components:
= fQ(i)
f, tv(i)]2
m dv/dt(i)
(15)
Within the model, the primary difference in the simulations of
dynamometer and road operation is in the handling of the mass in
computing total acting force by equation (2) or (15). If road
operation is to be simulated, then the gravitational mass of the
vehicle is entered; the equivalent mass simulated by the dynamom-
eter flywheels is entered for dynamometer simulations. There is
also a difference between these simulations in the estimation of
the effective equivalent masses of the rotating tire-wheel-brake
assemblies, which are required for calculation of the inertia
component of total acting force.
In either type of simulation, if an experimentally measured or
calculated value of the effective equivalent mass of one rotating
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overcome part of the acting rolling and aerodynamic resistances,
but there is still a net positive force to be overcome.
When the vehicle is in the "B"-mode of operation, the total
net power demand, P = FV, is added to the cumulative total just as
is done in "A"-mode. However, the individual contributions to the
total energy demand resulting from rolling resistance and aerody-
namic losses must be treated differently than when in "A"-mode.
The tire and aerodynamic energy demands cannot be simply added to
their respective component sums, since this results in the sum of
these energy demand components exceeding the total vehicle demand.
Consequently, the proportion of the corresponding steady-speed
energy demand that is required is calculated, and this proportion
of the rolling resistance and aerodynamic terms is added to their
respective component sums. That is, the actual total acting force
is given by:
F[V(i)] = f0 + f2 [V(i)]2 + m dV/dt(i) (18)
where /dt(i) is negative. During vehicle operation at the
corresponding steady speed, the total acting force would be:
F'[V(i)] = f0 + f2 [V(O]2 (19)
The proportion of the total steady-speed force that is required at
V(i), in "B"-mode, is therefore the ratio of the actual total force
to the corresponding steady-speed force:
F[V(i)]/F'[V(i)] (20)
Thus, it is this proportion of the rolling resistance and
aerodynamic losses that are added to the respective component sums:
FT' = FTtF(V(i))/F'(V(i))] (21)
FA' = FA[F(V(i))/F'(V(i))] (22)
A A
In "B"-mode, the inertia term of equation (18) is negative; no
energy is being demanded of the engine to overcome inertia.
Therefore, the component sum representing energy demand due to
inertial effects (kinetic energy) is not incremented.
In the event that the inertia component of force is negative
and -F > F + F , so that F < 0, no power is demanded from
the engine. This is indicated in the model as "C"-mode, and is
physically interpreted as the vehicle braking. In "C"-mode, none
of the component sums representing individual energy demands are
incremented .
All of these calculations in the model are performed in
SI units; therefore, integration of power demand over time to yield
energy demand reduces to simply summing the power demands for each
second (without problems with units and conversions). Similarly,
summing V(i) in m/s yields the total distance traveled in meters.
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It should be noted that it is the existence of the condition
identified in the program as "B"-mode that necessitates the sec-
ond-by-second calculations of the model. If either of these
simplifying assumptions are made: a) all of the kinetic energy of
vehicle motion is returned for use in overcoming rolling resistance
and aerodynamic losses, or b) none of this kinetic energy is
returned for useful work; then the equations used to determine
energy demand reduce to a set of definite integrals that depend
only on the characteristics of the driving cycle. Since the
vehicle parameters would have no effect on the solution of these
integrals, they can be solved once for any given cycle. The
solutions of these integrals and the vehicle parameters could then
be combined algebraically to yield the tractive energy requirement
of the vehicle over that cycle.
C. Output
The program output can be considered in three parts: the
vehicle information, the energy demand and its breakdown, and
auxiliary information. These are briefly discussed below.
The vehicle information listed includes the identifying
numbers (a case number for that run and an arbitrary vehicle
identification number). The input information is listed for
reference, and as a check on input accuracy. If vehicle design
parameters were supplied, they are listed with the calculated
values of the force equation coefficients. If the force equation
coefficients were derived from road or dynamometer coastdown data,
they are listed along with backcalculated values for the vehicle
design parameters from equations (lOa) and (Ha). The data in this
block are labeled to indicate what was supplied as input and what
was calculated by the program.
Energy demand has already been discussed; the total and each
of the contributing terms are labeled and listed. In addition,
the algebraic sum of all of the inertia component energy terms is
printed. In any driving cycle with equal initial and terminal
velocities (zero, for the EPA cycles), the true algebraic sum of
all kinetic energy terms is zero. Therefore, the value printed
should be near zero; any significant deviation from zero is indica-
tive of errors in the modeling program.
A few other lines of information are also output. The
time (sec) spent in each of the three "modes" of operation dis-
cussed earlier is listed. The time spent in "A"-mode is a function
of the acceleration characteristics of the driving cycle used,
and is vehicle-independent. For the EPA urban and HFET cycles,
"A"-mode consumes 544 sec and 319 sec, respectively. The division
of the remaining time between the "B" and "C"-modes is dependent on
the mass, the tire rolling resistance, and the aerodynamic drag of
the specific vehicle.
Distance traveled over the cycle is computed in meters and
converted to miles, and both are printed. The maximum power
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demanded by the vehicle at the drive wheels is listed, along with
the time of its occurrence within the cycle. The maximum power
demands for vehicles over the LA4 cycle occur during the 195th or
196th seconds, when accelerating at a rate of approximately 3
mph/sec from velocities of 30-35 mi/hr. Different vehicles experi-
ence peak power demand in the HFET cycle at several different
times, depending on the relative contributions of the aerodynamic
(V ) and inertial (dv/dt) terms.
D. Basic Error Check
A check for gross error in the computer program consisted
of modeling the energy demand of two base-value vehicles and
several odd variations of those vehicles. The base vehicles
used for this were a 1980 model Volkswagen Rabbit, representing
a small car, and a 1981 model Ford F150 4x4 pickup truck, repre-
senting a relatively large LDT. The three primary vehicle de-
scriptors (m, RRC, CDA) were then set to zero, singly and in
pairs, and the corresponding energy demands modeled. In these
configurations, the energy demands of the vehicles can be checked
algebraically without using the model.
A vehicle having a mass of zero, while maintaining its as-
sociated gravitational weight, would require no kinetic energy over
the cycle: the inertia component F of total acting force would
always be zero. (Maintaining the gravitational weight associated
with the original mass is necessary to keep the energy required for
overcoming rolling resistance from being affected.) Elimination of
the kinetic energy requirement means that the total energy demand
becomes the sum of the energy required to overcome the rolling
and aerodynamic resistances.
If the base vehicle maintains its mass and weight, but is
assumed to have a frontal area or drag coefficient of zero so that
C A = 0, then no energy is required to overcome aerodynamic drag.
Similarly, if the rolling resistance of the tires and tire-wheel-
brake assemblies is zero while mass, weight, and aerodynamic
characteristics are unchanged, then no energy will be required for
overcoming rolling resistance.
Setting two of these three primary descriptors equal to
zero at a time, three other "dummy" vehicles are generated.
Each of these last three vehicles have a total energy demand
equal to one of the components: rolling resistance, aerodynamic
drag, or kinetic. Running these "dummy" cases through the model
revealed no errors in the handling of equation (15) and its
terms.
To this point, discussion has focused on the concepts that
form the basis for the calculation of energy demand, and on imple-
mentation of the model as a computer program. The last sections of
the report present several suggested applications of the program.
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IV. Uses of the Model
The use of vehicular energy demand modeling can be divided
into two general groupings: prediction of the relative energy
requirements of vehicles of the future, and as an aid in both the
selection of vehicles for test programs and the evaluation of
test results.
A. Future Vehicle Performance
As was briefly discussed in Section II, specification of four
vehicle design parameters (mass, frontal area, coefficients of
rolling resistance and aerodynamic drag) allows calculation of the
force equation coefficients, and hence of cycle energy demand. One
major advantage of any modeling exercise is the ability to consider
systems that may not be available for direct empirical investiga-
tion. One of the first uses of this model was to predict the fuel
economy that may be possible with current and future optimized
technology vehicles.
Assumptions. Several assumptions were made to simplify and
enhance prediction of fuel consumption from modeled energy demand
of the optimized vehicles. Foremost among these was the use
of a continously variable transmission (CVT). Such transmis-
sions have already been successfully installed in some European
vehicles, and are currently under further development by Borg-
Warner.[6] Furthermore, it was assumed that the CVT would be
controlled, probably through the use of microprocessors, to
always seek the point of maximum engine efficiency possible under
the required loading. A final related assumption was that the
transmission and drivetrain system had a constant efficiency of
ninety percent; that is, only one-tenth of the engine power avail-
able at the flywheel is lost before reaching the axle of the drive
wheels.
Under these assumptions the model can be used to directly
calculate fuel consumption, if fuel consumption rates are given as
a function of demanded power. This information can be obtained
from a simple one—dimensional engine map. A set of points repre-
senting fuel consumption as a function of power demand are taken
from this map, and linear interpolation is used to determine fuel
consumption at intermediate levels of power demand.
Optimized Vehicles. Three general size categories of vehicles
were chosen for this investigation. In order of increasing size
and weight, these were (i) two-passenger vehicles, (ii) four-
passenger vehicles, and (iii) five-or-six-passenger vehicles and
light-duty trucks, combined in one group. For each of these
classifications based on size, two levels of technology, described
as current best (CB) and advanced technology (AT) were considered.
The technological level refers to values taken for the four design
parameters required to calculate the coefficients of the force
equation. The CB values have been achieved in vehicles available
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today, although not necessarily all simultaneously in a single
model. Advanced technology is better, in the sense of lowering
energy demand, than technology in use today; however, this can be
achieved within the framework of current technology. The values
chosen for the design parameters of these vehicles are presented in
Table 1.
A few comments regarding the values assumed for the vehicle
parameters for the current best (CB) and advanced (AT) levels of
technology should be noted. In the case of vehicle mass, there are
production vehicles representing each of the three size classes
discussed having masses near or below the masses listed for the CB
vehicles. In the two-passenger category, the MY1980 Daihatsu Max
Cuore, with a mass of 545 kg, [7] is already nearer to the AT than
to the CB mass. The four-passenger MY1980 Audi L, with a carrying
capacity of about 1,000 lb, has only 910 kg mass.[7] This is
almost exactly the mass assumed for the CB four-passenger vehicle.
One version of the Volkswagen Jetta, the GLI, can carry nearly as
great a load (948 Ibs), yet its mass is less than 800 kg in a
2-door version. The mass of the MY1980 Volkswagen front-wheel-
drive diesel pickup truck, a vehicle fitting the largest of
the three size categories discussed, is only 928 kg.[8]
Rolling resistance of automobile and light truck tires is
frequently expressed as a rolling resistance coefficient (RRC).
The RRC indicates the units of rolling resistance force (lb, N)
per thousand units of vertical load. The assumed current best
value, 0.008, is already being attained, at Least in some low
rolling resistance tires. In an ongoing EPA test program to
measure the rolling resistance of tires, data collected to date
indicate that there are tires widely available in today's market-
place with flat-surface RRCs in the range of 0.0082 to 0.0090, [9]
when tested in accordance with the EPA Recommended Practice for
Determination of Tire Rolling Resistance Coefficients (80 percent
of design load, at 35 psi).[10] The continuing efforts by the tire
industry to reduce rolling resistance seem likely to result in
tires having RRCs at or below the 0.007 assumed for advanced
technology.
Aerodynamic drag coefficients lower than the assumed current
best value of 0.4 are available in some vehicles today, and coeffi-
cients lower than the assumed advanced technology value of 0.3 will
be available in the relatively near future. Recent research
conducted by Volkswagenwerk AG indicates that reductions in drag
coefficients of as much as 45 percent over today's range (about
0.35 to 0.55) should be achievable with mass-produced passenger
cars.[11] Ford Motor Company is continuing development of a
prototype vehicle, currently known as Probe, which has a drag
coefficient of 0.22.[12] On the basis of these statements, the
assumed values of 0.4 (CB) and 0.3 (AT) certainly appear feasible.
The reductions in vehicle frontal area listed in Table 1 are
relatively small. Lower vehicle masses and improved aerodynamic
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Table 1
Vehicle
Size
Class
Two-
passenger
Four-
passenger
5 and 6-
passenger
and
'personal1
light
trucks
Assumed
Level of
Technology
Current
best (CB)
advanced
(AT)
CB
AT
CB
AT
Mass*
(kg)
680.4
476.3
907.2
635.0
1134.
793.8
C A2
RRC D (m )
0.008 0.4 1.7
0.007 0.3 1.6
0.008 0.4 1.7
0.007 0.3 1.7
0.008 0.4 2.0
0.007 0.3 1.9
C°2 fO f?
(m ) (NJ (kg/m)
0.68 53.3 0.398
0.48 32.7 0.281
0.68 71.1 0.398
0.51 43.6 0.298
0.80 88.9 0.468
0.57 54.5 0.334
Engine
Max imum
Power
(hp)
25
18
31
23
38
28
Scaling
Factor
0.357
0.257
0.443
0.329
0.543
0.400
* Values in this column are test weights. Curb weights would be approximately 136 kg
(300 Ib) lower.
-------
design are likely to result in the assumed decreases in frontal
areas.
Engine Sizing. Maximum power outputs required for the engines
of these six vehicles were calculated to allow adequate performance
with very little excess power. The minimum performance conditions
were (i) that the vehicle be capable of a 55 mi/hr cruise on any
roadway having no more than a five percent grade, and (ii) that
zero to 50 mi/hr acceleration take no longer than fifteen seconds.
The first of these conditions proved to be the more stringent: if
the engine is capable of maintaining the vehicle speed at 55
mi/hr on a five percent grade, then zero to 50 mi/hr acceleration
will take approximately thirteen seconds.
The power required to meet the most severe of these conditions
was then increased to allow for the power demand of accessories
that do not contribute to vehicle motion. The increase for acces-
sories was two hp for the two-passenger vehicle, three hp for the
four-passenger, and four hp for the 5/6-passenger cars and personal
recreational light trucks. These values represent estimates of the
maximum accessory power demand, not the actual power being demanded
for accessories while driving. In estimating energy demand and
fuel economy for these vehicles, it was assumed that an average
in-use accessory power demand of 0.5 hp was operating continuously.
The total power requirements were then rounded up to the next
integer horsepower levels. The maximum power output of the engines
derived from these requirements ranged from 18 hp for the advanced
technology two-passenger vehicle to 38 hp for the current best
technology 5/6-passenger vehicle. These values are listed in Table
1.
Fuel Consumption. The final step necessary was "development"
of fuel consumption versus power output maps for the optimized
engines of these vehicles. The logical starting point was a
small, fuel-efficient engine for which the required data are
currently available. One such engine is the seventy horsepower
turbocharged prechamber diesel engine manufactured by Volks-
wagen. [13] However, the rated power of this engine, 70 hp, is well
in excess of the maximum power requirements of all six of the
optimized vehicles when driven over the EPA driving cycles.
Consequently, the engine maps for these vehicles were obtained by
linear scaling of this map. That is, if an engine with a maximum
power of 30 hp was required, it was assumed that this engine would
develop 30 hp with the same thermal efficiency that the 70 hp
engine had at 70 hp. Similarly, the scaled-down engine was assumed
to have the same thermal efficiency at one-half maximum power as
did the 70 hp engine at half power.
Since the 70 hp engine map used in deriving fuel consumption
as a function of power demand is a prechamber engine, and direct-
injection (Dl) engines are more fuel-efficient than indirect-
injection (IDI) engines, full vehicle/engine optimization suggests
-------
the use of DI engines. There is evidence that the fuel consumption
of a DI diesel engine is approximately twelve percent lower than
that of a comparable IDI diesel engine. [14]
To simulate the maximum fuel economy improvements possible,
the fuel consumption rates from the 70 hp engine map were multi-
plied by 0.88 (reduced by 12 percent) before being entered as data
for the model. In other words, it is assumed that the engines of
these six optimized vehicles will be DI engines, and as such will
operate with the same decrease in fuel consumption relative to IDI
engines that is seen today.
After the power demand P(i), including the 0.5 hp accessory
load, has been computed for a given second t=i of the driving cycle
it is sent, along with the table of fuel consumption versus de-
manded power, to a linear interpolation subroutine. The subrou-
tine determines the interval of power demand within the table that
contains P(i) and interpolates when necessary to determine the fuel
consumption rate. This rate (g/kWh) is multiplied by the power
demand (kW) and divided by 3600 (s/h) to yield the fuel consumption
(g) during the i second.
The resulting value for fuel consumption is returned to the
main program and added to the cumulative .fuel consumption.
This completes the calculations for the i second, and the
programs goes on to evaluation of the (i+l)th second. Fuel
consumption is determined by this method for all of the time
that the vehicle is in "A"-mode (accelerating or cruising).
This method is also used to determine fuel consumption when
the vehicle is in "B"-mode (powered deceleration), except for the
case described in the following section.
Idle Fuel Flow Rate. There are several situations encountered
in the course of the EPA cycles where the method described above
cannot be used to determine fuel consumption. These are: (i)
idling, when the vehicle velocity is zero, (ii) operation in
"C"-mode, when the calculated power demand is negative, and (iii)
those seconds of operation in "B"-mode where the power demand is so
small (approximately 0.6 kW or less) that the interpolated value of
fuel consumption is less than the idle fuel flow rate.
In these three situations, an idle fuel flow rate of 0.12
gal/hr (0.107 g/s) is assumed. The conversion of the measured 0.12
gal/hr idle fuel flow rate to 0.107 g/s is based on density of
7.078 Ib/gal for diesel #2 fuel. This density is in turn based on
an assumed API gravity of 35", corresponding to the midpoint of the
range of API gravity (33° to 37°) specified for diesel #2 as an EPA
test fuel.
The 0.12 gal/hr idle fuel flow rate was measured in tests
conducted at EPA on an Integrated Research Volkswagen (IRVW)
safety vehicle.[15] This vehicle was equipped with a 70 hp turbo-
charged diesel engine, which is equal in maximum power to the
engine of the map used to derive the table of fuel consumption as a
-------
function of power demand. Since the maximum powers of these
engines are equal, the idle fuel flow rate was adjusted in the same
way that the fuel consumption values at given power demands were
adjusted: The base value for idle fuel flow was multiplied by the
ratio of the maximum power output of the engine sized for the
vehicle to the maximum power output (70 hp) of the engine used in
the determination of fuel consumption as a function of power
demand .
When the vehicle is operating in "C"-mode, the scaled idle
fuel consumption is added to the cumulative fuel consumption
without calling the interpolation subroutine. The other two
situations are treated within the subroutine: Before a one-second
fuel consumption value is returned to the main program, it is
checked against the scaled idle flow rate. If the calculated fuel
consumption is less than that rate, the scaled idle flow rate is
returned instead. This ensures that fuel consumption in any second
is never less than the scaled idle fuel flow in one second.
Testing the Method. The general method was tested by using
data representing a Volkswagen Rabbit. Input data was in the form
of vehicle design parameters, as shown below:
mass 1077.3 kg
RRC 0.0120
CA 0.77 m
The rolling resistance coefficient was chosen as representa-
tive of a low (but not exceptionally low) rolling resistance tire,
while the values of mass and C A actually describe a Rabbit.
The fuel consumption versus power demand map was from a 50 hp
naturally aspirated Volkswagen diesel engine. [13] This engine is
very near in power to the 52 hp diesel engine that is available in
MY1981 Rabbits manufactured by VWOA,[7] and hence the fuel con-
sumption figures were not scaled. Accessory load (0.5 hp) and idle
fuel flow rate (0.107 g/s) were treated in the same way as for the
six optimized vehicles.
The FE projections from the energy demand model were 53 MPG
for the LA4 cycle and 61 MPG for the HFET cycle. The urban FE
value represents an increase of approximately 25 percent over the
42 MPG achieved by the most fuel-efficient of the MY 1981 Rabbits.
[16] Since fuel economy increases of 20 percent are possible
through use of CVTs,[6l the modeling approach does not appear to be
overly optimistic.
Fuel economy (results). The fuel economy projections for the
six optimized vehicles are shown in Table 2, along with the cor-
responding energy demands. The model indicates that fuel economy
in the range of 90 MPG could be obtained by the two-passenger CB
-------
Table 2
Urban Cycle
HFET Cycle
Estimated
Vehicle
Size Class
Two-
passenger
Four-
passenger
•
5 or 6-
passenger
and 'personal'
Assumed level
of technology
current best
(CB)
advanced
(AT)
CB
AT
CB
AT
Energy
demand
(MJ)
2.81
1.93
3.43
2.38
4.21
2.88
Fuel
Economy
(MPG)
diesel gas
92
127
77
105
64
89
83
114
69
94
57
80
Energy
demand
(MJ)
4.88
3.36
5.38
3.84
6.48
4.46
Estimated
Fuel
Economy
(MPG)
. diesel gas
87
123
79
109
66
94
78
111
71
98
59
85
light trucks
-------
technology vehicle; this increases to approximately 120 MPG for the
advanced technology two-passenger vehicle. The increases in FE for
the AT vehicles over the CB vehicles, in the other size classes,
were also in the 35 to 40 percent range.
To estimate gasoline-equivalent fuel economy, the greater heat
content per unit volume of diesel #2 fuel over typical gasoline was
taken into account. The ratio of these heating values (138,700
BTU/gal for diesel #2, and 125,000 BTU/gal for gasoline[17]),
138.7/125 = 1.11, was multiplied by the cycle fuel consumption to
estimate gasoline-equivalent fuel consumption. The resulting
gasoline-equivalent fuel economy projections are also shown in
Table 2.
An aspect of the optimization of all four parameters (m, RRC,
C , A) that was not anticipated was the reversal of the ranking
or urban and highway fuel economy from the commonly accepted
order. For all of the vehicles in the 1981 Gas Mileage Guide[16],
highway FE is greater than urban FE. This relation also holds for
the two larger size classes of vehicles used in these projections,
although the gap between urban and highway FE for these vehicles is
relatively small. For the two-passenger vehicles, both CB and AT,
projected city FE exceeds projected highway FE. .
Table 3 shows the relative contributions of kinetic and
aerodynamic energy demand to total energy demand for these six
vehicles, over both of the EPA cycles. The kinetic energy demand
dominates the urban cycle, while aerodynamic drag dominates on the
highway cycle. The fuel economy reversal of the two cycles occurs
because for the chosen optimized values of the vehicle parameters,
the decreases in the kinetic energy requirements for urban driving
are much greater than the decreases in the aerodynamic energy
requirements for expressway driving.
In addition to the use of the model to estimate potential
improvements in energy demand and fuel economy, there are other
uses that apply to future and current vehicles, and to testing.
Sensitivity of energy demand to changes in the primary vehicle
parameters can be investigated, as discussed in the next section.
The last section briefly touches on some of the other possible
applications of the model.
B. Sensitivity Analysis
An energy demand model can be useful in investigating the
impact on energy demand of changes in different vehicle para-
meters. The effect of small variations in aerodynamic character-
istics (C A), for example, may be obscured in the "noise" of data
from actual tests. This assumes that two vehicles that are identi-
cal except for the parameter of interest can be found for testing;
this is often not the case, and in some instances (e.g., change
frontal area only) it may be impossible.
-------
Table 3
Vehicle
Size
Class
Two-
passenger
Four-
passenger
5/6-passen-
ger & light
truck
Assumed level
of technology
Current best(CB)
Advanced (AT)
CB
AT
CB
AT
LA4
EK
E
0.508
0.519
0.555
0.559
0.565
0.578
cycle
EA
E
0.278
0.285
0.221
0.239
0.210
0.218
HFET
IK
E
0.162
0.164
0.195
0.192
0.203
0.206
cycle
!A
E
0.607
0.620
0.536
0.565
0.521
0.538
where:
E
EA
total energy demand over cycle (at drive wheels)
kinetic energy requirement
aerodynamic energy requirement
-------
Table 4 presents the results of running an abbreviated sensi-
tivity analysis using the basic energy demand model. The four-
passenger vehicle with "current best technology" design parameters
from the previous section was selected as the vehicle for this
analysis.
First, the vehicle has its energy demand modeled using the
values of mass, RRC, and C A as given in Table 1. The energy
demands over both the LA4 and HFET cycles are then used as base
values, along with the maximum power demand in each cycle. The
CB four-passenger vehicle is then run through the model several
additional times; in each of these runs, one of the three vehicle
descriptors is either increased or decreased by ten percent. The
results of the additional modelings are compared with the baseline
results to examine the sensitivity of energy demand to the changes
in the design parameters.
The numerical results of these modelings are listed in Table
4, along with the percent changes in energy demand and maximum
power demand associated with ten percent changes in mass, RRC, and
C A. Over the LA4 cycle, ten percent changes in vehicle mass
resulted in approximately seven percent changes in energy demand.
Ten percent variations in aerodynamic behavior, as characterized by
C A, caused changes in the vicinity of three percent in energy
demand; and ten percent changes in rolling resistance, as charac-
terized by the RRC, changed energy demand by about two percent.
In the HFET cycle, with its much greater average speed and
relatively minor accelerations and decelerations, changes in the
aerodynamic parameter C A caused the greatest changes in total
energy demand: approximately six percent, for ten percent varia-
tions in C A. Increasing or decreasing the vehicle mass by ten
percent changed energy demand by just less than four percent. The
percentage effects of rolling resistance changes were almost the
same as for the LA4 cycle, around two percent.
C. Additional Applications
Selection of Vehicles for Testing. Another potential use of
an energy-demand model is assistance in selecting candidate vehi-
cles for some testing programs. Consider a hypothetical example:
Assume that a test program has been planned to investigate the
differences between dynamometer simulation accuracy for front—wheel
drive (FWD) and rear-wheel drive (RWD) passenger cars; and further
that sufficient test data exist to suggest the FWD vehicles experi-
ence greater loading than do RWD vehicles when tested on dynamo-
meters. The primary objective of this hypothetical test program
is to determine if FWD vehicles actually are more severely loaded
on the dynamometer relative to RWDs.
By entering the available test data in this model and com-
puting the energy demands, valuable insight could be gained as to
which vehicles would best be chosen for testing. Pairs of vehi-
cles, one FWD and one RWD, that exhibit similar internal and
-------
Table 4
Baseline vehicle parameters:
mass 907
RRC 0
C A 0
-------
external characteristics but have modeled energy demands that
differ greatly would be good test candidates, as would any FWD
vehicle whose modeled energy demands differed widely depending on
whether road-derived or dynamometer-derived data were input. By
this exercise, the vehicles that are most likely to demonstrate the
suggested problem will be selected for testing. (This is cited
only as an example. The FWD/RWD simulation accuracy is dependent
on the distribution of vehicle weight between the front and rear
axles.)
In a similar vein, this model could aid in the discretionary
selection of vehicles for confirmatory testing. For all test
vehicles, the required information for modeling energy demand on
the dynamometer is available. Vehicles that display ratios of
modeled energy demand to fuel economy (MJ/MPG) that are unusually
high or low would be obvious candidates for confirmatory testing.
The question that can be answered using the model is: Based
on the modeling parameters, which of the vehicles of the possible
test group are most likely to exhibit the highest levels of NOx
emissions and the lowest fuel economy? Consider a pair of vehi-
cles sharing engine and transmission/drivetrain characteristics in
common, one of which will be a discretionary choice to be tested.
In such a case, vehicle A may have a greater mass than vehicle B,
while vehicle B has a higher value for total dynamometer power
absorption. By modeling the energy demand of these vehicles
and choosing the vehicle with greater energy demand for confir-
matory testing, the lower of the two in fuel economy (and probably
the greater in NOx emissions) will be tested.
Test result guidelines. When a fuel economy-related test
program is planned, the test vehicles could be run through the
model before testing commenced. The results of the pre-test
modeling can serve as guidelines in evaluation of the test data,
flagging test results that deviate beyond reasonable allowances
from the modeled output. Such a pre-test exercise might allow
earlier detection and correction of errors that otherwise may
have gone undetected, and been suspected only at the conclusion of
the program. Another benefit is that more test time can then be
concentrated in areas, or on vehicles, where apparently anomalous
results are occurring.
This is not a complete list of the potential uses of a model
of this type. In general, it is attractive because it provides
insight into many aspects of vehicle energy demand at low cost.
-------
References
1. Hamming, R.W., Numerical Methods for Scientists and
Engineers, McGraw - Hill, 1962.
2. "The Measurement of Passenger Car Tire Rolling Resis-
tance," SAE Information Report J1270, October 1979.
3. "EPA Recommended Practice for Determination of Vehicle
Road Load," Attachment I to OMSAPC Advisory Circular 55B, December
6, 1978.
4. "Development of the Federal Urban Driving Cycle," by
Ronald E. Kruse and Thomas A. Huls, SAE Paper 730553, May 1973.
5. "Amendments to the Report on Development of a Highway
Driving Cycle for Fuel Economy Measurements," by C. Don Pausell,
EPA-AA-ECTD-74-2, April 1974.
6. "Belt Drive CVT for 1982 Model Year," Automotive En-
gineering, Vol. 88 No. 2, February 1980.
7. Automobile Club of Italy, World Cars 1980, Herald Books,
1980.
8. "Automotive Trendsetters - Fuel Economy Reigns Supreme,"
Automotive Industries, Vol. 160 No.11, November 1980.
9. "Rolling Resistance Measurements - 106 Passenger Car
Tires," by Gayle Klemer, EPA-AA-SDSB-81-3, to be published.
10. "EPA Recommended Practice for Determination of Tire
Rolling Resistance Coefficients," by Glenn D. Thompson, March 1980,
amended August 1980.
11. "Necessity and Premises for Reducing the Aerodynamic Drag
of Future Passenger Cars," by R. Buchheim, K.-R. Deutenbach, and
H.-J. Luckoff, SAE Paper 810185, February 1981.
12. "The Fords in Our Future," Automotive industries, Vol.
161 No. 3, March 1981.
13.. "Data Base for Light-Weight Automotive Diesel Power
Plants," by B. Wiedemann and P. Hofbauer, SAE Paper 780634, June
1978.
14. "Sofim Small High-Speed Diesel Engines - D.I. Versus
I.D.I.," by V.G. Carstens, T. Isik, G. Biaggini, and G. Cornetti,
SAE Paper 810481, February 1981.
15. "Evaluation of Two Turbocharged Diesel Rabbits," by
Edward A. Earth and James M. Kranig, EPA-AA-TEB-80-4, October
1979.
-------
References (cont'd)
16. "1981 Gas Mileage Guide - EPA Fuel Economy Estimates,"
First Edition, September 1980.
17. Oak Ridge National Laboratory, Transportation Energy
Conservation Data Book: Edition 4, ORNL-5654 for U.S. Department of
Energy, September 1980.
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18
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20
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33
34
35
36
37
38
39
40
41
42
43
44
/iK
tD
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60"
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
APPENDIX A
««»«« LDV ENERGY DEMAND MODEL **»»»
VARIABLE DIMENSIONS: VMASS, IMASS(KG); CDA(M»»2>; RHO(KG/M«*3)i
Dl(M); D2(MI); V» DVDT, VMEAN(M/SM AOtMI/HK-SH A2(HR/MI-S)I
FO, FTOT, FCON, FVSQ» FORCE, FORCE2, TIREF, AEROFt FINER(N)I
F2(KG/M); POWERt POrt£R2» TIREP, AEROP» PINER, AHPW(W)* TlMEt
TMAX» A, B, C(S); KW, SKW(KW); ENERGY, TIRENG, AEROE, POSKIN,
NETKIN(J); ACC, POWHP, PMAX, AHP(HP); FUEL, SFUEL(G)» IDLE,
SIDLE(GXS); FC(G/KW-HRM MPG(MI/GAL).
i/o ASSIGNMENTS:
REAL V(2000)
INTEGER A, B, C, I,
INTEGER NCAR, NSEC,
6 = OUTPUT FILE
5 = INPUT FILE:
4 = INPUT FILE:
3 = INPUT FILE:
2 = INPUT FILE:
DRIVING CYCLE
VEHICLE DATA
NCAR, NSEC, DTYP
FC/PWR TABLE
REAL VMASS, IMASSf
REflL 01t D2, DVDT,
REAL TIREF* TIREP*
REAL AEROF* AEROP,
REAL FORCE* POWER,
REAL FORCES, POWER2,
J, K»
DTYPt
PMAX
VMEAN
TIRENG
AEROE
ENERGY
POWHP
L
VEHID,
TMAX
REAL»8 FINER, PINER, POSKIN, NETKIN
REAL F2» RRC, CDA, RHO
REAL AHP, AHPW, TIME
REAL AO, A2, FCON* FVSQ, FTOT
INTEGER NMAP, FLAG
REAL KWC15), FC(15), MPG» FUEL* SFUEL, IDLE
REAL SKW(15), SCALE, SIDLE, BTU, MAXHP, MAPHP
A,B,C USED TO DETERMINE TIME SPENT IN EACH MODE:
A-MODE: FORCE > 0 5, FINER > 0
B-MODE: FORCE > 0 & FINER < 0
C-MODE: FORCE < 0 & FINER < 0
A = 0
B •= 0
C •= 0
READ IN KW/FC TABLE FOR INTERP
READ(2,100) MAPHP, NMAP
READ(2,103) (KW(I)fFC(I)t 1=1,NMAP)
IDLE = 0.107
BTU = 1.11
RHO = 1.17
NCAR = NUMBER OF CASES IN RUN
NSEC = LENGTH OF DRIVING CYCLE
DTYP = 1 (DYNAMOMETER COASTDOWN DATA)9
2 (ROAD COASTDOWN DATA), OR
3 (VEHICLE DESIGN PARAMETERS)
READ(3,106) NCAR, NSEC, DTYP
READ DRIVING CYCLE, CONVERT MI/HR TO M/S
READ(5,109) (V(I)» I=1»NSEC)
-------
APPENDIX A (cont'd)
61 DO 1 I = 1, NSEC
62 V(I) = 0.447«Vd)
63 1 CONTINUE
64 c
65 c LOOP: ONCE PER VEHICLE
66 C
67 DO 10 K = 1, NCAR
68 C
69 WRlTE(6tll2) K
70 C
71 C TYPE OF INPUT DATA
72 C
73 IF (DTYP.EQ.3) GO TO 3
74 IF (DTYP.EQ.2) 60 TO 2
75 C
76 C DYNAMOMETER COASTDOWN DATA
77 C
78 REftD<4,115) VEHID» MAXHP, VMASS. AHPt TIME
79 FTOT =
-------
APPENDIX A (cont'd)
T^T] c
122 C SCALE FC/KW ARRAY, IDLE PC
123 c
124 SCALE = MAXHP/MAPHP
125 SIDLE = IDLE»SCALE
126 DO 5 L = 1» NMAP
127 SKW(L) = KW(L)«SCALE
128 5 CONTINUE
129| WRITE<6,142) SCALE
130 C
131 C INITIALIZE RUNNING SUMSt PMAX» TMAX TO ZERO
132 C
133 Dl = 0.
134 AEP.OE = 0.
135 NETKIN = 0.
136 POSKIN = 0.
137 TIRENG = 0»
138 ENERGY = 0.
139 ENGINE = 0.
[1401 SFUEL = 0.
141 PMAX = 0.
142 TMAX = 0
143 C
144 C LOOP: ONCE PER SEC OF CYCLE
145 C
146 00 9 1 - It NSEC
147 C
148 -C CALCULATE DVDT, VMEAN, & DISTANCE TRAVELLED
149 C ,
150 IF (I.EQ.l) GO TO 11
151 J = 1-1
152 DVDT = V(I)-V(J)
153 VMEAN = (V(I)*V(J))/2.
154 GO TO 22
155 11 CONTINUE
156 DVDT = V(I)
157 VMEAN = V(I)
158 22 CONTINUE
159 01 = Dl+VMEAN
160 C
161 C CALCULATE FORCES AT ITH SECOND
162 C
163 TIREF = FO
164 AEHOF = F2
-------
APPENDIX A (cont'd)
C ADO ACCESSORY LOAD TO POWER DEMAND
POWHP = POWHP+0.5
C
IF (POWHP.GT.PMAX) TMAX = I
IF (POWHP.GT.PMAX) . PMAX = POWHP
POwt.R2 = PUWHP*745.7
CALL INTERP(SKW»FC»POWER2»SIDLE»NMAP»FUEL»FLAG)
SFUEL = SFUEL+FUEL
IF (FLAG.EU.l) WRITE(6,199) I
TIREP = TIREF»VMEAN
PINER = FINER^VMEAN
AEROP = AEROF»VMEAN
TIRENG = TIRENG+TIREP
NETKIN = NETKIN+PINER
POSKIN = POSKIN+PINER
AEROE = AEROE+AEROP
ENERGY = ENERGY+POWER
GO TO 8
C
C FORCE IS POSITIVE AND FINER IS NEGATIVE: PROPORTION
C ENERGY DEMAND TO ROLLING AND AERODYNAMIC RESISTANCES
C
6 CONTINUE
B = 8*1
FORCE2 = T1REF+AEROF
TIREF = TlRtF»(FORCE/FORCE2)
AEROF = AEROF*(FORCE/FORCES)
TIREP = TIREF»VMEAN
PINER = FINER*VMEAN
AEROP = AEKOF»VMEAN
POWER = FORCE2*VMEAN
POWERS = POWER/0.9
POWHP = POWER2/745.7
21^ C
215 C ADD ACCESSORY LOAD TO POWER DEMAND
216 POWHP = POWHP+0.5
217 C
218 IF (POwHP.GT.PMAX) TMAX = I
219 IF (POWHP.GT.PMAX) PMAX = POWHP
220 POWER2 = POWHP*74.5.7
221 CALL lNTERP(SKW,FCtPOWER2»SIDLE»NMAPfFUEL»FLAG)
222 SFUEL = SF.UEL*FUEL
223} IF (FLAG.EQ.l) WR'ITE (6,199) I
22<* TIRENG = TIRENG*TIREP
225 NETKIN = NLlMN + PINER
226 AEROE = AEROE+AEROP
227 ENERGY = ENERGY+POWER
228 GO TO 8
229 C
230 C FORCE IS NEGATIVE: CALCULATE INERTIA TERMS AS CHECK
231 C
232 7 CONTINUE
233 C = C+l
23^ PINER = FINEROVMEAN
235 NETKIN = NETKIN+PINER
r?3T] SFUEL = SFUEL*SIDLE
237 C
238 C (THREE BRANCHES REJOINED)
239 C
240 8 CONTINUE
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
APPENDIX A (cont'd)
9 CONTINUE
OUTPUT: BREAKDOWN OF ENERGY DEMANDED
WRITE(6t145) ENERGY,TIRENG,AEROE,NETKINtPOSKIN
COMPENSATE FOR ESTIMATED CVT EFFICIENCY
ENERGY = ENERGY/0.9
WRlTE(6,l4b) ENERGY
02 = D1/16U9.34
WKITE(6,151) 01, 02
WRTTE(6,154) A, B» C
WRITE(6,157) PMAX, TMAX
CONVERT PC TO FE
SFUEL = SFUEL/3218.
MPG = D2/SFUEL
WRlTE(b,160) SFUEL, MPG
SFUEL = SFUEL*BTU
MPG = D2/SFUEL
WKITE(6,163) SFUEL, MPG
RESET "MODE" INDICES
A = 0
B a 0
C = 0
10
100
103
106
109
112
115
118
121
124
127
130
133
136
139
142
145
148
151
154
157
160
163
199
HP'
END OA LOOP
CONTINUE
FORMAT(F5.1,16)
FORMAT(F5.1,F6.i)
FORMAT(315)
FORMATU6F5.1)
FORMAT('CASE NUMBER',14)
FORMAT(15,F5.ltF10.ltF5.ltFl0.2)
FORMAT('VEHICLE #',I5,5X,'MASS:•,F7.1,• KG',5X,'MAX HP:',F5.1,
FORMATUX,'FO =',F7.1,' N',5X,'F2 =',F7.4,» KG/M',10X,'(CALC)')
FORMAT(3X,'AHP =',F5.1,« HP',4*,'55-45 CD TIME:»,F6.2»' S',4X,'(DAT
FORMAT(3X,'RRC =',F8.5,4X,'CDA =',F6.3,» M»»2»»10X,'(CALO')
FORMAT(I5,F5.1,F10.1,F10.4,E12.4)
FORMAT(3X,»AO =»,F7.4,' MI/HR-S',3X,•A2 =»,E12.V,' HR/Ml-S',5X,'(DA
FORMAT(I5.F5.1,F10.1»F10.5,F10.3)
FORMAT(3Xt'RRC = • ,F8.5,4X,'CDA =»,F6.3,» M»»2',1IX,•(DATA)«)
FORMAT(3X,«(SCALING FACTOR',F6.4,')«)
FORMAT('ENERGY DEMANDS: TOTAL:•,E12.4,3X,'TIRE:',E12.4,3X,»AERO:',
,E12.4,3X,'POSK:',E12.4)
(TOTAL:»»E12.4,3X,'AT ENGINE, W/ 90* EFF CVT)')
FORMAT(16X,
FORMATU7X,
FORMATU7X,
FORMAT(17X,
FORMAT(17X,
FORMAT(17X,
FORMAT(3X,«
RETURN
END
DISTANCE:»,8X,F7.1,» M»,bX,F5.2,« MI')
TIME IN MODE:' , OR = IDLE FC RATE)
343 C
344 IFUEL = (IFUEL*IH)/3600.
345 IF (IFUEL .LT. IFLOW) IFUEL = IFLOW
346 GO TO 204
347 203 CONTINUE
348 IFtjEL =
------- |