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I. Purpose
The purpose of this study is to develop equations to predict the
dynamometer adjustment forces appropriate to simulate the on road ex-
periences of light duty trucks.. To accomplish this, equations of road
load versus speed were obtained from a diverse class of light duty
trucks. These data were then converted to dynamometer adjustment forces
appropriate to simulate the on road experience of a vehicle.
II. Introduction
When vehicle exhaust emission tests or vehicle fuel consumption
measurements are performed on a chassis dynamometer, the dynamometer is
usually adjusted to simulate the road experience of the vehicle. Specifi-
cally the dynamometer must simulate the road load of the vehicle. In
this report the vehicle road load is defined as the component of force
in the direction of vehicle motion which is exerted by the road on the
vehicle driving wheels. As defined, the road load force is the force
which propells the vehicle. In the standard case, when a vehicle is
moving with a constant velocity vector on a level surface, this force is
equal in magnitude to the sum of the rolling resistance and the aero-
dynamic drag of the vehicle. Unfortunately, neither this road-tire
force, nor the equal magnitude tire-road force can be directly measured
because of the virtual impossibility of instrumenting the tire-road
interface. Consequently, all experimental methods involve indirect
measurements and some corrective process.
Commonly used methods for road-load determination are: the decelera-
tion or coast down technique, drive line force or torque measurements,
and manifold pressure measurements. The coast down method was selected
as the approach best suited for this study since a method easily adaptable
to a diverse class of vehicles was required. The concept of the coast
down technqiue is to determine the rate of deceleration of a freely
coasting vehicle; then, knowing the mass of the vehicle, the road-load
force may be calculated by Newton's second law, f = ma. Previous experi
mental work at the EPA has demonstrated similar results are obtained
with the coast down technique and with drive shaft torque meters.
Fifteen diverse light duty trucks were chosen as the experimental
sample. These trucks were chosen to approximately represent the sales
weighting of light duty trucks. Each of the 15 trucks was tested with
varying payloads, such that the vehicle test weights ranged from the
empty vehicle weight to the GVW. This resulted in a total of approxi-
mately 50 track tests.
The track measurements include the dissipative losses of the vehicle
tires, wheel bearings and drive train. To determine a road value appro-
priate for adjusting a chassis dynamometer, the dissipative losses from
the drive train and driving tires must be subtracted from the total
system measurements. These dissipative losses were measured using a 48"
diameter roll electric dynamometer.
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III. Discussion
This section discusses the specific physical measurements which
must be performed to yield the dynamometer adjustment information. This
section is included since some of the desired parameters must be deter-
mined indirectly; consequently the reason for some of the measurements
may not be apparent.
The discussion is presented in three subsections. The system energy
section discusses the general aspects of the problem and introduces the
concept of equivalent effective mass. The track measurements determine
the acceleration of the vehicle. The mass measurements provide the
remaining information necessary to calculate the total road load of the
vehicle system.
A. System Energy
The introduction states that the vehicle mass and the vehicle
deceleration under freely rolling conditions are the general parameters
which must be obtained to determine road-load with the coast down tech-
nique. This section will discuss in detail what measurements must be
performed to obtain these data.
The total energy of the decelerating vehicle system is the sum of
the translational kinetic energy of the vehicle and the rotational
kinetic energy of any vehicle components in rotational motion. For all
mechanical components of the wheels and drive train, the rotational
velocity is proportional to the vehicle velocity; therefore, the energy
of the system may be written as:
E = 1/2 mv2 + 1/2 (Z I.a2.)v2 (1)
i
Where:
E = the total system energy
m = the vehicle mass
v = the vehicle speed .
I. = rotational inertia of the i rotating component
a. = the proportionality constant between the rotational
velocity of the i rotating component and the vehicle
speed
Differentiating equation (1) with respect to time, and comparing the
resulting expression for power with the similar time derivative of a
purely translational system, the generalized force on the system may be
expressed as:
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3
F = ( m + Z I.a2 )A (2)
X
Where:
F = the generalized system force
A = the translational acceleration of the system
Defining M as the "total effective mass of the system", where:
M = m + E I. a2. (3)
Equation (2) now has the familiar form
F = MA (4)
2
The I I. a . term is identified as the "equivalent effective mass" of the
rotating components and may be designated by:
m = I I. a2. (5)
eq i i
The equivalent effective mass, defined by equations (3) and (5), is
simply one approach to include the effect of the rotational kinetic
energy of the system. Equations (2) through (4) indicate that the
acceleration of the system, the vehicle mass and the equivalent mass of
the rotating components are the parameters which must be measured to
determine the road load force.
B. Acceleration
Experimentally, it is not practical to measure the vehicle accelera-
tion directly; however, the acceleration may be determined from the
vehicle speed. The vehicle acceleration can be calculated by numerically
differentiating the velocity versus time data. This is theoretically
undesirable for two reasons. The non-analytical differentiation process
is inherently noise sensitive and this can be a problem when attempting
a least squares fit to the differentiated data. Also, since the accelera-
tion must be derived from the velocity, the initially random errors in
the velocity versus time data may not yield normally distributed errors
in the acceleration versus velocity. A better approach is to assume a
model for the acceleration versus speed equation and then perform analy-
tical operations on this equation to convert it to the form of a speed
versus time function. This expression may then be directly fitted to
the velocity versus time data to obtain dv/dt as a function of vehicle
velocity. The latter approach was chosen. The exact method used is
an extension of the approach used by Korst and Whiteland is discussed in
detail in reference^-.
C. Mass
The required masses are the gravitational mass and the equivalent
effective mass of the rotating components. Equation (5) indicates that
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the rotational inertia is the primary measurement necessary to determine
the equivalent effective msss of the rotating components.
1) Gravitational Mass
The gravitational mass of the system may be easily measured by a
vehicle scale.
2) Effective Equivalent Mass of the Drive Wheels and Drive Train
The effective equivalent mass of the drive wheels and drive train
was calculated using a coast down method to determine the drive wheel
and drive train inertia. This technique was chosen because it gives
a measure of rotational inertia of all drive train components. The
rotational inertia of the system is given by the familiar equation:
-r do> ,-,.
T - I ^ (6)
where:
I = the rotational inertia
T = the torque necessary to motor the system
u> = the angular velocity of the system
Assuming that the torque is a function of velocity, the variables of
equation (6) may be separated and the integrals formed:
where:
o>1 = the initial angular velocity
« = the final angular velocity
t.. = the initial time
t~ = the final time
Integrating the left hand side and solving for I yields:
(t - t )
1 (8)
A djo
W2J T
Equation (8) gives the inertia as a function of the torque required
to motor the tire and wheel. However the effective equivalent mass is
actually the desired quantity. Substituting the definition of effective
equivalent mass and
T = FR
u) = v/R {''
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where
-5-
R = the rolling radius of the tire
F = the force at the tire roll interface
v = the simulated translational velocity of the vehicle
into equation (8) yields:
,2
(10)
leq
y
v2' F~
where
Req = the effective equivalent mass of the drive train
and driving tires
At is the time interval
R = the tire rolling radius
F = the force at the tire roll interface
v1 = the initial simulated vehicle speed
v~ = the final simulated vehicle speed
It should be noted that both F and At of equations (10) are negative
since the drive train is decelerating. Equations (10) indicate that the
dissipative forces of the drive train and the time required for the
drive train to coast over a known speed range are the parameters necessary
to calculate the drive wheel and drive train effective equivalent mass.
3) Equivalent Effective Mass of the Vehicle Non Driving Wheels
The technique of motoring, followed by coast down, was not
used for the non-driving wheel effective mass determination because of
the very low forces required to motor the front wheels. The equivalent
effective masses of the front wheels were determined by the three wire
torsional pendulum technique. With this method, the object is suspended
by three wires, or placed on a platform suspended by three wires. The
platform is rotated through a small angle, released and the period of
oscillations timed. The tension in the supporting cables, induced by
the mass of the object, causes a restoring torque on the oscillating
system, the inertia of the object controls the acceleration of the
system and, hence, the period of the oscillation. The rotational inertia
of the pendulum system is to a good approximation, given by:
n
p p
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where
2
g = the graviational constant, 9.80 m/sec
H = the length from the center of the pendulum to the point
of attachment of the supporting wires
L = the length of the supporting wires
m = the total mass of the pendulum and any object on
the pendulum
t = the time period of one oscillation of the system
Equation (11) indicates that the mass of the pendulum plus tire and
the period of oscillation of the system are the parameters required to
determine the rotational inertia of the front wheels by this method.
The effective equivalent mass can then be easily obtained from equation
(5) and the rolling radius of the tire.
IV. Data Collection
This section discusses the test vehicles, the instrumentation used
to collect the data and the test facilities.
The test vehicles were 15 light duty trucks, 10 pick-up style
trucks and 5 vans. These vehicles were selected on a sales weighted
basis, and ranged in size from approximately 4000 Ibs GVW to 8000 Ibs
GVW. The vehicles were procured either by renting or by requesting
participation from the automotive manufacturers; 87% were obtained from
manufacturers and the remaining 13% were rented. Each vehicle was
tested with various payloads so that the test weights ranged from the empty
vehicle weight to approximately the GVW. Table 1 of Appendix A identifies
each vehicle; gives the estimated EPA inertial weight category and the
vehicle frontal area. The EPA inertia weight categories were estimated
since many of these vehicles are not currently certified in a light duty
class. The inertia weight category was estimated by adding 100 to 150
pounds to the test weight of the empty vehicle plus driver. Since the
test driver weighed from 150 to 200 pounds this is equivalent to adding
300 pounds to the empty vehicle weight. The resulting weights were
factored into inertia weight categories in increments of 500 pounds in the
usual EPA manner. That is for example, all vehicles with weights between
3,250 and 3,750 pounds were assigned the inertia weight category of 3500
pounds.
The vehicle frontal areas were obtained from the manufacturers
whenever this information was available. For those vehicles where the
frontal area was not available from the manufacturer, the frontal area
was determined by polar planimeter measurements of photographs.
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7
A. The Track Measurements
The speed versus time data are the only measurements that are
required on the test rack. Ambient conditions were, however also
monitored to allow correction to a set of standard ambient conditions.
1) Test Facility and Test Procedure
All vehicle speed versus time data were collected on the skid pad
of the Transportation Research Center of Ohio, in East Liberty, Ohio.
This facility is a multilane, concrete, straight track with large turn
around loops at each end. Approximately 1 kilometer of this straight
track has a constant grade of 0.5% and this section was used for all
measurements.
Prior to the coast down measurements, the vehicle tires were
adjusted, when cold, to the manufacturers recommended pressures. The
cold tire pressures were recorded, as were the tire pressures immediately
after the coast down tests. After adjustment of the tire pressures, the
vehicles were warmed up for approximately 30 minutes at about 50 mph.
Twenty coast downs were recorded for each vehicle at each test
weight; ten in each direction of travel on the test track. Ten coast
downs were conducted by accelerating the vehicle to approximately 65
mph, then shifting into neutral and recording speed versus time as the
vehicle freely decelerated. The remaining ten coast downs were conducted
in the same manner; however, the initial speed was approximately 40 mph.
The two series of coast downs were necessary because the 1 km of section
of track with constant grade was insufficient to coast most vehicles
from 60 mph to a terminal speed near ten mph.
2) Velocity Instrumentation
The vehicle speed was measured by a police type Doppler radar. The
instrumentation contained a noise discriminator system which rejected
the Doppler pulse count any time the period between pulses differed
significantly from the previous pulse separation.
Modifications were made to the standard configuration to increase
the range. The length of the antenna horn was increased and aluminum
corner reflectors, or strips of aluminum foil, were placed inside the
target vehicle windows. These modifications increased the range from
about 0.5 km to approximately 1.0 km. The Doppler frequency counter
gate time was also increased from approximately 30 msec to 300 msec in
an attempt to improve the system precision. This modification did
increase the speed resolution; however, it also increased the total
period the discriminator evaluated the Doppler signal for extraneous
noise. The system noise is basically random; therefore, the probability
the discriminator will reject a measurement of the Doppler frequency is
linear with the counter gate time. The increase in the precision of
each measurement was accompanied by a decrease in the number of speed
versus time points measured during the coast down. Also, the range was
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-8-
greatly reduced since the probability of radar signal noise increased as
the distance from the transmitter to the target increased. This modifi-
cation was subsequently rejected and the final configuration of the
system provided a range of about 1 km with a resolution of + 1 mph.
A count of the Doppler frequency was recorded each second during
the coast downs on a seven track magnetic digital tape recorder. This
recorder and the support electronics were placed in a small van, parked
on the track berm. Electric power was provided by an alternator, bat-
tery bank, and inverter on this van. An example of the speed versus
time record of a light duty truck coast down is given in Figure 1.
60 T
50
HO J-
i
SPEED
( !Ti P h )
30.
20 '
to
0 J-
SPEED vs TIME
VEHICLE ID: ?7fji
TEST WEIGHT: 51 so it
-4-
-4-
£0
H 0 60
TIME (sec)
SO
100
3)
Figure 1
Ambient Conditions
Coastdowns were conducted only when steady winds were less than 15
km/hr (9.3 mph) with peak wind speeds less than 20 km/hr (12.4 mph).
Wind speed during the test period was measured with a photochopper type
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six-cup anemometer. The anemometer was located near one side of the
test track, at one end of the 1 km test section. These data were re-
corded at one second intervals on the same magnetic'tape as was used to
record the vehicle speed. During test periods the ambient temperature
was in the range of 5°C (41°F) to 35°C (95°F). The barometric pressure
was between 102 kPa (30.2 in Hg) and 94 kPa (27.9 in Hg). The air moisture
content ranged from 0.29 to 0.73 gm H20/gm dry air. These slowly varying
ambient parameters were recorded, by an observer, on a data sheet associated
with each vehicle.
B. The Dynamometer Measurements
The dynamometer measurements are conceptually simple since the
desired information is force data, and the dynamometer could be used to
measure forces directly. The dynamometer used was one of the EPA light
duty vehicle electric dynamometers. This dynamometer is a G.E. motor-gen-
erator type with a 48" diameter single roll. During these experiments
the normal 0-1000 Ib. load cell of the dynamometer was replaced with a
more sensitive 0-300 Ib load cell.
Prior to all measurements the cold tire pressures were adjusted to the
manufacturers recommended pressures. Again, the cold pre-test pressures
and the hot post-test pressures were recorded. The vehicle weight was
adjusted to approximate the vehicle weight during the corresponding track
measurement. The dynamometer force measurements were conducted on both
the front and rear axles of the vehicle. During the rear axle measure-
ments the transmission was shifted into neutral, as it was during the
track coastdowns.
The vehicle was placed on the dynamometer, and then the vehicle and
dynamometer were warmed up for 30 minutes at approximately 50 mph.
After warm up, the torque necessary to motor the dynamometer and vehicle was
measured at speeds from 60 to 10 mph in 5 mph decreasing speed intervals.
For each measurement steady state dynamometer speed and torque signals
were recorded on a strip chart for a period of approximately 100 seconds.
The stabilized values were then read from the strip chart by the dynamometer
operator.
After the measurements were completed with the full vehicle weight
resting on the dynamometer rolls, the vehicle was then lifted until the
vehicle tires were just contacting the dynamometer: roll. The vehicle
tires were considered to be just touching the dynamometer roll if a
person could, with difficulty, manually cause the tire to slip on the
roll when the roll was locked. With this test configuration the torque
versus speed measurements were repeated as before. Finally, the torque
required to motor only the dynamometer was recorded in the same manner.
The dynamometer speed data were converted to the units of m/sec.
All torque data were converted to force in newtons at the roll tire
interface. A scatter plot of the data from one truck, after conversion
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to force at the tire-roll interface and subtraction of the force neces-
sary to motor the dynamometer, is given as an example in Figure 2. In
addition, the difference between the force measurement when the full
weight of the vehicle was on the dynamometer and the force measurement
when the tire was just contacting the dyno roll, is also given in Figure
2.
REflR flXEL FORCE MEflSUREMENTS
VEHICLE ID: ??01
TEST WEIGHT: SISOlb
fORCE(NT)
MO.OOO
300.000
210.000
200.000
1SO.OOO
100.000
SO.000
0.0
. 2 = VEHICLE FULL WEIGHT
' 3 = TIRE DISSIPFfTIUE FORCE '
4 = VEHICLE JUST TOUCH I'NG
2
3
* *
2
3
4
4
2 2
3 3
4
4
2 2
3
3
4 4
2
3 3
4 4
2
1 3
4
4
0.0
5.000 10.000 13.000 20.000 15.000 JO.000
SPEDl«/$fCI
Figure 2 (a)
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-11-
FROMT flXEL FORCE MEflSUREMENTS'
VEHICLE ID: 7701
TEST WEIGHT: sisoib
FORCE I NT I
HO,000
300.000
2)0.000
200.000
100.000
$0.000
0.0 -
I 1
5. =' VEHICLE r
6 = TIRE DISS
7 = VEHICLE J
i i
5
s
» 6
i ^
i S
« 6
-.7 7-4
! !!*<
5 S
6 6
7
1 1
JLL WEIGHT '
IPflTIVE FORCE -
JST TOUCHING
5 S
6 6
7_..7_.
t
S
6
6
T r 7»aaT
S »
6 4
~~T T-
0.0 S.OO* 10.000 IS.COO 20.000 SS.OOO .(0.000
Figure 2(b)
C. Masses
1) The Gravitational Masses
The gravitational mass was measured by weighing each vehicle, with
the driver, immediately after the coast downs. The vehicle scale of the
TRC was used for all vehicle mass determinations. TRC personnel indi-
cated calibration checks on this scale have repeatedly been within + 10
pounds in the 0 to 10,000 pound range.
2) Equivalent Effective Mass of the Drive Wheels and Drive
Train
In order to calculate the equivalent effective mass of the drive
wheels, differential gears, drive shaft and transmission output shaft
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gears, the dissipative forces of the drive train and the time required
for the drive train to coast through a speed interval must be known.
The drive train dissipative forces are obtained in the dynamometer
measurements, therefore only the method of measuring the coast down time
intervals is discussed.
Immediately after the dynamometer force measurements of the rear
axle, several white stripes were chalked on each vehicle driving tire.
The vehicle tire speed could then be monitored by observing these chalk
stripes with a stroboscopic tachometer. The appropriate frequencies
corresponding to 60 mph and 10 mph were determined by observing the
tachometer when motoring each vehicle with the dynamometer at these
speeds. The vehicle, drive train with the transmission in neutral, was
motored to approximately 65 mph by the dynamometer. The vehicle was
lifted from the dynamometer and the time interval required for the
vehicle to decelerate from '60 mph to 10 mph was timed using a stop
watch. The initial and final speed points were determined by observing
the frequency output of the strobocopic tachometer. Five time intervals
were recorded for each drive wheel.
3) Front Wheel Effective Mass
The vehicle front wheels the rotational inertia was measured using
a three wire torsional pendulum. This pendulum was constructed from a
triangular shaped plywood platform suspended from three 1/8 inch stranded
steel cables. The physical parameters of the platform were:
the distance from the axes of rotation to the
suspension point = 0.532 m
the length of the suspension wires = 4.79 m
the mass of the platform, including hardware
was 2.74 kg.
For the determination of the rotational inertia a vehicle tire and
wheel, usually the spare, was placed on the platform. The platform was
rotated approximately 0.5 radians and released. The time required for
10 oscillations was then timed with a stop watch. This measurement was
repeated 4 times and then averaged.
The mass of each tire was then measured by weighting on a platform
scale. This scale was a "shipping clerks" scale with a maximum capacity
of 1000 Ib, and a resolution of + 0.5 Ib.
V. Data Analysis
A. Track Data
The usual form of a vehicle deceleration curve is assumed to be a
constant plus a term proportional to the velocity squared. However the
effect of a steady head-tail wind will appear as a linear-term. Also,
the drive train losses were expected to be approximately linear in
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4
velocity and some published tire data have indicated the inclusion of a
linear term may be theoretically desirable. For these reasons, a model
equation was chosen of the form:
2
dv/dt = aQ + a.jV + a2v
Terms were added to equation (12) to account for any effects of wind and
track grade. The variables of the resulting equation can be separated
and integrated to yield an expression for time as a function of velocity.
Since these functions are inverse trigonometric or hyperbolic functions,
their inverse may be taken to yield velocity as a function of time.
These functions were fitted to the coast down data by the method of
least squares to determine the a_, a.., and a« of equation (9). The
mathematics of thi's technique is discussed in detail in Reference 2
and in the EPA Recommended Practice for Road Load Determination.
2
Since the a« coefficient multiplies the v it was assumed to rep-
resent the aerodynamic drag of the vehicle. The aerodynamic drag is
proportional to the air density; therefore all a_ coefficients were cor-
rected for differences between the ambient conditions during the test,
and a set of standard ambient conditions chosen to be:
temperature 20°C (68°F)
barometric pressure 98 kPa (29.02 in Hg)
humidity 10 gm H_0/kg dry air (70 gr H_0 dry air)
The corrected acceleration coefficients for all vehicle tests are
presented in table 1 of Appendix B. The vehicle tire pressures for the
track measurements are give in table 2 of Appendix B.
B. Dynamometer Data
The dynamometer measurements determine the dissipative losses of
the driving tires and the drive train, and supply the necessary data to
determine the rotational inertia of the rear wheels and drive train.
The dynamometer measurements are conceptually simple since the dynamo-
meter used, a 48" roll GE electric chassis dynamometer, measures the
forces directly. The only arithmetic necessary is to convert from the
force values at the dynamometer load cell to the force at the tire-roll
interface. This conversion is simply the ratio of the length of the
moment arms. In addition a conversion to MKS units of force was made at
this time.
The data for the tire dissipative losses, the wheel bearing losses,
and the drive train dissipative losses were all scatterplotted versus
speed. These plots indicate the wheel bearing and drive train losses
are linear with speed, while the tire losses are approximately constant
with speed. Consequently a linear least squares regression was fitted
to each data set of the drive train and rear tire losses, the rear tire
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-14-
losses, the drive train losses and the front tire losses. The coeffi-
cients from these regression analyses are given in Tables 1 through 4
respectively of Appendix C.
The vehicle tire pressures for the dynamometer measurements are
given in Table 5 of Appendix C.
C. The total Effective Equivalent Mass of the Vehicle
The total effective equivalent mass of the vehicle is the sum of
the gravitational mass of the vehicle and the effective equivalent mass
of the drive tires, drive train and the non driving wheels.
1) The Gravitational Mass
The gravitational mass was determined by the vehicle scale at the
TRC. These data are presented in Table 1 of Appendix D.
2) The Drive Train Effective Equivalent Mass
The equivalent effective mass of the vehicle drive train and drive
tire was determined from the drive train coast down measurements.
Equation (11):
I1?
V2
was directly evaluated by numerical integration. Since F was measured
at equally spaced speeds, and known to be quite nearly linear, the
simple equally spaced trapezoidal integration algorithm was used. The
results of this integration, the effective equivalent mass of the drive
train is given in Table 1 of Appendix D.
3) The Front Wheel Effective Equivalent Mass
The inertia of the pendulum with the front tire-wheel combination
was calculated from equation (12) using the measured period of oscilla-
tion and the tire plus pendulum masses. The inertia of the tire wheel
combination was then determined by subtracting the inertia of the pendu-
lum from the total system inertia. The pendulum inertia was determined
both theoretically and experimentally and these results were in agreement
with 3%.
The effective equivalent mass of the front wheels was then calculated
by equation (5), that is:
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mc = 2I/R2 (14)
feq
where
mf = the effective equivalent mass of both front wheels
I = the rotational inertia of a single wheel-tire
The rolling radii of the tires were determined by measuring the
height of the loaded tire, from the contact patch to the top of the
tread and dividing by two. Previous experiments at the EPA have shown
this technique is a very good simple static measurement of the dynamic
rolling radius. Five to ten tires of each tire size were measured and
the average rolling radius used for all tires of that size. These
average rolling radii are given in Figure 3.
Rolling Radii versus Tire Size
Nominal Tire Size Average Rolling Radii
14 inches 0.31 m
15 inches 0.34 m
16 inches 0.37 m
16.5 inches 0.35 m
Figure 3
The use of a standard rolling radius for each nominal tire size
introduces some error, but this is slight compared to the total vehicle
mass and it simplifies the calculation by reducing the number of measured
parameters which need to be maintained. The use of the spare tire on
the torsional pendulum also neglects the rotational inertia of the brake
disk or drum. Several preliminary measurements which included brake
disks and drums indicated the effective equivalent mass of the brake is
only 10% of the effective equivalent mass of the wheel-tire combination.
Since a single wheel-tire combination has typical equivalent mass of 15
kg, neglecting the 10% effect of the brake introduces a probable error
of only 3kg in the total vehicle mass. This is less than the probable
error in the measurement of the vehicle gravitational mass or the probable
error in the determination of the equivalent effective mass of the drive
train and rear tire.
The equivalent effective masses of the vehicle non-driving wheels
are presented in Table 1 of Appendix D with the other mass terms. Also
included in Table 1 is total equivalent effective mass of the vehicle
system, the sum of the gravitational mass and the effective equivalent
masses of the driving and nondtiving wheels.
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VI. Results
The total vehicle road load is given by equation (4) as the product
of the acceleration and the total system effective mass. The coefficients
of this force were calculated and are presented in Table 1 of Appendix
E. Also presented in Table 1 of Appendix E is the total road load force
and power at 50 mph.
The total vehicle road load force is the sum of the tire rolling
resistances; the dissipative losses of the drive train, wheel bearings,
and brake drag; and the aerodynamic drag of the vehicle.
FTOT = ftire + fmech + faero (15)
where
F = the total vehicle road load force
tire = the sum of the tire rolling resistances
f , = the mechanical dissipative losses
mech
f = the aerodynamic drag
aero } &
The total vehicle road load force includes the dissipation in the
drive train from the rear wheel up to the point where the drive train is
decoupled from the engine. When the vehicle is being tested on a dyna-
mometer, the vehicle engine is required to overcome the drive train and
driving tire losses prior to supplying power to the dynamometer. Conse-
quently these losses should not be included in the dynamometer adjustment
force. The drive train losses are independent of the choice of a dyna-
mometer, however, the tire rolling resistance will depend on the type of
dynamometer. Therefore, to develop the appropriate dynamometer adjust-
ment force, tire losses for that particular dynamometer must be subtracted
from the total road measurements, in addition to the drive train losses.
A. Force Coefficients for Road Simulation on a Small Twin Roll
Dynamometer
In order to calculate a force appropriate for adjusting a small
twin roll dynamometer two assumptions must be made about tire power
dissipation on a small twin roll dynamometer.
Assumption 1: Two on the rolls equals four on the road"
It is commonly stated that two tires dissipate as much energy on a
small twin roll dynamometer as four tires dissipate on a flat surface.
However, measurements on sufficiently large tire sample to prove or
disprove this concept have not yet been reported in the literature.
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There is some theoretical basis for this statement , and one study has
reported the power consumption of a bias ply tire on a small twin roll
dynamometer to be very nearly twice the power consumption of the same
tire, at the same inflation pressure, on a flat road. This same study,
however, reported the power consumption of a radial tire on a small twin
roll dynamometer to be significantly greater than the power consumption
of the same tire or a flat road surface. The problem is further compli-
cated since most discussions have been directed toward light duty vehicle
tires. The truck tire is frequently constructed with a greater number
of carcase plies and it is typically operated at higher inflation pres-
sures. Truck tires, at the present time, are predominantly bias ply
construction.
Assumption 2: Power dissipation on a large single roll is proportional
to road power dissipation.
The assumption that tire power dissipation on a large single roll
dynamometer is greater than, but proportional to, the power dissipation
a flat surface is much better documented. The relationship between tire
losses on a large single roll and a flat surface, when determined by 7
torque or power consumption measurements, has been shown theoretically
to be given by:
F - ~ (16)
where
F = the rolling resistance of the tire on a flat road surface
F^ =the rolling resistance of the tire on a cylindrical
dynamometer surface
r = the rolling radius of the tire
R = the radius of the dynamometer roll
The theoretical treatise used to develop equation (16) has also been
used to predict the relationship between tire rolling resistances on a
large single roll and on a flat surface when the measurements are
obtained directly from spindle force transducers. This relationship has
been experimentally tested and appears reasonably valid.
To calculate a dynamometer power absorber setting for a twin roll
dynamometer, the above two assumptions were used. The rolling radii
given in Figure 3 were inserted into equation (16). The correction
factor, /14-r/R ranged from .814 to .789. Since this value was very
nearly constant the value 0.8 was used to convert the rolling resistance
measurements for all front and rear tires to estimates of the tire
rolling resistance on a flat road.
To obtain the force coefficients appropriate for adjusting a small
twin roll dynamometer the estimate of the flat surface tire rolling
resistances for both front and rear tires were subtracted from the total
-------
-18-
road forces as required by assumption 1. In addition, the drive train
losses were also subtracted. The resulting coefficients are given in
Table 2 of Appendix E as are the force and horsepower at 50 mph.
A significant purpose of this study is to develop equations to
predict the appropriate dynamometer power absorber setting as a function
of some easily measured vehicle parameter. The ability to predict the
small twin roll dynamometer power absorber setting as a function of
vehicle frontal area, test mass and the EPA inertia weight category will
be discussed in the following sections.
1) Frontal Area as a predictor of dynamometer power absorber
setting.
The assumptions regarding tire rolling resistance on a small twin
roll dynamometer, and the resulting corrections to the total road load
force, remove all tire dissipation from the small twin roll dynamometer
adjustment force. In addition, the drive train losses are subtracted,
therefore equation (15) shows only a portion of the mechanical losses,
the non-driving wheel bearing losses, and the non-driving wheel brake
drag remain in addition to the aerodynamic drag. These remaining mechani-
cal losses are probably weakly dependent on the vehicle mass since the
vehicle bearing and brake size depend on vehicle mass. However, the
random nature of these forces, especially the brake drag, will predominate
over any systematic effects for a sample size of 15 vehicles. Consequently
the remaining mechanical losses can be expected to appear as random
"noise" superimposed on the primary force of the aerodynamic drag.
Since the aerodynamic forces predominate in the small twin roll
dynamometer adjustment, an aerodynamic model is the logical choice for
predicting this dynamometer adjustment force. The aerodynamic drag of
the vehicle is theoretically given by:
where
F = the aerodynamic drag force
p = the air density , ,
C = the drag coefficient of the vehicle
v = the vehicle velocity
If the drag coefficients of the vehicles are approximately con-
stant, then the drag force, and hence the power should be linear in
frontal area. In Figure 4, the plot of twin roll dynamometer adjust-
ment power versus frontal area, the vehicles with frontal areas below
-------
30.000
POWER
(HORSEPOWER)
-19-
FWIN ROLL DYNAMOMETER ADJUSTMENT P'OWER AT 50 MPH
VERSUS
VEHICLE FRONTAL AREA
24.000 * ?
*?
»« 2
* 2* if »'
». '. ' "3*
3 S*
18.000 * 7 3 32
4
12.000 * ?
?0.000 ifd.uOO
24.000 3?.000
FRONTAL AREA (SQUARE FT)
Figure 4
-------
-20-
2
34 ft are pick up trucks while the remaining vehicles are vans. For
the pick up trucks the dynamometer power absorber setting at 50 mph
does appear to be linear with frontal area, however the data occur in
two major groups with no intermediate points. The power absorber
setting for vans may also be linear with frontal area, however since no
vans with small frontal areas were included in the test fleet this
cannot be empirically determined. These vans were not included since
few, if any, such vehicles are currently being sold.
A simple regression line could be fitted to the dynamometer power
absorber setting versus frontal area, however if a linear model were
chosen this would under estimate the power absorber setting for the
large pick up trucks and overestimate the setting for vans. If a non-
linear model were chosen this could adapt to the reduced road load of
the large frontal area vans, but would be inappropriate for any possible
pick up trucks with large frontal areas. To avoid this dilemma the
frontal area variable was "factored" into two variables one giving the
frontal areas of the pick up trucks only, and a second variable having
the values of the frontal areas of the vans only. This is approximately
equivalent to separating the data into two groups, vans and pick ups. A
general linear regression of these independent variables was first
performed. As theoretically predicted, the intercept was nearly zero
and there was relatively little statistical confidence that the inter-
cept was not zero. Consequently a linear regression was performed
forcing the regression line through zero. The results of this regression
are:
Regression of Twin Roll Dynamometer Adjustment Power
at 50 mph versus Vehicle Frontal Area
Regression model: H = a A + b A
p pu van
H = the dynamometer power absorber setting (Horsepower)
2
A = the frontal area of the pick up trucks (ft )
2
A = the frontal area of the vans (ft )
van
a = .633 hp/ft2
b = .511 hp/ft2
sample size 54
2
multiple correlation coefficient .856 R = .733
standard error of the regression 1.59
-------
-21-
The two prediction equations are:
H = .633 A for pick up trucks
P
H = . 511 A for vans
P
where
2
the vehicle frontal area (ft )
The square of the correlation coefficient indicates the proportion
of the variation of the data which is explained by the proposed model.
In this case 73% of the variation of the data is explained by the model.
The standard error of the regression is similar to a standard deviation;
approximately 68% of the data may be expected to lie within plus or
minus one standard error of the regression line. In this case approxi-
mately 68% of the measured data points are within 1.6 hp of the regression
line.
It must be remembered that equations (18) include the non-aerody-
namic losses associated with the front wheel. Consequently these forces
are greater than wind tunnel measurements of vehicle aerodynamic drag.
Measurements of wheel bearing, brake drag, and tire aerodynamic drag of
light duty trucks indicate these losses are approximately 1.8 horsepower
at 50 mph. Consequently the powers of equations (18) are approximately
9% greater than the aerodynamic drag of the vehicle.
2) Vehicle Test mass as a Predictor of the Dynamometer Power
Absorber Setting.
The vehicle test mass was defined as the total mass of the vehicle
including the driver and any payload. Figure 5, the plot of dynamometer
power absorber setting at 50 mph versus vehicle test mass,indicates the
power absorber setting increases with increasing test mass until about
2000 kg. Above 2000 kg the power absorber setting is approximately
constant. This occurs because the measurements at the higher test
masses resulted from increasing the vehicle payload with sandbags. Since
sand is relatively dense, the height of the sandbags never exceeded
the height of the sides of the pick up truck bed. Consequently the
payload does not directly affect the aerodynamic drag significantly in
the case of pick-up trucks and has no direct effect on the aerodynamic
drag of a van. Any aerodynamic effect which might occur from increasing
the vehicle payload would be an indirect result from changes in the
vehicle ground clearance or the aerodynamic angle of attack.
Increasing the vehicle payload does.increase the tire rolling resis-
tance. However, the assumptions about the rolling resistance of tires
on a twin roll dynamometer, and the resulting corrections to the total
road load force attempt to remove the tire rolling resistance from the
-------
-22-
TWIH ROLL DVHflMOMETER flDJUSTMENT POWER flT 50 MPH
UERSUS
TOTflL UEHICLE TEST MflSS
30.0UO *
^4.000
18.000 *
POWER
(HORSEPOWER)
12.000 *
lUOO.O i'^nO.O 3^*0 O.U
TOTflL UEHICLE TEST MfiSS (KG)
Figure 5
-------
-23-
dynamometer adjustment. Investigating the calculated twin roll dynamome-
ter power absorber settings,given in Appendix E, demonstrate the calcu-
lated dynamometer power absorber settings for different test masses of
each vehicle were generally within + 1 horsepower of the mean power
absorber setting for that vehicle. Furthermore, the value of the power
absorber settings do not systematically increase or decrease with changes
in the vehicle test mass. This demonstrates that the data analysis has
quite successfully removed the tire rolling resistance.
Since the test mass of any vehicle can vary significantly without
systematic effect on the dynamometer power absorber setting, the test
mass is not a logical parameter to use to predict the dynamometer power
absorber setting. In addition the data analysis indicates increasing
the payload of a vehicle does not adequately simulate vehicles of larger
mass. The simulation is inadequate because an increase in payload does
not affect the aerodynamic drag, while vehicles which are heavier when
empty tend to be physically larger and hence have larger aerodynamic
drag forces.
3) Inertia Weight Category as a Predictor of the Dynamometer
Power Absorber Setting.
The scatter plot of the dynamometer power absorber setting at 50
mph versus the EPA inertia weight category of the vehicle, Figure 6,
places all calculated power absorber settings for each vehicle at a
single abscissa position. This position is approximately the curb
weight of the vehicle plus 300 pounds. This approach is consistent with
the previously demonstrated test mass independence of the calculated
twin roll dynamometer power absorber setting.
The data plotted in Figure 6 appear approximately' linear in EPA
inertia category, except for the notable exception of the heaviest
inertia category vehicle. This vehicle is a GM van. Because of this
exception, a linear regression would under estimate the dynamometer
power absorber settings for the majority of vehicles which are in the
4000 to 5000 pound categories, while still over estimating the dynamome-
ter power absorber setting for the heaviest vehicle. Furthermore, a
linear model is not theoretically logical since the twin roll dynamometer
power absorber setting represents the aerodynamic drag of the vehicle,
and there is no theoretical reason to anticipate the aerodynamic drag
increases linearly with inertia weight.
A theoretically based model can be developed based on several
logical assumptions. The first assumption is that, because of similari-
ties in manufacturing technology, the density of light duty trucks is
approximately constant. Stated as ah equation, the assumption is:
W *> V (19)
-------
-24-
TWIN ROLL DYNAMOMETER ADJUSTMENT POWER AT 50 MPH
VERSUS
INERTIA WEIGHT CATEGORY
30.000
24.000 * - 2
3
? 2
* 4 ' *
2000.0 3600.0 5200.0
SdOO.O 4400.0 6000.0
INERTIA WEIGHT CATEGORY (LB)
Figure 6
-------
-25-
where
W = the inertia weight category of the vehicle (ie: the
empty weight plus a standard small payload)
V = the volume of the vehicle
The vehicle volume is approximately equal to the product of the three
major dimensions. The second assumption is that each of the major
vehicle dimensions may be expected to increase approximately equally
with an increase in weight. Consequently each major dimension is pro-
portional to the cube root of the vehicle weight. That is:
L * W 1/3 (20)
where
L = any of the major vehicle dimensions of height width and
length.
The twin roll dynamometer power absorber setting is primarily the aero-
dynamic drag of the vehicle. The aerodynamic drag is proportional to
the frontal area which is approximately equal to the product of the
vehicle height and width. Consequently the twin roll dynamometer power
absorber setting should be proportional weight of the vehicle to the
two-thirds power.
' H ^ W 2/3 (21)
P -
The previous arguments are hardly rigorous, therefore a model of
the form: '
H = aWX (22)
P
was chosen which allowed the exponent to vary. This model will predict
a dynamometer power absorber setting of zero horsepower for a vehicle of
zero mass, which is theoretically appropriate. Also, if x is less than
1, the model predicts the slope of the horsepower versus weight curve
will decrease as the weight increases. This is also theoretically
logical; and consistent with the observed data;
The model, equation (21), unfortunately cannot be conveniently
fitted to the data by least squares process. The fitting process is
difficult since the normal equations resulting from the least squares
criterion are non-linear. These equations can be solved simultaneously
by numerical methods however a simplier approach is to "linearize" equa-
tion (22) by the following logarithimic transformation.
In H = In a WX '
P x
= Ina + InW ,,,,
= Ina + xlnW
-------
-26-
Identifying In H as the dependent variable and In W as the independent
variable, equation (23) can now be fitted by a simple linear regression.
The results of this regression are:
Regression of Twin Roll Dynamometer Power at 50 mph
versus
Vehicle Inertia Weight Category
Regression model In H = In a + x In W
In H = the natural logarithm of the dynamometer power absorber
setting (horsepower)
In W = the natural logarithm of the vehicle inertia weight
category.
In a = -2.531
x = 0.6509
Sample size 54
2
Multiple correlation coefficient .767 R = .589
Standard error of the regression .1137
Converting to the form of the original model, the prediction equation
is:
H = .0796 W°'651 (24)
The correlation coefficient of the regression may indicate this regression
does not fit the data as well as the previous area based regression
model, however the statistics of this regression cannot be readily
interpreted since they are the statistics of the regression performed on
the transformed parameters.
In order to evaluate the inertia weight prediction model versus the
model using frontal area as the predictor of the dynamometer power
absorber setting, the prediction equations are plotted in figures 7, and
8. Also plotted in these figures are mean values of the calculated
power absorber settings for each vehicle versus the predictor variable.
Plotting only the mean values reduces the number of points plotted so
that the vehicle types may be identified. These mean values are given
in Table 3 of Appendix E.
Figure 7, the plot of the power absorber setting versus inertia
weight category shows the fitted model to be a very reasonable appearing
choice for these data. However the worst case error of the fitted line
-------
-27-
Mean Twin Roll Dynamometer Power Absorber Setting at 50 mph
versus
Vehicle Inertia Weight
30
20 -
Power
(horsepower)
10 -
Regression Line
H - .0769 W°-651
P
O
2000
O = Pick Up Trucks
D = Vans
3000 4000 5000
Inertia Weight (Ib)
6000
Figure 7
-------
-28-
from the data is about 4.5 horsepower. There are two additional cases
of errors of about three horsepower and 4 errors of approximately two
horsepower. The average dynamometer setting is about 18 horsepower,
therefore a two horsepower error is an error slightly greater than 10%.
Figure 8, the plot of power absorber setting versus frontal area,
with the vehicles divided into two categories, shows the worst case
error in this approach is only approximately 2.5 horsepower. In addition
there is only one other data point which is farther than two horsepower
from the regression lines.
An additional problem in the treatment of vans when using inertia
weight as the predictor of the dynamometer power absorber setting is
also apparent from Figures 7 and 8. The inertia weights of the vans
tested varied by 2000 pounds or about 40% of the mean inertia weight of
the vans. The dynamometer power absorber setting only varied about 1.5
horsepower or less than 8%. Consequently the inertia weight regression
equation predicts significantly different dynamometer power absorber
settings for different inertia weight vans, while no significant difference
was observed. Figure 8 indicates no differences should be expected in
the power absorber setting for the vans since the frontal areas, and
hence the aerodynamic drag of the vehicles were approximately equal.
The prediction model based on vehicle frontal area correctly predicts
nearly equal dynamometer power absorber settings for all of the vans in
the test fleet.
It is concluded that the prediction system based on the vehicle
frontal area, when the vehicles are divided into the categories of vans
and pick ups, is significantly better than a prediction system based on
the vehicle inertia weight categories. Both models had two parameters
which were fitted to the data, therefore the advantage of frontal area
as a predictor of the dynamometer power absorber setting is not merely
the result of a more flexible model.
The dynamometer adjustment powers could be regressed against both
frontal area and weight. Since this would introduce an additional
degree of freedom in the model, the prediction precision might appear
better. There is, however, no physically logical reason to expect
significant mass and frontal area dependence. The mass is a reasonably
successful predictor of the dynamometer adjustment primarily because of
a high intercorrelation between mass and frontal area. This inter-
correlation would make the relative magnitudes of the effects attributed
to weight and frontal area characteristic of the specific sample in-
vestigated. This approach was not seriously considered because of this
problem of relative coefficient instability. If frontal area and mass
are to be included in the same regression, the mass contribution should
be constrained so that it cannot exceed the effect anticipated for the
mechanical losses of the front wheel. With this constraint, the addi-
tion of mass to the prediction system cannot be expected to significantly
improve the prediction accuracy for the reasons discussed earlier. It
-------
-29-
Mean Twin Roll Dynamometer Power Absorber Setting at 50 mph
versus
Frontal Area
30 T
20
Regression
Lines
Power
(horsepower)
Hp
Hp
10
.633A
.511A
D = Vans
o = Pick Up Trucks
10 20 30
Frontal Area (Square Ft)
40
50
Figure 8
-------
-30-
would complicate the prediction system and was therefore not considered.
It may be desirable to consider the approach of constrained mass
plus frontal area prediction system in the future if a single prediction
equation is to be applied to very diverse vehicles, or if it is desirable
to isolate the pure aerodynamic drag. An example of the first case
would be if a single equation were to describe all road vehicles. A
possible reason for the second argument would be to allow into tunnel
measurements of aerodynamic drag to be directly introduced with the
dynamometer adjustment equation. Wind tunnel measurements can be in-
corporated in the current prediction system, but would require corrections
for the mechanical losses of the non-driving wheels.
B. Large Roll Dynamometer Adjustment Force
Equations to predict the power absorber settings for large single
roll dynamometer are developed since these equations may be useful at
the present, or in future work. Since the majority of EPA testing is
conducted on small twin roll dynamometers it is assumed that whatever
prediction system is chosen for the twin roll dynamometer will also be
used for large single roll dynamometers. Therefore only the necessary
modifications to the small twin roll dynamometer prediction equations,
will be developed.
The appropriate adjustment force for a large roll dynamometer can
be obtained directly since the tire and drive train dissipative losses
were measured on this dynamometer. To obtain the force coefficients
appropriate for adjusting a 48" roll dynaometer, the coefficients of the
tire and drive train losses, given in Table 1 of Appendix C, were sub-
tracted from the total force coefficients, given in Table 1 of Appendix
E. The resulting net force coefficients, representing the sum of the
non-driving tire and wheel bearing losses plus the vehicle aerodynamic
drag, are presented in Table 3 of Appendix E. The forces at 50 mph and
the appropriate power setting for a large single roll dynamometer to
simulate the vehicle road load at 50 mph are also presented in Table 3.
The differences between the small twin roll dynamometer power
absorber loads and the power absorber adjustment for a large single roll
is primarily the front tire rolling resistances. Since tire rolling
resistances are approximately proportional to the vertical load on the
tire, the differences in the power absorber loads should be linear in
the vehicle test mass. The power absorber setting for a small twin roll
dynamometer, given in Table 2 of Appendix E was subtracted from the
power absorber setting appropriate for a large single roll dynamometer,
given in Table 3 of Appendix E. The difference is scatter plotted in
figure 9 versus the vehicle test mass.
The scatter plot of the differences in the dynamometer power ab-
sorber settings indicate these data are approximately linear in the
vehicle test mass, although a significant amount of data scatter is
present. A regression, using the model that the tire rolling resistance
is proportional to the vehicle test mass was performed. The results of
-------
-31-
OIFFERENCES RFTWF.EN LARGE SINGLE ROLL DYNAMOMETER ADJUSTMENT
AND SMALL T^lIN ROLL DYNAMOMETER ADJUSTMENT AT 50 MPH
VERSES
VEHICLE TEST MASS
0000 *
0 0 0 0 *
'.">() on *
1.0000 +
*
tt « *
0. . * .; .
1000.0 2200.0 3400.0
1^00.0 ?rtO().0 4000.0
VEHICLE TEST MASS (KG) , . '
Figure 9
-------
-32-
this regression are:
Regression of the Differences in Dynamometer Power Absorber Settings
versus
Vehicle Test Mass
Regression model: H = aM
H = the difference in dynamometer power absorber settings
(horsepower)
M = the vehicle test mass (kg)
a = 0.000887
Sample size 54
2
Correlation coefficient 0.46 R = 0.215
Standard error of the regression 0.702
The results of this regression are appended to the prediction
equations (17) and (23). The dynamometer power absorber setting, pre-
dicted by the vehicle frontal area and weight is given by:
H = .633 A + .0004W for pick up trucks
1
P
P (25)
H = .511 A + .0004W for vans v '
where
2
A = the vehicle frontal area (ft )
W = the vehicle weight (Ib)
A factor of 1/2.2 has been introduced since the independent variable
vehicle mass in kg, while equations (25) use the vehicle weight in
pounds.
Similarly equation (24) is augmentical to:
H = .0796W0'651 + .0004W (26)
P
Since equation (25) and (26) depend strongly on equations (18)
and (24) it is concluded that the prediction system based on vehicle
frontal areas, equation (25) is the most accurate.
VII. Conclusions
If light duty trucks are divided into two classes, pick-up trucks
and vans, then vehicle frontal area is a significantly better predictor
of the appropriate dynamometer power absorber setting than is the vehicle
-------
-33-
weight. Since the power absorber adjustment of a twin roll dynamometer
primarily represents the aerodynamic drag of the vehicle, frontal area
is also the physically logical predictor. Therefore, it is concluded
that frontal area is the preferred predictor.
There are, however, disadvantages in predicting the dynamometer
power absorber setting from the vehicle frontal area. The major dis-
advantage is that a second parameter must be associated with each ve-
hicle, since the vehicle weight must be retained to adjust the flywheel
inertia simulation. In addition frontal areas are more difficult to
measure than vehicle weight. Several common methods exist for frontal
area measurement; such as polar planimetery of photographs or cutting
and weighing photographic images. Automated methods, such as computer
scanning of photographs are also in use by the automotive industry.
However, all photographic methods require the time necessary to develop
the photographic print. The final print size should be at least 8 x 10
inches to minimize errors in the area measurements which precludes the
use of currently available instant print processes. Fully automated
techniques, such as computer scanning of a television image or photocell
scanning of the vehicle shadow are feasible, but may involve expensive
equipment.
It must be noted that the vehicle frontal area is significantly
better than weight in predicting the dynamometer power absorber setting
only when light duty trucks are divided into subclasses of vans and
pick-up trucks. While this is relatively simple, it introduces the
vehicle shape as a predictor of the dynamometer power absorber setting.
Implicitly, the division of vehicles is a very simple means of estimating
the relative drag coefficients. This is of no major technical significance,
and conceptionally parallels the separation of light duty truck dynamome-
ter settings from those of light duty vehicles. It is, however, a
distinct philosophical variation from past methods.'
A potential advantage of a prediction system which considers vehicle
shape factors is that it enables introduction of possible refinements.
It is possible to design either vans or pick-up trucks with better
aerodynamic characteristics than current designs. Within a system based
on vehicle shape, these designs can be encouraged. The current test
sample of 15 vehicles is not sufficiently large or diversified to allow
extensive empirical treatment of light duty truck shapes; however,
sufficient information may be available from vehicle manufacturers.
Also, theoretical treatment from the literature of road vehicle aerody-
namics is also possible. Reference 9 is given as one of the more exten-
sive recent publications on road vehicle aerodynamics.
VIII. Recommendations
A dynamometer power absorber setting based on light duty truck
frontal area is recommended. The possible improvements in accuracy of
-------
-34-
this approach are considered sufficient to warrant the increase in
complexity. Since EPA receives criticism about the accuracy of our
dynamometer measurements, such a relatively simple improvement should
not be ignored.
It is further recommended that the distinction between pick-up
trucks and vans be made on the basis of those characteristics of the
vehicles which are responsible for aerodynamic differences. If the
vehicle dynamometer power absorber adjustment is specified in terms of
vehicle "shape factor" this will allow convenient expansion and re-
finements as more information becomes available.
-------
-35-
References
1. R. A.White and H. H. Korst, "The Determination of Vehicle Drag
Contributions from Coast-down Tests." Society of Automotive
Engineers, 720099, New York, N.Y. 1972.
2. G. D. Thompson, "The Vehicle Road Load Problem - Approach by
Non-Linear Modeling." ISETA Fourth International Symposium on
Engine Testing Automation, Vol. II. Published by Automotive
Automation, Croydon, England.
3. G. D. Thompson, EPA Report, unpublished.
4. J. D. Walter and F. S. Conant, "Energy Losses in Tires." Tire
Science and Technology, TSTCA, Vol. 2, No. 4, November 1974.
5. S. Clark, University of Michigan, unpublished discussions.
6. W. fi. Crum, "Road and Dynamometer Tire Power Dissipation." Society
of Automotive Engineers, 750955.
7. S. K. Clark, "Rolling Resistance Forces in Pneumatic Tires."
University of Michigan Report DOT-TSC-76-1, prepared for Department
of Transportation, Transportation Systems Center, Cambridge, Mass.,
January 1976.
8. D. J. Schuring, "Rolling Resistance of Tires Measured-Under Tran-
sient and Equilibrium Conditions on Calspan's Tire Research Facility."
DOT-TSC-OST 76-9, March 1976.
9. A. J. Scibor-Rylski, "Road Vehicle Aerodynamics," John Wiley and
Sons, New York, 1975.
-------
APPENDIX A
VEHICLE TKST FLEET IDENTIFICATION
-------
TABLE 1
ID
5902
7001
7101
7201
7301
7402
7502
7602
7701
7901
8002
8206
8306
8507
9003
VEHICLE TYPE E»
\
FORD F-100
CHEV CHEYF.NNE 20
CHEV SCOTTSDALE 10
CHEV CHEYENNE 10
CHEV G-20 VAN
FOHD F-100 4X4
FORD F-2SO
FORD F-100 R XLT
CHEV G-10 VAN
CHEV G-30 VAN
FORD E-150 VAN
TOYOTA HILUX SR-5
TOYOTA HILUX 2
DATSUN
DODGE TRADESMAN 100 VAN
3A INERTIA
rfT. CLASS
(LU)
4500
5000
4500
4500
4000
5000
4500
4500
4500
6000
4500
3000
3000
2500
4000
FRONTAL AREA
(FT»»?)
31.4(F)
32.0(GM)
31.6(GM)
31.6(GM)
37.0(GM)
31.4(F)
33.6(F)
31.4(F)
37.0(GM)
37.0(GM)
37.7(F)
21.2(EPA>
21.2(EPA)
21.2(EPA)
35.1 (EPA)
-------
APPENDIX B
TRACK MtASLWEMENTS
-------
TABLE 1
AMRIENT COPPECTED ACCELERATION COEFFICIENTS
ID
7101
7001.
77;01;
5902
8206
5902
7001
7502
7402
7001
7001
7901
7001
7301
7402
7201
7701
5902
8002
7201
7301
8002
8206
8507
8002
7301
7502
7901
7502
7001
830*
8507
9003
9003
9003
7701
7201
7101
7901
8002
7701
7502
8206
7201
7301
7101
740?
7b02
7101
7901
7001
8306
8306
8507
WT
(LB)
4110
6050
4500
4270
2750
4330
4930
,4540
5540
5530
4630
5690
5500
4560
5760
5110
4990
5020
4370
5480
5050
5530
4050
3^00
6320
f.4?0
5500
7900
6240
8190
3^90
3370
3970
4380
4810
5620
6060
5020
7040
5010
5980
5020
3550
4540
4060
4500
5110
5030
5330
6060
6490
4140
2700
2560
AO
t-0?
0. 3367E-0?
0.1036F-01
-O.S306E-03
0.^485K-0?
(i.6?M7f.-0?
0.764^E-0?
U.2564E-02
0.5966E-04
0.3926E-02
0.9399E-02
U.3739E-02
0.8017E-02
0.6857E-0?
0.9948E-02
0.3603E-0?'
0.9136E-02
0.4081E-0?
0.6517E-0?
0.6162E-02
0.<*669FJ-02
0.1190E-01
0.85653-02
A 2
( l/i-1)
0.41ie.E.-03
0.12HBE-03
O.V136E-03
0.2577E-03
0.3516F-03
0.1712E-03
0.3653E-03
0.4456E-03
0-.3774H-03
0.421 'if -03
0.202^e-03
0.40^4E-il3
0.326HK-03
0.43ca^-.-o3
0.22H?E-03
0.2279E-0'H
n.3S^lh-0 }
0 , Ui+o 0 fc - 0 3
0.'J01SF-l)3
0.384-3
n.4221t-o:'«
0.179«E-'03
0.5140E-03
0.1136E-03
0. 1920E-03
n.2047fc-03
0.2221E-03
0.4946E-03-
0.2649E-03
0.2351E-03
0.31J6E-03
0.2499E-03
0.3856E^03
0.2024£r03
0.3729EV03
0.154flE,-03
0.3279E-03
0.1909E-03
0.1420E-03
0.2295E-03
0.1881E-03
0.2637t-03
-------
TAHLF. 2
TIRF. PRESSURES
in
5902
5902
5902
7001
7001
7001
7001
7001
7001
7001
7101
7101
7101
7101
7201
7201
7201
7201
7301
7301
7301
7301
7402
7402
7402
7502
7502
7502
7502
7602
7701
7701
7701
7701
7901
7901
7901
7901
8002
8002
8002
8002
8206
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
WT
(LH)
4330
4270
5020
4620
4930
5530
5500
6050
6490
8190
4110
4500
5020
5330
4540
5110
5480
6060
4060
4560
5050
6420
5110
5540
5760
4540
5020
5500
6240
5030
4500
4990
5620
5980
5690
6060
7040
7900
4370
5010
5530
6320
2750
3550
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
BEFORE
FRONT REAR
(PSI)
30
36
36
35
35
35
35
35
35
35
32
32
32
32
28
28
28
28
30
30
30
30
32
32
32
35
35
35
35
36
32
32
32
32
45
45
45
45
32
32
32
32
20
20
20
20
20
20
21
21
21
30
30
32
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
(PST
30.
40.
40.
60.
*0.
60.
60.
60.
60.
60.
32.
32.
32.
12.
12.
32.
32.
12.
32.
12.
3-?.
32.
32.
32.
32.
45.
45.
4b.
45.
40.
32.
32.
32.
12.
60.
60.
60.
60.
40.
40.
40.
40.
?0.
20.
30.
20.
20.
32.
26.
42.
42.
30.
30.
32.
)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o
0
0
0
0
0.
0
0
0
0
0
0
0
0
0
0
0
u
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
LEFT
FPUNT
(PS
34
3b
40
3H
30
39
39
3H
39
40
34
35
35
34
30
31
30
29
32
32
32
32
37
37
37
39
3d
18
39
40
35
35
33
36
<+^
49
51
49
3b
35
36
37
22
22
23
23
22
24
24
24
25
32
33
35
i)
.5
.5
.5
.5
.5
.0
.5
.H
.5
.0
.8
.0
.5
.8
.5
.0
.5
.3
.5
.5
.0
.5
.5
.0
.0
.5
.fi
.0
.5
.?
.5
.0
.5
.0
. 0
.0
.0
.5
.0
.0
.5
.0
.5
.5
.0
.0
.0
.5
.5
.0
.0
.0
.5
.0
AFTFP
H'TGHT I.FFT
(-KOMT . RFAR
(PS
34
39
*0
3H
3b
39
39
3tt
40
39
34
35
35
35
30
10
30
2k*
3?
33
3?
.\rL
37
I/
17
3-*
3«
\-i
40
4'J
3 1
3*
13
3b
a^
4tt
49
44
34
34
36
37
?.t
??.
??.
?.?
21
24
?4
?4
25
32
3}
15
I)
.4
.0
.5
.H
.0
.0
.6
.7
.0
.5
.0
.0
.5
.0
.0
.5
.5
.0
.5
.0
. o
.H
.5
.0
.0
. 5
. 5
.?
.0
.0
.0
.5
.?
.0
.4
.rt
.(1
.0
17
^
.0
.0
.0
.0
.3
. 5
. 5
.0
. 0
.0
.5
.5
.5
.0
(PSI)
14.7
42.2
44.3
64.5
64.0
*2.0
^6.0
^5.7
*7.5
70.5
15.0
15.0
15.0
35.0
14.5
35.0
15.0
33.0
34 . 5
14.5
14.5
16.0
16.5
17.0
37.5
4H .0
47.5
48 . ,)
51.0
45.0
35.0
35.0
13.2
36.0
f>3.5
^4.5
^7.0
h5.5
42.0
43.5
45.0
45.5
23.0
?3.0
34.0
??.5
23.3
36.5
28.0
44 . 5
47.0
32.5
?3.5
35 . 0" "
RIGHT
(PSI)
34. S
42.2
45.0
65.0
65.5
65.5
66.0
65.4
66.5
6^.b
.14.5
35.0
1^.0
35.2
34.5
34.5
34.5
33.0
14.5
3S.O
34.^
36.5
3b.5
37.0
36. S
<*7.5
4H. 0
4Q.O
50.5
^*+.5
35.0
35.0
33.2
35.0
6«. 7
65.0
65.5
65.0
43. f
. 41.5
44 .5
*i5.S
22.0
21.5
33.0
?2.0
?2.S
36.0
?7.3
43.7
47.2
33.0
33.5
35^ U
-------
APPEND I* C
DYNAMOMETER MEASUREMENTS
-------
i
DRIVE TRAIN * RFAR TIkE
KEGkESSTON COEFFICIENTS
ID
7101
7101
7101
7101
7201
7201
7201
7201
7502
7502
7502
7502
7602
7602
7602
8002
8002
8002
800?
820b
8206
8306
8306
8306
8S07
85C7
8507
9003
9003
9003
590?
5902
5902
7001
7001
7001
7001
7001
7001
7301
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901
WT
(LH)
4110
4500
S020
5330
5480
4540
5110
6060
4540
5020
5500
6240
5040
4430
5530
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
4310
5020
5500
4620
4930
5530
6050
6490
8190
4060
4560
5050
6420
5110
5540
5760
4500
4990
5620
5980
5690
6060
7040
7900
A
(NT)
125.089
142.537
Ib3.138
176.577
147.625
94.002
120.296
170. 82b
126.443
149.018
170.187
212.167
132.137
115.029
156.920
79.075
104.432
83.967
121.000
81.356
135.113
8S.214
128.722
152.310
10U.22f
113.064
143.116
96.395
110.992
1P2.549
105.970
135.467
1*3.721
127.M9S
119.84L4
160.010
146.015
172.954
251.360
83.631
95.228
114.625
195.448
157.907
163.957
172.719
109.004
106.903
116.962
130.141
121.809
133.591
160.318
200.388
B
(KG/SEC)
1.907
2.218
2.473
2.081
1.704
2.297
2.601
2.007
2.814
2.951
3.685
2.824
1.656
1.510
1.471
3.480
3.995
4.311
4.973
?.150
2.290
2.253
2.343
2.400
2.213
2.145
2.404
2.009
1.914
2.225
2.939
2.922
2.760
1.958
1.841
1.823
2.995
3.11.1
3.301
1.685
1.584
1.665
2.476
3.445
3.215
3.372
1.846
2.312
2.690
2.818
2.681
2.955
2.992
2.728
-------
TABLE 2
RFAR TIRF
REGRESSION COEFFICIENTS
ID
7101
7101
7101
7101
7201
7?01
7201
7201
7502
7502
7502
7502
7602
760?
7f>02
8002
BOO?
8002
8002
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
5902
5902
5902
7001
7001
7001
7001
7001
7001
7301
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901
WT
(LB)
4110
4500
5020
5330
5480
4540
5110
6060
4S40
5020
5500
6240
5040
4430
5530
4370
5010
5S3U
6320
2750
4050
?700
3490
4140
2560
3370
3900
3970
4380
4910
4310
5020
5500
4620
4930
5530
6050
6490
8190
4060
4560
5050
6420
5110
5540
5760
4SOO
4990
5620
5980
5690
6060
7040
7900
A
(NT)
84.692
102.140
122.740
136.180
116.237
62.614
88.909
139.43*
88.802
111.373
132.542
174.522
101.56V
84.462
126.352
70.134
95.492
75.027
112.060
56.494
110.251
61.014
104.522
128.109
77.627
90.466
120.517
83.001
97.598
109.156
65.601
95.098
123.353
76.22B
88.175
108.342
94.346
121. 28h
199.693
64.873
76.469
95.867
176. 69u
135.962
142.012
150.774
68.629
66.529
76.588
89.767
88.516
100.298
127.025
167.096
P
(KG/SEC)
.239
.549
.804
.412
-.236
.357
.661
.067
.229
.366
1.099
.239
. 1 0 1)
-.045
-.084
.349
.864
1.180
1.842
.200
.340
-.020
.070
.127
-.324
-.392
-.133
.325
.230
.542
-.633
-.650
-.R12
-.48.0
-.597
-.614
.55tt
.673
.«63
-.087
-.187
-.107
.705
2.803
2.573
2.730
.214
.680
1.058
1.186
.353
.627
.663
.400
-------
TABLE 3 .
DRIVE TPAIN
DEGRESSION! COEFFICIENTS
ID
7101
7101
7101
7101
7201
7201
7201
7201
7502
7502
7502
750*
7602
760?
7602
8002
BOO/?
H002
8002
8206
8206
*306
8306
rt.306
6H07
BSO 7
8b07
90 OJ
9003
9003
5902
5902
5902
7001
7001
7001
7001
7001
7001
7301
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901
WT :
(LB)
4110
4500
5020
5330
5480
4540
5110
6060
4540
5020
5500
6240
5040
4430
5S30
4370
5010
5530
6320
2750
4050
2700
3490
4l90
6060
7040
7900
A
(NT)
40.398
40.398
40.398
40.398
31.388
31.388
31.388
31.388
37.645
37.645
37.645
37.645
30.568
30.568
30.56*
8.940
8.940
8.940
8.940
24.862
24.862
24.200
24.200
24.200
22.598
22.598
22.59*
13.39<*
\ 13.39*+
1 13.39<>
40.36S
40.369
40.369
51.66H
51.666
51.66J-
51.668
51.66B
51.668
18.758
18.758
18.758
18.758
21.946
21.946
21.946
40.374
40.37<*
40.374
40.374
33.293
33.293
33.293
33.293
B
(KG/SEC)
1.668
1.668
1.668
1 .668
1.940
1.940
1.940
1.940
2.586
2.586
2.586
2.586
1.555
1.555
1.55S
3.131
i.KU
3.131
3.131
1.950
1.950
?.273
H.^73
s.d.'?3
^.S37
2 . 5 'M
2.537
1 .^8^
1 .^8*4
1.684
3.b72
3.572
j.57^
2.437
2.^37
2.437
2.437
2.437
2.437
1.772
1.772
1.772
1.772
.642
.642
.642
1.632
1.632
1.632
1.632
2.328
2.328
2.328
2.328
-------
TABLE 4
F*ONT TIRE
DEGRESSION COEFFICIENTS
ID
7101
71C1
7101
7101
7201
7201
7201
7201
7502
7502
7502
7502
7*02
7602
7602
800?
8002
8002
8002
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
5902
5902
5902
7001
7001
7001
7001
7001
7001
7301
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901
WT
(LB)
4110
4500
5020
5330
5480
4540
5110
6060
4540
5020
SSOO
6240
5040
4430
5530
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
4310
5020
5500
4620
4930
5530
6050
6490
8190
4060
4560
5050
6420
5110
5540
5760
4500
4990
5620
5980
5690
6060
7040
7900
A
(NT)
100.119
101.676
96.805
102. 69B
73.717
74.04J
71.504
75.010
53.455
78.66b
72.612
138.780
116.928
111.475
128.301
125.442
123.561
133.580
151.644
54.797
61.980
68.994
75.065
75.603
53.466
56.870
70.427
136.528
148.811
159.544
132.806
132.485
145.088
110.863
108.425
1 1 b . 7 ? y
118.585
129.009
132.334
94.076
107.055
109.559
117.703
» & » « » «
ttttttttao
tnnnnn*
99.552
109.240
111.976
1 13.440
132.923
121.567
145.946
173.943
R
(KG/SEC)
.147
.376
.54a
.705
.2*4
.941
,S8/
.592
-.047
.021
.671
-.413
. 66(1
. 9 1 0
1.112
-.570
.636
. 760
.204
.367
.171
.107
.146
.222
-.591
-.294
-.SO 3
-.634
-.418
-.405
.737
1.966
2. 543
.088
.391
.514
.r>3<*
.41^
.513
.447
.543
.858
1.015
« «««»»
tt fe « » » tt
.535
.372
563
.552
-.204
-.043
.103
.405
-------
TABU: 5
TIRE PRESSURES
HEFORF
ID
5902
5902
5902
7001
7001
7001
7001
7001
7001
7101
7101
7101
7101
7201
7201
7201
7201
7301
7301
7301
7301
7402
7402
7402
7502
7502
7502
7502
7602
7602
7602
7701
7701
7701
7701
7901
7901
7901
7901
8002
8002
8002
8002
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
WT
(IB)
4330
5020
5500
4;620
4930
5530
6050
6490
8190
4110
4500
5020
5330
4540
5110
5480
6060
4060
4560
5050
h4
-------
APPENDIX D
MASSLS
-------
TABLE 1
VEHICLE MASSES
ID
7101
7101
7101
7101
7301
7201
7201
7201
7502
7502
7502
7502
7602
7602
7602
8002
8002
8002
8002
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
5902
5902
5902
5902
7001
7001
7001
7001
7001
7001
7001
7301
GRAV
MASS
(KG)
1868.2
2045.5
2281.8
2422.7
2490.9
2063.6
2322.7
2754.5
2063.6
2281.8
2SOO.O
2836.4
2286.4
2013.6
2518.2
1986.4
2277.3
2S13.6
2B72.7
1250.0
1940.9
1227.3
1586.4
1881.8
1161.6
1S31.8
1772.7
1804.5
1990.9
2186.4
1940.9
1968.2
2281.8
2500.0
2100.0
2240.9
2500.0
2513.6
2750.0
2950.0
3722.7
1345.5
DTT EFF
MASS
(KG)
33.811
33.811
33.811
33.811
64.657
64.657
64.657
64.657
42.007
42,007
42.007
42.007
43.537
43.537
43.537
30.971
30.971
30.971
30.971
31.074
31.074
20.605
20.605
20.605
30.183
30.183
30.183
42.142
42.142
42.142
46.852
46.852
46.652
46.852
55.724
55.724
55.724
55.724
55.724
55.724
55.724
50.140
t
FT EFF
MASS
(KG)
26.04
26.04
26.04
26.04
31.75
31.75
31.75
31.75
44.30
44.30 .
44.30
44.30
27.34
27.34
27.34
31.92
31.92
31.92
31.92
20.75
20.75
22.91
22.91
22.91
22.80
22.80
22.80
19.64
19.64
19.64
26.90
26.90
26.90
26.90
46.67
46.67
46.67
46.67
46.67
46.67
46.67
28.90
TOTAL VEH
MASS
(KG)
1928.0
2105.3
2341.7
2482.6
2587.3
2160.0
2419.1
2851.0
2149.9
2368.1
2586.3
2922.7
2357.2
2084.5
2589.1
2049.3
2340.2
2576.5
2935.6
1301.8
1892.7
1270.8
1629.9
1925.3
1216.6
1584.8
1825.7
1866.3
2052.7
2248.1
2014.7
2041.9
2355.6
2573.8
2202.4
2343.3
2602.4
2616.0
2852.4
3052.4
3825.1
1924.5
-------
(TABLE 1 CONTINUED)
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901
7901
2072.7
2295.5
2918.2
2322.7
2518.2
2618.2 ,
2045.5
2268.2
2554.5
2718.2
2586.4
2754.5
2977.3
3200.0
3590.9
50.140
50.140
50.140
43.537
43.537
43.537
41.779
41.779
41.779
41.779
56.206
56.206
56.206
56.206
56.206
28.90
28.90
28.90
28.81
28.81
28.81
27.16
27.16
27.16
27.16
38.04
38.04
38.04
38.04
3H.04
2151.8
2374.5
2997.2
2395.0
2590.5
2690.5
2114.4
2337.1
2623.5
2787.1
2680.6
2848.8
3071.5
3294.2
3685.2
-------
APPENDIX E
VFHICLE ROAD LOAD
AND
DYNAMOMFTFR ADJUSTMENT TO SIMULATE VEHICLE ROAD LOAD
-------
TABLE
TOTAL VEHICLE
ID
5902
5902
5902
7001
7001
7001
7001
7001
7001
7101
7101
7101
7101
7201
7201
7201
7201
7.301
7301
7301
7301
7402
7402
7402
7502
7502
7502
7502
7602
7602
7602
7701
7701
7701
7701
7901
7901
7901
7901
8002
8002
8002
8002
8206
820,6
8306
8306
8306
8507
8507
8507
9003
9003
9003
WT
(LB)
4330
5020
5500
4620
4930
5530
6050
6490
8190
41 10
4500
5020
5330
4540
5110
5480
6060
4060
4560
5050
6420
5110
5540
5760
4540
5020
5500
6240
4430
5030
5540
4500
4990
5620
5980
5690
6060
7040
7900
4370
5010
5530
6320
2759
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
FO
(NT)
0.1bl8E+03
0.3710E+03
0.2811E+03
0.4?26E+03
0.4404E+03
0.5^2SE+03
0.3419F+03
0.3796E+03
0.4S43E+03
0.2630E+03
0.1571F+03
0.2266F+03
0.2682E+03
0 . 1 412K. + 03
0.1694F+03
0.2«23E+03
0.1960E+03
0.1672E+03
0.2636E+03
0.2112E+03
0.3825E+03
0.3637E+03
0.4h72E+03
0.3834E+03
0.3105E+03
0.2653E+03
0.4087E+03
0.3256E+03
0.9496F. + 02
0.1640E+03
0.2093E+03
0.2361E+03
0.2373E+03
0.2283E+03
0.2534E+03
0.2973E+03
0.1764E+03
0.3S67E+03
0.3058E+03
0.1300E+03
0.2874E+03
0.2837E+03
0.2567E+03
0.1575E+03
0.2535E+03
0.1167E+03
0.2295E+03
0.2408E+03
0.1999E+03
0.2495E+03
f).2812E + 03
0.2787E+03
0.1751E+03
0.3332F>,03
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
^0
El
2924E
4426E
19b7E
1679E
8227E
93341:.
230 OE
188 IE
1997E
7670E
2094E
1802E
1013F.
1732E
1815E
3837E
1792E
1320E
6348E
1689E
6198E
8629E
38?4E
1758E
6215E
1989E
1060 E
2469E
2743E
21S4E
2173E
1173E
1040L
1177E
1094'E
2705E
1857E
844hE
1776E
1776E
1396E
6730E
1606E
8115E
5689E
1512E
9299E
+ 02
+ 01
+ 0?
+ 02
+ 01
+ 0 0
+ 02
+ 02
+ 02
+ 01
+ 02
+ 02
+ 02
+ 02
+ 02
+ 01
+ 02
+ 02
+ 01
+ 02
+ 01
+ 01
+ 01
+ 02
+ 01
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 01
+ 02
+ 01
+ 02
+ 02
+ 00
+ 01
+ 02
+ 01
+ 01
+ 02
+ 01
8989E+01
1042E
1041E
1057E
6284E
2127E
1193E
+ 02
+ 02
+ 02
+ 01
+ 02
+ 01
I
POA1J LOAD
F?.
.0.349 E
H.1036F
0 . S^78E
0 .4459F
0.8560E
0.1 101F
0.3^73E
0.4333F
0.5747E
0.7936E
0.4260E
0.4793E
'0 . 8 i 4 ). E
0.539VE
0.5514F
0.9955E
0 . 5473F
0.7422F
0.9434E
0.6076E
0.9219E
0.893 IE
+ 0 0
+ 01
+ 00
+ 00
+ 00
+ 01
+ 0 0
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
0.^77
-------
TABLE 2
TWIN SMALL POLL DYNAMOMETER
ID
5902
5902
5902
7001
7001
7001
7001
7001
7001
7101
7101
7101
7101
7201
7201
7201
7201
7301
7301
7301
7301
7402
7402
74Q2
7502
7502
7502
7502
7602
7602
7602
7701
7701
7701
7701
7901
7901
7901
7901
8002
8002
8002.
8002
8206
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
WT
(LH)
4330
5020
5500
4620
4930
5530
6050
6490
8190
4110
4500
5020
5330
4540
5110
5480
6060
4060
4560
5050
6420
5110
5540
5760
4540
5020
5500
6240
4430
5030
5540
4500
4990
5620
5980
5690
6060
7040
7900
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
-0.
0.
0.
0.
0.
n.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
o.
0.
0.
0.
-0.
-0.
-0.
0.
0.
0.
0.
0.
-0.
n.
-0.
-0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
-0.
0.
FO
(NT)
4729E
1486E
2598E
2213E
23.1 5F
300BF
1199E
1277E
1370E
7475E
4635F.
8966E
367QF.
4B70E
9682E
9R95E
6946E
2128E
9R02F.
2*10E
1282E
1394E
229QE
1382E
1S90E
7562E
2069E
3731E
9?36E
4137E
2*99E
+ 02
+ 03
+ 02
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 02
+ 02
+ 01
+ 02
+ 00
+ 01
+ f>2
+ 01
+ 02
+ 02
+ 02
+ 03
+ 03
+ 03
+ 03
+ 03
+ 02
+ 03
+ 02
+ 02
+ 02
+ 02
6118E+02
5631E
3708E
5046E
8686E
3^39E
1050E
3242E
3540E
1032E
1079E
3664E
4360E
9085E
1151E
6163E
5363E
7243E
1090E
1058E
8968E
3542E
1048E
+ 02
+ 02
+ 02
+ 02
+ 02
+ 03
+ 00
+ 02
+ 03
+ 03
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 02
+ 03
+ 03
+ 02
+ 02
+ 03
0.
-0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-u.
Fl
2558E+0?
1990E+00
1461E+02
1467E+02
5955E+C1
3?9uE+01
1961E+0?
1550E+02
1643E+02
5693E+01
1853E+02
1527E+0?
7568E+01
1434E+02
1521E+02
1859E+01
1545E+02
11146+02
429PE+01
1452E+0?
3050E+01
5212E+01
2340E+00
1386E+02
3484E+01
1699E+02
6598E+01
2224E+02
2518E+02
1937E+02
1935E+02
1396E+02
7926E+01
8842E+01
7917E+01
2580E+00
1577E+02
5506E+01
1479E+02
1481E+02
4191E+01
2047E+01
1129E+02
5711E+01
3330E+01
1278E+02
6853E+01
6436E+01
8615E+01
8422E+01
8541E+01
4847E+01
1974E+02
2987E+01
F2
0.3496F>00
0.1036E+01
0.5873E+00
0.445^ + 00
O.fe56ijr +00
0.1101F+01
0.367'if-~ + 00
0.4333F+00
0.5747E+00
0.7936F+00
0.4260E+00
0.4793E+00
0 . 8 1 4 1 F + 0 0
6.5397E+00
0.5514E+00
0.9955F+00
0.5473F+00
0.7422F+00
0.9434F+OH
0.6076E+00
0.9219E+00
0.8931E+00
0.9776E+00
0.6139E+00
0.9580E+00
0.5S67F+00
0.7128F. + 00
0.4298E+00
0.2393F+00
0.3^49E+00
0.3916E+00
0.1932E+01
0.827(SF + 00
0.8223E+00
0.7382E+00
0.1084F+01
0.5439E+00
0.7315E+00
0.6061F.+00
0.6179F+00
0.1157E+01
0.9441 F+ 00
0.7361E+00
0.457^E+00
0.532bF+oO
0.2390E+00
0.4346F+00
0.4419E+00
0.3209E+00
0.3556E+00
0.3606F+00
0.7878E+00
0.3691E+00
0.1156E+01
0
n
0
n
0
0
0
0
0
n
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
n
0
0
0
0*
0
. 0
0
0
0
0
0
0
0
0
F50
(NT) ,
.6991E
.6M6E
.6462E
.7718E
.7921E
.7772E
.7416E
.6906E
.7914E
.59R4E
.5806E
.5898E
.6125E
.S906E
.6251E
.6378E
.6118E
.6410.E
.6652E
.6561E
.6S69E
.7021E
.7226E
.7547E
.7155E
.7335E
.7105E
.7491E
.5900E
.5739E
.6031E
.7142E
.6469E
.6457E
.5962E
.6341E
.5899E
,?935E
.6329E
.6Q42E
.5875E
.6252E
.6S67E
.3999E
.^313E
.3934E
.4319E
.4182E
.4253E
.4749E
.4769E
.5915E
.5901E
.6155E
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
HP50
(HP)
20.954
19.830
19.368
23.132
23.742
23.294
22.228
20.699
23.719
17.935
17.403
17.67b
18.358
17.701
18.735
19.115
18.337
19.212
19.937
19.664
19.689
21.042
21.657
22.620
21.^44
21.985
21.294
22.453
17.684
17.200
18.077
21.407
19.388
19.353
17.868
19.005
17.679
17.788
18.971
18.108
17.608
IB. 739
19.683
11.987
12.928
11.792
12.944
12.535
12.746
14.233
14.292
17.729
17.685
16.449
-------
SINGLE
TABLE 3
LARGE ROLL
DYNAMOMETER
ID
5902
5902
5902
7001
7001
7001
7001
7001
7001
7101
7101
7101
7101
7201
7201
7?01
7201
7301
7301
7301
7301
7402
7402
7402
7502
7502
7502
7502
7602
7602
7602
7701
7701
7701
7701
7901
7901
7901
7901
8002
8002
8002
8002
8206
8206
8306
8306
8306*
8507
8507
8507
9003
9003
9003
WT
(l.H)
4330
5020
5500
4620
4930
5530
6050
6490
8190
4110
4500
5020
5330
4540
5110
5480
6060
4060
4560
5050
6^20
5110
5540
5760
4540
5020
5500
6240
4430
5030
5540
4500
4990
5620
5980
5690
6060
7040
7900
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
FO
(NT)
4583E+02
2355E+03
1174E+03
2947E+03
3006E+03
3725E+03
1959E+03
2066E+03
2029E+03
1379E+03
1456E+02
6346F+02
9162E+02
4720E+02
43
9657E+02
1871E+03
2058E+03
3032E+03
2107E+03
1B41E+03
1163E+03
2385E+03
1134E+03
2007E+02
3186E+02
5P38E+02
1271E+03
1304E+03
1113E+03
1233E+03
1755E+03
4281E+02
1964E+03
1054E+03
5093E+02
1830E+03
1997E+03
1357E+03
7614E+02
1184E+03
3149E+02
1008E+03
8849E+02
9967E+02
1364E+03
1381E+03
1R23E+03
6411E+02
2107E+03
0
0
0
0
0
-0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0
0
0
0
0
0
0
0
0
-0
0
'0
0
0
0
0
0
0
0
0
0
0
-0
F 1
.2630E
. 1504E
.168 IE
.1483E
.6386E
.2756E
.2000E
.1570E
.1667E
.5763E
1872E
.1555E
.8CI49E
.1502E
.155SE
.2133E
.1S91E
.1151E
.4764E
1522E
.3722E
.5184E
.6090E
.1421E
.3401E
.1694E
.6915E
.2187E
.2592E
.1988E
.2026E
.1358E
.8088E
.9080E
.8122E
+ 02
+ 01
+ 02
+ 02
+ 01
+ 01
+ 02
+ 02
+ 0?
+ 01
+ 02
+ 02
+ 01
+ 02
+ 02
+ 01
+ 02
+ 02
+ 01
+ 02
+ 01
+ 01
+ 00
+ 02
+ 01
+ 02
+ 01
+ 02
+ 02
+ 02
+ 02
+ 02
+ 01
+ 01
+ 01
.2400E-01
.1562E
.5454E
.1503E
.1428E
.3855E
.2419E
. 1 1 69E
.5965E
.3399E
.1287E
.6956E
.6589E
.8207E
.8265E
8166E
.4275E
.1936E
.3418E
+ 02
+ 01
+ 02
+ 02
+ 01
+ 01
+ 02
+ 01
+ 01
+ 02
+ 01
+ 01
+ 01
+ 01
+ 01
+ 01
+ 02
+ 01
E?
0.3496E+00
0.1036E+01
0.587HE.+00
0.4459E+00
0.8560E+00
0.1101E+01
0.3673F+00
0.4333F.. + 00
0.57W + 00
0.7936F+00
0.4260E+00
0.4793E+00
0.8141E+00
0.5397E+00
0.5514F. + 00
0.9955F+00
0.5473F+00
0.7422E+00
0.9434F+00
0.6076E+00
0.9219E+00
0.8931E+00
0.9776F+00
0.6139E+00
0.9580E+00
0.5567E+00
0.712HE+00
0.4298E+00
0.2393E+00
0.3649F. + 00
0.3916E+00
0.1932E+01
0.8276E+00
0.8228E+00
0.7382E+00
0.1084E+01
0.5439F. + 00
0.7315E+00
0.6061E+00
0.6179E+00
0.1157E+01
0.9441E+00
0.7361E+00
0.4578E+00
0.5326E+00
0.2390E+00
0.4346E+00
0.4419E+00
0.3209F+00
0.3556E+00
0.3606E+00
0.7878E+00
0.3691E+00
0.1156E+01
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
o.
0.
0.
0.
0.
0.
0.
0*
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
F50
(NT)
80B3E
7867E
7867E
8489E
87I09E
B609E
8 2.6 5 E
7740E
B626E
6631E
6458E
6504E
6782E
6526E
6721E
6796E
6542E
7117E
7461E
7404E
7307E
7678E
«052E
H349E
7386E
7730E
7491E
816HE
6788E
6585E
7008E
7887E
7246E
7253E
6735E
7175E
6635E
6837E
7441E
6787E
6747E
7254E
7512E
4 38 IE
4604E
4384E
4733E
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
*63
+ 03
+ 03
+ 03
+ 03
+ 03
4565E+03
4434E
4988E
5007E
6714E
6811E
7117E
+ 03
+ 03
+ 03
+ 03
+ 03
+ 03
HP50
(HP)
24.226
23.577
23.579
25.444
26.102
25.801
24.771
23.197
25.853
19.875
19.356
19.492
20.326
19.558
20.143
20.369
19.608
21.330
22.362
22.190
21.902
23.012
24.133
25.023
22.137
23.167
22.453
24.482
20.344
19.73*
21.004
23.640
21.717
21.738
20.l'87
21.505
19.886
20.491
22.303
20.343
20.223
21.741
22.515
13.132
13.799
13.141
14.187
13.682
13.289
14.950
15.008
20.122
20.413
21.331
-------
TABLE 4
MEflM URLUES OF THE
SMflLL TWIM ROLL DVMRMOMETER
POWER RBSORBER SETTINGS RT 50 MPH
TO
5902
7001
7101
7?01
7301
7402
760?
7701
7Q01
8002
8306
BS07
9003
EPA INFRTIA'
WT. CLASS
(LR)
4500
5000
4500
4000
5000
4500
4500
4500
6000
4500
3000
3000
2500
4000
FRONTAL AREA
(FT*«2)
MEAN POWER
50 MPH
(HORSEPOWER)
31.4(F)
32.0(GM)
31.6(GM)
31.6(GM)
37.0(GM)
31.4(F)
33.6(F)
31.4(F)
37.0(GM)
37.0(GM)
37.7(F)
21.2(EPA)
21.2(FPA)
21.2(EPA)
35.1 (EPA)
20.051
22.802
17.R43
18.472
19.625
21.773
21.794
17.654
19.504
18.361
18.534
12.457
12.424
13.757
17.954
------- |