EPA-AA-SDSB  79-26
                           Technical  Report
           A Track to Twin Roll Dynamome'ter Comparison  of
                 Several Different Methods  of Vehicle
                          Velocity Simulation
                                  by
                              John Yurko
                               June 1979
                                NOTICE
Technical Reports do not necessarily represent final EPA decisions or
positions.  They are intended to present technical analysis of issues
using data which are currently available.  The purpose in the release of
such reports is to facilitate the exchange of technical information and
to inform the public of technical developments which may form the basis
fo 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 Radiation
                 U.S. Environmental Protection Agency

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                                  -2-
ABSTRACT

     The current EPA test procedure for fuel economy and emissions
testing uses a twin roll dynamometer, obtaining a speed signal from the
rear roll and simulating the forces at the front roll.  With the rolls
coupled only by the drive wheels of the vehicle, the front roll travels
approximately 2% slower than the rear roll at steady-state 50 mph, re-
sulting in approximately a 4% overprediction of fuel economy. Coupling
the rolls externally equalizes the roll speeds at a value which better
simulates the road velocity and therefore better predicts the fuel
economy.  This report describes the test program and data analysis which
led to these conclusions.

FOREWORD

     The EPA has conducted a test program in order to determine the most
representative method for simulating the road velocity of a vehicle on
a Clayton twin-roll dynamometer.  The three methods of simulating the
road velocity on the twin-roll dynamometer are:

     (1)  Using the velocity of the rear roll, which is the current
          method,

     (2)  Using the velocity of the front roll,

     (3)  Operating with the rolls coupled.

     To determine which of these three methods most closely represents
the road experience of a vehicle, steady-state tests were conducted on a
track and compared to dynamometer tests using each speed simulation
method.  The same vehicle was used for all phases of the test program.
This report describes the test program, reports the results, and recom-
mends the most appropriate method of velocity simulation on a twin-roll
dynamometer.

SUMMARY

     The results of the road to dynamometer comparison show that the
road velocity is best simulated when the front and rear rolls of the
dynamometer are coupled.  With  the rolls coupled, the simulated velocity
was within 0.025% of actual road velocity.  With the rolls uncoupled,
the rear roll velocity over credited the vehicle speed by approximately
1.0% while the front roll under credited the  speed by about 1.0%.
Coupling the rolls reduced measured  fuel economy by approximately 4%  in
comparison with the current method of using the rear roll speed.  This
is consistent with the 1% speed errors in each roll, since the force  is
proportional to the velocity squared.  In conclusion, coupling the rolls
is technically the best method  of simulating  the vehicle velocity and
should  improve EPA fuel economy predictions.

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                                  -3-
I.   INTRODUCTION

     When a vehicle is tested for fuel economy and emissions on a
Clayton twin-roll dynamometer, there is a difference between the velo-
cities of the front and rear rolls of the dynamometer.

     Therefore, the speed sensor location can have a significant effect
on fuel economy and emissions testing.  Steady-state tests have shown
that the rear roll travels approximately 1.0 mph faster than the front
roll at 50 mph (1).  This occurs because the drive wheels of the vehicle,
which are cradled between the two rolls, act as the only coupling be-
tween the two rolls when a vehicle is driven on the dynamometer.  The
power absorber and inertia flywheels, which simulate the road force
experienced by a vehicle, are connected to the front roll.  This causes
a greater tangential force at the tire/front-roll interface than at the
rear-roll interface, resulting in a smaller effective rolling radius in
the tire with respect to the front roll as opposed to the rear roll.

     Externally coupling the rolls eliminates the difference in velo-
cities of the two rolls.  Therefore, this has been considered as an
alternative method for simulating the vehicle speed.  Locating the speed
sensor on the front roll has also been suggested, since the forces and
the velocity would then be associated with the same surface.  To de-
termine which method would best simulate the actual road velocity of a
vehicle, a test program was conducted.  The following discussion de-
scribes the track tests, the dynamometer tests, and the road to dyna-
mometer comparison which were used to determine the optimum method for
measuring the simulated velocity of a vehicle.

II.  DISCUSSION

     The test program consisted of three portions: 1) track portion 2)
dynamometer portion, and 3) data analysis.  The track portion was con-
ducted at the Transportation Research Center of Ohio  (TRC).  The dyna-
mometer portion was conducted at the EPA laboratory in Ann Arbor.  One
vehicle, a 1978 Mercury Montego, was used for all testing.  Steady-state
tests were conducted on both  the track and the dynamometer, for four
different sets of radial tires which are listed in Appendix A-l.

     A.   Track Portion

     Prior to each  test, the vehicle was weighed with a full tank of
indolene test fuel, complete  instrumentation, and two operators.  After
a 20-minute warm up at 50 mph around an oval trackj data were collected
during one lap of  the track for approximately  10 minutes  at steady state
50 mph.  Both left  and right  rear wheel speeds, left  and  right  rear
wheel torques, and  a fifth wheel speed were recorded  at a  once/second
rate.  Total fuel  flow and distance  traveled were also measured.  Am-
bient temperature,  barometric pressure, wind velocity and  wind  direction
were monitored during the tests.  Tire  temperatures were  recorded before
and after each test.  Immediately following the steady state test,  10

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                                  -4-
coastdowns were conducted in accordance with the EPA recommended prac-
tice for determination of road load for light-duty vehicles.   A detailed
description of all the equipment used is given in Appendix A-2.

     B.   Dynamometer Portion

     The goal was to reproduce the exact road torque and speed condi-
tions for each test on the dynamometer.  In order to obtain the necessary
precision, we instead chose to use a 9-point speed/torque test matrix,
and then to interpolate the dynamometer data to the road datum.

     For the dynamometer tests, it was decided to warm-up the tires so
that they would be at approximately the same conditions as are vehicle
tires during typical EPA tests.  This was chosen since the results would
be more representative of conditions during EPA tests than would result
from a 20 minute 50 mph steady-state warm-up and there would be reduced
probability of tire failures.  This approach also resulted in tire
temperatures which were closer to the road tire temperatures than would
have occurred with the 20 minute steady-state warm-up.

     The test cycle chosen consisted of a tire warm-up of one complete
FTP cycle followed by three consecutive 5 minute steady-state measure-
ments at a single horsepower.  At this time a 15 minute cool down period
was provided before the dynamometer adjustment was changed, then the
first 505 seconds (bag one) of the LA4 cycle was driven to precondition
the tires and three more steady-state measurements were obtained.  This
cycle of a cool'down followed by a preconditioning was repeated until
all data necessary for the 9 point matrix were obtained.  The  15 minute
cool down followed by the 505 seconds of preconditioning was chosen on
the basis of tire temperature measurements, to be appropriate  to yield
approximately the same tire temperatures as were obtained after one
complete LA-4 cycle starting with a cold tire.  No tire failures were
observed in this program, either as a result of the warm-up cycle or the
measurement conditions.

     The vehicle was tested with each set of tires at three steady-state
speeds, nominally:  1) 50 mph, 2) 40 mph, and 3) 55 mph.  For  greater
precision the actual measured velocities were used in the data analysis.
The 55 mph point was chosen instead of 60 mph since, at 60 mph the tire
temperature increased rapidly, indicating possible tire failure prob-
lems.  Data were collected during each steady state test for 5 minutes
at a once/second rate.  As in  the track portion, both rear-wheel torques
and rear-wheel  speeds were recorded.   Instead of a fifth wheel speed,
the front and rear dynamometer roll speeds were recorded.  Fuel flow and
rear roll distance traveled were also measured.  Each steady state was
followed by a vehicle/dynamometer coastdown from 55 mph to 45  mph and
the coastdown time was recorded.  The  dynamometer  coastdown times were
only used for a fuel economy comparison as described in Section III.
The steady-states and the coastdowns were repeated at each speed for
three  different indicated dynamometer  power absorber settings:  1) 11.4
HP, 2)  12.4 HP, 3) 10.4 HP,  in that order.  This test sequence is sum-
marized in the  9-point test matrix shown in Figure  1.  The 11.4 HP value

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                                            -5-
                                       Figure 1
                                Dynamometer Test Matrix
            12.4
Dyno Power
Absorber
Setting (HP)
            11.4-
            10.4.
                            40
50           55
                              Nominal Steady State Velocity (MPH)

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                                   -6-
approximately represented the road load of the vehicle, with the midrange
set of tires, as determined by matching the road and dynamometer coast-
down times.  The 10.4 and 12.4 test values were chosen to cover the
range of road loads, observed with different tires.  For greater pre-
cision, actual wheel torques and wheel speeds were used to match the
dynamometer test to the road.  This was done by a linear regression
which is described in Section IIC.

     The entire configuration was then repeated, for each tire set, with
the front and rear rolls coupled by a motorcycle chain, and sprockets
connected to each roll.  A detailed description of the test sequence
including warm-up cycles for the dyno portion is given in Appendix B.
All the equipment used in the dyno portion was the same as the equipment
used in the track portion with the exception of replacement of some
minor damaged components and the additional equipment associated with
the dynamometer.  These are included in the equipment list of Appendix
A-2.

     C.   Data Analysis for Road to Dynamometer Comparisons

     For each set of tires, one 50 mph steady-state test was conducted
on the road.  For each test, mean rear wheel angular speeds, mean rear
wheel torques, and a mean fifth wheel speed were calculated.

     Conceptually, the intent was to reproduce the rear wheel torque and
speed conditions of the vehicle which were observed on the road, for
each set of tires on the dynamometer.  Under these conditions, the
different possible speed measurements would be sampled, and that method
of measurement which best agreed with the road fifth wheel velocity
would be selected as the most appropriate method of measuring the dyna-
mometer simulated speed.

     The conceptual approach could not be used directly because of the
experimental precision considered necessary to resolve the small velo-
city variations among the different methods of dynamometer speed simula-
tion.  Therefore, we chose  to use the 9-point steady-state speed/torque
test matrix described in Figure 1.

     The data obtained at these points uses the interpolated velocity to
obtain a roll velocity corresponding to the conditions observed during
the road tests.  The interpolation was conducted by means of a multiple
linear regression using the mean  of the data at each point of the test
matrix.

     First, as discussed, the mean values of each  rear wheel angular
speed, each rear wheel torque, and each dynamometer roll velocity, with
rolls  coupled and uncoupled was calculated for every steady-state test.
An  example of these data for one  of the nine point matrices is graphi-
cally  shown in Figure  2.  The interpolation of these data to the observed
road point was accomplished by regressing each roll velocity versus  the
sum of the mean rear wheel  angular speeds and the  sum  of the mean rear
wheel  torques, over each 9-point  test matrix, yielding the  coefficients
for the  following equations:

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                                     -7-
                                      Figure 2
                              Tire 4 With Rolls  Coupled



       Sum of  the Rear Wheel Torques vs.  Sum of  the  Rear Wheel Angular Speeds

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                                  -8-
     VRR ' VWL + V + bR(TL + V + CR
                   V + V*L + V + CF
     Vcoup = ac(WL + WR) + bc(TL + TR) + CG                      (3)
Where:
     V   = mean rear roll velocity
      KK
     V   = mean front roll velocity
      FR
     V     = mean rear roll velocity with rolls coupled
      coup
     W  = mean left wheel angular speed
      J-j
     W  = mean right wheel angular speed
      K
     T  = mean left wheel .torque
     T  = mean right wheel  torque
      R



      's    's    's
     a  , b  , c   = unique sets of regression coefficients for

                      each  roll condition and each 9-point test

                      matrix
     The road values of mean wheel  torques and speeds were inserted into

equations  (1),  (2), and (3) for each set of tires to obtain the simulated

road velocity for each method of speed measurement interpolated to the

road conditions.  The predicted road velocities as given by the above

equations, were then compared to the actual mean road velocity for the

same set of tires:
     VRR/Road = 3R(\ + VRoad + V*L + VRoad + CR
     VFR/Road = V\ + VRoad + bF(\ + ^Road + CF

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                                  -9-
     VcOup/Road = aC(\ + VRoad + bC(fC + VRoad + CC
Where:
      ^T,/,,   , = Road velocity as simulated by the rear roll at the
      RR/Road       ,    J44..
                road conditions
     V   ,„   , = Road velocity as simulated by the front roll at the
                road conditions
     V     /„   , = Road velocity as simulated with the rolls coupled
      coup/Road


     a,b,c = the set of coefficients obtained from the regressions of
             the dynamometer data for each tire  (different for the rear
             roll, front roll, and coupled roll predictions)


     Sample calculations and the original data,  including the regression
coefficients are given in appendix C.

III. RESULTS

     The results of all tests on the radial and bias belted tires are
given in Table  1.

     The mean deviation from the actual  road velocity for the radial
tires was  +1.10% using the  rear roll velocity simulation, -1.07% using
the front  roll, and -0.22%  with the rolls coupled.  Where, a positive
deviation  corresponds to an observed dynamometer velocity greater than
the road velocity under the same wheel condition.

     For the bias-belted tires, the rear roll deviated by +1.23% from
the road,  the  front roll deviated by -0.04%, and the coupled rolls
deviated by +0.40%.

     Overall,  the rear roll was in error by +1.15%, the  front roll by
-0.71%, while  the error with the rolls coupled was only  -0.02%.  Therefore,
on  the average  and particularly for radial tires the coupled mode most
closely simulated the road.

     Since coupling the rolls improved the vehicle velocity simulation,
the vehicle fuel economy effect of this  change was investigated.  In the
majority of EPA fuel economy tests, alternate dynamometer adjustments,
obtained by the coastdown  technique, are used.   Also the coastdown
method is  used  in dynamometer calibration, and therefore, would account
for the increased friction  of the  coupling mechanism.  Consequently, a
comparison of  vehicle fuel  economy, obtained with dynamometer adjust-

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                                  -10-

ments, which produced equal coastdown times, was considered the most
appropriate approach to evaluate the fuel economy effect of coupling the
dynamometer rolls.  This comparison could easily be made since, during
the dynamometer portion of this test program, vehicle dynamometer coast-
down times were recorded immediately following the fuel consumption
tests.

     Figure 3 shows the 50 MPH fuel consumption of the vehicle, equip-
ped with radial tires, plotted versus the coastdown time obtained for
both the uncoupled and coupled tests.  This plot indicates that coupling
the dynamometer rolls results in a 2 to 6 percent increase in measured
fuel consumption for the same vehicle-dynamometer coastdown time.  For
example, at a coastdown time of 14.0 sec, the fuel consumption was
approximately 7150 cc/km with the rolls uncoupled and about 7450 cc/km
with the rolls coupled, a difference of approximately 4%.

     The fuel economy results obtained in this test program are all from
steady-state measurements.  However, the results are consistent are pre-
liminary investigations of the effect on transient cycles.  For example,
computer modeling has estimated the transient cycle fuel economy effect
to be about 4%.(2)  Limited empirical data from transient cycle tests
also indicate the effect to be about 4%.(3)

IV.  CONCLUSIONS

     Operating with the rolls coupled most closely simulates the road
experience of a vehicle using radial tires, and therefore, provides the
most accurate method of testing for fuel economy.  The current EPA
method  for simulating the vehicle velocity, using the rear roll speed,
causes  an over prediction of steady-state 50 mph fuel economy by approx-
imately 4%.  This occurs because the velocity error results in both an
underloading of the energy demand from the vehicle and an overcredit of
the distance travelled.

     The same mechanism occurs during transient cycles and in this
instance, inertial forces applied to the vehicle are also inappropri-
ately low because of  the velocity error.  Computer modeling and limited
empirical data indicate the  transient cycle fuel economy errors re-
sulting from this velocity error are also about 4%.  It should be.noted
that  these conclusions are based on data from vehicles equipped with
radial  tires, however this is  the most important case.  It is estimated
that  over 70% of  the vehicles  tested at EPA are equipped with radial
tires.

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Tire
 No.

 1
 2
 3
_4	

Mean
% Deviation
 Road Velocity
 Predicted by
the Front Roll
	(mph)

     50.05
     49.72
     50.18
     50.26

     50.05
     -1.07
     Table 1

  Radial Tires

   Road Velocity
   Predicted by
   the Rear Roll
       (mph)

       51.19
       50.58
       51.43
       51.38

       51.15
       +1.10
 Road Velocity
Predicted with
 Rolls Coupled
	(mph)

     50.45
     50.00
     50.85
     50.61

     50.48
     -0.22
Observed Road
  Velocity
    (mph)

    50.81
    50.10
    50.83
    50.62

    50.59
 ..Predicted - Observed.   ,__
 (	—	-:	) x 100
      Observed
 6
 7
Mean
% Deviation
     50.53
     50.55

     50.54
     -0.04
Bias Belted Tires

       51.16
       51.20

       51.18
       +1.23
     50.82,
     50.70

     50.76
     +0.40
    50.51
    50.60

    50.56
Mean
% Deviation
     50.22
     -0.71
     TOTALS

       51.16
       +1.15
     50.57
     -0.02
Error analysis indicated that on the average, we were 95% confident that
the predicted values were accurate to within +0.23 mph.
                                                                                              50.58

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                                          -12-
                                         Figure 3
                           Coupled vs'Uncoupled Fuel Consumption
                              Plotted Against Coastdown Time
                                    (with radial tires)
                                             Tire 1:       • - uncoupled     Q - coupled
                                             Tire 2:       A - uncoupled     A ~ coupled
                                             Tire 3:       • - uncoupled     O - coupled
                                             Tire 4:       if- uncoupled     fa - coupled
     7800 -'
                                                 coupled
4
 u
 O
 c
 O
•H
 CO
 e
 o
 0)
 3
7200
     6600 - -
              upper limit
              to uncoupled
                lower limit
                to uncoupled
                  13.0
                                      14.0

                              Coastdown Time (sec)
15.0

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                                 -13-
                              References
1.   Richard Burgeson, Myriam Torres,  "Tire Slip on the Clayton Dyna-
     mometer",  EPA Technical Support Report, LDTP 78-02,  March 1978.

2.   John Yurko, "Computer Simulation of Tire Slip on a Clayton Twin
     Roll Dynamometer", EPA Technical Support Report, SDSB 79-10,
     February 1979.

3.   Conversation with Don Paulsell, of the EPA Ann Arbor Laboratory,
     March 1979.

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                                 -14-
                             Appendix  A-l
Tire
 No.

  1
  2
  3
  4
  6
  7
          Tire

       Michelin-X
       Firestone 721
       Firestone 721
       Multimile Supreme
       Uniroyal Fastrak
       Uniroyal Fastrak
Tire
Type
Radial
Radial
Radial
Radial
Bias Belted
Bias Belted
Tire
Size
GR78xl5
GR78xl5
GR78xlA
GR78xl5
G78xl5
G78xl5
                                Vehicle
1976
Mercury Montego
w/ 29,000 accum.  miles

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                                 -15-
                             Appendix A-2
 Type of Data
Being Collected

Drive wheel torques
  (analog voltage output)

Wheel angular velocities
  (frequency output)

Conversion of frequency
  to analog voltage

Collect and digitize
  analog signals for
  output to a recording
  device
     Equipment

Lebow torque sensor
  Model No. - 7510

Disc/Rotaswitch pulse
  Encoders

Anadex frequency to
  voltage converter

Fluke datalogger
  Model 2240B
Record data
Techtran Data Cassette
  Model 8400
Record fuel flow
Fluidyne Flowmeter
  Model 1250T
Tire temperatures
Wahl Heat Spy
  Infared thermometer

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                                 -16-
                              Appendix B

                       OVERVIEW OF TEST SEQUENCE
                        (eg. using tire no. 3)
1.    Tire no. 3 mounted, pressure set to 45 PSI.

2.    Tires broken in with 1 FTP.

3.    Allowed to cool at least 4 hours.

4.    Reset pressure to 45 PSI.

5.    Vehicle rear axle weight approximately 2290 Ib with driver and
     full gas tank.

6.    Set dynamometer inertia to 5000 Ibs.

7.    Set dynamometer horsepower to 11.4 horsepower.

8.    Set fixed data to 350114.

9.    Conduct 1 FTP, then obtain tire temperatures.

10.  Insert  tape in techtran, ready for scan at 1 second intervals
     (Tape labeled: uncoupled 350114, 3501124).

11.  Conduct a 5-minute Steady State at 50 mph, collect data.

12.  Conduct a coastdown, collect 55 to 45 mph time only.

13.  Record  tire temperature during or right after coastdown, reset
     fixed data to 340114.

14.  Conduct a 5-minute Steady State at 40 mph, collect data.

15.  Conduct a coastdown.   (NOTE:  be sure to collect data only during
     the 5-minute Steady State.  All data collection devices should
     be reset before new Steady State speed is set.)  Collect coast-
     down time and tire temperatures.

16   Reset fixed data  to 355114, conduct a Steady State at 55 mph
     for 5 minutes collecting data.  Stop data, conduct a coastdown,
     record  time and tire  temperatures.  Increase speed above 60 mph.

17.  Life vehicle, conduct  a  dynamometer only coastdown, check zero,
     adjust  on torque  meter.  Record  55  to 45 mph time.  Reset horse-
     power to  12.4, fixed  data  to 350124.  Tires should be allowed to
     cool 15 minutes starting from when  the vehicle was lifted.

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                                 -17-
                          Appendix B (cont.)


18.  Conduct a 505 second warm up, record tire temperature.

19.  Repeat 11 and 12.

20.  Reset fixed data to 340124.

21.  Repeat 14 and 15.

22.  Reset fixed data to 355124.

23.  Repeat 16.

24.  Repeat 17.  Reset horsepower to 10.4 after dynamometer coast-
     down, fixed data to 350104,  allow 15 minutes cooling, rewind
     tape and insert new one.  (Tape labeled: Uncoupled, 350104).

25.  Conduct a 505 second warm up, repeat 11 and 12.

26.  Reset fixed data to 340104.

27.  Repeat 14 and 15.

28.  Reset fixed data to 355104.

29.  Repeat 16.

30.  Conduct dynamometer only coastdown, recheck zero drift.  Rewind tape.

31.  Steps 1 through 30 complete a tire for  the uncoupled config-
     urations.  Approximately 3 to 4 hours of testing and 2 cassette
     tapes are required.  If nothing is done to the vehicle but to let
     it set for an hour (say for lunch), you should be able to start at
     step 6 with rolls coupled and fuel tank filled, and conduct steps 6
     through 30 to complete a tire type.

     Steps 1 through 31 will be repeated for each tire set.

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                                -18-
  Test

 350114
 340114
 355114
 350124
 340124
 355124
 350104
 340104
 355104
                            Appendix C-l

                               Tire 3
               9-Point Test Matrix Data on Dynamometer
                        with Rolls Uncoupled
RRV
(mph)
50.116
39.979
55.125
49.955
40.091
55.074
50.068
40.166
54.881
FRV
(mph)
49.170
39.423
53.932
48.556
39.183
53.421
48.857
39.375
53.459
(W +W )
(rev/sec)
21.598
17.239
23.672
21.402
17.198
23.508
21.415
17.181
23.426
(T.-KT-)
(ft.-l§s.)
155.892
120.743
181.191
167.662
125.286
187.087
149.114
112.087
164.744
 351114
 341114
 356114
 351124
 341124
 356124
 351104
 341104
 356104
        With Rolls Coupled

50.031        50.075
40.109        40.130
55.030        55.084
49.870        49.902
39.936        39.948
55.011        55.045
49.990        50.041
40.029        40.040
55.031        55.079
21.710
17.340
23.941
21.618
17.306
23.894
21.678
17.312
23.821
178.241
138.261
206.123
177.924
131.293
202.540
159.231
118.504
183.033
        Regression Coefficients
(Vi = a (WT  + WJ  +  b  (TT
                                              TR)
                                    C)
   Vi
                b x 10
                                               R-SQR
2.3808
2.3639
2.3320
-0.26600
-1.2120
-0.46453
-0.58549
-0.078181
+0.23591
.99934
.99991
.99991
Rear Roll
Front Roll
Coupled Roll

  (WT + W_,) road = 22.03 rev/sec and (T_. + T_ ) road = 162.98 ft.-lb
    Li    K                             K    LJ

  (R-SQR signifies the confidence in the fit of the regression.  For
  example, R-SQR = .99991 means a 99.991% confidence in the fit.)

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                                 -19-
                             Appendix C-2





                   Example Calculation Using Tire  3

               Rear Roll Velocity with the Rolls Coupled





     V     = a (WT + W_) + b (TT + T_) + C
      coup       L    R        L    R


from linear regression with RRV from appendix  C-l  as  the  dependent variable:  :





     a = 2.3320, b = -0.46453 x 10~2, c=0.23591



therefore, applying the coefficients to the road data results:





     V     .    . = 2.3320 (W_ + WD) road + -0.46453 x  10~2 (f_ + f_)  road + 0.23591
      coup/road            L    R                            L     R




     where:



     (WT + W_.) road = 22.03, and (T_, + TT ) road =  162.98
       Li    K                      K    ij




     therefore:



     V     .    ,= 50.85
      coup/road


this compares  to the actual road velocity:





     V    . = 50.83
      road


(These correspond to the results given in Table  1. Section III  of this

report.)

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                               -20-
                           Appendix  C-3

                              Tire  1
                9-Point  Test  Matrix  on Dynamometer
                      with Rolls Uncoupled

Test
150114
140114
155114
150124
140124
155124
150104
140104
155104

151114
141114
156114
151124
141124
156124
151104
141104
156104
RRV
(mph)
50.073
40.002
54.950
50.001
40.019
54.982
49.971
39.946
55.021

50.044
39.983
54.937
50.032
40.058
55.088
49.927
40.035
54.945
FRV
(mph)
49.995
39.340
53.651
48.694
39.163
53.488
48.865
39.218
53.681
with Rolls Coupled
50.100
40.006
55.042
50.071
40.066
55.125
49.963
40.042
54.998
(B + 5>
(Li / K. \
rev / sec)
20.902
16.690
22.893
20.800
16.643
22.848
20.782
16.618
22.849

21.164
16.828
23.239
21.139
16.861
23.278
21.068
16.829
23.175
Regression Coefficients
Vi
Rear Roll
Front Roll
Coupled Roll
a
2.4586
2.3336
2.3689
b x 102
-0.48606
-0.10248
-0.29440
c
-0.37559
-0.56480
0.50768
                                                          (ft.  -  Ibs.)

                                                            165.847
                                                            127.049
                                                            188.137
                                                            167.585
                                                            122,969
                                                            187.133
                                                            146.920
                                                            111.007
                                                            168.222
                                                            181.263
                                                            150.630
                                                            205.630
                                                            175.900
                                                            128.142
                                                            210.694
                                                            158.839
                                                            114.663
                                                            180.070
                                                              R-SQR

                                                             .99988
                                                             .99750
                                                             .99996
      (WT  + VL)  road = 21.27, and (TT  + Tj  road = (150.616)
             K
                                         K
(R-SQR signifies the confidence in fit of the data by the regression)

-------
                               -21-
                           Appendlx C-4

                              Tire 4
                9- Point Test Matrix on Dynamometer
                       with Rolls Uncoupled
 Test

450114
440114
455114
450124
440124
455124
450104
440104
455104
451114
441114
456114
451124
441124
456124
451104
441104
456104
  Vi

Rear roll
Front roll
Coupled roll
RRV
(mph)
49.960
39.968
55.013
49.990
40.007
55.120
49.956
39.952
55.054

49.697
40.636
54.887
49.929
40.589
54.918
49.983
40.074
55.295

a
2.3939
2.3838
2.3781
FRV (WL + WR)
(mph) (rev / sec)
48.951
39.374
53.765
48.780
39.238
53.680
48.907
39.287
53.873
with Rolls Coupled
49.847
40.733
55.113
50.084
40.688
55.084
50.126
40.175
55.484
Regression Coefficients
b x 102
0.12847
-0.78016
-0.64562
20.864
16.623
22.849
20.786
16.591
22.849
20.754
16.575
22.856

20.999
17.021
23.223
21.154
17.048
23.268
21.086
16.810
23.359

c
0.071297
0.57721
0.84438
 (T  + T )
(ftV - 1&0

  152.446
  115.488
  176.968
  156.114
  114.620
  178.410
  142.134
  107.053
  165.278
  160.798
  119.410
  189.825
  173.993
  125.797
  200.720
  151.774
  109.630
  175.490
    R-SQR

   .99973
   .99977
   .99992
        (WT + WD) road = 21.35 and  (TT + Tj road =  155.603
          L    K                     L    K

-------
                               -22-
  Vi
                           Appendix C-5

                              Tire 2
             9- Point Test Matrix Data on Dynamometer
                       with Rolls Uncoupled


Test
250114
240114
255114
250124
240124
255124
250104
240104
255104
RRV

(mph)
49.880
39.949
54.976
49.921
40.014
55.061
49.945
39.887
55.121
FRV

(mph)
48.803
39.251
53.764
49.108
39.561
54.018
49.237
39.492
54.222
(WT + W_)
L R
(rev / sec)
20.916
16.773
22.994
20.980
16.863
.23.037
21.036
16.820
23.209
(T_ + T_)
L R
(ft. - Ibs)
159.274
123.905
182.863
165.863
123.553
189.958
147.109
108.334
165.357
                        with Rolls Coupled
251114
241114
256114
251124
241124
256124
251104
241104
256104
50.197
40.167
55.121
50. 009
39.980
54.958
49.925
40.111
55.061
50.340
40.251
55.290
50.132
40.056
55.139
50.061
40.194
55.218
21.404
17.071
23.511
21.347
16.993
23.455
21.243
17.025
23.437
174.465
130.972
198.727
172.235
124.866
197.955
161.941
123.351
186.192
Rear roll
Front roll
Coupled roll
       Regression Coefficients
                    2
  a           b x 10             c             R-SQR

2.3000         1.1332         -0.085243       .99987
2.3081         0.17002         0.40039       .99984
2.4186        -0.91726         0.045152       .99996

-------
                               -23-
                           Appendix C-6

                              Tire 7
              9-Point Test Matrix Data on Dynamometer
                       with Rolls Uncoupled

Test
750114
740114
755114
750124
740124
755124
750104
740104
755104
RRV
(mph)
49.996
39.878
55.081
50.054
39.947
54.917
50.108
40.084
55.158
FRV
(mph)
49.435
39.562
54.341
49.396
39.576
54.065
49.549
39.773
54.473
(WL + WR)
(rev / sec)
21.102
16.891
23.189
21.114
16.915
23.090
21.136
16.994
23.312
(TT + T_)
(ftV - l§s)
154.821
114.676
178.088
156.746
112.423
177.521
142.726
106.785
165.109
                        with Rolls Coupled
751114
741114
756114
751124
741124
756124
751104
741104
756104
50.123
39.894
55.142
50.028
40.034
54.957
49.947
40.041
54.966
50.281
39.994
55.391
50.168
40.117
55.104
50.100
40.131
55.129
21.368
17.040
23.513
21.333
17.101
23.415
21.289
17.102
23.372
166.150
121.278
191.962
167.352
118.877
191.912
157.123
113.344
177.934
  Vi
Rear roll
Front roll
Coupled roll
Regression Coefficients

        b x 102
R-SOR
2.3246
2.3209
2.4311
0.84300
0.20201
-0.59811
-0.32574
0.12043
-0.83437
.99992
.99994
.99998
           (WT  + WD) road
             L    R
      21.59 and (T_ + T ) road = 159.165
                  R    L

-------
                                        -24-
                                   Appendix C-7

                                      Tire 6
                     9-Point Test  Matrix Data on Dynamometer
                              with Rolls Uncoupled

Test
650114
640114
655114
650124
640124
655124
650104
640104
655104
RRV
(mph)
50.078
40.077
54.923
50.029
40.036
55.033
50.133
39.972
54.979
FRV
(mph)
49.485
39.786
54.293 .
49.440
39.712
54.272
49.597
39.665
54.303
cwL + v
(rev / sec)
20.599
1.6.552
22:551
20.537
16.527
22.574
20.624
16.483
22.519

-------