-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:

ei 2
aero = 2 Cp AV (17)
where
F ero = the aerodynamic drag force
i = the air density
cy = the drag coefficient of the vehicle
Vv = 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


, TABLE 1
AMAIENT COFRECTED ACCELERATION CUEFFICTENTS

ID wT “AO al a2
(LB) (M/SEC#H2) (1/SEC) (17a

71021 4110 061364E400 0.397RE-02 0.41166 -02
7001." 6050 001199E+00 0.8064E-02 0.12n8F-03
7101" 4500 OollI7TE+00 -0.5550E-02 9.9136E-03
$902. 4270 0e1464E+00 067684E-02 9.2577E-03
8206 2750. ‘Oek210E+00 =0266234F-02 9.35166 =-03
5902 “4330 067434E=01 061432E-01 9.171 28-03
7001 4930. 961879E+00 0.3511E-02 0,3653£-03
7502 4540 061444E+00 0.2891E-02 0.44566 -03
7402 S540 061803E+00 OolS76ES02 0.3774F-03
7001 ‘5530 0e2035E+U0 =003568E-03

7001 ‘4620 0e1919E+00 © 0.7623E-02

7901 $690 Well09E400 O.100GE=02 0, 40445 -03
7001 5500 921833E+U0 062363E-07 0.3264 R05
7301 4560 Oe1225E*%00 De2950E$02 0.4304r-04
7402 5760 9e1425E+00 026534 -02 ?

7201 $110 O.7TOOLE-01 Oe75O1E-07 -9,22796-93
7701 4990 DelLOISE4+00 Oe4450E R07 ALA54e]b R03
$902 5020 NeASTSE*GO OelLH7IFH02 OH eeauHk-n3
8002 4370 966343E-01 O6866RR-02 9.9015F-03
7201 5480 OelN9IE+00 Oe l4n3F -02

7301 S050 N,8B896E-01 0.711 3k -02

8002 $530 MoLLOLEF00 Geel ?t-ur

8206 4050 061339E+00 0.30066 -02

8507 3900 elS40E400 Oe574]F <2

8002 6320 DB74GE@01 0-547] £9? 250% -03
7301 6420 Del27T6E+O0 Ne2O5HF-07 .507THE-03
7502 5500 Ne1580E+00 06409KF-02 0.2754 -43
7901 7900 DeB29TE<“U1 06481KF 02 9, 16465E-08
7502 6240 Me111GE+00 = 06A449F m2 061471603
7001 8190 OeLLBBE+00 O65222F-02 0.1503 -03
8306 3490 Mel40B8E+00 O065705E-02 1.2O64E H03
8507 3370 VelSTGEF00 0.556% =02 2 244E=03
9003 3970 Oe1493E+00 063367802 0.4221b-03
9003 4380 O.8530E“U) Uel036F-01 9.1798E=03
9003 4810 061482E4+00 -0.5306F=03 9.591406 -03
7701 5620 VeB7OGEH0) 064485 =02 1.3135E-03
7201 6060 DeORTSE01 Web2H7F HDA O.1920E-03
7101 5020 Ve967TBEH01 De 7AYHE R02 0.20476 -63
7901 7040 0e1083E+00 UeeS64b-u2 1.2221F-03
8002 5010 el226E+00 065966E-04 9.494666-03
7701 5980 9.9093E-01 9.43926E-02 0,2649F-03
7502 $020 061120E+00 0.8399F=02 9.2351E+03
8206 3550 O61387E+00 v.37T39E-02 0.3146E=03
7201 4540 0-6536E-01 0.8017E-02 1.2499E=03
7301 4060 0.8686E-01 066B57E-02 1.3856B03
7101 4500 Oe7461E=01 0.49943F=-02 0.2024E03
7402 $110 Oe1519E+00 0.3603E=02: 0.3729E%03
Tone 5030 0-6956E-01 9.9136F-02 .1548E=03
7191 5330 0-1080E+00 0-6403)E-02 9.3279F=03
7901 6060 0-6192E=01 O.A517E-02 9.1909F<03
7001 6490 Ne1264E+00 066162E-02 0.1420E-03
8306 4140 Oe1251E+00 0.64669F=-02 1.2295E-03
8306 2700 )69182E-61 0.1190E-01 . 9.1881E=93

6507 2560 0-1643E+00 0285653-02 0.26376 +93


-35-
References

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.

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.

G. D. Thompson, EPA Report, unpublished.

J. D. Walter and F. S. Conant, "Energy Losses in Tires." Tire
Science and Technology, TSTCA, Vol. 2, No. 4, November 1974.

S. Clark, University of Michigan, unpublished discussions.

W. B. Crum, "Road and Dynamometer Tire Power Dissipation."

of Automotive Engineers, 750955.

S. K. Clark, "Rolling Resistance Forces in Pneumatic Tires."

Society

University of Michigan Report DOT-TSC-76-1, prepared.for Department
of Transportation, Transportation Systems Center, Cambridge, Mass.,
January 1976. .

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.

A. J. Scibor-Rylski, "Road Vehicle Aerodynamics," John Wiley and
Sons, New York, 1975.


ID.

7101
7101
7102
7102
7201
7201
7201
7201
7Ss02
7502
7502
7502
7602
7602
7602
6002
8002
ROO?
600d
8206
8206
A306
8306
8306
B507
8507
8507
9003
9003
9903
9902
5902
$902
7001
7001
7001
7001
7001
7001
7301
7301
7301
7301
7402
7402
7402
7701
7701
7701
7701
7901
7901
7901
7901

TABLE

3

ORIVE TRAIN
REGRESSION COEFFICIENTS

eww www en eee ewe we we wesw eeewee ances

wT
(LB)

4110.
4500

5020
$330
5480
4540
5110
6060
4540
so20
5500
6240
5040
4430
5530
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4Al0
4310
5020
5500
4620
4930
5530
6050
6490
8190
4060
4560
soso
6420
5110
5540
5760
4500
4990
5620
5980
5690
6060
7040
7900

A

(NT)
40.398
40.398
40.398
40.398
31.388
31.388
31.3868
31.2388
37.645
37.645
37.645
372645
30.568
30.568
30.56%

8.940

Be940

8.946

8.940
24.862
24.862
242200
24.200
24.200
220598
226598
226594K
13.394
134394
13.394
40.369
40.369
40.369
51.66
51.666
51.664
51.668
51.668
51.668
18.756
18.758
18.756
18.758
21.946
21.946
212946
40.374
40.374
40.374
40.374
332293
33.293
33.2293
33.293

4
(KG/SEC)

1.668
1.668
1.568
1.668
1.940
1.940
1.940
1.940
2.586
2.586
2.586
20586
1.555
1.555
1.555
30131
$0131
3131
3013)
1.956
1295
22273
20°73
de2dl3
60937
ae



-12-

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 1b, and a resolution of + 0.5 1b.

Vv. 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


1D

s9n2
7001
719)
7201
7301
7402
702
7602
7701
7901
anne
8206
8306
8507
9093

TABLE 4

MEAN VALUES OF THE

SMALL TWIN ROLL DYNAMOMETER
POWER ABSORBER SETTINGS AT 59 MPH

Era INERTIA
wTe CLASS
(LA)

4500
5000
4500
4500
4000
5000
4500
4500
4500
6000
4so0
3000
3000
2500
4000

FRONTAL AREA

(FT##2)

3164(F)
32.0(GM)
31.6(GM)
3166 (GM)
37.0 (GM)
31.4(F)
33.6(F)
31.4(F)
3760(GM)
3720 (GM)
3767(F)
2162(EPA)
2162(FPA)
2162(EPA)
35.1 (EPA)

MEAN POWER
50 MPH
(HORSEPOWER)

20.051
22.802
17.843
18.472
19.625
21.773
21.794
172654
19.504
18.361
18.534
126457
12.4246
13.757
17.954


1d

5902
5902
5902
7001
7001
7001
7001
7001
7002
7101
7101
7101
7101
7201
7201
7201
7201
7301
730)
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
(La)
4330
5020
$500
4620
4930
5530
6050
6490
8190
4110
4500
5020
5330
4540
$110
5480
6060
4060
4560
5050
6420
5110
5540
5760
4540
5020
5500
6240
4430
5030
S540
4500
4990
5620
5980
$690
6060
7040
7900
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4810

FO
(NT)
~004729F +02
0.1486 +03
0.2598E +02
0.22136+03
0623156 +03
043008E +03
041199E403
0.12776 403
0413706403
06 747SE +02
=0.4635E+02
0.8966E +01
0.3670F +02
0-4870F +00
0.9682E4N1
069895E +02
~0 69466401
062128E+n2
0.9R02E +02
0.28106 +02
061282F +03
0+1394F+03
0+2290E+03
061 382E +03
0.1590£+03
0.75626 +02
022069E +03
063731E+02
=0,9236E +02
=0.4137E+02
~0..2499F +02
046118E+02
0.S631E+02
0.3708E +02
0.5046F +02
068686E +02
=0 0 3439F +02
021050E+03
-063242F 400
=0.3540E +02
0.10326 +03
0.1079E+03
0e3664E+02
0-4360E +02
0.9085E+02
~O.1151E+02
0.6163F +02
0.5363E +02
0672436 +02
061090£+03
0.1058E+03
0.8968E +02
-0.3542E +02
0.10486 +03

TARLF 2
TWIN SMALL ROLL DYNAMOMETER

Fl

0.255RE +02
-0.1990E+00
61461E +02
0414676402
0.595SE401
-0.3290F +01
061961 E402
0.1550 +02
0.1643E +02
0.5693E+01
061 853E+02
0.1527E +02
0.7568E+01
061434E +02
0.1521E+02
0.1A59E+01
0615456 +02
0.1114E+02
0.42926 401
0614526402
0-3050E+01
052126401
062340E+00
061 386E +02
0,.3484E401
0.1699E +02
066598E+01
062224 +02
0.25136+02
0.1937E+02
041935E+02
-0.1396E +02
0.7926E +01
0.88426 +01
0.7917E+01
0.25806 +00
0.15776 +02
0-SS06E+01
061479E+02
0.1481E+02
-0.4191E 401
0.2047E+01
0611296 +02
O.S71IE+O1
063330E+01
0.1278€+02
0.6853€+01
0.64366 +01
0.8615E+01
0.8422E+01
0.8541E+0)
0.4847E+01
0.1974E +02
-0.2987E +01

Fe

0.3495F +00
9-1036E+01
0. S87RE +00)
0.44596 +00
O-6560F+00
GellOLF +0)
0030736 +00
0.4333F+00
OeS747E+00
0-7936F +00
0e4260E +00
9.47936 +06
OeB141F +09
0.5397E +00
GeSSI4E+00
0 .9955F +09
065473F +00
06 7422F 400
0.9434F +00
0.6075E+00
069219F +00
068931F +00

“0e977HF 400

066139E+00
0.9585F+00
0.5567F +00
O47128F +00
0e4298E+00
0.23936 +00
0.3649F +00
0-3916E +00
0.1932F+01
0.8276E +00
0 «622B8E +00
0.7382E +00
0.10846 +01
0.5439F+00
0.731SE+00
O66061F +00
06179F +06
O.LIS7TE+01
0.9441F+00
0-7361E +00
0e4573E +00
065326F+00
0.2390E+00
0043465400
0.4419E+00
0.3209F +00
0.3556E+00
0.3606EF +00
0.7478E+00
0.3691E+00
0-1156F +01

N-6991E+03
1661 6E +03
0 66462E+03
9.7718E+03
067921E +03
Ne 77T2E+03
967416E+03
0.6906E+03
9.7914E4+03
0 .S59R4E +03
9 SK06E +03
0 .58938E+03
0.6125F+03
0-5906E+03
0.6251E+03
9.6378E+03
966118E+03
906410E+03
9 e6652E+03
0.6561E+03
0-6569E+03
06 7021E+93
0-7226E+03
Oe 7TS47E+03
0.7155E+03
9.7335E+03
0e7105E+03
06 7491E+03
0.5900E+03
9.5739F +03
0e6031E +03
9e7142E+03
0 -64F9E+03
0.6457E+03
0.95962F +03
0e46341E+03
0-5899E+03
9.5935E+03
9 h329E +03
9.6042E +03
0.5875E+03
0 e6252E+03
066567E+03
%s3999E+03
0 24313E+03
0.3934E+63
964319E+03
0 .41R82E+03
024253E+03
0.47496 +93
0e4769E4+03
0¢SG15E+03
0.S90LE+03
9.6155E+03

16.337
19.212
19-937
19.664
19.689
21.042
21.657
22-620
216444
21.985
216294
222453
17.684
17.200
18.077
212407
196368
19.353
17.868
19.005
172679
172788
18.971
18.108
17.608
18.739
19.683
11.987
12.928
11.792
126944
12.535
12.746
14.233
14.292
17.729
17.685
15.449


APPENDIX €
VEHICLE ROAD LOAD
AND
DYNAMOMETER ADJUSTMENT TO SIMULATE VEHICLE ROAD LOAD


-22-

TWIN ROLL DYNAMOMETER ADJUSTMENT POWER AT 59 MPH
VERSUS
TOTAL VEHICLE TEST MASS

30.000 +

+
24.000 + +

a tht
+ * ae
+ eo ee +
* 2 oe
* oe Bee *
18.000 + ee 200 42 ae #2. *
. * e
~ POWER . + oo
CHORSEPOWER) * ®
s w 2

12.000 + 2

+
6.0000 +

+
Oe +

Se ee ee ee coe ee a ce oe cane’
1000.0 e000 BOG ea
1590.0 adel) eO0n.G

TOTAL VEHICLE TEST MASS (KG)

Figure 5


TABLE 2
TIRE PRESSURES

REFORE AFTER
mn wT FRONT’ REAR LEFT &TGRT FFT RIGKT
FRONT FRONT , REAR REAR
(Li) (PST) (PST) (PSL) (PST) (PST) (PST) -
$902 4330 30.9 300 34.5 3404 34.7 34.5
5902 4270 36.0 40.0 36.5 B90 4262 4202
5902 5020 36.0 40.0 40.5 4005 44.3 45.0
7001 4620 35.0 60.0 34.5 3428 44.5 65.0
7001 4930 35.9 60.0 3865 Bee = 45400 6505
7001. $530 35.0 60.0 39.0 39.0 F200 6565
7001 5500 35.0 60.0 39.5 34926 9600 6600
7001 6050 35.0 60.0 380K 3467 4567 6504
7001 6490 35.0 60.0 3945 40.0 67.5 6605
7001 8190 35-0 60.0 4.0 3905 7005 6905
7101 4110 32.0 32.0 34.8 34.0 4520 3465
7101 4500 32.0 32.0 35.0 35.0 3520 35.0
7101-5020 - 32.0 32.0 39,5 35.5 35.0 35.0
7101 5330 3220 32.0 34.8 35-0 . 3520 3502
7201 4540 — 28.0 32.0 30.8 3920 24.5 3465
7201 5110 28.0 32.0 31.0 39.5 35.0 34.5
7201 5480 28,0 32.0 30.5 3065 35.0 34.5
7201 6060 28.0 R20 29.3 2490 33.9
7301 4060 30.9 32.0 32.5 32.5 34.5
7301 4560 30.0 32.0 32.5 33649 34.5
7301 $050 30.9 32.0 32.0 37.9 9 3425
7301 6420 30.0 32.0 32.5 Bee 3H00
7402 5110 32.0 32.0 37.5 3765 3He5S
7402 5540 32.0 32.0 37.0 are 47.0
7402 5760 32.0 32.0 37.0 37.0 3765
7502 4540 35.0 45.0 3965 a4 GHeD
7502 5020 35.0 45.0 34.0 3oe5 4765
7502 5500 35.0 45.0 34.0 390? Gel
7502 6240 35.0 45.0 39.5 40.0 51.0
7602 5030 36.0 40.0 40.2 4Ueu 450
7701 4500 32.9 32.0 35.5 3409 3520
7701 4990 32.0 32.0 3500 3405 35.0
7701 S620 32.9 32.0 33.5 R362? 33.2
7701 5980 32.0) 32.0 36.0 3509 36.0
7901 5690 4500 60.0 49.0 4964 4305
7901 6060 45.0 60.0 49.0 45 F405
7901 7040 45.0 60.0 S1.0 49.0 47.0
- 7901 7900 45.0 60.0 49.5 4A 65.5
8002 4370 32.0 40.0 3360 A403 4200
8002 5010 32.0 4020 35.0 34a. 4365
8002 5530 32.0 40.0 3665 Riraiy 45.0
8002 6320 32.0 40.0 37.0 37.69 4565
8206 2750 20.0 70.0 22.5 eee 2320 2
8206 3550 20.0 20.0 22.5 P20 2320 2165
8206 4050 20.0 3020 23.0 ? 34.0 3300.
8306 2700 20.0 20.0 23.0 2225 220d
8306 3490 20-0 20.0 22.0 2363 22.5
8306 4140 20.0 32.0 24.5 24ei) 36.5 3600
8507 2560 21.0 26.0 24.5 ?4.0 = 2860 2723
8507 3370 21.0 42.0 24.0 24.0 44.5 43.7
8507 3900. 21.0 42.0 25.0 25.5 4720 47.2
9003 3970 30.0 30.0 32.0 32.5 32.5.
9003 4380 30.0 30.0 33.5 33.5 (3365

9003 4810 32.0 3260 35.0 35.0 | 38.0


~3-

F= (m+ 1,07 )A (2)
i
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 Io (3)

Equation (2) now has the familiar form
F = MA (4)

The 2 I a? term is identified as the "equivalent effective mass" of the
rotating cOmponents and may be designated by:

- 2
Meg = EI, (5)

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’.

Cc. Mass

The required masses are the gravitational mass and the equivalent
effective mass of the rotating components. Equation (5) indicates that


-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 vehiclés 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, théoretical 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 drea is recommended. The possible improvements in accuracy of


30.000

24.000

18.000

POWER
(HORSEPOWER)

12.000

Ae0000

-19-

TWIN ROLL DYNAMOMETER ADJUSTMENT POWER AT 50 MPH

NFM

VERSUS

VEHICLE FRONTAL AREA

#2
oe

NNW SN
_*

3e
St
32

Se ee ee eee Sones

20.000

enev0i
24.000

32.000

FRONTAL AREA (SQUARE FT)

Figure 4

30.090

4000


-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:

1/3

Louw (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 tno the
two-thirds power.

www 7/3 ; _@y

The previous arguments are hardly rigorous, therefore a model of
the form: ‘

Hy = aw* (22)
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.

Inf. =inawe ~ :

P x
= 1lna + 1nW (23)

lina + xlnW


-21-
The two prediction equations are:

yy = 633 A for pick up trucks
4, =,511A for vans

(18)

where
A = 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


-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.


-16-

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.

F, =f

TOT tire + fnech + f aero (15)

where

Foor = the total vehicle road load force

feire = the sum of the tire rolling resistances

£

the mechanical dissipative losses
mech

f oero = the aerodynamic drag
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 dissipdte 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.


-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.

69 T
a SPEED vs TIME
50 om VEHICLE ID: 7791
an | TEST WEIGHT! 51901b
we
‘
4ot "a,
SPEEO wn
Cmphd oe,
30.7 om
2g
i+
4 sy yy ly
fl 2g 40 6h $0 100
TINE (sec?
Figure 1

3) 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


-31-

OIFFERENCES BETWEEN LARGE SINGLE ROLL DYNAMOMETER ADJUSTMENT

520000

40060

3.0000

POwEH

(AURSEPOWER) —

200000

1.0000

0.

VERSES
VEHICLE TEST MASS

1600.0 2AM.

VEHICLE TEST MASS (KG)

Figure 9

AND SMALL TWIN ROLL DYNAMOMETER ADJUSTMENT AT SO MPH

*

e
* *
2 + e
a ? Pe oe
* ee aoe
oe | oe
eo aoe *
ee
# we *
* + ? ee
*
* *
s
beeen Hoenn tec tenn teen ten nn terme tome n teen tennant
220060 340009

4000.0


-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


=5-

where
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 (et, - ty)

Teq® = —t
vof 1 d(v/R)
2 FR
(10)
_ At
Req fo ay
Vo F

where

TMReq = 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

= the initial simulated vehicle speed

Vy = 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:

2
r= 2L- ot? qa)
amb PP


-4-

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:

dw

tela (6)

where:
the rotational inertia

the. torque necessary to motor the system
the angular velocity of the system

a
oun

Assuming that the torque is a function of velocity, the variables of
equation (6) may be separated and the integrals formed:

1a] 1 dw :
J dt =1 of ae (7)

where:

the initial angular velocity
the final angular velocity
the initial time

the final time

ee

NENE

me

Integrating the left hand side and solving for I yields:

(t, - ty)
r-—t 2 (8)

1 dw

wf >

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
w= v/R (9)


-17-

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
torque or power consumption measurements, has been shown theoretically
to be given by:

FL = Fy/ (16)

R r
v zt
1+e

where

FR = the rolling resistance of the tire on a flat road surface

Fy =the rolling resistance of the tire on a cylindkical
dynamometer surface

ry = 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 spigdle 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, Yl+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


-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


-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 thé 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 an equation, the assumption is: .

wvv (19)


Technical Support Report for Regulatory Action

Light Duty Truck Road Load Determination

by

Glenn D. Thompson

September 1976

Notice

Technical support reports for regulatory action do not necessarily
represent the final EPA decision on regulatory issues. They are inten-
ded to present a technical analysis of an issue and recommendations
resulting from the assumptions and constraints of that analysis. Agency
policy constraints or data received subsequent to the date of release
of this report may alter the recommendations reached. Readers are
cautioned to seek the latest analysis from EPA before using the infor-
mation contained herein.

Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Source Air Pollution Control
Office of Air and Waste Management
U.S. Environmental Protection Agency


TABLE 5
TIRE PRESSURES

REF ORF. AFTED
10 wT FRONT = PEAR LERT RIGHT LEFT: RIGHT
FRONT FRONT | PEAR: FEAR
(LB) (PST) (PST) (PST) (PST) (PSI) (PST)
5902 4330 36.0 +4020 42.2 42.0 4609 470
5902 5020 40.0" 43.4 4305 4703) GAG)
5902 5500 36.0 4000 42.0 42.0 4763: 45.0
7001 4620 35.0 6060 - 4065 4005 54S
7001 4930. 35.0 * 60.0 4262 42.0 (6500. 6408
7001 5530 35.0 (60.0 42.5 42.5 65.5. 45.0
7001 6050 35.0 60.0 42.8 42.4 70.60 49.5
70016490 35.0 -60.0 4200 4168 =6900° 6765
7001 8190 35.0 - 6060 4205 4340 © 75.0) 7365
7101 4110 32.0  ° 32.0 3764 37260 35.0 3464
71014500 © 32.0 32.0 37.0 37.4: 34.5: 34.5
7101 5020 32.0 | 3260 3764 3700 3500. 3504
7101 5330 32.0- 3260 37.0 3720 37.0
7201 4540 28.0 32.0 33.7
7201 5110 28.9 32.0 33,8 34.0: 34.4
7201 5480 28.0 © 3260 32.6 34.0 3.0)
7201 6060 28.9 32.0 32.0 Wed Bed
7301 460 30.0 3240 3700. 3A el)
7301 4560 ~ 30.0 32.0 34.0 34,0 47.5 360d
7301 5050 32.0 37.0 RTD
7301 6420 30.0 3260 35.0 35.0 34.0. 2.0
7402 5110 32.0 : 3960-3765
7402 $540 32.0 32.0 42.0 41.0
7402 5760 32.0 41.5 41.0
7502 4540 35.0 45.0 43.0 Z 4B eG GHG
7502 5020 35.0 45.0 42.6 49.6 4906
7502 5500 35.0 45.0 41.6
7502 6240 35.0 45.0 41.6 50.0, 50.4
7602 4430 36.0 4060 41.8 4700' 4606
7602 5030 36.0 40.0 42.0 47
7602 5540 36.0 40.0 43.6 470°
7701 4500 32.0 3260 38.0 Wwe0
7701 4990 32.0 3260 38.0 3665
7701 5620 32.0 32.0 39.0 3H.0
7701 5980 32.0 3260 39.8 3768
7901 5690 45.0 6000 52.0 4965
7901 6060 45.0 6060 52.0 70.5
7901 7040 45.0 60.0 54.0 72.2
7901' 7900. 45.0 60.0 $2.0 7208
8002 4370 32.0 40.0 33.5 43.2
8002 5010 32.0 40.0 36.5 4362 4320
8002.5530 32.0 4060 37.4 4402 4406
8002 6320 32.0 40.0 36.5 45.0 4546
8206 2750 20.0 20.0 21.8 22.0 22.8
8206 4050 20.0 30.0 24.8 3502 3462
8306 2700 20.0 20.0 24.2 2504 = 5a
8304 3490 20-9 2000 + 24.2 28.8
8306 4140 20.0 32.0 24.2 3902
8507 2560 21.0 26.0 26.0 28.6
8507 3370 21.0 42.0 28.4 50.5
8507 3900 21.0 4260 2864 5302
9003 3970 30.0 30.0 35.5 3660
9003 4380 30.0 30.0 36.0 35.0

9003 4810 32.0 32.0 37.5 34.0 38.5


-10-

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.

REAR AXEL FORCE MEASUREMENTS
VEHICLE ID: 7701
TEST WEIGHT: 51991b

FORCECNT)

350.000 ¢-. + + eemnt: oe
' : : :

2 = VEWICLE FULL WEIGHT !

poosoon B= TIRE SISSTIFATIVE ’
4 = WEHTC H

(250.000 «-- !
1

at

:

200.000

150.000

100.000

50,000

1
4
1
1
1
1
1

0.0 5.000 10,000 15.000 20,000 25.000 40-000
‘SPEED inssecy

Figure 2 (a)


-9-

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 H,0/gm dry air. These slowly varying
ambient parameters were recorded, by an observer, on a data sheet associated
with each vehicle.

Be 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 1b. load cell of the dynamometer was replaced with a
more sensitive 0-300 lb 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


TABLE 1

ORIVE TRAIN * REAR TIKE
REGRESSTON COEFFICIENTS

(NT)
125-089
142.537
163.134
176.577
147.625

94.002
120.294
170.826
126.443
149.018
170.187
2120167
132.137
115.029
156.920

79.075
1042432

83.967
121.000

81.356
1352113

85.214
128.722
152.310
100.22¢
113.064
143.116

964395
110.992
122.549
105.970
1350467
163.721
127.895
139.843
160.010
146.015
1722954
251.360

83.631

95.226
114.625
195.448
157.907
1632957
172.719
109.004
106.903
116.962
130.141
121.809
133.59)
160.318
200.388

8
(KG/SEC)
16907
20218
2.473
2.081
1.704
20297
20601
22007
203814
2.951
32685
20824
1.656
1.510
1.471
3-480
3.995
4.311
4.973
22150
22290
20253
20343
2-400
20213
20145
20404
2.009
16914
2.225
2.939
2092?
22760
1.958
1.841
1.823
20995
3e111
3-301
16685
12584
12665
20476
34445
36215
3.372
1.846
20312
2.690
2.818
2.681
2.955.
2.992
2.728


-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


APPENDIX D

MASSES


~29-

Mean Twin Roll Dynamometer Power Absorber Setting at 50 mph
versus

Frontal Area

30
20 F
Regression
Lines
Power . 1
(horsepower) Hp = .633A ee
Hp = .511A 2
10 o= Vans
o = Pick Up Trucks
0 +

10 20 30 40 50

Frontal Area (Square Ft)

Figure 8


where

g = the graviational constant, 9.80 m/sec”

& = 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 lbs GVW to 8000 lbs
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.


~20-

34 ee? 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: 4H, =a Aou +b Avan
Ay = the dynamometer power absorber setting (Horsepower)
ou = the frontal area of the pick up trucks (et?)
Avan = the frontal area of the vans (£t”)

a = .633 hp/et?
b= «511 hp/tt?
sample size 54
multiple correlation coefficient .856 R” = ,733

standard error of the regression 1.59


TABLE 1

1D VEHICLE TYPE "EPA INERTIA “FRONTAL AREA
WT. CLASS
(Lis) (FT##2)
5902 FORD F-10900 4500 31.4(F)
7001 CHEV CHEYENNE 20 5000 32.0(GM)
7101 CHEV SCOTTSDALE 10 4500 31.6 (GM)
7201 CHEV CHEYENNE 10 4500 3166(GM)
7301 CHEV G-2U VAN 4000 37.20(GM)
7402 FORD F=100 4x4 5000 Ble4(F)
7502 FORD F-250 4500 33.6(F)
7602 FORD F-100 R XLT 4500 3164(F)
7701 CHEV G-10 VAN 4500 37.0(GM)
7901 CHEV G=30 VAN 6000 37.0(GM)
8002 FORD £-150 VAN 4500 3707(F)
8206 TOYOTA HILUX SR=5 3000 2162(EPA)
8306 TOYOTA HILUX 2 3000 21-2(EPA)
8507 DATSUN 2500 21.2(EPA)

9003 DODGE TRADESMAN 100 VAN 4000 35e1 (EPA)


APPENDIX 8

TRACK MEASUREMENTS


10

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
B206
8206
8306
8306
8306°
8507
8507
8507
9003
9003
9003

WT
(LB)
4330
5020
5500
4620
4930
5530
6050
6490
8190
4110
4500
5020
5330
4540
5110
5480
6060
4060
4560
$050
6420
5110
$540
S760
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

FO
(NT)
0.45R83E+02
0e2355E+03
Del L74E+03
062947E+03
0+3006F +03
063725E +03
001959E+03
1e2066E+03
9.2029E+03
061379E+03
0-1456F +02
0063246F +02
0.9162E +02
0.4720F+02
06491 0E+02
001347F+03
Oe2517E+N2
0eR357E+02
061 684E+03
0-9657E+02
OolB71LE+03
02058F +03
0230326403
Ne2107E+03
0-1841E+03
021163E+03
062385E +03
001134£+03
-0-2007E+02
063186E+02
0e5238E+N2
061271E+03
021304E+03
061113403
061233£+03
001755E+03
0.4281E+02
001964E+03
921054E+03
0e5093E+02
021830F+03
0-1997E+03
061357E+03
06 7614E+02
0011846 +03
0e3149E+02
0.1008E+03
0 eB8849E 402
0.9967E+02
061364E+03
0-13K81E+03
001R23E+03
Ne6411E +02
02107F +03

TABLE 3
SINGLE LARGE ROLL DYNAMOMETER

Fl

0.26306 +02
061504E+01
O1681E+02
061483E+N2
0.6386E6+01
-0.2756E +01
0-2000E+02
061570E+02
0.1667E+02
0.5763F+01
O.1872E+02
061555E +02
0.8049E+01
0.1502E+02
0-1555E+02
062133E+01
0-1591E+02
OoLIS1E+02
0e4764E +01
001522E+02
0-3722E+01
OeS1LB4E +0)
0.6090E+00
061421E+02
0.3401E+01
0-1694E+02
0-6915E+01
062187E+02
062592E +02
061988E+02
0-2026E+02
-021358E +02
0.8088E+01
0-9080E+01
068122E+01
0-2400E-01
0.1562 +02
0-5454E +01
0-1503E+02
0+1428E+02
-0.3855E+01

062419E +01 -

0611096402
0-59465E401
0.3399E+01
0.1287E +02
0.69566 +01
0.6589E+01
068207E+01
0.8265E+01
0-8166E+01
0.4275E+01
01936E+02
-0.3418E+01

F?

0.3496F +00
0.10346F +01
0.547HF +00
064459F +00
0.8560F +00
O.L1OLE+01
063673F +00
024333F+00
O.S747F +00
0.7936F +00
0 e4260E+00
064793F +00
O.8141E+00
0.5397E+00
U6S514E+00
0 e9955F +00
0.5473F +00
0.7422 +00
069434F +00
0-6076F+00
0.9219E+00
O.B931E +09
0.9776F +00
0.61396 +00
029580F+00
025567E+00
0.7128E+00
0.4298F +00
0«2393E+00
023649F +00
063916E+00
021932E+01
0.8276F+00
0e8228E +00
067382E+00
061084E+01
0.5439F +00
0.7315E+00
9-6061E+00
0661 79F+00
O-LISTE+01

°0.9441E+00
06 7361E+00

064578E+00
0653266400
0.2390E+00
04434656 +00
064419E +00
0.3209F +00
0.3556E+00
0.3606E +00
0.7878E+00
0.36916 +00
0.1155E+01

FSO
(NT)
0 .B0R3E +03
0.7867E+03
0.7867E+03
0 6A4R9E +03
0.8709E+03
9 .BA09E +03
068265E+03
067740E+03
0686266 +03
0.6631E+03
0 645BE+03
066504E+03
066782E+03
0.65266 +03
Oe6721E+03
OeAT9IBE+03
9.6542E 403
Oe7TLI7E+03
0-7461E+03
00 7404E+03
0-7307E+03
9.7678E+03
0.80526 +03
0.#349E+03
0. 7386E+03
067730E+03
067491E+03
0eB8@168E4+03
0.6788E +03
1 66585E+03
0-7008E+03
0-7887E+03
0.7246E+03
067253E+03
066735E+03
Oe71L75E+03
1 66635E+03
0 e6837E+03
96 7441E+03
066787E+03
0.6747E+03
027254E +03
Ox?S12E+03
0e4381E+03
064604F.+03
064384E+03
0.4733E+03
0-4565E+03
024434E+03
0.4988E+03
0-5007E+03
066714E+03
0e6811E+03
Oe7TLI7E+03

HP5SO
(HP)
24226
23-577
23-579
250444
26.102
25.801
246771
23-197
25853
19,875
19.356
19.492
206326
19.558
200143
200369
19.608
21.330
220362
220190
212902
232012
24.133
252023
226137
23-167
22.453
24.482
200344
19.734
212004
23-640
21.717
21.738
206187
21.505
19.886
20-491)
222303
202343
20.223
21.741
226515
13.132
13.799
13.2141
14.187
13.682
13.289
14.950
15.008
20.122
200413
21.331


-26-

Identifying In H. as the dependent variable and In W as the independent
variable, equatibn (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 1n 4 =Inat+txinW

in H_ = the natural logarithm of the dynamometer power absorber
P setting (horsepower)

in W = the natural logarithm of the vehicle inertia weight
category.

Ina = -2,531
x - = 0.6509

Sample size 54

Multiple correlation coefficient .767 R2 = .589

; Standard error of the regression .1137

Converting to the form of the original model, the prediction equation
is:

H, = 0796 yo: 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


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 mv? + 1/2 (5 107 wv? (1)
i
Where:
E = the total system energy
m = the vehicle mass
v = the vehicle speed th
Ty = 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:


TABLE 4
FRONT TIRE

HEGRESSTON COEFFICIENTS

ID wT A R

(L8) (NT) (KG/SEC)

7101 4110 100.119 0147
7101 4500 101.675 2376
7101 5020 96.805 0544
710) 5330 102.698 2705
7201 5480 736717 024
7201 4540 74.043 294)
7201 S110 71.504 258/
7201 €060 75.010 2592
7502 4540 S$3.455 6047
7502 5020 78.666 2021
7502 5500 720612 e671
7502 6240 136.740 0413
7402 5040 116.926 2666
TA02 4430 111.475 910
7602 5530 124.301 10112
8002 4370 1256442 0 -=2570
8002 Solu 123.561 2636
8002 5530 1332580 -760
8002 6320 151.844 2204
8206 2750 54.797 0367
8206 4050 61.980 e171
6306 2700 68.994 0107
8306 3490 752065 2146
8306 4140 750603 2222
8507 2560 53.466 =.591
8507 3370 560870 9-6 294
8507 3900 700427 9 =.503
9003 3970 136.528 9-634
9003 4380 148.811 -.418
9003 4a10 159.544  =.405
5902 4310 132.806 2737
5902 5020 1320485 = 14.966
5902 5500 145.086 26543
7001 4620 110.863 208K
7001 4930 108.425 239)
7901 5530 116.727 2514
7001 6050 118.585 236
7001 6490 129.009 2416
7001 8190 132.334 0513
7301 4060 94.076 2447
7301 4560 1072055 0543
7301 5050 109.559 2358
7301 6420 1176703 14015
7402 S110 th te th th te te ah te te ae te
7402 5540 PRE ED Beh th th th ae
7402 S740 th tb th th te te $e de th th te ae
7701 4500 996552 — 2535
7701 4990 199.240 2372
7701 5420 111.976 0563
7701 5980 113.440 2552
T9OL 5690 132.923 +2204
7901 6060 121.567 = -,.043
7901 7040 145.946 2103

7901 7900 173.943 0405


1D

7101
7101
71021
7101
7201
7201
7201
7201
7502
7502
75902
7502
7602
7602
7602
8002
8002
8002
8002
826
8206
8306
8306
8306
8507
8507
8507
9003
9003
9003
5902
5902
5902
7001
7001
Tool
7001
7001
7001
7301
7301
7301
7301
7402
740?
7462
7701
7701
7701
7701
7901
7901
7901
7901

TABLE 2
REAR TIRE

REGRESSION COEFFICIENTS

wT
C6)
4110
4500
5020
5330
5480
4540
5110
6060
4540
sv20
£500
6240
5040
4430
553u
4370
5010
5530
6320
2750
4050
2700
3490
4140
2560
3370
3900
3970
4380
4310
4310
S020
5500
4620
4930
$530
6050
6490
8190
4060
4560
5050
6420
5110
5540
5760
4500
4990
5420
$980
5690
6060
7040
7900

A
(NT)
84.692
102.140
122.740
136.180
116.237
62.614
88.909
139.434
AB.B02
111.373
132.542
174,522
101.569
84.462
126.352
70.134
95.492
752027
112.060
56.494
110.251
61.014
104.522
128.109
77.627
90.456
120.517
83.001
97.596
109.156
65.601
95.098
123.353
76.226
88.175
108.342
94.346
121.286
199.693
64.873
766469
95.8667
176.690
135.962
142.012
150.774
68.629
660529
766588
89.767
84.516
100.298
127.025
167.096

R
(KG/SEC)
0239
0549
0804
0412
0236
0357
061
20487
2229
0366
12099
0239
e100
- 2045
72084
0349
0864
12180
1.842
0200
2340
72020
070
2127
70324
= 2392
20133
°325
2230
2542
72633
72650
e812
2480
20597
e614
0558
0673
0863
2087
7.187
-.107
-705
20403
26573
2.730
0214
2680
1.058
1-186
2353
0627
2663
2400


-13-
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:

dv/dt = ay + ayy + av (12)
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 this technique is discussed in detail in Reference 2

and in the EPA Recommended Practice for Road Load Determination.

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 #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 ftom 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


-15-

m= 2U/R" (14)

feq +

where

seq = 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 nondriving wheels.


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.

Il. 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.


SPPENDIX A

VEHICLE TEST FLEET IDENTIFICATION


30.000

24.000

13.000

12.000

20000

~24-
TWIN ROLL DYNAMOMETER ADJUSTMENT POWER AT 50 MPH

VERSUS ——
INERTIA WEIGHT ‘CATEGORY

+ 2
3
2 2
. 4 2
3 2
’ 5 :
+: a x >
2
+
? .
“ 3
+ 2
+
.
+
+
$ wwe tent eee tweet temo toon toesentosentoement
2000.0 3600.0 5200.0
280020 440060 : - 6000.0

INERTIA WEIGHT CATEGORY (UB)

Figure 6


Abstract

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. Speci-
fically, if the dynamometer measurements are to accurately reflect on-
road operation of the vehicle, the dynamometer must supply the appro-
priate load; that is, the force required to drive the vehicle on a level
surface as a function of the vehicle speed. In this study, road load
versus speed data were obtained from 15 light duty trucks. The road
load of each truck was determined for different payloads, resulting in a
total of approximately 50 road load measurements. The coast down techni-
que, in which the forces acting on a freely decelerating vehicle are
deduced from the speed-time history. of the deceleration, was used for
all track measurements.

When a vehicle is operated on a chassis dynamometer, the vehicle
must overcome the dissipative losses of the drive train and tires before
power is transmitted to the dynamometer. Therefore, to derive a dyna-
mometer setting appropriate to simulate the road experience of a vehicle,
these losses must be subtracted from the total system losses measured on
the track. Measurements of the dissipative forces of the driving tires,
the drive train, the non-driving tires, and the non-driving wheel bear-

ings were performed on a 48 inch diameter single roll electric dynamo-
meter.

The dynamometer load settings, resulting from the subtraction of
the dissipative losses of the drive train and the driving tires from the
total system measurements, are presented. These data are regressed
first against vehicle frontal area and then against vehicle inertia
weight category to develop equations to predict the dynamometer load
settings.

It is concluded that the dynamometer load settings predicted on the
basis of vehicle frontal area are the most accurate. In addition to
greater accuracy, the frontal area based prediction system is more
flexible in allowing possible refinements and improvements within the
framework of the system. While it is recognized that a prediction
system based on vehicle frontal areas is more complex to implement, this
approach is recommended.


TABLE 1
VEHICLE MASSES

wee ewww neem ewer ewe w werner een wewn en eeowmenoeweoooe

1D GRAV OTT EFF “FT EFF TOTAL VEH
MASS MASS MASS MASS
(KG) (KG) (KG) (KG)
7101 1868.2 33.811 26.04 1928.0
7101 2045.5 33.811 26004 21053
7101 2281.8 33.811 26.04 2341.7
7101 «© 2422.7 33.811 26.04 2482.6
7201 2490.9 64,657 31.75 2587.3
7201 2063.6 64.657 31.75 2160.0
7201 2322.7 64.657 31.75 241901
7201 2754.5 64.657 31.275 2851.0
7502 2063.6 42.007 44.30 2149.9
7502 2281.8 42.007 44.30 . 2368.1
7502 250020 422007 44.30 2586.3
7502 2836.4 42.007 44.30 2922.7
7602 2286.4 43,537 27.34 2357.2
7602 201366 43.537 27.34 2084.5
7602 2518.2 - 43.537 27.34 258961
8002 1986.4 30.971 31.92 2049.3
8002 2277.3 30.971 31.92 2340.2
8002 2513.6 30.971 31.92 2576.5
8002 287267 30.971 31.92 2935.6
8206 1250.0 31.074 20.75 1301.8
8206 1840.9 31.074 20.75 1892.7
8306 1227.3 20.605 22.91 1270.8
8306 1586.4 20.605 22.91 1629.9
8306 1681.8 20.605 22.91 1925.3
8507 1163.6 30.183 22.80 1216.6
8507 1531.8 30.183 22.80 1584.8
8507 1772.7 302183 22.80 1825.7
9003 1804.5 42.142 19.64 1866.3
9003 1990.9 42.142 19.64 2052.7
9003 2186.4 42.142 19.64 2248.1
5902 1940.9 46.852 26.90 2014.7
5902 1968.2 46.852 26.90 2041.9
$902 2281.8 46.852 26-90 235546
5902 2500.0 46,852 26.90 2573.8
7001 2100.0 55.724 46.67 2202.4
7001 224069 55.724- 46.67 234363
7001 2500.0 55.724 46.67 260264
7001 2513.6 55.724 “46.67 2616.0
7001 2750.0 55.724 46.67 2852.4
7001 295020 55.724 46.67 305204
7001 3722.7 55.724 46.67 382561

7301 1345.5 50.140 28.90 1924.5


-32-

this regression are:

Regression of the Differences in Dynamometer Power Absorber Settings
versus
Vehicle Test Mass

Regression model: A, = aM
H_ = the difference in dynamometer power absorber settings
P (horsepower)
M = the vehicle test mass (kg)

a 0.000887

Sample size 54

Correlation coefficient 0.46 Rr = 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:

4H, = .633 A + .0004W for pick up trucks

A, = .511 A + .0004W for vans | (5)
where

A = the vehicle frontal area (et?)

W = the vehicle weight (1b)

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:

9-651 §  oooaw (26)

H. = .0796W
Pp
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


APPENDI¥ C

DYNAMOMETER MEASUREMENTS


-27-

Mean Twin Roll Dynamometer Power Absorber Setting at 50 mph
versus

Vehicle Inertia Weight

30

Regression Line

H. = .0769 worO5t (e) 8
20 p

ie
Power
(horsepower)
10 4 O= Pick Up Trucks
O= Vans
0 + + + +
2000° 3000 4000 5000 6000

Inertia Weight (1b)

Figure 7


-11-

FRONT AXEL FORCE MEASUREMENTS

VEHICLE 10: 7701

TEST WEIGHT? 51991b

FORCEWNT)
SSoco0 r

1
300,000 ++
'

1
t

worn

1
250,000 +

1

0.0 $6000 = 10,000 15.c0e 26,000
SPEEDUN/S EC)

Figure 2(b)

Cc. Masses

1) The Gravitational Masses

23.000 30.000

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


(TABLE 1 CONTINUED)

7301 2072.7 50.140 28.90 2151.8
7301 2295.5 50.140 28.90 2374.5
7301 2918.2 50.140 28.90 299762
7402 2322.7 43.537 28.81 2395.0
7402 2518.2 43.537 28.81 2590.5
7402 2618.2 . 43.537 28.81 2690.5
7701 2045.5 41.779 27.16 2114.4
7701 2268.2 41.779 27016 233761
7701 2554.5 41.779 27.16 2623.5
7701 2718.2 41.779 27.16 2787.1
7901 2586.4 56.206 38004 2660.6
7901 2754.5 56.206 “38.04 2848.8
7901 2977.3 56.206 38204 3071.5
7901 320020 56.206 38.04 3294.2

7901 3590.9 56.206 35.04 368562


(NT)
DelSLRE +03
0.3710F +93
Oe2K1LIE+03
0 .4226E +03
0 64404F +03
0.53256 +03
06341 9F +03
063796E +03
0 64543E+03
0.2630E+03
O.1S7TIF +03
00 2766F +03
0026826 +03
0.14126 +03
0.1694F +03
0e2823F+03
01960F +03
De1A72F +03
062636 +03
0021126 +03
9 3825E+03
003637E+03
0e4H72E +03
063834E +03
0631056403
002653E+03
040876403
0237256E+03
0 29496F +02
0-1640E+93
022093E+03
002361F +03
002373E+03
0.22836 +03
062534E +03
0 62973E+03
N01 764F403
063567F +03
0.3958E+03
001300E+03
De2R74E+N3
%e2k37E+03
0-2567E+03
0615756403
0-2535E 403
OL 167E+03
062295F +03
062408E+03
01999E +93
022495F +03
0e2812E+03
062787E+03
Oe.17S5S1F +03
0033326 +03

TAKLE.
TOTAL VEHICLE

Ueed24t +0?
0.4426E +01
Vel IS7TE+02
0.1679E+02
Uek22TE+O1
70 eI344E +00
0e2300E +02
Oo1BALE +02
0e1997E+02
0.7670K +01
0.20946E+02
001802E+02
0-1013E +02
0.1732E+02
01815640?
0e3837E+01
001 792E+02
0.1320E+02
0.63486 +01
0+1689E +02
0661 98E +01
0 e8629E+01
03624E+01
O61758E+02
0e6215E+01
0e19R9E+02
O-1060E+02
062469F +02
0.2743E +02
Ne2154E+02
0-2173F+02
wOeL173E+02
001040E+02
OsL1L77E+02
0.1094E+02
0e2705F +01
Oe1L457E+02
0eB44HE+01
0.1776b+02
Ool776E+02
00}396E +00
026730E+01
0-1606E+02
0.8115E+01
0.5689E+01
001512E+02
069299E+01
0e8989E+01
021042E+02
0.1041E+02
0-1057E+02
0-6284E+01
0.2127E+02
=001193E+01

OAI4VE

1
POAD Lodo

0.369 F400
0,10346F+01
0.52 TAR +O0
9.4459F +06
OeHSODE +00
0.1101E+0)
0e3673E +00
0044338400
0.57476 400
0.7936F +00
0.4260E +00
004793E+00
ao
0.5397E+00
0.5514F +00
0-9955E +00
0.5473F +00
06 7422F +00
0.9434F +00
0 eA075E +06
9.9219E+00
0-8931E+00
O.977THE+00
0.6139F +00
O.95R0F +00
06S567E +00
Oe7L2HE +00
0 e429KRE +00
0.2393F +00
0.3649F+00
0e3915F +00
001932F +01
OeB27THF +00
0.8228 +00
0.7382F +00
OL OB4E+01
N.5439EF +00
)e7315E+00
0.6061E+00
O61 79F +00
Del IS7E+O1
9-9441E 400
06 7SO1F +00
0e457HF +00
0.5326F +00
0.2390£+00
004346E+00
064419F +00
0.3209F+00
0.3556E+00
063606F+00
0.7878F +00
0.3691E+00
0.1156F+01

(NT)
9.9799F +03
O.GS77E+03
G.1012E +04
eI D21E+04
061 057E +04
Nel OF2E+04
Vel OBIE +4
Nel Q1L6E+04
Del) RAE +04
0.P309F 403
0.83R0E+03
OeHORRE+ U3
NePO14E +03
06 797RE+03
0 oPSN4E+03

90 4653E4+03

NBTSTE+O3
0 e8923E +03
Ne9H16E +03
0.1003E+04
0.1041E+04
0e1083E+04
0 e92R0E+03
0.9879E +03
9e1002E+04
N.1092E+04
0 6P276E +03
DeF2TSE +03
008905E+03
069387E+03
0.8K31E+03
0.9023E+03
0.8667E +03
0.8993E +03
0.2630E+03
9e9109E+03
0.1005F. +04
Oe8357TE+03
eB ABTE+03
0 -90S7TE+N3
B<9834E+03

“9 .S675E+03

O.6467E403
OeS7T41E +03
1 26544E4+03
066625E+03
06S931E+03
0.6597E+03
066976E+03
0 e&126E+03
9.°348E +03
0 -8634E+03

30331

30.601

316530
31.630
31.141

302451

352607
24.904
25.116
262040
2Te017
23.912
25.484
252935
262075
24.961

26.276
260744
292420
302062
31.201
320459
276814
292609
302032
32.729
24.305
24.802
260690
286135
260468
27644
25.977
260954
25-866
272301

39.122
25-0047
266037
270145
29.474
17.009
19.383
17.207
19.614
192856
17.776
19.772
20.908
24.355
25.020
260489



-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):

TReq 7 x - (13)
play
Vo F

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: