LDTP -11-1
Technical Support Report for Regulatory Action
Prediction of
Vehicle Reference Frontal Area
by
Harriet W. Goodall
Glenn D. Thompson
November 1977
NOTICE
Technical support reports for regulatory action do not necessarily
represent the final EPA decision on regulatory issues. They are intended
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 re'ached. Readers are cautioned to
seek the latest analysis from EPA before using the information 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
-------
-2-
Abstract
Beginning with the 1979 model ye"ar, the dynamometer power absorp-
tion to simulate the vehicle road load during exhaust emission certifi-
cation testing and fuel economy measurements will be predicted by the
vehicle reference frontal area.
This report develops an equation to estimate the vehicle reference
frontal area using the overall vehicle height and width. The reference
area data and the overall height and width data used in this analysis
were supplied by the vehicle manufacturers.
It is concluded that the product of the overall vehicle height,
width and the coefficient, 0.80, yields a good approximation of the
actual vehicle reference frontal area. Using this approximation, there
is 80 percent confidence that the predicted value will be within +1.0
square feet of the actual reference frontal area. This is approximately
5 percent of the reference area of a typical vehicle.
This equation is recommended as a method for evaluation of sub-
mitted reference area data or for predicting vehicle reference frontal
areas when empirical data are not available.
-------
-3-
Purpose
This report proposes an equation to estimate the vehicle reference
frontal area using the overall vehicle height and width as parameters.
This equation may be useful for estimating vehicle reference areas when
measured values are not available, or for preliminary evaluation of the
accuracy of submitted reference area data. This report documents the
data sources and methodology used in developing the proposed equation.
Introduction
In a previous technical support report, "Prediction of Dynamometer
Power Absorption to Simulate Light-Duty Vehicle Road Load", (1)* it was
concluded that the prediction model which utilizes the vehicle reference
frontal area is the preferred approach. This method will be used to
determine the dynamometer adjustment for exhaust emission certification
and fuel economy tests beginning with the 1979 model year (2).
When this regulation was first proposed, General Motors commented
that the vehicle reference frontal area could be adequately predicted by
the product of the overall vehicle height and the vehicle width times
0.8. This report provides a thorough analysis and documentation of this
method of predicting the vehicle reference frontal area.
Discussion
Beginning with the 1979 model year, the vehicle reference frontal
area will be used to determine the dynamometer adjustment for EPA exhaust
emission certification and fuel economy testing. For this purpose, the
vehicle reference frontal area is defined as the area of the orthogonal
projection of the vehicle onto a plane perpendicular to the longitudinal
axis of the vehicle. This area is usually determined by analysis of
engineering drawings, projection techniques from the actual vehicle, or
planimeter measurements from photographs. Any of these methods are
capable of yielding accurate results. However, unless a well automated
system is used they can be time consuming. For example, the photographic
approach requires the time delay of the development and printing of the
photographic negative. Therefore, methods to predict the reference area
from the overall vehicle height and width were considered desirable and
worth investigating.
Reference area, overall height and overall width data were requested
from the appropriate manufacturers for all vehicles used in the EPA road
load project. The test fleet is described in Table 1 of the Appendix.
These vehicles were selected to approximately represent the sales
weighting of light-duty vehicles. The submitted reference area, height
and width data are given in Table 2 of the Appendix.
* Numbers in parentheses designate references at the end of the paper.
-------
-4-
The model used to predict the vehicle reference area using the
vehicle height and width was:
A = aHW (1)
where A = the vehicle reference area
H = the overall vehicle height
W = the overall vehicle width
a = a constant to be determined
by the regression analysis
Equation 1 was chosen since the area should obviously be propor-
tional to the product of the overall vehicle height and width. A con-
stant term was not included in the model since any vehicle with vanishing
height or width must have a zero reference area. Equation 1 was fitted
to the reference area data and the vehicle height and width data by the
least squares method. The results of this regression were:
Regression of Height Times Width
versus
Vehicle Reference Area
Regression Model: A = aHW
A = the vehicle reference area
H = the overall vehicle height
W = the overall vehicle width
a = 0.80
Sample Size = 67 „
Estimate of the Standard Error = 0.80 ft
Correlation Coefficient = 0.95
It should be noted that the regression coefficient is dimension-
less. Therefore, the coefficient 0.80 is valid independent of the
system of units. However, the system of units must be dimensionaly
consistent. That is, the area must have the same units as the product
of the height and width.
The data and the resulting regression line are plotted in Figure 1.
The plot demonstrates the strong relationship between the reference area
and the product of the vehicle height times width. The estimate of the
standard error is approximately equivalent to one standard deviation of
the residuals. Therefore, 68% of the data is expected to be within +
0.80 square feet of the regression line. Figure 1 indicates there is
only one datum which differs from the regression line by a much greater
amount. The residuals of the measured values minus the predicted values
of the regression were computed and are given in Table 3 of the Appendix.
These residuals demonstrate that this atypical vehicle was an AMC Pacer.
For this vehicle the predicted value was in error by 2.6 square feet or
12.1 percent.
-------
-5-
Figure 1 - Scatter Plot of Reference Area Data
versus
Overall Vehicle Height Times Width
2 4
26.000 * » #
2
2 3* *
24.000 * »»
62 2
*
3
22.000 *
OJ
o
2 20.000 *
CU
Pi
4 « ««
18.000 *
2
«• 2 *
4. «
16.000 *
20.000 26.000 3?.000
23.000 29.000 35.000
Height Times Width (ft2)
-------
-6-
The general reference area shape of the Pacer is shown in Figure 2
along with the reference area shape of a more typical vehicle. Is is
apparent from this figure that it is the wide "belt line" of the Pacer,
together with the more rounded shape of the vehicle which causes the
observed atypical results.
Conclusions
It is concluded that the Equation;
A = 0.80HW
is a good prediction of the actual vehicle reference area. There is
approximately 80 percent confidence that the true vehicle reference area
is within + 1.0 square feet of the predicted value. There are, however,
some atypical vehicles for which the prediction errors are much larger.
Recommendations
The equation can be useful in evaluating submitted reference area
data. It may also be useful for predicting reference areas when empirical
data are not available. It is recommended that the equation be used in
this manner.
It is not recommended that the prediction equation be used in the
regulatory process because of the inaccuracies in the case of atypical
vehicles. If used in the regulatory process, the equation would penalize
vehicles with the frontal surfaces similar to the AMC Pacer. However,
there may be aerodynamic advantages of such rounded configurations.
In addition, if the product of the overall height and width were
used in the regulatory process, manufacturers might tend to produce the
largest reference area vehicles possible within a given height times
width. It is considered inappropriate to impose this design oriented
pressure when the vehicle reference area is considered the important
parameter, not the vehicle height or width.
-------
-7-
Figure 2 - Comparison of the Reference Area of a
More Typical Vehicle to the Reference Area
of the AMC Pacer
-------
References
1. G.D. Thompson, EPA Technical Support Report for Regulatory Action,
"Prediction of Dynamometer Power Absorption to Simulate Light-Duty
Vehicle Road Load", April 1977.
2. "Control of Air Pollution from New Motor Vehicles and New Motor
Vehicle Engines," Federal Register, Vol. 42, No. 176, September 12,
1977.
-------
APPENDIX
-------
VEHICLE
IDENTIFICATION
NUMBER
101
201
301
401
502
601
804
901
1001
1102
1201
1301
1401
1501
1601
1702
1802
1901
2102
2203
2301
2401
2502
2602
2706
2802
2906
3011
3102
3212
3304
3402'
3505
3613
3908
4014
4102
4202
4402
4507
4607
4701
4801
4903
5103
5203
5303
5403
5503
5603
5601
5701
5802
6002
6102
6202
6302
6402
6502
6702
6802
6909
8101
8401
9101
MODEL
YEAR
1974
1975
1975
1975
1975
1975
1974
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1975
1973
1975
1975
1975
1975
1975
1975
.1975
1975
.1.975
1975
1975
1975
1975
1975
.1975
1975
1975
1975
1975
1975
1975
1.975
1975
1975
1.975
1975
1975
1975
1.975
1975
1975
1975
1975
1975
1975
1.975
1975
1.976
1975
1975
1975
TABLE 1
TEST FLEET
MANUFACTURER
Chevrolet
Chevrolet
Pontiac
Pontiac
Ford
Oldsmobile
American Motors
Chevrolet
Chevrolet
Ford
Buick
Buick
Buick
Buick
Chevrolet
Ford
Ford
Buick
Mercury
Plymouth
Buick
Buick
Lincoln
Mercury
Toyota
Mercury
Toyota
Saab
Ford
Triumph
American Motors
Ford
Volkswagen
Honda
Mazda
Fiat
Mercury
Ford
Ford
Datsun
Da t sun
Pontiac
Oldsmobile
Dodge
Plymouth
Plymouth
Plymouth
Plymouth
Chrysler
Chrysler
Pontiac
Oldsmobile
Ford
Mercury
Ford
Ford
Ford
Ford
Ford
Ford
Ford
Volvo
Chevrolet
Oldsmobile
Chevrolet
MODEL BODY
NAME STYLE
Impala Sedan
Chevelle Sedan
Firebird Sedan
Ventura Sedan
Pinto Sedan
Cutlass Sedan
Gremlin Sedan
Impala Stationwagon
Vega Sedan
Granada Sedan
Century Sedan
Special Sedan
Skylark Sedan
Apollo Sedan
Monza Sedan
Mustang Mach 1 Sedan
Mustang Sedan
Skyhawk Sedan
Capri II Sedan
Valiant Sedan
LeSabre Sedan
Estate Stationwagon
Continental Sedan
Capri Sedan
Corolla Sedan
Comet Sedan
Celica Sedan
99 Sedan
Mustang Mach 1 Sedan
TR6 Convertible
Pacer Sedan
Maverick Sedan
Rabbit Sedan
CVCC Sedan
RX-3 Stationwagon
128 Sedan
Montego Sedan
Gran Torino Sedan
LTD Sedan
280Z Sedan
B210 Sedan
Lemans Sedan
Cutlass SupremeSedan
Dart Sedan
Valient Custon Sedan
Gran Fury Sedan
Scamp Sedan
Valiant Sedan
New Yorker Sedan
Newport Sedan
Lemans Sedan
Delta 88 Sedan
Granada Sedan
Montego Sedan
LTD Sedan
Torino Sedan
Granada(l)Sedan
LTD Sedan
Torino Stationwagon
Gran Torino Stationwagon
Gran Torino Sedan
264DL Sedan
Corvette Sedan
Toronado Sedan
Corvette (2) Sedan
TEST
WEIGHT
(LBS)
4560
4100
3640
3520
2800
4250
2970
5250
2680
3510
4140
4020
3720
3910
3490
3000
3020
3200
2570
3600
4870
5590
5450
2350
2470
3320
2760
2710
3320
2650
3330
3320
2170
1900
2680
2180
4560
4570
4860
3110
2310
4230
4330
3610
4260
4840
3680
3620
5120
4840
4320
4770
3760
4500
5020
4420
3800
5060
5210
5000
4600
3290
3850
5170
3820
(1) Same vehicle as 5802.
(2) Same vehicle as 8101, however head lamps up.
-------
TABLE 2
REFERENCE AREA ESTIMATES
ID
101
201
301
401
502
601
804
901
1001
1102
1201
1301
1401
1501
1601
1702
1802
1901
2102
2203
2301
2401
2502
2602
2706
2802
2906
3011
3102
3212
3304
3402
3505
3613
3908
4014
4102
4202
4302
4402
4507
4607
4701
4801
4903
5001
5103
5203
5303
5403
5503
5601
5603
5701
5802
6002
6102
6202
6302
6402
6502
6702
6802
6909
8101
8401
9101
HEIGHT
(INCH)
54.50
53.80
49.10
53.20
50.60
54.10
54.35
58.10
50.00
53.20
54.10
54.10
54.20
54.20
49.80
49.70
50.00
50.20
51.00
54.70
54.60
58.40
55.30
50.70
53.54
52.90
52.86
56.69
49.70
54.09
55.06
52.90
55.50
52.16
55.12
54.09
52.60
53.30
54.70
53.70
51.38
50.79
53.40
54.10
53.80
53.40
54.70
56.50
53.50
54.70
54.40
53.40
54.80
54.50
53.20
52.60
53.70
52.60
53.20
53.70
54.90
54.90
53.30
56.69
48.10
53.20
48.10
WIDTH
(INCH)
79.50
76.60
73.00
72.40
69.40
76.70
61.82
79.50
65.40
74.00
79.00
79.00
72.40
72.40
65.40
70.20
70.20
65.40
66.90
71.00
79.90
79.90
80.25
64.80
64.96
70.50
63.78
66.53
70.20
62.60
76.60
70.50
63.40
59.25
60.80
62.60
79.30
79.00
79.60
79.50
64.96
60.83
77.40
76.70
71.80
77.40
71.00
80.20
71.80
71.00
80.40
77.40
80.40
79.90
74.00
79.30
79.50
79.30
74.00
79.50
79.00
79.00
79.00
67.32
69.00
79.70
69.00
** CALCULATED REFERENCE AREA
* REFERENCE AREA
SUPPLIED
AREA*
(FT)
24.20
23.30
20.70
21.90
19.40
23.30
19.04
24.40
18.40
22.60
23.30
23.30
21.90
21.90
18.70
19.50
19.50
18.70
18.90
21.59
24.20
24.40
25.90
19.00
18.40
21.60
17.70
20.67
19.50
18.30
21.05
21.60
20.00
16.97
18.19
17.40
23.40
24.20
26.00
25.00
17.64
17.22
23.30
23.30
21.50
23.30
21.59
24.38
21.37
21.59
24.30
23.30
24.52
24.20
22.60
23.40
25.00
23.90
22.60
25.00
25.60
25.60
24.20
22.07
17.20
23.90
17.20
AREA**
(FT)
30.09
28.62
24.89
26.75
24.39
28.82
23.33
32.08
22.71
27.34
29.68
29.68
27.25
27.25
22.62
24.23
24.37
22.80
23.69
26.97
30.30
32.40
30.82
22.81
24.15
25.90
23.41
26.19
24.23
23.51
29.29
25.90
24.44
21.46
23.27
23.51
28.97
29.24
30.24
29.65
23.18
21.46
28.70
28.82
26.83
28.70
26.97
31.47
26.68
26.97
30.37
28.70
30.60
30.24
27.34
28.97
29.65
28.97
27.34
29.65
30.12
30.12
29.24
26.50
23.05
29.44
23.05
USING HEIGHT TIMES WIDTH
BY THE MANUFACTURER
-------
TABLE 3
CALCULATED REFERENCE AREA
ID
101
201
301
401
502
601
804
901
1001
1102
1201
1301
1401
1501
1601
1702
1802
1901
2102
2203
2301
2401
2502
2602
2706
2802
2906
3011
3102
3212
3304
3402
3505
3613
3908
4014
4102
4202
4302
4402
4507
4607
4701
4801
4903
5001
5103
5203
5303
5403
5503
5601.
5603
5701
5802
6002
6102
6202
6302
6402
6502
6702
6802
6909
8101
840.1
9101
AREA*
(FT)
24.20
23.30
20.70
21.90
19.40
23.30
19.04
24.40
18.40
22.60
23.30
23.30
21.90
21.90
18.70
19.50
19.50
18.70
18.90
21.59
24.20
24.40
25.90
19.00
18.40
21.60
17.70
20.67
19.50
18.30
21.05
21.60
20.00
16.97
18.19
17.40
23.40
24.20
26.00
25.00
17.64
17.22
23.30
23.30
21.50
23.30
21.59
24.38
21.37
21.59
24.30
23.30
24.52
24.20
22.60
23.40
25.00
23.90
22.60
25.00
25.60
25.60
24.20
22.07
17.20
23.90
17.20
* REFERENCE
+ CALCULATED
AREA+
(FT)
24.25
23.06
20.06
21.55
19.65
23.22
18.80
25.85
18.30
22.03
23.91
23.91
21.96
21.96
18.23
19.52
19.64
18.37
19.09
21.73
24.41
26.11
24.83
18.38
19.46
20.87
18.66
21.10
19.52
18.94
23.60
20.87
19.69
17.29
18.75
18.94
23.34
23.56
24.37
23.89
18.68
17.29
23.13
23.22
21.62
23.13
21.73
25.36
21.50
21.73
24.47
23.13
24.66
24.37
22.03
23.34
23.89
23.34
22.03
23.89
24.27
24.27
23.56
21.35
18.57
23.72
18.57
RESIDUAL
(FT)
-0.045188
0.239273
0.644741
0.346036
-0.252381
0.078122
0.241720
-1.448642
0.101289
0.570640
-0.614828
-0.614828
-0.056842
-0.056842
0.473807
-0.023460
-0.136266
0.328771
-0.188352
-0.141230
-0.214397
-1.706484
1.066610
0.620713
-1.058999
0.730928
-1.162740
-0.432741
-0.023460
-0.643316
-2.550583
0.730928
0.307332
-0.321517
-0.559934
-1.543316
0.057258
0.639704
1.633949
1.109345
-1.037416
-0.071517
0.174812
0.078122
-0.118425
0.174812
-0.141230
-0.977131
-0.127561
-0.141230
-0.170800
0.174812
-0.136123
-0.166051
0.570640
0.057258
1.109345
0.557258
0.570640
1.109345
1.330639
1.330639
0.639704
0.717475
-1.372668
0.178553
-1.372668
%DIFF
-0.187
1.027
3.115
1.580
-1.301
0.335
1.270
-5.937
0.550
2.525
-2.639
-2.639
-0.260
-0.260
2.534
-0.120
-0.699
1.758
-0.997
-0.654
-0.886
-6.994
4.118
3.267
-5.755
3.384
-6.569
-2.094
-0.120
-3.515
-12.117
3.384
1.537
-1.895
-3.078
-8.870
0.245
2.643
6.284
4.437
-5.881
-0.415
0.750
0.335
-0.551
0.750
-0.654
-4.008
-0.597
-0.654
-0.703
0.750
-0.555
-0.686
2.525
0.245
4.437
2.332
2.525
4.437
5.198
5.198
2.643
3.251
-7.981
0.747
-7.981
AREA SUPPLIED BY THE MANUFACTURER
REFERENCE
AREA FROM THE REGRESSION
------- |