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 ------- |