MC 75-02 Standards Development and Support Technical Report Motorcycle Useful Life by Thomas Cackette June 1975 Notice Technical support reports for regulatory action do not necessaily represent the final EPA decision on regulatory issues. They are intended to present a technical analysis of an issue and conclusions and/or 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 conclusions rea.ched. 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 ------- Distribution List Motorcycle Technical Support Reports for Regulatory Action D. Alexander E. Brune T. Cackette J.P. DeKany C.L. Gray D. Hardin K. Hellman W. Houtman T. Huls R. Jenkins E. Rosenberg R. Stahman E.G. Stork G. Thompson M. Williams ------- Abstract A useful life mileage for motorcycles has been determined using Gallup motorcycle owner survey data and registration information. The useful life mileage is 12000 km for motorcycles with engine displace- ments between 49 and 170 cubic centimeters, and 30000 km for motorcycles with displacements of 170 cubic centimeter or greater. Prepared By Project Manager Motorcycle Regulations Branch Chief ^j f /ivision, Director Standards Development //Emission Control and Support \*/ Technology Division > /•"] (-*' ------- Introduction To determine the durability test requirements for motorcycles, it is necessary to know their useful life mileage. While the Clean Air Act defines the useful life of motor vehicles to be 5 years or 50,000 miles, which ever is greater, it is the opinion of the Office of General Councel that "The Statutory Definition of Useful Life as 50,000 miles would not apply to motorcycles" (Ref. 6). The following analysis defines useful life "as the mean (average) mileage a motorcycle can be expected to accumulate during its life- time. The discussion presents the analysis technique, the detailed calculations, and a description of the data and associated assumptions, Discussion Definition of Useful Life Mileage The useful life mileage of a motorcycle is defined as the mean Caverage) mileage a motorcycle can expect to accumulate over its life- time, and is given by equation 1, 00 J MR(t) *Pr(t) dt = useful life mileage 1) o where: MR = yearly distance traveled at a given age t Pr = probability of survival at a given age t Equation 1 can be approximated by the following summation over discrete intervals. oo I MR^ *Pri = useful life mileage 2) Examining equation 2 reveals that the largest contribution to the useful life mileage occurs for the newer motorcycles whose probability of survival, Pr, is high. This is a desirable feature of the equation because more data is available for the newer motorcycles and fewer assumptions in processing these data are required. The term MR^, the distance traveled in year i, is evaluated using Gallup survey data of motorcycle accumulated mileage and age. The desired quantity is the average number of miles accumulated in a year by motorcycles of age i. This can be evaluated from equation 3, ------- -2- i-1 MR* = W± - I MR. 3=1 = AM± - f^i±-i 3) where: AMjf = total accumulated mileage for a motorcycle of age i Note that MRj_ is not the accumulated mileage divided by the age, This would give the average miles per year traveled over the age interval, and not the miles per year traveled in year i, The. term Pr^, the probability of survival, is evaluated using registration data and the survey results. Pr^ is defined as the number of motorcycles of age i in operation today divided by the number originally sold new. The number of motorcycles of age i still operating can be estimated from the Gallup survey results. The number originally sold new is obtained from registration data. The Gallup Data The Motorcycle Industry Council (MIC) commissioned the Gallup Organization to perform a survey of motorcycle owners. The Gallup Organization surveyed 4187 motorcycle owners nationally who owned a total of 4800 motorcycles. Mini cycles were excluded from the survey. The data were weighted according to the distribution of motorcycle ownership in the country, giving 9888 weighted responses. The EPA received a tape of the survey data, from which the data in this report were obtained. The survey asked motorcycle owners to go look at their odometers and report the mileage. If the owner refused, or there was no odometer or it was not working, a mileage estimate was obtained. The accumulated mileage data were analyzed and it was determined that those people who estimated mileage and had no odometer or working odometer on the average estimated accumulated mileage higher than the rest of the owners. There- fore this group was eliminated from the data base. All motorcycles used only for off road riding were also excluded because this type of motor- cycle is not covered by the emission regulations. A final exclusion was the 1974 model year motorcycles. It was felt that the mileage accumulation rate of new motorcycles would be high, and thus projecting a yearly mileage based upon less than one years usage was not valid. The data supported this conclusion. Thus the data base was reduced to street and dual purpose motorcycles of 1973 and older model year with working odometers. ------- -3- Using this data base the following information relating to useful life mileage was determined: Accumulated mileage versus age (AM.^) , yearly mileage (MR^) versus age, and the number of motorcycles still in existence versus age (numerator of Pr^) . Registration Data The remaining term to be evaluated in the useful life equation is the number of new motorcycles sold each year (denominator of Pr^) . The required data were obtained from new (first time) motorcycle registrations. In general the data set of street and dual purpose motorcycles selected from the Gallup data is the set of registerable motorcycles. Thus the two data sources have a consistent base and can be used together to calculate ^ , New motorcycle registration data are available only back to 1967, requiring estimates to be made for the older model year motorcycles. Fortunately motorcycles older than 1967 contribute less than 20 percent of the useful life mileage, and therefore errors made in estimating new registrations are minimized. The procedure used to estimate new motor- cycle registrations is presented in Appendix I. Table I presents the new motorcycle registration data versus model year, the number of motorcycles of a given model year still operating, and the calculated value of Pr, TABLE I ALL ENGINE SIZES > 50cc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1st time registra- tions, N! * 103 1190 1006 928 751 550 437 287 587 545 317 225 153 107 106 Ref. 1 // still operating R± * 103 1153 1029 755 499 311 236 175 150 118 46 31 16 10 6 Ref. 2 (Also see Appendix II) Probability of Survival, Pr^ .97 1.02 .81 .66 .57 .54 .61 .26 .22 .15 .14 .10 .09 .06 ------- In Table I the motorcycle age is also presented. The Gallup survey was taken in the last half of May 1974. Since this is approximately the time at which them median sale of a given model year motorcycle occurs, the average age of a motorcycle will be equal to the model year subtracted from 1974. Splitting the Data into Displacement Categories The proposed regulations divide motorcycles into two engine dis- placement categories, those between 49 and 170 cubic centimeters and those greater than or equal to 170 cc, i.e. 'small' and 'large' motor- cycles. An examination of accumulated mileage versus engine displacement category indicated small motorcycles have a significantly shorter useful life mileage than large motorcycles, and thus a displacement category dependent useful life mileage was required. A single non-displacement related use- ful life mileage would have unfairly penalized small motorcycles. The Gallup data were easily split into displacement categories since engine size was a question asked in the survey. The 1974 to 1967 new registration data also contained displacement information. The older registration data contained no displacement data, requiring an estimate of the displacement distribution. The estimate was made by extrapolating the trend towards purchasing larger motorcycles and from motorcycle import data. Again the older motorcycles contribute a small percent of the useful life mileage, and thus the effect of an estimate error is small. Table II presents the registration data for each displacement category. N-^ is the number of new first time registrations, which approximates the number of new registerable motorcycles sold. TABLE II SPITTING DATA INTO DISPLACEMENT CATEGORIES 3 Fraction Ni * 103 U± * io3 * 10 > 170 cc 50 _< cc <170 cc > 170 1973 1190 .73 321 869 72 1006 .71 292 714 71 928 166 316 612 70 751 .54 346 406 69 550 .51 270 280 68 437 . .51 214 223 67 287 .48 149 138 66 587 .42 340 247 65 545 .38 338 207 64 317 .33 212 105 63 225 .30 158 68 62 153 .30 107 46 61 107 .30 75 32 60 106 .30 74 32 59 102 .30 71 31 ------- Table III shows the calculations to determine the probability of survival, Pr.», for each displacement category. R^ is determined from the Gallup survey data. (See Appendix II) TABLE III PROBABILITY OF SURVIVAL M , , v 50 < cc < 170 cc > 170 Model Year — — Hi ii Pri Ni Ri Pri 1973 321 345 1.07 869 809 .93 72 292 296 1.01 7l"4 734 1.03 71 316 233 -74 612 522 .85 70 346 216 .62 406 283 .70 69 270 125 .46 280 186 .66 68 214 88 .41 223 148 .66 67 149 79 .53 138 96 .70 66 340 69 .20 247 81 .33 65 338 66 .20 207 52 .25 64 212 25 -12 105 20 .13 63 158 8 .05 68 22 .32 62 107 2 -02 46 14 .30 61 75 2 .03 32 8 .25 60 74 2 -03 32 A >12 59 71 1 -01 31 1 .03 N^ = number of new registerable motorcycles, Ref. 1 R^ = number of registerable motorcycles still operating, Ref. 2 Pr-£ = RI/NJL = probability of survival cc = cubic centimeter engine displacement Yearly Mileage Rate As described by Equation 3, the miles traveled per year is calculated using total accumulated mileage, which was obtained from the Gallup survey data. Because there are only a few sample responses for the older motor- cycles, the mean accumulated mileage for old motorcycles tends to show large variations from model year to model year. To overcome this dif- ficulty, a least squares second order polynomial was fit through all the data points, and accumulated mileage was calculated from the fit equation. Figure 1 shows the average accumulated mileage versus model year and the best fit equation which has the form: 2 Accum. miles = ao + ai * year + &2 * year ------- Calculation of the Useful Life Mileage Equation 2 is now used to calculate the useful life mileage. The annual mileage rate is obtained from equation 3 and the curve fit accumulated mileage of Figure 1. The probability of survival is obtained from Table III. The calculations, presented in Tables IV and V, result in useful life mileages of 10633 km for motorcycles between 49 and 170 cc, and 28232 km for motorcycles greater than or equal to 170 cc. Recommended Useful Life Mileage for Use in the NPRM For the actual specification of useful life mileage in the motorcycle regulations, it is considered appropriate to round up the calculated values. The rounded values result in even increments for durability testing and maintenance intervals. The relatively short distances required do not put an unreasonable burden upon the manufacturers. It is also felt that once manufacturers are required to demonstrate motorcycle durability, the designs tend to improve, and the useful life mileage will increase beyond the levels upon which these calculations were based. The recommended useful life mileages are: / Calculated Recommended Values for Regulations 50<^cc<:170 10633 km 12000 km cc >170 28232 km 30000 km ------- _i_4-!-:-U-i---i-U. - .- ..i •.!.;-: p..;.. :_n. . i O'. CURMS" FIT MifA/J MIL?/-..';: ------- Table IV Useful Life Mileage - 50 1 cc < 170 Model Year 1973 72 71 70 69 68 67 66 65 64 63 62 61 60 59 Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AM± 2160 3369 4495 5537 6495 7370 8161 8869 9493 10034 10490 10864 11153 11359 11482 MEL 2160 1209 1126 1042 958 875 791 708 624 541 456 374 289 206 123 Pri 1.07 1.01 .74 .62 .46 .41 .53 .20 .20 .12 .05 .02 .03 .03 .01 MIL * Pr± 2311 1221 833 646 441 359 419 142 125 65 23 8 9 6 1 E = 6608 miles =10633 km AM, accumulated miles calculated from Figure 1, miles MR. = yearly mileage rate from equation 3, miles per year i Pr = probability of survival from Table III ------- Table V Useful Life Mileage - cc >170 Model Year 1973 72 71 70 69 68 67 66 65 64 63 62 61 60 59 Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AM. 4342 6767 9121 11402 13611 15748 17813 19807 21728 23577 25354 27059 28692 30252 31741 MR^ 4342 2425 2354 2281 2209 2137 2065 1994 1921 1849 1777 1705 1633 1560 1489 Pr. i .93 1.03 .85 .70 .66 .66 .70 .33 .25 .13 .32 .30 .25 .12 .03 M^ * Pr..^ 4038 2498 2001 1597 1458 1410 1446 658 480 240 569 512 408 187 45 Z =17546 =28232 miles km ------- 10 Other Useful Life Mileage Estimates The only other estimate of useful life mileage based on extensive survey or registration data was made by JAMA (Ref. 3) for motorcycle usage in Japan. The results of this survey are: 51 to 125 cc 15100 km 126 to 250 cc 21000 km >251 cc 24200 km The results, although higher for the small motorcycles and lower for the large motorcycles, compare favorably with the results obtained herein. The motorcycle manufacturers, in their comments to the ANPRM, typically suggested 20000 km for large motorcycles and 10000 km for the smaller motorcycles. These values for useful life mileage were not supported by significant data. Useful Life Age The average useful age for a motorcycle can be calculated from the age and probability of survival data. The useful life age is given by equation 4. CO ( Pr(t)dt 4) o or for one year intervals, 00 E PrjL 5) The useful life age is: 5.5 years 50 <^ cc < 170 7,3 years cc >^ 170 ------- 11 References 1. Motorcycle Industry Council "facts and figures", titled: "Distribution of Total New U.S. Motorcycle Registrations", (source: R.L. Polk & Co.). 2. Gallup Organization Inc., Survey of Motorcycle Owners, 1974, (Data processed by EPA from a tape of the survey results). 3. Japan Automobile Manufacturers Assoc. Inc., "A Survey Report on the Use of Motorcycles," December 1974. 4. R.L, Polk & Company, New Registration Data, 1967-1973. 5. Gallup OrganiEation Inc., "Survey of Motorcycle Ownership, Usage, and Maintenance", conducted for MIC, January 1975, pg 4. 6, "Ramification of Current Definition of Motorcycles and Determination of Useful Life for Motorcycles", William F. Pederson, Attorney OGC to Rodney W. Jenkins, Staff Assistant MSAPC, June 20, 1974. ------- Appendix I To determine the probability of survival, Pr^, the number of new registerable motorcycles sold per year needs to be known. These data are available only back to 1967. Therefore for years prior to 1967, an estimate based on other available data was made. The available data are: New first time registrations 1967-1973 Total U.S. registrations 1960-1973 plus 1953 The approach is to calculate, using the above data for 1967 to 1973, the percent of the registered population which fails to register the fol- lowing year. This is defined as the retirement rate of the population. The mean for 1967 to 1973 is calculated and used as an assumed retirement rate for 1966 to 1958. Thus the number of new registerable motorcycles for these years can be back calculated. The calculations are shown in the following table. The subscript refers to the year. Those values below the solid line are from calcula- tions containing assumed data. D.-. , the number of previously registered motorcycles not registered the next year is assumed to be the number of motorcycles retiring in year j . Dj is calculated from year j + 1 data since if a registered motorcycle retires in year j it will not be reflected until year j + 1 registration data. I j , the increase in total registrations per year, contains all new first time registered motorcycles minus those that retired. Thus for the years in which new registration data, N.S , is available, the retirement rate , %Dj, can be calculated. The calculation procedure is as follows: For 1967 to 1973 data - Ij = TJ - T.« i increase in total registrations Dj = NJ+I - Ij+i # retiring; N.+1 known %Dj = Dj/Tj For 1958 to 1966 data, back calculate assuming %Dj = .15 is a constant %Dj = .15 retirement rate assumed constant DJ = .15 * TJ i retiring Dj 4- Ij+i # new first time registrations NJ is then used as the number of new registerable motorcycles sold for years 1966 to 1958. ------- Table A-l Motorcycle Registration Data - All cc's Yeat ' 1973 72 71 70 69 68 67 66 65 64 63 62 61 , 60 59 58 T. = J N. = J V D. = 3 %D. = T. * 10 J 4353 3802 3345 2815 2316 2101 1953 1753 1382 985 786 660 596 575m 552 * 529 (D N. * 10 .1 1190 1006 928 751 550 437 287 587 545 317 225 153 107 106 102 total U.S. registrations as of I. A 10 J 551 457 530 499 215 148 200 371 397 199 126 64 21 23 23 D. A 10 5 J 639 549 398 252 335 289 87 207 148 118 99 89 86 83 79 t D. 1 Mean 15 5 . 15 ' 15 15 15 15 15 15 15 end of year, ref. 1 number of new first time registrations, ref. 4 increase in total registrations = T. - T., number of previously registered but not registered in year j : VT. V estimate based on linear change between 1960 and 1953 ------- Appendix II The method of converting the Gallup survey data to estimates of national population is accomplished as follows. Based on the estimated number of households in the U.S., the number of households owning motorcycles, and the number of motorcycles per household having a motorcycle, an estimate of the number of motorcycles in the U.S. is obtained. (Ref. 5) This includes all types of motorcycles except minicycles. # of motorcycles in U.S. as of June 1974 7,064,000 (+312,000) Weighted number of motorcycles in survey 9888 Conversion of weighted data to national estimate = 7,064,000/9888 = 714.40 In the useful life calculations, the responses to those people not having a working odometer or no odometer were excluded. This involves about 8% of the registerable population and thus the conversion factor must be corrected. The conversion factor used in projecting a nation- wide estimate (R^) from the Gallup data is: conversion factor = 714.40 * 1.08 * 771.6 and, R^ = (771.6) * (weighted responses) ------- |