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
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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
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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
>
/•"]
(-*'
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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,
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-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.
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-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
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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
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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
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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
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_i_4-!-:-U-i---i-U. - .- ..i
•.!.;-: p..;.. :_n. . i
O'.
CURMS" FIT
MifA/J MIL?/-..';:
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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
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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
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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
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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.
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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.
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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
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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)
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