car occupant life expectancy: car mass and seat belt effects

Risk Analysis, Vol. 2, No. 4, 1982

Car Occupant Life Expectancy: Car Mass and Seat Belt Effects

Leonard Evans' and Dennis E. Blumenfeld'

Received July 7, 1982; revised October 9, 1982

Average human life expectancies for the U.S. resident population are calculated using tabulated population and survival rate data. These life expectancies are recalculated assuming elimination of various types of motor vehicle fatalities using Fatal Accident Reporting System (FARS) data. The differences between the original and recalculated values provide estimates of life expectancy reductions due to the motor vehicle fatalities. These estimates are combined with prior work relating the likelihood of an occupant fatality to car mass, so that reductions in life expectancy are determined as a function of car mass. The estimates of life expectancy reductions are also used to determine the effect of seat belt use on life expectancy. The estimates, which are based on data for 1978, assume that survival rates remain unchanged. Estimates of the changes in life expectancy associated with switching from a large (1 800 kg) car to a small (900 kg) car, and switching from not using to using a seat belt are presented as functions of the age at which an individual makes the switch.

KEY WORDS automobile crashes; accident fatalities; automobile mass; seat belts.

1. INTRODUCTION

Previous studies have estimated how the relative likelihood of a driver or occupant fatality in motor vehicle crashes depends on car mass(') and seat belt use.(2) The purpose of the present work is to express such effects in terms of differences in longevity or, equivalently, differences in life expectancy. To fur- ther place the results in perspective, effects of pedestrian and motorcycle rider fatalities on longevity are also determined.

Some estimates of the effects of motor vehicle fatalities on longevity appear in the l i t e r a t ~ r e ( ~ * ~ ) in tables listing various life-shortening factors. As motor vehicle fatalities were only a small component of these studies, the separate effects of motor vehicle crashes have not been examined in detail, nor are

'Transportation Research Department, General Motors Research Laboratories, Warren, Michigan 48090.

numerical details of the calculations published. Here we present a calculation based on Fatal Accident Reporting System (FARS) data,(5) which allow a detailed study of the different types of motor vehicle fatalities.

2. REDUCTION IN LONGEVITY DUE TO MOTOR VEHICLE CRASHES

Reductions in longevity due to motor vehicle

1. Population data-U.S. Bureau of the Censud6)

2. Survival rate data-National Center for Health Statisticd7)

3. Fatal Accident Reporting System (FARS) data-National Highway Traffic Safety Ad- mini~tration(~)

All three sets of data used are for the U.S. in 1978.

crashes are determined using three sources of data:

259 0272-4332/82/1200-0259$03.~/lQ1982 Society for Risk Analysis

260 Evans and Blumenfeld

Table I. Average” Life Expectancies at Birth (Years)

Males Females All

Average life expectancy

Average life expectancy recomputed assuming (base case) 69.493 71.183 73.309

elimination of motor vehicle deaths to: All persons 10.332 11.544 13.932 car occupants 69.927 77.426 73.658 Car drivers 69.199 17.294 13.521 Pedestrians 69.615 11.245 13.405 Motorcycle riders 69.593 71.194 73.368

‘Average is over entire U.S. resident population (1918).

This year was chosen because the car mass versus fatality likelihood study(’) used 1978 FARS data. The first two data sources, which provide tabulations of population estimates and survival rates by age and sex, are used to calculate the average life expectancies at birth. The results are shown in the top row of Table I for the entire population and for males and females separately. These average life expectancies, which are well known but are independently calculated here to provide a consistent comparison frame- work, are referred to as the “base case.” The details of this and other longevity calculations are given in Appendix A.

The average life expectancies are then recalculated, using the FARS data on motor vehicle fatalities by age and sex to infer what life expectancy would have been if various types of motor vehicle fatalities had not occurred. These recomputed values are shown in Table I. The resultant increase in average life expectancy over the base case gives the expected increase in life expectancy due to eliminating the particular type of motor vehicle crash fatalities. For example, if all car occupant fatalities were eliminated, the average U.S. life expectancy would increase from 73.309 years to 73.658 years, a net increase of 0.349 years, or 127 days. This is essen- tially equivalent to the statement that car occupant fatalities reduce average life expectancy by 127 days.

By applying the same calculations, reductions in average life expectancy at birth due to various motor vehicle fatalities are derived from the values in Table I. These reductions are shown in Table 11.

Estimates of reductions in average life expectancy at birth due to all motor vehicle fatalities and to pedestrian fatalities are given in ref. 3, based on 1974 National Safety Council data. The estimates are in close agreement with those in Table I1 (207

days vs. 227 days, and 37 days vs. 35 days, respectively).

Schwing@) has shown that approximate estimates of longevity reduction can be obtained by simply multiplying the crude mortality rate by a given constant. Longevity reductions obtained from that approach are consistently lower than those gven in Table 11, by between 13% for male car driver fatalities and 35% for female pedestrian fatalities. The differences are not surprising given that motor vehicle fatalities preferentially affect young people to a greater degree than the various causes of death on which Schwing’s relationship is based.

Table I1 gives reductions in life expectancy averaged over the entire U.S. resident population due to various types of motor vehicle crashes. For example, if all motorcycle rider fatalities could be eliminated, the average U.S. life expectancy at birth would increase by 22 days. Naturally, the increase in life expectancy per motorcycle rider is much larger than this, since only a small fraction of the population are motorcycle riders.

Similarly, to determine the average reduction in life expectancy per car driver, we must divide the reduction in life expectancy averaged over the entire U.S. population by an estimate of the fraction of the

Table 11. Reduction in Average” Life Expectancy at Birth Due to Motor Vehicle Fatalities (Days)

Persons killed Males Females All

All 306 132 221 car occupants 158 89 121 Car drivers 112 41 80 Pedestrians 45 23 35 Motorcycle riders 3 1 4 22

“Average is over entire U.S. resident population.

Car Occupant Life Expectancy 241

Table 111. Reduction in Average Life Expectancy at Birth for a Carpriver (Days)

Males Females All

Reduction in life expectancy averaged over population (from Table 11) 112 41 80

Percent drivers 94% 75% 84% Reduction in life expectancy

per car driver 119 55 95

population who, at some stage in their lives, may be classified as drivers.

Such a calculation is shown in Table 111. The estimates of percent drivers in Table I11 were obtained from Highway Statistics(') which gives the percentages of the population of driving age that have driver licenses. We assume a steady state situa- tion in which these values are also estimates of the probability that a person just born will someday drive. We assume that 100% of the U.S. population may be classified as car occupants, so that average reductions in life expectancy due to car occupant deaths given in Table I1 over the entire U.S. population are also the average values per car occupant.

3. EFFECT OF CAR MASS ON LONGEVITY

The longevity reductions due to fatalities of car occupants (Table 11) and drivers (Table 111) depend on the mix of cars on the nation's roads in 1978. Prior work'') has shown that fatality likelihood depends on car mass. By combining the results in Tables I1 and I11 with the prior car mass results,(') the reductions in longevity due to using cars of different masses can be calculated, as discussed in detail in Appendix B. The results of the calculation are shown in Table IV, which gives estimates of reductions in life expectancy at birth due to motor vehicle fatalities for a car driver who drives exclusively throughout his life a car of the indicated mass.

The corresponding results for occupants are shown in Table V. The effects are necessarily larger for occupants than for drivers because an occupant may be either a driver or a passenger.

Note that the top row in Tables IV and V refers to the reduction in longevity averaged over the 1978 car fleet. This is close to (but not identical to) the reduction associated with the car of average mass for the 1978 fleet (1596 kg).

Table IV. Reductions in Average Life Expectancy at Birth for a Car Driver Who Drives Exclusively a Car of Indicated Mass

Reduction in average life expectancy driven at birth (days)

Car exclusively

Male Female All drivers drivers drivers

(Average values

1800 kg car 98 45 78 1400 kg car 132 61 106 900 kg car 194 89 155

Change from 1800 kg car to 900 kg car 96 44 17

from Table 111) ( 1 19) (55) (95)

Table V. Reductions in Average Life Expectancy at Birth for a Car Occupant (Driver or Passenger) Who Uses Exclu-

sively a Car of Indicated Mass

Car exclusively Reductions in average life expectany used at birth (days)

Male Female All occupants occupants occupants

(Average values from Table 11) (158) (89) ( 127)

1800 kg car 129 13 104 1400 kg car 175 99 141 900 kg car 257 145 207

Change from 1800 kg car to 900 kg car 128 12 103

The data in Tables IV and V refer to reductions in life expectancy at birth. Clearly, the reductions in life expectancy at older ages are smaller. Age depen- dence is included in the longevity calculations given in Appendices A and B. Expected change in driver life expectancy due to switching from exclusive driving of a 1800 kg car to exclusive driving of a 900 kg car is shown in Fig. 1 as a function of the age at which the driver makes such a switch. The curves do not decrease monotonically with age, but peak at the age at which individuals begin to drive. Correspond- ing information for an occupant who switches from exclusive use of an 1800 kg car to exclusive use of a 900 kg car is shown vs. age of occupant at the time of the switch in Fig. 2.

The reduction in longevity associated with switching to a smaller car decreases rapidly as the driver passes beyond the high accident risk years of the late teens and early twenties.

To place the reductions in life expectancy calculated here in perspective, some comparisons are shown


_ _ _ Males

Reduction i n Average Life Expectancy for a Car Driver (Daysi

I Females \-\,

Car Drivers

- - ......................... U' 1 I I I I I 1 I 1 I

0 10 20 30 40 u) 60 70 80 90 100

Age at which Swttch Occurs(Years)

Fig. 1. Reduction in average life expectancy for a car driver due to switching from exclusive driving of a car of mass 1800 kg to exclusive driving of a car of mass 900 kg, shown as a function of age at which switch occurs.

Redudion in Average U t e w e c t a n q for a Car Occupant (Days)

"I Males

Car Occupants

Age 1 which Switch -6 mars)

Fig. 2. Reduction in average life expectancy for a car occupant due to switching from exclusive use of a car of mass 1800 kg to exclusive use of a car of mass 900 kg, shown as function of age at which switch occurs.


Table VI. Reductions in Longevity Due to Various Factors

Reduction in average life expectancy

Factor (days) Source

{ EEdes Cigarette smoking

Heart disease

Car occupant fatalities: Average (1978 car fleet) Use of “small” car (900 kg) Use of “large” car (1800 kg) Switch from “large” car ( 1 800 kg)

to “small” car (900 kg)

2250

ref. 3 1300 900

127 Table V of this report

103

in Table VI with data on reductions in longevity due to other factors.(3)

4. EFFECT OF SEAT BELT USE ON LONGEVITY

The calculations of longevity reductions due to fatalities of car drivers can also be used to estimate the effect of seat belt use on driver longevity. Table V shows that, as a result of motor vehicle fatalities, a driver’s life expectancy at birth is reduced, on average, by 95 days. This result is an average for all drivers-males and females, seat belt users and non- users. If we assume that use of a seat belt reduces the

probability of a fatality by 50% (based on estimates in ref. 2), and that 14%(’’) of drivers in 1978 were users, it follows that the average life expectancy reduction due to driver fatalities for a nonuser driver is given by 95/( 1 - 0.5 X 0.14) = 102 days. The reduction in longevity due to car crashes for a user is half this value, 51 days. The decision to be always a user as compared to always a nonuser accordingly gener- ates an increase in life expectancy at birth equal to (102 - 5 1) days = 5 1 days. Corresponding calculations for males and females separately give 64 days and 30 days, respectively. In each case, the increase in life expectancy due to always wearing a seat belt is 0.5/( 1 - 0.5 X 0.14)X (reduction in life expectancy due to fatalities), assuming the same usage rate of 14%.

7 0 7 Males \ _---- \ \

All \ 60-

Increase i n Average Life Expectancy for a Car Driver (Days) 2o -

30 - . ...... ... ....... .

10-

0, I I I I 1 I I I I 1

0 10 20 3l 40 50 60 70 80 90 100

Age al which Driver Becomes a Seal Belt User, (Years)

Fig. 3. Increase in average life expectancy for a car driver due to becoming a seat belt user as a function of driver age.


Note that these life expectancy increases reflect averaging over the 1978 car mix. Occupants of smaller cars obtain larger benefits because of the higher fatality risks associated with smaller cars.

As in the analysis of car mass effects, the life increasing effects of changing from being a nonuser to becoming a user depend on the age at which the change is made, as shown in Fig. 3.

The curves in Fig. 3 are identical, within a scaling factor, to those in Fig. 1, in both cases being proportional to the reduction in driver life expectancy due to fatalities as a function of driver age. Figure 3 shows the large increase in average life expectancy due to seat belt use for drivers in the high accident risk years of the late teens and early twenties, and the rapid decrease in the benefit of seat belt use for ages beyond these years.

Note that the only seat belt benefit considered above is fatality reduction. Benefits due to injury prevention and reduction are not included. Use of a seat belt may make the difference between no injury and many years of disability-a possibility not re- flected in the above data.

APPENDIX A

Details of Calculation of Reduction in Average Life Expectancy Due to Motor Vehicle Crashes

Average life expectancy can be obtained from a basic characteristic of the population, the survival function, S ( a ) , defined as

S ( a ) = Probability that an individual survives to age a .

Note that S(0) = 1 by definition. We assume a steady state mortality rate; that is, the rate at which people of a given age die remains constant over time, and hence S ( a ) does not depend on time. It can be readily shown that the average life expectancy at birth, Lo, is given by

Equations A1 and A2 can be evaluated numerically from tabulated data giving values the survival function S ( a ) for different ages a.

The probability m(a, a + A a ) that an individual dies (from any cause) between ages a and a + Aa years can be obtained in terms of S ( a ) as follows: (Probability of surviving to age a + h a ) =

(Probability of surviving to age a )

X (Probability of not dying between

age a and a + Aa)

that is

S ( a + A a ) = S ( a ) [ l - m ( a , a + A a ) ] (A3)

Hence

(A4) S( a ) - S ( a + A a )

m ( a , a + A a ) = s ( 4

If a population at a given time contains P ( a , a + Aa) individuals between ages a and a + Aa years, then we expect

D ( a , a + A a ) = P ( a , a + A a ) - m ( a , a + A a )

(A51

of them will die within the next Aa years. Suppose that, of these D(a, Q + A a ) deaths, F(a, a + A a ) were fatalities in motor vehicle crashes. Then if such fatalities could be prevented, the number of deaths would be

D ’ ( a , a + A a ) = D ( a , a + A a ) - F ( a , a + A a )

(A6)

The reduced number of deaths, D’(a, a + Aa), results in a reduced probability of dying between ages a and a + Aa, m’(a, a + Aa), given by

m ’ ( a , a + A a ) = D ’ ( a , a + A a ) / P ( a , a + A a ) Lo = @x) dx (Al)

647) It can also be shown that the average life expectancy at age a, L(a) , is given by which in turn results in a changed survival function

(i.e., probability of surviving to age a ) , S‘(a), gven fmS(x) dx by

S’(a + h a ) = S ’ ( a ) [ l - m’(a , a + Aa)] (A8)


with S’(0) = S(0) = 1. The increased average life expectancy at birth that would result if fatalities in motor vehicle crashes cduld be prevented, LA, is then given by

LA = /mS’( x ) dx 0

and the increased average life expectancy at age a, L’(a), is given by

ImS’( x ) dx

The reduction in average life expectancy due to motor vehicle crashes is therefore

for the average life expectancy at birth, and

R ( u ) = L ’ ( u ) - L ( u ) (m for the average life expectancy at age a.

Equation (A7) above involves the assumption that the number of fatalities F(a, a + Aa) is suffi- ciently small that its effects on the number of individuals P ( a , a + Aa) in the population can be ignored.

Average life expectancies were calculated from data on the three quantities S ( a ) , P ( a , a + Aa), and F(a , a + Aa). Tabulated data on the survival function S ( a ) are given in ref. 7 and on resident population P ( a , a + Aa) in ref. 6, for the U.S. in 1978. The motor vehicle fatalities F(a, a + Aa) were obtained from the 1978 FARS data,(5) provided on tape by the National Highway Traffic Safety Administration. For each of the three quantities, the data are tabulated in one year increments of age (i.e., for ha = 1 year).

The tabulations for S ( a ) and P ( a , a + Aa) are given for ages a from 0 to 85 years. The probability of dying, m(a, a + Aa), for this age range was calculated using Eq. (A4). Values of the survival function S ( a ) for ages a greater than 85 years were obtained by assuming that the probability of dying m ( a , a + Aa) increased linearly with age a for a = 85 years and over, the rate of increase being determined by the average life expectancy, Lo, given in ref. 7. The population P ( a , a + Aa) for each age a beyond age a = 85 years was obtained by assuming that the combined population figure given for age 85 and over decreased with age a in proportion to the survival

function S( a). In the motor vehicle fatalities data, the number of fatalities for unknown age were distrib- uted among the different ages in proportion to the number of fatalities at each age; i.e., the number of fatalities F(a, a + Aa) were each multiplied by a constant factor so that the total number of fatalities excluding fatalities for unknown age was the same as the original total including such fatalities.

Table A1 shows the data for the population, P ( a , a + A a ) , the survival function, S ( a ) , and the motor vehicle fatalities, F( a, a + Aa), extended and adjusted as described above and also the quantities calculated from these three sets of data using Eqs. (Al) through (A12). The last three columns of Table A1 give, respectively: the average life expectancy at age a including motor vehicle fatalities, L ( a ) ; the average life expectancy at age a excluding motor vehicle fatalities, L’(a); and the difference between them, R ( a ) . The average life expectancies at birth, L, and LA, are given by the values of L (a) and L’( a) in the first row of Table A1 (i.e. for age a = 0).

The data for S(a) , P ( a , a + Aa), and F(a, a + ha) given in ref. 7, ref. 6, and FARS,”) respectively, also provide separate tabulations for males and females. The FARS data on motor vehicle fatalities, F(a, a + ha), are, in addition, broken down by type of person killed. Using these breakdowns of the data, separate calculations were made of the average life expectancies excluding motor vehicle deaths to car occupants, car drivers, pedestrians, and motorcycle riders, in each case for males and for females. The results of the calculations are given in Tables I and I1 of the main text.

APPENDIX B

Details of Calculation of Car Mass Effects on Longevity

In ref. 1 the relative likelihood, F( m), of a driver fatality in a car of mass m (m in kg) is expressed as

F ( m ) = 4.58exp( -0.000 764 m). (Bl)

The values given by Eq. (Bl) are relative to a value of one for a 1992 kg car, the heaviest of six car mass categories used in ref. 1.

By weighting Eq. (Bl) by the distribution of masses of cars in the 1978 car fleet, we determine that


the driver of the “typical” car in the 1978 car fleet was 1.42 times as likely to be killed as was a driver of a 1992 kg car.

ity by

R ’ ( m ) = (4.58 R/1.42)exp( -0.000 764 m ) Suppose that, due to motor vehicle crash fatali-

ties, driving the “typical” car in the 1978 car fleet = 3.23 Rexp( -0.000 764 m)

reduces longevity byR days. Then, driving a 1992 kg car will reduce longevity by R/1.42 days. More generally, driving a car of mass m will reduce longev-

where R’(m) is in days. Illustrative values calculated using Eq. (B2) with

R = 119, 55 and 95 days (the values in Table 111) and

Table AI. Quantities Involved in Average Life Expectancy Calculation

3203000 3160000 2962000 3039000 3013000 3083000 3287 000 3603000 3481000 3441000 3535000 349800 0 3624000 3845000

1.00000 0.98621 0.98528 0.98456 0.98399 0.98351 0.98310 0.98273 0.98240 0.9821 1

0. 0. 0 . 0. 0. 0. 0 . 0. 0. 0. 0. 0. 0 . 0. 0.

01379 00094 00073 00058 00049 00042 00038 0 0 0 3 4 00030 00025 00023 00023 00029 00041 00056

209 210 279 260 26 7 292

.2

.2

.6

.5

.6

.7

44169.4 2979.9

43960.1 2769.7

0.01372 0.00088 0.00064 0.00049 0 . 0 0 0 4 0 0.00032

1.00000 0.98628 0.98541 0.98478 0.98430 0.98391 0.98359

73.309 74.327 74.396 74.448 74.489 74.523 74.552 74.578 74.600 74.620 74.637

73.932 74.954

227 229

2164.5 1759.4 1469.8

1884.9 1498.9 1202.2 992.5

75. oi8 75.065 75.100 75.128 75.150 75.169 75.186 75.201 75.214 75.225 75.235 208 75.248 206 75.268 204 75.294 201 75.327 197 75.360 190 75.393 180 75.426 168 75.462 157 75.505 147 75.549 137 75.596 127 75.645 119 75.696 75.745 75.794 75.842 75.889 75.937 75.986 76.036 76.085 76.136 76.190 76.247 76.308 76.372 76.442 76.517 76.597 76.684 76.778 76.879 76.988 77.104 77.229 77.363 77.507 77.661 77.826 78.001 78.118 78.383 78.587

227 225 223 221 218

1285.2 334 298 253 232 222

. o

.7

.5

.4

1237.1 90S.i 1209.9 911.1 1027.6 774.1 875.9 643.6

0.00027 0.00025 0.00022 0.00019 0.00017 0.00016 0.00021 0.00031 0 . 0 0 0 4 4 0.00055 0.00055 0.00058 0.00058 0.00064 0.00077 0.00082 0.00089 0.00093

0.98332 0.98307 0.98285

216 214 212 21 1 209

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

0.98186 0.9816 3 0.98140 0.98112 0.98072 0.98017 0.97944 0.97855

. 3

.5

.6

. 1

.8

.8

.6

.8

.9

. 3

828.1 605.8 0.98267 0.98250 253

272 362 484

819.6 1034.0 1567.6 2292.0 3082.6 3784.7 4481.9 4824.8 5167.6 5528.3 5573.9 5474.8 5344.4

566.1 761.4

1205.5 1807.2

74.652 74.666 74.684 74.709 74.743 74.787 74.840 74.900 74.965 75.033 75.103 75.174 75.247 75.319 75,388 75.455 75.520 75.583 75.645 75.705 75.765 75.824 75.884 75.945 76.008 76.074 76.142 76.215 76.291 76.373 76.460 76.554 76.654 76.761 76.875 76.997 77.127 77.266 77.414 77.573 77.741 77.921 78.111 78.310 78.518

0.98234 0.98213 0.98183 4087000

4139000 4165000 4258000 4211000 4240000 4313000 4176000

0 . 0. 0.

00074 00091 00105

813 1476 2020 2385

2268.8 0.98139 2308.0 2461.1 2438.8

0.98085 0.98031 0.97974 0.97752 0.

0. 0. 0. 0.

~~~~~

00115 00122 00128 00133 00138 00138

0.97640 0.97521 0.97396 0.97266 0.97 132 0.96998 0.96865 0.96735

2452 2195 2147 1947

2715.2 3332.5 3426.4 3527.5 3609.3

0.97918 0.97855 0.97779 0.97699 0.97612 0.97521

.8

. 5

.4 3974000 3874000 3926000 378000 0 3635000 3594000 3473000 3477000 3675000 3751000

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 . 0 . 0. 0. 0 . 0. 0. 0. 0 . 0 . 0. 0 . 0 . 0 . 0. 0 . 0. 0. 0.

i735 .1 .5 .8 .2 .6 .1 .8 . 3 .8 .2 .9 .8 . 5 .4 .9 . 7 .8 .7 .7 .4 .4 .3 .4 .4 . 5 . 3 .2 . 3 . 5 .2 . 5 . 3 . 3

00137 00134 00132

1462 1338 1234 1128

5383.2 5073.0 4809.8 4687.5

3920.6 3734.2 3575.6 3558.9 3486.5 3558.0 3934.8 4206.2 3100.2 3339.3 3739.5 4318.3 4054.8 4225.6 4415.1 4772.7 5231.6 5600.2 6222.7 6767.5 7307.9 8161.2

10100.3 11780.0 12682.7 14156.1 15526.7 17197.7

20015.5 21197.9

8973.8

ia883.9

0.00100 0.00099 0.00098 0.00099 0.00100 0.00102 0.00107 0.00112 0.00113 0.00120 0.00129 0.00142 0.00151

0.97424 0.97328 0.97232

112 106 100 94

00130 0.96481 0.96355 0.96229

00131 00131 00132 00134

1049 4535.6 4546.7 4850.1 5035.1 3812.4 4007.2 4383.2 4913.8 4640.3 4728.6 4874.7 5248.5 5700.4 6065.9 6632.1 7185.0 7707.2 8565.6 9383.2

10520.8 12179.3 13065.0 14557 . S 15950.2 17581.9 19319.5 20411.8 21599.2

0.97I36 0.97038 0.96939 0.96835 0.96727

988 915 a28

89 85 81 77 73 69 66 63 60 58 55 52 50 47 45 4 3 41 39 37 35 34 32 31 29 28 27 25

0.96102 0.95973 0.95840 0.95702 0.95557

275100 0 2783000 2893000

00139 512 667 643 595 585 502 459 475 468 465 409 417 399 4 0 4 409 4 2 0 399 382 401 423 384 4 3 5 396 401

00144 00152 00161

0.96618 0.96502 0.96377 3049000

2683000 2530000 240 10 D O

0.95403 0.95238 0.95060 0.94867 0.94657 0.94427 0.94176 0.93900 0.93598 0.93268 0.92907 0.92512 0.92080 0.91608 0.91091 0.90526

0.89243 0.88527 0.87761

0.1~9910

ooi73 . . . . - . . 0.96240

00187 00203 00221 00243

0.00167 0.00184 0.00201 0.00223 0.00245 0.00275 0.00303 0.00334

0.96095 0.95934 0.95758 0.95565 0.95352

0.94857 0.94569

0.95iia

2346000 22820 0 0 2263000

00266 00293 00322 2234000

2186000 2213000 2207000

00353 00387 00425 00467

0.94253 0.93905 0.93524 0.93104 0.92643 0.92135 0.91580 0.90973 0.90313 0.89605 0.88844

0.00369 0.00407 0.00448 0.00496 0.00548 0.00603 0.00662 0.00726 0.00784 0.00848 0.00913

4 7 68 2S76000 49 2315000 50 2347000 51 2344000 52 2370000 53 54 55 -

2253000 oosij 00564 00620 00680 00742

2408000 2359000 2323000

00802 00865 00930


Table AI. Continued.

56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109 110

2332000 2239000 2252000 2095000 1975000 1889000 1864000 1873000 1834000 1810000 1755000 1715000 1723000 1574000 14880 0 0 1357000 1272000 1180000 1067000 973000 843000 847000 815000 693000 615000 582000 564000 523000 463000 321043 286579 253522 222251 193058 166156 141673 119664 100117 82962 68083 55327 44519 35466 27970 21835 16871 12900 9761 7308 5412 3965 2874 2059 1459 1022

218228000

0.869450 0.860750 0.851350 0.841080 0.829810 0 .a17440 0.804010 0.789660 0.774620 0 -759020 0.742920 0.726210 0.708730 0.690240 0.670560 0.649710 0.627720 0.604490 0.579920 0.553970 0.526710 0.498280 0.468900 0.438820 0.408320 0.377660 0.347120 0.316960 0.287470 0.259910 0.231116 0.204457 0.179237 0.155695 0.133999

0.096505 0.080741 0.066906 0.054906 0.044620 0.035903 0.028602 0.022557 0.017609 0.013606 0.010404 0.007872 0.005893 0.004365 0.003198 0.002317 0.001661 0.001177 0.000825

0.01001 0.01092 0.01206 0.01340 0.01491 0.01643 0.01785 0.01905 0.02014 0.02121 0.02249 0.02407 0.02609 0.02851 0.03109 0.03385 0.03701 0.04065 0.04475 0.04921 0.05398 0.05896 0.06415 0.06950 0.07509 0.08087 0.08689 0.09304 0.09935 0.10735 0.11535 0.12335 0.13135 0.13935 0.14735 0.15535 0.16335 0.17135 0.17935 0.18735 0.19535 0.20335 0.21135 0.21935 0.22735 0.23535 0.24335 0.25135 0.25935 0.26735 0.27535 0.28335 0.29135 0.29935 0.30735

375.2 369.2 398.3 353.1 388.3 335.0 393.3 329.9 311.8 350.0 301.8 328.9 345.0 285.7 311.8 286.7 298.7 278.6 252.5 258.5 206.2 243.4 259.5 196.1 198.2 174.0 136.8 148.9 130.8 116.7 82.5 73.4 51.3 40.2 37.2 12.1 21.1 11.1 9.1 6.0 2.0 3.0 0.0 0.0 0 . 0 0.0 0 . 0 0 . 0 0.0 0 . 0 0 . 0 0 . 0 0.0 0 . 0 0 . 0

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23334.8 24451.5 27166.3 28071.8 29441.4 31035.0 33268.7 35673.5 36934.8 38392.9 39474.0 41280.3 44951.2 44877.6 46267.0 45928.8 47072.8 47962.1 47745.6 47879.8 45502.2 49941.5 52282.4 48166.7 46179.2 47064.2 49003.9 48660.0 45998.8 34463.8 33056.8 31271.9 29192.5 26902.5 24482.9 22008.8 19547.0 17155.0 14879.2 12755.3 10808.2 9053.0 7495.8 6135.3 4964.2 3970.6 3139.3 2453.4 1895.2 1447.0 1091.9 814.2 600.0 436.9 314.3

22959 24082 26768 27718 29053 30700 32875 35343 36622 38042 39172 40951 44606 44591 45955 45642 46774 47683 47493 47621 45296 49698 52022 47970 45981 46890 48867 48511 45868 34347 32974 31198 29141 26862 24445 21996 19525 17143 14870 12749 10806 9049 7495 6135 4964 3970 3139 2453 1895 1447 1091 814 600 4 3 6 314

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0.00985 0.01076 0.01189 0.01323 0.01471 0.01625 0.01764 0.01887 0.01997 0.02102 0.02232 0.02388 0.02589 0.02833 0.03088 0.03363 0.03677 0.04041 0.04451 0.04894 0.05373 0.05868 0.06383 0.06922 0.07477 0.08057 0.08664 0.09276 0.09907 0.10699 0.11506 0.12306 0.13112 0.13914 0.14713 0.15526 0.16317 0.17124 0.17924 0.18726 0.19531 0.20328 0.21135 0.21935 0.22735 0.23535 0.24335 0.25135 0.25935 0.26735 0.27535 0.28335 0.29135 0.29935 0.30735

0.880335 0.871668 0.862293 0.852043 0.840770 0.828402 0.814938 0.800565 0.785459 0.769774 0.753595 0.736774 0.719181 0.700563 0.680715 0.659692 0.614061 0.637504

0.589247 0.563019 0.535464 0.506692 0.476962 0.446517 0.415608 0.384535 0.353554 0.322920 0.292968 0.263944 0.235706 0.208585 0.182917 0.158933 0.136819 0.116689 0.098572 0.082487 0.068362 0.056 109 0.045602 0.036695 0.029236 0.023057 0.017999 0.013907 0.010634 0.008046 0.006024 0.004462 0.003269 0.002369 0.001698 0.001203 0.000843

78.734 78.959 79.196 79.449 79.719 80.010 80.320 80.643 80.976 81.315 81.658 82.006 82.364 82.736 83.124 83.529 83.950 84.390 84.852 85.337 85.846 86.379 86.936 87.514 88.112 88.730 89.366 90.020 90.689 91.371 92.077 92.805 93.551 94.315 95.094 95.888 96.696 97.515 98.345 99.185

100.035 100.893 101.759 102.632 103.512 104.399 105.291 106.188 107.091 107.998 108.910 109 .826 110.745 111.669 112.595

78.800 79.022 79.256 79.505 79.774 80.061 80.368 80.689 81.019 81.356 81.696 82.043 82.399 82.768 83.155 83.559 83.978 84.417 84.876 85.360 85.867 86.399 86.954 87.530 88.127 88.743 89.378 90.031 90.698 91.380 92.084 92.811 93.556 94.319 95.098 95.891 96.698 97.516 98.346 99.186

100.035 100.893 101.759 102.632 103.512 104.399 105.291 106.188 107.091 107.998 108.910 109.826 110.745 111.669 112.595

24 23 22 21 20 19 18 17 16 15 14 13 13 12 1 1 1 1 10 10 9 8 8 7 7 6 5 5 4 4 4 3 3 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

m = 900, 1400, and 1800 kg are shown in Table IV of the main text.

If a driver were to switch from driving a 1800 kg car to driving a 900 kg car, his life expectancy would decline by

In the above R need not be confined to the average reduction in longevity at birth. It may repre- sent expected reduction in longevity at any age, which is available, as R(a), in the life expectancy calculation (see Table AI). Hence, to determine reductions in life expectancy as a result of a driver of age a transferring from a 1800 kg car to a 900 kg car we use Eq. (B3) with values of R = R ( a ) as determined by the method described in Appendix A.

3.23 R[exp( -0.000 764x900)

- exp( - 0.000 764 x 1 SOO)] = 0.81 R (B3)


In the above, we have assumed that Eq. (Bl), which was derived for all drivers, applies equally to both male and female drivers. To estimate the effect of car mass on occupant longevity, we now assume that Eq. (Bl), which was derived for one specific occupant, the driver, also applies to all occupants. The above assumptions are considered reasonable because Eq. (Bl) gives relative likelihoods vs. car mass. They are forces associated with changes in speed that largely contribute to the fatalities, and all occupants, regardless of sex or seating position, are subject to effects due to these changing with car mass.

Assuming Eq. (Bl) holds for car occupant fatalities, and that 100% of the population in the US. may be classified as car occupants, Eqs. (B2) and (B3) apply to car occupant longevity reductions with the values of R given in Table 11. Illustrative values are shown in Table V.

ACKNOWLEDGMENTS

We thank W. W. Meyer and R. C. Schwing, General Motors Research Laboratories, for helpful discussions.

REFERENCES

1 . L. Evans, Car mass an likelihood of occupant fatality, SAE Technical Paper No. 820807 (Society of Automotive Engineers, Warrendale, Pennsylvania, June 1982).

2. G. Grime, The protection afforded by seat belts, TRRL Sup- plementary Report 449 (Transport and Road Research Laboratory, Crowthorne, Berkshire, England, 1979).

3. B. L. Cohen and I-S. Lee, A catalog of risks, Health Physics 36,

4. S . H. Preston, N. Keyfitz, and R. Schoen, Causes of Death: Life Tables for National Populations (Seminar Press, New York,

5. A. A. Sebastian, Fatal accident reporting system, SAE Techni- cal Paper No. 810322 (Society of Automotive Engineers, War- rendale, Pennsylvania, February 1981).

6. U.S. Bureau of the Census, Estimates of the population of the United States, by age, race andsex: 1976 to 1979, Current Population Reports, Series P-25, No. 870 (Washington, D.C., January 1980).

7. National Center for Health Statistics, Vital Statistics of the United States, 1978, Volume ZZ, Section 5: Life Tables (US. Department of Health and Human Services (DHHS) Publica- tion No. (PHS) 81-1104, Hyattsville, Maryland, 1980).

8. R. C. Schwing, Longevity benefits and costs of reducing various risks, Technological Forecasting and Social Change 13,

9. Federal Highway Administration, Highway Statistics 1978 (U.S. Department of Transportation, Washington, D.C., 1979, p. 34).

10. Opinion Research Corporation, Highlights of four research studies: 1. safety belt usage among drivers (ORC Study No. 51495, Princeton, New Jersey 08540, prepared for National Highway Traffic Safety Administration, March 1980).

707-722 ( 1 979).

pp. 768-771, 1972).

333-345, (1979).

car occupant life expectancy: car mass and seat belt effects

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