The unformatted htm text below is from

Copyright © 2004 by Leonard Evans

Information about

How to purchase

Table of Contents



The text below is © Leonard Evans.  Portions totaling not more than 400 words my be freely used with appropriate citation.
For more extensive use, permission in writing must be first obtained by emailing the author 

11 Occupant protection

This  html version contains only the text (no figures, tables equations, or summary and conclusions) To check printed book appearance see pdf version of Chapter 1 or pdf version of Chapter 16.

Why people get hurt in crashes - basic biomechanics
Biomechanics is the science that provides a bridge between medicine and engineering. It examines relationships between injuries and the mechanical forces that produce them in traffic crashes. , Trauma surgeons use the terms penetrating trauma and blunt trauma to distinguish between injuries produced by different types of impacts. Penetrating trauma occurs when small objects exert sufficient localized force to penetrate the human body, obvious examples being knife or bullet wounds. Blunt trauma occurs when a force applied over a large area of the body is sufficiently great to damage the body's structure, such as occurs when someone falls from a height. Nearly all injuries to vehicle occupants or pedestrians are from blunt trauma.
Consider a hypothetical situation in which a completely rigid vehicle traveling at 50 km/h crashes head-on into a perfectly rigid immovable horizontal barrier. Assume that the vehicle stops on impact, and does not bounce back from the barrier. After the vehicle strikes the barrier, its occupants would, in accord with Newtonian mechanics, continue to travel at 50 km/h until impacted upon by a force. Occupants, if not otherwise restrained, would move forward out of their seats until they struck the interior of the now stationary vehicle at a speed of 50 km/h. This impact provides the force that changes their speed from 50 km/h to zero. The magnitude of the force depends on the degree to which the body compresses on impact. If the body compressed, say, 10 cm, the average force on it would be about 100 times that due to gravity (represented by 100 G). This is equivalent to the person being compressed under a weight of about 100 times his or her own weight for a brief period, and is likely to prove fatal. It is the collision of the occupant with the vehicle interior, the so-called second collision, that causes injuries, not the earlier first collision of the vehicle striking the barrier. A third collision has also been defined as the impact of internal organs with the structure of the body.
A person falling from a fourth floor window would strike the ground at a speed similar to that in the example above, and experience injury forces similar to those of the vehicle occupants if the ground were of a substance like concrete that did not compress much on impact. While evolution has provided humans with a protective fear of heights, no corresponding fear exists for the relatively new experience of traveling at speeds faster than can be produced by muscle power (page 192).
Goal of occupant protection
The reduction in speed divided by the time over which it takes place defines deceleration. Injury-producing forces are proportional to the deceleration experienced by the occupant. Occupant protection aims at reducing these forces by spreading the occupant's changes in speed over longer times. The theoretical best protection would be for the occupant to slow down from the initial vehicle speed to zero speed at a constant deceleration using the entire distance between the occupant's body and the vehicle's point of impact. In the previous example of an initial speed of 50 km/h, and assuming the driver is seated 2.5 m behind the front bumper, the resulting average deceleration would be 4 G, uncomfortable but unlikely to produce even a minor injury. The engine and other rigid components make it impossible to get close to this ideal. However, two approaches have led to major advances in occupant protection. These are vehicle engineering changes and occupant protection devices.
Vehicle design and occupant protection
In the hypothetical example the vehicle was completely rigid, the worst case for occupant protection. In fact, even without occupant protection considerations, it is not feasible to make a completely rigid vehicle - the structure is always going to crumple to some extent under severe impact. However, how it crushes is important for occupant protection. Consider two extreme possibilities. First,
the completely rigid case in the example. The occupant's seat stops instantly and the unrestrained occupant continues forward at a speed of 50 km/h until striking the vehicle interior. Now assume the other extreme in which all structure in front of the occupant offers no resistance and compresses offering less resistance than cotton candy. The occupant will continue moving forward in the normal seating position, unhindered until arriving at the barrier. The occupant will then be slowed from 50 km/h to stationery on impact with, in effect, the barrier. So, although the sequence of events is different, the outcome is the same - the occupant, traveling at the vehicle's prior speed, strikes a solid stationery object.
Vehicle crush characteristics between these two extremes substantially enhance occupant protection. For unconstrained occupants (those without airbags or safety belts) the goal is that impact with the vehicle interior should occur while the vehicle is still moving forward, thereby reducing the impact speed between occupant and vehicle interior. The remainder of the vehicle's slow down until stopped should be over as long a time as possible, which is achieved by designing the vehicle to be not too stiff (resisting crushing) or too soft (easily crushed).
Intensive research, including models taxing even the largest computers, has been devoted to designing vehicle structures that crush in ways that improve occupant protection. There is no single best design, not even in principle. Instead, there is a different best design for each impact speed. A design that provides the best protection at very high impact speeds will be stiffer than one that provides the best protection at lower impact speeds. Thus difficult trade-offs are unavoidable, especially between reducing severities of major injuries or severities of moderate injuries, which are far more numerous (Chapter 2) and therefore cause more societal harm.
While the structure in front of occupants should crush as much as possible in a severe crash, it is also important that occupants be protected in a strong compartment, referred to as a safety cage. The goal here is provide a survival space that helps prevent intrusion of other objects, such as the front of another vehicle in a side impact. A direct impact on the human body from an external object presents a particularly high risk. While the safety cage is designed to crush as little as is feasible, the remainder of the vehicle should contain crumple zones designed to crush in controlled ways.
One specific vehicle design change that reduces driver fatality risk by 6% is the collapsible steering column. In a frontal crash the chest of an unrestrained driver strikes the steering wheel, which, when sufficient force is applied, is designed to move forward because of a collapsible section included in the steering column. The driver's chest continues to move forward in contact with the steering wheel, rather than stopping more rapidly as would occur with a rigid column.
Padding on objects likely to be struck also increases the distance over which the occupant's speed changes.
Occupant protection devices
Devices designed for the specific purpose of reducing the occurrence and severity of injuries in crashes, as distinct from general improvements in the engineering of the vehicle, are referred to as occupant protection devices. These include safety belts, airbags, and helmets. Some devices are referred to as passive, meaning that they are supposed to provide protection without requiring any actions by road users, who need not to be aware of their existence. Active devices provide protection only when their users do specific acts, such as fastening safety belts or wearing motorcycle helmets. The term occupant restraint is often used in place of occupant protection device, which is fine for belts but hardly includes helmets.
Occupant protection devices spread the change in speed of occupants over longer times. For example, in the example of a car crashing into a barrier, a safety belt (also called a seat belt) would have applied forces keeping the body more fixed to the seat. The belt helps the occupant "ride-down" the crash, so that impact with the steering wheel or instrument panel is less likely or less severe. Safety belts also prevent occupants from being ejected from vehicles during crashes. An ejected occupant might travel outside the vehicle at close to the vehicle's pre-crash speed, continuing at that speed until stopped by striking something in the roadway environment.
Airbags are restraint systems consisting of a bag that inflates rapidly when sensors detect an abrupt change in vehicle speed indicative of a crash. For a frontal airbag this is typically a delta-v in the range 10 to 20 km/h. Instead of striking the steering column or instrument panel, the occupant rides down the crash in contact with the airbag, which additionally spreads the impact forces over a larger area. A belted occupant can receive additional protection from an airbag because it may reduce loading forces on the belt. The airbag is a supplemental system - it is designed to be used in conjunction with the safety belt.
Effectiveness definitions
The effectiveness of an occupant protection device is defined in general terms as the percent reduction in some specified level of injury (such as fatality) that would result if a population of occupants changed from all not using the device to all using it, all other factors remaining unchanged. Equivalently, effectiveness is the percent reduction in risk an average occupant obtains when changing from non-use to use, without otherwise changing behavior. Three distinct effectiveness measures must be considered:
1. Severity-specific effectiveness, defined as the percent reduction in injuries (in crashes of a specified type) at a specific severity, or within a narrow range of severities.
2. When-used effectiveness, defined as the percent reduction in injuries that occurs when the device is used, taking into account the mix of severities in traffic.
3. Field effectiveness, defined as the percent reduction in injuries taking into account the use rate for the device and the mix of severities that occurs in traffic.
The severity-specific effectiveness depends only on the particular crash type, on the engineering of the device, and on the biomechanical properties of the human body. The when-used effectiveness depends on the types and severities of crashes that occur in actual traffic. The term effectiveness most often means when-used effectiveness. Field effectiveness is identical to when-used effectiveness only when the device is always used. When the device is not used at all times, field effectiveness is less than when-used effectiveness. When-used effectiveness applies in general, because even nominally passive devices are not always used. Airbags may be disconnected or not replaced after deployment, and automatic safety belts may still not be fastened. The collapsible steering column is a truly passive device - most drivers are so unaware of its existence that it is generally considered more part of the vehicle engineering than an occupant protection device.
Concepts central to all occupant protection devices
Figure 11-1 illustrates basic concepts that apply to occupant protection devices in general. Crash severity, S, is a variable that increases with impact speed and could be, for example, delta-v as introduced in Chapter 2. For expository convenience the formalism is discussed in terms of driver fatalities and safety belts, although the concepts are equally applicable to any occupant, any protection device, and any injury level.

Figure 11-1. Schematic representation of how the risk of death might increase with crash severity for belted and unbelted occupants. The effectiveness is computed from the schematic risk curves using Eqn 11-2.

If fN (S) is the probability that an unbelted driver is killed in a crash of severity S, and fY (S) is the probability that a belted driver is killed, the ratio
depends on the protection provided by the safety belt. (The subscripts indicate use, Yes or No). The variable R has many desirable mathematical properties, including always being greater than zero, and providing easily computed errors in terms of the errors in fN (S) and fY (S). While calculations are in terms of R, there are advantages in presenting results in terms of the percent effectiveness, which, for the case of severity-specific effectiveness, is defined as
At very low severities, S < S1, there is essentially no risk of a fatality to a driver, whether belted or unbelted. As the probability of death without the belt is zero, the belt cannot reduce this probability further. Because fN(S) = 0 when S < S1, effectiveness is not defined in this low severity region.
As severity increases, it reaches a value S1 at which the probability that an unbelted driver is killed begins to exceed zero. Because the belt is designed to reduce risk, the probability that a belted driver is killed begins to exceed zero only at some higher severity S2. In the region S1 < S < S2 effectiveness is 100% because fY(S) = 0 but fN(S) > 0.
As severity increases further, it reaches a value S3 at which the probability of death to the unbelted driver becomes 100%, but the belted driver's risk remains less than 100%, leading to an effectiveness of 100[1- fY(S)]. Eventually severity reaches a value S4, at which even a belted driver's fatality risk becomes 100%, so that fN(S) = fY(S) = 100%, and effectiveness is zero. The bold curve showing the dependence of effectiveness on severity is mathematically derived from the assumed probabilities of death plotted for belted and unbelted drivers.
Laboratory evaluations of occupant protection devices tend to measure the severity-specific dependence at some chosen level of severity. As crash tests are difficult and expensive, the chosen level tends to be at a severity for which
the device was primarily designed. Tests are less likely to be conducted
at substantially higher or lower severities. Considerations such as these may have contributed to a history of disappointing field results relative to expectations based largely on laboratory tests, because in actual use there are likely to be many crashes at such extreme levels of severity that there is little opportunity for mitigation of injuries. In addition, a surprisingly large number of crashes are of a bizarre nature not readily encompassed in any laboratory-testing program.
When a crash is of such extreme severity that death cannot be prevented, then force reductions produced by occupant protection devices provide no benefits. In this regard, fatality is a unique level of injury, because for all other levels, reductions in forces lead to reductions in injuries. This general consideration suggests that the effectiveness of an occupant protection device is likely to be lower for fatalities than for injuries, though specific factors might lead to an opposite result.
An important inference from Fig. 11-1 is that the effectiveness of occupant protection devices decreases as severity increases. It is 100% at the lowest severities, and decreases monotonically to zero at the highest severities.
The above formalism does not apply in all respects to airbags. There is a designed threshold severity, SA, below which the airbag does not deploy. At severities just above the threshold, some occupants, such as short females, will be at increased risk, so that effectiveness is negative for them. Apart from the discontinuity at S = SA, airbags fit the pattern in Fig. 11-1.
Severity-specific effectiveness from data
The data used to produce Fig. 11-2 are the same NASS data used to produce Fig. 2-1 (p. 27). The belted drivers are wearing the integrated lap/shoulder belt system that became standard on all Model Year 1974 or later US cars. Some of the effectiveness values are negative because of noisy relationships resulting from small sample sizes (raw data from Ref. ). However, the data show effectiveness of belts for drivers declining with increasing severity, as expected from the theoretical considerations above.

Figure 11-2. The probability of fatality to unbelted and belted drivers estimated from the same data used for Fig. 2-1 (p. 27). The square symbols represent the effectiveness computed using Eqn 11-2.5 The open squares indicate insufficient data (less than 3 fatalities) to estimate an error in the effectiveness estimate.

Another example derived from data is given in Fig. 11-3 in which severity is measured using the Collision Deformation Code. This severity measure is based on a police officer identifying the best match between the appearance of the crashed car and a series of photographs of cars damaged in crashes of increasing severity. A declining effectiveness with increased severity is apparent. Effectiveness is determined with most precision at mid-range severities in Figs 11-2 and 11-3. At low severities there are few fatalities as risk is low, while at very high severities there are few fatalities because there are few crashes of very high severity (Fig. 2-1, p. 27).

Figure 11-3. Safety-belt effectiveness computed using Eqn 11-2 versus severity estimated by Collision Deformation Code. The open symbols indicate insufficient data (less than 3 fatalities) to estimate an error.5,
Difficulties in estimating safety belt effectiveness
The relationships in Figs 11-1 to 11-3 depend mainly on the engineering of the occupant protection device and the response of the human body to crash forces. They do not indicate the risk reduction the devices provide to populations that use them. If all traffic crashes were in the low severity region S < S2 , then the device would be 100% effective and the population using it would experience no fatalities. On the other hand, if all crashes were of severity S > S4 , then the device would have no effect on fatalities. The when-used effectiveness depends strongly on the distribution of actual severities that occur in traffic.
These distributions are known for the data used to produce Figs 11-2 and 11-3.5 The when-used effectiveness is the weighted average of the severity-specific effectiveness, with weights equal to the number of unbelted fatalities at each severity. This does not produce the most precise estimates of when-used effectiveness because of the high uncertainty of severity-specific effectiveness estimates at high and low severities. More precise estimates can be derived from the much larger samples in FARS data. Because FARS does not have a useful measure of severity, the when-used effectiveness is estimated by other means. Whatever methods are used to estimate when-used effectiveness, there are intrinsic problems regardless of the quantity of data available.
Miscoding of belt use
In Chapters 6 and 10 we encountered problems from incomplete coding of alcohol measurements in FARS, leading to many missing values. For safety belts there is an even greater problem. Belt use is coded, but incorrectly. If miscoding were random, it would not bias effectiveness estimates. However, it departs systematically from randomness in a way that creates major problems. After the first US law requiring belt use was in effect in 1984, survivors of crashes became motivated to tell police officers that they were belted when they were not. Police officers are inclined to accept questionable survivor self-reports, as the alternative is to issue belt-law violations at fatal-crash scenes where officers have more pressing duties. When belt use is coded, it is therefore biased for survivors, but not for fatally injured occupants. The old rule that "Dead men don't tell lies" leads to at least some of the data being unbiased.
Effectiveness is estimated by comparing the percent of belted occupants who survive to the percent of unbelted occupants who survive. Coding an unbelted survivor as belted inflates the belted survivors total, while at the same time depletes the unbelted survivors total. Thus, miscoding one survivor generates two misclassifications, each of them biasing effectiveness estimates in the same upward direction. The result is that even a small percent of miscoding inflates effectiveness estimates by substantial amounts. The effect of this bias is apparent in many publications that accept post-law data as valid and report implausibly high effectiveness estimates.
Other clear evidence of miscoding is provided by estimating the effectiveness of the same belt system at different times. (p 13) Effectiveness of belts in model year 1980-1985 cars was estimated at 47% using 1977-1985 FARS data, but
at 63% using 1986-1999 data. As it is implausible for the same belt system
to become more effective as it gets older, the large difference is likely due to data miscoding.
There are two approaches to the problem of miscoded data. First, use only pre-1984 data, as there was little reason to miscode in the pre-law era. While excluding post-law data leads to smaller samples, enough data remain for many evaluations. Second, attempt to correct for miscoding biases. An approach was developed in which a universal exaggeration factor was determined by examining how belt effectiveness estimates increased after belt laws were introduced.7 Basically, using the example above, a measurement of 63% was interpreted to be really 47%, and other measured values were multiplied by a factor of 63/47. Applying this made it possible to use the large quantities of post-law data. The disadvantage is that estimates do not follow directly from the data, and involve a scaling factor known only approximately. This largely precludes quantitative estimates of errors. In what follows we show mainly results derived directly from pre-law data, but augmented by some additional results based on inferences from post-law data.
When-used effectiveness of safety belts
When-used effectiveness of safety belts in preventing fatalities to drivers and right-front passengers of cars was estimated using FARS data for the pre-law years 1975-1983. Only cars of model year 1974 or later were included because all such cars came equipped with the integrated lap/shoulder system, also called a three-point belt system. Henceforth safety belt refers to this familiar system. Prior to model year 1974, lap and shoulder belts were generally separate, so that 'belted' could mean that one or the other, or both, were fastened.
The double pair comparison method was used. Following the procedures described in Chapter 6, data for cars containing, say, belted drivers as subject occupants and unbelted right-front passengers as control occupants, were extracted from FARS data, and the ratio of belted drivers killed to unbelted passengers killed was computed. From a second set of crashes, the ratio of unbelted drivers to unbelted right-front passengers was computed. From the ratio of these two ratios, the when-used effectiveness, E, of the belts was estimated. Henceforth, effectiveness means when-used effectiveness. The study used 711 belted driver and 716 belted right-front passenger fatalities, together with over 30,000 fatally-injured unbelted occupants. In the pre-law period observed belt use was about 14%, with use in fatal crashes even less.
The subject and control data were disaggregated into three age categories, and occupants in all car seats (front and rear, and in center seats) were used as control occupants. In using this method to estimate belt effectiveness it is crucial that the control occupant be disaggregated by belt use. If this were not done, then the control occupant accompanying a restrained subject occupant would be more likely to survive a crash than a control occupant accompanying an unrestrained subject occupant, in violation of the assumptions of the method, because belt use by one occupant in a vehicle is highly correlated with use by other occupants.
The combination of control occupants used led to 46 estimates of E. Computing weighted averages provided the following estimates of fatality- reducing effectiveness:
E = (42.1 ± 3.8) % for drivers
E = (39.2 ± 4.3) % for right-front passengers
The slightly higher precision of the driver estimate is due to larger sample sizes. Vehicles with no right-front passenger, but with rear or center-front passengers still provided belt-effectiveness estimates for drivers.
Fatality reducing mechanisms
Safety belts protect vehicle occupants in two ways; they prevent ejection, and they reduce the frequency and severity of occupant contact with the vehicle interior. The when-used effectiveness, E (percent), can be written as the sum of two components,
where J is the percent reduction in fatalities to an unbelted population if ejection were eliminated, assuming that those prevented from ejecting had the same fatality risk as those not ejected in similar crashes, and I represents the percent reduction in fatalities from preventing or reducing the severity of impact with the vehicle interior. The equation assumes that safety belts eliminate ejection, a more than adequately correct assumption for present purposes, even though the data in Fig. 3-13 (p. 51) show about 7% of fatally injured car drivers who were ejected were wearing belts.
The fraction of fatalities that would be eliminated if ejection were prevented was estimated by applying the double pair comparison method to 1975-1986 FARS data to estimate the ratio of the risk of death if ejected to the risk of death if not ejected. For drivers, the risk of death if ejected is 3.82 times the risk of death in the same crash if not ejected. The data showed that 25.3% of unbelted drivers who were killed were ejected. If these drivers had not been ejected, then J = (1 - 1/3.82) 25.3% = 18.7% of fatally injured drivers would not have been killed. Substituting this value into Eqn 11-3 gives that the interior impact reduction component of belt effectiveness is 23.4% (given that E = 42.1%). These values and their associated errors, together with the corresponding information for right-front passengers, are presented in Table 11-1. Almost half of the effectiveness of the lap/shoulder belt in preventing fatalities comes from eliminating ejection.
The reduction due to eliminating ejection is in good agreement with the 19% value derived from post-law data.7(p 32) The same data show that eliminating ejection from light trucks would prevent 32% of fatalities, a major contribution to the 60% overall effectiveness reported.7(p 28)
Effectiveness by direction of impact
Table 11-2 shows belt effectiveness by direction of impact, and the contribution to that effectiveness from eliminating ejection. Belts reduce fatalities for all principal impact points, much of the effectiveness being due to eliminating ejection. Much of the fatality reduction in rear impacts is from eliminating ejection. Similar effectiveness estimates are found in post-law data, where a 57% effectiveness is reported for rear impacts.7(p 28) The universal exaggeration factor used to rescale estimates based on post-law data assumed an unbiased effectiveness of 45%, somewhat higher than the 42% value used here. As a consequence, inferences from the post law data will tend to be about (45/42) = 1.07 times higher than if a reference value of 42% had been selected.
Belts are (77 ± 6) % effective in preventing driver fatalities in non-collisions, of which 63% is due to ejection elimination, leaving I = (14 + 6) %. Non-collisions normally imply rollover not initiated by striking a clearly identifiable object, such as a tree or other vehicle.
Table 11-3 uses 1978-1983 FARS data to estimate effectiveness in rollover crashes. Note the 82% effectiveness when rollover is the first event. The major portion of this, 64%, is from eliminating ejection. Belts reduce risk in all crashes involving rollover by 69%, with the major contribution from eliminating ejection. When no rollover is involved, 7% of belt effectiveness is due to ejection elimination.
Table 11-3. Belt effectiveness, E, and the contribution from ejection elimination, J, according to rollover status.11

Other factors
Because effectiveness depends on the mix of crashes it will be different for different sub-populations, depending on their use patterns. The dependence of effectiveness on a number of factors has been measured with the results summarized below.
Driver age. Effectiveness declines with increasing driver age, from about 50% in late teens to about half that value at age 80.7(p 36), , (p 235) As shown in Fig. 7-18 (p. 164), the percent of fatalities that are rollovers declines steeply as drivers age. Since belts are most effective at preventing fatalities in rollovers and the fatal crashes of older drivers tend not be to rollovers, it is to be expected that belt effectiveness will decline with increasing driver age.
Single- versus multiple-vehicle crashes. E = (62.2 ± 5.2) % for single-vehicle crashes compared to E = (29.5 ± 8.4) % for two-vehicle crashes. The post-law data gave 64% compared to 35%.7(p 18) The higher effectiveness in single-vehicle crashes is due to the larger contribution of rollover to single-vehicle crashes.
Two-door versus four-door cars. The estimates are E = (48.2 ± 6.1) % for two-door cars compared to E = (37.6 ± 9.9) % for four-door cars.14 This difference is consistent with the higher rollover rates of two-door cars (Fig. 4-2, p. 65).
Car mass. Two investigations using unrelated methods failed to show any clear
relationship between belt effectiveness and car mass.13(p 236),14, An analysis of post-law FARS data gives a weak indication that effectiveness was higher for the lightest vehicles,7(p 18) as did another study. The larger role of rollover in light-car crashes would contribute to higher effectiveness. Any mass effect is small, so, to a reasonable approximation, it can be concluded that belts reduce risk in light and heavy cars by about the same 42%. The absolute risk reduction is, of course, greater in the lighter car because of its higher risk to occupants whether belted or not.
Car model year. There are no discernable effects in the 1975-1983 FARS data.13(p 237) The same model year cars show higher effectiveness in post-law FARS, a clear indication of miscoding effects.
Driver compared to right-front passenger effectiveness. The pre-law results nominally indicate higher effectiveness for drivers than for right-front passengers (42%, compared to 39%). A larger difference of 48% compared to 37% is found in post-law data,7(p 34) and another study reports higher effectiveness for drivers.6 The evidence taken together supports that belt effectiveness is higher for drivers than for right-front passengers.
Other levels of injury. The above has focused exclusively on fatalities. All the technical problems that make it difficult to estimate fatality effectiveness apply also for injury effectiveness estimates. Injury data have additional limitations, making estimates additionally uncertain. There are many estimates of belt effectiveness for injuries, especially using post-law data. They vary from values much higher than for fatalities to values much lower than for fatalities. In the aggregate, estimates tend to be similar, but perhaps somewhat higher, than fatality estimates. Percent changes in injuries after passing belt laws are in some cases higher and in other cases lower than the percent changes observed for fatalities.

Effectiveness of other occupant protection devices 

While the integrated lap/shoulder belt in front seats is the occupant protection system providing the most benefit to the most people, other occupant protection systems make important contributions to reducing fatalities.
Lap-only belts in rear seats
Prior to the mid 1980s the normal occupant protection system in the rear seats of cars in the US was a lap-only belt. A study to estimate the fatality-reducing effectiveness of this system confronted sample sizes sharply reduced by lower occupancy rates, lower fatality risks, , and lower wearing rates. In order to obtain usable sample sizes, the 1975-1983 data used to estimate front-seat belt effectiveness was augmented by FARS data for 1984 and 1985. The inclusion of some immediate post-law data was considered a less serious problem than
for front seats because rear-seat occupants were not covered by the early belt laws, and biasing effects are less important in the context of estimates with much lower precision. The study found that lap-only belts reduced fatality
risk of passengers seated in rear outboard seats (left and right, but not center)
by (18 ± 9) %.
A later study using post-law data to estimate effectiveness for lap-only and lap/shoulder belts in rear seats reported substantially higher effectiveness than (18 ± 9) % for lap only belts. However, the results are likely biased substantially upwards by miscoding in post-law data.
Prior to the study that found (18 ± 9) % effectiveness,17 the most widely accepted estimate was that lap-only belts reduced fatality risk by 30 to 40%. The lower than expected effectiveness led General Motors to announce in June 1986 that it would install lap/shoulder belt systems in rear seats of all its passenger vehicles. Ford and Chrysler later announced similar policies. Later, lap/shoulder belts were required by NHTSA regulations. Prior to these changes there were some vehicles (mainly from Europe) on US roads with rear seat shoulder belts.
A further study examined the portion of the effectiveness that was due to ejection elimination, with the results
E = (18 ± 9) % (when-used effectiveness).
J = (17 ± 1) % (contribution from eliminating ejection).
I = ( 1 ± 9) % (contribution from reducing impact with interior).
The results indicate that the effectiveness of the lap-only belt derives almost entirely from eliminating ejection from the vehicle. A similar estimate of E = (17 ± 8) % was reported in another study using similar methods and data.
Rear seat belts not only protect rear-seat passengers - they also protect front-seat occupants by reducing the risk of direct impacts from unrestrained rear passengers and by reducing the loading forces on the backs of front seats. The phenomenon has been called "the flying mother-in-law effect." Two studies found that the presence of an unrestrained rear occupant increases the risk to an unrestrained front-seat occupant by 4%. , When the front-seat occupant is restrained, the risk increase from the unrestrained rear occupant is 20%.25 A published study contains the following: "The risk of death of belted front-seat occupants with unbelted rear-seat passengers was raised nearly five-fold." This absurd result is another sad reflection of the way that traffic-safety research has not developed professional structures parallel to those in the traditional sciences to keep nonsense out of professional literature.
Motorcycle helmets
Helmet effectiveness in preventing fatalities to motorcycle drivers and passengers was estimated by applying the double pair comparison method to FARS data for 1975-1986. Motorcycles with a driver and a passenger, at least one being killed, were used. In order to reduce as much as possible potentially confounding effects due to the dependence of survivability on gender and age, the analysis was confined to male drivers (there were insufficient female driver data), and to cases in which the driver and passenger age did not differ by more than three years. It was found that helmets are (28 ± 8) % effective in preventing fatalities to motorcycle riders, the effectiveness being similar for male and female passengers, and similar for drivers and passengers. By applying essentially the same method to 1982-1987 FARS data, another study obtained a near identical effectiveness estimate of 29%.
A motorcyclist not wearing a helmet is 31 times as likely to be killed as a car occupant for the same distance of travel, based on 2001 data. Because of the 28% effectiveness of the helmet, for the same distance of travel, a motorcyclist who wears a helmet is only 22 times as likely as a car occupant to be killed. A helmeted motorcyclist is more likely to be killed than an unbelted drunk driver traveling the same distance in a small car.
Motorcycles have traditionally been associated with young males, inspiring the quip, "Buy your son a motorcycle for his last birthday." Motorcycle fatalities in the US increased from 2,055 in 1997 to 3,126 in 2002, a more than 50 percent rise in five years. What is most remarkable about the increase is that the major component is from drivers older than 35, who registered a more than 100% increase from 738 deaths in 1997 to 1,491 deaths in 2002. In both periods 89% of all motorcyclists killed were male drivers, the remainder being passengers and female drivers. The reduction in helmet wearing rates, from 63% in 1994 to 58% in 2002,37(p 9) contributed, but only modestly, to the increased fatalities. The main factor was an increase in older motorcyclists. The 753 additional deaths of male motorcycle drivers over 35 years old in 2002 compared to 1997 exceed the total number of annual traffic fatalities in many countries. Sweden, for example, had a total of 554 traffic fatalities in 2001.
Motorcycles in the US are used primarily for recreation rather than transportation, underlining the role of non-transportation motives in traffic safety discussed in Chapter 9. For all the vehicles on the roads of the US, the average crash risk is one crash per 12 years. Most of these involve just property damage or no more than minor injury. This is because of the inherent stability of vehicles with more than two wheels, and the protection provided by the safety cage and the vehicle structure. A helmeted motorcyclist is at high risk of serious injury when involved in any type of crash, and an unhelmeted motorcyclist is at even higher risk. The Highway Safety Act of 1966 prohibits the agency that is now NHTSA from recommending the banning of any category of vehicle on the grounds of safety. Although improvements in protection for motorcyclists in crashes are already incorporated in motorcycles, and additional improvements are always being sought, there seems no possibility that motorcycle riding can ever be other than an extremely high-risk activity relative to other risks in traffic.
NHTSA has produced a series of estimates of the effectiveness of frontal airbags in reducing driver fatality risk using two methods of analysis. The first considered crash-involved cars equipped with driver airbags but without passenger airbags. Although this combination was not generally produced after the mid 1990s, the cars with it remained in service and were available for analysis for many subsequent years. The ratio of driver fatalities to passenger fatalities was compared to the corresponding ratio for earlier similar cars with no driver airbags, thus providing a measure of the effect of the airbag. The second approach used the ratio of drivers killed in frontal crashes to drivers killed in non-frontal crashes for cars with and without airbags. As airbags are designed to deploy only in frontal crashes, this ratio estimates effectiveness. Both methods provided consistent estimates. The average values from both methods appear in the first row in Table 11-4. The same method produced the values published in 2001 shown in the second row.

Table 11-4. Airbag effectiveness estimates.

The third row shows results of a study published in 2002 that estimates the effectiveness of driver airbags by taking advantage of the increasing availability of passenger airbags. Vehicles containing a driver and a right-front passenger, at least one being killed, were selected from FARS 1990-2000 data. Many of the model year 1987-2001 vehicles included in the study had a driver airbag but no passenger airbag. These cases provided the core information to estimate effectiveness of driver airbags. Vehicles, which had no airbags, or airbags for both the driver and passenger, provided data to control for other driver-passenger differences in risk, unrelated to risk changes associated with driver airbags. Because there are no vehicles with passenger airbags but without driver airbags, the method cannot estimate airbag effectiveness for passenger air bags. The results, shown in row 3 of Table 11-4, are consistent with the NHTSA estimates to within the published errors.
All the studies summarized in Table 11-4 estimate airbag effectiveness for belted and unbelted drivers. Miscoding of belt use has no more than a modest influence on the airbag effectiveness estimates. Indeed, the method which compares frontal to side fatalities uses only fatalities, for which belt use is considered to be correctly coded.
The combination of safety belt plus airbag cannot be estimated using pre-law data, as there were few airbags until the 1990s. However, it can be estimated by considering a population of cars without airbags driven by unbelted drivers. Assuming that this population experiences 100 driver fatalities, the number of deaths that would have occurred if all the cars had airbags, or if all the drivers were belted, can be estimated as shown in Fig. 11-4. The result is that the effectiveness of the belt plus airbag combination is 47%. At zero belt use, the airbag prevents 12 of the original 100 deaths, whereas at 100% belt use the airbag prevents 5 of the original 100 fatalities. The next chapter will be devoted to more on airbags because of the central role they have played in US safety policy.
Figure 11-4. An initial population of drivers in cars without airbags sustains 100 driver fatalities. The figure shows the revised numbers of fatalities that would have occurred if different occupant protection scenarios had been in effect.

Summary of effectiveness estimates
The estimates derived here are summarized in Table 11-5. There are other occupant protection devices not listed, mainly because quantitative estimates parallel to those presented are not available, usually because evaluation is even more difficult than it was for the devices shown. There is copious evidence that bicycle helmets reduce risk, probably by an amount not substantially different from that shown for motorcycle helmets. Fatalities to bicyclists are included in FARS only if they occur in a crash involving a vehicle with an engine. FARS for 2002 records 662 bicycle fatalities compared to 3,126 motorcycle fatalities. There are many types of infant and baby seats with much evidence supporting that they provide major risk reductions in crashes. Effectiveness of airbags in light trucks is similar to that for cars.32
Estimating field effectiveness
If when-use effectiveness of a device is E, but no one uses it, then field effectiveness is zero. If everyone uses it, then field effectiveness is identical to when-used effectiveness E. For any active occupant protection device, the percent of users is always between these extremes, and estimating field effectiveness presents a number of problems.
Naive calculation
If a fraction, ui, of random members of a population consisting exclusively of non-users were to convert to using a device, the fractional reduction in casualties, F, that would result is
This will reduce an original N casualties to a new lower N (1 - Eui) casualties. If at some later time the use rate increases to a new value, uf, then the fractional reduction in casualties compared to the already lowered number is
where Du, the increase in use, is given by
These equations estimate far larger casualty reductions than are observed. The reason is that the assumption that users are random members of the population is grossly in error.
Selective recruitment
This term refers to the phenomenon that those who become users of an active occupant protection system are not recruited randomly from the population of non-users. Instead, users differ from non-users in many ways that influence safety. Two effects are:
1. When non-wearers crash, they have more severe crashes.
2. Non-wearers are more likely to crash.
Crash severity and belt use
Figure 11-5 shows the percent of crash-involved drivers who were belted versus the severity of their crashes. The two graphs use the same measures of severity and data used to produce Figs 11-2 and 11-3. Both graphs, despite the different periods, driver populations, and severity measures show consistently that the more severe the crash, the less likely is the driver to be belted. The very drivers most in need of protection when crashes do occur are the very ones least likely to wear belts.

Figure 11-5. The more severe the crash, the less likely the driver is to be belted. The different absolute belt use rates reflect different periods when overall use rates were different (post-law on left plot, pre-law on right).5,6
Crash risk and belt use
If the effectiveness of belts in preventing fatalities is known, a number of inferences can be made from FARS data. Calculation details are given below because the approach has applications beyond the present case of inferring belt use in crashes. The inferences use only data for fatally injured occupants, for which belt-use coding is fairly reliable.
Inferring crash risks of unbelted relative to belted drivers from FARS data.  Table 11-6 shows fatalities to drivers of cars (body type 1-10) killed in daytime crashes (6:00 am to 7:59 pm) from FARS 2002. Only drivers coded as either unbelted or using the lap and shoulder belt system are included.
It is helpful to introduce the notion of a set of potentially lethal crashes, defined as a set of crashes by unbelted drivers in which 100 unbelted drivers are killed. If all the drivers had instead been belted, then 100 (1 - E) belted driver fatalities would result. The number of potentially lethal crashes by unbelted drivers, CN is proportional to the number of unbelted fatalities, KN. For convenience, we take the constant of proportionality to be unity, so that CN = KN for unbelted drivers. For belted drivers

where KY is the observed number of belted fatalities, and CY is the inferred number of potentially lethal crashes by belted drivers. The total number of potentially lethal crashes, CTOTAL, is given by
Dividing the number of crashes by belted drivers by the number of crashes by all drivers defines an inferred belt use rate in severe crashes, uINFERRED, given by
A finding that uINFERRED is lower than the belt use rate estimated by roadside observations, uOBSERVED, implies that unbelted drivers are crashing at greater rates than belted drivers. It can be shown that
Substituting the observed daylight wearing rate for car drivers of 78% in 2002, , (p 4) and the inferred wearing rate of 67.6% into Eqn 11-11 gives that, for all crashes, unbelted drivers have crash risks 70% higher than those of belted drivers. For single-car crashes, for which the higher effectiveness E = 62% is used, the result is that unbelted drivers have single-car crash risks 114% higher than those of belted drivers. This fits the pattern discussed previously (p. 164-166 and in Chapter 10 on alcohol) that any driver risk-increasing factor will be more prevalent in single-vehicle than in multiple-vehicle crashes.
Empirical values of R. The two values of R derived in Table 11-6 appear in the first two rows of Table 11-7. The other rows show seven previously published R values.35 Three use FARS 1975-1983 data. The driver fatality value was estimated using the calculation described above with uOBSERVED = 14%, a belt use rate that remained stable during the pre-law period covered by the data. Miscoding makes it impossible to use post-law FARS data to obtain estimates based on drivers involved in crashes killing pedestrians or motorcyclists. For example, FARS 2002 codes 1,672 belted and 238 unbelted drivers involved in crashes in which pedestrians were killed but the driver was uninjured. These data nominally imply an implausible 88% wearing rate, and therefore provide clear evidence that unbelted drivers are claiming to be belted.
The last four rows in Table 11-7 are from studies (described in Chapter 13) in which approaching cars were photographed on Michigan roads. - For all cases in Table 11-7 unbelted driver involvement rates are 28% to 114% higher than those for belted drivers. The tendency for the values relating more to single-vehicle crashes to be higher than the values relating to multiple-vehicle crashes is another illustration of risk-increasing behavior having a larger impact on single-vehicle crashes.
Calculating fatality reductions from increased belt use
The higher crash risks of unbelted compared to belted drivers suggests a continuous relationship between propensity to not wear belts and crash risk. Consider all the drivers in a population rank ordered from the most to the
least willing to wear a belt. Conceptually, belt wearing might increase continuously from 0% to 100% in response to varying rewards and punishments. Increasing punishments for not wearing would result in belt-wearing by drivers with ever-increasing reluctance to wear - and correspondingly ever increasing risk of crashing.
Let us assume that a driver's crash risk can be represented by
where r is a variable increasing from 0 to 1, reflecting the driver's rank ordered willingness to wear a belt and c0 is the risk for the safest driver. The safest driver is the most willing wearer with r = 0, and the least willing wearer has r = 1. While a number of exponents were explored analytically, the data presented below show that N = 2 is an appropriate choice. To simplify subsequent equations we let b = 3l, where l is a parameter to be determined from data, so that Eqn 11-12 becomes
At a given population belt use rate, u, all the drivers with r < u will be wearers, and all with r > u non-wearers. Integrating Eqn 11-13 gives
The bottom 7 items in Table 11-7, which have an average value R = 1.53, were all for a belt use rate of 14%. Substituting R = 1.53 and u = 0.14 gives l = 0.47. For u = 0.78, Eqn 11-14 gives R = 1.65, compared to 1.70 and 2.14 in Table 11-6. The value of R computed by Eqn 11-14 varies relatively little (from a minimum of 1.47 at u = 0 to a maximum 1.65 at u = 0.77) because with increasing belt use, numerator and denominator both increase. As u increases the average risk of the non-user population increases as it loses its safest drivers, while the average risk of the user population also increases as riskier drivers join it. Of course, the average risk of the entire population goes down as belt wearing increases.
The above equations allow us to express the percent reduction, F, in fatalities when belt use increases from ui to uf as
where Du = uf - ui is the increase in belt use rate. Substituting l = 0 reproduces the naive Eqn 11-5. If belt use is initially zero and increases to 100%, substituting ui = 0 and uf = 1 gives F = E, the definition of when-used belt effectiveness. Below we always use l = 0.47, and generally E = 0.42.
I have previously reported an equation producing results identical to those of Eqn 11-15. The earlier equation was derived by a similar approach to that used here, but the present derivation is more direct and simple leading to a simpler equation. 41,13(p 258)
Selective recruitment is expected. Eqn 11-13 with l = 0.47 (and r = 1) indicates that the crash risk of the most reluctant belt wearer is 2.41 times that of the most willing, a result to be interpreted in terms of populations rather than individuals. The individual highest risk driver has a crash risk above that of the safest driver by a much larger factor. Unwillingness to wear a belt is an unhealthy behavior, and individuals showing one unhealthy behavior are more likely to exhibit other unhealthy behaviors, leading one to expect non-wearers to have higher crash risks. When belt laws apply, non-wearers violate traffic law. Violators of one traffic law are more likely to violate other traffic laws, so it would be surprising if non-wearers did not have crash rates substantially higher than those of wearers. Selective recruitment is to be expected, and it would be remarkable if it did not occur.
Fatality changes compared to zero belt use
A simple case is estimating fatality reductions at a given belt use rate compared to zero wearing. This is obtained by substituting ui = 0 so that Eqn 11-15 simplifies to
which is plotted in Fig. 11-6. Also shown as a dashed line is the linear reduction in fatalities that would occur in the absence of selective recruiting. The data points are all inferred from FARS data using the approach in Table 11-6, except that data are not restricted to daytime hours. The bullet symbols are published estimates based on 1988 and earlier FARS data when belt wearing rates were lower. ,13(p 269)

Figure 11-6. Calculated reductions in driver fatalities when belt use increases from 0 to ui. The curve is Eqn 11-16 and the dashed straight line is the naive calculation ignoring selective recruitment. The points are calculated from FARS data for individual years for which the belt-use rate was measured.

It should be stressed that the data are not directly observed fatality reductions, but inferences from fatalities. The inferences use the same effectiveness as in the equation to plot the curve, so there is some circularity in the process. Also, points are plotted at the observed daytime belt use rate37(p 4) even though the rates averaged over the whole day are lower. Using only daytime fatalities runs into a problem because the when-used effectiveness is estimated using data for the entire day. Direct comparison with observed reductions is not possible because no jurisdiction has ever had a zero belt use in the "before" period of a before/after study, so that fatality reductions from an initial zero use cannot be measured directly. Changes in fatalities have been measured after belt wearing laws generated abrupt increases in wearing rates, thus providing actual fatality reductions that can be compared with the predictions from Eqn 11-15.
Belt wearing laws
Safety belts were first introduced into automobiles in the 1950s based on solid biomechanical understanding that they would reduce risk in crashes. Even though belts of some type were being installed in most of the world's new vehicles by the 1960s, wearing rates were low in all countries, and it seemed they would remain low unless wearing was required by law.
The first mandatory belt wearing law in a jurisdiction with a substantial driver population came into effect on 22 December 1970 in Victoria, a state in Australia. (Malawi and the Ivory Coast had formally included belt wearing in their legal statutes, but not otherwise acted.) In 1971 belt use increased in Victoria from about 15% to about 50%, and a reduction of about 12% in deaths to affected occupants (drivers and left-front passengers) was reported. Substituting ui = 0.15 and uf = 0.50 into Eqn 11-15 gives F = 12.2%, the first entry in Table 11-8. The closeness of the agreement between the two is fortuitous given the uncertainties in the observed fatality change and belt use rates, and in the equation.

Table 11-8. Comparison of fatality reductions estimated by Eqn 11-15 with observed reductions from introducing mandatory belt wearing.

Influenced by reports of casualty reductions from the Victoria law, many jurisdictions eventually passed belt wearing laws. Such laws are in place in all US states except New Hampshire, in all Canadian provinces, in all Australian states, and in nearly all of the world's countries.
Switzerland provides a particularly interesting case, because the law that became applicable in January 1976 was repealed by voter petition in July 1977 but became effective again after October 1977.13(p 268) The following changes in fatalities were recorded:
- after law first passed fatalities decreased
- after law was repealed fatalities increased
- after law reinstated fatalities decreased
A review of 33 US studies found that US belt laws in various US states reduced fatalities by a median 9%, and injuries by a median 2%. The laws were found to increase belt use by a median 33%. If one assumes that the laws increased belt use from pre-law rates of 14% to post-law rates of 47% (a reasonable average for the extended period covered by the studies), substituting ui = 0.14 and uf = 0.47 into Eqn 11-15 gives F = 11.2%.
The UK's belt wearing law
The belt wearing law that came into effect on 31 January 1983 in the UK has three factors favoring effective evaluation that are not available for any other jurisdiction. First, belt use was closely monitored at 55 traffic census sites operated by the Department of Transport, generally from 8:30 am to 4:30 pm, before and after the law came into effect. Second, a large increase in belt use occurred in a few months, from about 40% to about 90%. Third, the UK, with over 16 million cars in 1983, provides one of the largest populations of occupants affected by a single law.
Despite uniquely favorable conditions, evaluating the UK's law has not been without difficulties or controversy. There were claims that the increased safety provided by belts encouraged drivers to take more risks, thereby reducing the safety benefits to the drivers while increasing risks to other road users. The simplest evaluation, a count of casualties in an 11-month period before the law to an 11-month period after the law showed a 23% reduction in fatalities and a 26% reduction in serious injuries to occupants covered by the law. Because of claims that such reductions could be due to other concurrent changes, the Department of Transport invited two outside distinguished statisticians to examine the monthly time series of casualties to various road users. They found an 18% fatality reduction for drivers and a 25% reduction for front-seat passengers, together with fatality increases to rear-seat passengers, pedestrians and bicyclists. In the much larger sample of injuries they found larger injury reductions to occupants covered by the law without systematic increases to those not covered. The extensive well-documented discussion (printed after their paper) is uninhibited by the politeness that often does such disservice to the search for truth in the US.
Additional evidence of the efficacy of the law was provided by a 15% reduction in traffic crash patients brought to hospitals, a 25% reduction in those requiring admission to wards, and a similar fall in bed-occupancy. Larger reductions are found for front-seat passengers than for drivers. I suspect that some front-seat passengers migrated to rear seats rather than wear belts, which explains reduced front-seat casualties and increased rear-seat casualties.
There were additional evaluations,13(p 262-265) justifying a consensus view that the law reduced fatalities to covered occupants by about 20%, and that the increases in pedestrian and bicycle fatalities with no corresponding increase in injuries were probably spurious effects in small samples (see also p. 301). Substituting ui = 0.40 and uf = 0.90 into Eqn 11-15 gives F = 26.5% (Table 11-8). The lower observed than computed reduction likely reflects that nighttime wearing rates were lower than the observed daytime 90% rate, and that the crashes of unbelted drivers were of higher severity.
Primary and secondary laws
Laws requiring belt use are of two types. Primary laws allow police officers to stop drivers based solely on an observed safety belt violation. Secondary laws allow officers to enforce the belt law only if the driver is first stopped for some other violation. In 2002, eighteen states in the US had primary laws. An analysis of direct observations of belt use in 2002 and inferences from fatalities as described above finds that the change from secondary to primary enforcement increased daytime belt use rates from 70% to 83%. Substituting ui = 0.70 and uf = 0.83 into Eqn 11-15 gives F = 9%.
Calculating fatality reductions from increased belt use
The complexity of evaluating even the UK law shows how much more difficult it is to measure casualty reductions reliably in other jurisdictions which have fewer vehicles and do not experience large rapid changes in belt use when laws are passed (or strengthened). A real fatality reduction of, say 4%, represents an important safety benefit, but is essentially impossible to measure directly in the face of total fatalities changing for so many other reasons.
I believe the best approach available to estimate fatality changes that cannot be observed directly is to use Eqn 11-15. This equation incorporates a coherent interpretation of many of the key effects relevant to how changes in belt use rates affect casualties, and it fits reasonably well available observed changes in casualties from large changes in belt use.
One of the many derivations that can be made from Eqn 11-15 is shown in Fig. 11-7, which shows the percent reduction in fatalities that would result if belt use rate increased by 5%. The relationship computed from the naive Eqn 11-5 is also shown. It is not a straight line because even when selective recruitment is ignored and the same percent increase in belt use always produces the same absolute reduction in fatalities, the initial number of fatalities becomes less with increasing belt use.
If belt use is zero, increasing it by 5% reduces fatalities by only 1.4% because the first 5% of drivers to use belts will be the safest drivers. However, if belt use is 95%, increasing it by 5% reduces fatalities by 5.5%. The higher the belt use rate, the greater is the benefit of increasing it further by the same amount. One might refer to the effect as the law of increasing returns.
Benefits of belt laws
Many decades of experience with belt-use laws shows that after they are passed, use increases, but then generally declines from its immediate post-law peak. The pattern typical of US states was an increase from under 20% in the pre-law period to about 50% immediately after passage, but then dropping to about 40%. Rates increase in response to increased enforcement and additional law changes, especially the change from secondary to primary enforcement. Rates also increase in response to persuasion in media messages, and a general incorporation of belt use into the social norm. In Canadian provinces, use rates were typically 50% some time after laws were passed in the mid 1970s, but have increased in response to various measures to around 90%.
While Eqn 11-15 estimates different fatality reductions dependent on initial belt use rates, a fatality reduction is always estimated to result from an increase in belt use. Any measure that increases belt use is expected to reduce fatalities. When use rates are already high it becomes more difficult to increase them further, but the benefits of doing so also increase. Adopting primary laws and enforcing them vigorously will prevent many deaths.
Repeal of mandatory motorcycle helmet wearing laws
Following the Highway Safety Act of 1966, the US Federal Government made passage of mandatory helmet wearing laws for motorcycle drivers and passengers a precondition for the states to receive highway construction funds. All but three states passed such laws. In 1976, in response to pressures from many states, the US Congress revoked the financial penalties for non-enactment of helmet wearing laws. In the next few years, just over half of the states repealed their laws; half repealing and half not provides the optimum "natural experiment" to compare repeal and non-repeal states.
Each point plotted in Fig. 11-8 estimates the increase in motorcyclist fatalities in an individual state. This was computed by comparing the number of fatalities after repeal to the number before repeal to this same ratio for all the states that left their wearing laws in place. The numbers along the horizontal axis give the states ordered by date of repeal, from 21 May 1976 for Rhode Island to 1 January 1982 for Louisiana. There are 27 data points for 26 states because Louisiana repealed its law, then passed another, which was subsequently also repealed. Nominally, 24 of the points indicate that fatalities increased after repeal, compared to 3 indicating a decrease, so the data provide extremely strong evidence that repeal led to a substantial increase in fatalities. The weighted average of all 27 values is (25 ± 4) %.

Figure 11-8. Change in motorcyclist fatalities in US states after 27 helmet wearing laws were repealed. Plotted from data in Ref. 54, which names the states.

Wearing rates (night and day) were estimated for drivers at 88% in states with laws compared to 42% for states without laws.13(p 272) Substituting E = 28, ui = 0.88 and uf = .42 into Eqn 11-15 gives F = -18%. The corresponding calculation for passengers, with use rates of 80% in law states compared to 23% in no-law states, gives F = -19%. The predicted increases of 18% and 19% are somewhat lower than the observed increase of 25%. It has been speculated that wearing laws discouraged some motorcycle travel, an effect which would amplify fatality changes when laws were passed or repealed. Eqn 11-15 was of course derived for safety belts, and is applied to motorcycle helmets because there is little possibility of deriving a corresponding equation based on motorcycle data.
Occupant-protection issues
The history of occupant-protection devices and laws requiring their use has included technical errors and much controversy. There were many early estimates of belt effectiveness based on comparing the percent of driver fatalities who were belted to the percent of drivers who were unbelted. Such calculations led to published effectiveness estimates as high as 90%, which in turn generated predictions of large reductions in casualties from increases in belt use. The failure to observe such reductions gave rise to much speculation, including the claim that drivers were negating the benefits of belts by increased risk taking.
Do drivers using occupant protection devices change their behavior?
This question has a very easy and certain answer, namely yes. However, neither this question nor its answer is of much importance. The two important questions are
1. In what direction - more risk or less risk?
2. By how much?
The answer to the first question is not known. Note that this question refers to changes in behavior when an individual driver fastens a belt, and should not be confused with the unrelated finding that non-users have higher crash risks than users, because that comparison is between different drivers.
One can provide a more substantive answer to the second question, namely, not much. The reason is that the agreement of so much data with Eqn 11-15 is sufficiently good to preclude the possibility of any additional large effect. The possibility that drivers might drive substantially more carelessly because of the additional protection a belt provides cannot be dismissed as unreasonable, but it is rejected by data.
It is of course certain that the act of wearing a belt does influence driver behavior to some degree because of the universal principle that anything of which we are aware affects our behavior. The act of fastening might reduce crash risk by reminding drivers that there are risks associated with driving, or increase risk because of reduced harm expected if a crash were to occur. Data collected in a test-track experiment suggested that the same drivers increased speed by about 1% when belted compared to when unbelted. Any actual small speed increase would reduce the effectiveness of belt wearing laws, and could contribute to the general tendency for observed reductions to be somewhat less than predicted.
It was claimed that the UK belt wearing law led drivers to take increased risks in traffic, which killed more pedestrians and other road users.48 The small samples of fatality data did indeed indicate increases. However, no other reports have associated increased pedestrian or other road user casualties with increased belt wearing. FARS data would be suitable for such investigations. Belt use rates can be inferred as in Table 11-6 for 50 states each year since 1975, so an enormous data pool is available to examine pedestrian fatalities relative to changes in belt use rates. While I would not attach high priority to such a study, it has more value than many studies that are performed.
Are there cases in which occupant protection devices kill?
This is another question with an easy and certain answer, namely yes. It requires no data to prove it - logic suffices as the following analogy establishes. Every year a number of pedestrians walking on the sidewalk are killed by out-of-control vehicles. These are cases in which walking on the sidewalk led to death, while walking in the center of the fastest traffic lane would have been safer (well, certainly not less safe). We choose the sidewalk not because it is always, under all circumstances, safer, but because it is, on average, safer. The same reasoning applies to all measures that reduce risk, including use of safety belts.
In many cases those killed do indeed receive their injuries from safety belts. A naive interpretation might be that the belt therefore killed the occupant. The more likely situation can be explained in terms of many people falling from different heights onto a concrete surface, resulting in many deaths. If a mattress were placed on top of the concrete, fewer deaths would occur. However, an examination of the fatalities and injuries would find that 100% of them had been caused by severe contact with a mattress.
While the above general principles apply, the specific situation remains that in a severe crash a belted occupant may receive injuries of a different type, and in different parts of the body, than would have occurred without the belt. In some cases the injuries might be more severe than without the belt. When a belt injury occurs it is generally difficult to estimate what the outcome would have been, absent the belt. Fractures of the sternum and sprained necks appear to have increased following the British belt wearing law.51 Tharaco-lumbar spine injuries and serious cervical spine injuries increased following the French belt law. The injuries that increased in frequency might be substitutes for more serious injuries if no belt had been worn. Part of the effectiveness of airbags is through reducing injuries from safety belts.
The effectiveness of a device being say, 12%, means that a population of non users that sustained 100 deaths would have sustained 12 fewer deaths if all members of the population had been users. It does not mean that 12 of the original 100 people killed would have survived, while 88 of the original 100 killed would still have died. In principle, the device could save every one of the original 100, but kill a different 88 who would have survived without it, still giving 12% effectiveness. Effectiveness measures the difference between deaths with and without the device, but does not convey information about deaths that could have been caused by the device.
There are occasional claims that unbelted occupants landed uninjured in haystacks after being ejected from vehicles in which they would otherwise have perished. Some non-wearers state such anecdotes to justify not wearing. Ejection increases the probability of being killed by a factor of 3.8. Occasional good outcomes from ejection are as inevitable as occasional good outcomes from walking in the middle of the road. It is imprudent to let either influence behavior.
There is one occupant protection device that is of a different nature from the others. Airbags inject additional energy into the crash event that may cause harm that would not otherwise occur. NHTSA reports that, as of July 2003, there were 231 confirmed deaths caused by airbag deployments in crashes that would otherwise not have been life threatening.
Objections to occupant protection laws
Laws requiring the use of safety belts and helmets differ in a fundamental way from those against speeding and drunk driving. There is near universal agreement that governments have a high priority duty to protect citizens from being harmed by the actions of others. However, people not using occupant protection devices increase risk to nobody but themselves (except for the possibility of the small effects discussed above). Claims that wearing a belt helps a driver better control a vehicle in an emergency are not supported by any evidence, and seem to be grasping at straws to avoid the problem addressed in this section. The claim that motorcycle helmets increase crash risk by restricting peripheral vision is more plausible, but still unconvincing.
The fact that non-wearing hurts no one except the non-wearer has inspired objections to wearing laws, especially of motorcycle helmets, on the grounds that government has no right to restrict a citizen's right to do things that do not harm others. However, non-wearing does impose costs on others. All motorized societies have medical systems that treat those injured regardless of how they got injured. Non-participation is not an option. One cannot conceive of a contract in which a person would accept personal responsibility for not wearing a belt or helmet by agreeing to forgo medical attention if involved in a crash. Not only would this be ethically difficult, but it would also be impossible to administer. Non-wearers consume additional medical and rescue resources, making such resources possibly unavailable to others needing help. The belt-wearers who pay part of the many additional costs imposed on them by non-wearers are being merely prudent in using the legal system to coerce non-wearers into wearing. This is a question legitimately decided by the political process, and can be addressed without bringing up any issue of government paternalism. If the voters are willing to subsidize skiers and rock climbers, but not non-wearers, this is their legitimate choice. They are under no obligation to avoid sensible policies just to fit some critic's notion of consistency. Quantitatively, the costs imposed by belt and helmet non-wearers are enormous compared to those imposed by all the other subsidized risk takers.
Advances in safety belt technology
There have been ongoing efforts to improve the performance of the lap/shoulder belts installed in all 1974 and later model year vehicles. The two most specific advances are pretensioning devices, which pull belts snug as a crash begins, and load limiters, which allow belts to yield slightly during a crash to reduce the risk of injuries from the belt. Approximately 63 percent of model year 2002 cars and light trucks had pretensioners, and 84 percent had load limiters. These are shown to reduce forces on anthropometric dummies in laboratory tests in which vehicles crash into barriers.
While such changes are expected to provide reduced risk in actual crashes, it is not possible to measure the differences from field data. This should be clear in the light of the problems of determining effectiveness for the entire vehicle population. Statistical uncertainty is not the only problem, but it presents a major hurdle. The overall belt effectiveness is (42 ± 4) %, so that if the population were divided into two equal subpopulations, the uncertainty in the estimate for each would be about 6%. Thus it would be difficult to observe any difference between the populations unless it exceeded 10%, an unrealistic expectation. Similar comments apply to attempts to address differences in the effectiveness of the belts in vehicles from different manufacturers. The best one can do is to rely on engineering inference and judgment. However, the earlier comments about how laboratory tests tend to overestimate field effects should be kept in mind.
Are more accurate and more precise estimates of belt use possible?
The (42 ± 4) % estimate for the effectiveness of belts in reducing car driver fatality risk is based on pre-1984 FARS data, and therefore on cars of model year 1984 or earlier. In the time that has elapsed since then, does additional information suggest a higher or lower value? There are two reasons to suspect that the true effectiveness might have been a little lower. First, even after taking into account selective recruitment, reductions in fatalities have still tended to fall short of predictions based on 42% effectiveness. Second, before belt wearing laws, belt wearing was considered socially desirable. Many surveys found that the percent of respondents who claimed to always wear belts far exceeded the percent observed actually wearing them. A small tendency for unbelted survivors to indicate that they were belted even before non-wearing was illegal seems probable. The technical improvements in belts have likely increased effectiveness, perhaps to close to the 42%. NHTSA uses a slightly higher effectiveness of 45%. Although the difference between the two is smaller than anything that can be measured, I consider the lower estimate provides a marginally better general fit to what is known.
The introduction of Event Data Recorders offers the possibility of more accurate and more precise estimates of belt effectiveness. Because of the need to determine whether or not to deploy an airbag, tens of millions of vehicles on the roads by 2003 already had such devices. They record many variables including the pre-crash speed and whether a belt was worn. Belt wearing is based on sensors in the belt system, so that there is the potential to provide, for the first time, substantial quantities of objective data on belt use by surviving occupants. Questions of privacy and ownership of data have precluded (at time of writing) the use of the data for research purposes.
Theoretical limits of crash protection
Before 1905 the question: "What is the theoretical fastest speed an object can travel?" would have produced a different answer than would be given today. In the earlier period the answer would likely start by stressing that while there is no theoretical limit, all sorts of engineering and other constraints place practical limits on attainable speeds. Today the answer would likely start by stating that no matter what is done, it is not possible to travel faster than the speed of light.
There is a somewhat analogous theoretical barrier which occupant protection cannot penetrate. The limit flows from the fact that the forces on occupants in vehicles that crash cannot be made less than limits dictated by physical laws. Consider a driver sitting 2.5 meters from the front bumper of a car that crashes head-on into an immovable hard barrier. The theoretical safest situation would be for the driver to decelerate at a constant rate over the entire 2.5 meters, arriving in contact with the barrier at zero speed. If the car's speed is v km/h, then the value of the constant deceleration is v2/635 G, where G is the deceleration due to gravity. For v = 252 km/h the result is 100 G, a value which some literature indicates is the limit the human body can withstand.3 While 252 km/h is not of much relevance in normal traffic safety, there are nonetheless 19 car models available in the US claiming higher top speeds. The assumption that the driver arrives at the barrier rests on the quite implausible assumption that the engine and other components in front of the driver compress to zero thickness. Any more realistic assumption will indicate a much lower maximum survivable speed. There are indications that some individuals can withstand forces well in excess of 100 G, leading to higher estimated maximum survivable impact speeds.
The example is given to show that there is a theoretical limit, even if it cannot be reliably estimated. Crashes can be of such high severity that it is impossible to make them survivable, even in principle. A main reason why many spectacular high-speed crashes by racing cars are survived is because the vehicles come to rest over very long distances and extended times. It is the reduction in speed over long distances that provides the spectacular pictures. Unsurvivable crashes are not spectacular. From the beginning to the end of the crash the vehicle travels a meter or so. The crash lasts about one tenth of a second, which to the unaided eye appears instantaneous.

Summary and conclusions (see printed text)

References for Chapter 11Numbers in [ ] refer to superscript references in book that do not correctly

 show in this html version.  To see how they appear in book see the pdf version of Chapter 1.

 [1] Naahum AM, Melvin JW, editors. Accidental Injury: Biomechanics and Prevention. New York, NY: Springer-Verlag; 1993.

[2] Mackay GM. A review of the biomechanics of impacts in road accidents. In: Amrosio JAC et al., editors. Crashworthiness of Transportation Systems: Structural Impact and Occupant Protection. Netherlands: Kluwer Academic Publishers; 1997, p. 115-138.

[3] Crawford H. Survivable impact forces on human body constrained by full body harness. Report prepared for UK Health and Safety Executive. Report HSL/2003/09; September 2003.

[4] Kahane CJ. Evaluation of current energy-absorbing steering assemblies. SAE paper 820473. Warrendale, PA: Society of Automotive Engineers; 1982. (Also included in Occupant Crash Interaction with the Steering System. SAE special publication SP-507; 1982, p. 45-49).

[5] Evans L. Safety-belt effectiveness: The influence of crash severity and selective recruitment. Accid Anal Prev. 1996; 28: 423-433.

[6] Campbell BJ. Safety belt injury reduction related to crash severity and front seated position. J Trauma. 1987; 27: 733-739.

[7] Kahane CJ. Fatality reduction by safety belts for front-seat occupants of cars and light trucks: Updated and expanded estimates based on 1986-99 FARS data. Report DOT HS 809 199. Washington, DC: US Department of Transportation, National Highway Traffic Safety Administration; Dec. 2000.

[8] Evans L. The effectiveness of safety belts in preventing fatalities. Accid Anal Prev. 1986; 18: 229-241.

[9] Evans L. Double pair comparison – a new method to determine how occupant characteristics affect fatality risk in traffic crashes. Accid Anal Prev. 1986; 18: 217-227.[10] Evans L, Frick MC. Potential fatality reductions through eliminating occupant ejection from cars. Accid Anal Prev. 1989; 21: 169-182.

[11] Evans L. Restraint effectiveness, occupant ejection from cars and fatality reductions. Accid Anal Prev. 1990; 22: 167-175.

[12] Evans L. Airbag effectiveness in preventing fatalities predicted according to type of crash, driver age, and blood alcohol concentration. Accid Anal Prev. 1991; 23: 531-541.

[13] Evans L. Traffic Safety and the Driver. New York, NY: Van Nostrand Reinhold; 1991.

[14] Evans L, Frick MC. Safety belt effectiveness in preventing driver fatalities versus a number of vehicular, accident, roadway and environmental factors. J Safety Res. 1986; 17: 143-154.

[15] Evans L. Fatality risk for belted drivers versus car mass. Accid Anal Prev. 1985; 17: 251-271.

[16] Partyka SC. Belt effectiveness in passenger cars by weight class. In: Papers on Car Size – Safety and Trends. Report DOT HS 807 444. Washington, DC: National Highway Traffic Safety Administration; June 1989, p. 1-35.[17] Evans L. Rear seat restraint system effectiveness in preventing fatalities. Accid Anal Prev. 1988; 20: 129-136. (Also see Evans, L. Rear compared to front seat restraint system effectiveness in preventing fatalities. SAE paper 870485. Warrendale, PA: Society of Automotive Engineers. (Also included in Restraint Technologies – Rear Seat Occupant Protection. SAE special publication SP-691; 1987, p. 39-43).[18] Evans L, Frick MC. Seating position in cars and fatality risk. Am J Pub Health. 1988; 78: 1456-1458.

[19] Smith KM, Cummings P. Passenger seating position and the risk of passenger death or injury in traffic crashes. Accid Anal Prev. 2004; 36: 257–260.[20] Morgan C. Effectiveness of lap/shoulder belts in the back outboard seating positions. Report DOT HS 809 945. Washington, DC: US Department of Transportation, National Highway Traffic Safety Administration; June 1999.

[21] National Highway Traffic Safety Administration. Final regulatory impact analysis, Amendment of FMVSS 208, passenger car front seat occupant protection. Washington, DC; 11 July 1984.

[22] Evans L. Restraint effectiveness, occupant ejection from cars, and fatality reductions. Accid Anal Prev. 1990; 22: 167-175.

[23] Kahane CJ. Fatality and injury reducing effectiveness of lap belts for back seat occupants. SAE paper 870486. Warrendale, PA: Society of Automotive Engineers; 1987. (Also included in Restraint Technologies: Rear Seat Occupant Protection. SAE special publication SP-691; 1987, p. 45-63).

[24] Park S. The influence of rear-seat occupants on front-seat occupant fatalities: The unbelted case. General Motors Research Laboratories, Research Publication GMR-5664; 8 January 1987.

[25] Cummings P, Rivara FP. Car occupant death according to the restraint use of other occupants: A matched cohort study. J Am Medical Assoc. 2004; 291: 343-349.

[26] Ichikawa M, Nakahara S, Wakai S. Mortality of front-seat occupants attributable to unbelted rear-seat passengers in car crashes. Lancet. 2002; 359: 43-44.

[27] Evans L, Frick MC. Helmet effectiveness in preventing motorcycle driver and passenger fatalities. Accid Anal Prev. 1988 ;20: 447-458.

[28] Wilson DC. The effectiveness of motorcycle helmets in preventing fatalities. Report DOT HS 807 416. Washington, DC: National Highway Traffic Safety Administration; March 1989.

[29] National Highway Traffic Safety Administration. Traffic Safety Facts 2001. Report DOT HS 809 484. Washington, DC: US Department of Transportation; December 2002.

[30] International Road Traffic and Accident Database (OECD) (2001).

[31] Kahane CJ. Fatality reduction by air bags: Analysis of accident data through early 1966. Report DOT HS 808 470. Washington, DC: National Highway Traffic Safety Administration; 1996.

[32] National Highway Traffic Safety Administration. Fifth/Sixth Report to Congress: Effectiveness of occupant protection systems and their use. Report DOT HS 809 442. Washington, DC: US Department of Transportation; November 2001.

[33] Cummings P, McKnight B, Rivara FP, Grossman DC. Association of driver air bags with driver fatality: A matched cohort study. Brit Med J. 2002; 324: 1119–1122.[34] Evans L. Human behavior feedback and traffic safety. Hum Factors. 1985; 27: 555-576.

[35] Evans L. Belted and unbelted driver accident involvement rates compared. J Safety Res. 1987; 18: 57-64.

[36] Glassbrenner D. Safety belt use in 2003. Report DOT HS 809 646. Washington, DC: US Department of Transportation, National Highway Traffic Safety Administration; Sept. 2003.

[37] Glassbrenner D. Safety belt and helmet use in 2002 – Overall results. Report DOT HS 809 500. Washington, DC: US Department of Transportation, National Highway Traffic Safety Administration, September 2002.[38] Von Buseck CR, Evans L, Schmidt DE, Wasielewski P. Seat belt usage and risk taking in driving behavior. SAE paper 800388. Warrendale, PA: Society of Automotive Engineers; 1980. (Also included in Accident Causation. SAE special publication SP-461; 1980, p. 45-49).

[39] Evans L, Wasielewski P. Risky driving related to driver and vehicle characteristics. Accid Anal Prev. 1983; 15: 121-136.

[40] Wasielewski P. Speed as a measure of driver risk: Observed speeds versus driver and vehicle characteristics. Accid Anal Prev. 1984; 16: 89-103.

[41] Evans L. Estimating fatality reductions from increased safety belt use. Risk Analysis. 1987; 7:


[42] Partyka SC, Womble KB. Projected lives savings from greater belt use. Washington, DC: National Highway Traffic Administration Research Notes; June 1989.

[43] Andréasson R. The Seat Belt: Swedish Research and Development for Global Automotive Safety. Sweden, Uppsala: Claes-Göran Bäckström; 2000.

[44] Trinca GW. Thirteen years of seat belt usage – how great the benefits. SAE paper 840192. Warrendale, PA: Society of Automotive Engineers; 1984. (Also included in Restraint Technologies: Front Seat Occupant Protection. SAE special publication P-141; 1984, p. 1-5).[45] Grimm AC. International restraint use laws. Ann Arbor, MI: University of Michigan Transportation Research Institute. UMTRI Research Review. 1988; 18: 1-9.

[46] Andreassend DC. Victoria and the seat belt law, 1971 on. Hum Factors. 1976; 18: 563-600.

[47] Guide to community preventive services: System reviews and evidence based recommendations. Effectiveness of safety belt use laws. December 2002.

[48] Adams JGU. Smeed’s law, seat belts and the emperor's new clothes. In: Evans L, Schwing RC, editors. Human Behavior and Traffic Safety. New York, NY: Plenum Press; 1985, p. 193-248.[49] Harvey AC, Durbin J. The effects of seat belt legislation on British road casualties: A case study in structural time series modeling. J Royal Statistical Soc. 1986; A149: 187-210.

[50] Discussion of the paper by Professors Harvey and Durbin. J Royal Statistical Soc. 1986; A149: 211-227.

[51] Rutherford WH, Greenfield T, Hayes HRM, Nelson JK. The medical effects of seat belt legislation in the United Kingdom. Research Report number 13. London, UK: Her Majesty's Stationery Office, Department of Health and Social Security, Office of the Chief Scientist; 1985.

[52] Chaudhary NK, Preusser DF. Lives lost by states’ failure to implement primary safety belt laws. Report prepared for the National Safety Council’s Air Bag & Seat Belt Safety Campaign; November 2003.[53] Transport Canada. Results of Transport Canada’s July 2001 Survey of Seat Belt Use in Canada. Fact Sheet # RS 2001–07; October 2001.[54] Chenier TC, Evans L. Motorcyclist fatalities and the repeal of mandatory helmet wearing laws. Accid Anal Prev. 1987; 19: 133-139.

[55] Janssen W. Seat-belt wearing and driver behavior: An instrumented-vehicle study. Accid Anal Prev. 1994; 26: 249-261.

[56] Salmi LR, Thomas H, Fabry JJ, Girard, R. The effect of the 1979 French seat-belt law on the nature and severity of injuries to front-seat occupants. Accid Anal Prev. 1989; 21: 589-594.

[57] Counts for air bag related fatalities and seriously injured persons.

[58] Waltz MC. NCAP Test improvements with pretensioners and load limiters. Traf Inj Prev. 2004; 5: 18-25. (Also available as Report DOT HS 809 562. National Highway Traffic Safety Administration; March 2003.

[59] National Highway Traffic Safety Administration. Event data recorders, summary of findings by the NHTSA EDR working group, final report; August 2001.

[60] All cars – cars are our life.