V. Why Choose SSF ?

A. Description of Metrics

The agency, vehicle manufacturers and others have used various "metrics" and driving maneuvers to characterize the rollover resistance of vehicles in particular situations. Metrics are usually measurements of dimensional, mass and inertial properties of vehicles or calculations combining these properties in ways intended to represent rollover resistance. They have also taken the form of the results of simple static tests such as tilt table ratio or the combination of static measurements and simple driving maneuver tests such as "stability margin". In its ongoing rollover studies, the agency has used several metrics including Static Stability Factor, Tilt Table Angle or Ratio, Critical Sliding Velocity and Side Pull Ratio and various driving maneuvers including J-turn and fishhook maneuvers and sinusoidal steering.

Each of these indicators of rollover resistance has both advantages and disadvantages, and several would be acceptable candidates for comparative consumer information. The agency favors static stability factor because it is applicable to both tripped and untripped rollover. The causal basis for its good correlation to crash outcomes is clear. It is relatively simple for consumers to understand and can be measured inexpensively with good accuracy and repeatability. Also, changes in vehicles to improve static stability factor are very unlikely to cause unintended consequences.

The Static Stability Factor (SSF) of a vehicle is one half the track width, t, divided by h, the height of the center of gravity above the road. The inertial force which causes a vehicle to sway on its suspension (and roll over in extreme cases) in response to cornering, rapid steering reversals or striking a tripping mechanism, like a curb, when sliding laterally may be thought of as a force acting at the center of gravity (c.g.) to pull the vehicle body laterally. A reduction in c.g. height increases the lateral inertial force necessary to cause rollover by reducing its leverage, and the advantage is represented by an increase in the computed value of SSF. A wider track width also increases the lateral force necessary to cause rollover by increasing the leverage of the vehicle's weight in resisting rollover, and that advantage also increases the computed value of SSF. The factor of two in the computation "t over 2h" makes SSF equal to the lateral acceleration in g's at which rollover begins in the most simplified rollover analysis of a vehicle represented by a rigid body without suspension movement or tire deflections. In this form, it is easy to compare to the related metrics, Tilt Table Angle and Side Pull Ratio, which are similar except for the inclusion of suspension movement and tire deflections.

Figure 5-1

A simple test of rollover resistance is to place a vehicle entirely on a table which tilts about a longitudinal axis and raises one side of the vehicle higher than another. As the table continues to tilt, it eventually reaches an angle at which the high side tires lift from the table, and the vehicle rolls over if not restrained. The critical angle is called the Tilt Table Angle. The trigonometric function, tangent, of this angle is the Tilt Table Ratio (TTR), which is the ratio of the component of the tilted vehicle's weight which acts laterally to overturn it, to the component perpendicular to the table which resists overturning. For an idealized vehicle without suspension movements, the TTR is the same as the SSF. The suspension movements of actual vehicles reduce the TTR about 10 to 15 percent relative to the SSF.

Figure 5-2

The Side Pull Ratio (SPR) is the lateral force acting at the vehicle's c.g. necessary to cause two wheel lift, divided by the vehicle's weight. It is determined by a test which is conceptually identical to the tilt table test but which uses an externally applied lateral force to cause the wheels on one side of a vehicle parked on a horizontal surface to lift up. It exercises the vehicle suspension more realistically because the whole weight of the vehicle remains on its suspension. In the tilt table test, the vehicle can rise somewhat relative to the table surface because the component of the vehicle weight which compresses the suspension springs steadily diminishes as the angle of the table increases. For an idealized vehicle without suspension movements, the SPR also is the same as the SSF. Again, the suspension movements of actual vehicles reduce the SPR relative to the SSF by about 10 to 15 percent.

Figure 5-3

Critical Sliding Velocity (CSV) is a metric tied directly to tripped rollover. It is a calculation of the lateral velocity necessary to cause a rigid body representation of a vehicle to overturn upon impact with a rigid tripping mechanism. It includes the c.g. height, track width, mass and roll mass moment of inertia of the vehicle in the calculation.

Stability Margin is a metric directed toward on-road untripped rollover. It is the difference between the Side Pull Ratio of a vehicle and its maximum lateral acceleration in g's, as measured in a steady state cornering test. The steady state cornering test consists of finding the maximum speed the vehicle can maintain while following a circular path. The idea is that if the cornering acceleration the vehicle can produce is less than the SPR, it would not be possible for a rollover to occur simply as a result of steering maneuvers. GM recommends a margin of 0.2 g's because lateral accelerations in maneuvers with rapid steering reversals and/or brake release in a curve can be greater than those measured in a steady state test.

B. Tripped and Untripped Rollover

The terms on-road and off-road rollover are sometimes thought of as surrogates for tripped and untripped rollover. Off-road rollover does not refer to vehicles rolling over while trying to negotiate difficult trails away from public roads. It refers to vehicles leaving the road in the course of a crash and rolling over off the pavement. Usually, but not always, a curb, a soft shoulder, a ditch, loose gravel, a guard rail or another tripping mechanism initiates the rollover. In contrast, most people associate only the frictional force between the tires and the pavement rather than a tripping force with on-road rollover involving a single vehicle. This is also called maneuver-induced rollover.

Past NHTSA studies of crash data from the state of Maryland (1)

and NASS (2) suggested that between and 8 and 10 percent of single-vehicle rollover crashes were on-road rollover. However, a recent study of audited NASS CDS data (a data sampling system with projection factors to represent the national trends) estimated that while over 13 percent of rollovers in single-vehicle crashes occur on-road or on a paved shoulder, only 4.2 percent are untripped. Examples of on-road tripped rollovers are instances in which potholes or differences in pavement level acted as tripping mechanisms and the more common instances in which the wheel rim dug into the pavement (possibly as a result of tire de-beading). The study also estimated that only 0.2 percent of rollovers are untripped and off-road.

The agency has conducted studies of on-road untripped rollover because these events are considered egregious by the public and because the prospects of developing objective, repeatable and realistic vehicle tests of untripped rollover appeared to be more favorable than for tripped rollover, in which the circumstances are limitless. Many of the vehicle attributes that improve resistance to untripped rollover also improve resistance to tripped rollover. Certainly, a low c.g. and a wide track width are beneficial in resisting rollover in general.

However, even objective and repeatable steering maneuver tests present a dilemma. Suppose the first vehicle responds to steering maneuvers up to a high test speed and two wheel lift occurs. Suppose the second vehicle spins out or plows out at a significantly lower speed, but two wheel lift does not occur. Which vehicle has better performance in rollover resistance? If untripped on-road rollover is the only criterion, the second vehicle has demonstrated better performance because it cannot be controlled through a test maneuver severe enough to cause two wheel lift. But the test tells us nothing about the far more likely risk of tripped rollover. We do not know how the second vehicle would have performed under the same lateral acceleration that caused two wheel lift in the first vehicle.

Stability Margin shares the dilemma for vehicle comparisons described above. The SPR component of stability margin compares vehicles on an equal basis that would be meaningful for tripped or untripped rollover, but the subtraction of the maximum on-road lateral acceleration limits the applicability of the margin to on-road untripped rollover. Simply fitting the same vehicle with lower traction tires increases the stability margin without making any difference when a tripping mechanism is encountered. Even when the scope of interest is limited to on-road untripped rollover, Stability Margin is unsuitable for comparative purposes. A greater stability margin does not necessarily mean more safety. A margin in excess of the minimum necessary to avoid untripped rollover may simply represent poor cornering capability.

The steering maneuver tests studied by the agency were consistent with SSF, TTR and CSV. The only vehicles that experienced two wheel lift in the maneuvers were those at the lower range of the metrics. However, the steering maneuver tests studied do not distinguish between those vehicle attributes that increase rollover resistance in all circumstances and those applicable only in the narrow risk category of on-road untripped rollover. Therefore, the steering maneuver tests recently studied are not considered as appropriate for general consumer information on rollover as SSF, TTR or CSV.

C. Correlation and Causation

Correlation means that two events generally occur together. However, the fact that event B occurs when event A occurs does not mean that event B occurs because event A has occurred. Thomas Sowell, the economist and columnist, notes that youngsters who voyage on the Queen Elizabeth II or ride on the Concorde tend to make more money as adults, but that we don't recommend buying tickets for these as a way to increase a child's earning potential. Childhood luxury trips are correlated to future earnings, but do not cause the higher income.

A causal relationship, on the other hand, means that event B occurs because event A has occurred. These events are not simply linked in time, like in a correlation, but event A is a necessary element for event B to occur. In a simple form, the plant grows because of the light. Light is not the only thing needed for the plant to grow, and the plant may die even if it receives plenty of light, but there is a causal relationship between inadequate light and plant death.

Just as with light and plants, a low SSF is not the only thing that is needed for a rollover and a rollover may occur even if a vehicle has an excellent SSF, but there is a causal relationship between SSF and rollover. At the initiation of either tripped or untripped rollover, the moment arm for the principal overturning force is the c.g. height, and the moment arm of the principal restoring force is the track width divided by two. In the case of tripped rollover, the severity of the impact with a tripping mechanism determines the principal overturning force. Depending on the circumstances, roll moment of inertia, suspension deflections, tire properties and other vehicle properties influence rollover - but never to the exclusion of c.g. height and track width. Among the many causal factors included in mathematical models of various rollover scenarios, c.g. height and track width are always present and usually exert the most influence.

While the vehicle properties represented by SSF, TTR, SPR and CSV are directly and causally related to vehicle rollover, that alone does not prove that the vehicle properties exert enough influence to be noticed in the context of the driver and roadway variables. Especially in the context of tripped rollover, the circumstances of the crashes and the nature of the tripping mechanisms may be nearly unique from crash to crash. Examination of a large number of crashes may be necessary to detect even powerful influences with any degree of certainty. Statistical correlation of the metrics to the rate of rollover occurrences of representative vehicles in actual crashes is the usual method of determining their influence. The agency has demonstrated significant correlations between SSF, TTR and CSV and the rate of rollovers per single-vehicle crash in past studies of the crash reports recorded by particular states (3), (4). The agency has consistently found that given a single-vehicle crash, the SSF, TTR or CSV of the vehicle is a good statistical predictor of the likelihood that it will roll over. The number of single-vehicle crashes has been used as an index of exposure to rollover because it eliminates the additional complexity of multi-vehicle impacts and because about 82 percent of light vehicle rollovers occur in single-vehicle crashes.

The statistical study described in the Appendix to this notice was undertaken to develop a relationship between SSF and rollover rate representative of the whole country rather than a particular state. The average rollover/single-vehicle crash rate varies from state to state because of differences in reporting thresholds for single-vehicle crashes and real differences in road conditions, vehicles and drivers. A relationship between rollover rate and SSF normalized to the national rollover rate and to a nationally representative set of driver and road use variables was developed as a basis for a comparative rating system for rollover risk in the event of a single-vehicle crash. We had available crash reports of 185,000 single-vehicle crashes from six states from 1994 to 1997 in which it was possible to determine the make/model of the vehicles and whether rollover occurred in the course of a single-vehicle crash, and for which SSF data were also available. We also had the NASS GES data sampling system, with far fewer but nationally representative crash reports, to determine the national average rollover rate for the population of vehicles investigated in the state reports.

The study of state reports of single-vehicle crashes was performed as a regression analysis, in which the square of the coefficient of regression (the R2 statistic) indicates the degree to which the differences between the data samples can be explained by the independent variables. In this case, the R2 calculated for the rollover rates of about 100 vehicle make/models as a function of SSF ranged from 0.53 to 0.76 across the states. This means that between 53 percent and 76 percent of the differences in rollover rate of the subject vehicles can be explained by differences in SSF.

However, an analysis using only SSF does not preclude the possibility that cross correlations of SSF with other factors could create a level of correlation beyond the causal relationship of SSF to rollover. For example, if the drivers of vehicles with low SSF were generally more aggressive, the degree of correlation could be raised by the greater chance of these vehicles leaving the road at high speed. Likewise, if vehicles in a particular range of SSF were operated more often than others on poor road surfaces, their exposure to tripping mechanisms as well as their rollover resistance would be reflected in a correlation with SSF. Because of the possibility that the apparent influence of SSF on rollover could be due in part to cross correlations, the agency also performed a stepwise regression analysis in which the available variables describing driver and road characteristics were given the first opportunity to explain the differences among vehicles in rollover rate. In this analysis, cross correlations would reduce the apparent influence of SSF because part of its effect would have already been included in a cross correlated driver or road variable. The driver and road use characteristics recorded in the crash reports of the various states included gender, age, alcohol involvement, number of occupants, day or night, stormy weather, road speed limit over 50 mph, bad road or road surface, rural location, curve, and hill. When only the driver and road use variables, but not the SSF, for each vehicle were considered, it was found that their cumulative information could explain between 53 and 69 percent (differing with State) of the variability between vehicles in rollover rate. When SSF was added to the available driver and road characteristics, the explanatory power of the information increased to between 85 and 90 percent. The addition of SSF explained between 64 and 80 percent of the variability remaining after consideration of the driver and road variables.

The six-state model that included all 185,000 single-vehicle crashes yielded similar results. When only the SSF of the vehicles is considered (with a correction for systematic differences between States) the R2 statistic was 0.73; when the driver and road variables rather than SSF were entered, the R2 statistic was 0.58; and when the SSF was added to the driver and road variables R2 statistic rose to 0.88. In the direct correlation, SSF appeared to explain about 72 percent of the variability in rollover rate between crash experiences of about 100 vehicle/make models in six states. If cross correlations between the vehicle SSF and driver and road variables cause the direct correlation to be optimistic, the same cross correlations would diminish the apparent influence of SSF in the stepwise regression in which the driver and road variables alone were entered first. However, SSF remained influential in the stepwise regression with the power to explain 72 percent of the remaining variability after the entry of the driver and road use variables. (Note: The similarity of 72 and 73 percent in the two analyses is merely a coincidence. While 73 percent is the R2 statistic in the direct correlation, 72 percent is the ratio (0.88 - 0.58)/(1.0 - 0.58) in the stepwise analysis.)

Rollover is a very complex event, heavily influenced by driver and road characteristics as well as vehicle properties. The most important non-vehicle variable may be the speed at which the vehicle leaves the roadway, for which some of the driver and road use variables are only broadly indicative. However, the directly causal influence of SSF is sufficient to explain a large portion of the variability among vehicles in real-world crash experiences in either a direct correlation or stepwise analysis of the variability remaining after consideration of driver and road use variables. It is not lost in the noise of complex circumstances, and its explanatory power exceeds the cumulative explanatory power of all other available driver and road use variables in most instances.

The same analyses using TTR or CSV would be expected to yield similar results based on past agency studies. In fact, CSV might show slightly higher correlations because most rollovers are tripped. However, the choice of a rating metric was not made simply for incremental gains in R2 among metrics, since each one provides a high level of correlation to rollover crash rates. The simplicity and generality of SSF have value in a rating system intended for consumers. In addition, there is only modest room for improvement over a metric which already explains 73 percent of the variability in rollover rates left after application of driver and road use variables.

In some analyses, the inclusion of wheelbase, which is simple, improves the correlation coefficient. Wheelbase has not been included here because, unlike the components of SSF, it does not have a direct causal relationship with rollover. It may be a surrogate for roll moment of inertia, yaw moment of inertia, or pitch moment of inertia, each of which may influence rollover in certain circumstances. Alternatively, wheelbase may be a surrogate for owner demographics within certain vehicle classes. We have chosen not to include factors which correlate to rollover through cross correlation to other undefined factors.

D. Simplicity and Measurability

The principle of SSF is obvious. The fact that an object which is more top heavy or narrower at its base can be turned over more easily is encountered repeatedly in common experience and is intuitive for most consumers. Track width is a straightforward dimensional measurement which can be measured very accurately given sufficient care, and special fixtures and calipers can be constructed to make the task easy. In past comments to the agency, lack of repeatability of c.g. height measurement between various labs was cited. However, improvements in equipment and technique have taken place. The agency's own lab and a contractor using similar equipment report errors no greater than one half of one percent in c.g. height measurement of vehicles (5).

Tilt Table measurements expressed either as TTR or TTA also have the advantage of accuracy and relative ease of measurement. The process of tilt table measurement should make intuitive sense to the public, but the conversion from an angle to a trigonometric ratio may not. The reporting of the angle is less complicated, but it creates a non-linear measurement that does not increase as rapidly as the actual improvement of rollover resistance expressed in TTR.

CSV would be easier for the public to understand were it the result of a full scale vehicle test rather than the computation of a simplified model. While the public should understand track width and c.g. height, the additional concept of roll moment of inertia is outside common experience. The simplified model also results in CSVs that are unrealistic in absolute value, though useful for comparison of vehicles. The computation predicts that lateral speeds of 10 to 15 mph are sufficient for tripped rollover of virtually all light vehicles from large cars to compact SUVs. The low threshold may not appear to be credible to consumers who have experienced hard curb contact with only wheel and tire damage and may trivialize the information by causing consumers without such experience to conclude that all vehicles will turn over so easily that differences between vehicles are not worth consideration.

In fact, the lateral speeds for tripped rollovers of actual vehicles in common circumstances would always be greater than the computed CSV. Instead of being available to raise the vehicle's c.g. to the rollover point, much of the kinetic energy from the vehicle's lateral speed would be dissipated by tire contact with the ground, stored or dissipated in tire and suspension deflections, and dissipated in the permanent deformation of vehicle suspension components and of the tripping mechanism. The calculation of CSV requires a measurement of roll moment of inertia in addition to the measurements needed to calculate SSF, but that is not an obstacle. The agency's own lab and a contractor using similar equipment report errors no greater than two percent in roll moment of inertia measurements of vehicles.

Side Pull Ratio has intuitive appeal if one can understand that the inertial forces which cause tripped or untripped rollover can be represented by forces applied in a laboratory with a cable pulling at the c.g.. However, it is difficult to coordinate the movement of the outboard end of the cable with vehicle roll motion and to avoid applying extraneous vertical forces. For this reason SPR is often estimated from SSF with modifying factors for the roll stiffness of the vehicle and its general suspension type.

The simplicity and relative ease of measurement of SSF and TTR are advantageous for consumer information.

E. Unintended Consequences

In comments to the 1992 ANPRM on rollover issues, several manufacturers pointed out that some changes that could improve a vehicle's tilt table performance may degrade its control and handling attributes. Aspects of suspension design, such as choices of front to rear roll stiffness ratio and overall roll stiffness, could be different from those now chosen to balance ride quality, handling, tire wear and other important features if they were influenced by a desire to maximize TTR. Commenters to the same docket claimed that measurements of c.g. height were difficult and not repeatable in comparison to the tilt table measurement.

These comments presented the agency with a dilemma. The most practical rollover resistance metric from a measurement viewpoint, TTR, had the potential to introduce new trade-offs for suspension designers. Obviously, the agency does not want vehicle manufacturers to depart from designs which they believe optimize safe handling and directional control. Improvements in the methods of measuring the c.g. height of vehicles have occurred that resolve the concerns raised in the comments. SSF is now as practical and repeatable a measurement as TTR.

Changes in track width or c.g. height to improve SSF do not require trade-offs of handling and control. In general, those particular changes would make it easier to achieve good handling. A potential trade-off discussed in the agency's 1987 denial of a rulemaking petition for a minimum level of SSF was the possibility of manufacturers reducing the strength of the upper structure of vehicles in order to lower the c.g.. At that time, FMVSS No. 216 on roof crush resistance did not apply to SUVs, vans or pickup trucks. Beginning with the 1995 model year, the roof crush resistance of light trucks including SUVs and vans has been included in the regulation, making that potential choice to compromise safety even less likely.

1. E. A. Harwin and L. Emery; "The Crash-avoidance Rollover Study: a Database for the Investigation of Single-vehicle Rollover Crashes;" 12th International Technical Conference on Experimental Safety Vehicles, Goteburg, Sweden, May 29-June 1, 1989; Vol 1, p.470-477.

2. "Technical Assessment Paper: Relationship between Rollover and Vehicle Factors"; NHTSA; July 1991. Computation of untripped rollover based on 1989 NASS.

3. Ibid

4. E.A. Harwin and Howell K. Brewer; "Analysis of the Relationship between Vehicle Rollover Stability and Rollover Risk using the NHTSA CARDfile;" NHTSA, 1989.

5. Heydinger, G.J., et al; "Measured Vehicle Inertial Parameters - NHTSA's Data through November 1998;" Society of Automotive Engineers 1999-01-1336; March, 1999