QUASI-ANALYTIC ACCELERATION INJURY RISK FUNCTIONS: APPLICATION TO CAR OCCUPANT RISK IN FRONTAL COLLISIONS

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1 QUASI-ANALYTIC ACCELERATION INJURY RISK FUNCTIONS: APPLICATION TO CAR OCCUPANT RISK IN FRONTAL COLLISIONS Denis Wood 1, Ciaran Simms 2, Colin Glynn 3, Anders Kullgren 4 and Anders Ydenius 4 1. Denis Wood Associates, Isoldes Tower, 1 Essex Quay, Dublin 7, Ireland , , dpw@iol.ie. 2. Centre for Bioengineering, Trinity College Dublin. 3. Dept. of Mechanical and Manufacturing Engineering, Trinity College Dublin. 4. Folksam Research, S23, SE Stockholm, Sweden. Abstract. There is continuing controversy regarding the role of car mass in occupant risk. Injury risk is influenced not only by the vehicle deformation characteristics and the occupant restraint system, but also by the size and mass of both case and partner cars. Recent research has shown that injury is better correlated with mean car acceleration than with velocity change. Injury risk relations for belted/unbelted drivers in all crashes with AIS 3+ and fatal injuries were derived from US data using a modified Joksch [7] type risk equation. These risk equations are shown to compare with recent Swedish AIS 2+ and AIS 3+ frontal collision data and with US frontal collision fatality data. The derived AIS 3+ and fatality risk functions, in conjunction with car population stress/density characteristics, were combined with US, German and Japanese car mass and collision velocity distributions to predict the variation in fatality and AIS 3+ injury risk with car mass and mass ratio using Monte Carlo simulation techniques. The resulting predictions were compared to published real world accident risk versus car mass data for each country, and a high degree of correspondence obtained. The results show that empirically derived car population structural characteristics and injury risk functions satisfactorily explain the real world fatality and injury versus mass effect. Key words: mean acceleration injury and fatality risk functions, car occupant risk, car mass effect, and frontal collisions.

2 2 Denis Wood1, Ciaran Simms2, Colin Glynn3, Anders Kullgren4 and Anders Ydenius4 1. INTRODUCTION: The influence of car mass and size on injury causation in frontal collisions remains in dispute. Mechanics dictates that case car acceleration in two-car collisions declines with increasing case car mass, but structural properties of both vehicles determine the shape of the acceleration pulse. Further, increased case car mass increases risk for the partner car occupants. In moderate severity collisions, the acceleration of a restrained occupant is a reflection of the vehicle acceleration [1]. In high severity collisions, intrusion influences injury. For unrestrained occupants, injury is due to contact with the car interior and vehicle ride down inertial loading. Real world data indicates that, for similar severity of frontal collision, injury risk increases with vehicle structure acceleration [2-3], despite reduced intrusion. Folksam [4,5] used on-board collision recorder data to show that the mean vehicle acceleration (ā) is a better predictor of injury risk than velocity change ( ν). 50ms moving average vehicle acceleration based injury criterion is used to evaluate safety barriers [6]. This paper presents analytic injury risk functions based on mean car acceleration during impact. These functions are combined with recent real world car population structural behaviour data [8-9-10] to predict the variation in injury risk with car mass in frontal collisions. 2. INJURY RISK FUNCTION: Joksch [7] proposed the empirical injury risk function given by equation 1a, where ν critical is the lower limit of ν for which risk equals 1.0. For > ν critical, P i =1. Following recent research [4,5], it is now proposed that injury risk is a function of mean acceleration, see equation 1b, in which ā critical is the lower limit of ā for which risk equals 1.0. The empirical constants ā critical and n are derived by regression of real world injury risk data. v Pi ( v) = v (1a), critical n a Pi ( a) = a (1b) critical n 3. RISK FACTORS IN FRONTAL COLLISIONS: The independent variables in frontal collisions are

3 Quasi-analytic Acceleration Injury Risk Functions: Application to Car Occupant Risk in Frontal Collisions 3 distribution of vehicle masses structural and crashworthiness characteristics of the vehicles interactive structural effects and configuration of the vehicles distribution of collision velocities risk versus ā distributions for restraint use/ non-use. The distribution of car masses in any car fleet is obtained from analysis of the records of the registered fleet in service. 3.1 Structural characteristics of car population Wood et al [8-9] analyzed real world collision recorder data from 269 single and two-car collisions (overlap > 25%, collision direction 11-1 o clock) and showed that the mean real world behaviour of individual car types could be described by empirically derived statistically robust power regressions. Further, the scatter in the real world responses results from the distributions of overlap, vehicle crush profiles and structural interaction effects, while the mean curves reflect the mean structural responses [10]. Analysis [8-9, 11] showed that the fundamental structural parameter for cars is the crumpling stress/density ratio, σ/ρ, which is independent of car size and mass and is equivalent to the specific energy absorption capacity, āl. Power regressions for individual car types and also for a mean car type of the form da ( d L) da a. L = σ ρ = C. (2a) a va. L = C va. V (2b) show high statistical correlation, where C da is the key stress/density parameter, which is independent of mass, while d a is a function of C da with a secondary mass influence [9]. These relations have been applied to successfully predict peak barrier force versus vehicle mass for 64 km/hr tests with offset deformable barriers [9]. 3.2 Collision velocity distribution The independent velocity parameter is collision closing speed. However, the available data is for damage-plus collisions and is in the form of velocity change, ν, which, as shown in equation 3, is a dependent variable being a function of mass and collision closing speed.

4 4 Denis Wood1, Ciaran Simms2, Colin Glynn3, Anders Kullgren4 and Anders Ydenius4 M 2,1 v1,2 = V CCS (3) M 1 + M 2 In countries with in-depth accident research, the ν and vehicle mass distributions for tow away-plus collisions are known. The log form of equation 3 yields: ln( v1,2 ) = ln( M 2,1 ( M 1 + M 2 )) + ln( V CCS ). Therefore, provided the mass and ν distributions can be satisfactorily described by logarithmic statistical distributions the mean and variance of the collision closing speed, respectively, can be obtained, [ ln( )] ln( v ) CCS [ 1,2 ] [ ln( M 2,1 ( M 1 M 2 )] mean / var mean / var V = + (4) ) mean / var Analysis of ν and mass distribution data for the US [13-14] showed both can be represented by log distributions, thus allowing derivation of the V ccs distribution. 4. INJURY PROBABILITY FUNCTIONS: 4.1 Real world data Evans [13] detailed injury probability for belted and un-belted drivers in all car crashes. Using the US car mass [14] and V CCS distributions and the car population stress/density, σ/ρ, characteristics [8-9], mean accelerations for each risk level in [13] were found using Monte Carlo methods. The data was regressed using the form of equation 1b for AIS 3+ injuries and fatalities for belted/unbelted drivers, see table 1. Table 1 Injury & Fatality Risk : Regression Parameters Case ā critical (g) n r 2 N Belted Driver Fatality Belted Driver AIS 3+ Injury Unbelted Driver Fatality Unbelted Driver AIS 3+ Injury Folksam Belted AIS 2+ Injury Figure 1 shows the data and regression lines for driver fatality risk. Regressions for AIS 3+ injury risk were determined similarly. All regressions have high correlations and the values of ā critical are similar (from

5 Quasi-analytic Acceleration Injury Risk Functions: Application to Car Occupant Risk in Frontal Collisions g for AIS 3+ unbelted to 20.05g for unbelted fatalities). Statistical analysis shows that there is no significant difference in ā critical for AIS 3+ injuries and ā critical for fatalities nor between belted and unbelted drivers. Folksam Research [5] reported risk probability for AIS 2+ belted front seat occupants based on 72 frontal injury collisions, including some cases with airbags. The regression parameters are detailed in table 1. Figure Application of risk equations to frontal collisions The suitability of the US accident data (containing some side/rear impact cases) for application in frontal collisions was statistically analysed. Comparison of ā critical for US AIS 3+ injuries with ā critical from the Folksam AIS 2 + shows no significant difference (t = 0.54). The regression exponent for the Folksam AIS 2 + risk is, as expected, less than that for the AIS 3+ unbelted which is less than the AIS 3+ belted, both being less than the exponents for fatalities. Evans [15] reported fatality risk versus ν for frontal collisions for belted and unbelted drivers between 1982 and Using the proportions of belted drivers over this period [16] and the described procedures (refer 4.1) the predicted fatality risk was computed using the regression data in table 1. Figure 2 shows the comparison. Correlation analysis shows a coefficient of determination, r 2 = with a proportionality coefficient = and standard error = Figure 3 compares the derived AIS 3+ belted injury relation with recent Folksam AIS 3+ injury risk data derived from 18 AIS 3+ frontal injury collisions. Analysis shows that there is no significant difference between the risk equation and the Folksam data (P > 5%).

6 6 Denis Wood1, Ciaran Simms2, Colin Glynn3, Anders Kullgren4 and Anders Ydenius4 Figure 2 Figure 3 5. MASS EFFECTS - DISCUSSION: In the analysis and graphs that follow, mass ratio is the defined as the ratio of heavier vehicle mass to the lighter vehicle mass. Figure 4 compares the relative fatality risk to drivers as a function of car to car mass ratio in frontal collisions for for the US [17] with the predictions using the fatality risk functions in table 1 and the ratio of reported seatbelt use [16]. The predicted injury risk versus mass ratio and the real world data closely match (t = -1.06). Figure 4 Figure 5 Figure 5 compares the relative AIS 3 + injury risk to drivers as a function of car to car mass ratio in Japan [18] from with the model predictions, showing close correspondence ( t= 0.95). Ernst et al [19] reported on the variation in AIS 3+ injury car mass in rural two car frontal collisions in Rhine Westphalia between 1984 and The V CCS distribution for Rhine Westphalia was not available, instead overall

7 Quasi-analytic Acceleration Injury Risk Functions: Application to Car Occupant Risk in Frontal Collisions 7 data for West Germany for the period was used [20]. Figure 6 shows the real world variation in AIS 3+ risk with car mass compared with the predicted results for 50% ile collision closing speeds between 51 km/hr and 62 km/hr. The absolute risk is very sensitive to the magnitude of the 50% ile V CCS. A 50% increase in injury risk for all cars results from a 20% increase in 50% ile Vccs - from 52km/h to 62 km/h. Figure 6 shows that predicted risk varies with mass in a similar manner to the real world data and bounds the data. Figure 7 shows the close match between real world variation in risk with mass normalized for the 50% ile German car mass (1050 kg). Statistical analysis of the normalised data for different 50% ile closing speeds shows no significant difference between the real world data and the model predictions, see figure 7. Figure 6 Figure 7 6. CONCLUSIONS The derived mean car acceleration based injury risk functions are shown to apply to frontal collisions. The risk functions in combination with car population structural characteristics derived from real world crash recorder data are shown to satisfactorily predict the variation in injury and fatality risk with car mass and mass ratio. REFERENCES 1. Wood D.P. and Simms C.K. Communication on: Edwards,MJ., Davies, H., Thompson, A. and Hobbs, A. Development of test procedures and performance criteria to improve compatibility in car frontal collisions Proc. IMechE 2003, Vol. 217, Part D, pp , pub. Proc. IMechE, Vol. 218, Part D, pp , 2004.

8 8 Denis Wood1, Ciaran Simms2, Colin Glynn3, Anders Kullgren4 and Anders Ydenius4 2. Prasad P., Laituri TR., Sullivan K. Estimation of AIS3+ thoracic injury risks of belted drivers in NASS frontal crashes Proc. IMechE 2004, Vol. 2118, Part D, pp Prasad P., Smorgonsky L. Comparative Evaluation of Various Frontal Impact Test Procedures, Pub. Society of Automotive Engineers, (SAE) 1995, paper Kullgren, A. Crash Pulse Recorder Results from Car Acceleration Pulses in Real Life Frontal Impacts Proc IRCOBI Conference Sept 11-13, 1996, Dublin. 5. Ydenius, A., Kullgren A. Pulse Shapes and Injury Risks in Frontal Impacts based on Real Life Crashes Proc IRCOBI Conference Sept , Munich. 6. Gabauer D., Gabler H.C. A Comparison of roadside crash test occupant risk criteria using event data recorder technology Proc IRCOBI Conference Sept 2004, Graz. 7. Joksch, HC., Velocity change and fatality risk in a crash a rule of thumb, Accid. Anal. Prev., Vol. 25, pp , Wood DP., Ydenius A., Adamson D. Velocity changes, Mean accelerations and Displacements of some car types in Frontal collisions Int. J of Crashworthiness, Vol. 8, No 6, pp , Wood DP., Adamson D., Ydenius A. Car frontal Collisions: Occupant compartment forces, Interface forces and Stiffnesses" Int. J of crashworthiness, Vol. 9, No 3, pp , Wood DP., Glynn C., Simms CK. Frontal collision behavoiur: Comparison of Onboard Collision Recorder Data with Car Population Characteristics accepted for publication Int. J of Crashworthiness, 26 November Wood DP., Simms CK Car size and injury risk: a model for injury risk in frontal collisions Accid. Anal Prev. Vol. 34, pp , Edwards MJ., Davies H., Thompson A., Hobbs A. Development of test procedures and performance criteria to improve compatibility in car frontal collisions Proc. IMechE 2003, Vol. 217, Part D, pp Evans L. Driver Injury and Fatality Risk in Two-Car crashes versus Mass Ratio Inferred using Newtonian Mechanics Proc. Accid Anal and Prev. Vol. 26, No5, pp , US Department of Transportation, National Highway Traffic Safety Administration FARS 90 Fatal Accident reporting system 1990 US Department of Transportation, Evans L. Car size and safety: a review focused on identifying causative factors, Proc of the 14 th ESV Conference, Munich, Germany May 1994, Vol. 1, pp , Evans L. Private communication Joksch HC., Fatality risks in collisions between cars and light trucks US Department of transport, Washington D.C Mizuno K., Umeda T., Yonezawa H. The relationship between car size and occupant injury in traffic accidents in Japan, SAE paper , Ernst G., Bruhning E., Glaeser KP., Schmid M. Compatibility problems of small and large passenger cars in head-on collisions 13 th ESV Conference, Paris, Paper S1-0-12, Appel H., Krabbel G., Meissner T. Safety of city cars conflict between ecology, economy, road traffic benefits and safety Forum of European Road Safety Institutes, September 1992, Berlin, Paper BER.NR.487/92.