Comparison of Onboard Collision Recorder Data with Car Population ...

Frontal Collision Behaviour: Comparison of Onboard Collision Recorder Data with Car Population Characteristics D P Wood†, C Glynn‡ and C Simms‡ Journal of Crashworthiness, vol 10 no 1 pp 61-73, 2005 †

‡

Denis Wood Associates, Isoldes Tower, 1 Essex Quay, Dublin 8 Dept. of Mechanical & Manufacturing Engineering, Trinity College, Dublin

Abstract: The acceleration and displacement responses of cars in frontal collisions depend on the severity of the collision, the collision partner, the overlap between the case car and the collision partner and the crush pattern. A previously validated geometric crush model is combined with generalized full width barrier characteristics for the car population, the distributions of overlap in frontal collisions, and distributions of crush profiles (segmental and triangular) to obtain the frontal collision characteristics of the car population. The resulting frontal collision response characteristics are shown to encompass the real-life characteristics obtained from onboard collision recorders for 16 car types in 269 collisions.

NOTATION ā ⋅L L d ∆V g d/L INTRODUCTION The accelerations and crush displacements of cars during collisions depend on the nature of the collision and the overlap between the colliding car and its collision partner. These variations are clearly demonstrated by Agaram et al. [1] in their review of mean acceleration characteristics of cars in staged tests: full width, rigid barrier, full width car-to-car, and various overlap car-to-car tests. This data shows, as expected from impact mechanics, that mean accelerations increase with increasing overlap. Recent analysis of data obtained from onboard collision recorders for actual crashes [2, 3], derived empirical mean acceleration and displacement characteristics for individual car types, which were robust, with high coefficients of determination and which were primarily a function of collision severity. The indications were [3] that the empirical characteristics obtained reflected the pattern of overlap distribution in real-life frontal collisions and that the mean empirical responses represented the frontal collision behaviour at the 50%ile overlap. In this paper a geometric crush model is combined with a generalised representation of the full width barrier behaviour of the car population, and data for the pattern of overlap in real-life collisions to determine the mean normalized acceleration, ā⋅L, velocity change, ∆V, and normalized displacement, d/L, characteristics of the car population in car-to-car frontal collisions. The resulting overall statistical relations characterizing the behaviour of the car population are compared with those derived for the car population from onboard collision recorders as reported in [2].

BACKGROUND Theory Frontal Barrier Characteristics Full width barrier data of impact speed and normalised dynamic displacement, d/L, from 224 tests of 70 car types designed between the early 1950s and mid 1980s was analysed, for velocities up to 27 m/s (97 km/h, 60 mph). A power regression between velocity and normalised crush, d/L, yielded the result:

∆Vm / s

d  = 71 ⋅   L

0.85

d  ∆Vm / s = 71(1±0.1×t ) ⋅   L

[4] 0.849⋅(1± 0.0255×t )

The coefficient of determination, r2 = 0.874, and the one standard error ranges for the coefficient and exponent are 68.0 to 74.0 and 0.83 to 0.87, respectively. Onboard Collision Recorder Data Based on analysis of twelve car types, in 258 frontal collisions, Wood et al. [2] obtained overall mean characteristics for the car population in terms of ā⋅L, ∆V and d/L, relationships. (Data for a further four car types, N = 11, was insufficient to derive individual car type regressions.) The theoretical basis for this approach, set out in [2], is for a specific class of vehicle, in this case cars, that the stress-density ratio, σ ρ , is independent of size, and that normalised acceleration, ā⋅L, and velocity change, ∆V, are functions of collision severity, measured in terms of normalised displacement, d/L. The mean empirical relationships obtained [2] were:

a ⋅ Lm 2 / s 2

d  = 923.2 ⋅   L

0.49

[1]

a ⋅ Lm 2 / s 2 = 69.5 ⋅ (∆Vm / s )

0.73

d  ∆Vm / s = 43.0 ⋅   L

[2]

0.74

[3]

For the onboard collision recorder data analysed, the 99th percentile velocity change, ∆V, was less than 20 m/s. Comparison of Full Width Barrier and Onboard Collision Recorder Data CHARACTERISATION OF FRONTAL COLLISIONS

Frontal Crush Shapes Examination of the profiles of the fronts of cars after impacting, both real-life and staged collisions has lead researchers [4 to 11] to characterise the crushed profiles as either segmental or triangular. The crush face thus takes either a diagonal profile or a segmental shape, as illustrated in Figure 1. In all cases the non-struck side pivots or hinges at the attachment between the rear of the engine compartment and front of the occupant compartment. Typically, the proportion of segmental to triangular crush profiles in real life collisions is 60% to 40% [9]. Overlap Distribution The patterns of overlap in frontal collisions (from 11 o’clock to 1 o’clock) have been reported for both segmental and triangular crush profiles [4 to 11]. Analysis of this data shows that cars which develop a segmental crush shape, have an overlap distribution between 25% and 100%, with a 50th percentile overlap of 56%. (It should be noted that for collisions with an overlap below 25%, neither front chassis rail is engaged in the crushing process, and the collisions are essentially sideswipe in nature.) By contrast, for triangular crush profiles the 50th percentile overlap is 60%, while 95% of triangular profile frontal deformed cars have overlaps of 67% or less [6]. It should be noted that the mechanisms which result in segmental or triangular crush profiles are not fully understood, but are considered to depend on the detailed structural characteristics of the colliding pairs, the particular collision overlap, orientation and severity. The same car type will have either a segmental or triangular profile depending on collision circumstances. GEOMETRIC CRUSH MODEL Wood, Doody and Mooney [13] derived a geometric crush shape model for frontal impacts and applied it to both velocity estimates from residual crush profiles for accident reconstruction purposes, and to dynamic crush modelling of individual cars where the full width rigid barrier response of the individual cars was combined with the geometric model to predict the car behaviour in 45% overlap and 30˚ angled barrier tests [15 to 18]. The essentials of the geometric crush model are that • the length of the car front is inextensible; • the non-struck side of the car hinges at the front of the occupant compartment; • the deformation energy is absorbed in longitudinal crush (bending effects are ignored); • the energy absorbed is a function of the mean crush depth. Figure 2 illustrates the manner in which mean crush depth is computed across the deformed crush profile. The equations for geometric crushing are detailed in Wood et al. [13] and Glynn [14]. Validation Wood [15 to 18] applied the geometric model to the dynamic crush behaviour of eight car types in 45% overlap and 30˚ angled barrier tests at 13.9 m/s (50 km/h) and at 15.6 m/s (56 km/h) speeds. In each case the full width barrier characteristics of the car type were used to compute the 45% overlap and 30˚ angled barrier responses. Figures 3 and 4 show the comparison between

model and test data for two of the cars. There is a high degree of correspondence between the model and the test results. OVERALL FRONTAL RESPONSES Methodology Monte Carlo simulation techniques were used to calculate the overall frontal collision response of the geometric model for velocity changes up to 27 m/s (the limit of the available full width barrier data) and to derive equation [4]. The ratio of crush profile between segmented and triangular profiles was taken as 60% to 40%, the distribution of collision overlaps as shown in Figure 5, the full width barrier characteristics detailed in equation [4], were used to relate velocity change to mean crush depth (d/L), while the geometric shape model was used to relate centre of gravity displacement to mean crush depth (d/L). The acceleration regression, āL, was then computed from the velocity change, ∆V, and normalised displacement, d/L, data. A total of 500,000 runs were made (i.e. 500,000 collision simulations). COMPARISON OF RESULTS Comparison of equations [5] to [7] from the geometric model for the car population with equations [1] to [3] derived from the onboard collision recorder data for twelve car types, shows that the corresponding coefficients and exponents are higher for the geometric model than obtained from the onboard recorders. However, all of the onboard data is bounded by the scatter plot data obtained from the geometric model; refer to Figures 6 to 8. The mean regression curves are compared in Figures 9 to 11. The differences are small. At low velocity change, ∆V, and low normalised displacement, d/L, the mean response for the geometric model is less than for the onboard recorder, while at high velocity changes the geometric model results are higher. The maximum differences at low velocity change values occur in the range 3.2 m/s (for āL = f (∆V)), to 5.9 m/s (for ∆V = f (d/L)). The maximum difference in mean acceleration (expressed in ‘g’ units for the mean population car length, L = 4.26 m [19]) is -0.69 g, while the difference in velocity change is -0.3 m/s. The maximum differences at high speed occur at 27 m/s (the limit of the full width barrier data for overall population). Here, the difference in mean acceleration is 0.99 g for the acceleration versus normalised displacement regression (ā⋅L -v- d/L), 2.69 g for the acceleration versus velocity change regression (ā⋅L -v- ∆V), and 0.87 m/s for the difference in velocity change (∆V -v- d/L). Table 1 summarises the comparison between the two sets of equations. The mean difference for the ā⋅L versus ∆V and ∆V versus d/L relations are negligibly small, while mean difference between the ā⋅L versus ∆V relations is 0.55 g. Table 2 shows the difference in proportionate or percentage terms. VARIATION OF Cda , Cdv and Cva COEFICIENTS WITH OVERLAP DISCUSSION The comparison the geometric model prediction for the response of the car population in frontal collisions and the onboard collision recorder data (16 cars, N=269); refer Figures 6 to 8; shows

that the population model encompasses the onboard recorder results. Comparison of the mean regression relations derived from the two sets of data shows a high degree of agreement with only small differences. In the circumstances, it can be concluded that the overall population characteristic derived from the onboard collision recorder data reflects the pattern of distribution of overlap between collision partners in frontal collisions. Figures 12 and 13 show the variation in mean acceleration versus velocity change, for both segmented and triangular crush profiles with overlap. The relationships were derived on the basis of a 10% overlap range for each nominal overlap, i.e. for a nominal overlap of 50% the range used was 45% to 55%, uniform distribution basis. This data shows, for a velocity change, ∆V, of 15 m/s, that as overlap increases from 30% to 100%, the mean acceleration increases from 450 m2/s2 (10.8 g) to 730 m2/s2 (17.5 g) for the cars which develop a segmental crush profile during impact, and from 410 m2/s2 (9.8 g) to 730 m2/s2 (17.5 g) for cars which sustain a triangular crush shape. Whether a car develops a segmental or triangular crush profile in the course of a collision depends on the precise circumstances of the individual collision and all car types sustain both crush patterns. Also, as detailed in [2, 3] the stress-density, σ ρ , characteristics of individual car types are distributed about the population mean. Figures 14 and 15 show the scatter plot distribution for a nominal 50% overlap (45% to 55%), for both segmental and triangular crush profiles. The scatter plots show that there is a 2.1 to 1.0 range between maximum and minimum acceleration levels due to the variation in characteristics of individual car types. The factors include the detailed structural design and global respective frontal stiffness. CONCLUSION The overall frontal collision response of the car population, obtained from the geometric crush profile model, and generalised frontal barrier characteristics of the car population, and that obtained from analysis of onboard recorders of 16 car types in 269 frontal collisions, are, for all practical engineering purposes, identical, and thus confirm that the characteristics obtained from the onboard collision recorder reflects the characteristics of the car population in frontal collisions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

Agaram, V., Xu, L., Wu, J., Kostyniuk, G. and Nusholtz, G. ‘Comparison of Frontal Crashes in Terms of Average Acceleration’, SAE paper 2000-01-0880, Society of Automotive Engineers 2000. Wood, D P., Ydenius, A. and Adamson, D. ‘Velocity changes, mean accelerations and displacements of some car types in frontal collisions’, International Journal of Crashworthiness, 2003, Vol. 8, No. 6, pp 591-603. Wood, D P., Adamson, D. and Ydenius, A. ‘Car Frontal Collisions: Occupant Compartment Forces, Interface Forces and Stiffnesses’, submitted for publication February 2004. Kallina, I., Zeidler, F. and Scheunert, D. ‘Safe or unsafe in road accidents? Can this question be answered by comparing Crash Test results?’, Comparative Crash Tests within the EC, pp 95-104. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Tsuda, Y. and Yamanoi, T. ‘Technical consideration on the current status of crash tests in the case of head on collisions’, Comparative Crash Tests within the EC, pp 105-114. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Ardoino, P. ‘Crash testing: A way to improve or to rate the safety?’, Comparative Crash Tests within the EC, pp 115-124. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Hackney, J R. ‘Comparative analysis of occupant protection as measured in Crash Tests in the USA’, Comparative Crash Tests within the EC, pp 124-164. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Hobbs, C A. ‘The need for a deformable impact surface for frontal impact testing’, Comparative Crash Tests within the EC, pp 171-184. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5.

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Appel, H., Lutter, G. and Sigmund, T. ‘The relevance of crash tests to real road collisions’, Comparative Crash Tests within the EC, pp 185-204. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Frampton, R J., Hill, J R. and Mackay, G M. ‘The relevance of current crash tests to real world collisions in the UK’, Comparative Crash Tests within the EC, pp 205-232. Published Verlag TÜV Rheinland GmbH, Köln. ISBN 3-8249-0145-5. Harms, P. ‘Crash injury investigation and injury mechanisms in road traffic accidents’, State-of-the-art Review, Transport Research Laboratory. Published HMSO, 1993, ISBN 0-11-5511814. Wood, D P. and Simms C. “Car Size and Injury Risk: A model for injury risk in frontal collisions”, Accident Analysis and Prevention, Vol. 34(1), pp93-99, 2002. Wood, D P., Doody, M. and Mooney, S. “Application Of A Generalised Frontal Crush Model Of The Car Population To Pole And Narrow Object Impacts” SAE Paper 930894. Glynn, C. ‘Geometric Crush Model of Cars: Comparison with Real-Life Responses’, Final Year Project, Dept. of Mechanical and Manufacturing Engineering, Trinity College, Dublin, 2004. Wood, D P. and O’ Riordain, S. “Car Frontal Crush - A New Perspective” 1996 IRCOBI Conference September 11 - 13 Dublin. Wood, D P. and Mooney, S. “Car Size and Relative Safety: Fundamental Theory and Real Life Experience Compared” 1996 IRCOBI Conference September 11 -13 Dublin. Wood, D P. and Mooney, S. “Modelling of Car Dynamic Frontal Crush” SAE paper 970943. Wood, D P. “Comparison of Modelled and Actual Car Dynamic Frontal Crush” SAE Paper 980027. Wood, D P. “Collision Speed Estimation Using a Single Normalised Crush Depth Impact Speed Characteristic” SAE Paper 920604.

Table 1: Summary of Comparisons ∆V for max. difference at low speed Max. difference Max. difference at 27 m/s (97 km/h) ∆V for difference = 0 Mean difference RMS difference

ā⋅L -v- d/L 3.9 m/s -0.63 g +0.98 g 15.7 m/s -0.04 g 0.50 g

Table 2: Proportional Difference (2 m/s to 27 m/s) ā⋅L -v- d/L ā⋅L -v- ∆V Difference at 2 m/s -20.0 % -23.4 % Difference at 27 m/s +6.1 % +14.7 % Mean difference -2.4 % +1.9% RMS difference +6.9 % +9.5 %

ā⋅L -v- ∆V 3.2 m/s -0.69 g +2.69 g 11.3 m/s 0.55 g 1.19 g

∆V -v- d/L 5.9 m/s -0.30 m/s +0.81 m/s 15.6 m/s 0.04 m/s 0.31 m/s

∆V -v- d/L -10.5 % +3.0 % -1.3 % +3.5 %

APPENDIX 1 THEORY APPENDIX 2 GEOMETRIC MODEL DERIVATION (CORRECTED SEG DERIVATION + DBAR-DCG DERIVATION FOR TRIANG)

For mathematical generality and simplicity the dimensions in figure A2.1, along with the mean crush ( d ), are normalised to the width of the car, W, and are represented by,

P' =

d d P S W ' , S' = , 1= , d' = and d max = max . W W W W W

(A2.1)

Using simple geometry the normalised mean crush ( d ' ) can be related to the normalised ' ) as maximum crush ( d max

 cosα  ' ' − d ' = d max  1− P 2  

(

2

(A2.2)

α = π − µ −φ − β

where

and where

)

(

(A2.3)

) ( ) )( ) (

2   ' 2 ' ' 2 1 P S d − + − − S' 2  max µ = cos  ,  2 1 − P ' 1 − P ' 2 + S' − d ' 2  max   −1

(

(

) ( ( ) (

) ( ) (

)

) ( ) (

2 2 2  2 1 − P ' + S' − d 'max + L' − d 'max − L' − S'  φ = cos  2 1 − P ' 2 + S' − d ' 2 . 1 − P ' 2 + L' + d ' max max  −1

and

(A2.4)

) )

  2  

2

 (1 − P ' )  β = tan −1  ' . '  (L − d max ) 

(A2.5)

(A2.6)

For a segmental crush profile the centre of gravity displacement (dcg) is equal to the maximum crush ( d max ). Therefore, a relationship between dcg and d is found by replacing dcg for d max in equation A2.2, and rearranging.

 cos α  ' dcg ' = d ' +   1− P  2 

(

)

2

(A2.7)

For a triangular crush profile, the centre of gravity displacement (dcg) can be related to the mean crush ( d ) by looking at the dcg- d max relationships for the two extreme cases of 0% overlap and 100% overlap. For 0% overlap, shown in figure A2.2a, it can be seen that the centre of gravity displacement (dcg) is equal to the maximum crush (dmax). For 0% overlap,

d max = dcg .

For 100% overlap the dcg – dmax relationship is more complicated. Assuming that car 1 and car 2 are identical in figure A2.2b and therefore L1 is twice the length of both cars (L), then the centre of gravity displacement (dcg) is

(A2.8)

'

dcg ' =

'

'

( L1 − L 2 ) L = L' − 2 . 2 2

(A2.9)

If the normalised width of the car front (ab) is 1, then '

Therefore,

For 100% overlap,

L2 cos α . = L' − d 'max + 2 2

(A2.10)

cos α   dcg ' = L' −  L' − d 'max +  2  

(A2.11)

d 'max = dcg ' +

cos α . 2

(A2.12)

Combining equations A2.8 and A2.12 a relationship between d 'max and dcg as a function of overlap is found,

d 'max = dcg ' + OL.

cos α 2

(A2.13)

where OL is the overlap with values ranging from zero for no overlap to one for one hundred percent overlap. Substituting equation A2.13 into equation 2.2 and taking P’ as zero, we obtain a relationship between the centre of gravity displacement (dcg) and the mean crush ( d ) for a triangular crush profile.

dcg ' = d ' + (1 − OL )

Figure A2.1

cos α . 2

a – 0% Overlap b – 100% Overlap Figure A2.2

(A2.14)

Figure 1

Figure 3

Figure 5

Figures 6 & 7

a

b

c Figure 8

a

b

c Figure 9

a

b

c Figure 10