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Simplified method for evaluating energy loss in vehicle collisions
Accident Analysis and Prevention 41 (2009) 633–641
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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Simplified method for evaluating energy loss in vehicle collisions Dario Vangi ∗ Department of Mechanic and Industrial Technologies, Faculty of Engineering, University of Florence, Via S. Marta, 3 – 50139 Florence, Italy
a r t i c l e
i n f o
Article history: Received 18 June 2008 Received in revised form 5 January 2009 Accepted 20 February 2009 Keywords: Energy loss Accident reconstruction EES Crush measurement Vehicle impact
a b s t r a c t A method is proposed for the evaluation of energy loss in road vehicle collisions. The energy loss evaluation is an essential task to reconstruct the dynamics of a road accident. The proposed method combines the simplicity of visual evaluation, typical of the method based on EES (equivalent energy speed), with flexibility, in order to evaluate the energy loss on any kind of vehicle deformation profile, of the methods based on measuring residual crush. The method is based on linearizing the damage profile, so that it is possible to predetermine the analytical expression of the kinetic energy loss in relation to only two parameters that characterise the shape of the damage. The stiffness of the vehicle is determined by estimating the geometric parameters of the damage starting from a photograph of generic damage, with documented EES, on a vehicle of the same model as the one under investigation. The proposed method was validated performing crash tests and using data from crash tests found in the literature. The method estimate with sufficient accuracy the kinetic energy loss in deformation on vehicles. The method, thanks to its simplicity and versatility, can constitute a valid alternative to the classic procedures for evaluating energy loss commonly utilised. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction In reconstructing the dynamics of a road accident and the impact phase, the ordinary methods employed (based on analysis of forces and deformations or based on momentum equations) require knowledge of the energy loss in vehicles damages. This energy can be estimated starting from evaluation of the work done by the contact forces, through knowledge of the force-deformation law or of the equivalent stiffness (coefficients A and B or k1 and k2 (Campbell, 1974; Fonda, 1999; Siddal and Day, 1996; McHenry and McHenry, 1986; Nystrom et al., 1991; Neptune et al., 1992)) and through measurement of the deformations. An alternative method, widely used in Europe, is based on comparing the vehicle damage with similar damage for which the energy loss is known. In general, comparison is based on the EES (equivalent energy speed) parameter (Schreier and Nelson, 1987; Zeidler et al., 1985). These methods have some limitations. The one based on visual comparison of the damage (EES) is not applicable in every case, since it is not always possible to find vehicles similar in dimensions, mass and stiffness, which have undergone damage similar in severity and position, and for which the EES is certified. As regards instead the methodology based on measuring the residual crush
∗ Tel.: +39 055 4796505; fax: +39 055 4796505. E-mail address: dario.vangi@unifi.it. 0001-4575/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.aap.2009.02.012
(Campbell, 1974; McHenry, 2001), the stiffness coefficients specific to a given type of vehicle are not always available and the stiffness values taken from tables found in the literature often refer only to American cars and are, moreover, divided into broad bands, at times too broad. A method is proposed here, termed the “triangle method”, which combines the simplicity of visual evaluation, typical of the method based on EES, with flexibility of measuring residual crush method in order to evaluate the energy loss on any vehicle deformation profile. The proposed method is based on linearizing the damage profile, i.e. on approximating damage of any kind with rectangular and triangular shape. For these configurations it is possible to predetermine, according to Campbell’s method (Campbell, 1974), the analytical expression of the kinetic energy loss in relation to only one or two parameters that characterise the shape of the damage. The stiffness characteristics of the vehicle are instead determined by estimating the geometric parameters of the damage starting from a photograph of generic damage (reference damage), with documented EES, on a vehicle of the same model as the one under investigation. 2. Theory In analysing residual crush in vehicles subject to road accidents, it has been noted that the deformation profiles, although often highly irregular, can be linearized by approximating the
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Nomenclature A B b0 b1 C C1 , C2 Ci Ed EdA EdB EES f KA KB L100 Ld M PDOF V V¯ XA XB
stiffness coefficient (zero residual crush force) stiffness coefficient (slope of the force–crush curve) impact speed which produces no residual crush slope of impact speed vs. crush linear curve damage depth parameter in linearized profiles damage depth parameters in trapezoidal profiles singular damage depth measurement in Campbell’s method energy loss energy loss by vehicle energy loss by barrier equivalent energy speed–speed in a rigid barrier crash test which produce the same crush correction coefficient to account for the PDOF longitudinal stiffness of the vehicle stiffness of the barrier frontal width damage width vehicle mass principal direction of force pre-impact velocity post-impact velocity average crush depth of the vehicle in a 40% offset crash test with deformable barrier average crush depth of the deformable barrier in a 40% offset crash test
Greek symbols ˛ coefficient to account for EES in a 40% offset damage ε coefficient of restitution
damaged area with triangular, rectangular or trapezoidal geometries, as shown in Figs. 1 and 2. This approximation make it possible to predetermine the analytical expression of the energy loss based on only two parameters, which characterise the shape of the damage: the depth C and the width Ld .
These parameters can also be adequately quantified by visual analysis of suitable photographic documentation of the damage. For correct evaluation of the depth C, it should be taken into account, albeit in qualitative manner, that the shape by which the damage is approximated must be equivalent to the latter not so much in geometry (area) as in terms of energy (the same damaged area, but with greater depth, absorbs more energy, energy being proportional to the square of depth). The expression of energy loss in the various cases of damage approximation is analysed below. 2.1. Triangle In cases where the deformed area of the vehicle can be approximated by a triangle, the energy loss can be expressed by the ratio between the width of the deformed area Ld and the width of the car front L100 , the maximum deformation C and the coefficients characteristic of the vehicle b0 and b1 (Campbell, 1974): Ed = Ld
M L100
b20 2
+
b2 C 2 b0 b1 C + 1 2 6
f
(1)
where f indicates the corrective factor introduced to account for the fact that the principal direction of force (PDOF) is not generally normal to the axis of the vehicle (Crash User’s Guide, 1981; Smith and Noga, 1982; Woolley et al., 1985; McHenry, 2001; Vangi, 2009). Utilising the following expression (McHenry, 1976) for the correction coefficient f = 1 + tg2 (PDOF) = 1/cos2 (PDOF), (1) becomes: M Ld Ed = cos2 (PDOF) L100
b20
b2 C 2 b0 b1 C + + 1 2 2 6
(2)
The coefficient b0 , which represents the velocity below which no permanent deformation is produced in impact against a fixed rigid barrier, can be considered with good approximation as constant and, equal to 8 km/h (2.2 m/s) for any type of vehicle (King et al., 1993; Nystrom et al., 1991; Strother et al., 1990). The parameter b1 varies instead in relation to the vehicle’s stiffness characteristics, and is the parameter to be determined. Recalling that energy loss can be expressed as Ed =
1 M(EES)2 2
Fig. 1. Approximating damage on vehicles with areas of triangular, trapezoidal or rectangular shape.
Fig. 2. Examples of real damage that can be approximated with geometries (a) triangular and (b) rectangular.
(3)
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Fig. 3. Diagram “C”—Triangle: graph of parameter EES cos(PDOF)(L100 /Ld )0.5 versus depth of damage of triangular shape C, for various values of coefficient b1 .
Fig. 4. Diagram “A”—Rectangle: graph of parameter EES cos(PDOF) versus depth of damage of rectangular shape C, for various values of coefficient b1 .
it is possible, by equalising (3) to (2), to obtain the following equation:
obtain a satisfactory balance between the energy loss for both areas, the trapezoidal and the triangular one
EES cos(PDOF)
L100 = Ld
b20 + b0 b1 C +
b21 C 2 3
C = C2 + 0.7C1 (4)
To simplify the method and make it fully applicable without having to perform calculations, we can diagram Eq. (4), which becomes a bundle of lines originating at the point of coordinates (0, b0 ), with parameter b1 (see Fig. 3).
(8)
At this point we can express energy loss through (2) and obtain an equation for EES similar to (4), where Ld = L100 :
EES cos(PDOF) =
b20 + b0 b1 C +
b21 C 2 3
(9)
whose diagram is again the one shown in Fig. 3. 2.2. Rectangle 2.4. Damage deriving from 40% offset crash test In cases where the deformed area of the vehicle can be approximated by a rectangle, the energy loss can be expressed by the deformation depth C of the rectangle, the width of the deformed area Ld = L100 (constant along its entire perimeter) and the stiffness coefficients characteristic of the vehicle b0 and b1 : M Ed = cos2 (PDOF)
b20 2
+ b0 b1 C +
b21 C 2
2
(5)
Recalling (3) we can write:
EES cos(PDOF) =
b20 + 2b0 b1 C + b21 C 2
(6)
The deformation deriving from a 40% offset crash test against a barrier or impactor is also analysed, since it is a very commonly used test, so that images of damage with documented EES are available. In the case of 40% offset crash test against a barrier, deformation in the vehicle occurs as diagrammed in Fig. 6. This deformation is characterised by a portion of direct damage, deriving from contact between the vehicle’s front end and the barrier, whose width is 40% of the width of the front end L = 0.4 L100 , and a portion of indirect damage whose width can be approximated, for almost all vehicles, as equal to L/2. This approximation derived from the observation of many EURONCAP (European New
(that is analogous to the classical equation V = b0 + b1 C), which can be diagrammed as shown in Fig. 4. 2.3. Trapezoid In cases where the deformed area of the vehicle can be approximated by a trapezoid, the energy loss can be expressed by the width of the deformed area Ld = L100 , the maximum deformations C2 and minimum deformations C1 = kC2 (k ≤ 1) and the stiffness coefficients characteristic of the vehicle b0 and b1 : Ed =
M Ld cos2 (PDOF) L100
b20 2
+
b2 C 2 (1 + k + k2 ) b0 b1 C(1 + k) + 1 2 6
(7) To reduce the number of parameters in (7), the area of the trapezoid can be approximated by the area of an equivalent triangle as regards energy loss, having the same width, and as length C the sum of the maximum crush C2 and the minimum crush C1 multiplied by a factor of 0.7 (see Fig. 5). This factor is empirically determined to
Fig. 5. Approximating trapezoidal area with triangular area equivalent as regards energy loss.
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Fig. 6. Approximation with trapezoidal area of damage deriving from impact against a barrier at 40% offset.
Car Assessment Programme—www.euroncap.com) 40% offset crash tests. The vehicle’s energy loss (indicated as EdA , to distinguish it from the globally energy loss Ed , which also includes any energy loss by the deformable barrier) can thus be expressed as the sum total of a portion of damage of rectangular shape plus a portion of triangular shape EdA = M
L
L100
+M
L/2 L100
b20 2
+ b0 b1 C +
b20 2
+
b21 C 2
b0 b1 C + 2
6
EdA = M
0.7b21 C 2 b0 b1 C 0.3b20 + + 2 3
(10)
(11)
To determine the equation that relates the EES to the maximum deformation C measurable on the vehicle, we must distinguish between the case of non-deformable barrier and deformable barrier (e.g., EURONCAP tests). In the case of non-deformable barrier, the vehicle’s EES is equal to the impact velocity of the crash test (ignoring elastic restitution). In the case of deformable barrier, part of the kinetic energy possessed by the vehicle is dissipated in deformation of the barrier. The energy dissipated by the barrier, linearizing its mechanical behaviour, is EdB =
1 KB XB2 2
(12)
with KB the stiffness of the barrier and XB the displacement (deformation) of the barrier. This displacement, in the real case of non-uniform deformation, corresponds to a displacement calculated as weighted average on the depth of crush of the barrier. The vehicle’s energy loss is EdA
1 = KA XA2 2
from which, recalling the definition of the coefficient of restitution and considering that the barrier is fixed: 1 M V 2 (1 − ε2 ) 2
EdA =
(16)
(13)
(14)
1 1 1 KA XA2 = MV 2 (1 − ε2 ) − KB XB2 2 2 2
(17)
from which, substituting KB obtained from (12) and with some algebraic manipulation, we have Ed =
1 XB KA XA2 1 + 2 XA
=
1 MV 2 (1 − ε2 ) 2
(18)
The energy dissipated by the vehicle is, comparing (13) with (18): EdA =
1 MV 2 ˛2 2
with ˛2 = (1 − ε2 )
(19)
XA XA + XB
(20)
The EES of the vehicle, in the case of impact against a deformable barrier, is thus EES = V˛. In the case of 40% offset crash test against a deformable barrier, of the EURONCAP type, from analysis of the relationship between XA and XB we can determine, from (20), a mean value of ˛ around 0.92, within a range of 0.9–0.94. The value of 0.92 agrees also with the EES value reported in the Autoexpert Hungary data base (EES = 58–60 km/h) for the EURONCAP crash tests (V test = 64 km/h; EES = V˛.). To determine the relationship between EES and the maximum deformation C measurable on the vehicle, we may utilise, in place of (3), the equation: Eda =
with the symbols having obvious meanings and the same considerations applying to deformation. Since at each instant of the impact, the force exchanged is the same for the vehicle and the barrier, we have KB XB = KA XA
(15)
The energy dissipated by the vehicle EdA , will thus be:
The corrective factor f is not introduced, due to the inclination of the forces in relation to the vehicle’s axis, since typically the PDOF in this type of test is only a few degrees and the f factor may be considered unitary. Since L = 0.4 L100 the above equation can also be written as
1 1 MV 2 − M V¯ 2 = Ed 2 2
Ed =
2 b21 C 2
From the law of conservation of energy we may write:
1 MV 2 ˛2 2
(21)
where in the case of non-deformable barrier, it is assumed that ˛ = 1. We obtain:
EES = V˛ =
0.6b20 + b0 b1 C +
1.4b21 C 2
3
which can be diagrammed as shown in Fig. 7.
(22)
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3.2. Step 2 When the damage to the vehicle under investigation can be approximated by a triangular shape: • In diagram “C”, on the same stiffness curve identified in step 1, in correspondence to the value of the deformation C estimated on the vehicle under investigation, determine the value of the parameter:
EES cos(PDOF)
L100 Ld
• Having estimated the PDOF and the relationship L100 /Ld , determine the value of EES. Fig. 7. Diagram “B”—Offset 40%: graph of parameter EES = V˛ versus damage depth C, for various values of coefficient b1 in damage deriving from 40% offset crash test. ˛ = 1 for non-deformable barrier and ˛ = 0.92 for deformable barrier type EURONCAP.
3. Procedure for determining energy loss by the triangle method Having determined the relationships between EES and the damage parameters, for the various geometries by which any damage on a vehicle can be approximated, we may proceed as follows to determine the energy loss of a vehicle. (1) Evaluate the geometric parameters of the damage taken as reference and determine the stiffness curve on the proper diagram (triangular, rectangular, trapezoidal or 40% offset). (2) Evaluate the geometric parameters of damage to the vehicle under evaluation (triangular or rectangular approximation) and determine the value of EES from the proper diagram. (3) Calculate the deformation energy.
When the damage to the vehicle under investigation can be approximated by a trapezoidal shape, it is treated as if it were triangular, with maximum depth of the equivalent triangle equal to: C = C2 + 0.7C1 , where C1 is the shorter side of the trapezoid. When the damage to the vehicle under investigation can be approximated by a rectangular shape: • In diagram “A”, on the stiffness curve identified in step 1, in correspondence to the value of the deformation C estimated on the vehicle under investigation, determine the value of the parameter: EES cos(PDOF) • Having estimated the PDOF, determine the value of EES. 3.3. Step 3 The value of the energy loss can be computed by
The procedure can be applied either starting from the above formulations, or by utilising diagrams “A”, “B” and “C” directly, without the need for calculations. Utilising the diagrams, the various steps are analysed below: 3.1. Step 1 A crash test is available, with known EES: Evaluate the deformation C of the damage:
1 2
× M × EES 2
4. Application Some examples to show the applicability of the proposed method are presented, which cover the common situations of energy loss computation in road accident reconstruction. 4.1. Example 1—estimation based on photographs of 100% offset crash
Determine the EES (ignoring the restitution, EES can be assumed equal to the impact velocity V for 100% offset crashes, while EES = V˛, with ˛ = 0.92 for 40% offset crashes). Consider PDOF = 0. Determine on the diagram (diagram “A” for 100% offset crash test against rigid barrier, diagram “B” for 40% offset crash test against either rigid or deformable barrier) the stiffness line on which lies the point identified by the pair of values C and EES.
We wish to estimate the EES of a Volvo S40 for which we have a photograph of the damage (Fig. 8). This is the damage under investigation. The photograph has been taken from the catalogue Autoexpert Hungary to which an EES value of 16 km/h has been assigned. Based on analysis of the photograph of the vehicle, the damaged area is approximated by a triangular shape and the following parameters are estimated:
If no crash test is available, but only photographs of damage of any kind with documented EES:
• maximum deformation: 20 cm, • width of deformed area: 90% of front end, • PDOF = 10◦ .
• Estimate the deformation depth C of the damage, approximating it with a triangle, rectangle or trapezoid (in the latter case, consider C = C2 + 0.7C1 ) and width Ld . • Estimate the PDOF. • Determine on the diagram (diagram “A” for rectangular damage and diagram “C” for triangular damage) the stiffness line on which lies the point identified by the pair of values C and EES.
As reference damage, we may consider a 100% offset crash test against a rigid barrier, taken from the NHTSA database (crash no. 5544), with EES 11 m/s (see Fig. 9). This is the reference damage. It is assumed that PDOF = 0. From the photograph of the vehicle subjected to crash test, damage of rectangular shape with C = 0.3 m is estimated. The
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deformation of 20 cm on the vehicle, we determine the value
EES cos(PDOF)
L100 = 5 m/s Ld
Considering that the width of deformation is about 90% of the total width (Ld /L100 = 0.9) and PDOF = 10◦ , we obtain a value of around 17 km/h for EES, which is very close to the value documented for the damage in question, 16 km/h. 4.2. Example 2—estimation based on photograph of 40% offset crash against deformable barrier
Fig. 8. Documentation of damage to vehicle whose energy loss is to be determined in examples 1 and 2.
deformation depth could also have been determined from the measurements given in the crash test report. Utilising graph “A”, suitable for the damage of rectangular shape, we identify the line on which lies the point identified by the pair of values EES cos(PDOF) = 11 m/s and C = 30 cm: 5th curve starting from the top. On diagram “C”, suitable for the damage of triangular shape, on the same curve (5th from the top) and in correspondence to a
We wish to estimate the EES of the same Volvo S40 used in example 1, but having available as reference a 40% offset crash against a deformable barrier (EURONCAP) at V = 64 km/h (17.8 m/s). From a photograph of the vehicle subjected to crash test, damage of rectangular shape is estimated with C = 0.65 m (see Fig. 10). It is assumed that PDOF = 0. Utilising graph “B”, suitable for damage from a 40% offset crash, we identify the line on which lies the point identified by the pair of values C and V˛ (with ˛ = 0.92 we have V˛ = 17.7 × ˛ = 16 m/s − deformation C = 65 cm): between the 4th and 5th curve from the top. On diagram “C”, suitable for damage of triangular shape, on the same curve (between the 4th and 5th from the top) and in correspondence to a deformation of 20 cm on the vehicle, we determine
Fig. 9. Vehicle subjected to crash test and evaluation of damage depth in the equivalent rectangular area.
Fig. 10. Vehicle subjected to crash test and evaluation of damage depth in trapezoidal area.
D. Vangi / Accident Analysis and Prevention 41 (2009) 633–641
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Fig. 11. Documentation of damage to vehicle whose energy loss is to be determined in example 3.
Fig. 12. Documentation of reference damage taken from “Auto Export Hungary” database with documented EES of 27 km/h.
the value
bottom) and in correspondence to a deformation of 20 cm on the vehicle, we find the value
EES cos(PDOF)
L100 = 5.2 m/s Ld
Considering that the width of the deformation is approximately 90% of the total width (Ld /L100 = 0.9) and PDOF = 10◦ , we obtain a value of about 17.7 km/h for EES, close to the value documented for the damage in question, namely 16 km/h, and to the value calculated in example 1. 4.3. Example 3—estimation based on photograph of real accident with documented EES We wish to estimate the EES of a Fiat Punto for which we have a photograph of the damage (Fig. 11). The figure, to which an EES value of 24 km/h was assigned, was taken from the Autoexpert Hungary data base. Based on analysis of the photograph of the vehicle under investigation, the damaged area is approximated by a rectangular shape and the following parameters are estimated: • maximum deformation: 20 cm, • width of deformed area: 100% of front end, • PDOF = 0◦ .
EES cos(PDOF) = 6.1 m/s = 22 km/h which coincides with the EES, since PDOF = 0. The documented value of the damage in Fig. 13 is EES =24 km/h, close to the value determined with the triangle method. 5. Limits and applicability The method, being derived directly by the Campbell’s method, is subject to the same limitations, namely the reference damage must include the same structures than in the case under inspection, particularly referring to the vertical extent and position (frontal, lateral, and rear) of the damage. The validity of the linear approximation of the damage can be verified comparing the approximate profile with the real one and evaluating the corresponding energy loss. For this purpose, sets of random numbers were generated, representing the classic 6 Ci measurements (Tumbas and Smith, 1988) of crush depth utilised in the Campbell method; the difference between the energy loss calculated starting from the Ci measurements and on the linearized profile was then evaluated.
We do not have available a crash test as reference damage, but a photograph of the same vehicle, taken from the “Auto Export Hungary” data base, but with damage of strikingly different shape and EES of 27 km/h = 7.5 m/s (see Fig. 12). Based on analysis of the photograph of the reference damage, the damaged area is approximated by a triangular shape and the following parameters are estimated: • maximum deformation: 50 cm, • width of damaged area: 80% of front end, Ld /L100 = 0.8, • PDOF = 0◦ . Utilising graph “C”, suitable for damage of triangular shape, we identify the line on which lies the point identified by the pair of values C and EES cos(PDOF) L100 /Ld (EES 7.5 m/s − deformation 50 cm, Ld /L100 = 0.8, PDOF = 0): between the 2nd and 3rd curve starting from the bottom. On diagram “A”, suitable for the damage of rectangular shape, on the same curve (between the 2nd and the 3rd starting from the
Fig. 13. Example of profile randomly generated with 6 crush depths.
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In the random Ci generation, to avoid non-realistic profiles, difference in the crush depth between one measurement and the subsequent was kept less than the mean value of the 6 measurements divided by 1.5. This value was determined by trial and error procedure, to provide realistic crush profiles. The profile was linearized utilising both a single line and two broken lines (for V-shaped profiles, as occur in cases of impact against poles or trees, for example), utilising the best-fit lines of the points. An example of a profile randomly generated is given in Fig. 13. Around 20,000 simulations were performed, varying the following parameters: • • • •
Pattern of damage profile (Ci measurements). Width of car. Width of damaged area. Stiffness parameters of the car, within the values available in the stiffness tables of NHTSA.
The percentage frequency histograms of mean deviation of the real profile from the approximating line and the histogram of percentage errors in energy loss calculation are shown in Fig. 14. The maximum profile deviations are about 23 cm. The mean error in calculating energy loss is around 2.5%, the maximum is 12%. These results confirm that approximating any damaged profile with a line or pair of lines, even in the presence of differences of 20 cm between the original and the linearized profile, produces acceptable errors in calculating energy loss. This is true all the more so considering the general approximations of the method of Campbell or the method of EES in the evaluation of the energy loss. For an experimental validation of the proposed methodology, crash tests were conducted on the track of the University of Florence – Department of Mechanics and Industrial Technologies, on vehicles of the models Fiat Panda and Fiat Uno, in order to have a sure value of energy loss to be compared with the estimations obtained by the proposed method. Each type of vehicle was tested in crashes
Fig. 14. Histogram of deviation of the real profile from the approximating line in cm (triangular marks) and histogram of percentage error (round marks) energy calculation.
against a fixed rigid barrier: (A) at 100% offset, (B) at 40% offset and (C) with barrier tilted 45◦ . By way of example, the values of the real and the estimated EES for the Fiat Uno vehicle are compared in the three following cases: (A–B) Estimation of EES of 100% offset crash starting from damage of 40% offset crash. (A–C) Estimation of EES of 100% offset crash starting from damage of crash with barrier tilted 45◦ . (B–A) Estimation of EES of 40% offset crash starting from damage of 100% offset crash. (B–C) Estimation of EES of 40% offset crash starting from damage of crash with barrier tilted 45◦ .
Table 1 Data from experimental crash tests on Fiat Uno type vehicle. Fiat Uno
A-offset 100%
B-offset 40%
C-tilted 45◦
a
Vehicle mass (kg)
Pre-impact velocity (km/h)
Post-impact velocity (km/h)
800
54.4
5.4
91,204
61
91,142
54
800
45.5
2.7
63,896
13
63,883
45
840
46.2
25.0
69,171
20,255
36,316a
33
The energy balance is computed also the energy loss by friction between barrier and car, 12,600 J.
Pre-impact kinetic energy (J)
Post-impact kinetic energy (J)
Energy loss j
EES (km/h)
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Table 2 Comparison between experimental EES versus calculated ones. Reference EES (km/h)
Deformation (cm)
Curve
Estimated EES (km/h)
Evaluation of EES Case A (EES = 54 km/h) Case B 45 Case C 33
59 31
5th from bottom 5th from bottom
56 56
Evaluation of EES Case B (EES = 45 km/h) Case A 54 Case C 33
57 31
4th–5th from bottom 5th from bottom
42 44
Evaluation of EES Case C (EES = 33 km/h) Case A 54 Case B 45
57 59
4th–5th from bottom 5th from bottom
33 35
(C–A) Estimation of EES of crash with barrier tilted 45◦ starting from damage of 100% offset crash. (C–B) Estimation of EES of crash with barrier tilted 45◦ starting from damage of 40% offset crash. The data and results of the crash tests on the model Fiat Uno are reported in Table 1. For the cases presented above, the experimental EES values and those calculated through the triangle method are compared in Table 2. The results show excellent match between the estimated and the real values, thus validating the applicability of the method. Regardless of shape of the damages, the EES–Crush dept relationship is linear. So, any error in the reference EES propagate linearly over the computed EES, amplified by factor C investigated/C reference, where C reference is the reference damage dept and C investigated is the dept of the damage under investigation. Note that, for applying this method, it is unnecessary to know the stiffness coefficients of the vehicles, which are subject to error and can significantly influence the evaluation of energy loss (Wang and Gabler, 2007; Jang et al., 2003), since evaluation is again based on visual estimation of deformations, similar to the method based on EES. 6. Conclusions This study presents a method alternative to the existing ones commonly employed to evaluate the energy loss in damage occurring to vehicles in road accidents. The new method, called “triangle method”, combines the simplicity of visual comparison, typical of the method based on EES, with flexibility in evaluating the energy loss on any deformation profile of a vehicle, typical of the Campbell’s method. The new methodology is applicable starting from photographic documentation with certified EES of damage of any kind, even differing in shape and severity from the one in question, taken from a generic crash test or even from a real accident on the same type of vehicle as the one under investigation. The damage of the vehicles is approximated by a triangular, rectangular or trapezoidal geometry, allowing the analytical expression of energy loss to be determined on the basis of only two parameters, which characterise the geometry of the damage: the depth C and the width Ld , which can be adequately quantified also by visual analysis of suitable photographic documentation of the damage. The approximation deriving from linearization of the damage profile has been evaluated as regards both geometry and energy, by performing numerical simulations and comparing the energy loss in the two cases: considering the profile in typical cases of damage deriving from real crashes, and considering the linearized profile. The difference between the energy values calculated utilising linear approximation as compared to the traditional measurement with six measurement stations was found to be minor, averaging about 2.5%.
Having noted the low value of the error introduced through linear approximation of the damage profile on the vehicles, the proposed method was validated utilising both crash tests conducted at the University of Florence Department of Mechanics and Industrial Technologies and data from crash tests found in the literature or from real accidents where the energy loss value was known. Based on the results, it was concluded that the new method can be used to estimate with sufficient accuracy the kinetic energy loss in deformation on vehicles consequent to road accidents. The method has been described in a course held by the University of Florence for 50 traffic accident experts, with a test in which the participants were requested to apply it in estimating the energy loss of vehicles involved in accidents. The results have confirmed that the method, thanks to its simplicity and versatility, can constitute a valid alternative to the classic procedures for evaluating energy loss commonly utilised. References Campbell, K.E., 1974. Energy Basis for Collision Severity. Environmental Activities Staff, General Motors Corp., SAE Paper 740565. Crash 3 User’s Guide and Technical Manual, Pub. No. DOT HS 805732, NHTSA, Washington, DC, 1981. Fonda, A.G., 1999. Principles of Energy Loss Determination. Fonda Engineering Associate, SAE Paper 1999-01-0106. Jang, T., Grzebieta, R.H., Rechnitzer, G., Richardson, S., Zhao, X.L., 2003. Review of car frontal stiffness equations for estimating vehicle impact velocities. In: Proceedings of the 18th International Technical Conference on Enhanced Safety of Vehicles, Nagoya, Japan, May. King, D.J., Siegmund, G.P., Bailey, M.N., 1993. Automobile Bumper Behavior in Lowspeed Impacts, SAE Paper No. 930211. McHenry, B.G., 2001. The Algorithm of CRASH. McHenry Software, Inc. McHenry, R.R., 1976. Extensions and Refinements of the CRASH Computer Program Part I: Analytical Reconstruction of Highway Accidents, DOT HS-801 832. McHenry, R.R., McHenry, B.G., 1986. A Revised Damage Analysis Procedure for the CRASH Computer Program. McHenry Consultants, Inc., Cary, NC, SAE Paper 861894. Neptune, J.A., Blair, G.Y., Flynn, J.E., 1992. A Method for Quantifying Vehicle Crush Stiffness Coefficients. Blair, Church & Flynn Consulting Engineers, SAE Paper 920607. Nystrom, G.A., Kost, G., Werner, S.M., 1991. Stiffness Parameters for Vehicle Collision Analysis. Failure Analysis Associates, Inc, SAE Paper 910119. Schreier, H.H., Nelson, W.D., 1987. Applicability of the EES-accident Reconstruction Method with MacCAR©, SAE Paper 870047. Siddal, D.E., Day, T.D., 1976. Updating the Vehicle Class Categories, Engineering Dynamics Corp., SAE Paper 960897. Smith, R.A., Noga, J.T., 1982. Accuracy and sensitivity of CRASH, U.S. Department of Transportation, National Highway Traffic Safety, SAE Paper 821169. Strother, C.E., Woolley, R.L., James, M.B., 1990. A Comparison Between NHTSA Crash Test Data and CRASH3 Frontal Stiffness Coefficients, SAE Paper 900101. Tumbas, N.S., Smith, R.A., 1988. Measurement Protocol for Quantifying Vehicle Damage from an Energy Basis Point of View, Tumbas and Associates—U.S. Naval Academy, SAE Paper 880072. Vangi, D., 2009. Energy loss in vehicle to vehicle oblique impact. International Journal of Impact Engineering 36 (March (3)), 512–521. Wang, Q., Gabler, H.G., 2007. Accuracy of vehicle frontal stiffness estimates for crash reconstruction. In: Proceedings of the 20th International Technical Conference on Enhanced Safety of Vehicles, Lyon, France, June. Woolley, R.L., Warner, C.Y., Tagg, M.D., 1985. Inaccuracies in the CRASH3 Program, Collision Safety Engineering, SAE Paper 850255. Zeidler F., Schreier H.H., Stadelmann R., 1985. Accident Research and Accident Reconstruction by the EES-accident Reconstruction Method, SAE Paper 850256.
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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Simplified method for evaluating energy loss in vehicle collisions Dario Vangi ∗ Department of Mechanic and Industrial Technologies, Faculty of Engineering, University of Florence, Via S. Marta, 3 – 50139 Florence, Italy
a r t i c l e
i n f o
Article history: Received 18 June 2008 Received in revised form 5 January 2009 Accepted 20 February 2009 Keywords: Energy loss Accident reconstruction EES Crush measurement Vehicle impact
a b s t r a c t A method is proposed for the evaluation of energy loss in road vehicle collisions. The energy loss evaluation is an essential task to reconstruct the dynamics of a road accident. The proposed method combines the simplicity of visual evaluation, typical of the method based on EES (equivalent energy speed), with flexibility, in order to evaluate the energy loss on any kind of vehicle deformation profile, of the methods based on measuring residual crush. The method is based on linearizing the damage profile, so that it is possible to predetermine the analytical expression of the kinetic energy loss in relation to only two parameters that characterise the shape of the damage. The stiffness of the vehicle is determined by estimating the geometric parameters of the damage starting from a photograph of generic damage, with documented EES, on a vehicle of the same model as the one under investigation. The proposed method was validated performing crash tests and using data from crash tests found in the literature. The method estimate with sufficient accuracy the kinetic energy loss in deformation on vehicles. The method, thanks to its simplicity and versatility, can constitute a valid alternative to the classic procedures for evaluating energy loss commonly utilised. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction In reconstructing the dynamics of a road accident and the impact phase, the ordinary methods employed (based on analysis of forces and deformations or based on momentum equations) require knowledge of the energy loss in vehicles damages. This energy can be estimated starting from evaluation of the work done by the contact forces, through knowledge of the force-deformation law or of the equivalent stiffness (coefficients A and B or k1 and k2 (Campbell, 1974; Fonda, 1999; Siddal and Day, 1996; McHenry and McHenry, 1986; Nystrom et al., 1991; Neptune et al., 1992)) and through measurement of the deformations. An alternative method, widely used in Europe, is based on comparing the vehicle damage with similar damage for which the energy loss is known. In general, comparison is based on the EES (equivalent energy speed) parameter (Schreier and Nelson, 1987; Zeidler et al., 1985). These methods have some limitations. The one based on visual comparison of the damage (EES) is not applicable in every case, since it is not always possible to find vehicles similar in dimensions, mass and stiffness, which have undergone damage similar in severity and position, and for which the EES is certified. As regards instead the methodology based on measuring the residual crush
∗ Tel.: +39 055 4796505; fax: +39 055 4796505. E-mail address: dario.vangi@unifi.it. 0001-4575/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.aap.2009.02.012
(Campbell, 1974; McHenry, 2001), the stiffness coefficients specific to a given type of vehicle are not always available and the stiffness values taken from tables found in the literature often refer only to American cars and are, moreover, divided into broad bands, at times too broad. A method is proposed here, termed the “triangle method”, which combines the simplicity of visual evaluation, typical of the method based on EES, with flexibility of measuring residual crush method in order to evaluate the energy loss on any vehicle deformation profile. The proposed method is based on linearizing the damage profile, i.e. on approximating damage of any kind with rectangular and triangular shape. For these configurations it is possible to predetermine, according to Campbell’s method (Campbell, 1974), the analytical expression of the kinetic energy loss in relation to only one or two parameters that characterise the shape of the damage. The stiffness characteristics of the vehicle are instead determined by estimating the geometric parameters of the damage starting from a photograph of generic damage (reference damage), with documented EES, on a vehicle of the same model as the one under investigation. 2. Theory In analysing residual crush in vehicles subject to road accidents, it has been noted that the deformation profiles, although often highly irregular, can be linearized by approximating the
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Nomenclature A B b0 b1 C C1 , C2 Ci Ed EdA EdB EES f KA KB L100 Ld M PDOF V V¯ XA XB
stiffness coefficient (zero residual crush force) stiffness coefficient (slope of the force–crush curve) impact speed which produces no residual crush slope of impact speed vs. crush linear curve damage depth parameter in linearized profiles damage depth parameters in trapezoidal profiles singular damage depth measurement in Campbell’s method energy loss energy loss by vehicle energy loss by barrier equivalent energy speed–speed in a rigid barrier crash test which produce the same crush correction coefficient to account for the PDOF longitudinal stiffness of the vehicle stiffness of the barrier frontal width damage width vehicle mass principal direction of force pre-impact velocity post-impact velocity average crush depth of the vehicle in a 40% offset crash test with deformable barrier average crush depth of the deformable barrier in a 40% offset crash test
Greek symbols ˛ coefficient to account for EES in a 40% offset damage ε coefficient of restitution
damaged area with triangular, rectangular or trapezoidal geometries, as shown in Figs. 1 and 2. This approximation make it possible to predetermine the analytical expression of the energy loss based on only two parameters, which characterise the shape of the damage: the depth C and the width Ld .
These parameters can also be adequately quantified by visual analysis of suitable photographic documentation of the damage. For correct evaluation of the depth C, it should be taken into account, albeit in qualitative manner, that the shape by which the damage is approximated must be equivalent to the latter not so much in geometry (area) as in terms of energy (the same damaged area, but with greater depth, absorbs more energy, energy being proportional to the square of depth). The expression of energy loss in the various cases of damage approximation is analysed below. 2.1. Triangle In cases where the deformed area of the vehicle can be approximated by a triangle, the energy loss can be expressed by the ratio between the width of the deformed area Ld and the width of the car front L100 , the maximum deformation C and the coefficients characteristic of the vehicle b0 and b1 (Campbell, 1974): Ed = Ld
M L100
b20 2
+
b2 C 2 b0 b1 C + 1 2 6
f
(1)
where f indicates the corrective factor introduced to account for the fact that the principal direction of force (PDOF) is not generally normal to the axis of the vehicle (Crash User’s Guide, 1981; Smith and Noga, 1982; Woolley et al., 1985; McHenry, 2001; Vangi, 2009). Utilising the following expression (McHenry, 1976) for the correction coefficient f = 1 + tg2 (PDOF) = 1/cos2 (PDOF), (1) becomes: M Ld Ed = cos2 (PDOF) L100
b20
b2 C 2 b0 b1 C + + 1 2 2 6
(2)
The coefficient b0 , which represents the velocity below which no permanent deformation is produced in impact against a fixed rigid barrier, can be considered with good approximation as constant and, equal to 8 km/h (2.2 m/s) for any type of vehicle (King et al., 1993; Nystrom et al., 1991; Strother et al., 1990). The parameter b1 varies instead in relation to the vehicle’s stiffness characteristics, and is the parameter to be determined. Recalling that energy loss can be expressed as Ed =
1 M(EES)2 2
Fig. 1. Approximating damage on vehicles with areas of triangular, trapezoidal or rectangular shape.
Fig. 2. Examples of real damage that can be approximated with geometries (a) triangular and (b) rectangular.
(3)
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635
Fig. 3. Diagram “C”—Triangle: graph of parameter EES cos(PDOF)(L100 /Ld )0.5 versus depth of damage of triangular shape C, for various values of coefficient b1 .
Fig. 4. Diagram “A”—Rectangle: graph of parameter EES cos(PDOF) versus depth of damage of rectangular shape C, for various values of coefficient b1 .
it is possible, by equalising (3) to (2), to obtain the following equation:
obtain a satisfactory balance between the energy loss for both areas, the trapezoidal and the triangular one
EES cos(PDOF)
L100 = Ld
b20 + b0 b1 C +
b21 C 2 3
C = C2 + 0.7C1 (4)
To simplify the method and make it fully applicable without having to perform calculations, we can diagram Eq. (4), which becomes a bundle of lines originating at the point of coordinates (0, b0 ), with parameter b1 (see Fig. 3).
(8)
At this point we can express energy loss through (2) and obtain an equation for EES similar to (4), where Ld = L100 :
EES cos(PDOF) =
b20 + b0 b1 C +
b21 C 2 3
(9)
whose diagram is again the one shown in Fig. 3. 2.2. Rectangle 2.4. Damage deriving from 40% offset crash test In cases where the deformed area of the vehicle can be approximated by a rectangle, the energy loss can be expressed by the deformation depth C of the rectangle, the width of the deformed area Ld = L100 (constant along its entire perimeter) and the stiffness coefficients characteristic of the vehicle b0 and b1 : M Ed = cos2 (PDOF)
b20 2
+ b0 b1 C +
b21 C 2
2
(5)
Recalling (3) we can write:
EES cos(PDOF) =
b20 + 2b0 b1 C + b21 C 2
(6)
The deformation deriving from a 40% offset crash test against a barrier or impactor is also analysed, since it is a very commonly used test, so that images of damage with documented EES are available. In the case of 40% offset crash test against a barrier, deformation in the vehicle occurs as diagrammed in Fig. 6. This deformation is characterised by a portion of direct damage, deriving from contact between the vehicle’s front end and the barrier, whose width is 40% of the width of the front end L = 0.4 L100 , and a portion of indirect damage whose width can be approximated, for almost all vehicles, as equal to L/2. This approximation derived from the observation of many EURONCAP (European New
(that is analogous to the classical equation V = b0 + b1 C), which can be diagrammed as shown in Fig. 4. 2.3. Trapezoid In cases where the deformed area of the vehicle can be approximated by a trapezoid, the energy loss can be expressed by the width of the deformed area Ld = L100 , the maximum deformations C2 and minimum deformations C1 = kC2 (k ≤ 1) and the stiffness coefficients characteristic of the vehicle b0 and b1 : Ed =
M Ld cos2 (PDOF) L100
b20 2
+
b2 C 2 (1 + k + k2 ) b0 b1 C(1 + k) + 1 2 6
(7) To reduce the number of parameters in (7), the area of the trapezoid can be approximated by the area of an equivalent triangle as regards energy loss, having the same width, and as length C the sum of the maximum crush C2 and the minimum crush C1 multiplied by a factor of 0.7 (see Fig. 5). This factor is empirically determined to
Fig. 5. Approximating trapezoidal area with triangular area equivalent as regards energy loss.
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Fig. 6. Approximation with trapezoidal area of damage deriving from impact against a barrier at 40% offset.
Car Assessment Programme—www.euroncap.com) 40% offset crash tests. The vehicle’s energy loss (indicated as EdA , to distinguish it from the globally energy loss Ed , which also includes any energy loss by the deformable barrier) can thus be expressed as the sum total of a portion of damage of rectangular shape plus a portion of triangular shape EdA = M
L
L100
+M
L/2 L100
b20 2
+ b0 b1 C +
b20 2
+
b21 C 2
b0 b1 C + 2
6
EdA = M
0.7b21 C 2 b0 b1 C 0.3b20 + + 2 3
(10)
(11)
To determine the equation that relates the EES to the maximum deformation C measurable on the vehicle, we must distinguish between the case of non-deformable barrier and deformable barrier (e.g., EURONCAP tests). In the case of non-deformable barrier, the vehicle’s EES is equal to the impact velocity of the crash test (ignoring elastic restitution). In the case of deformable barrier, part of the kinetic energy possessed by the vehicle is dissipated in deformation of the barrier. The energy dissipated by the barrier, linearizing its mechanical behaviour, is EdB =
1 KB XB2 2
(12)
with KB the stiffness of the barrier and XB the displacement (deformation) of the barrier. This displacement, in the real case of non-uniform deformation, corresponds to a displacement calculated as weighted average on the depth of crush of the barrier. The vehicle’s energy loss is EdA
1 = KA XA2 2
from which, recalling the definition of the coefficient of restitution and considering that the barrier is fixed: 1 M V 2 (1 − ε2 ) 2
EdA =
(16)
(13)
(14)
1 1 1 KA XA2 = MV 2 (1 − ε2 ) − KB XB2 2 2 2
(17)
from which, substituting KB obtained from (12) and with some algebraic manipulation, we have Ed =
1 XB KA XA2 1 + 2 XA
=
1 MV 2 (1 − ε2 ) 2
(18)
The energy dissipated by the vehicle is, comparing (13) with (18): EdA =
1 MV 2 ˛2 2
with ˛2 = (1 − ε2 )
(19)
XA XA + XB
(20)
The EES of the vehicle, in the case of impact against a deformable barrier, is thus EES = V˛. In the case of 40% offset crash test against a deformable barrier, of the EURONCAP type, from analysis of the relationship between XA and XB we can determine, from (20), a mean value of ˛ around 0.92, within a range of 0.9–0.94. The value of 0.92 agrees also with the EES value reported in the Autoexpert Hungary data base (EES = 58–60 km/h) for the EURONCAP crash tests (V test = 64 km/h; EES = V˛.). To determine the relationship between EES and the maximum deformation C measurable on the vehicle, we may utilise, in place of (3), the equation: Eda =
with the symbols having obvious meanings and the same considerations applying to deformation. Since at each instant of the impact, the force exchanged is the same for the vehicle and the barrier, we have KB XB = KA XA
(15)
The energy dissipated by the vehicle EdA , will thus be:
The corrective factor f is not introduced, due to the inclination of the forces in relation to the vehicle’s axis, since typically the PDOF in this type of test is only a few degrees and the f factor may be considered unitary. Since L = 0.4 L100 the above equation can also be written as
1 1 MV 2 − M V¯ 2 = Ed 2 2
Ed =
2 b21 C 2
From the law of conservation of energy we may write:
1 MV 2 ˛2 2
(21)
where in the case of non-deformable barrier, it is assumed that ˛ = 1. We obtain:
EES = V˛ =
0.6b20 + b0 b1 C +
1.4b21 C 2
3
which can be diagrammed as shown in Fig. 7.
(22)
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3.2. Step 2 When the damage to the vehicle under investigation can be approximated by a triangular shape: • In diagram “C”, on the same stiffness curve identified in step 1, in correspondence to the value of the deformation C estimated on the vehicle under investigation, determine the value of the parameter:
EES cos(PDOF)
L100 Ld
• Having estimated the PDOF and the relationship L100 /Ld , determine the value of EES. Fig. 7. Diagram “B”—Offset 40%: graph of parameter EES = V˛ versus damage depth C, for various values of coefficient b1 in damage deriving from 40% offset crash test. ˛ = 1 for non-deformable barrier and ˛ = 0.92 for deformable barrier type EURONCAP.
3. Procedure for determining energy loss by the triangle method Having determined the relationships between EES and the damage parameters, for the various geometries by which any damage on a vehicle can be approximated, we may proceed as follows to determine the energy loss of a vehicle. (1) Evaluate the geometric parameters of the damage taken as reference and determine the stiffness curve on the proper diagram (triangular, rectangular, trapezoidal or 40% offset). (2) Evaluate the geometric parameters of damage to the vehicle under evaluation (triangular or rectangular approximation) and determine the value of EES from the proper diagram. (3) Calculate the deformation energy.
When the damage to the vehicle under investigation can be approximated by a trapezoidal shape, it is treated as if it were triangular, with maximum depth of the equivalent triangle equal to: C = C2 + 0.7C1 , where C1 is the shorter side of the trapezoid. When the damage to the vehicle under investigation can be approximated by a rectangular shape: • In diagram “A”, on the stiffness curve identified in step 1, in correspondence to the value of the deformation C estimated on the vehicle under investigation, determine the value of the parameter: EES cos(PDOF) • Having estimated the PDOF, determine the value of EES. 3.3. Step 3 The value of the energy loss can be computed by
The procedure can be applied either starting from the above formulations, or by utilising diagrams “A”, “B” and “C” directly, without the need for calculations. Utilising the diagrams, the various steps are analysed below: 3.1. Step 1 A crash test is available, with known EES: Evaluate the deformation C of the damage:
1 2
× M × EES 2
4. Application Some examples to show the applicability of the proposed method are presented, which cover the common situations of energy loss computation in road accident reconstruction. 4.1. Example 1—estimation based on photographs of 100% offset crash
Determine the EES (ignoring the restitution, EES can be assumed equal to the impact velocity V for 100% offset crashes, while EES = V˛, with ˛ = 0.92 for 40% offset crashes). Consider PDOF = 0. Determine on the diagram (diagram “A” for 100% offset crash test against rigid barrier, diagram “B” for 40% offset crash test against either rigid or deformable barrier) the stiffness line on which lies the point identified by the pair of values C and EES.
We wish to estimate the EES of a Volvo S40 for which we have a photograph of the damage (Fig. 8). This is the damage under investigation. The photograph has been taken from the catalogue Autoexpert Hungary to which an EES value of 16 km/h has been assigned. Based on analysis of the photograph of the vehicle, the damaged area is approximated by a triangular shape and the following parameters are estimated:
If no crash test is available, but only photographs of damage of any kind with documented EES:
• maximum deformation: 20 cm, • width of deformed area: 90% of front end, • PDOF = 10◦ .
• Estimate the deformation depth C of the damage, approximating it with a triangle, rectangle or trapezoid (in the latter case, consider C = C2 + 0.7C1 ) and width Ld . • Estimate the PDOF. • Determine on the diagram (diagram “A” for rectangular damage and diagram “C” for triangular damage) the stiffness line on which lies the point identified by the pair of values C and EES.
As reference damage, we may consider a 100% offset crash test against a rigid barrier, taken from the NHTSA database (crash no. 5544), with EES 11 m/s (see Fig. 9). This is the reference damage. It is assumed that PDOF = 0. From the photograph of the vehicle subjected to crash test, damage of rectangular shape with C = 0.3 m is estimated. The
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deformation of 20 cm on the vehicle, we determine the value
EES cos(PDOF)
L100 = 5 m/s Ld
Considering that the width of deformation is about 90% of the total width (Ld /L100 = 0.9) and PDOF = 10◦ , we obtain a value of around 17 km/h for EES, which is very close to the value documented for the damage in question, 16 km/h. 4.2. Example 2—estimation based on photograph of 40% offset crash against deformable barrier
Fig. 8. Documentation of damage to vehicle whose energy loss is to be determined in examples 1 and 2.
deformation depth could also have been determined from the measurements given in the crash test report. Utilising graph “A”, suitable for the damage of rectangular shape, we identify the line on which lies the point identified by the pair of values EES cos(PDOF) = 11 m/s and C = 30 cm: 5th curve starting from the top. On diagram “C”, suitable for the damage of triangular shape, on the same curve (5th from the top) and in correspondence to a
We wish to estimate the EES of the same Volvo S40 used in example 1, but having available as reference a 40% offset crash against a deformable barrier (EURONCAP) at V = 64 km/h (17.8 m/s). From a photograph of the vehicle subjected to crash test, damage of rectangular shape is estimated with C = 0.65 m (see Fig. 10). It is assumed that PDOF = 0. Utilising graph “B”, suitable for damage from a 40% offset crash, we identify the line on which lies the point identified by the pair of values C and V˛ (with ˛ = 0.92 we have V˛ = 17.7 × ˛ = 16 m/s − deformation C = 65 cm): between the 4th and 5th curve from the top. On diagram “C”, suitable for damage of triangular shape, on the same curve (between the 4th and 5th from the top) and in correspondence to a deformation of 20 cm on the vehicle, we determine
Fig. 9. Vehicle subjected to crash test and evaluation of damage depth in the equivalent rectangular area.
Fig. 10. Vehicle subjected to crash test and evaluation of damage depth in trapezoidal area.
D. Vangi / Accident Analysis and Prevention 41 (2009) 633–641
639
Fig. 11. Documentation of damage to vehicle whose energy loss is to be determined in example 3.
Fig. 12. Documentation of reference damage taken from “Auto Export Hungary” database with documented EES of 27 km/h.
the value
bottom) and in correspondence to a deformation of 20 cm on the vehicle, we find the value
EES cos(PDOF)
L100 = 5.2 m/s Ld
Considering that the width of the deformation is approximately 90% of the total width (Ld /L100 = 0.9) and PDOF = 10◦ , we obtain a value of about 17.7 km/h for EES, close to the value documented for the damage in question, namely 16 km/h, and to the value calculated in example 1. 4.3. Example 3—estimation based on photograph of real accident with documented EES We wish to estimate the EES of a Fiat Punto for which we have a photograph of the damage (Fig. 11). The figure, to which an EES value of 24 km/h was assigned, was taken from the Autoexpert Hungary data base. Based on analysis of the photograph of the vehicle under investigation, the damaged area is approximated by a rectangular shape and the following parameters are estimated: • maximum deformation: 20 cm, • width of deformed area: 100% of front end, • PDOF = 0◦ .
EES cos(PDOF) = 6.1 m/s = 22 km/h which coincides with the EES, since PDOF = 0. The documented value of the damage in Fig. 13 is EES =24 km/h, close to the value determined with the triangle method. 5. Limits and applicability The method, being derived directly by the Campbell’s method, is subject to the same limitations, namely the reference damage must include the same structures than in the case under inspection, particularly referring to the vertical extent and position (frontal, lateral, and rear) of the damage. The validity of the linear approximation of the damage can be verified comparing the approximate profile with the real one and evaluating the corresponding energy loss. For this purpose, sets of random numbers were generated, representing the classic 6 Ci measurements (Tumbas and Smith, 1988) of crush depth utilised in the Campbell method; the difference between the energy loss calculated starting from the Ci measurements and on the linearized profile was then evaluated.
We do not have available a crash test as reference damage, but a photograph of the same vehicle, taken from the “Auto Export Hungary” data base, but with damage of strikingly different shape and EES of 27 km/h = 7.5 m/s (see Fig. 12). Based on analysis of the photograph of the reference damage, the damaged area is approximated by a triangular shape and the following parameters are estimated: • maximum deformation: 50 cm, • width of damaged area: 80% of front end, Ld /L100 = 0.8, • PDOF = 0◦ . Utilising graph “C”, suitable for damage of triangular shape, we identify the line on which lies the point identified by the pair of values C and EES cos(PDOF) L100 /Ld (EES 7.5 m/s − deformation 50 cm, Ld /L100 = 0.8, PDOF = 0): between the 2nd and 3rd curve starting from the bottom. On diagram “A”, suitable for the damage of rectangular shape, on the same curve (between the 2nd and the 3rd starting from the
Fig. 13. Example of profile randomly generated with 6 crush depths.
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In the random Ci generation, to avoid non-realistic profiles, difference in the crush depth between one measurement and the subsequent was kept less than the mean value of the 6 measurements divided by 1.5. This value was determined by trial and error procedure, to provide realistic crush profiles. The profile was linearized utilising both a single line and two broken lines (for V-shaped profiles, as occur in cases of impact against poles or trees, for example), utilising the best-fit lines of the points. An example of a profile randomly generated is given in Fig. 13. Around 20,000 simulations were performed, varying the following parameters: • • • •
Pattern of damage profile (Ci measurements). Width of car. Width of damaged area. Stiffness parameters of the car, within the values available in the stiffness tables of NHTSA.
The percentage frequency histograms of mean deviation of the real profile from the approximating line and the histogram of percentage errors in energy loss calculation are shown in Fig. 14. The maximum profile deviations are about 23 cm. The mean error in calculating energy loss is around 2.5%, the maximum is 12%. These results confirm that approximating any damaged profile with a line or pair of lines, even in the presence of differences of 20 cm between the original and the linearized profile, produces acceptable errors in calculating energy loss. This is true all the more so considering the general approximations of the method of Campbell or the method of EES in the evaluation of the energy loss. For an experimental validation of the proposed methodology, crash tests were conducted on the track of the University of Florence – Department of Mechanics and Industrial Technologies, on vehicles of the models Fiat Panda and Fiat Uno, in order to have a sure value of energy loss to be compared with the estimations obtained by the proposed method. Each type of vehicle was tested in crashes
Fig. 14. Histogram of deviation of the real profile from the approximating line in cm (triangular marks) and histogram of percentage error (round marks) energy calculation.
against a fixed rigid barrier: (A) at 100% offset, (B) at 40% offset and (C) with barrier tilted 45◦ . By way of example, the values of the real and the estimated EES for the Fiat Uno vehicle are compared in the three following cases: (A–B) Estimation of EES of 100% offset crash starting from damage of 40% offset crash. (A–C) Estimation of EES of 100% offset crash starting from damage of crash with barrier tilted 45◦ . (B–A) Estimation of EES of 40% offset crash starting from damage of 100% offset crash. (B–C) Estimation of EES of 40% offset crash starting from damage of crash with barrier tilted 45◦ .
Table 1 Data from experimental crash tests on Fiat Uno type vehicle. Fiat Uno
A-offset 100%
B-offset 40%
C-tilted 45◦
a
Vehicle mass (kg)
Pre-impact velocity (km/h)
Post-impact velocity (km/h)
800
54.4
5.4
91,204
61
91,142
54
800
45.5
2.7
63,896
13
63,883
45
840
46.2
25.0
69,171
20,255
36,316a
33
The energy balance is computed also the energy loss by friction between barrier and car, 12,600 J.
Pre-impact kinetic energy (J)
Post-impact kinetic energy (J)
Energy loss j
EES (km/h)
D. Vangi / Accident Analysis and Prevention 41 (2009) 633–641
641
Table 2 Comparison between experimental EES versus calculated ones. Reference EES (km/h)
Deformation (cm)
Curve
Estimated EES (km/h)
Evaluation of EES Case A (EES = 54 km/h) Case B 45 Case C 33
59 31
5th from bottom 5th from bottom
56 56
Evaluation of EES Case B (EES = 45 km/h) Case A 54 Case C 33
57 31
4th–5th from bottom 5th from bottom
42 44
Evaluation of EES Case C (EES = 33 km/h) Case A 54 Case B 45
57 59
4th–5th from bottom 5th from bottom
33 35
(C–A) Estimation of EES of crash with barrier tilted 45◦ starting from damage of 100% offset crash. (C–B) Estimation of EES of crash with barrier tilted 45◦ starting from damage of 40% offset crash. The data and results of the crash tests on the model Fiat Uno are reported in Table 1. For the cases presented above, the experimental EES values and those calculated through the triangle method are compared in Table 2. The results show excellent match between the estimated and the real values, thus validating the applicability of the method. Regardless of shape of the damages, the EES–Crush dept relationship is linear. So, any error in the reference EES propagate linearly over the computed EES, amplified by factor C investigated/C reference, where C reference is the reference damage dept and C investigated is the dept of the damage under investigation. Note that, for applying this method, it is unnecessary to know the stiffness coefficients of the vehicles, which are subject to error and can significantly influence the evaluation of energy loss (Wang and Gabler, 2007; Jang et al., 2003), since evaluation is again based on visual estimation of deformations, similar to the method based on EES. 6. Conclusions This study presents a method alternative to the existing ones commonly employed to evaluate the energy loss in damage occurring to vehicles in road accidents. The new method, called “triangle method”, combines the simplicity of visual comparison, typical of the method based on EES, with flexibility in evaluating the energy loss on any deformation profile of a vehicle, typical of the Campbell’s method. The new methodology is applicable starting from photographic documentation with certified EES of damage of any kind, even differing in shape and severity from the one in question, taken from a generic crash test or even from a real accident on the same type of vehicle as the one under investigation. The damage of the vehicles is approximated by a triangular, rectangular or trapezoidal geometry, allowing the analytical expression of energy loss to be determined on the basis of only two parameters, which characterise the geometry of the damage: the depth C and the width Ld , which can be adequately quantified also by visual analysis of suitable photographic documentation of the damage. The approximation deriving from linearization of the damage profile has been evaluated as regards both geometry and energy, by performing numerical simulations and comparing the energy loss in the two cases: considering the profile in typical cases of damage deriving from real crashes, and considering the linearized profile. The difference between the energy values calculated utilising linear approximation as compared to the traditional measurement with six measurement stations was found to be minor, averaging about 2.5%.
Having noted the low value of the error introduced through linear approximation of the damage profile on the vehicles, the proposed method was validated utilising both crash tests conducted at the University of Florence Department of Mechanics and Industrial Technologies and data from crash tests found in the literature or from real accidents where the energy loss value was known. Based on the results, it was concluded that the new method can be used to estimate with sufficient accuracy the kinetic energy loss in deformation on vehicles consequent to road accidents. The method has been described in a course held by the University of Florence for 50 traffic accident experts, with a test in which the participants were requested to apply it in estimating the energy loss of vehicles involved in accidents. The results have confirmed that the method, thanks to its simplicity and versatility, can constitute a valid alternative to the classic procedures for evaluating energy loss commonly utilised. References Campbell, K.E., 1974. Energy Basis for Collision Severity. Environmental Activities Staff, General Motors Corp., SAE Paper 740565. Crash 3 User’s Guide and Technical Manual, Pub. No. DOT HS 805732, NHTSA, Washington, DC, 1981. Fonda, A.G., 1999. Principles of Energy Loss Determination. Fonda Engineering Associate, SAE Paper 1999-01-0106. Jang, T., Grzebieta, R.H., Rechnitzer, G., Richardson, S., Zhao, X.L., 2003. Review of car frontal stiffness equations for estimating vehicle impact velocities. In: Proceedings of the 18th International Technical Conference on Enhanced Safety of Vehicles, Nagoya, Japan, May. King, D.J., Siegmund, G.P., Bailey, M.N., 1993. Automobile Bumper Behavior in Lowspeed Impacts, SAE Paper No. 930211. McHenry, B.G., 2001. The Algorithm of CRASH. McHenry Software, Inc. McHenry, R.R., 1976. Extensions and Refinements of the CRASH Computer Program Part I: Analytical Reconstruction of Highway Accidents, DOT HS-801 832. McHenry, R.R., McHenry, B.G., 1986. A Revised Damage Analysis Procedure for the CRASH Computer Program. McHenry Consultants, Inc., Cary, NC, SAE Paper 861894. Neptune, J.A., Blair, G.Y., Flynn, J.E., 1992. A Method for Quantifying Vehicle Crush Stiffness Coefficients. Blair, Church & Flynn Consulting Engineers, SAE Paper 920607. Nystrom, G.A., Kost, G., Werner, S.M., 1991. Stiffness Parameters for Vehicle Collision Analysis. Failure Analysis Associates, Inc, SAE Paper 910119. Schreier, H.H., Nelson, W.D., 1987. Applicability of the EES-accident Reconstruction Method with MacCAR©, SAE Paper 870047. Siddal, D.E., Day, T.D., 1976. Updating the Vehicle Class Categories, Engineering Dynamics Corp., SAE Paper 960897. Smith, R.A., Noga, J.T., 1982. Accuracy and sensitivity of CRASH, U.S. Department of Transportation, National Highway Traffic Safety, SAE Paper 821169. Strother, C.E., Woolley, R.L., James, M.B., 1990. A Comparison Between NHTSA Crash Test Data and CRASH3 Frontal Stiffness Coefficients, SAE Paper 900101. Tumbas, N.S., Smith, R.A., 1988. Measurement Protocol for Quantifying Vehicle Damage from an Energy Basis Point of View, Tumbas and Associates—U.S. Naval Academy, SAE Paper 880072. Vangi, D., 2009. Energy loss in vehicle to vehicle oblique impact. International Journal of Impact Engineering 36 (March (3)), 512–521. Wang, Q., Gabler, H.G., 2007. Accuracy of vehicle frontal stiffness estimates for crash reconstruction. In: Proceedings of the 20th International Technical Conference on Enhanced Safety of Vehicles, Lyon, France, June. Woolley, R.L., Warner, C.Y., Tagg, M.D., 1985. Inaccuracies in the CRASH3 Program, Collision Safety Engineering, SAE Paper 850255. Zeidler F., Schreier H.H., Stadelmann R., 1985. Accident Research and Accident Reconstruction by the EES-accident Reconstruction Method, SAE Paper 850256.