E L S E V I E R JSAE Review 15 (1994) 215 221

Energy loss and delta-V in vehicle collision: car-to-car side impact

H i r o t o s h i I s h i k a w a

Japan Automobile Research Institute Inc.. 2530 Karima, T~'ukuha ('itv, lharaki. 305 Japan

Received 17 February 1994

Abstract

The relationship between energy loss and delta-V in vehicle collision is formulated from a two-dimensional car-to-car impact model. In order to understand the energy loss, impulse and delta-V at collision, sixteen car-to-car side impact tests were conducted and analyzed according to this formula, in which the generalized impulse ratio (GlR) was used as an index indicating the collision type. The energy loss and impulse measured from the tests are presented with GIR. A new method of estimating the delta-V from energy loss alone is also introduced and validated by comparison with the actual delta-V at the tests.

1. Introduction

In automobile collision analyses, the term "del ta -V ( A V ) " is used as an indicator of impact severity because it approximates the impact speed between the occupant and vehicle interior. Delta-V is defined as the velocity change of a car compartment during collision and is determined in several ways. If an extensive recording of pre-crash and post-crash data, such as braking marks, skid marks, final rest positions and so on is available, we can estimate the pre-impac~ speed and post-impact speed and can then determine the delta-V at collision. However, it may often be quite difficult to estimate the pre-impact speed and post-impact speed in a real world collision. One practical method which has been developed in delta-V calculations is the algorithm used in CRASH3 [1], a well-known and widely used program for accident reconstruction.

CRASH3 uses the damage measurements of vehicles to estimate the energy loss and introduces the relationship of energy loss to delta-V. The algorithm used in CRASH3 is based on the Campbell method [2] which states that energy loss can be approximated by using residual crush measure- ments,

For CRASH3-related programs, it is necessary to define the impulse vector location and angle relative to the vehi- cle structure, the so-called Principal Direction of Force (PDOF). CRASH3 requires the PDOF to be determined prior to the simulation with the assumption of perfectly inelastic impact. PDOF is defined empirically and is con- sidered to be quite difficult to determine from the vehicle

deformation profile. Due to the uncertainty of PDOF and to the unrealistic assumption of perfectly inelastic impact, the average error to be expected from CRASH3 is gener- ally claimed to exceed 20% [3]. However, no one has proposed a practical method to improve the accuracy of CRASH3 in terms of delta-V calculation. Consequently, a new method of calculating the delta-V from energy loss is formulated based on a previously presented two-dimen- sional impact model [4,5].

This paper introduces a theory explaining the relation- ship between energy loss and delta-V and proposes a new method for delta-V estimation from energy loss. The new method is evaluated with 16 car-to-car side impact tests. Additionally, the energy loss and impulse analyzed from the tests are presented with the Generalized Impulse Ratio (GIR) . GIR is used as an index indicating the collision type [5]. Some assumptions and oversimplifications cur- rently used in automobile accident analyses are also dis- cussed and evaluated based on test results of energy loss and impulse with GIR.

2. Impact model and theory

The car-to-car impact model is a two-dimensional plane model as shown in Fig. I. Each vehicle has one mass and three degrees of freedom, and the following assumptions are made:

(1) Conservation of momentum is maintained during the collision so that the tire force and other external forces are negligible.

t)389-4304/94/$07.0t) ~;!) 1994 Society of Automotive Engineers of Japan. Inc. and Elsevier Science B.V. All rights reserved SSDI 0389-43(t4t ~4 )IIIH) 16-M JSAE9434181

216 H, l s h i k a w a , ' J S A I ( R e m e w I'~ ( 1 ~ 4 ) 2 1 5 - 2 2 1

n

Fig. 1. Car-to-car two-dimensional impact model.

t

(2) Vehicle mass, center of gravity and yaw moment of inertia do not change before or after the impact.

(3) Resultant impulse is concentrated at the impact center.

A normal-tangential coordinate system is selected such that the origin is located at the impact center. The n-axis is normal and the t-axis is tangential to the impact surface.

The impact model is described by six equations. Four equations are derived from the law of conservation of momentum, and two equations are obtained from the nor- mal and tangential restitution coefficients at the impact center. A detailed explanation and derivation of these equations appear in the previous reports [4,5].

2.1. Normal and tangential restitution coefficients

The normal and tangential restitution coefficients at the impact center restrict the vehicle motion at the end of impact. These restitution coefficients are defined by Eq. (1) as follows:

e n = -- R D S / R D S o ,

e t = - R S S / R S S o ( l )

where

P ~ S 0 = W2(}n - A 2 0,)20 -- V10 n + a~ ¢010,

R D S = V2n - - a 2 0 ) 2 -- Vln + al~ol,

RSS o = V2o t + b 2 oa2o - Vio t - b~ co~o,

R S S = V2t + b 2 t o 2 - V l t - b l o l .

2.2. General formula for two-dimensional impact

Eq. (2) represents the two-dimensional impact model with the normal and tangential restitution coefficients and

can be called a general formula fol two-dimensional im- pact analysis. The analytical solution of Eq. (2) yields the linear impulse components. P and loss. /51 , as shown in Eqs (3),-(:~

• t l l l t t

1

t}

0

(tl~ D ,

I.

f ~ 1 "

t~ t Yll I t? l , k. ;

( I [ j 12t?11

I

() H t n

t?l~ q

h i m ! m l k ~

( I I I !1 ttt

t ',. and the energy

t~, ~1 ill 2 K~

(i

iJ

ot

i

O. ??l~ Ill k

H

t& r * , 1'°~, ] (21

I Pn = (1 - m , m t m 2) { m " R D S ° ( I + e , )

+ m n m t m o R S S o ( 1 + e~)},

1 ['~ (1 - m , m t m ; ) { m " m t m ° R D S ° ( l + e , )

--~ mr RSS o ( 1 + e t ) ),

l Et = ( l _ m n m t m ~ ) { ½ m , R D S , ~ ( I - - e ~ )

+ 5mtRSSS(1 - e? )

+ m , m t m o RDSo n s s o ( 1 - e,~ e t ) }

where

"~ln m l '~2nm 2 ')/it m l ~2t rn2 m, = , nl t = ,

'Ylnml + "Y2nm2 3/ltml + T2tm~

alb~ aeb2 k{ !

m° m l k ? m2k 2 ~;~ + a~

k? Y:'~ k ~ + a ~ ' Y,t k [ + h ~ Yzt

(3)

(5)

The energy loss is maximized when both the normal and tangential restitution coefficients are zero. This is called a perfectly inelastic impact. The energy loss in collisions cannot exceed E L m~x" EL max is the maximum energy loss theoretically determined from the impact con- figurations and thus can be called a theoretical maximum energy loss:

1 Et ...... = (1 - m.mtm~, ) (½m~RDS~ + ½mtRSS o

+ m n m t m o R D S o R S S o ), (6 )

H. Ishikawa /JSAE Reciew 15 (1994) 215-221 217

-~ p A V i =

m i

, I +en -4,

e~ / 2mr EL - -

]/2mnEL l - e n

1+ et I - e e

Fig. 2. Impulse-ellipse.

The energy loss becomes minimum or zero when both the normal and tangential restitution coefficients are one. This is called a perfectly elastic impact.

In a typical collision analysis, the normal and tangential restitution coefficients can be restricted to

- l < e ~ < l , - l < e ~ < l .

2.3. Energy loss and delta-V

From Eqs. (3)-(5), the relationship between the energy loss and the linear impulse components can be written as

1 - % 1 - e t P ~ + Pt 2

2m~EL(1 + en) 2mtEL(1 + et)

(1 -- enet)m o + EL(I + en)( 1 + et ) P.et = 1. (7)

Eq. (7) represents the ellipse shown in Fig. 2. This ellipse can be called an impulse-ellipse. The vector from the origin to the ellipse represents the resultant linear impulse, and the dotted vectors represent the maximum and minimum impulses. Fig. 2 indicates that the impulse is variable given the same energy loss. From the energy loss relationship derived from Eq. (7), the maximum and mini- mum values of delta-V are defined as follows:

/'max Pmin AFt max -- AWi rain -- ( 8 )

mi m i

where

Pmax = 2{mnmtEL(1 + en)(1 + e , ) (mn(1 + e n ) ( 1 - - e t )

+ m , ( l - e n ) ( 1 + e t ) - { { m n ( 1 + e n ) ( 1 - et )

- - m t ( 1 - - e n ) ( l + e , ) } 2

2,,1/2 ~ - 1 } 1/2 ' + 4 m ~ m ~ m 2 ( 1 - e n e t ) ) )

Pmin=2{mnmtEL(1 + e n ) ( l + e t ) ( m n ( l + G ) ( 1 - - e t )

+rot(1 - e n ) ( 1 + e t ) + { { r a n ( 1 + e ~ ) ( 1 - et)

--mt(1--en)(l +et)} 2

,) '} +4m2nm~mo( 1 _ enet)2}l/2 ,/2.

Impulse direction and restitution coefficients are neces- sary to determine delta-V from energy loss in a typical collision analysis. When the impulse direction is not avail- able, the maximum and minimum delta-Vs can be calcu- lated from Eq. (8) using energy loss.

When both the impulse direction and restitution coeffi- cients are missing, an assumption of zero restitution coeffi- cients derives a rough estimation of delta-V from energy loss as follows:

Pmax 0 q- Pmin 0 A Vcstimated = 2m ( 9 )

where

Pma×O=2{mnmtEL(mn+mt-{(m° mr) 2

+4m2om~m2}l/2)-l) '/e,

Pmi°o=2{m,m, EL(m, +mt+{(mn--mt) 2

9 2 2~1/2~ 1} I / 2 - +4m•mtmol )

In the next section, the delta-V from Eq. (9) is com- pared to the measured delta-V from collision tests to verify the validity of Eq. (9).

2.4. Generalized Impulse Ratio (GIR)

Parameters RDSo, RSSo, mn, m t and mo are defined automatically from the initial conditions at impact. The impulse components, Pn,, and /:'to, which are obtained by letting e n = 0 and e t = 0 in Eq. (2), can also imply the generality and depend on the impact condition. Thus, the ratio, Pto/Pno, can be called a Generalized Impulse Ratio (GIR) and can be used as an index indicating the collision type. GIR coincides with the equivalent friction coefficient when the impact is perfectly inelastic (e n = e t = 0) or perfectly elastic (e n = c t = 1), or when the normal and tangential restitution coefficients are identical (en = e t).

Pto mnmtmoRDSo + m~RSS o GIR= =

P,o mnRDSo + mnmtmoRSSo

.~ 1 H. lshikawa /'.ISAL Ret:iew I s ( l uu4J 2 t5-221

3. C a t - t o - c a r s ide i m p a c t tests

To obtain the relationship between energy loss and delta-V, a total of sixteen car-to-car side impact test.,,. including side-swipe collisions and corner-to-corner colli- sions, were analyzed using the impact model described above. The test conditions and the method of defining the impact center are described in the previous reports [5]. The cars used in the tests were Japanese passenger cars weigh- ing about 1000 kg and one small Japanese car weighing about 600 kg.

3.1. Energy loss and impulse

EUEo (%) !00

50

o! O

Impact angle I

<[:.. 75 deg. i i

O : 90 deg . ~-j 135 deg. / ~ 1F,O deg.

F_; A o o

i 2 S 4 :; GIR

I:ig. 4 t , !~, ~ ~,'[R

Fig. 3 shows the relationship of energy toss to impulse. According to Eq. (7), the impulse magnitude is propor- tional to the energy loss, and their relationship is character- ized by the combination of restitution coefficients. If the energy loss is the same, the impulse is proportional to the restitution coefficients. The impulses in the 135-degree and 150-degree side impacts were relatively small compared to those in the 75-degree and 90-degree side impacts when the energy toss was the same. This results from the facl that the tangential restitution coefficients in 135-degree and 150-degree side impacts tend to become smaller than those in 75-degree and 90-degree side impacts [5].

Figs. 4 and 5 show the relationship of energy loss to GIR at different impact angles. The initial kinetic energy (E 0) and the theoretical maximum energy loss (E~ ....... ) are used to normalize the energy loss (E~.) at collision in these figures.

As shown in Fig. 4, E ~ / E o ranged from 10% to 50% in 16 tests. The E L / E o varied according to the collision type and tended to decrease as GIR increased. The relationship of E L / E o to GIR was not so clear as the relationship of E~. /EL max tO GIR. It appears that the E t . / E o ratio could be less than 10% when the GIR exceeds 5.

The relationship of E t / E ~ . . . . . . to GIR was distinctive. Specifically, the E L / E L ...... ratio decreased drastically as GIR became greater than 2. When the GIR was less than l, the energy loss became nearly identical to the theoretical maximum energy loss except in two cases. One of the two cases was a low-speed, corner-to-corner impact, the other all impact involving a small car. in which the normal restitution coefficients exceeded (~.3. The theoretical maxi- mum energy loss is obtained ,,,,'hen the collision is per- fectly inelastic. A number of impact models for accident reconstruction use the assumption of perfectly inelastic impact for simplicity in deriving system equations. The test result indicates that this assumption will not apply m side impacts when GIR exceeds one, or to corner-to-corner impacts.

Figs. 6 and 7 show the relationship of impulse to GIR

at different impact angles. Pu and P0 are used to normal- ize the impulse (P ) in each impact configuration. As shown in Fig. 8, PR is a resultant impulse theoretically determined assuming a perfectly inelastic impact of two particles. P~ is a resultant impulse theoretically deter-

P (KN s) 12

i i Impaci angle

~:: 75 deg. -J ~ ~ O! 90 deg.

. . . . . . . . . . . . . . . . . . . ': / i "13 aeo /'. / : -

: ~ L~: 150 deg

....... i ........

(J " : / :

0 20 40 60 80 100 EL (KJ )

Fig. 3. Impulse vs. Energy loss.

E , /E ~m.x (%) 150

1 O0

50

i

oo:

F_5

A

lmpact~ angle ~C' 75 deg. o . 90 ~eg-. [ ] : 135 deg. ~, ] 150 deg.

t L i

0 1 2 3 GIR

Fig. 5. l'. I / E : . . . . v,,. G I R .

[] O

,!

H, lshikawa /JSAE ReHew 15 (1994) 215-221 219

P/PR (%) 100

80

60

40

20

0

UQ"C' i ! i Impact angle

: ~ ! 75 deg. O

O i o O i 90 deg.

. . . . . . . . . o . . . . . Ozx ~ . . . . . . . . . . : . . . . . . . . . . D i l 3 5 d e g :

O Z& 1150 deg. . . . . . . o . . . . . . . . . . . . . . . : : . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . o . . . . . i . . . . . . . . . . . . . ; o . . . .

I I

0 1 2 3 4 GIR

Fig. 6. P/PR VS. GIR.

P/Po (%) 150

100

50

Ooi o°,9

OA

Impact' angle

75 deg. 0 90 cle.g:.

. . . . . . . . . . . t S i i 3 ; ,Jeg. A ' 150 deg.

A . . . . . . . . . . . . i ,-O .......

ZX D

I I

1 2 3 4 5 GIR

Fig. 7. P/P , vs. GIR.

mined assuming a perfectly inelastic impact of two rigid bodies. P, PR and P, are written as follows:

mlm2 ,, v PR -- ~ V]" o + V~ - 2Vl.V2o cos Ocl ,

m~ + m ,

P0 = v"P,,~, + P,~,.

There was a distinctive relationship between P / P k and GIR. P/Pr~ decreased drastically from 90%.to 10% as GIR increased from 0 to 4. A model for two-particle impact with zero restitution coefficient has been applied in simple analyses of automobile collisions, since the vehicle mass, initial impact velocity and impact angle at collision define PR without reference to the impact center and vehicle moment of inertia. If this application is valid, P / P R should become 100% regardless of impact condition or GIR. The test result indicated that this particle impact model can only be applied when GIR is less than 0.5, though it may cause more than 10% error in impulse calculation. Simplification is necessary for accident recon- struction. However, those assumptions and oversimplifica- tions in impact models may cause unacceptable errors in collision analyses.

According to the definition of Po, P / P o should exceed 100% when both the normal and tangential restitution coefficients are positive. When both the normal and tan-

gential restitution coefficients are negative, P / P o should become less than 100%. The assumption of perfectly in- elastic impact in vehicle collision makes P / P o be 100%. The relationship of P / P o to GIR in Fig. 7 shows that this assumption will not apply in most cases of side impact analyses.

3.2. Impulse-ellipse for indication of collision type

Two-dimensional car-to-car collisions are classified into four types based on combinations of normal and tangential restitution coefficients [4,5].

(1) e n > 0 a n d e t > 0 , (2) e n > 0 a n d e t < 0 , (3) e n < 0 a n d e t > 0 , (4) e n < 0 a n d e t < 0 . Three out of the four collision types in the 16 car-to-car

side impact tests are shown in Fig. 9. In this figure, impulse-ellipses derived from Eq. (7) are used to graphi- cally represent the collision type. In Fig. 9 a set of two ellipses are drawn for the same energy loss in each test condition. The bold-line ellipse is obtained with measured restitution coefficients, the thin-line ellipse with zero resti- tution coefficients. The thin-line ellipses can be obtained automatically from Eq. (7) with the vehicle mass, yaw moment of inertia, C.G. position and energy loss at colli- sion, assuming zero restitution coefficients. Consequently,

~, m2 _ "20

m Vl°"v'°"~'~

m~ + m 2

v , - - , / r E + - 2V, cos07, Fig. 8. Two-particle impact and definition of Pr~.

q g .

220 tL lshikawa / .ISAE Review 15 (1994) 21~-22 l

-10

Test No.7

en=0.12 et=0.16'

Pn[lO~] Test No.5 Pn[10,,3] Test No.6 Pn[10,'9]

1 0 [ =et=0 1 % et=0 t0 j en=et=-o

! ~ ' ~ ' ! ~ " _ __ ~ i ~ J f en=-0.18 / _,n l GIR=0.61 e n = 0 . 3 3 ~ GIR=1.76 et=-o.86 GIR=3.09

-10 et=-o.45 -10[ . . . . . . . .

(2) en>0, et<0 (1) en>0, et>0 (3) en<0, et<0 [Unit: Ns]

Fig. 9. Typical impulse-ellipses in car-to-car side impacts.

the thin-line ellipse can be called a standardized impulse- ellipse. If both the standardized impulse-ellipse and the actual impulse-ellipse are drawn, various kinds of two-di- mensional automobile collisions can be classified into four groups graphically. The arrow from the origin to the bold-line impulse-ellipse indicates an impulse vector, and the angle (0) a friction-angle representing equivalent fric- tion coefficient (/x) at the impact center.

3.3. Estimation of delta-V ( A V) from energy loss

Fig. 10 shows the relationship of estimated delta-V from Eq. (9) to measured delta-V in 16 side-impact tests. Except for the two cases indicated by arrows, the differ- ences between the estimated and measured delta-Vs were less than 2 m / s . The GIRs in these two cases were greater than 3. The delta-V estimated by Eq. (9) tended to differ significantly from the measured delta-V as GIR increased. This is because the assumption of zero restitution coeffi- cients at the impact center cannot apply in automobile collision analysis when GIR becomes greater than 1 [5].

10 Struck Car o 75 deg.

~-~8 o 90 deg.

i i i o i [] 135 deg

i .......... . .......... !,,. ........ . .......... • ...........

~ ~ Zx 150 deg.

o 4 i i i iiiiiiiiiiiiiiiiiii[iiiiiiiiii o

0 2 4 10 Delta-V measured (m/s)

Fig. 10. Comparison of delta-Vs, measured and estimated.

However, Eq. (9) can be a useful method for roughly estimating delta-V only from energy loss in collision anal- ysis.

CRASH3 uses a formula for calculating the energy loss from vehicle deformation. The coefficients in the formula are obtained from collision tests and presented for many car models for front, side and rear impact [6]. Accuracy of calculating the energy loss during collision can be im- proved by using this method. However, the accuracy of delta-V estimation may become poor as GIR increases as long as the assumption of zero restitution coefficients is used in the CRASH3 algorithm, tn order to improve the accuracy of delta-V estimation, it is necessary to estimate restitution coefficients from vehicle deformation severity.

4. Conclusions

By using a previously presented two-dimensional im- pact model, sixteen car-to-car side impact tests were ana- lyzed in detail to understand the energy loss, impulse and delta-V at collision. The results are summarized below.

( t ) The relationship of energy loss to delta-V can be formulated by an equation of ellipse or impulse-ellipse.

(2) The impulse-ellipse can be used to derive the maxi- mum and minimum values of delta-V from the energy loss at collision without referring to the principal direction of force.

(3) A method, Eq. (9), can be used to roughly estimate delta-V only from energy loss, in which the maximum error for delta-V estimation was less than 2 m / s when GIR was less than 3.

(4) Automobile collisions can be classified graphically by drawing both the standardized impulse-ellipse and the actual impulse-ellipse.

H. lshikawa /JSAE Review 15 (1994) 215-221 221

(5) The impact mode l of two part icles can be applied to

automobi le col l is ion analysis only when GIR is less than

0.5, though it may cause more than 10% error in impulse

calculat ion if zero restitution coeff ic ients are assumed.

(6) The assumption of perfectly inelastic impact or

c o m m o n veloci ty constraint at the impact center is only

permiss ible in a l imited impact condi t ion where GIR is

less than 1.

5. Notation

o = opposite,

i, 1, 2 = vehic le number,

n = normal,

t = tangential,

max = max imum,

min = min imum,

L = loss,

R = resultant,

tel = relative,

cl = collision.

m = mass,

V = veloci ty ,

w = angular veloci ty ,

k = radius of gyration,

P = impulse,

a, b = c.g. position,

e = restitution coefficient ,

E = energy,

/.t = equivalent fr ict ion coeff icient ,

RDS = relat ive deformat ion speed at impact center,

RSS = relat ive sl iding speed at impact center,

A = difference symbol ,

0 = angle;

(Subscripts)

0 = initial, original,

References

[1] Crash3 User's Guide and Technical Manual, Pub. No. DOT HS 805732, NHTSA, February 1981; revised April 1982.

[2] Campbell, K., Energy Basis For Collision Severity, SAE Paper 740565.

[3] Woolley, R.L., Warner, C.Y. and Tagg, M.D., Inaccuracies in the CRASH3 Program, SAE Paper 850255.

[4] Ishikawa, H, Kinematics of Automobile Collision - - A Negative Restitution Coefficient and a Rotational Restitution Coefficient for Analysis of Two-Dimensional Impact (in Japanese), JSAE Transac- tions Vol. 4, pp. 101-106 (1991).

[5] lshikawa, H., Impact Model for Accident Reconstruction-Normal and Tangential Restitution Coefficients, SAE Paper 930654.

[6] Prasad, A.K., Energy Absorbing Properties of Vehicle Structures and Their Use in Estimating Impact Severity in Automobile Collisions, FISITA 92, FISITA No. 925209 (1992).