By Brian G. McHenry

©McHenry Software, Inc.

The acronym CRASH stands for the __C__omputer __R__econstruction
of __A__utomobile __S__peeds on the __H__ighway. The CRASH computer
program is an accident reconstruction program. With CRASH you input the vehicle
properties, the impact and rest positions, and the vehicle damage measurements.
The program produces approximations of the vehicle speeds at impact the impact
speed change or Delta-V (DV).

The
**Impact Speed Change (****DV)****
**is defined as the impulsive change in vehicle speed (i.e., produced by an
impact) that occurs along the direction of action of the principal collision
force^{[1]}.

The magnitude and direction of the impact speed-change of a vehicle, that occurs during a collision, serve as primary descriptors of impact severity, since they reflect the effect of the ratio of the masses of the two colliding bodies as well as that of the closing speed. The impact speed-change is expressed in miles per hour and the clock direction from which the principal force was applied is generally stated.

For example, a 20 MPH, 06 o’clock impact speed-change would correspond to a principal force acting from the 06 o’clock direction (i.e., a longitudinal rear-ender) with a sufficient impulse (i.e., time-integral of applied force) to produce a 20 MPH impact speed-change of the subject vehicle.

In a central, collinear collision, the impact
speed-change of vehicle #1, DV_{1}, and the closing velocity, (V_{10 }–V_{20}),
are related as follows:

_{} MPH

Where V_{10}-V_{20} = closing velocity, MPH

W_{1} = weight of vehicle #1, lbs.,

W_{2} = weight of vehicle #2, lbs., and

e = coefficient of restitution.

The terms barrier-equivalent speed and impact speed-change are sometimes used interchangeably. However, this is appropriate only for that portion of the impact speed-change that precedes restitution.

A further discussion of impact speed-change is
presented in **Figure 1** from **Reference
**[2].

Figure 1 The
significance of Impact Speed Change

In 1952, a pioneer program in highway safety research, the Automobile Crash Injury Research program (ACIR), was created with the objective of determining injury causation among occupants of cars involved in accidents, in order that the injuries might be prevented or mitigated through improved vehicle design. By the mid sixties, 31 states had participated in the program and provided over 50000 cases for study. The main criterion for classifying severity in the ACIR program was through the use of comparison pictures of damaged vehicles.

Also during the 60's the digital computer was coming of age. Mainframe computers, which filled entire floors of buildings and cost hundreds of thousands to millions of dollars had evolved into time-sharing, batch processing machines. These were used in conjunction with 9 track tapes, card punch machines and terminals to provide to scientists, engineers and others number crunching capabilities unlike any utility ever before imagined. The digital computer quickly became an integral part of scientific research and development.

In September 1966, President Lyndon Johnson signed the National Traffic and Motor Vehicle Safety Act and the National Highway Safety Act. These established the authority to develop both the Federal Motor Vehicle Safety Standards (FMVSS) and the National Traffic Safety Agency (currently known as the NHTSA). As part of signing the legislation President Johnson stated that "auto accidents are the biggest cause of death and injury among Americans under 35". In 1965, 50,000 people were killed on the nation’s highways in auto accidents.

The SMAC computer program was initially created as a feasibility study by researchers at Cornell Aeronautical Lab (currently known as Calspan). The researchers at Cornell were interested in demonstrating the feasibility of a mathematical model of automobile collisions which could achieve improved uniformity and accuracy in the interpretation of evidence in automobile accidents. SMAC applications would give more accurate indications of collision severity. This would help to establish priorities, provide monitoring and assist in establishing the regulatory role of the government.

At the time of the creation of SMAC, limitations in the detail and the accuracy of the ACIR study had spawned a number of different exploratory approaches to the ACIR objectives. The SMAC program was evaluated as a possible tool for the investigative teams. SMAC is an "open-form" accident reconstruction program. A requirement of "open-form" programs like SMAC is that the user must initially estimate the impact speeds. The program also generally requires iterations to achieve an acceptable match of the accident evidence. One of the difficulties which arose in setting up SMAC simulations by the investigative teams was that the initial estimate of the speeds were not always obvious. Also, the user had to provide vehicle properties and specifications, many of which were not readily available. Those requirements, combined with the relatively high cost per run for a SMAC simulation run, required that a pre-processor be created which could provide the initial estimate.

The CRASH computer program was initially created to assist SMAC users in determining first estimates of the impact speeds. The original CRASH program utilized both piecewise-linear trajectory solution procedures and a damage analysis procedure to provide an initial estimate. The CRASH program was subsequently adopted by NHTSA as an integral part of the National Accident Sampling Study (NASS) investigations. The rationale for the use of the CRASH program was that for statistical studies, the average error in severity determinations is more important than any individual errors. The CRASH program, with it's question and answer mode, vehicle categorization, single step solutions procedure, and most importantly low cost, redirected the NHTSA interest from SMAC towards the CRASH computer program.

From the CRASH3 User’s Guide and technical manual, NHTSA, US Dept of Transportation:

“The CRASH3 program is a simplified mathematical analysis of automobile accident events. As is the case with any such analytical procedure, certain simplifying assumptions have been made to reduce the complexity and the operating cost of the program. Any accident event that violates the CRASH3 program’s simplifying assumptions either degrades the accuracy of the solution, or, in the extreme, completely invalidates it. Thus, while CRASH3 users do not need to know the minute details of the analysis procedure, it behooves them to know the major simplifying assumptions so that accidents that violate them may be either avoided or handled with special techniques.”

· Ballistic Post-Impact Trajectory

CRASH3 assumes that the vehicles spin out to rest with constant rolling resistances, no active steering, and over a single friction surface, although a secondary friction surface may be specified in the trajectory simulation option.

· Point of Common Velocity During Impact

CRASH3 assumes that at some time instant during the impact, the contact point on both vehicles reaches a common velocity. There are certain situations, notably sideswipes, when this is not the case and a CRASH3 analysis will not be successful.

· Flat, Single Friction Surface Traversal

CRASH3 is a two-dimensional analysis. The program assumes both vehicles traverse the same friction surface.

· Quantization of Vehicle Properties

CRASH3 maintains tables of vehicle properties that divide the vehicle population into discrete categories.

· Uniform Crush Stiffness

CRASH3 assumes uniform individual crush stiffnesses for the side, front and back of a vehicle. The crush stiffnesses have been empirically derived from data generated in crash tests. Obviously the uniformity notion does not account for the fact that a vehicle side is fairly stiff near the axles but less so near the doors. Again, this is a compromise of complexity, convenience and cost.

The original CRASH program utilized both piecewise-linear trajectory solution procedures and a damage analysis procedure.

· CRASH Trajectory Algorithms

· CRASH Damage Analysis Algorithms

**©McHenry Software, Inc.**

On the basis of *Conservation of Momentum*,
serves as the theoretical basis for reconstruction of impact speeds in
vehicle-to-vehicle collisions.

For the moment we will assume that the system is isolated and will ignore the external forces produced by the tires and other possible sources, such as gouging and scraping of vehicle components on the ground, during the collision. The magnitudes of these external forces are normally small when compared with the magnitude of the forces of the collision. However, they can not be totally ignored.

A trajectory analysis is used to determine each
vehicle’s velocity and direction subsequent to the collision, thereby providing
a definition of the ** system** momentum at separation. This can then be used to define
the

Our presentation of trajectory analysis will begin with the simplest form of vehicle motion, linear motion without yawing:

For the simplest case of straight-line travel without yawing rotation and with constant drag forces, the corresponding change in velocity can be approximated with analytical relationships for constant deceleration:

V=V_{0}
- at (1)

From integration of (1),

S = V_{o} t - 1/2 at^{2} (2)

_{} (3)

Substitution of (3) into (2) yields

_{} (4)

Solution of (4) for V yields

V^{2} = V_{o}^{2} - 2aS (5)

where

V = Velocity

V_{0} = Initial velocity

a = Acceleration

t = Time

S = Distance

In applications of equation (5), a distinction must be
made between the prevailing average friction coefficient, m, and
the deceleration, a. If the full 100%
friction coefficient is utilized, i.e., wheels locked or pure lateral travel, a
=mg
ft/sec^{2}.

For longitudinal motions with one or more wheels not
fully locked and/or sideslip angles less than 90 degrees, , the friction
utilization will be less than 100 percent and, thereby, a < mg
ft/sec^{2} .

In the case of a vehicle coming completely to rest
without further obstacle contacts, V_{f} = 0, and equation (5) becomes:

V_{o}^{2} = 2aS (6)

The decrease of speed with travel distance, for the
case of constant deceleration, is depicted in **Figure
2**.

Figure 2
Speed Decrease with travel at Constant Deceleration

A space-fixed coordinate
system is necessary to define measured spinout trajectories for analysis (e.g.,
**Figure
3**). The
relationship of the X' and Y' axes in** Figure 3 **reflects the aeronautical convention for
three-dimensional coordinates, in which the Z' axis points downward. In the selected coordinate system, the Y'
axis is directed to the right of the X' axis and the angle Y is
measured in the clockwise direction with respect to the X' axis.

Figure 3 Space Fixed Coordinate system

While the position and orientation of the space-fixed reference coordinate system for a given case are arbitrary, it is generally desirable to relate them to permanent reference points at the accident scene (e.g., curb lines, utility poles, etc.).

The position data used in trajectory calculations refers to the location of the vehicle center of gravity, something which is not readily measurable at the accident scene. The reconstructionist must interpret tiremark evidence and/or measurements to wheel locations and from these data ascertain the center of gravity location.

In simple spinout
motions, the actual distances traveled to rest can be approximated, with reasonable
accuracy, by straight lines between the separation and rest positions. The separation velocities can be estimated on
the basis of the total work done by each vehicle against tire-terrain friction
forces between separation and rest. The
rate of energy dissipation by tire forces is dependent on the heading direction
of the vehicle in relation to its direction of motion and on the extent of
rotational resistance at the individual tires.
For example, in a broadside slide, all tires produce important resistance
forces. In forward or backward motion,
only those tires with applied brakes, damage effects, large steered angles or
driveline braking produce significant drag forces. At a given sideslip angle, or over a limited
range of a changing sideslip angle, the motion resistance can be approximated
in the manner depicted in **Figure 4**. For the case of rotation about a vertical axis
(i.e., yawing rotation) a vehicle alternates between the two conditions of
motion.

Several different conditions of the vehicle tires may exist which can produce different extents of rotation during a spinout and therefore produce differing amounts of energy dissipation. Either the wheels may be freely rotating or there may be some resistance to rotation due to either vehicle damage or connection to a driveline (which produces the drag on the vehicle that is called ‘driveline braking’).

With freely rotating
wheels, the linear and angular velocities of a vehicle are decelerated
alternately as the heading direction changes with respect to the direction of
motion. When the vehicle slides
laterally, the side forces at the front and rear tires tend to have the same
direction despite the existence of a yawing velocity (**Figure
5(a)**).
Therefore, during this phase of motion, the angular velocity tends to
remain constant while the linear velocity is decelerated. When the longitudinal axis is aligned with the
direction of the linear velocity, the side forces at the front and rear tires
act in opposite directions and the angular velocity is decelerated while the
linear velocity tends to remain constant **(Figure 5(b))**. The general nature of the alternating
decelerations is depicted in **Figure 6.**

The other situation which can occur is if one or more of the wheels has rotational resistance. In that situation the linear velocity is decelerated, generally at different rates, during both phases of the spinout motion. The amount and location of the wheel drag on a vehicle directly affects its behavior. A vehicle with all wheels locked tends to decelerate at a faster rate than one with less than all wheels locked. Also, the location of the locked wheel with respect to the velocity direction and heading ( i.e., lateral vs. longitudinal) of a vehicle in a spinout affects the characteristics of its angular deceleration time history.

Differences which are
related to wheel rotation drag become most apparent when either the amount of
yaw rotation is greater than 60 degrees and/or the vehicle spends a significant
amount of time in a near longitudinal side-slip. A random sampling of angular
velocity time histories for four different cases with either none, one, two,
three, or four wheels with drag is illustrated in **Figure
7 **from **Reference**
[3].

Figure 4 Approximation of Motion Resistance in Sideslip

Figure 5 Tire Forces During Spinout

Figure 6 Linear and Angular (Yawing) Velocity vs. Time (no braking)

Figure 7 Random sampling illustrating angular velocity deceleration variations due drag

*(For conditions with 0,1,2,3 and 4 wheels with drag (from Reference 3))*

In the following an
analytical procedure is presented for approximating the linear and angular
velocities of a vehicle at the start of its motions subsequent to a collision,
which was first defined by Marquard in **Reference
[4]**, and
which served as a starting point for corresponding aspects of the CRASH
computer program **(Reference [5]). **The cited procedure takes into account
the fact that the linear and angular (i.e., yaw rotation) displacements of a
four-wheeled vehicle subsequent to a collision occur under conditions of
intermittent deceleration when the wheels are free to rotate. By approximating
the linear and angular deceleration rates of a vehicle with either (1) all
wheels freely rotating or (2) all wheels locked during the different phases of
a spinout motion, Marquard developed approximate relationships for the
relationship between the total linear and angular displacements during the
travel from separation to rest. He then
estimated the corresponding linear and angular velocities of the vehicle at separation from its collision
partner, for two cited cases of rotational resistance at the wheels. The
procedure has been generalized in the following to include intermediate
conditions of rotational resistance at the wheels.

A technique for generating initial estimates of the collision separation conditions:

**INPUTS**

_{} Rest position and
orientation

(feet and degrees)

_{} Position and
orientation at separation

(feet and degrees)

a + b = Wheelbase, inches

k^{2}
= Radius of
gyration squared for complete vehicle

in
yaw, in^{2}

^{ }_{} = Nominal
tire-ground friction coefficient

_{} = Decimal
portion of full deceleration

_{}

g = Acceleration of gravity

= 386.4
inches/sec^{2 }

**1.0
**_{} inches

**2.0
**_{} radians

**3.0
**_{}

**4.0
**_{} **GO TO 10.0**

**5.0
**_{}

**6.0
**_{}

**7.0
**_{}

**8.0
**_{} deg/sec

**9.0
**_{} inches/sec

**GO TO 12.0**

**10.0
**_{} deg/sec

**11.0
**_{} inches/sec

**12.0
**_{} inches/sec

**13.0
**_{} inches/sec

**14.0
** Return
with starting values: u_{S, }v_{S} inches/sec

_{} degrees/sec

Note that the above calculations can be simplified by means of the following steps:

Let

_{} (7)

Then

_{} deg/sec (8)

_{} inches/sec (9)

Several possible shortcomings in the cited technique
for the generalized case have been investigated (see **Reference 3).** This technique should be considered a first
approximation technique for the estimation of separation conditions which will
produce better approximations than conventional constant deceleration
techniques (i.e., V^{2 }=2as).

The following option were implemented in CRASH during various phases of the development. The main objective in the implementation of the options was to improve the correlation with full-scale tests.

· Point on Curve

· End of Rotation

· Trajectory Simulation Option

The SPIN2 procedure of the original CRASH program uses as a starting point the relationships developed by Marquard [[6]]. The Marquard procedure takes into account the fact that the linear and angular (i.e., yaw rotation) displacements of a four‑wheeled vehicle subsequent to a collision each occur under conditions of intermittent deceleration when the wheels are free to rotate. By approximating the linear and angular deceleration rates of a vehicle with either (1) all wheels freely rotating or (2) all wheels locked during different phases of spinout motion, Marquard developed approximate relationships between the total linear and angular displacements during the travel from separation to rest and the corresponding linear and angular velocities of a vehicle at separation from its collision partner, for the two cited cases of rotational resistance.

In the CRASH program [**11**],
the SPIN2 routine was developed to extend the relatively simple Marquard
relationships to include the cases of partial braking and/or damage-locked
individual wheels. Evaluations of the resulting, modified relationships by
means of trial applications to spinout trajectories generated with SMAC [3] revealed several shortcomings of the initial SPIN2
relationships. First, a residual linear velocity frequently exists at the end
of the rotational (i.e., yawing) motion. Next, the general shapes of plots of
linear and angular velocity vs. time changed substantially as functions of the
ratio of linear and angular velocity at separation from the collision. Finally, the
transitions between the different deceleration rates of linear and angular motions were found to occur gradually rather
than abruptly. Slope changes in the plots of linear and angular velocity vs.
time were found to generally occur in the form of rounded "corners"
in the curves.

To improve the accuracy
of approximations of separation velocities, provisions for the introduction of
a residual linear velocity at the end of the rotational motion and the
development of empirical coefficients, in the form of polynomial functions of
the ratio of linear to angular velocity at separation, were incorporated in the
SPIN2 analytical relationships of the CRASH program. Since the separation
velocity ratio is initially unknown, a solution procedure was developed whereby
several trial values of the ratio, based on an approximate equation, were used
to test multiple solutions.

The cited analytical
developments, reported in [**12**],
involved only limited efforts which were aimed primarily at demonstrating the
feasibility of the CRASH concept.
Polynomial functions to generate empirical coefficients were developed,
on the basis of 18 single-vehicle SMAC runs with relatively high linear and
angular velocities for starting (i.e., separation) conditions. In the more
common, real-life accident case, a relatively small rotation (i.e., yawing)
velocity may exist at separation. In such a case the initial direction of the
velocity vector with respect to the longitudinal axis of the vehicle will
obviously affect the sequence and the duration of the linear and angular
deceleration rates of the vehicle.

In consideration of
known shortcomings of the SPIN2 aspect of the CRASH program, a subcontract to
refine SPIN2 was undertaken in 1979 [3]. A representative sample of actual accident cases was selected from the
NCSS [[7]]
files for use in the study. A total of 50 cases were selected and then
reconstructed with the SMAC computer program. For each of the SMAC reconstructions,
separation information was used to formulate a basis for a refinement of the
SPIN2 empirical coefficients.

A careful examination
of the time-history plots of linear and angular velocities for all of the cases
in the sample revealed a significant number of cases in which the
SMAC-predicted behaviour deviated from the analytical assumptions upon which
the SPIN2 routine is based. Attempts were undertaken within the research
project to discriminate characteristics of separation conditions. Unfortunately,
only partial success was achieved in the attempts to accommodate deviations by
means of the use of logic and discriminators. As a result, a realistic
appraisal of residual scatter in the empirical fits led to the conclusion in [3]:

"To achieve a
general improvement in the reliability and accuracy of approximations of the
angular and linear velocities at separation, a step-by-step time history form
of trajectory solution should be implemented."

Subseqent work which has
been performed on investigation and refinement of the SPIN empirical
coefficients [Error! Bookmark not defined., [8], [9]] and the corresponding modifications to CRASH is
subject to the effects of ‘scatter’. Any proposed refinements of the SPIN
empirical coefficients and any reconstruction techniques which are based on the
refinements of the SPIN empirical approach will ultimately fail in some
applications to individual case reconstructions due to the possibililty that
the particular case being investigated may be characteristic of a
"scatter" point. The research cited in this paper strongly supports
the conclusion from 1981 that implementation of a trajectory solution procedure
should utilize an iterative time-history simulation.

The original form of the CRASH [[11], [12], [13], [14]]^{ }computer program, which
culminated in the CRASH3 version, was not intended to be a detailed, highly
accurate reconstruction program. Rather,
it was developed to serve as a simple preprocessor for the SMAC program. While the results of CRASH3 applications can
be useful in providing approximate measures of accident severity for use in
statistical studies, where the average error is most important, it has been
demonstrated in validation tests to produce results which when compared to
those of full-scale crash tests can include individual errors as great as 45%[**14**]. The possible error levels of the CRASH3
computer program are also generally applicable to the EDCRASH [[15],
[16], [17]]
computer program, since the CRASH3 program and the widely distributed EDCRASH
clone are essentially identical. No significant analytical refinements have
been made to the trajectory solution or trajectory simulation procedures of
EDCRASH. The EDCRASH program, while claiming to be “within **16**] is subject to
errors in individual speeds as great as 43.5% (Table 2, case 12, vehicle No. 1
[**16**]).
Any “improvement” of the EDCRASH results over CRASH3 is mainly due to the
“optimization” of the inputs to EDCRASH (to produce better correlation with __known__
results) and modification of the error reporting techniques [**16**].

The CRASH3
program also includes an exploratory *trajectory
simulation *option solution procedure based on the SMAC trajectory model. The
optional *trajectory simulation*
procedure (USMAC) includes routines from the trajectory portion of the SMAC
program to permit time-history simulations in CRASH of the spinouts of the
individual vehicles from separation to rest.

The USMAC *trajectory
simulation* model is a three degree of freedom (X, Y, PSI) mathematical
representation of planar motion. The
tire side force calculations are based upon a nondimensional side force
function whereby the small-angle properties of the tires "saturate"
at larger angles. The "friction circle" concept is used to
approximate the interactions between side and circumferential (braking or
tractive) tire forces. The "friction circle" concept is based on the
assumption that the maximum value of the resultant tire friction force is
independent of its direction relative to the wheel plane.

The purpose of
the USMAC routine in CRASH3 was to serve as a check of the SPIN2 approximations
of separation speeds. An optional iterative procedure was also included in the
CRASH3 *trajectory simulation option*
to automatically adjust the SPIN2 separation velocities in an attempt to reduce
errors in the predicted vs. actual final rest positions. The initial form of the trajectory iteration
routine was implemented merely to demonstrate feasibility and was not
thoroughly tested and evaluated. The costs of a CRASH run increased ten-fold by
the use of the exploratory iterative trajectory solution procedure (USMAC)
(e.g., [[18]] , circa. 1976, p1.,"The
computer costs … of the CRASH program …range from approximately $1.00 to $10.00
per case. The upper end of the indicated cost range corresponds to a run in
which the option for testing and refining the trajectory analysis portion of
the calculation has been exercised").
There was no further NHTSA sponsored development of the original
exploratory implementation of the USMAC routine.

By the mid 1990’s, with the prevalence of extremely
powerful and inexpensive Pentium PC’s, and therefore the availability of
virtually unlimited computer resources, consideration was given to internal
research by McHenry Consultants, Inc. to further develop the *trajectory simulation* routine of the
CRASH3 program. The objective in our
refinements of the CRASH3 accident reconstruction procedures has been to
simplify the input requirements of the program while providing a significantly
improved correlation of the reconstruction results with known test
results. A secondary consideration in
the form of the refinement has been to limit the total computational time for
convergence on a solution to a reasonable amount of time.

Effective refinements of the *trajectory simulation* procedure can substantially increase the
usefulness of the simple “closed-form” CRASH3 accident reconstruction procedure
by producing a general refinement of the *trajectory
solution* procedure. The CRASH3 *trajectory
solution* procedure requires a minimum amount of input information about the
accident scene and vehicles. An effective improvement of the *trajectory solution* procedure can be
expected to substantially improve the correlation or "validation" of
the CRASH3 model when comparing the reconstruction results with full-scale test results. A 1989
study [**16**] concluded that the original form of the CRASH3/EDCRASH *trajectory simulation* option can
actually degrade the *trajectory solution *results
of the CRASH3 program.

A secondary task required in order to further refine
and enhance the *trajectory solution*
procedure of the CRASH3 program was a reactivation and refinement of the
angular momentum solution procedure.
The original CRASH program included conservation of linear momentum in
the trajectory based solution to determine the impact speeds based on the
separation velocities. A contract performed on CRASH2 to implement an angular
momentum solution achieved mixed results [[19]]. A major hurdle for any procedure
which includes an angular momentum solution is the need to approximate movement
of the vehicles during the collision. In the CRASH2 formulation the impact and
separation positions and headings were assumed to be identical. The research in
[**19**]
revealed that the accuracy of an angular momentum solution procedure for
accident reconstruction which includes the assumption of no movement between
impact and separation will produce unacceptable error levels (>>20%) in
many cases.

Other analytical accident reconstruction techniques which include provision for an angular momentum solution procedure and/or which are based on conventional momentum analyses, include the somewhat subjective input requirement that either a vehicle-to-vehicle contact "point" [[20]], or a "point of maximum engagement" [[21]] or an "impact center" [[22]] be specified. The additional input is required to compensate for the cited solution procedure’s lack of an independent determination of separation positions and orientations.

The requirement that the user specify either an arbitrary impact contact "point" or an arbitrary "point of maximum engagement" detracts from the objectivity of the reconstruction techniques.

**Figure 5**
demonstrates representative changes in positions and orientations during the
contact phase of collisions.

Figure 8 Impact and Separation Positions and Orientations for RICSAC Test#12 and Test#1

The subjective choice of a “point” can produce a large variation in the predicted results. During “validation,” when the results are known, the user has some guidance in choice of the subjective “point.” In real-world applications, where the answer is not known, the determination and arbitrary specification of a “point” can and will produce a wide range of predicted results. The normal input requirements of accident reconstruction programs of damage dimensions and approximate impact configurations should provide more than adequate information for any accident reconstruction program to independently achieve the function of any contact “point” or “point of maximum engagement” without user intervention. The movement of the vehicles between impact and separation can be initially approximated, for example, by moving the vehicles in their initial directions of motion to positions where the damage regions match. The procedure to determine a separation position should be automated to prevent subjective variations between users in the positions of match and therefore the results.

Other assumptions of the cited techniques [**20,21,22**] which may detract from the validity of their
impact models for objective application to accident reconstruction are:

·
During the impact no consideration is given for *tire-to-ground
“external” forces*

·
The ** impact duration** and time for
exchange of momentum is assumed to be infinitesimally small.

**TIRE-TO-GROUND "EXTERNAL" FORCES**: The
effects of tire-ground forces must be considered in a motor vehicle collision
reconstruction. During the early development of the SMAC program [[23],
[24]] tests were performed to determine the effects
of external tire forces on the collision solution procedure. It was concluded
that “The conventional assumptions that
the effects of vehicle deformations and of tire forces can be neglected in
analytical reconstructions of collisions can lead to significant errors. This
is particularly true for intersection-type collisions at low to moderate
vehicle speeds, in which prolonged or multiple contacts and significant
movements of the involved vehicles occur” and that "therefore it is
essential in a general procedure for reconstruction calculations that both the
collision and tire forces be considered simultaneously."

**IMPACT DURATION:** The duration of a motor
vehicle collision cannot be assumed to be infinitesimally small. Normally the exchange of momentum requires 50 to 125
milliseconds. Significant changes in positions and orientations can occur
during the collision which can produce changes in the collision moments acting
on the collision partners. Any accident
reconstruction solution procedure which contains the assumption of an
instantaneous exchange of momentum should be carefully evaluated.

Datasets were prepared of the 12 RICSAC tests and run
with the CRASH3/EDCRASH programs and the results are depicted in **Figure
9** and **Figure 10.
**These figures represent the __starting point__ for the ** refined
CRASH3** research project and they demonstrate the general inability of
the CRASH3/EDCRASH programs to consistently reconstruct.

Figure
9
Initial comparison of reconstructed __DV__
of CRASH3/EDCRASH Trajectory Solution vs. SMAC

Figure 10 Initial comparison of
reconstructed __Impact Velocity__ of CRASH3/EDCRASH Trajectory Solution vs.
RICSAC Test

A comparison of the ** refined CRASH3** trajectory
solution procedure with the RICSAC tests is presented in

Figure
11 Comparison of reconstructed __DV__
of *refined CRASH3* Trajectory Solution
vs. SMAC

Figure 12 Comparison
of reconstructed __Impact Velocity__
of *refined CRASH3* Trajectory
Solution vs. RICSAC Test Data

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Damage analysis procedures (e.g., SMAC and CRASH computer programs) were originally focused on interpolation/extrapolation of the early available crash test results, most of which were in the DV range of 25 to 45 MPH.

Combined assumptions of (a) linearity of DV_{c}
(i.e., the DV
preceding restitution) as a function of residual crush and (b) a DV_{c}
intercept near 5 MPH, at which no residual damage occurs, have served as the
basis for extrapolations outside the range of available test data.

The cited assumptions, combined with either (a) neglect of restitution (CRASH, EDCRASH) or (b) a crude approximation of restitution (SMAC, EDSMAC) have limited the reliability of damage-based DV results obtained with current techniques, near the lower end of the range for airbag deployments. As a result, it is necessary to supplement such damage-based reconstructions with separate analyses based on conservation of linear and/or angular momentum and on work-energy principles, until such time that validated refinements of the existing damage analysis procedures are developed and made available.

Another aspect of damage analysis that has been the focus of recent attention is that of offset frontal collisions. While the CRASH type of damage analysis permits the direct entry of induced damage along with contact damage, the original form of the SMAC type of damage analysis does not include induced damage.

In the following, a brief review of the history and of the analytical basis of damage analysis is presented. It is followed by a presentation and discussion of preliminary results of recent extensions to damage analysis procedures.

The early Automotive Crash Injury Research (ACIR) study (**Reference** [25])**,** which was initiated in 1952 and aimed
at (1) identification of injury causes and (2) measurement of the effectiveness
of countermeasures, relied on relatively gross evaluations of vehicle damage as
a basis for the classification of exposure severity. Photographs of the damaged vehicles were
compared with reference photographs to segregate individual cases into four
accident categories (front, side, rear and rollover) and five categories of
severity (minor, moderate, moderately severe, severe and extremely
severe). Travel speeds were based on
police estimates.

In 1969, a "Tri-Level Accident Research Study"
was initiated in which a Vehicle Deformation Index (VDI) similar to that defined in
SAE J 224a was adopted as a more refined damage descriptor (**Reference** [26])**.**

During the late ‘60’s and early '70's, a number of
technical papers in the field of highway safety indicated that reasonably
accurate estimates of the speed-changes that occur in wide-contact collisions
could be obtained through the use of simple linear relationships between the
impact speed-change and the extent of residual crush (e.g., **References** **26, [27]**,
[28],
[29], [30]**).**
While such relationships obviously constitute a gross simplification of
complex automobile structures, they were found to be capable of yielding impact
speed-change results with approximately a plus or minus 10 percent accuracy
when applied to a limited number of staged collisions** **(e.g**., Reference [31]).** In a more comprehensive evaluation** (Reference [32]) ,** it was found that the 95
percent confidence limits on individual calculations of delta-V ranged from 9
to 25 percent.

In **Reference 31**, empirical linear fits to the crush properties of
six different size categories of late ‘60’s and early ‘70’s vintage vehicles
are presented and discussed. It should
be noted that, in many of the cited empirical fits, a very limited number of
staged collision data points were found to be readily available. Further staged collision data were collected
and summarized in **References [33]
**and** [34]** for the purpose of supporting
refinements of the fits presented in **Reference**
**31**.

The use of linear relationships may be viewed as a simple empirical process for interpolation and extrapolation of the results of staged collisions. The application process must include provisions to account for the impact configuration, the “effective” mass and stiffness of the struck object, the contact area and irregular damage profiles. Clearly, the cited factors must be considered in any interpretation of collision damage. Such an interpretation procedure can be extended to accommodate nonlinear crush properties when sufficient crash-test results are available to permit the fitting of more exact empirical relationships. For example, it appears that bilinear fits might yield more accurate application results when a large DV range is included in the fitted data.

The general form of the existing linearized fits is
depicted in** Figure 13**. With this
assumed form of crush resistance, the energy absorbed by vehicle crush may be
obtained by double integration of equation 1** (Error! Reference source
not found.).**

F = A + BC Lb/in/in (1)

where A = Unit width Force Level for ‘no residual damage’, lb/in.

B
= Linear Force-Deflection Rate, lb/in^{2}.

C = Residual Crush, Inches.

F = Crush Resistance per Unit Width, lb/in.

the double integration of the equation is:

_{} (2)

where E = Energy Absorbed, inch lbs.

C = Residual crush, inches.

L = Length of contact damage area, inches.

Figure 13 **Assumed Linear Form of Crush Resistance**

For application of Equation (2) to a damaged vehicle,
the damage dimension format of **Figure 14** may be used.
In **Figure 14**, a uniform vertical damage profile is
depicted. It should be noted, however,
that the existing empirical fits** **(**Reference 34**) are based on the maximum extent damage profile.

Integration of equation (2) yields

_{} (3)

where G = constant of integration.

If the linear slope, B, is assumed to exist in the
non-damage range of the applied force, the constant of integration, G, is equal
to the work done in reaching the maximum force value for no-damage, the
variable A. Thus, for a full frontal
impact into a rigid barrier, an elastic deflection equal to A/B and involving
an energy absorption of A^{2}/2B per unit width will exist at C=0. Therefore, G=A^{2}/2B.

Integration of Equation (3) yields

_{} (4)

Since _{}Cd_{} is equal to the plan view contact damage area, in^{2}
(see** Figure
14)** and _{} is equal to the first
moment of the plan view contact damage area about the line defining the
original (undeformed) surface, in^{3} (see** Figure
14),** equation (4) may be expressed as

E = Aa + Bb + GL inch lb. (5)

where

a = Plan view contact damage area, in^{2}.

b = First moment of the plan view contact damage area about the line defining

the original undeformed
surface, in^{3}.

G = Constant
of integration »
A^{2}/2B.

L = Length of contact damage area, inches.

_{}

For the case of symmetrical, full-frontal impacts, Equation (4) becomes

_{} (6)

If the absorbed energy is equated to the corresponding dissipated kinetic energy of the subject vehicle,

_{} (7)

_{} (8)

where DV = Impact speed-change preceding restitution

Figure 14
Damage Dimensions

Equation (8) may be restated

_{} (9)

Therefore, in this special case (i.e., symmetrical, full-frontal) the impact speed-change DV is a linear function of the residual crush (C) and has an intercept at

_{} in/sec

The relationship is depicted in **Figure
15**.

_{0} and b_{1}
for the intercept and slope of plots similar to **Figure
15**, and he has presented some representative
values. It is of interest to relate his
variables to A, B and G.

_{} (10)

_{} (11)

where

M_{s}= Standard test mass, lb sec^{2}/in.

Solution of (10) and (11) for A and B yields

_{} (12)

_{} (13)

_{} (14)

_{}

Application of equations (12), (13) and (14) to the frontal barrier test
data presented by **Reference 29**) yields the results presented in **Table
1**.

Table 1 Frontal Barrier Test Data (Based on Reference 9)

It should be noted that the crush coefficients for
CRASH, (A, B & G) and those for _{0}, b_{1}), represent *virtual*
crush resistance properties. The simplifying assumption of these techniques is
to use the *residual *crush to compute
the energy absorbed up to the point of a common velocity to determine the
equivalent barrier impact speed. The crush is the residual crush that will
exist *after* the vehicle undergoes
dynamic crush and restitutes to its residual deformation. It does not give any
indication of the actual stiffness of the structure of the vehicle.

Consider two vehicles with the same residual crush for
a given impact speed into a barrier (for example, at 30 MPH). One vehicle is
structurally very stiff and deforms dynamically only up to approximately the
residual amount (i.e., very little or no restitution). On the other hand, the
other vehicle is structurally very soft. It initially deforms to a value twice
that of the residual value after which it’s structural properties produce a
restoration of the front structure to produce a residual crush equal to that of
the very stiff vehicle. By the simplifying assumptions of a CRASH-type of
damage analysis, both vehicle’s have the same *virtual *stiffness (Same A & B and/or b_{0} & b_{1}),
whereas in reality the structures of the two vehicles are very different. Do not make the mistake of referring to the
stiffness of a particular vehicle on the basis of its CRASH-type crush
coefficients. A careful examination of the actual tests on which the CRASH-type
crush coefficients are based should be performed to determine the actual crush
properties.

The damage-analysis technique of the CRASH computer
program produces an approximation of the __approach-period__ portion of the
impact speed-change, rather than the total impact speed-change. The clearly defined selection of analytical
approach (**Reference
**[35])
was based on a lack of definitive information, in 1975, on the actual magnitude
and variation of the coefficient of restitution as a function of both deflection
extent and position on the vehicle periphery.
The resulting underestimate of the total impact speed-change in low
speed collisions, where restitution effects are greatest, was fully recognized
and acknowledged in **Reference 35.**

Figure 15
Speed-Change vs. Residual Crush in Full-Frontal Symmetrical Impacts

In 1987, a proposed revision to the Damage Analysis
Procedure for the CRASH computer Program was presented in **Reference [36]**. In the paper it was noted that
Smith and Noga (**Reference 32**) properly conclude that the damage algorithm of
the CRASH computer program tends to underestimate low DV values as a result of
the neglect of restitution effects. The original formulation of the CRASH3
program (**Reference** **35**) addressed only the speed change ( DV) up
to the point of common velocity. The omission of restitution effects in CRASH
was based on several important considerations: First, the original formulation
of CRASH had limited objectives in terms
of accuracy. It was developed primarily as a pre-processor for use with the
SMAC accident
reconstruction program (**Reference [37]**).
Second, at the time of the CRASH formulation (1975), restitution effects of
vehicle structures were not found to be sufficiently well defined to support
the added complexity of inclusion of a provision to model restitution. The
simplifying assumption which included the neglect of restitution was clearly
pointed out in the original Crash documentation (**References [38],35**).

The widespread use of the damage analysis portion of
CRASH3, as a primary technique rather than a simple pre-processor, justified a
re-examination of the analytical formulation of CRASH. The proposed revised
algorithm for Crash, “CRASH4”, included the original Crash stiffness
Coefficients, A & B, as well as four new internal coefficients, K_{1},
_{2}*virtual* Crush Stiffness based on a relationship between the
residual Crush and absorbed energy for a given crash test speed. The new
internal coefficients in CRASH4 were included to provide a means of
accommodating variations in the restitution properties of vehicle structures.

When we examine a damaged vehicle, the damage that we observe is called the residual or permanent damage. This permanent damage is the result of a dynamic collision event. During the collision the vehicle normally deforms a certain amount greater than the observed final residual damage. The amount that a vehicle initially deforms is called the peak or maximum dynamic crush. This period of the collision is also referred to as the period of deformation, which refers to the time from initial impact to the point of maximum deformation. It is during this time that the maximum collision forces and resulting impulses act on the vehicles. Subsequent to the peak dynamic deformation, the vehicles begin the restitution phase. The restitution phase is the time from the maximum deformation condition to the instant at which the bodies separate. During this period additional forces and therefore additional impulse acts on the vehicles as some of the structure restores or springs back. The rate, both in terms of force level and duration, at which the vehicle structure restores from the peak dynamic damage to the final residual damage determines the amount of additional impulse the vehicle undergoes during the restitution phase. The restitution phase acts to increase the accident severity by prolonging the acceleration exposure while also reducing the amount of residual damage. This accounts for an inherent error in the simplifying assumptions of a damage analysis procedure which ignores the restitution phase of a collision.

The amount of restitution and the rate at which a
vehicle restitutes can produce a range of variation of collision severity
between different vehicles for a given residual crush on a vehicle. The
magnitudes of the increases in the __total __speed change (using CRASH4 and
including a range of hypothetical restitution properties) over the impact
speed-change for the __approach__ period only (using CRASH3 with its
assumption of no restitution) may be seen from **Reference 36 **to range from 3.9% to 15.5% at 30 inches of
static crush and from 8.9% to 58.2% at 10 inches of static crush.

To date there has been only a limited number of crash tests performed which include an investigation of the restitution properties of vehicle structures. Therefore there is too limited an amount of data available to include directly the effects of restitution in the CRASH type of analysis. However, any reconstruction which utilizes a CRASH3 based damage analysis procedure should consider the possibility that significant restitution effects may have been ignored.

The relationship between the impact speed-changes and
the maximum absorbed energy is made more understandable by consideration of the
fact that the impact speed-change is determined by the __impulse__ of the
collision force while the absorbed energy is determined by the work done by the
collision force.

_{}

_{} (31)

_{} (32)

At the end of the approach period, the relative velocity, dd/dt, is near zero while the collision force, F(d), is at its maximum value. Thus, the change in absorbed energy, equation (31), is very small while the total impulse, equation (32) increases rapidly.

In most side impact cases the maximum extent of damage involves override of the sill structure. Also, most of the available side impact test results have not included direct contacts on the wheels. The need for a “zoned” approach to empirical fits for side structures is clearly indicated, but it is presently precluded by data limitations. The effects of side impacts at wheel locations and of sill structure contacts are compensated, to some extent, by the fact that the energy absorbed by the two involved vehicles is summed in the approximation of speed-changes. Contacts with the more resistant portions of the struck vehicle produce a greater deformation and, thereby, a greater energy absorption by the striking vehicle.

In the case of side impacts, determination of the
energy absorption by vehicle crush is somewhat more complicated than the case
of end impacts. First, the
"effective" mass at the point where a common velocity is
reached must be determined from the impact configuration and the inertial
properties of the two colliding bodies.
The present version of the** CRASH**
computer program includes the assumption that the common velocity is reached at
the centroid of the damaged area **(Reference
[39]).** Next, energy absorption produced by a
tangential component of the collision force must be subtracted from the total,
since the fitted empirical crush characteristics apply only to the intervehicle
force component perpendicular to the involved side or end**.**

For cases in which the principal force is not perpendicular to the involved side or end, the analytical relationship defining the maximum relative displacement makes use of the crush resistance and deflection along the line-of-action of the resultant force. In other words, the effective peripheral crush resistance that is used in the derivation of equations is in the direction of the resultant force. Therefore, the calculation of absorbed energy must reflect this fact.

If the specified direction of the principal force is
assumed to be approximately correct, a corresponding tangential force component
must have existed during the deflection.
In **Figure 16**, the components of a resultant intervehicle force
are depicted.

It may be seen that

_{} (33)

The work done in the direction of the resultant force may be determined from

_{} (34)

Application of (34) to the calculation of absorbed
energy yields a correction factor (1 + tan^{2}a) for the effective crush
stiffness in oblique collisions. Note
that the maximum value of a is limited to plus or minus 45 degrees in the **CRASH3** computer program. Further refinement and discussion of the
energy correction factor can be found on page 32.

The moment arms of the resultant force on the two vehicles determine the effective masses acting at those vehicle points that achieve a common velocity during the collision (assumed to be the centroids of the damaged areas). Thus, the accuracy of DV results corresponding to given damage patterns is directly affected by the moment arm approximations.

In **Figure 17** the moment arms of the resultant collision force
are depicted. It is essential, or
course, in applications of the described technique that the specified
directions of the principal force on the two interacting bodies combined with
the heading directions of the vehicles are consistent with oppositely directed
forces (i.e., ±180°). Additional internal checks have been added to
the CRASH3 program to insure such compatibility of inputs.

The following relationships defining the approach-period
speed changes of the two vehicles are derived in **Reference** [40].

_{} (35)

_{} (36)

where

(see **Figure
17**)[bm1]

Figure 16
Force Components in Oblique Collision

Figure 17
Moment Arms of Resultant Collision Force

Since 1990, TRC of Ohio, Inc. under the sponsorship
of NHTSA has undertaken the task of performing a large number of crash tests of
late model vehicles in support of and as justification for a refinement of the
CRASH3 damage analysis procedure for the reconstruction of automobile
collisions. The crash tests performed as a part of the research utilized the
repeated test technique (**References [41]**,
[42]**).**

Papers authored by Prasad (**References**
[43], [44],
**42**, [45], [46]**)** as a part of the NHTSA investigation
discuss a CRASH3 “reformulation,” “new
algorithm” and “new model” based on the results of the significant number of
crash tests of late model vehicles.

The reports address three separate topics related to the CRASH algorithm:

(1) Forced intercepts.

(2) Custom-fitted coefficients.

(3) Abandonment of A, B and G.

The first two items have already been proposed or
adopted by researchers and/or entrepreneurs in the field (e.g., **References [47]**, [48], [49], [50], [51]**)**
and, therefore, they are not new concepts.
The first two items clearly should be adopted in a needed update of the
existing CRASH3 coefficients (see discussion).
The last item is an arbitrary, conceptual revision which cannot improve
accuracy (see** Reference 45,** p.17, 2nd paragraph).

In the following paragraphs, the individual topics are addressed in greater detail:

If a straight line is fitted through a clustered group
of data points for delta-V versus the uniform or average value of residual
crush (for known contact widths) that are all in the range of 30 to 35 MPH, the
delta-V intercept at zero residual crush will __clearly__ not be reliable
(e.g., see “natural” intercept in **Figure 18**).
Therefore, in the case where __actual data__ from low speed
collisions are not available, a forced intercept will be preferable to an
unreliable one based on the slope of a linear fit through closely spaced, relatively high-speed points. This conclusion has been reached in a number
of related publications **(e.g.,
References 47, 49)** and, therefore, it is not a new concept. Among the three topics addressed in the
subject report, this one should clearly receive early attention in a needed
update of the existing CRASH3 coefficients.
However, such an update __must not__ be based on __single data
points__ combined with the forced intercepts.

While the concept of a forced intercept may be
accepted as a __necessity__ with existing data limitations, the related use
of real data points must include __all available__ test results. Note that some individuals have based linear
fits on __single data points__, combined with forced intercept.

A judicious engineering approach to the empirical
fitting process will clearly require the use of __more than one__ actual
data point for a given collision direction on a given vehicle. The scatter that occurs in crash test data
makes the use of a single test result, combined with a forced intercept, a
highly unreliable basis for a linear fit.

For example, in a litigated matter, an EDCRASH (**Reference** **48**) customer relied on an unrealistically low crush
resistance for ‘70’s vintage Plymouth, when available NHTSA crash test data for
the specific vehicle and other closely related models clearly indicated that
the EDCRASH fit was based on a forced intercept combined with a __single NHTSA
data point__ that was sufficiently different from the other data to be
doubtful** **(see** Figure
19).**

Thus, __all applicable data__ must be utilized in
the case of a forced intercept in order to minimize errors in slope, (i.e., b_{1})
related to the __scatter__ of the test data.
Such straight line fits can simply utilize a linear regression technique
that includes a forced intercept. In
this manner, b_{1}, for full contact, fixed rigid barrier collisions
can be directly obtained (e.g., see solid line in **Figure
18**). Note
that crush__ corrections__ for variations in test weights are required when
multiple data points are used to obtain a linear fit of delta-V versus residual
crush.

The proposed abandonment of A, B and G in favor of b_{0}
and b_{1}, is a separate topic which has no direct bearing on the use
of a forced intercept. In fact, A, B,
and G are retained in **Reference 47 ** while
forced intercepts are used. The fact
that b_{0} and b_{1} have been defined in terms of A, B and G
and vice versa, since 1975** **(e.g., **Reference 31**) makes that general topic a superficial and
arbitrary one.

Figure 18 Comparison if “natural” and forced intercept
fit for Delta-V vs Crush

It is obvious that custom-fitted crush coefficients
can generally yield more accurate damage interpretations than those
coefficients based on fits by vehicle categories (particularly for the crash
conditions on which they are based) (**Reference**
**45,** p.20, paragraphs 3&4, p. 23, paragraph 4, p.
24, paragraph 1). **References 49**, **50**, and **51** make that point in relation to the reconstruction
of “specific accidents” (i.e., litigated matters). Unfortunately, the concept may not be
applicable to NASS because of limitations in available crash test data and
practical considerations regarding the storage of individual crush properties for
the entire

In **Reference [52] and [53]**, an analytical approach is defined
which potentially could achieve significant accuracy improvements while
retaining the categorization of vehicle, by segregating stiffness and
restitution properties. Thus, the approach
of **Reference** **52 and 53** may be more applicable to the needs of NASS than
the custom-fitting of individual crush properties.

Figure 19 Comparison of CRASH3 Category and Linear Regression fit for
a Plymouth Fury

In the original CRASH approach, __absorbed energy__
was selected as the basis for fitting empirical crush coefficients, in
recognition of the fact that the __test weights__ of given makes and models
of vehicle are generally not __identical__ in available test data (e.g.,
empty vehicle vs. four test dummies).
Also, the technique was designed to __not__ be limited to uniform
crush, central collisions against fixed barriers** **(e.g., **Reference 31**). Thus,
while the crush properties are assumed to be the same in different tests of a
make and model of vehicle, the extent of crush must be related to the actual
energy absorption rather than to speed-change alone (e.g., effective mass in
oblique collisions, irregular damage profiles, actual test weights).

A cited review of the ‘reformulation’ of CRASH3 by
Prasad indicates that it consists mainly of the addition of new crash test data
points and a rework of the formula to use different symbols. All the
simplifying assumptions of CRASH3 are retained and __no additional refinements__
are introduced.

A comparison of the Crush coefficient symbols related
to the ‘reformulation’ by Prasad, the original CRASH3 coefficient symbols and
the

**Campbell**** **: b_{o }=_{ }MPH or IN/SEC

_{ }b_{1}
= MPH/IN or IN/SEC/IN

**McHenry**
(CRASH3): A = LB/IN

B = LB/IN^{2}

**Prasad**: d_{0 }=_{ }

_{ }d_{1} = _{}

**Conversions
between:**

A = d_{0 }* d_{1} * 0.57101 LB/IN

B = d_{1}^{2} * 1.45036 LB/IN^{2}

_{} _{}

_{} _{}

_{} where

M_{s}=
Standard test mass, lb. sec^{2}/inch.

The reformulation proposed and used by Prasad was basically to change the units of the Crush Coefficients:

McHenry:(Crash3 ): Force per unit width

Prasad: Energy Dissipated per unit width.

Continuing efforts to refine existing procedures for damage analysis have included developments related to the topics of (1) an energy correction factor to approximate the effects of tangential friction forces in oblique collisions, and (2) restitution effects. In the following, a brief summary is presented along with measures of the magnitudes of the cited effects.

Crush properties of vehicles are measured and fitted
for crush directions that are perpendicular to the involved end or side of a
vehicle. However, in an oblique
collision, a component of the tangential friction force acts to increase the
effective crush resistance in the direction of crushing and thereby, the
absorbed energy (**Figure 20**).
Therefore, an Energy Correction Factor (ECF) is needed for applications
of crush coefficients to oblique collisions.

Figure 20 Application of Fitted Crush Properties

In the early development of CRASH (**Reference** **40**)
the need was recognized and a simplistic ECF was defined in the form of (1 +
tan^{2} a),
where a
is the angle of crushing relative to a perpendicular to the involved end or
side of the vehicle.

As application experience increased and evaluations
were made of results at large angles, a, the ECF was limited to
the angular range of ±45 degrees, so that the maximum value of the ECF was
limited to 2.000 (e.g., **Reference** **39**).

On the basis of a recognition of the limitations on
energy absorption that are imposed by realistic levels of tangential friction,
a revised form of the ECF was proposed in 1986 (**Reference** **52**).
Applications of the ECF by the author since that time have generally
been restricted to the angular range of ± 45 degrees so that only a
limited evaluation of the effects of the revised ECF was possible.

The topic has recently been revisited. A detailed review of the earlier analytical assumptions and the corresponding derivation of relationships has led to the proposed form of the modified ECF being further revised, on a purely analytical basis, to the following:

ECF = (1.0 + m_{v}
tan a) (1)

It is proposed that the angular range of the ECF should be limited to ± 60 degrees, so that the maximum value of ECF is limited to approximately 1.95.

The analytical derivation of Equation (1) is contained in the literature.

During a motor vehicle collision, the maximum dynamic deformation generally exceeds the residual deformation. Subsequent to the peak dynamic deformation, the collision partners begin a restitution phase as the deformed structures restore kinetic energy, or “spring” back. The restitution force level and duration determine the impulse that acts on the collision partners during the restitution phase.

When an accident vehicle is examined, the residual, or
permanent, deformation is observed and/or measured. The original form of damage analysis in CRASH
does not include provisions for the effects of restitution. The original SMAC collision routine includes
a simplified restitution model which is cumbersome to apply, can be sensitive
to time increment size, and tends to over-predict the residual damage. The
resulting effects on the accuracy of damage-based reconstructed values of DV,
for the case of direct, central barrier collisions, ranges from approximately
10 to 30% underestimates, depending on properties of the specific vehicle and
the extent of residual crush. For the
case of oblique, non‑central collisions, a similar range of effects is
anticipated on the basis of indirect measures of corresponding restitution
values [**1, 2**]^{[54]}.

At the present time, crush coefficients for vehicle
collision analysis are predominantly based on impact speeds and damage
measurements from rigid, fixed barrier crash tests. The residual damage is correlated with the
impact speed by means of fitted linear relationships. In general, there is no consideration given
to the effects of restitution in applications of the fitted crush
coefficients. However, the ignored
effects of restitution on the total impact speed‑change, corresponding to
a given amount of residual crush, are compounded by the fact that restitution
acts to __reduce__ the amount of residual deformation, for a given maximum
dynamic crush, while also acting to __increase__ the total impact speed
change. Thus, substantially different
vehicles can share nearly equal slopes and intercepts in CRASH-type plots of
the approach period speed-change as a function of residual crush. This can
occur even though the actual exposure severity for a given residual crush may
be significantly different.

Available information on the restitution behavior of
automobile structures (e.g., **References**
[55], [56], [57],
[58]) is limited. However, the general nature of the measured
behavior has served as the basis for the development, in **Reference 52 and 53**, of corresponding analytical relationships.

The purpose of that development has been an attempt to refine the existing crush property descriptors by segregating the effects of stiffness and restitution. The overall objective is, of course, to achieve improved accuracy in damage-based reconstruction results.

In the CRASH implementation of restitution, the
restored energy for each of the collision partners is separately calculated by
means of integration across the damage interface. The resulting values are added and then
combined with the total absorbed energy for application in the calculation of DV_{1}
and DV_{2}.

The effective overall coefficient of restitution in a given collision includes effects of the width and location on each vehicle of the contact area, the detailed damage profiles and the individual unit-width crush properties of the collision partners. This combination of effects is believed to constitute a realistic analytical representation of the actual physical system during the unloading process.

Progress toward a rigorous and complete validation study to support a general release of the developments is data-limited at the present time.

©McHenry Software, Inc.[1] See “Collision Deformation
Classification,” Society of Automotive Engineers Technical Report J224a, 1972,
for further discussion of the principal collision force and its direction of
action.

[2] Knipling, R.R., Kurke,
D.S., “**NASS Field Techniques – Volume IV
– CRASH MEASUREMENTS**”,

[3] McHenry, R.R., McHenry,
B.G., **"National Crash Severity
Study - Quality Control - Task V:
Analysis to Refine Spinout Aspects of CRASH", ** Contract DOT-HS-6-01442, January 1981

[4] Marquard, E., **“Progress in the calculations of Vehicle
Collisions”, **Automobiletechnische Zeitschrift, Jarq. 68, Heft 3, 1966

[5] McHenry, R.R., **"User's
Manual for the Crash Computer Program, Part 2 - Final Report", **Calspan
Report No. ZQ-5708-V-3, Contract No.
DOT-HS-5-01124, January 1976.

[6] Marquard, E.,“Progress in
the calculations of Vehicle Collisions” Automobiletechnische Zeitschrift, Jarq.
68, Heft 3, 1966

[7] Kahane, C.J, et al,
"The National Crash Severity Study", Sixth International Technical
Conference on Experimental Safety Vehicles (1976) 495-516

[8] Fonda, A.G.,

[9] Fonda, A.G., "Energy
and Major Diversion in Accident Reconstruction", SAE Paper 96-0888

[10] McHenry, B.G., McHenry,
R.R.,“CRASH-97 - Refinement of the
Trajectory Solution Procedure”, SAE
Paper No. 970949; also published in __1997 SAE Transactions, Vol 106;
Journal of Passenger Cars__;

[11] McHenry, R.R., “The CRASH
Program - A simplified Collision Reconstruction Program” Proceedings of the Motor Vehicle Collision
Investigation Symposium, Calspan, 1975

[12] McHenry, R.R**. **Lynch, J.P., “User’s Manual for the
Crash Computer Program” Calspan Report
No. ZQ-5708-V-3, Contract No. DOT-HS-5-01124, Jan 1976

[13] NHTSA,“CRASH3 User’s Guide
and Technical Manual”, Revised Edition, National Highway Traffic Safety
Administration, DOT-HS-805732, April
1982

[14] ** **Tsongos, N.G.,** **“CRASH3 Technical Manual”**, **

[15] Day, T.D., Hargens, R.L.,
“Differences Between EDCRASH and CRASH3”, SAE Paper 85-0253

[16] ** ** Day, T.D., Hargens, R.L., “Further Validation
of EDCRASH Using the RICSAC Staged Collisions”, SAE Paper 89-0740

[17] Day, T.D., Siddall, D.E., “Validation of
Several Reconstruction and Simulation Models in the HVE Scientific
Visualization Environment”, SAE Paper 96-0891

[18] McHenry, R.,R., Lynch,
J.P., "CRASH 2 User's Manual", Contract DOT-HS-5-01124, Calspan
Report ZQ-HS-5-01124, November 1976

[19] McHenry, R.R., Lynch, J.P.,
“Revision of the CRASH2 Computer Program”, US DOT HS-805-209, September 1979

[20] Limpert, R., Andrews, D.F.,
"Linear and Rotational Momentum for Computing Impact Speeds in Two-Car
Collisions (LARM)" , SAE paper 91-0123

[21] Steffan, H., Moser,
A.,"The Collision and Trajectory Models of PC-CRASH", SAE Paper
96-0886

[22] Ishikawa, H., "

[23] McHenry, R.R.,
"Development of a Computer Program to Aid the Investigation of Highway
Accidents”**, **Contract FH-11-7526,
December 1971, Calspan Report VJ-2979-V-1,NTIS PB# 208537

[24] McHenry, R.R.,"A
Computer Program for Reconstruction of Highway Accidents", SAE Paper
73-0980, Proceedings of the 17^{th} Stapp Car Conference, November 1973

[25] McHenry, R.R., **“Automotive
Crash Injury Research “Estimated Traveling Speed and Fatalities”**, Cornell
Aeronautical Laboratory Report No. VJ-2721-R1, Jan 1969

[26] McHenry, R.R., **“Tri-Level Accident Research Study”,**
Calspan Report No. ZM-5086-V-2, May 1973

[27]** ****“Analytical
Approach to Automobile Collisions”, **SAE paper 68-0016

[28] Mason, R.P., Whitcomb, D.W. , **“The
Estimation of Accident Impact Speed”, **Cornell Aeronautical Laboratory
Report No. YB-3109-V-1, August 1972

[29] Campbell, K.L., **“Energy Basis for Collision Severity”,** ** **SAE
paper 74-0565, 3rd International Conference on Occupant Protection, Troy,
Michigan, July 10-12, 1974.

[30] McHenry, R.R., **"Determination of Physical Criteria for Energy Conversion System**", Bureau of Public Roads, Program Review
Meeting of R&D of Traffic Systems,

[31]** **McHenry,
R.R.,**"Yielding-Barrier Test Data
Base - Refinement of Damage Data Tables in the Crash Program"**, Calspan Report No. ZR-5954-V-1, DOT-HS-5-01124December 1976.

[32] Smith, R.A, Noga, J.T. , **“Accuracy and Sensitivity of CRASH**”, SAE paper 82-1169.

[33] McHenry, R.R., J.P.Lynch, D.J.Segal.,**"Research Input for Computer
Simulation of Automobile Collisions"**,
Contract DOT-HS-7-01511, Calspan Corporation Report No. ZQ-6057-V-1,June
1977

[34] Monk, MW, Guenther, D., **“Update of CRASH2 Computer Model Damage
Tables”,** DOT-HS-806446, March 1983

[35] McHenry, R.R., **"User's
Manual for the Crash Computer Program, Part 2 - Final Report"**, Calspan
Report No. ZQ-5708-V-3, Contract No.
DOT-HS-5-01124, January 1976.

[36] McHenry,R.R, McHenry, B.G., **“A
Revised Damage Analysis Procedure for the CRASH Computer Program”, **SAE paper
86-1894, also in __SAE Transactions 1986__

[37] McHenry, R.R., **“A Computer Program for Reconstruction of Highway Accidents”,** Proceedings of the 17th Stapp Car Crash
Conference, SAE paper 73-0980,

[38] McHenry, R.R., **“The CRASH Program - A simplified Collision
Reconstruction Program”, **Proceedings of the Motor Vehicle Collision
Investigation Symposium, Calspan, 1975

[39] NHTSA, **“CRASH3 User’s Guide and Technical Manual”,** Revised Edition,
National Highway Traffic Safety Administration, DOT-HS-805732, April 1982.

[40]** **McHenry,
R.R., **"Analytical Reconstruction of
Highway Accidents Extensions and Refinements of the Crash Computer
Program"**, Calspan Report No. ZQ-5708-V-1, Contract No. DOT-HS-5-01124, January 1976.

[41] Warner, C.Y., Allsop, D.L.,
and Germane, G.J.,“A Repeated Crash Test Technique for Assessment of Structural
Impact Behavior”, SAE paper 860208

[42] Prasad, A.K., **“Energy dissipated in Vehicle Crush - A
study Using the Repeated Test Technique”, ** SAE paper 90-0412

[43] Prasad, A.K., **“CRASH3
Damage Algorithm Reformulation for Front and Rear Collisions”,** SAE paper
90-0098

[44] Prasad, A.K., **“Energy absorbing properties of vehicle
structures and their use in estimating impact severity in automobile
collisions”, ** IME paper 925209,
C389/421

[45] Prasad, A.K., **“CRASH3 Damage Model Reformulation”,** Report No. VRTC-87-0053, Vol. I & II,
November 1987

[46] Prasad, A.K., **“Energy
Absorbed by Vehicle Structure in Side-Impacts”, **TRC of

[47] Navin, F., MacNabb,
M., “**CRASH3 and Canadian Test Data**”, SAE Paper No. 870499, February
1987.

[48] Day, T.D., Hargens,
R.L., **“An Overview of the Way EDCRASH Computes Delta-V”,** SAE Paper 870045, February
1987.

[49] Day, T.D., Hargens, R.L., **“Vehicle Crush Stiffness Coefficients for
Model Years 1970-1984”,** EDC Library Reference No. 1043, August 1987.

[50] Strother, C.E., et al, **“Crush Energy in Accident Reconstruction”, **SAE
Paper 860371, February 1986.

[51] Struble, D.,**“Generalizing CRASH3 for Reconstructing
Specific Accidents”, **SAE paper
87-0041

[52] McHenry, R.R., McHenry,
B.G., **"A Revised Damage Analysis
Procedure for the CRASH Computer Program"**, SAE paper 861894, Proceedings of the 30th
Stapp Car Crash Conference, Society of Automotive Engineers Transactions, 1986

[53] McHenry, R.R., McHenry,
B.G.**“Effects of Restitution on the
Application of Crush Coefficients”**,
SAE Paper No. 970960

[54] Numbers in brackets [ ]
indicate references at end of paper

[55] Smith, R.A., Tsongos,
N.G., "**Crash Phase Accident Reconstruction**”, SAE paper 860209.

[56] Navin, R., MacNabb, M.,
Miyasaki, G., “**Elastic Properties of
Selected Vehicles**”, SAE paper
880223.

[57] Hight, P.V., Lent-Koop, D.B., Hight, R.A.,“**Barrier Equivalent Velocity, Delta V and
CRASH3 Stiffness in Automobile Collisions**”,
SAE paper 850437

[58] Antonetti, V.W., “**Estimated the Coefficient of Restitution**** of Vehicle-to-Vehicle Bumper
Impacts**”, SAE paper 980552.