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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 can
be obtained through the use of simple linear relationships between the
impact speed-change and the extent of residual crush (e.g., References
34, 50-52, 3). 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
46). In a more comprehensive evaluation (Reference
53), it was found that the 95 percent confidence limits on individual
calculations of delta-V ranged from 9 to 25 percent.
When a damaged vehicle is examined, the damage observed
is called the residual or permanent damage. This permanent damage observed
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 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 vehicle begins 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 an 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 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.
For a given amount of residual crush, the amount of restitution and the rate at which a vehicle restitutes can produce a range of variation of collision severity between different vehicles. The magnitudes of the increases in the total speed change (using the proposed CRASH4 damage analysis algorithm of Reference 26 and including a range of hypothetical restitution properties) over the impact speed-change for the approach period only (using the original CRASH3 algorithm with it's assumption of no restitution) were demonstrated in Reference 26 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.
In 1987, a proposed revision to the damage analysis procedure
for the CRASH computer Program was presented (Reference
26). In the paper it was noted that Smith and Noga (Reference
47) properly conclude that the damage algorithm of the CRASH computer
program tends to underestimate low delta-V values as a result of the neglect
of restitution effects. The original formulation of the CRASH3 program
(References 48, 49) only addressed the speed change
(Delta-V) 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
collision reconstruction program (Reference 1).
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 assumptions which included the neglect of restitution was
clearly pointed out in the original Crash documentation (References
To date (1995) there has been no significant 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 add to the predicted speed change
a variable of approximately +10% at 30 inches of residual crush
to +25% at 10 inches of residual crush for the predicted total
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 35, 36). The repeated test technique is based on the assumption that a vehicle deforms under repeated impacts in a manner similar to that for a single test at a higher speed involving the same absorbed impact energy. The technique was used as an economical method for obtaining several data 'points' for a given vehicle at a range of speeds. Among the possible sources of errors in the method are the effects of restitution (due to multiple tests being run on a vehicle at low speeds), velocity sensitivity of the structure, and the general changes to the structural properties due to repeated loadings.|
Papers authored by Prasad (References 36-40) as a part of the NHTSA investigation and refinement of collision reconstruction techniques 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 words "reformulation," "new algorithm" and "new model" overstate the actual contents of the crash reports and related research. The reports address three separate topics related to the CRASH algorithm:
The first two items have already been proposed or adopted by researchers and/or entrepreneurs in the field (e.g., References 41-45) and, therefore, they are not new concepts. The first item 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 36, p. 17, 2nd paragraph).
In the following paragraphs, the individual topics are addressed in greater detail:|
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 test on
which they are based) (Reference 36: p.20, paragraphs
3&4, p. 23, paragraph 4, p. 24, paragraph 1). References
43, 44, and 45 make that point in relation to the reconstruction of
"specific collisions" (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 US population.
In Reference 26 and 56 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 26 and 56 may be more applicable to the needs of NASS than the custom-fitting of individual crush properties.|
The reformulation proposed and used by Prasad was basically
to change the units of the Crush Coefficients from:
This brief review of the CRASH damage analysis algorithm and the NHTSA 'reformulation' by Prasad indicates that the 'reformulation' consists mainly of the addition of new crash test data points (which one might only consider 'new data') and the use of different symbols in the CRASH formulas. All the simplifying assumptions of CRASH are retained and no additional refinements have been introduced.
For additional information on the application of crush
coefficients in collision reconstruction, please also read our recent SAE
paper 97-0960 entitled "Effects of Restitution
in the Application of Crush Coefficients"
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