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Computerized Reconstruction of Accident Speeds on the Highway, EXtended uses conservation of momentum and energy to find initial speeds from initial headings and trajectories to rest. It is based
on the U S Department of Transportation's classic CRASH program of the
1970's, but with significant improvements in accuracy and versatility.
For purposes of comparison CRASHEX reverts on command to the original
assumptions of CRASH, yielding an alternate set of outputs based on
identical inputs.
While the speed of each of two vehicles
prior to impact is readily found -- even graphically -- by
conservation of momentum, given the speed of each upon separation and
all four directions, those pivotal speeds at separation are difficult to
evaluate for a vehicle which "spins," or travels more or less
sideways while yawing, with fluctuating deceleration. The problem is to
assign the yawing vehicle a rate of deceleration with reasonable accuracy. Rather than
to simply ignore this problem or rely on experience-based user
estimates, CRASH has a built-in base of experience in the form of
mathematical curve fits to a family of mathematically modeled spins. In
comparison with any momentum-based treatment which lacks such built-in
routines, CRASH (in its several embodiments) offers significantly better
accuracy of reconstruction in all but the simplest cases of travel to
rest.
In the early 80's, however, the not necessarily complete CRASH treatment was "frozen" by DOT for use only as an unchanging mass-data statistical yardstick with which to establish the efficacy of federal safety mandates. Nevertheless, being in the public domain, it is available from various sources and, in part due to its superior treatment of spin, is at least in the U S a mainstay of single-event accident reconstruction. For such purposes, any and all possible improvements in the treatment could and should be adopted.
Generally the inaccuracies of the older version do not make a critical difference; the unimproved treatment is often “good enough” as a basis
for a forensic opinion. But, how can the expert know when that is
true? At the very least, a final check of CRASH against CRASHEX is
needed to be sure that the more exact values -- which the opposing
expert might unexpectedly present -- do not alter alter the essence
of the opinion.
CRASHEX is also needed whenever the effects of
parameter mis-measurement on the reliability of the CRASH (or other)
result will be brought into question - - which will become increasingly
likely as awareness of this concept in general, and Daubert challenges
in particular, become more common.
While both CRASH and CRASHEX find the speeds of approach of two moving vehicles to impact (the V0's)
and the speed changes (the delta-V's) during impact both by momentum
(given site data) and by energy (given damage data), CRASHEX alone
- recites
the delta-V redundancy, the shear ratio, and the coefficient of
restitution -- as quality ratings which tell you whether the solution
is internally consistent and physically valid.
- includes the effects of tire forces acting during impact.
- These forces are included in CRASHEX just as they are in SMAC; and indeed by use of the same model of tire behavior.
While such differences may be small in instances of large travel to rest
after impact, tire force effects otherwise could swing the balance of
useful opinion.
- The expert might best then select CRASHEX as the preferred means of reconstruction.
- solves the case of obstacle impact. This is so whether the obstacle is a stationary vehicle or an immovable barrier.
The sole computerized alternative to time-reversed
momentum-and-energy-based treatment is a simulation, a time-forward
mathematical re-enactment using simple kinematics and good models of
tire response to operating conditions, such as that provided by SMAC,
from the same DOT source. This approach requires for its initiation a
hopefully good guess as to its initial state, or (as was the original
intent) a prior run of CRASH or the like. If in good agreement they
have confirmed each other. Due to the robustness of the kinematic and
tire models, such agreement is probably more significant than agreement
with error-prone observation of staged collisions.
CRASHEX in any event goes on to add a statistical treatment
of deviations of measurement not otherwise offered regardless of
treatment. Given a carefully chosen "best" solution, the user can enter
(from a look-up) the 5% likely (2 SD) error of measurement of every
input and find each individual effect on each output and the likely
total effect of all these component uncertainties. The result is the
"less than 1-in-40" likely high and likely low extremes of your
solution. The expert is then prepared to answer with confidence all
reasonable What-If questions about his or her opinion.
The utility of CRASHEX lies firstly in its more-accurate treatment of
both impact and post-impact travel, secondly in the insight gained
through a greater number of associated outputs, and thirdly in the
provision of Finite Difference Analysis for evaluation of the
statistical span of values about the mean approach speeds. Furthermore,
that numerical span is directly transferable from CRASHEX to CRASH or
SMAC or any other preferred basis of testimony, because the bell curve
expressing the distribution of values of each approach speed is a
function of the actual event and its investigation, not of the method
of reconstruction. Its span thus must be the same for all means of
reconstruction, even if it is centered on a somewhat different mean.
The same bell curve applies even to a simulation, which practically
speaking cannot be solved for that result.
CRASHEX executes so rapidly that the program's total run time of consists almost entirely of the user's input time at the keyboard plus the printer's output
printing time. CRASHEX thus can in a few hours of use add the “final
polish” to a reconstruction already developed over days and months of
investigation and analysis. This is why it is available on (and only
on) a short-term, low-cost, essentially time-share basis. The usage fee
can be charged to your client as an item of expense, no more per day
than you charge for an hour of your services. You list it for later
reimbursement when you bill for your services.
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