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AUTOMOBILE
COLLISION
RECONSTRUCTION:
A LITERATURE
SURVEY
BARRY
D. OLSON
CRAIG
C.
SMITH
RESEARCH
REPORT
63
FEBRUARY
1979
TEXAS
OFFICE
OF
TRAFFIC
SAFETY
RESEARCH
REPORTS
PUBLISHED
BY
THE
COUNCil
FOR
ADVANCED
TRANSPORTATION
STUDIES
1
An
Integrated
Methodology
for
Estimating
Demand
for
Essential Services
with
an
Application
to
Hospital
Care. Ronald Briggs, Wayne
T.
Enders,
James
A. Fitzsimmons, and Paul Jenson,
April
1975
(DOT·TST-75·81).
2
Transportation
Impact
Studies: A ReView
with
Emphasis
on
Rural Areas. Udvard Skorpa, Richard
Dodge,
C.
Michael
Walton,
and John
Huddleston
,October
1974
(DOT-TST-75-59).
4
Inventory
of
Freight
Transportation
in
the
SouthwestlPart
I:
Major
Users
of
Transportation
in
the
Dallas·Fort Worth Area. Eugene Robinson,
December
1973
(DOT-TST-75-29).
5
Inventory
of
Freight
Transportation
in
the
Southwest/Part
1/:
Motor
Common
Carrier Service
in
the
Dallas-Fort Worth Area.
J.
Bryan Adair and
James
S.
Wilson,
December
1973
(DOT-T5T·75-30).
&
Inventory
of
freight
Transportation
in
the
SouthweSt/Part
III:
Air
Freight Service
in
the
Dallas-Fort Worth Area. I. Bryan
Adair,
June
1974
(DOT-
T5T-75-31l.
7
Political
Decision
Processes, Transportation
Investment
and
Changes
in
Urban
Land
Use: A Selective
Bibliography
with
Particular Reference
to
Airports
and
Highways.
William
D.
Chipman,
Harry
P.
Wolfe,
and
Pat
Burnett,
March
1974
(DOT-T5T-75·28l.
9
Dissemination
of
Information
to
Increase Use
of
Austin
Mass Transit: A
Preliminary
Study.
Gene
Burd,
October
1973.
10 The
University
of
Texas
at
Austin:
A Campus
Transportation
Survey. Sandra Rosenbloom,
Jane
Sentilles Greig, and
lawrence
Sullivan Ross,
August
1973.
11
Carpool
and
Bus
Matching
Programs
for
The
University
of
Texas at
Austin.
Sandra Rosenbloom and Nancy
J.
Shelton,
September
1974.
12
A
Pavement
Design
and
Management
System
for
forest
Service
Roads-A
Conceptual
Study. Final
Report-Phase
I. Thomas G. McGarragh
and
W.
R.
Hudson,
July
1974.
13
Measurement
of
Roadway Roughness
and
Automobile
Ride
Acceleration
Spectra.
Anthony
J.
Healey and
R.
O.
Stearman,
luly
1'974
(DOT-TST·
75-140).
14
DynamiC
Modelling
for
Automobile
Acceleration
Response
and
Ride
Quality
over
Rough
Roadways.
Anthony
J.
Healey, Craig
C.
Smith, Ronald
O.
Stearman, and Edward Nathman,
December
1974
(DOT-TST-75-141).
15
Survey
of
Ground
Transportation Patterns at
the
Dallasifort
Worth
Regional
Airport,Part
I:
Description
of
Study.
William
J.
Dunlay,
Jr"
Thomas
G. Caffery,
lyndon
Henry,
and Douglas
W.Wiersig,
August
1975
(DOT-T5T·7&-78).
16
The
PrediLtion
of
Passenger
Riding
Comfort
from
Acceleration
Data. Craig C. Smith, David
Y.
McGehee,
and
Anthony
J.
Healey, March 1976.
17 The
Transportation
Problems
of
the
Mentally
Retarded. Shane Davies and John W. Carley, December
1974.
18
Transportation·Related
Constructs
of
Activity
Spaces
of
Small
Town
Residents.
Pat
Burnett,
John Betak, David Chang, Wayne Enders, and
Jose
Montemayor,
December
1974
(DOT·T5T-75-135).
19
The
Marketing
of
Public
Transportation:
Method
and
Application.
Mark
Alpert
and Shane Davies, January (DOT-T5T.75·142).
20
The Problems
of
Implementing
a
911
Emergency
Telephone
Number
System
in
a Rural Region. Ronald T.
Matthews,
February
1975.
23
Forecast
of
Truckload
freight
of
Class I
Motor
Carriers
of
Property
in
the
Southwestern
Region
to
1990.
Mary
lee
Gorse, March
1975
(DOT-
lST·
75-138).
24
forecast
of
Revenue Freight Carried
by
Rail
in
Texas
to
1990. David
l.
Williams,
April
1975
(DOl·TST-75-139).
28
Pupil
Transportation
in
Texas. Ronald Briggs, Kelly
Hamby,
and David
Venhuizen,
July
1975.
30
Passenger Response
to
Random
Vibration
in
Transportation
Vehicles-Literature
Review. A.
J.
Healey, June
1975
(DOT·TST-75-143).
35
Perceived
Environmental
Utility
Under
Alternative
Transportation
Systems: A
Framework
for
Analysis.
Pat
Burnett,
March
1976.
36
Monitoring
the
Effects
of
the
Dallas/Fort
Worth Regional
Airport,
Volume
I:
Ground
Transportation Impacts.
William
J.
Dunlay, Jr.,
lyndon
Henry,
Thomas G. Caffery, Douglas
W.
Wiersig,
and
Waldo
A. Zambrano,
December
197&.
37
Monitoring
the
Effects
of
the
Dallasifort
Worth Regional
Airport.
Volume
II:
Land
Use
and
Travel Behavior.
Pat
Burnett,
David Chang, Carl
Gregory,
Arthur
Friedman,
Jose
Montemayor,
and Donna Prestwood, July
1976.
38
The
Influence
on
Rural
Communities
of
Interurban
Transportation
Systems,
Volume
II:
TransportatIOn
and
Community
Development:
A
Manual
for
Small
Communities.
C.
Michael
Walton,
John
Huddleston,
Richard
Dodge,
Charles Heimsath, Ron
linehan,
and John Betak, August
1977.
39
An
Evaluation
of
Promotional
Tactics
and
Utility
Measurement
Methods
for
Public
Transportation Systems.
Mark
Alpert,
linda
Golden,
lohn
Betak,
James
Story, and C. Shane Davies,
March
1977.
40
A Survey
of
Longitudinal
Acceleration
Comfort
Studies
in
Ground
Transportation
Vehicles.
l. l.
Hoberock,
July
1976.
41
A Lateral Steering Dynamics
Model
for
the
Dallas/fort
Worth AIRTRANS. Craig
C.
Smith and Steven
lsao,
December
1976.
42
Guideway
Sidewall
Roughness
and
Guidewheel
Spring
Compressions
of
the
Dallas/Fort Worth AIRTRANS.
William
R.
Murray
and Craig C.
Smith,
August
1976.
43
A Pavement
Design
and
Management
System
for
Forest Service
Roads-A
Working
Model.
Final
Report-Phase
II.
Freddy
l.
Roberts,
B.
Frank
McCullough,
Hugh
J.
Williamson,
and
William
R.
Wallin,
February
1977.
44
A
Tandem-Queue
Algorithm
for
Evaluating
Overall
Airport
Capacity.
Chang-Ho
Park and
William
J.
Dunlay, Jr., February 1977.
45
Characteristics
of
Local Passenger Transportation Providers
in
Texas. Ronald Briggs, January
1977.
46 The
Influence
on
Rural
CommUnities
of
Interurban
Transportation
Systems.
Volume
I: The
Influence
on
Rural
Communities
of
Interurban
Transportation
Systems. C.Michael
Walton,
Richard
Dodge,
John
Huddleston,
John Betak, Ron
linehan,
and Charles Heimsath,
August
1977.
47 Effects
of
Visual
Distraction
on
Reaction
Time
in
a
Simulated
Traffic
Environment.
C.
Josh
Holahan,
March
1977.
48
Personality Factors
in
Accident
Causation. Deborah Valentine,
Martha
Williams,
and Robert
K.
Young,
March
1977.
49
Alcohol
and
Accidents.
Robert
K.
Young,
Deborah
Valentine.
and
Martha
S.
Williams,
March
1977.
50
Alcohol
Countermeasures.
Gary D. Hales, Martha
S.
Williams,
and Robert
K.
Young, July
1977.
51
Drugs
and
Their
Effect
on
Driving
Performance.
Deborah
Valentine,
Martha
S.
Williams,
and Robert
K.
Young,
May
1977.
52
Seat Belts: Safety
Ignored.
Gary D. Hales, Robert
K.
Young, and Martha
S.
Williams,
June 1978.
53
Age-Related
Factors
in
Driving
Safety. Deborah Valentine, Martha
Williams,
and Robert
K.
Young, February
1978.
54
Relationship
Between
Roadside Signs
and
Traffic
Accidents:
A
field
Investigation.
Charles
J.
Holahan,
November
1977.
5S
Demographic
Variables
and
ACCidents. Deborah
Valentine,
Martha
Williams,
and Robert
K.
Young, January
1978.
56
Feasibility
of
Multidisciplinary
Accident
Investigation
in
Texas.
Hall.
Fitzpatrick, Craig
C.
Smith, and
Walter
S.
Reed,
September
1977.
57
Modeling
the
Airport
Terminal
Building
for
Capacity Evaluation
Under
Level-of-Service Criteria. Nicolau
D.
Fares
Gualda and
B.
F.
McCul·
lough,
forthcoming
1979.
58
An
AnalySiS
of
Passenger Processing Characteristics
in
Airport
Terminal
Buildings.
Tommy
Ray
Chmores
and
B.
F.
McCullough,
forthcoming
1979.
59
A User's
Manual
for
the
ACAP
Model
for
Airport
Terminal
Building
Capacity Analvsis. Edward V. Chambers
III,
B.
F.
McCullough,
and Randy
B.
Machemehl,
forthcoming
1979.
60
A
Pavement
Design
and
Management
System
for
Forest Service
Roads-Implementation.
Final
Report-Phase
III.
B.
Frank
McCullough
and
David
R.
luhr,
January 1979.
61
Multidisciplinary
Accident
Investigation.
Deborah
Valentine,
Gary D. Hales, Martha
S.
Williams,
and Rouert K.Young,
October
1978.
&2
Psychological
Analysis
of
Degree
of
Safety
in
Traffic
Environment
DeSign. Charles
J.
Holahan, February
1979.
&3
Automobile
Collision
Reconstruction:
A Literature Survey. Barry D.
Olson
and Craig
C.
Smith,
forthcoming
1979.
b4
An
Evaluation
of
the
Utilization
of
Psychological
Knowledge
Concerning
Potential
Roadside Dis tractors. Charles
J.
Holahan,
forthcoming
1979.
AUTOMOBILE
COLLISION
RECONSTRUCTION:
A
LITERATURE
SURVEY
Barry
D.
Olson
Craig
C.
Smith
Research
Report
63
February
1979
Prepared
by
Council
for
Advanced
Transportation
Studies
The
University
of
Texas
at
Austin
Austin,
Texas
78712
For
Texas
Office
of
Traffic
Safety
State
Department
of
Highways
and
Public
Transportation
Austin,
Texas
This
report
was
developed
by
the
Council
for
Advanced
Transportation
Studies
in
cooperation
with
the
Texas
Office
of
Traffic
Safety
in
the
interest
of
information
exchange.
The
University
of
Texas
at
Austin
and
the
Texas
State
Department
of
Highways
and
Public
Transportation
assume no
liability
for
its
use.
ii
1
...........
2.
•
ce"
••
I_No.
3.
R"ci"i_".
C
......
Mo
.
4.
Titl
....
SooIotitl.
S. R
__
, D"
••
February
1979
AUTOMOBILE
COL~ISION
RECONSTRUCTION:
6.
P
..........
O,
...
in,i_
eo.-
A
LITERATURE
SURVEY
I.
P
......
h
••
0.,,-:0";"
.......
N..
1
.....
...,.,
Barry
D.
Olson
and
Craig
C.
Smith
RR
63
9
..........
0...,1
......
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....
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......
10. •
...
Unit No. (TRAIS)
Council
for
Advanced
Transportation
Studies
The
University
of
Texas
at
Austin
11.
Con".",
..
,
G,_.
N ...
Austin,
Texas
78712
(77)
72-00-02
B
13.
T}'Ptt.'
A_'
....
Period
Co
••
,.d
12.
s.-_I
..
.....-,"_
....
,....,.
••
Texas
Office
of
Traffic
Safety
Research
Report
State
Department
of
Highways
and
Public
14. s,......ori
...
A,.nc,
eo.-
Transportation
Austin,
Texas
15. s....a-,.-y
No
...
.....
......
_.
A
great
number
of
papers
have
been
written
dealing
with
the
characteristics
of
automobile
collisions.
In
this
report,
the
principal
research
methods
which
are
used
are
reviewed
and
the
major
papers
dealing
with
each
method
are
surveyed.
Computer
techniques
which
have
been
developed
within
the
past
few
years
are
reviewed,
and
their
utility
and
limitations
are
discussed.
A
modular
approach,
in
which
individual
computer
modules
are
used
interactively
by
an
investigator
to
reconstruct
an
accident
in
separate
phases,
is
suggested
•
.
17.
It"'
.....
II.
Dlolri"tieoo
s_
Motor
Vehicle
Accidents,
Traffic
This
document
is
available
through
the
Safety,
Accident
Reconstruction,
Council
for
Advanced
Transportation
Automobile
Accident
Simulation,
Studies,
The
University
of
Texas
as
Computer
Reconstruction
of
Austin,
Austin,
Texas
78712.
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METRIC
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Of
EXECUTIVE
SUMMARY
I.
INTRODUCTION
Losses
suffered
by
the
American
public
from
automobile
accidents
have
been
a
growing
problem
for
the
last
fifty
years.
To
take
effective
action
to
reduce
such
losses,
traffic
safety
officials
need
good
information
about
these
accidents
and
their
causes.
Automobile
accident
reconstruction
can
potentially
provide
reliable
information
which
can
be
useful
in
the
admin-
istration
of
justice
for
individual
accident
cases
and
for
effecting
highway
legislation
or
automobile/highway
design
decisions
when
information
from
a
variety
of
accidents
is
taken
together.
A
great
number
of
papers
dealing
with
automobile
collisions
have
appeared
in
the
literature.
It
is
the
purpose
of
this
report
to
review
the
primary
reconstruction
techniques
described
in
the
literature
and
to
review
the
principal
papers
associated
with
the
methods.
II.
RECONSTRUCTION
METHODS
Because
of
the
great
variability
in
type
and
nature
of
automobile
collisions,
the
methods
of
reconstruction
also
vary.
One
approach
to
the
categorization
of
these
methods
is
according
to
the
physical
laws
or
mechanical
principles
upon
which
they
are
based.
The two
basic
principles
used
are
the
principle
of
impulse
and
momentum
and
the
principle
of
work
and
energy.
For
any
particular
accident
or
phase
of
an
accident,
the
principles
which
are
most
appropriately
applied
depend
upon
what
is
best
known
about
the
forces
acting
on
each
vehicle
through
each
accident
phase.
Because
some
principles
are
typically
more
appropriate
during
one
phase
than
another,
the
principles
are
discussed
relative
to
impact
and
trajectory
phases.
More
detailed
examination
of
any
phase
of
an
accident
is
possible
using
a
digital
computer
simulation,
and
simulation
techniques
have
there-
fore
been
developed
by
various
sources
during
the
past
few
years.
The
most
prominent
simulation
techniques
are
therefore
described
and
evaluated,
including
some
discussion
of
the
computer
programs
SMAC
and
CRASH,
which
v
were
developed
under
contract
to
the
National
Highway
Traffic
Safety
Administration.
In
general,
there
is
a
lack
of
computational
efficiency
in
these
programs
because
of
the
program
generality
required
to
simulate
a
large
variety
of
accidents.
III.
PRINCIPAL
CONCLUSIONS
AND
RECOMMENDATIONS
A
variety
of
automobile
accident
reconstruction
methods
are
presently
available.
Because
of
the
variability
among
accidents,
the
selection
of
the
reconstruction
principles
to
be
applied
in
analyzing
a
given
accident
should
be
on
the
basis
of
the
data
available
for
that
accident.
It
is
suggested
that,
to
facilitate
this,
a
computer
reconstruction
system
should
be
developed
in
modular
form.
Individual
program
modules
could
then
be
selected
based
upon
the
data
available,
and
thus
the
reconstruction
program
could
be
tailored
to
the
specific
reconstruction
problem
needs.
vi
TABLE
OF
CONTENTS
AUTOMOBILE
COLLISION
RECONSTRUCTION:
A
LITERATURE
SURVEY
I.
INTRODUCTION....
. .
II.
MECHANICAL
PRINCIPLES
A.
Impact
Phase:
Principle
of
Impulse
and
Momentum
• . . . .
B.
Impact
Phase:
Conservation
of
Mechanical
Energy
. . . . .
C.
Trajectory
Phases:
Conservation
of
Mechanical
Energy
. • • .
III.
SIMULATION
TECHNIQUES
IV.
CRITIQUE:
APPLICATION
OF
COMPUTER
SIMULATION
V.
SUMMARY
BIBLIOGRAPHY
ABOUT
THE
AUTHORS
.
vii
1
3
3
6
8
9
13
16
17
19
AUTOMOBILE
COLLISION
RECONSTRUCTION
A
LITERATURE
SURVEY
I.
INTRODUCTION
A
great
number
of
papers
dealing
with
the
characteristics
of
automobile
collisions
have
appeared
in
the
literature.
The
overall
motivation
for
pursuing
the
study
of
automobile
collisions
is
to
improve
the
safety
of
automobile
travel
through
a
better
understanding
of
the
predominant
characteristics
which
lead
to
accidents
and
influence
injury
severity.
Quantification
of
conditions
of
accidents
and
of
vehicle
and
occupant
behavior
has
led
to
many
improvements
in
the
design
of
vehicles
and
roadways,
as
well
as
being
an
aid
to
our
legal
system
in
administering
justice.
Simulation
of
vehicle
collisions
has
played
an
important
role
in
this
progress.
Yet,
substantial
potential
for
further
improvement
exists.
A
discussion
of
the
factors
affecting
occupant
injury
in
automobile
collisions
is
presented
by
Marquardt.
l
Marquardt
has
organized
these
factors
into
groups
of
vehicle-related
factors
~hose
relating
to
the
collision
external
to
the
occupant
compartment)
and
occupant-related
factors
(those
which
relate
to
occupant
compartment
interactions).
The
analysis
presented
shows
that
the
actual
injury
incurred
is
determined
by
occupant-related
factors
for
a
given
Peak
Contact
Velocity
(PCV).
Peak
Contact
Velocity
is
defined
as
the
maximum
relative
velocity
with
which
the
occupant
will
contact
the
vehicle
interior.
The
PCV
is
essentially
the
velocity
change
of
the
vehicle
during
the
crushing
phase,
when
the
vehicles
are
brought
from
their
original
velocities
to
a
common
velocity
in
the
forward
phase
of
impact.
Consequently,
the
determination
of
velocity
changes
in
vehicle
accidents
is
an
important
step
in
quantifying
injury
severity
potential.
The
actual
injury
is
a
function
of
many
occupant-related
factors,and
Marquardt
has
concluded
that
a
statistically
valid
sample
of
the
random
occupant
variables
is
necessary
for
drawing
conclusions
about
the
correlation
of
injuries
to
accident
conditions.
IJ.F.
Marquardt,
"Vehicle
and
Occupant
Factors
that
Determine
Occupant
Injury,"
SAE
paper
740303
(1974).
I
Although
accidents
staged
with
test
dummies
present
a method
for
generating
statistical
data,
a much
larger
number
of
accidents
exists
in
the
field.
With
the
development
of
simulation
techniques
applicable
to
the
reconstruction
of
field
accidents,
the
first
step
towards
tapping
this
data
has
been
made. The
National
Highway
Traffic
Safety
Administration
is
now
sponsoring
a
National
Crash
Severity
Study
to
obtain
the
first
statistical
data
using
a
computer
simulation
program
to
reconstruct
a
large
number
of
accidents
across
the
nation.
The
purpose
of
this
paper
is
to
present
a
survey
of
the
current
literature
available
with
respect
to
the
development
of
accident
simulation
techniques.
Before
dynamic
principles
and
simulation
techniques
are
discussed,
the
reader
is
referred
to
J.F.
Wilson's
article
"Two-Vehicle
Collision
Reconstruction:
A
Rational
Computer-Aided
Approach"
for
insight
into
2
the
reconstruction
problem.
For
the
two-vehicle
collision
model,
Wilson
presents
one
possible
set
of
system
parameters
(40
in
this
particular
case)
which
could
be
used
to
define
the
impact
and
post-impact
trajectory
phases
of
an
accident.
Depending
on
the
particular
accident,
the
available
evidence
(e.g.,
tracking
data
and
post-collision
inspections),
and
the
mechanical
principles
used
to
simulate
or
reconstruct
the
accident,
the
set
of
system
parameters
may
be
altered.
However,
Wilson's
classification
of
the
system
parameters
into
subsets
(most
certain,
less
certain,
least
certain,
and
definite
unknowns)
defines
a
logical
process
for
evaluating
parameters
for
any
given
accident.
As
indicated,
the
common
goal
of
simulations
is
generally
to
determine
initial
velocities
and
velocity
changes,
whether
the
motivation
is
an
interest
in
occupant
movement
and
injury
potential
studies,
legal
investigations,
or
other.
2
J.F.
Wilson,
"Two-Vehicle
Collision
Reconstruction:
A
Rational
Computer-
Aided
Approach,"
Vehicle
System
Dynamics 2
(1973).
2
II.
MECHANICAL
PRINCIPLES
The
reconstruction
of
vehicle
collisions
by
using
the
dynamic
principles
of
rigid
bodies
is
certainly
nothing
new.
With
the
introduction
of
the
digital
computer
the
capability
to
substantially
increase
the
complexity
of
the
reconstruction
existed
and
it
has
been
exercised.
However,
regardless
of
the
complexity
introduced,
a
basic
understanding
of
the
principles
of
impulse-
momentum
and
conservation
of
mechanical
energy
with
applicable
assumptions
is
needed.
Although
there
are
different
approaches
for
analyzing
a
collision,
in
general,
vehicle
collision
reconstruction
is
separated
into
distinct
phases
of
impact
and
pre-
and
post-collision
trajectory.
Consequently,
the
principles
as
applied
to
the
individual
phases
will
be
discussed
separately.
Note
should
be
made
that,
with
the
division
of
the
analysis
into
separate
phases
(events)
as
presented
here,
the
impact
phase
is
modeled
assuming
that
tire
forces
are
negligible
during
that
phase.
Although
this
assumption
is
3
reasonable
for
most
collisions,
as
noted
by
Grime
and
Jones
and
by McHenry,
McHenry
indicates
that
significant
errors
have
resulted
for
moderate-speed
intersection
collisions
in
which
multiple
contacts
occur.
A.
Impact
Phase:
Principle
of
Impulse
and
Momentu~
Most
introductory
dynamics
texts
present
a
discussion
of
the
appli-
cation
of
the
principle
of
impulse-momentum
(conservation
of
momentum)
to
the
basic
impact
problem.
Beer
and
Johnston
present
introductory
dis-
cussions
for
both
central
and
eccentric
impact.
4
A more
complete
yet
fundamental
treatment
of
the
principle
of
impulse-momentum
with
specific
reference
to
vehicle
collision
impact
can
be
found
in
Reizes.
5
More
detailed
presentations
of
the
principle
applied
to
the
impact
problem
can
be
found
in
3
G.
Grime
and
1.
S.
Jones,
"Car
Collisions--The
Movement
of
Cars
and
Their
Occupants
in
Accidents,"
Proceedings
of
Institute
of
Mechanical
Engineering
184
(1969-70);
R.R.
McHenry~
"Computer
Program
for
Reconstruction
of
Highway
Accidents,"
SAE
paper
730980
(1973).
4
F
•P•
Beer
and
E.R.
Johnston,
Jr.,
Vector
Mechanics
for
Engineers:
Dynamics 2nd
ed.
(New
York:
McGraw-Hill,
1972).
5
H
•
Reizes,
The
Mechanics
of
Vehicle
Collisions
(Springfield,
IL:
Charles
C. Thomas,
1973).
3
Emori
and
in
Goldsmith.
6
Several
assumptions
are
made
in
the
application
of
the
principles
of
rigid
bodies
to
vehicle
collisions.
In
traffic
accidents
the
bodies
(vehicles)
undergo
elastic
and
plastic
deformations.
Although
the
centers
of
gravity
of
the
bodies
are
affected,
the
locations
of
the
centers
of
gravity
do
not
change
radically
during
the
impact
phase
and,
therefore,
are
assumed
to
be
constant.
The mass moments
of
inertia
of
the
vehicles
are
also
assumed
to
be
constant
during
and
following
deformation.
Due
to
the
substantial
crushing
involved
in
severe
collisions,
portions
of
the
body
structure
(e.g.,
the
occupant
compartment)
take
an
appreciable,
though
still
short,
time
to
reach
a
common
velocity.
Consequently,
portions
of
the
body
structure
or
mass
may
undergo
a
change
in
velocity
before
the
rest
of
the
vehicle.
This
effect
is
not
modeled
in
detail
and
all
of
the
mass
of
the
vehicle
is
assumed
to
have
the
same
velocity
at
all
times.
In
current
simulations
only
two-dimensional
vehicle
motion
has
been
included.
Although
pitching
and
rolling
are
present
in
essentially
IIplanar"
accidents,
their
effects
are
typically
small
and
are,
therefore,
neglected.
The
influence
of
the
preceding
assumptions
are
considered
7
by Grime
and
Jones.
The
impact
phase
of
a
collision
can
be
further
broken
down
into
periods
or
subphases.
Immediately
following
a
collision,
the
relative
velocities
of
two
masses
will
tend
to
be
equalized
as
the
masses
continue
along
their
initial
trajectories
interacting
by
impulsive
forces.
Once a
common
velocity
is
reached,
the
forward
impact,
or
period
of
deformation,
of
the
collision
terminates.
At
this
instant,
reaction
forces
acting
to
separate
the
masses
are
present
if
at
least
one
of
the
masses
is
elastic
to
some
degree.
This
period
of
the
impact
is
commonly
called
the
period
of
restitution,
or
rebound.
It
ends
when
the
reaction
force
reduces
to
zero
at
vehicle
separation.
6
R.I.
Emori,
"Vehicle
Mechanics
of
Intersection
Collision
Impact,"
SAE
paper
700177
(January
1970);
W.
Goldsmith,
Impact
(London: Edward
Arnold,
1960)
•
7 .
Grl.me and
Jones,
"Car
Collisions."
4
The
ratio
of
the
forces
acting
during
the
period
of
restitution
to
those
during
the
period
of
deformation
is
called
the
coefficient
of
resti-
tution.
This
ratio
may
also
be
viewed
as
that
of
the
momentum
transfer
at
rebound
to
the
momentum
transfer
during
crush.
The
coefficient
of
resti-
tution
varies
between
zero,
for
a
perfectly
plastic
collision,and
one,
for
a
perfectly
elastic
collision.
The
principle
of
conservation
of
momentum
is
valid
regardless
of
the
value
of
the
coefficient
of
restitution.
In
general,
total
mechanical
energy
is
not
conserved
in
impact
problems
except
where
the
impact
is
perfectly
elastic.
Therefore,
the
coefficient
of
resti-
tution
serves
as
a
measure
of
energy
loss
as
previously
noted.
In
application
to
vehicle
collisions.
the
coefficient
of
restitution
tends
to
be
small.
depicting
the
almost
inelastic
behavior
of
crushing
automobiles.
The
coefficient
of
restitution
is
typically
on
the
order
of
0.05
to
0.1
for
symmetric
head-on
collisions
of
two
automobiles.
8
Consequently,
it
is
common
to
assume
perfectly
plastic
collisions
which
result
in
a
common
velocity
after
impact.
Confirmation
of
the
assumption
of
small
coefficients
of
restitution
is
given
by
Marquardt.
who
has
determined
that
a
change
of
the
coefficient
from
0.0
to
0.1
would
change
the
amount
of
energy
absorbed
9
by
only
one
percent.
Given
ample
evidence,
the
assumption
of
an
a
priori
coefficient
of
restitution
is
not
required,
and
it
is
possible
to
calculate
the
coefficient.
This
calculation
also
provides
a
subjective
check
on
the
accuracy
of
the
interpretation
of
the
available
evidence.
The
validity
of
the
assumption
of
a
perfectly
plastic
collision
may
be
subjectively
evaluated
by
considering
the
final
relative
positions
of
the
vehicles
involved.
lO
Caution
must
be
taken
in
considering
the
final
distance
between
two
vehicles
as
representative
of
the
degree
of
elastic
behavior
because
many
variables
which
enter
into
the
post-trajectory
phase
of
a
collision
affect
final
rest
positions.
8
Ibid
.
9
Marquardt,
ttVehicle
and
Occupant
Factors.
tt
10R.M.
Brach,
"An
Impact
Moment
Coefficient
for
Vehicle
Collision
Analysis,"
SAE
paper
770014
(February
1977).
5
Another
treatment
of
the
impact
phase
of
a
vehicle
collision
concentrating
on
an
approach
using
the
equations
of
impulse
and
momentum
is
presented
by
Brach.
II
Due
to
the
inability
to
exactly
locate
the
point
of
application
of
the
resultant
force
impulses
in
vehicle
collisions,
Brach
contends
that
the
resultant
of
the
total
surface
contact
forces
should
consist
of
both
force
and
moment
impulses
to
accurately
formulate
the
equations
of
impact.
For
a
physical
interpretation,
the
moment
can
be
considered
to
be
generated
by
the
mechanical
interlocking
of
parts
of
the
deforming
vehicles.
In
including
moment
impulse
in
the
formulation,
an
impulse
moment
coefficient,
similar
to
the
coefficient
of
restitution,
is
introduce~corresponding
to
angular
velocities.
The moment
coefficient
ranges
between
negative
and
positive
one.
At
negative
one
the
angular
impact
is
elastic,
at
zero
the
vehicles
have
zero
relative
angular
velocity
following
impact,
and
at
positive
one
no moment
is
transmitted
at
impact
relating
to
the
direct
central
impact
problem.
Brach's
paper
is
the
only
known
source
to
consider
surface
moment
impulse
in
the
context
of
vehicle
collisions.
Because
little
work
has
been
done
with
this
concept,
it
would
be
difficult
to
establish
a
priori
values
for
the
moment
coefficient
in
vehicle
collision
analysis.
When
ample
collision
evidence
is
known,the
moment
coefficient
can
be
treated
as
an
unknown
and
the
analysis
accuracy
can
be
improved.
Brach
presents
one
example
in
which
the
moment
coefficient
was
treated
as
an
unknown
and
calculated
to
equal
0.70.
There1atively
high
moment
coefficient
value,
approaching
the
direct
central
impact
value,
as
well
as
the
accuracy
of
collision
analysis
by
others
in
which
the
moment
impulse
is
ignored,
would
lead
one
to
question
the
need
for
this
approach
and
the
additional
complexity
it
introduces.
However,
the
theory
offers
improved
accuracy
and
additional
work
in
this
area
appears
warranted.
B.
Impact
Phase:
Conservation
of
Mechanical
Energy
Another
approach
to
the
analysis
of
the
impact
phase
of
vehicle
collisions
6
is
to
use
the
principle
of
conservation
of
mechanical
energy.
The summation
of
the
initial
kinetic
energies
before
impact
and
the
energy
absorbed
(negative)
by
plastic
deformation
during
the
period
of
deformation,
for
the
vehicles
involved,
must
equal
the
summation
of
the
kinetic
energies
of
the
vehicles
at
the
instant
the
period
of
restitution
ends.
To
use
this
balance
of
mechanical
energy
to
reconstruct
vehicle
collisions,
a method
for
determining
deformation
energy
terms
from
post-collision
crush
12
profiles
is
needed.
Wilson
uses
vehicle-to-vehicle
crush
data,
showing
that
the
mean
vehicle
crush
deformation
is
linearly
correlated
to
vehicle
impact
speed,
to
calculate
the
plastic
work.
13
An
identical
linear
correlation
based
on
barrier
test
data
for
frontal
impact
is
presented
by
Campbell
to
calculate
what
he
refers
to
as
an
Equivalent
Barrier
Speed (EBS)
for
estimation
of
the
energy
absorbed
by
plastic
deformation.
14
Equivalent
Barrier
Speed
is
commonly
defined
as
the
speed
at
which
equivalent
vehicle
damage
(based
on
equivalent
energy
absorption)
is
produced
in
a
fixed
barrier
test
of
the
same
vehicle.
Campbell
tabulates
the
coefficients
of
the
linear
equation
and
the
standard
weight
at
which
these
coefficients
were
determined
for
four
classifi-
cations
of
vehicles.
A
linear
force-deflection
model
which
reproduces
the
barrier
test
linear
relationship
using
the
same
coefficients
is
also
developed.
The
tabulated
data
are
valid
only
for
frontal
impact
due
to
the
limited
availability
of
additional
test
data;
however;
the
concept
is
valid
for
all
types
of
collisions.
Campbell
proposes
that
the
factors
involved
in
a
collision
could
be
used
to
classify
collisions
into
categories
where
EBS
formulations
valid
for
the
particular
categories
could
be
used.
To
arrive
at
the
additional
EBS
formulations,
test
programs
supplemented
by
accident
simu-
lations
are
needed.
l~.p.
Mason
and
D.W.
Whitcomb,
"The
Estimation
of
Accident
Impact
Speed,"
Cornell
Aeronautical
Laboratory
Report
No.
YB-3l09-V-l
(August
1972).
l3Wilson,
"Two-Vehicle
Collision
Reconstruction."
l4
K.
L
.
Campbell,
"Energy
Basis
for
Collision
Severity,"
SAE
paper
740565
0-974).
7
C.
Trajectory
Phases:
Conservation
of
Mechanical
Energy
The
trajectory
phases
of
an
accident
can
be
reconstructed
on
the
basis
of
conservation
of
mechanical
energy.
Following
vehicle
separation
at
the
end
of
the
period
of
restitution
of
the
impact
phase,
the
kinetic
energy
levels
possessed
by
the
individual
vehicles
are
reduced
to
zero
by
frictional
work
between
the
vehicle
and
roadway.
Thus
the
summation
of
translational
and
rotational
kinetic
energy
following
impact
and
of
the
frictional
work
(always
negative
work)
during
the
post-collision
trajectory
must
equal
zero.
Brief
presenta-
tions
of
the
principle
and
a means
of
calculating
the
total
frictional
work
can
be
found
in
Emori and
Taui
and
in
Wilson.
l5
McHenry
presents
another
discussion
of
post-impact-trajectory
analysis
based
on
energy
dissipation
by
frictional
work
between
vehicle
separation
and
rest
positions~6
Although
this
presentation
is
not
a
unique
solution
based
on
the
theory,
more
detail
of
the
development
is
provided.
Steering
is
not
considered
in
a
detailed
sense,
and,
in
the
initial
development,
a
piecewise
linear
idealization
of
the
linear
and
angular
velocity
time
histories
is
assumed
with
abrupt
changes
in
deceleration
rates
between
linear
and
angular
motion.
In
other
words,
when
the
vehicle
slides
laterally,
the
angular
velocity
is
assumed
constant
while
the
linear
velocity
is
decelerated,
and
the
opposite
is
assumed when
the
direction
of
linear
velocity
is
aligned
with
the
longitudinal
axis
of
the
vehicle.
By
approximate
integrations
of
the
idealized
velocity
versus
time
plots
and
rigid
body
mechanics,
approximate
linear
and
angular
deceleration
times
are
found.
Assuming
the
linear
and
angular
phases
of
motion
end
at
approximately
the
same
time,
equations
relating
the
separation
velocities
to
displacements,
the
friction
coefficient,
and
vehicle
geometry
are
derived.
Although
this
initial
development
has
been
found
to
have
several
shortcomingQ,
it
is
a
fairly
complicated
approach
and
offers
an
alternative
method
for
trajectory
analysis.
This
general
approach
as
well
as
a method
based
on
integration
of
equations
of
motion
will
be
further
discussed
later
in
this
paper.
l5
R
.1.
Emori
and
M.
Taui,
"Vehicle
Trajectories
After
Intersection
Collision
Impact,1I
SAE
paper
700176
(January
1970);
and
Wilson,
"Two-Vehicle
Collision
Reconstruction."
l6
R. R• McHenry, "A
Comparison
of
Results
Obtained
with
Different
Analy-
tical
Techniques
for
Reconstruction
of
Highway
Accidents,"
SAE
paper
750893
(1975).
8
Note
that
although
the
discussion
has
been
focused
on
post-impact-
trajectory
analysis,
the
principles
can
as
easily
be
applied
to
pre-impact
trajectories
in
order
to
find
initial
velocities
prior
to
braking
or
skidding.
Typically,
pre-impact-trajectory
analysis
is
simplified
because
angular
velocities
are
negligible.
III.
SIMULATION
TECHNIQUES
In
this
section
a
discussion
of
several
simulation
techniques
combining
available
evidence
and
mechanical
principles
are
presented.
As
described
in
the
previous
section,
alternative
methods
for
developing
simulation
techniques
exist,
and
the
techniques
presented
in
the
following
discussion
will
reemphasize
this
fact.
However,
the
simulation
techniques
discussed
are
not
limited
to
the
general
approaches
previously
presented.
Vehicle
collisions
have
been
reconstructed
for
some
time
with
hand
calculations
by
using
the
dynamic
principles
of
rigid
bodies,
as
previously
discussed.
Given
accident
layouts
with
tire
tracks,
impact
point,
and
rest
positions,
an
investigator
can
estimate
accident
conditions.
The
velocity
of
each
vehicle
at
the
termination
of
the
period
of
restitution
can
be
aproximated
by
using
conservation
of
mechanical
energy
and
assuming
friction
factors.
With
further
assumptions
and
the
principle
of
impulse
and
momentum,
the
impact
phase
can
be
analyzed
to
approximate
inital
contact
velocities.
If
tire
tracks
indicate
braking
or
skidding
before
impact,
conservation
of
mechanical
energy
can
again
be
used
to
approximate
initial
velocities.
By
varying
the
assumed
values
in
the
calculations
(e.g.,
friction
coefficients),
a
sensitivity
study
can
be
made
and
for
most
accidents
a
reasonably
accurate
reconstruction
is
obtainable.
Reizes
reconstructs
several
vehicle
collisions
with
hand
calculations.
17
Wilson
outlines
two
individual
algorithms
applicable
to
the
estimation
of
initial
speeds
and
the
post-impact-trajectory
lengths
of
an
accident.
18
The
algorithms
are
not
designed
to
be
used
together
as
modules,
as
the
input
and
outputs
between
them
are
not
consistent.
17Reizes,
Mechanics
of
Vehicle
Collisions.
18Wilson,
"Two-Vehicle
Collision
Reconstruction."
9
The
first
algorithm
has
outputs
of
initial
velocities,
post-impact
linear
and
angular
velocities,
and
the
force
impulse.
The
algorithm
is
based
on
the
conservation
of
mechanical
energy
in
combination
with
the
impulse-
momentum
principle.
This
approach
is
different
from
those
discussed
previously
in
that
the
force
impulse
is
left
as
an
unknown
and
the
coefficient
of
resti-
tution
is
not
introduced.
A
numerical
example
of
an
oblique
impact
is
used
to
illustrate
the
algorithm.
Another
example
of
a
central
impact
is
also
presented;
however,
in
this
case
the
algorithm
as
previously
presented
was
not
implemented.
Instead
Wilson
uses
the
conservation
of
mechanical
energy
in
combination
with
the
conservation
of
linear
momentum
where
the
force
impulse
has
been
eliminated
as
a
variable.
The
assumption
of
a
coefficient
of
restitution
is
not
noted,
although
its
use
is
implicit
in
the
assumption
of
a
common
post-impact
velocity,
which
is
equivalent
to
assuming
a
coefficient
of
restitution
equal
to
zero.
The
second
algorithm
for
trajectory
estimation
uses
a
vector
equation
describing
the
locations
of
the
vehicles
in
combination
with
equations
used
in
the
first
algorithm
to
arrive
at
admissible
solutions.
In
this
case
the
definite
unknowns
are
the
post-impact-trajectory
lengths.
Initial
velocities
are
classified
as
least
certain
and
are
input
with
lower
and
upper
bounds.
Numerical
examples
for
the
second
algorithm
are
not
presented.
Cal
span
Corporation
appears
to
have
done
more
in
the
area
of
accident
reconstruction
by
computer
simulation
than
anyone
else.
19
It
is
Calspan's
CRASH
computer
program
which
is
being
used
in
the
National
Crash
Severity
Study
mentioned
in
the
introduction.
The
Calspan
Reconstruction
of
Accident
~eeds
on
the
~ighway
(CRASH)
program
is
actually
a
refinement
of
a
routine
(START)
used
to
generate
initial
approximations
for
a much more
detailed
simulation
program
called
SMAC
(limulation
~odel
for
Automobile
£ollisions).
I
19R.
R
• McHenry,
"Development
of
a Computer
Program
to
Aid
the
Investigation
of
Highway
Accidents,"
Cornell
Aeronautical
Laboratory
Report
No.
VJ-2979-V-l
(December
1971);
R.R.
McHenry
et
aI.,
"Mathematical
Reconstruction
of
Highway
Accidents,11
Interim
Technical
Report
No. DOT-HS-800
801,
prepared
by
Calspan
Corp.
for
DOT
(January
1973);
McHenry,
"Computer
Program
for
Reconstruction";
McHenry,
"Comparison
of
Results";
and
R.R. McHenry
and
J.P.
Lynch,
"CRASH-2
User's
Manual,"
Cornell
Aeronautical
Laboratory
Report
No. ZQ-5708-V-4
(September
1976).
10
The
SMAC
program
is
an
algorithm
which
predicts
a
time
history
response
and
corresponding
evidence
(i.e.,
rest
positions,
damage,
and
tire
marks
and
tracks)
when
initial
approximations
of
the
collision
conditions
are
input.
In
the
reconstruction
of
accidents,
successive
iterative
runs
are
performed
until
an
acceptable
match
with
real
accident
evidence
is
obtained.
In
general,
the
uniqueness
of
SMAC
is
in
its
generality
and
the
extent
of
analytical
detail.
Equations
based
on
the
fundamental
physical
laws
and
empirical
relationships
are
used
to
balance
the
applied
and
inertial
forces
and
moments
acting
on
vehicles
throughout
an
accident.
Empirical
laws
are
introduced
to
treat
collision
and
tire
forces
simultaneously.
The
analytical
assumptions
which
are
made
for
the
collision
force
aspect
of
the
impact
and
differ
substantially
from
those
previously
discussed
are
outlina:l
by
11cHenry:
1.
the
vehicles
are
treated
as
rigid
bodies,
each
surrounded
by
a
layer
of
isotropic,
homogeneous
material
exhibiting
elastic-plastic
behavior;
2.
the
dynamic
pressure
in
the
peripheral
layer
increases
linearly
with
the
depth
of
penetration
relative
to
the
initial
boundary
of
the
deflected
surface;
3.
the
adjustable,
nonlinear
coefficient
of
restitution
varies
as
a
function
of
maximum
deflection.
The
"friction
circle
ll
concept
for
introducing
tire
forces,
which
is
a method
of
limiting
tire
forces
to
those
obtainable
by
coulomb
friction,
is
also
out-
20
linedby
McHenry.
The SMAC-predicted
time
histories
of
vehicle
responses
during
impact
and
spinout
trajectories
are
generated
by
step-by-step
integration
of
con-
tinuous
equations
of
motion
over
the
time
interval
of
the
accident.
A
21
derivation
of
the
equations
implemented
in
SMAC
is
outlined
by McHenry.
A
simpler
presentation
of
equations
of
motion
applicable
to
vehicle
collisions
20
McHenry,
"Computer
Program
for
Reconstruction."
2~cHenry,
"Development
of
a Computer
Program."
11
is
outlined
in
Appendix 2
of
the
paper
by
Grime
and
Jones.
22
Although,
as
McHenry
shows,
SMAC
is
obviously
more complex
in
its
treatment
of
collision
and
tire
forces
than
the
presentation
in
Grime
and
Jones,
the
integration
of
equations
of
motion
to
generate
time
responses
should
be
readily
apparent
from
either
reference.
The
SMAC
program
has
been
found
to
yield
± 5
percent
accuracy
in
velocity
estimation
in
certain
test
cases.
23
However, a
sufficiently
detailed
definiton
of
the
accident
is
required
to
obtain
this
level
of
accuracy
and
to
take
advantage
of
the
benefits
provided
by
SMAC
predictions.
There
are
numerous
examples
in
the
literature
of
application
of
SMAC.
24
The
development
of
the
CRASH
program
was
prompted
by
a
need
to
reconstruct
accidents
where
a
detailed
definition
of
the
accident
was
lacking.
Although
the
range
of
accuracy
with
CRASH
is
decreased
to
about
±
12
percent,
a 75
percent
cost
savings
per
run
is
obtained
and
the
program
inputs
are
less
detailed.
These
factors
provide
for
a
broader
application
potential.
A
discussion
of
CRASH
and
comparative
25
results
from
CRASH
and
SMAC
is
presented
by
McHenry.
The
CRASH
program
contains
two
methods
of
analyzing
accident
evidence.
The
first
method
is
an
extension
of
the
trajectory
analysis,
based
on
energy
26
dissipation
by
frictional
work,
introduced
earlier
in
this
paper.
Appli-
cation
of
this
trajectory
analysis
to
SMAC-generatedspinout
trajectories
revealed
that
shortcomings
existed
due
to
assumptions
and
idealizations
in
the
original
derivation.
Modifications
were
introduced
to
avoid
the
assumption
that
linear
and
angular
motion
terminated
simultaneously,
the
errors
intro-
duced
in
the
integration
of
the
velocity
plots,
and
the
assumptions
that
22Grime
and
Jones,
"Car
Collisions."
23
McHenry,
"Comparison
of
Results."
24
M.E.
James,
Jr.,
and
H.E.
Ross,
Jr.,
"Improvement
of
Accident
Simulation
Model,"
Texas
A&M
Research
Foundation
Report
No.
RF-3258-1
(November
1976);
McHenry,
"Development
of
a Computer
Program";
McHenry
et
ai.,
"Mathematical
Reconstruction";
and
McHenry, "Computer
Program
for
Rec;)nstruction."
25
McHenry,
"Comparison
of
Results."
26
Ibid
•
12
deceleration
rates
between
linear
and
angular
motions
changed
abruptly.
Although
the
details
of
the
modifications
are
sketchy,
it
is
apparent
that
SMAC
was
implemented
to
generate
empirical
relationships
used
in
the
result-
ing
equations.
By
combining
this
trajectory
analysis
with
an
impact
phase
analysis
based
on
the
impulse-momentum
principle,
the
change
in
velocity
during
impact
and
initial
impact
velocities
are
obtained.
The
second
analysis
method
in
CRASH
is
an
extension
of
Campbell's
damage
analysis
technique.
27
The
linear
damage
analysis
is
based
on a
spring-
mass-dissipator
system
using
potential
energy
relationships
and
conservation
of
momentum
to
derive
expressions
for
velocity
changes
during
the
impact
phase
as
a
function
of
the
absorbed
energy
in
crushing
deformation.
The
absorbed
energy
calculation
is
based
on
Campbell's
work
in
which
gross
approximations
are
made
for
the
empirical
coefficients
for
side
and
rear
collisions.
The
computa-
tion
of
the
absorbed
energy
is
accomplished
by
integration
of
the
energy
equations
by
trapezoidal
approximations
where
coefficients
are
shown
in
tables.
The
impact
phase
velocity
changes
calculated
with
the
two
analysis
methods
contained
in
the
CRASH
program
are
comparable,
although
the
trajectory
analysis
must
be
used
in
both
cases
to
calculate
initial
impact
velocities.
IV.
CRITIQUE:
APPLICATION
OF
COMPUTER
SIMULATION
The
first
computer
program
to
be
used
on
a
large
scale
for
accident
reconstruction
was
Calspan's
SMAC
program.
As
previously
noted,
the
SMAC
program
was
designed
to
be
very
general,
thus
allowing
its
application
to
a
large
spectrum
of
accidents,
assuming
sufficient
detailed
evidence
existed.
The
generality,
however,
causes
several
problems.
First,
the
program
is
of
significant
size,
requiring
a
large
computer
for
storage
and
computation.
At
The
University
of
Texas
at
Austin,
where
the
program
has
been
used
to
reconstruct
field
accidents,
it
was
advantageous
to
store
SMAC
and
do
computation
on a
CDC
6600,
while
input
and
output
were
handled
with
a
PDP
11/40.
Calspan
used
27
Campbell,
"Energy
Basis
for
Collision
Severity."
13
"
...
___
-~'!l
__
_
a
similar
approach
to
handle
the
program
at
one
time,
as
described
by
McHenry
28
et
al.
Second,
it
is
likely
that
the
complexity
and
analytical
detail
incorporated
into
the
program
are
not
required
to
obtain
comparable
accuracy
for
certain
accidents.
The
second
point
is
especially
true
when
detailed
evidence
is
not
available.
For
instance,
for
frontal
impact
accidents
at
high
speeds
a
simplified
reconstruction
using
the
assumption
of
a
coefficient
of
restitution
equal
to
zero
is
likely
to
be
of
sufficient
complexity
to
obtain
suitably
accurate
results.
Some
of
the
drawbacks
noted
above
for
the
SMAC
program
contributed
to
Calspan's
reasoning
for
developing
CRASH,
as
previously
noted.
The
alternative
methods
provided
with
CRASH
for
approximating
impact
phase
speed
change
make
it
possible
for
the
user
to
select
the
results
based
on
the
most
reliable
evidence
available.
At
the
same
time,
comparison
of
results
from
the
alternative
methods
provides
a
check
on
the
compatibility
of
the
various
evidence
items.
The
drawback
encountered
with
the
CRASH
program
is
the
loss
in
accuracy.
The
accuracy
loss
in
the
CRASH
trajectory
analysis
routine
is
due
to
the
use
of
approximations,
leading
to
idealized
velocity
versus
time
plots
for
the
derivation
of
the
energy
balance
equations
representing
the
trajectory
phase,
instead
of
direct
integration
of
equations
of
motion
during
this
phase.
In
SMAC
the
equations
of
motion
are
integrated
directly
over
the
trajectory
phase
as
well
as
the
impact
phase.
Integration
of
the
equations
of
motion
over
the
impact
phase
introduces
a number
of
disadvantages
due
to
the
short
interval
of
impact
time
during
which
rapid
changes
take
place,
as
the
integra-
tion
time
steps
must
be
very
small
to
maintain
accuracy.
Additionally,
SMAC
requires
a
great
deal
of
computational
effort
at
each
time
step
during
the
impact
phase
to
balance
the
pressures
acting
on
the
vehicles
across
the
impact
interface.
Therefore,
the
impact
phase
analysis
used
in
the
CRASH
program,
which
is
based
on
the
impulse-momentum
principle,
is
a
worthwhile
trade-off
for
simplification.
However,
for
the
trajectory
phase,
large
time
steps
are
28
McHenry
et
aI.,
"Mathematical
Reconstruction."
14
appropriate
and
interface
pressures
need
not
be
calculated,
making
the
trade-off
to
a
less
accurate
solution,
such
as
the
CRASH
program
trajectory
analysis,
questionable.
For
the
damage-based
approximations
of
the
CRASH
program,
based
on
29
Campbell's
work,
the
main
drawback,
as
previously
noted,
is
the
lack
of
experimental
data
for
other
than
frontal
impacts.
For
this
reason
it
may
be
desirable
to
rely
more
heavily
on
other
methods
of
approximation,
such
as
impulse-momentum
solutions.
However,
there
are
classes
of
accidents
for
which
impulse-momentum
methods
are
not
applicable,
(e.g.,
accidents
at
slower
speeds),
and
a method
based
on
damage
analysis
is
the
only
attractive
alternative.
In
this
case
the
CRASH
program
damage
analysis
is
as
good
as
one
may
expect
to
30
achieve
with
a
simplified
approach
and
is
suitable
for
most
cases.
The two
algorithms
developed
by
Wilson
are
similiar
in
nature
to
the
31
CRASH
program.
However,
both
of
these
algorithms
rely
on
calculating
the
total
plastic
work
using
a
linear
correlation
between
vehicle
impact
speed
and
mean
vehicle
crush.
32
It
is
not
evident
in
the
literature
that
the
validity
of
the
algorithms
has
been
substantiated,
and
it
is
extremely
doubtful
the
results
could
be
any
more
accurate
than
those
of
CRASH.
In
conclusion,
it
appears
that
a number
of
different
algorithms
or
modules
appropriate
to
different
classes
of
accidents
with
different
types
of
evidence
would
be
an
attractive
alternative
to
a
general
algorithm
for
application
to
a
wide
spectrum
of
accidents.
By
using
a
modular
approach
extended
to
apply
to
different
stages
of
any
particular
accident,
the
complexity
of
the
total
package
could
be
reduced
while
taking
advantage
of
the
specific
evidence
available
and
making
appropriate
simplifying
assumptions.
As
a
proposed
scheme
an
algorithm
package
including
a
trajectory
analysis
based
on
the
full
integration
of
equations
of
motion
and
an
impact
analysis
based
on
the
principles
of
impulse
and
momentum
could
be
used
to
reconstruct
accidents
with
full
impacts.
29
Campbell,
"Energy
Basis
for
Collision
Severity.,1
30
McHenry,
"Comparison
of
Results."
3~ilson.
"Two-Vehicle
Collision
Reconstruction."
32
Mason
and
Whitcomb,
"Estimation
of
Accident
Impact
Speed."
15
V.
SUMMARY
The
common
goal
of
vehicle
accident
simulations
is
generally
to
determine
initial
velocities
and
velocity
changes,
whether
the
purpose
is
occupant
movement
and
injury
potential
studies,
legal
investigations,
or
other.
To
explore
the
alternative
methods
of
accident
simulation
or
reconstruction,
an
understanding
of
the
application
of
the
principles
of
impulse-momentum and
conservation
of
mechanical
energy
with
applicable
assumptions
is
needed.
Dividing
the
vehicle
accident
into
separate
phases
of
impact
and
pre-
and
post-
trajectories,
the
basic
principles
and
assumptions
were
discussed
in
this
report
as
they
pertain
to
each
phase.
A
wide
variety
of
potential
simulation
algorithms,
combining
different
assumptions,
models,
and
mechanical
principles
exist.
S 1 1
. h
dId
b Wil 33 d C 1 C . 34
evera
a
gor1t
ms
eve
ope
y
son
an
a
span
orporat10n
were
discussed
and
critiqued.
It
is
the
authors'
opinion
that
a
package
of
modular
algorithms,
including
a
trajectory
analysis
based
on
the
integration
of
equations
of
motion
and
an
impact
analysis
based
on
the
principles
of
impulse
and
momentum,
is
the
most
advantageous
approach
to
vehicle
accident
simulation.
This
type
of
algorithm
package
would
be
applicable
to
different
phases
of
vehicle
accidents
under
different
circumstances
(accident
classifications)
and
is
an
approach
that
would
maintain
simplicity
and
take
full
advantage
of
applicable
assumptions
under
the
different
circumstances.
33Wilson,
"Two-Vehicle
Collision
Reconstruction."
34 .
See
note19.
16
BIBLIOGRAPHY
Baker,
S.J.
"Traffic
Accident
Investigation
Manual."
Evanston,
IL:
The
Traffic
Institute,
Northwestern
University,
1975.
Beer,
F.P.,
and
E:R.
Johnston,
Jr.
Vector
Mechanics
for
Engineers:
Dynamics.
2nd
ed.
New
York:
McGraw-Hill,
1972.
Bhushan, B.
"Analysis
of
Automobile
Collisions."
SAE
paper
750895,
October
1975.
Brach,
R.M.
"An
Impact
Moment
Coefficient
for
Vehicle
Collision
Analysis."
SAE
paper
770014,
February
1977.
Campbell,
K.L.
"Energy
Basis
for
Collision
Severity."
SAE
paper
740565,
1974.
Emori,
R. L
"Analytical
Approach
to
Automobile
Collisions."
SAE
paper
680016,
January
1968.
__
--=-="::"'::".
"Vehicle
Mechanics
of
Intersection
Collision
Impact."
SAE
paper
700177,
January
1970.
Emori,
R.I.,
and
D.
Link.
"A Model
Study
of
Automobile
Collisions."
SAE
paper
690070,
January
1969.
Emori,
R.
I.,
and
M.
Tau!.
"Vehicle
Trajectories
After
Intersection
Collision
Impact."
SAE
paper
700176,
January
1970.
Goldsmith,
W.
Impact.
London: Edward
Arnold,
1960.
Greene,
J.E.
"Computer
Simulation
of
Car-to-Car
Collisions."
SAE
paper
770015,
February
1977.
Grime,
G.,
and
I.S.
Jones.
"Car
Collisions--The
Movement
of
Cars
and
Their
Occupants
in
Accidents."
Proceedings
of
the
Institute
of
Mechanical
Engineers
184,
1969-70.
James,
M.E.,
Jr.,
and
H.E.
Ross,
Jr.
"Improvement
of
Accident
Simulation
Model."
Texas
A&M
Research
Foundation
Report
No.
RF-3258-l,
November 1976.
Marquardt,
J.F.
"Vehicle
and
Occupant
Factors
that
Determine
Occupant
Injury."
SAE
paper
740303,
1974.
Mason, R.P
.•
and
D.W.
Whitcomb. "The
Estimation
of
Accident
Impact
Speed."
Cornell
Aeronautical
Laboratory
Report
No.
YB-3l09-V-l,
August
1972.
McHenry, R.R. "Development
of
a Computer
Program
to
Aid
the
Investigation
of
Highway
Accidents."
Cornell
Aeronautical
Laboratory
Report
No.
VJ-2979-V-l,
December
1971.
17
______
. "Computer
Program
for
Reconstruction
of
Highway
Accidents."
SAE
paper
730980,
1973.
• "A Comparison
of
Results
Obtained
with
Different
Analytical
------
Techniques
for
Reconstruction
of
Highway
Accidents."
SAE
paper
750893,
1975.
McHenry,
R.R.,
and
J.P.
Lynch.
"CRASH-2
User's
Manua1."
Cornell
Aeronautical
Laboratory
Report
No. ZQ-5708-V-4,
September
1976.
McHenry,
R.R.,
D.J.
Segal,
J.P.
Lynch,
and
P.M.
Henderson
III.
"Mathematical
Reconstruction
of
Highway
Accidents."
Interim
Technical
Report
DOT-HS-800
801.
Prepared
by
Calspan
for
DOT.
January
1973.
Reizes,
H.
The
Mechanics
of
Vehicle
Collisions.
Springfield,
IL:
Charles
C.
Thomas,
1973.
Wilson,
J.F.
"Two-Vehicle
Collision
Reconstruction:
A
Rational
Computer-
Aided
Approach."
Vehicle
System Dynamics
2,
1973.
18
ABOUT
THE
AUTHORS
Barry
D.
Olson
is
presently
a
graduate
student
and
Research
Assistant
at
The
University
of
Texas
at
Austin,
where
he
will
receive
a
Master
of
Science
degree
in
Mechanical
Engineering
in
May
1979.
While
at
Texas
he
has
been
a
recipient
of
an
Alcoa
Foundation
Fellowship.
A
native
of
Wyoming,
he
received
a B.S.M.E. from
the
University
of
Wyoming
in
May
1975.
While
an
undergraduate
at
Wyoming
he
worked
for
Texas
Instrument~
Inc.,
in
Dallas,
Texa~
in
the
summer
of
1973
and
for
Eastman Kodak Company
in
Rochester,
New
Yor~in
the
summer
of
1974.
Following
his
graduation
from
the
University
of
Wyoming
he
worked
for
the
Trane
Company
in
La
Crosse,
Wisconsin,
as
a Development
Engineer
in
the
Commercial
Air
Conditioning
Division
before
entering
Graduate
School
at
Texas
in
September
1977.
Craig
C.
Smith,
presently
Assistant
Professor
of
Mechanical
Engineering
at
The
University
of
Texas
at
Austin,
holds
B.S.M.E.
and
M.S.
degrees
from
Brigham Young
University
and
a Ph.D.
degree
from
the
Massachusetts
Institute
of
Technology.
He
has
taught
courses
covering
a
variety
of
topics,
special-
izing
in
the
areas
of
systems
dynamics,
control
systems,
machine
design,
and
vibrations.
He
has
published
several
papers
and
reports
dealing
with
vehicle
and
systems
dynamics.
He
has
been
employed
during
summers
with
U.S.
Steel
Corporation,
Bell
Telephone
Laboratories,
and
IBM
Corporation
and
has
had
a
variety
of
industrial
consulting
experience.
He
presently
serves
as
Chairman
of
the
Technical
Panel
on System
Modeling
and
Identification
for
the
Dynamic
Systems
and
Control
Division
of
the
American
Society
of
Mechanical
Engineers.
He
is
also
a member
of
the
Society
of
Automotive
Engineers,
Sigma
Xi,
Phi
Kappa
Phi,
and
Tau
Beta
Pi
and
is
a
registered
Professional
Engineer
in
the
state
of
Texas.
19
RESEARCH
MEMORANDA
PUBLISHED
BY
THE
COUNCIL
FOR
ADVANCED
TRANSPORTATION
STUDIES
1 Human Response
in
the·Evaluation
of
Modal
Choice Decisions.
Shane
Davies, Mark Alpert,
and
Ronald
Hudson,
April 1973.
2 Access
to
Essential Services. Ronald Briggs,
Charlotte
Clarke,
james
Fitzsimmons,
and
Paul
jensen,
April 1973.
3
Psychological
and
Physiological Responses to
Stimulation.
D.
W.
Woolridge,
A.
J.
Healey,
and
R.
O.
Stearman,
August 1973.
4
An
Intermodal
Transportation System for
the
Southwest: A Preliminary Proposal. Charles
P.
Ziatkovich,
September
1973.
5 Passenger Travel Patterns
and
Mode
Selection
in
Texas:
An
Evaluation.
Shane
Davies, Mark Alpert. Harry Wolfe,
and
Rebecca
Gonzalez,
October
1973.
6
Segmenting
a Transportation
Market
by
Determinant
Attributes
of
Modal
Choice.
Shane
Davies
and
Mark Alpert,
October
1973.
7 The Interstate Rail System: A Proposal. Charles
P.
Ziatkovich,
December
1973.
8
Literature Survey
on
Passenger
and
Seat
Modeling
for
the
Evaluation
of
Ride
Quality.
Bruce
Shanahan,
Ronald Stearman,
and
Anthony Healey,
November
1973.
9 The
Definition
of
Essential Services
and
the
Identification
of
Key Problem Areas. Ronald Briggs
and
james
Fitzsimmons, january 1974.
10 A
Procedure
for
Calculating Great Circle Distances Between Geographic Locations.
J,
Bryan Adair and Marilyn Turnbull, March 1974.
11
MAPRINT: A
Computer
Program
for
Analyzing
Changing Locations
of
Non·Residential
Activities. Graham
Hunter,
Richard
Dodge,
and
C.
Michael Walton, March 1974,
12
A
Method
for
Assessing
the
Impact
of
the
Energy Crisis
on
Highway
Accidents
in
Texas.
E.
l.
Frome
and
C.
M,
Walton, February 1975,
13
State Regulation
of
Air
Transportation
in
Texas. Robert C. Means
and
Barry
A.
Chasnoff, April 1974.
14
Transportation Atlas
of
the
Southwest. Charles
P.
Ziatkovich,
S.
Michael Dildine, Eugene Robinson,
james
S.
Wilson,
and
J.
Bryan Adair, June
1974.
15
Local
Governmental
Decisions
and
Land-Use Change:
An
Introductory
Bibliography. William Dean
Chipman,
May 1974,
16
An
Analysis
of
the Truck
Inventory
and
Use Survey Data
for
the
West South Central States. Michael Dildine, July 1974.
17
Towards Estimating
the
Impact
of
the
Dallas-Fort Worth Regional
Airport
on
Ground
Transportation Patterns. William
J.
Dunlay, Jr.,
and
lyndon
Henry,
September
1974.
18
The
Attainment
of
Riding
Comfort
for
a Tracked
Air-Cushion
Vehicle Through
the
Use
of
an Active
Aerodynamic
Suspension. Bruce
Gene
Shanahan,
Ronald
O.
Stearman,
and
Anthony
J.
Healey,
September
1974.
19
Legal Obstacles
to
the
Use
of
Texas
School
Buses
for
Public Transportation. Robert
Means,
Ronald Briggs, John
E.
Nelson,
and
Alan
J.
Thiemann,
January 1975.
20
Pupil Transportation: A Cost Analysis
and
Predictive
Model.
Ronald Briggs
and
David
Venhuizen,
April 1975.
21
Variables
in
Rural Plant Location: A Case Study
of
Sealy, Texas. Ronald
linehan,
C. Michael Walton,
and
Richard
Dodge,
February 1975.
22
A
Description
of
the
Application
of
Factor Analysis
to
Land Use Change in
Metropolitan
Areas. John Sparks, Carl Gregory,
and
jose
Montemayor,
December
1974.
23
A Forecast
of
Air
Cargo
Originations
in
Texas
to
1990.
Mary
lee
Metzger
Gorse,
November
1974.
24
A Systems Analysis Procedure
for
Estimating
the
Capacity
of
an
Airport:
A Selected Bibliography. Chang-Ho Park, Edward
V.
Chambers
III,
and
William
J.
Dunlay, Jr., August 1975.
25
System 2000-Data Management
for
Transportation
Impact
Studies.
Gordon
Derr, Richard
Dodge,
and
C. Michael Walton,
September
1975.
26
Regional
and
Community
Transportation Planning
Issues-A
Selected
Annotated
Bibliography. John
Huddleston,
Ronald
linehan,
Abdulla
Sayyari, Richard
Dodge,
C. Michael Walton,
and
Marsha Hamby,
September
1975.
27
A Systems AnalysiS Procedure
for
Estimating
the
Capacity
of
an
Airport:
System
Definition,
Capacity
Definition
and
Review
of
Available
Models.
Edward
V.
Chambers
III, Tommy
Chmores,
William
J.
Dunlay, Jr., Nicolau D.
F.
Guald~,
B.
F.
McCullough, Chang-Ho Park,
and
John
Zaniewski,
October
1975.
28
The
Application
of
Factor Analysis
to
Land Use Change in a
Metropolitan
Area.
lohn
Sparks
and
lose
Montemayor,
November
1975.
29
Current Status
of
Motor
Vehicle
Inspection:
A Survey
of
Available Literature
and
Information.
lohn
Waller
lhrfurth
and
David
A.
Sands,
December
1975.
30
Executive Summary: Short Range Transit
Improvement
Study
for
The University
of
Texas
at
Austin.
C. Michael Walton, May 1976.
31
A Preliminary Analysis
of
the
Effects
of
the
Dallas·Fort Worth Regional
Airport
on
Surface Transportation
and
Land Use. Harry Wolfe, April 1974.
32
A Consideration
of
the
Impact
of
Motor
Common
Carrier Service
on
the
Development
of
Rural Central Texas. james S. Wilson, February 1975.
33
Modal
Choice
and
the
Value
of
Passenger Travel Time Literature: A Selective Bibliography.
Shane
Davies and Mark
I.
Alpert, March 1975.
34
Forecast
of
Air
Cargo Originations
in
Arkansas, Louisiana,
and
Oklahoma
to
1990.
Deborah
GoHra, April 1975.
35
Inventory
of
Freight Transportation
in
the
SouthweSt/Part
IV:
Rail Service
in
the
Dallas-Fort Worth Area. Charles
P.
Ziatkovich, Mary
l.
Gorse,
Edward
N.
Kasparik,
and
Dianne
Y.
Priddy, April 1975.
36
Forecast
of
Waterborne Commerce
Handled
by
Texas
Ports
to
/'1'10.
Stuart Metz Dudley, April
1'175.
37
Forecast
of
Refinery Receipts
of
Domestic
Crude
Oil
from Pipelines
in
the
West South Central States
to
1990.
Mary
l.
Gorse,
Dianne
Y.
Priddy,
and
Deborah
I.
Goltra, April 1975.
38
A Feasibility Study
of
Rail Piggyback Service Between Dallas-Fort Worth
and
San
Antonio.
ldward
N.
Kasparik, April 1975.
39
Land Value
Modeling
in
Rural
Communities.
lidvard
Skorpa, Richard
Dodge.
and
C. Michael Walton,
lune
1974.
40
Towards
Computer
Simulation
of
Political
Models
of
Urban Land Use Change. Carl Gregory, August 1975.
41
A Multivariate Analysis
of
Transportation
Improvements
and
Manufacturing
Growth
in
a Rural Region. Ronald
linehan,
C. Michael Walton,
and
Richard
Dodge,
October
1975.
42
A Transit
Demand
Model
for
Medium-Sized
Cities.
john
H.
Shortreed,
December
1975.
43
Recommended
Procedures
for
Evaluating
Medical
Services Transportation
in
Houston,
Texas. Mark Daskin, John
F.
Betak, Randy
Machemehl,
and
Ronald Briggs,
October
1978.
Council for Advanced Transportation Studies
THE
UNIVERSITY
OF
TEXAS
AT
AUSTIN