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1. Thesis and Dissertation Collection, all items
1976-06
The estimation of Lanchester attrition-rate
coefficients for an aggregated combat model
Lee, Yin-chu; Pi, Yu-kung
http://hdl.handle.net/10945/17749
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THE ESTIMATION OF LANCHESTER ATTRITION RATE
COEFFICIENTS FOR AN AGGREGATED
COMBAT MODEL
Lee, Yin-chu
•&ST
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
THE ESTIMATION OF LANCHESTER ATTRITION RATE
COEFFICIENTS FOR AN AGGREGATED
COMBAT MODEL
by
Lee, Yin-chu
and
Pi, Yu-kung
June 1976
Thesis Advisor
James G. Taylor
Approved for public release; distribution unlimited.
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The Estimation of Lan Chester Attrition- Rate Coeffi
cients for an Aggregated Combat Model
7.
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Master's Thesis
June 1976
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Lee Yin-chu
Pi Yu-kung
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PROGRAM ELEMENT. PROJECT, TASK
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Naval Postgraduate School
Monterey, California 93940
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Naval Postgraduate School
Monterey, California 93940
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Naval Postgraduate School
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necemmmry mnd Identity by block number)
Lanchester-type combat models
Markov- dependent fire
Estimation of Lanchester attrition-rate coefficients
Theater- level combat models
20.
ABSTRACT
(Continue on reverme aide
II
necmmmmrr end Identity by block number)
This thesis oonsiders the problem of estimating Lanchester attrition rate
coefficients for an aggregated Lanchester type theater level combat model,
BALFRAM, which has been used for various high level defense planning purposes.
Several alternative coefficient estimation methodologies are examined, with
their strengths, weaknesses, and problems of implementation in BALFRAM being
discussed.
Data requirements for coefficient estimation and approaches to
aggregation are also discussed.
DO .SS,
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Entered)
THE ESTIMATION OB LANCHESTEH ATTRITION-BATE COEFFICIENTS
FOB AN AGGBE6ATED COMBAT MODEL
by
Lee- 1£in-chu
Col, Bep. of China Air Force
M.E.A., Tamkang College, China, 1974
Pi, Yu-kung
Lt Col- Bep. of China Arm?
M.E.A., Tamkang College, China, 1974
Submitted in partial fulfillment of the
reguirements for the degree cf
BASTES OF SCIENCE IN OPEBATIONS BESEABCH
from the
NAVAL POSTGBADOATE SCHOOL
June 1976
LIBRARY
DUDLEY KNOX
PO
NAVAL
MONT
ABSTRACT
Tbis
Lanchestei
thesis
considers
attrition
—
the problem of estimating
rate
coefficients
for
an
aggregated lanchester-type theater- level combat model,
level
EAIFBAK, lihich has been used for various high
defense
planning
purposes.
Several
alternative
coefficiect- estimation methodologies are examined,
weaknesses, and problems of
nith their strengths,
Data
implementation in BALFRAM being discussed.
reguirements for coefficient estimation and approaches
to aggregation are also discussed.
TABLE OF CONTENTS
I.
II.
III.
INIfiOEDCTION
A.
RBI MODEL COMBAT
B.
OVIBVIER OF THESIS
7
8
.
MEIHCECICGIES FOR THE ANALYSIS CF CCBEAT
9
A.
11B GAMES
E.
SIMULATION
10
C.
ANALYTIC MODELS
11
9
EilFfiAM
13
A.
GENERAL DESCRIPTION
13
E.
SYSTEM APPLICATION
14
C.
D.
1.
System Organization
2.
Systea Operation..
-
...
..
16
....
16
Lanclieste^s Classic Combat Models.
16
2.
Differential Fight Laws
19
a.
Square Law....
b.
Linear Lav....
-
19
20
EALEBAM PBOCESS
21
1.
Scenario Geography
23
2.
Force Characteristics
23
3.
Contingency Logic
-
•
24
a.
Battle Logic
25
b.
Movement Logic
25
Inputs and Outputs
NODH Program
a.
b..
DCSF Program
26
Capabilities.
27
UTILIZATION OF BALFRAM IN REP. OF CHINA
ESTIMATION CF ATTRITICN-RATE COEFFICIENTS
A.
14
1.
5.
E.
..»
HMBEMATICAL BACKGROUND
4.
IV.
7
MABKOV EEPENDENT FIRE
26
26
30
33
33
¥.
¥1.
E.
ECNDEB'S METHOD
34
C.
CliBK'S MODEL
37
DATA BECUIREMENT FOB COEFFICIENT ESTIMATION
40
A.
HISTORICAL DATA
40
E.
LCGISTICS DATA
42
C.
WEAPON DATA
43
D.
QUALITATIVE DATA
44
AGGBECATICN OFFOBCES
45
A.
HCTIONAI UNIT
B.
FIBEPCWEB SCOBES
C.
TEE OSE OF SATELLITE MODELS
D.
TEE APPLICATION OF EONDEB«S APPROACH IN
45
,
46
-
47
EAIFBAM.
48
VII.
FISAI EEMABKS
LIS! OF EIGUBES
LIST OF EEFEBENCES
50
,
52
,
•
53
INTRODUCTION
I.
A.
SHY KCDEI CCMEJST
came
war
A
has
been
a
military
whatever means, cf
more
cppcsirg
forces,
defined
(8)
as "a simulati.cn, by
operation
conducted
involving
using
tfco
data
rules,
or
and
prccedures designed to depict an actual or assumed real life
It is a systematic method of studying military
situation."
prctlems and can provide
identifying
errors
or
a
means
gaining
of
shortcomings,
experience,
and improving skills
without paying the penalties of the real world.
One
the significant values of war gaming is ttat it
cf
can provide an impelling stimulus to innovation,
and
creativeness
.
It
challenges and motivates
different
kinds
establishes
a
an
responsible
mcti^aticn
environment
that
participant.
Thus
cf war games have been used extensively to
train officers in military forces throughout the world.
Ancther
advantage
of war gaming is that a war garce can
be played on any hypothetical terrain which may not te areas
ccctrolled by the nation sponsoring the game, as must te the
case in field tests and maneuvers that employ real
fcrces.
Any
military
nation may employ war gaming tc assess or test
contingencies
military
requirements
military
fcrces must be anle tc cope to ensure the security
and
and survival cf the nation.
the
with
which
B.
OVEBvIJ* CE THESIS
paper is composed of seven chapters. In chapter
This
war gaming
is
Chapter
2
gives
combat.
These are
mcdels.
Chapter
discussed
three
its
different
values
methods
simulation
games,
nar
3
and
introduces
a
1,
described.
are
modelling
for
analytical
and
computerized analytical
model EALEBAfi and discusses its analysis use in the Bepublic
of
Chapter
China.
means
of
introduces Markov-dependent fire and
4
calculating
coefficient.
Chapter
the
5
attrition — rate
Lanchester
discusses the historical, logistic,
weapon and qualitative data which are required for input
simulation oi war gaming models.
Chapter
methodologies such as notional unit,
the
6
examines several
firepower
scores
and
of satellite models for the aggregation of fcrces,
use
and the prchlem area to apply Eonder*s approach in
Chapter
to
7
gives seme final remarks.
EAIFEAM.
METHODOLOGIES fOR THE ANALYSIS OF CO ME AT
II.
A.
WAR GAMES
war game, as defined by Ecnder
A
frcm
(2)
reality of a field experiment or
the
removed
field exercise
a
representing
wherein crly teams of players
step
is a
,
commanding
the
officers and their staffs are included.
Chinese people invented a game
called "Kei Chi" and it is still played tcday on a stjlized
map board with black and white colored stones and wen ty the
Ahcut 3QC0 B.C., the
flayer
succeeded
*ho
in outflanking his opponent. Perhaps
that was the origination of war games
the
seventeenth
development
military
Christopher
Heikhmamn
the "King's Game."
as
chess
century
came
of
to
[22]
it
was
in
games reflecting the
like
a
Eut
.
new
age.
In
1644,
01m developed a war chess called
It is said to have been highly
an aid in military training.
regarded
Since then various kinds of
military chess were invented in many different countries. In
1824, a war came was played before General Vcn Muffling, the
Chief cf General Staff of
players
rather
ecldly
Prussia.
He
first,
but
at
expanded en the map and move by move the
out
their
had
as
received
the operations
combatants
worked
plans, the old general's face lit up and at last
he broke cut with enthusiasm: "It's not a game at all,
training
the
fcr
it's
war. I shall recommend it enthusiastically to
the whole army £2) ."
This
was
the
beginning
of
the war game as a serious
military tursuit which was to spread to alacst every country
with
military pretensions.
But what is the usefulness of
war games?
but
the
It is net any information
from
them,
to combatants of tactical and
present
they
test
acquired
strategical knowledge. "The only difference from actual war
is
the absence of danger, of fatigue, of responsibility and
of the friction involved in maintaining discipline and these
factors
1S37)
all important in war." said Wilkinson
are
(1653 to
who was a British military reformer.
,
When
playing
called
so
free
regarding the effects of combat
games, assessments
war
decisions
other
and
were
subjectively by a control team of experienced military
made
officers. So
different
a
high variance of the results was expected
decision makers were used. And because it takes a
long time tc develop and to play a single game, it is not
feasible
if
a
mechanism for analyzing a broad spectrum of system
alternatives in
responsive manner to meet
a
planning
cycle
requirements
B.
SIHOIATICN
War games can te simulated also by using
To
this kind of model, the military process is studied
develop
and
computers^
microscopically
activities,
which
decomposed
are
into
basic
events
and
to be ordered in a logical seguence
Befpre being able to compute, the
computer
and programmed
.
must
with data and parameters such as firing rate,
be
fed
kill probabilities, etc. When
those
the
start
key
is
pressed,
events and activities of the different combat process
are essentially followed
in
a
specified
decisions based upon predetermined rules.
seguence
The final outcome
will be trinted cut at the end of simulation.
10
Baking
processes
ccmbat
Since
protabilistic
events
distributions
number
large
a
activities,
and
probability
reguire
contain
simulation
many
for
of
models
of the input
variables and generate the probability distributions fcr the
output
variables
results.
or
statistical
If
saapling
techniques involving the generation of pseudo random numbers
employed,
are
simulation
the
called
is
Monte
a
Monte Carlo simulation models are
simulation.
Carlo
employed
in
military plaining studies.
Hcnte Carlo simulations tend to be
games
war
tut
still
are
much
more
abstract
concrete
more
than
than, for
exanple, the Lanchester- type combat models discussed
below.
instance, two Marine Corps colonels fighting a war game
For
over Cuba are a much subtler model of
real campaign than
a
trying tc simulate the same thing. This is because
computer
the human brain can still perform a much
processes
than
the
variety
wider
cannot
it
qualitative
make
of
elaborate electronic computer.
most
computer can handle much more data with accuracy and
but
a
judgements
A
speed,
or deal with
intangible factors such as leadership and morale.
C.
ANALI1IC MCDEIS
Like
siirulaticns,
To develop a model
involvement.
study
the
events
models also have no player
analytic
activities.
and
mathematically.
Finally
then
He
one
integrates
of
the
we
first
process.
By
describe
them
these events and
assumed
mathematical
consistent
mathematical
activity descriptions into an overall
structure
kind,
and decompose it into its basic
process
ccmbat
this
of
operations, solutions can be obtained
which
will
indicate
the relationship between independent and dependent variables
of combat effectiveness.
When such a
11
relationship
can
be
developed,
obviously
it
sensitivity analysis
interpreting
contained
since
can
not
mathematical techniques, but
ottairable.
often
an
conduct
increased ease
the
of
in
combat dynamics are
the
examined
readily
solutions
analytical
provides
and
results,
the
in
simplifies
Sometimes
equations.
obtained by appropriate
be
approximations
numerical
are
provides substantial reductions in
This
cost and time for the conduct of military analysis.
Analytic
models
can
either
be
In the deterministic case,
prctabilistic.
deterministic
or
the same
of
set
values always produce the same set of output results;
input
while in the probabilistic case, seme of the input variables
have probability distributions and produce different results
Eeplications
ever the cutjut variables.
desirable
are
in
prcbabalistic case.
Combat is
a"
measurement.
process that does not readily lend itself to
operational
The
effectiveness
combat
of
systems are often times edicted by military personnel.
experimentally
not
are
Thus they should not be
verified.
used as an evaluation mechanism to provide
predictions
estimate
accurate,
effectiveness
combat
They should
decision lakers.
purposes
of
used
be
They
only
point
for use by
analysis
for
as to have a better understaning of the system
so
number
dynamics. For this purpose,
a
variations
variables
of
the
model
large
paranetric
of
required.
is
As
a
consequence, for such parametric studies analytic models are
preferred tc simulations and war games.
developed
Among many analytical models
States,
BAIFRAM
Methodology)
China
Force
(Balanced
Requirement
is the one which has been used by
military
personnel
as
a
ccntingency flans. BALFRAM will be
chapter.
12
the
in
tool
tc
discussed
United
Analysis
Republic
analyze
in
the
of
their
next
BALFRAM
Ill-
A.
GENEE4L EESCEIETICN
EALFBAM
(Balanced
Force
Requirement
Analysis
Methodology)
is a computer war gaming model. It consists of
scae
FORTBAfl
10,000
primarily
statements.
The
capabilities
force
requirements
and
can be analyzed and the effectiveness of force
levels and fcrce mixes can be evaluated.
The entire program
subprograms, namely, the NODH program and
two
of
The NODH program, when provided with
the DCSF program.
scenario
is
an analytical bookkeeping device which provides a
framework within which problems of
consists
program
tasic
the
abstracted from a hypothesized campaign
geccraphy
environment in terms of nodal points
and
lines
access
of
between nodes, will compute the matrices of minimum distance
between nodes and of next
distance.
characteristics
force
on
the
of
path
minimum
program, when provided with inputs of
DCSF
Ihe
nodes
and
contingency
logic
(tactical
decision rules) will move units over the scenario geography,
enabling them
computing
the
to
according
engage
outcome
of
the
to
the
engagements
scenario
according
and
to
appropriate fight laws designated by the user. The program
is
It is very flexible and may be used to
user oriented.
examine
In
a
wide range of military applications.
order
to use BALFRAH, scenario geography must first
be abstracted into nodes representing geographical
at
which
tattles
may
congruous EALFRAM terms.
take
place
and
locations
translated
into
Then fcrce characteristics and the
13
decision
tactical
rules
must
be formulated and described
through tte use of BALFRAM descriptors.
EAIFBAM
is
not
a
In
certain
complete war gaming model until
descriptors en fcrce characteristics and
sense,
a
set of
contingency
legic
has been prepared and assembled to compose a scenario.
B.
SXSTEH AEEIICAIION
!•
System Organization
A
in figure
simplified system organization cf EALFRAM is shown
1
as a tree type diagram.
14
SYSTEM SUPERVISOR
W
STOP
J
Descriptor
Processor
Surface Supervisor
A
T
Surface Matrix
Output
BATTLE SUPERVISOR
Next Event
Determinator
Figure
1
-
Survivor
Contingency
Determinator
Plan Processor
SYSTEM ORGANIZATION
15
It
scenario
shows the steps in control
ficm
time
the
inputs
and
execution
submitted
are
of
a
the
to
ccmputaticn center until the time final outputs are produced
alcng
functional
supervisors each
lines.
charge
in
idea
The
of
a
of
specific
having
step
three
in
the
execution piccess is veil conceived.
2-
$1§ ten Operation
In
order
use
to
scenario and translate it
First,
scenario
BALFRAM, the user must develop a
into
geography
NODH
serves
EALFRAM
inputs.
is submitted to the computation
center in natrix fcrm as inputs
from
congruous
to
NODH
program.
Outputs
geographical inputs to DCSF program.
as
Then ether ircuts (force characteristics, movement logic and
tattle
logic)
are
submitted
to the computation center as
Outputs from DCSF program are the
results of the scenario with respect to specific sets
inputs tc DCSE program.
final
of parameters. BALFRAM maintains no
and
NODH
tasis.
DCS*
files
data
except
base
the
are on a scenario to scenario
which
All outputs from both
NODH
and
program
DCSF
are
returned to the users.
C.
MATHEMATICAL EiCKGROOND
'•
Lancaster's Classic Combat Models
The
iiathematical foundation of BALEBAM rests en the
extention and enrichnent of Lanchester's classic
combat
1946)
between
two
was an English
opposing
forces.
aeronautical
16
theory
Lanchester
engineer,
who
of
(1668 to
believed
that "one cf the great questions at the root of all strategy
is that cf concentration;
resources
cf
a
concentration
the
of
field of operations
made
a
strength
of
naval or military, at cne point in the
whether
force,
whole
belligerent on a single purpose or object,
and concurrently the concentration of the main
his
the
To prove this
$5} ."
point,
Lanchester
simplified jnathematical analysis of the relation of
oppcsing fcrces in battle, He wrote the
equations" in
(1)
T9"14
famous
"Lanchester
under the assumption that:
Iwo oppcsing forces each capable
of
inflicting
casualties en the ether are engaged in combat,
(2)
Each unit
engaged
in
battle
are
within
the
firing range cf all pther enemy units, and
(3)
Ihen
Ecth sides use aimed fire.
the combat between the two oppcsing forces was
modelled by
dx/dt =-ay w£th x
(t = 0) =xo
(3. 1)
dy/dt =-bx with y(t=0)=y
where
x (t)
=the numbers of X force at time
y(t)=the numbers of
a=atrition rate of
b=attriticn rate of
and t=
Y
force at time
t
t
force
X
Y
force
denotes the time at which the battle begins.
17
from
Lanchester deduced his classical square
(3.1)
lav
t(x
2
2
=a(£-y2 (t))
-x (t))
which implies that if one
(3.2)
side
committed
more
forces
to
tattle at the very beginning, his casualties will be reduced
significantly.
He
by
histcry pf force level, x
and y(t)
(t)
were given
18
Cosh/abt-y /a/bSinh/abt
i (t) =2o
0(
(3.3)
Cosh/abt Xo/FTaSinh/abt
J (t) ~lo
If
assumptipn
is changed to be area fire, the
(3)
model beccmes
dx/dt =-axy with x(t = 0)=x o
(3.4;
dj/dt =-bxy with y(t=0)=yo
The state eguation is given by
t (Xo-x)
=a
the
flod
(3.5)
(y.-y)
time
histcry of, for example, the
X
force
level is given by
1
I
bx ~
}
asio <?xp[(ay
~bx
for bx °n yi ay °
T)
tJ
J
x(t) =-
———-—
X
I
-r
b
xn
for
t
18
bx 0=d
y
(3-6)
Cifferential Fig ht
2.
L§ws.
Fight laws define the number of surviving components
of
tasic differential fight
law. They are
linear
BAIFBAM contains two
as a function of time.
side
each
a
square
the
laws:
law
and
the
modified version of the Lanchester's
eguations.
a.
Sguare Law
The sguare law has the form
dx/dt=-ay-c with x(t = 0)=x
C3.7;
cy/dt=-bx-e with y(t=Q)=y„
where
the
x(t),
v (t)
excgenccs
incremental
,
a
and b are defined as in
parameter
firepower
capability
of
y
that
(3.1)
and
c
represents
is
the
to inflict attrition Or
virtue of the exogenous firepower available to y, and
x
e
by
is
defined sinilarly.
The state equation is given by
(fbxo* e//b)-(/bx+e//b)
2
=
(
/ay. + c//aj*- (/iy + c//i)
2
Analytic sulutions are always available and
(3.3)
are
given by
j (t)
=
(
(/"cx
+e//b)
Cosh/a~bt-(/ay e
+c//a)
Sinh /abt)//~b-e
C3.9)
I <t)
=
(
(
/ay +c//a)
Cosh
19
/a~bt- (/"Exo +e//b)
Sinh /ab t)//a-c
Ihe differential fight laws contain the implicit
assumption
area)
that
fire wfcich
exogenous fire is aimed (rather than
is subject to discussion.
this
linear Lav
t.
The linear law has the form
cx/dt=-axy-c with
x (t=0) =x
(3.10J
dy/dt=-bxy-e with
where
x,j f t,c,and
attrition of
surviving
side
components
is
dependent
both
of
assumption cf area fire:
receiving
=y
are as previously defined.
e
each
y (t=0)
sides.
the more
distributed
uniformly
on
The rate of
number
the
of
This is because the
components
in
area
an
fire, the more casualties
incurred; and the mere components firing intc the area,
the
mere casualties thay will inflict.
Ihe state equation is given by
t (x -x)
=a
(y -y)
for tc=ae
analytic suluticns
In case e=c=0,
(3.10)
(3.11,)
for
equation
eiist.
(a)
x
bx« =ay
(t)=x./(1+btXo
)
(3. 12)
J(t)=y./{1+atya
(t)
)
bx *ay
20
i <t)
= /a7br h/(exp
(
/abkt)-r)
(3.13)
j
<t)=/E7a€xp (/abkt)/(exp (/abkt)-
fcfaere
r=bxa/ay and k= /a7"by Vt/ax o
When
c
*
or both c, e * 0, no analytic
e *
0,
r)
solution exists and it is necessary to perform
solution of eguaticn
Kcte:
ether
numerical
a
(3.10).
Shen one side
uses
aimed
fire
area fire, one side suffers attrition at
uses
proportional to only the number of firers, while
at
a
proportional
rate
the
to
called
"nixed
the
a
the
the
rate
other
product of the number of
firers and the number of targets. The resulting
is
anc
combat
law
BALFRAM can also accommodate
law."
this situation.
D.
EALFBAS IICCISS
Although
EALFRAM
war gaming model,
language.
to
form
a
it is essentially a
order
has been prepared and
(descriptors)
hypothesized
scenario.
consist of three categories.
force
high
a
computer
conpiler
can be regarded as model only when a ccnplete
It
set of inputs
usually referred to as
is
characteristics,
decision rules)
.
Figure
They are
essential imputs
scenario
contingency
and
2
The
logic
shows the entire EiLFRAM
21
assembled
geography,
(tactical
process.
/ Q
\
u
/
H
>\
UI
h O
thfe
o.
< 2
2
O Q I
lil
/ H < \
(
< £ ^ >
\ a 2
/
\
\
to
Ui
M
u
\\ „E //
\
"2
1 .-•
o
J
i
as
Y
I
i
<
I
4
Q
uj
t— ui
2
O
—
30tt
^ < 2
2 a
O
O 2
UJ
.
CC
z>
h
<
H
CM
a'
M
H
22
Scenario Geography
1 •
abstracted from a projected
campaign envircnment into nodes and lines of access between
geography
Scenario
represent
ncdes
The
then.
specific locations.
even
represented
fcy
a
defined
areas
or
They can be located on land, on sea
or
air"
tie
"in
is
scenario
the
as
geographic
reguires.
ncde can range in size from
reguired
that
an infantry sguad to that reguired for a battle between
fcr
corps or field armies.
associated
their
and
The lines of
distances
access
sides
must
move.
between
represent
cottmunicaticn ever which the forces and
nodes
Given
a
can
be
logistics
both
of
The network
as detailed as reguired by the scenario.
netwerk cf nodes, the NODH program will compute
distance
network.
Geographical
swamps
and
of
The movement of combat units during the
shcrtest
risers
aodes
lines
the
course of battle most also follow these routes.
of
The area
route
between
irregularities
also
can
be
twe
any
nodes
such
as
in
the
the
mcuntains,
input to the network for
assessing the effects of force deployment
and
mobility
on
battle cutccne.
Fcrce Charac teri stics
2-
characteristics refer to the number, type and
nature of units each side can commit to battle, the nobility
of
rate at which each unit can move over the scenario
Perce
geography, the combat effectiveness in terms of the
atility
to inflict casualties on the enemy units,
and the breakpoint
in term cf the number of casualties each
unit
before being defeated.
cne.
It
retaining
can
its
consist
cwn
can
sustain
In BALFRAM, the unit is a conceptual
of
several
units
characteristics or
23
a
with
unit
each
fraction of
a
unit
which possess the same attrition
breakpoint
the
as
mobility
capability,
and
Units of different sizes can be
unit.
input into EiLJBAM as force equivalents of the standard unit
which is designated
They can be icpct into
the same prirciple applies.
either
as
single ship
a
As to ships and airplanes,
the user.
i>y
EilffiAM
or as naval
(or airplane)
(cr air
units.
force)
Ccntinqency Logic
3-
Ccntingency logic refers to the sequential
decision
rule
tactical
the way forces are to be employed during
or
example
typical
initial
the course
cf
deployment
would be what proportion of ground forces are to
deployed
be
piopcrticn
campaign.
front
to
combat
line
are
forces
cf
A
of
positions
and
what
to be held as reserves, and the
relative pcsition cr locations the front line units and
reserves
are
to
occupy.
An example of fcrce utilization
would be what proportion of tactical air
csed
close
for
combat.
air
the
fcrce
are
to
be
aix support and what proportion for air to
initial
After
deployment,
may
it
become
necessarj to change deployment policy or mission allocations
These
events
specific
contingent upon some
activities
contingent
might
which
provide
the
occur.
operational
priorities and novement logic which govern the way in
a
conducts
unit
which
its operation as the scetario progresses.
The general form cf contingent logic input statement is
some
condition
true,
the
specified
units
do
the
In developing logical operations, the users are
following."
cautioned
is
"if
to
be
consistent. Inconsistencies may cause one
logical step tc be negated by another.
types of contingency logic inputs,
namely, battle logic inputs and movement logic inputs:
They
There
are
two
can be summarized as follows.
24
a.
Eattle Logic
Eescrite
rattles are
tc
forces
involved
and
nodes
at which
cccur.
attrition
Specify
factors
and
criteria
for
tattle teminaticn
orders
Eermit
of battle of several units tc be
merged.
Specify
allocation
ef fectivecess
and
of
supporting weapons.
Ercportionally assign and redistribute fcrcss.
Eescrite
logistic
pipelines
and
interdiction
effects.
Vary
parameters
such
as
order
of
battle,
firepower, ncrility.
^Ffly principles of concentration.
t.
ecvement Logic
Cove units
from
node
to
node
contingent
on
arrival events.
Eelocate units contingent on defeat events or at
specified tine.
Eermit withdrawal if force ratic is unfavorable.
25
Cause one force to chase another.
Establish a sequential link up cf forces.
Eedeploy units after battle is wen.
PEBA
Trace ffovement of
tattle area)
(forward
of
the
.
Inputs and Outputs
**•
HCEH Program
a.
represent
Inputs to this program
abstracted
geography
in
matrix
form
representicg direct distance between nodes.
(1)
edge
the
scenario
with
elements
The outputs are
matrix cf direct distance between node pairs,
of minimuu distance between node pairs, and
(2)
matrix
matrix
(3)
of
next nodes ct the path of minimum distance.
LCSF Program
t.
Eeside
the
preprocessed
scenario
geography
inputs from KCEH program, additional inputs must be prcvided
to construct a EALPRAM scenario.
These include force levels,
motility, indices cf combat effectiveness, defeat
and
attrition rates.
also be developed and
logic
inputs.
the "end
cf
criteria,
The initial concept cf operation must
formulated
as
battle
and
aovement
The outputs include the "battle histcry" and
campaign
summary".
The
former
provides
a
chronological record of the scenario showing the location
objectives of forces, location and status of
anc next
26
tattles,
step.
and
size
the
surviving
latter,
The
casualties
forces involved at each tattle
of
resulting
both
on
sides,
from exogenous fire, and the duration
An output of
of the battle.
forces
sensitivity
analysis
results
can also te cbtained at the option of the user.
5
.
Capabilities
forces
heterogeneous
as
homogeneous,
EAIPEAM provides an aggregated approach to the simulation of
Treating
conventicnal
conflicts between two opposing forces composed
of ground, air and naval units. It can be used to assess the
capabilities cf the component ground, air and naval elements
in their coordinated support of a military operation
cr
to
ccapare
soundness of tactical decisions by examining the
tfce
effects cf alternative courses of action upon the outccme of
a
conflict.
theoretic sclutions tc
sensitivity
perform
program can also generate game
software
The
of
force
analysis
to
guantify
between input and output, thus
analyzing
tradeoffs
the
allocation
problems
providing
between
a
and
relationship
framework
for
forces
and
component
deriving optimal force level objectives.
simulation model for a
It can be used to model combat at the
unified high command.
theater level. There is no explicit statement on the level
however, the
it
can handle;
cf force cr number of units
EALIBkH
is
primarily
inputs
on
force
primary
a
and contingency
characteristics
logic in the form cf data cards usually do
not
exceed
300
per scenario.
&
analysis
typical
E2LFRAM
example
can
of
the
perform
kind
would
of
te
analysis
superiority, parity and I-force superiority
en
the
variations
of
Y- force
27
levels
sensitivity
the
X — force
as
shown
based
in the
following figure.
28
o
r-i
P
•P
CO
U
O
>
rt
CO
4-<
O
>
3 o
•H
CO -H
4J
Q
1.0
1.5
2.C
2.5
Y-Force Level Multiplier
Figure
3
-
SENSITIVITY ANALYSIS
29
3.0
i.
0TILI2A1ICN OF EALFRAM IS THE REPUELIC CI CHINA
EA1FBAM was first introduced to the Republic of China in
ISVO's.
early
Since
ccnjuncticn kith manual war
games
well
as
tattle
simultaneously
has
Because
games.
used
been
computer
in
war
manual war games can cnly represent the
as
reality
field
BALFRAM
then,
using
seme
to
extent,
same
the
playing
scenario
them
hopefully
would
elininate seme of the weaknesses of both.
A
lajor difficulty encountered in using EALFRAM was the
determination of attrition rate coefficients
types
of
(e.g.
Army)
different
for
EA1FRAM treats units from the same Service
units.
as being homogeneous regardles cf
their
weapon
characteristics and units frcm different Services (e.g. Army
and Air fcrce)
units
wherein
EA1JRAM
in
supposedly
brought
normalizing
The use of notional
as heterogeneous forces.
to
units from the same Service are
footing
equal
by
pooling
resources by the standard unit is
their
estimation
in the right direction toward the
and
a
step
attrition
of
However, it falls short cf achieving its
rate coefficients.
goal because cf the definition of homogeneity.
An
example
may help tc illustrate this point.
For example, if an infantry
standard
unit.
urit
division
is
used
divisions
notional units.
capability
cf
is
and
This means
an
the
given a value of 1.0, i.e. one notional
and
An armcred division is found to be eguivalent
infantry
as
armored
tc
two
given a value cf 2.0, i.e. two
that
the
casualty
inflicting
division is twice as that cf an
infantry division. However, in terms of other contr itutiens,
an
division may be worth more than two infantry
armored
divisions.
The
use
of
armored
30
divisions
fcr
the
exploitation
victories is a possible case. The
defeat of France by Germany in the Second Wcrld War is an
example cf such an instance. On the other hand, an infantry
tattle
of
division may te equivalent
to
armored
an
division
under
certain ccmfcat sitcations.
Due to its aggregate
respect
this
to
BALFRAM's
nature,
approach
with
problem was to leave the determination of
attrition-rate coefficients
suggest
that this wuold
user.
the
to
increase
seemed
It
to
flexibility
the
and
applicability of BAIFBAM in that the user was free to choose
the
attrition coefficients and simulate many types of
Military operationswhich
In view of the
objectives admirably.
by
command
of
at
was intended to be used, it had achieved its
BilFEAM
relatively
level
However, for more
effective
use
at
lcwer levels of command, BAIFRAM can be improved
employing
existing
other
methodologies
estimate
to
attrition-rate coefficients for different types of units and
under different sets of circumstances.
ICE
was the calculation of
encountered
(index cf combat effectiveness).
Another
status
the
difficulty
or
etc.)
,
the
was
large
a
reflects
ICE
condition
sustaining
experience,
of
a
unit
capability,
of ICE is primarily a matter of
determination
judgement and to
problem
effectiveness
ccmfcat
(training, motivation,
Eecause
extent
a
subjective
one.
The
further complicated when information regarding
the enemy troops concerning these factors is incomplete
can
net
be
relied
upon.
and
Under these circumstances, the
results cf the simulation could easily be tempered to please
would be
Th£ net result of all this
cne*s superior.
tantamount to the negation of
the
purpose
of
the
entire
effort.
One way cf attacking this problem would
methodology
for
estimating
the
31
ICE^
fce
to develop
a
of various types of
units with respect to quantitative and
which
have
a
qualitative
factors
direct bearing on the effectiveness of
to carry en combat.
It is
true
that
(measure
MCE
a
unit
a
of
effectiveness) for such factors is hard to decide on because
it is difficult to devise a acceptable ffesaurement of
these
factors iihich will provide a reasonable approximation to the
BAIIBAM took
ICE.
a
passive approach to this problem as
the case cf attrition- rate coefficients.
in
An active approach
would be to develop a methodology and incorporate it in
the
program for the estimation of ICE of various types cf units.
This is nest desirable on the part of the users.
EALEEAM,
In
ICE is a Multiplicative factor acting upon
the attrition-rate coefficient.
because
the
attrition— rate
It
may
net
coefficient
diainishing marginal return with respect to
ICE.
A
be
should
realistic
have
increasing
a
the
curve such as an exponential might be mere suitable
to descrite this relationship.
32
ESTIMATION OF ATTRITION-RATE COEFFICIENTS
IV.
In
utilization
the
essential
fart
is
of
Lanchester — type model, the
a
determine
to
numerical
values
for
attrition— rate coefficients frcm weapon system
performance data. Two significant developments in this field
appeared during the 1960's, namely, (1) the development of
Bethcdolccy fcr th€ prediction of Lanchester attrition — rate
coefficients frcm weapon system performance data by S.
the development of
Bender (3) and C.
Earfoot (l) and
(2)
methcdclcgy fcr the estimation of such coefficients from
will
Clark (6}
We
Monte Carlo sinulaticn output by G.
discuss these methodologies in this chapter.
Lanchester
.
A.
MABKCV EEEENDEKT FIRE
The purpose of firing a gun is to destroy a target.
the
distribution
hit
is
interest
of
in
weapon
So
system
analysis work. If we could assume that the bit probability
the
is
same for all rounds and each of them is independent
then
of the others,
the
Binomial
distribution
would
be
suitable for the hit distribution.
Let
E
be a random variable denotes the number of
rounds
ttrcet with each round has hit probability p, then
for firing n rounds, the probability that at least one round
hit
the
hit the target is given by
Pr<
B
1
1
)
=
1-Pr( H =
)
33
=
1-(
1-p f
(4.1;
many
circumstances this model is inadequate
because fire can be adjusted and aim pcints for rounds are
net statistically independent.
Eut
in
Bender assumed that
the
firing
process
is
a
Karkov
process that is the weapon system performance depending only
en the cutccne of the last round fired.
=
Erob
(
hit on first round
g =
Erct
(
iiiss
p
then eguaticn
Pr
E
(
>
1
paper
This
=
)
on round|miss en -previous rcund
(4.1)
)
Define
)
may be revised as
1-(
1-p
)
<f~',
for n
>
(4-2)
1
deal with this type of firing process
will
and called it Markov-dependent fire.
E.
ECNDEEȣ HETHCE
Becall
the Lanchester- type equations fcr combat between
two homogeneous forces
dx/dt = -ay with
x (t=0) =x<>
(4-3)
dy/dt =-bj with
In
this
model,
y (t=0)
a
=y
and
b
are
called
the Lanchester
represents the
a
attrtion-rat e coefficient. Fcr example,
rate at
which a single Y weapon system destroys X targets.
It has the diuensicn of
(X
casualties) /( (number of X units)
3±
•
(unit time))
Ecnder has defined A,
random variable, as the rate
a
of
destruction cf X target and its value is given by
A
=
where
to
(4-4)
l/l
is a randcm variable denotes the time for
T
kill
an
destruction
target.
X
would
"average"
The
rate
a
Y
firer
target
of
be the expected value of A, denoted ty
a
and
i = E< A
= E(
)
However, in
a
1/T
(A-S)
)
paper published in 1969,
out the average attrition of equation
Earfoot
(4.5)
pointed
is inadequate as
well as net ffathematically tractable. He suggested
defining
the average kill rate as the reciprocal of the expected time
to destroy
a
=
a
target.
1/E(T)
(4-6)
The reason is that in
distribution
function
Bender's
represents
model
the
the fractions or targets
killed fcr which each rate is used, then the
of the rates should be used.
probability
harmonic
If the probability distribution
function represents the fraction of the time that each
is
used,
arithmatic
the
then
mean
mean of
a
rate
set of attrition
rates will be appropriate.
Eguaticn
a,
(4.6)
agrees with the intuitive definition of
the average attrition rate is the ratio cf the number
targets
killed
in
a
number of battles to the time
large
interval over which the targets were killed.
are
killed and
i-1 and
i
t
of
If
n
targets
is the time interval between which targets
were killed, then
35
n
n
S*'
In a later paper
E( 1)
1
1
n
i
n
.
(4.7)
l
(£/>!
(u)
,
Bender suggested
a
way to calculate
as
B(T)=t*+trth *<th *tf)/PK +({tm+t f )/p). (<1-u)/P K +u-p,
)
C4.8)
where
time tc acguire targets
td =
ti
time tc fire the first round
=
time to fire
tj,=
a
round, given the .preceeding rcund was
hit
time tc fire a round, given the preceeding rcund was
tm =
a
a
aiss
projectile flight time
tj =
p,
first round hit probability
=
the conditional probability of kill, given a hit
pK =
conditional probability of a hit,
preceeding rcund fired hit the target, and
given
the
conditional probability of a
preceeding rcund fired missed the target.
given
the
u
p
=
=
Prof. Tajjlcr stated that if
36
the
hit,
following
assumptions
can te justified,
|
(D
t
=
(2)
ti
=th=t m =t = 1/v, where
(3)
p
=
C
u
=
p,
= ph
,
where
denotes the rate of fire,
v
ph
denotes the single shot
hit
probability, and
U-
<<*)
C
Then equation
E(T)
where
C.
(4.8)
can be simplified as follows
l/(v.p)
=
(4 g)
#
p
=
ph pK
CLARK'S MCEIL
G.
Clark
[6)
probability,
has added another factor, target
Lanchester- type
into
combat
development cf the COMAN (COMbat ANalysis)
The
model is
funcanental
a
ccnbinaticns.
models
in his
model.
concept used in constructing the CCMAN
rate
kill
acquisition
These
for
specified
rates
kiJl
firer/ target —type
are estimated from
simulation data and they provide insights as to the relative
effectiveness
of
various weapon types without resorting to
nuaerous siiulation runs.
Clark points out that for modelling purposes a target is
acguired by a firer when fire can be directed towards the
target's
position.
Acquisition
can
be
accomplished
visually detecting the target so that its position is
37
by
known
then directing fire at the position where the target is
and
actually located.
Ecwever
used.
are
This is the case when direct fire weapons
indirect fire weapons such as artillery
can be fired ever hill masses that obstruct
a
line of
sight
between the firer and acquired target position. So knowledge
of the exact target position can be acquired
by
firing
at
area for targets to be located until fire happens to
likely
be directed at an actual target position by chance.
effects
The
of
using the prctability that
are introduced by
acquisition
target
target
a
unacquired
is
as
a
parameter. Define
=
p
the
probability
unacquired by an individual
g
=
that
a
specific
X
target
is
firer, and
Y
the corresponding probability for a
I
target
X
firer
ccntinaticn,
then
dx/dt = -a5 (1-p x
)
dy/dt=-bx (1-q y
)
where a>C ,b>C,0$p<
1
and 0^q<1.
It can be seen that if
equation
(4. 10)
targets
are
readily
becomes
dx/dt=-ay
dy/dt = -t*
which is the familiar Lancheste^s square law.
38
acquired,
When individual targets become increasingly difficult to
acguire that is the probability of a target being unacguired
assume values close to one, the combat situation represented
by eguaticn
by
(4.10)
Lanchester
is equivalent to the situation envisioned
when
he
formulated
relationship is shown by expressing
function
cf
p
and
g
the
linear
eguaticn
law. This
(4. 10)
as
a
and expanded in a Taylor series about
the points p=1#g=1
dx/dt=f
(p)
=-ay(1-p x )
=-ay(f (1)+f«
(1)
<p-1)+f"0)/2!) (p-1) *.--)
=-ay <-x (p-1) ) =-axy (1-p)
similarly
(4.12)
dy/dt=-fciy (1-g)
39
1-
£ATA BE^UIREMENT 121 COEFFICIENT ESTIMATION
running
simulation or war gaming model, a wide
range cf factors must be considered. Though simplifying
parity assumptions can be made regarding common factors,
Id
a
guantified values must be provided to describe those factors
for which differences exist between the two opposing forces.
This gives rise to the problem of input
data
requirements,
which is crucial tc the estimation of attrition coefficients
for
different
types
of
under
units
different
combat
situations.
The data required for input to simulaticn or war
models
for
the
evaluation
military
cf
problems
gaming
can be
classified into four categories;
A.
HISTCEICil EAT*
Since
tte
formulation of the linear and square laws by
Lanchester in 1914, substantial amount of research work has
the area of mathematical modeling of ccmfcat.
been done
in
Efforts in this respect were primarily centered on the
enrichment of lanchester's theory of ccmtat,
which has teen validated to be adequate to represent the
dynamic process of classic combat by:
extention
and
Helmtcld using data on twenty seven battles which
occurred in the United States between 1759 to 1945 (also
(1)
several subseguent studies
(1Q) (14)
40
)
,
using
Engel
(2)
Seccmd Wcrld
Imo
the
Jima engagement data cf the
fcar,
iillard using data of the land battles of the years
(3)
1SC8, and
1618 to
Weiss using Anerican Civil War data.
(4)
However,
parameters
historical
Lanchester— type
using
cf
data
the
model must be very
combat
-
estimate
to
careful because:
data from different sources usually are
Historical
(1)
net consistent,
It
(2)
difficult
is
to decide hew tc count reserves,
reinf orcenent and saneuvering elements,
Casualties may in some instances have been estimated
(3)
by subtracting "stenjgth after battle" from
battle".
It
is
calculated
value
a
"strenth
from
before
two inaccurate
numbers hence large errors may by expecte.d, and
Ihe duration of engagement is unreliable,
(4)
usually it
is estimated by the author.
these
along
Furthermcre,
discussed th€ uselessness
future
types
ccmbat
of
developed
outcome
singulation
same
historical
of
predictions.
and
war
Helmbold
lines
gaming
for
data
(11)
has
aaking
Meanwhile, different
have
models
since the end of the Second World War.
been
While war
gaming technigues are being energetically extended tc fields
where
in
little
or no previous experience with the technigues
sophisticated
efforts
military
have
fprm
exists,
essentially
no
parallel
been made to compile and analyze data on past
engagements.
This
may
41
be
attributed
to
the
following reasons:
Shen nations were at war with each ether, they would
(1)
engulfed
so
te
in it that they could not afford
to divert
their effort tc data collection,
Ihough much can be and have been learned by studying
(2)
the successes and failures in past wars,
the chance to fight
had
a
a-
nations
few
have
war in the same general situation
second tise, and
Even
(3)
actual
if
cemtat
data
available, it was doubtful whether
significart
they
would
be
impact
military
on
doctrine
operations have been developed.
be
of
any
value to military analysis because of the rapid
advances in science and technology. New weapons
great
wars were
past
on
fought
concept
the
have
of
The kind of war which
will
weapons
will
equipped
forces
ty
and
which
these
with
definitely be different from past wars.
view
In
United usefulness
This
has
sinulaticn
validation
the
resides only in
led
of
models;
it
has
only
in predicting the outcome of future wars.
the
to
war
and
value of historical data
the
above,
the
cf
present
gaming
to
trend
of
using
ccnputer
generate data for military
analysis
E.
L0GIS1ICS EATA
particularly susceptitle to
guantificaticn. Appropriate data on practically every thing
that can be procured, transported, used and consumed exist
Logistics
imput
data
in seme tangible form.
food,
gasoline,
etc.,
are
Items such as equipment, ammunition,
fall into this category.
42
Data such
as distances, means cf transportation,
volume and weight
to
be transported,
tine in transit, etc., are readily available
can be
used
as
and
inputs.
Furthermore,
logistics
reguirement for each type of units can be established and
sithin
placed
preparaticn
reasonable
bounds.
This
processing for use.
and
is cct kncwn hew these
logistic
facilitate
will
However, currently it
factors
influence
combat
capability. In particular, there is no commenly accepted (or
used) prccedure
for modifying
combat capability due to
logistic shortfalls.
C.
UEAPCK ZilA
Weapon data include range, rate or fire, lethality, etc.
Using
characteristics, different types of weapens or
these
weapcn systems can be converted into input data by firepower
sccre
information
ef f
evaluated.
weapons,
of
problem
the
in
characteristics
one's
of
conventional
Hcwever,
and
the
Thus
cover
tactical
of
is complicated.
In
not
the
weapons can be compared and
case
the
protective
significant factors.
cases,
is
forces.
own
areas significant, but troop density
time,
most
In
obtained based en known data and
are
characteristics
ectiveress
methods.
weapon
enemy
en
Estimates
available.
weapon
appropriate
ether
cr
Net only are lethal
the
in
or
addition,
nuclear
area
expesure
at
the
also
are
contamination
effects
which deny the area to both friendly and enemy use must also
be considered.
Since tactical nuclear
weapens
have
never
been used in the past, their psychological effects in actual
ccmbat situation with respect to
the
fight of trccps involved is not known.
morale
43
will
to
Presumably estimates
can be made, but how close these estimates
real effects is not ascertainable.
and
can
be
tc
the
QOALIIAIITJE DA1A
D.
The term qualitative data
refers
to
factors
such
as
discipline, motivation, courage, morale, will to fight, etc.
By
prcfessioral military judgement,
these
factors
can
be
quantified values to represent different levels or
degrees using scaling method. Qualitatve standards
such as
outstanding, superior, good, etc., can be assigned numerical
assigned
values, shich can be
degrade
used
expected
tte
multipliers
as
performance
upgrade
to
But factors
of a unit.
such as the effects of shock and fatigue en
or
personnel;
the
resourcefulness, initiative, and leadership cf the
relative
opposing ccananders; the results of communication or command
control
failure
not
are
susceptible to guantif ication in
that each war is urique in its
own
right.
impact
The
of
factcrs on *ar outcome is immense and very difficult,
these
if net impossible,
to estimate. Probably BALfBAM is the enly
computer *ar gaming model which allows for the consideration
Though
cf some cf these factors.
factcrs
in
a
unfortunately,
inclusion
of
these
simulation or war gaming is essential tc the
representation
adeguate
the
of
ultimate
their
battlefield
impact
is
reality,
beyond
the
imagination cf the human mind.
The
prctlem
cf
data
complex and complicated.
have
been
established
requirements for war gaming is
Except where definite objectives
and quantitative data exist in some
tangible fcrm, the problem appears
to
be
magnitude and deserves a separate treatment.
44
cf
considerable
AGGREGATION OF FORCES
VI.
It was feinted out in the preceeding
validation
cf
chapter
that
Lanchester* s theory of combat had led
enccurageuent of development of simulation
and
war
the
to
the
gaming
models based en the enrichment and extension of that theory.
Such develotnent was clearly in response to the growing need
models
such
for
field
the
in
of
military analysis and
decision caking. New the problem which remains to be
is
the
acgregaticn
of
solved
forces when the forces involved on
either or tcth sides are composed of more than one unit
above division level. In the case of homogeneous forces
are
(i.e.
of
and
forces composed of identical units),
forces
is
not
a
problem;
however,
the
in
aggregation
the
case of
nenhomogeneecs forces, the problem is complicated and lather
difficult.
Several
methodologies
used to deal with the problem in
All
of
these
problem
a
the
been propesed and
nonhemogeneous
represent
methodologies
direction, but none provide
have
case.
steps in the right
satisfactory solution
tc
the
because each methodology has its strengths and none
lacks weaknesses. There is nc commonly accepted
methodology
in existence.
A.
N0TICSA1 ONIT
The concept cf notional unit
(16)
is one
cf
the
several
methodologies being used to address the problem of
aggregaticn cf forces. The major strength cf the approach
existing
that it takes into account all the resources (personnel,
Though there are ether
eguipment and weapons) of a unit.
is
45
to t€ considered,
factors
the approach appears to provide a
reasonable approximation to the
contributing
factors
concerned.
assigned
tc
cf
far
unit
is
what values should
be
of
a
at
approximation
reasonable
a
unit? Since the effectiveness of
a
depends en the type of target against which it is
contribution
the
major
as
different weapons or pieces of equipment in
tfce
arrive
capability
as
capability
the
to
Eowever, the problem is:
tc
order
problem
of
a
the
weapon
used
and
of equipment depends en the
piece
a
tc
ervironment in which it is employed, the cencept of notional
units must re applied with special care and emphasis en the
type of cemfcat in which a unit is
to
engaged
be
and
the
envirenment in which the unit will be fighting.
E.
FIBEECWEE SCORES
The firepewer scores approach appeals tc
(see Stockfisch
and
(17)
further
fcr a
further
references.)
discussion
relative firepower
The
to be based cc actual or experimental data
ccrtribution
the
of
certain
a
are
supposed
with respect to
elusive.
seems
However, the problem
standard weaken.
firepower
of
scores tc be assigned to each type of weapons
can
military
because cf its simplicity and ease of application.
analysts
scores
most
type
a
How
of weapen to a
Bilitary cperation be isolated and singled cut from the many
weapen
involved?
systems
Given
this
firepower sccres should be assigned to
can
a
be
weapon
dene, what
considering
the different types of targets against which a weapen nay be
used?
tank
Fcr example, consider the firepower scores for
gun
and
a
M14 rifle.
a
90MM
If the M14 rifle is chesen as a
standard weapen and assigned a value of 1 , what value should
be
assigned to the 90MM tank gun? If lethality, rate of
fire, motility, protection, type of targets are
seme
basis
cf
cemparison
considered,
exists and a value for the 90MM
46
tank gun may be derived. Military experience
expertise
and
familiarity with the weapons may provide a professional
judgement as to the reasonableness of the estimation, but
and
this nay
C.
as far as one can go.
fce
THE QSE CF SATELLITE MODELS
increased
In view cf the
techrigues
gaming
use
simulation
of
CCHANEX
combat)
model
(CCMiN
cf
and
battalion
sized
used
be
resolution
of
COMANEX is a satellite
conjunction with CABMONETTE,
in
simulation
combat
Carlo
units in crcund
lower
or
Monte
(a
Data
model.
a
high
relating
to
characteristics, combat environment, missicn, etc.,
weapons
particular
fcr a
CARMONETTE
Extended)
are examples of such models.
tc
problem
forces lies in the use of satellite mcdels.
cf
sinulaticn
war
in the analysis of military problens, it
appears tc the authors that the solution to the
aggregation
and
mix
performs
CAEMCNETTE
CAEMONETIE.
fcrces
opposing
of
a
input
are
to
prespecified number of
replications cf
the
replication,
time- sequenced casualty history identifying
a
the time at which
the
killer
type.
CCMAHEX which
a
It
battle.
outputs,
then
for
each
casualty occurred, the casualty type and
output
This
massages
the
in turn, input to the
is,
data
outputs
and
a
set
of
Lanchester-t jpe parameters which represent, essentially, the
kill rates fcr each firer/target combination in the battle.
paraneters are then used in DBM (Division Battle Kodel)
approach
ground ccmbat assessments. The advantage of this
The
traditional
over
scores
is
developed
that
by
methodology
CAHMONETTE
environment, including
frcii
and
weapon
the
based
unit
reflect
weapon
firepower
performance
measures
on
variations in the ccmbat
synergistic
effects
resulting
the entlcyment of various combinations cf weapons.
47
D.
THE APPLICATION CF BONDEB»S APPROACH IN EALFRAM
Though
EAIFRAC
heterogeneous
forces
reality it is
cnly
has
the
as
well
capability
homogeneous
as
homogeneous
a
handling
of
forces, in
because
model
of
the
aggregated fashicn in which it handles hetercgeneous forces.
Heterogeneous force in BALFRAM
ccoponent
different
refers
Services
frco
cf the armed forces,
the Army, Aii Force and Navy.
types
units
to
Units
namely,
classified
are
the
into
grcund, air or naval according tc the Services to
as
which they telcng.
Units which belong to
Service
same
the
treated as homogeneous though they may be equipped with
are
weapons cf different characteristics such as lethality, rate
of
range,
fire,
BALFRAM's definition of
protection, etc.
homogeneous and heterogeneous forces is different frcm
is
generally
assumed
ailitary analysts.
for
force to be
firepower,
researchers and
in his mathematical
For example,
hcacgeneous
identical
operation
most
between two homogeneous forces, Prof.
combat
defined
by
Gordon
units.
a
force
force
to
of
J.
acdels
Taylor
composed
force
a
Clark
M.
composed
mobility,
be
what
of
defined hetercgeneous
weapons
with
protection,
and
different
detection
characteristics in the general context of land combat.
Bonder extended Lancheste^s original formulation cf the
linear and scuare laws to incorporate target acquisition
time,
rate cf fire, and conditional kill probability in the
calculation cf Lanchester-type attrition-rate coefficients.
His
definition of homogeneous and heterogeneous forces was
also in the general context of land combat and agrees with
these
of
Ercf.
modeled the ccmbat
J.
Taylor
process
Gordon
and
in
a
M.
detailed
Clark.
fashion
Ecnder
while
Eonder initially used the
EALFRAM in ar aggregated fashicn.
arithmatic mean of the time required to destroy a target as
the
estimate of the Lanchester attrition-rate coefficient.
48
However, this
untractable,
approach
turned out to be mathematically
an explicit expression fcr the Lanchester
and
attritioE-rate coefficient could not be obtained.
Later
Barfoot suggested using the harmonic mean of
the time
required tc destroy
a
target as the estimate of the
average
attrition- rate coefficient. Bender modified his formulation
acccrding tc Earfcct*s suggestion.
Eoth
EAIFEAM
and
Bonder's
model
are
based'
extention and enrichment of Lanchester's theory
of
on
the
cemtat.
underlying difference in the definition of
hemegeneens and heterogeneous forces led to different basic
However,
the
in the two models. As a result, the application
assumptions
of
Ecnder's
challenge
apprcach
in
BALPRAM
presented
than was originally anticipated.
in the levels cf details covered in the two
ccnplicated
the
problem.
The
beyond the scope of this paper.
H9
a
greater
The differences
models
further
amount of work involved is
VII.
The study of war will
despite
become
never
efforts
striving
the
PINAL REMARKS
of
scientists and military analysts.
inability
operation
science
researchers,
reason
The main
is
Another reason is
vast number of variables present in a ccmbat situation.
These variables do
decree,
not
Heights
or
recur
fixed
in
relative
of
fashion,
importance.
amount,
Therefore,
although varicus kinds of wars have been fought in the
and
the
of man to predict how an individual will react in
stressful and cangerpus combat situation.
the
exact
an
most
past
Hill continue to be fought in the future,
likely
man's understanding of the process
of
never
will
war
be
adequate and complete.
In man's guest for insight into the process of war, both
formulation of combat models and techniques of
mathematical
simulation ard war gaming have been
the
been
area
extensively
used.
mathematical models, substantial interest has
of
maintained
since
theory
mathematcial
Lanchester
coefficients,
this
paper
published
first
his
Among the various methods
of warfare.
suggested for the estimation of
Lanchester
considered
— type
attrition
the Markov-dependent
fire and Ecnder's and Clark's models in particular.
area
In
In
the
of simulation and war gaming, sophisticated techniques
Now war
gaming
and
increasingly employed.
sinulaticn have become standard practices in the analysis of
this paper
Of all the existing models,
military problems.
have
been
discussed
EAIFBAM
feasibility
estimation
EAIfBAM.
of
in
applying
some
detail
Bonder's
and
explored
methodology
for
the
the
Lanchester attrition— rate coefficients in
It was found that BA1PRAM considers theater— level
cf
50
ccabat in a very aggregated fashion, while Ecnder s approach
Thus,
applies tc fire fights in a more detailed manner.
1
Benders
methodology
is
not
applicable
directly
aggregated constat model such as BALFRAM,
very
heterogeneous
example,
Hence,
a
conglomeration
division pr
apparently
a
a
corps
different
as
which
in
models
an
the
of forces found in, for
a
homogeneous
approach
must
force.
be used to
estimate attrition- rate coefficients in such Lanchester-type
force- planning models. This problem is a state-of-the-art
problem in
cemtat
modelling,
beyond the scope of this thesis.
51
and
further
discussion
is
LIST CF FIGURES
1.
System Organization
15
2.
EAIFEAM Erocess.....
22
3.
Sensitivity Analysis
29
52
LIST OF REFERENCES
1.
Lanchester
Attrition - Rate
Coefficient: Scjne Comments on Seth Bonders Paper and a
Suggested Alternate Method",
Cpns . Bes i# v.
17, p.
Earfoot,
C.
888 tc 6S4,
2.
the
13th
November,
v.
Ecnder,
S.
An Overview of Land Battle Modeling in
•
Proceedings
OS",
Sympcsiua,
3.
1969.
Bender,
S.
The
••
Coefficient",
Qpns.
,
15,
v.
1974.
Attrition— Bate
Lanchester
Res.
Operations
Arm y
s_.
73 to 88,
p.
The
"
U.
221 tc 232,
p.
.1967.
4.
Bender,
S.
Qpns.
5.
fles_.,
v.
18,
Mean
p.
Lanchester Attrition Eate",
179 to 181,
The oretic
Game
Chaiken,
P.
The
"
1970.
Analysis
Military
of
Ope rations Des cription of the B attlefie ld Mod els
to
43,
Stanfprd Research Institute,
flenlo
p.
25
Park, Ca.,
1966.
6.
Tie
Clark,
G.
Combat
Analysis
Model,
Ph.
D.
Dissertation, Tie Ohio State University, 1968.
7.
J.
Opnsj
8.
A.
Engel,
"
Res_.,
v.
Verification
2,
p.
of
163 to 171,
Lanchester's Law",
1954.
Simulation in Warx Business, and
McGraw Hill Book Coopany,
120,
V enture
fiausrath,
Politics, p.
A
1
to
1971.
9.
R.
Helmtcld, "Lanchester Parameters for Some Battles of
the Last Iwo Bundred Years," Combat Operations Research
53
lechnical
Group,
Operations,
Inc.,
-
CORG
SP
—
122,
Febrcary 1961.
10.
11.
Belmtcld,"Bistorical Data and Lanchester's Thecry of
Combat,
Eart II," Combat Operations Research Group,
Technical Operations, Inc.,
COBG-SP-190, August 1964.
B.
Helmbcld,
B.
Some
"
Observations
Lanchester's Theory for Prediction",
12,
12.
778 tc 781,
p.
Helnbold,
B.
EquaticDS",
12.
B.
14.
R.
14,
Belmfccld,
"
Res,.,
v.
13,
of
Bes^.,
v.
Lanchester's
cf
857 to 859,
p.
1965.
Attrition Model",
1
624 to 635,
p.
Cjcns^
1966.
"Decision in Battle: Breakpoint Hypotheses
Engagement
and
Modification
'Universal
A
Opns.
Use
1964.
A
Op^ns.
Belntold,
Res., v.
"
the
en
Termination
Data," B-772-PB, The RAND
Corporation, June 1971.
15.
F.
Lanchester, "Aircraft in Warfare: The Dawn cf the
fi.
Fourth
"Engineering
2138 tc 2148
Mahtematics,
422
98,
Principle
The
Bc.V.,
Arm
(see also p.
IV,
Vpl.
423
to
(reprinted on p.
(1914)
2148 to 2157)
Newman
J.
Concentration,
of
of The iorld of
(Ed.)
Siacn
,
and
Schuster, New Yprk, 1956).
16.
E.
Means,
C.
Phillips
and
Young,
S.
BALFBAE Oser
Manual for the Staff of the Commander in Chie f Pacific,
p.
1—1
to B-15,
1974.
Park, Ca.,
17.
J.
Stanford Research Institute, Menlo
Stockfisch, Models, Data, and Bar:
Study cf Conventional Forces,
Prepared for United States
p.
6
A
tc
Critique cf The
27,
A
Seport
Air Force Project Band
B-
1526-PB, Santa Monica, Ca., 1975.
18.
J.
Taylcr
Solution
of
and
G.
Varible
Brown,
"
Canonical Methods in the
Coefficient
54
Lanchester — Type
19.
Eguaticcs
cf
44 tc 4S,
1976.
J.
Hodern Warfare",
"Mathematical
Taylor,
Cpns. res., v.
Models
of Combat," L€cture
Notes for 0A4654, Naval Postgraduate School,
Ca.,
20.
J.
1 S
1
Bes_.,
21.
H.
v.
A.
1
22, p.
Heiss,
Hilscn,
Lanchester- Type Equations for
Opns.
with Variable Coefficients",
Solving
"
Rarfare
Civil War",
22.
Monterey,
5-
laylcr,
•Modern
24, p.
"
756 to 770,
1974.
Combat Model and Historical Data: Ihe OS
OjanSj.
ijar
Res^.,
v.
Gaming, p.
14,
p.
759 to 790,
13 to 29,
Ltd,Harircndsworth, Middlesex, England,
55
1966.
Penguin Ecoks
1970.
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Defense Documentation Center
Cameron Station
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2
Library (Code 0212)
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Dept of Operations Research & Admin Sciences
Naval Postgraduate School
Monterey, California 93940
1
Professor J. B. Tysver (Code 55Ty)
Dept of Operations Research & Admin Sciences
Naval Postgraduate School
Monterey, California 93940
1
Chairman, Code 55
Dept of Operations Research
Naval Postgraduate School
Monterey, California 93940
2
&
Admin Sciences
Col Lee, Yin-Chu
P.O. Box 7022-5
Taipei Taiwan
Republic of China
1
Lt Col Pi, Yu-Kung
P.O. Box 7022-5
Taipei Taiwan
Republic of China
1
Gen T. S. Yen
P.O. Box 7022-5
1
,
,
Taipei Taiwan
Republic of China
,
Professor Chien Lih
2
T-amkang College of Arts and Sciences
Tamsui Taipei Taiwan
Republic of China
,
,
1
Mr. E. H. Means
Stanford Research Institute
333 Ravenswood Avenue
Menlo Park, California 94025
56
138095
The estimation of
Lanchester attritionrate coefficients for
an aggregated combat
363 3 3
8
Thesis
U435 Lee
The estimation of
Lanchester attritionrate coefficients for
an aggregated combat
model
3
6
u
ise
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thesL435
The estimation
of Lanchester attntion-r
3 2768 002 12016 4
DUDLEY KNOX LIBRARY