ACCURACY MODELING OF THE 120MM M256 GUN AS A · PDF fileProviding America Advanced Armaments...
Transcript of ACCURACY MODELING OF THE 120MM M256 GUN AS A · PDF fileProviding America Advanced Armaments...
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Providing America Advanced Armaments for Peace and War
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ACCURACY MODELING OF THE 120MM M256 GUN AS A FUNCTION OF BORE CENTERLINE PROFILE
BRIEFING FOR THE GUNS, AMMUNITION, ROCKETS & MISSILES SYMPOSIUM - 25-29 APRIL 2005
RONALD G. GAST, PhD, P.E.SPECIAL PROJECTS TEAM, WEAPONS, SYSTEMS AND TECHNOLOGY DIRECTORATE
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
BACKGROUND AND MOTIVATION FOR THE CONDUCTION OF THIS STUDY
It is a well known fact that the centerline profile of the bore affects the in-bore dynamics and exit conditions of the projectile.
The exit state of the projectile serves as initial conditions to the projectile’s flight path to its intended target.
A relatively accurate and quick running model of this would be beneficial to assess accuracy, especially for the newer, lightweight ordnance weapons.
Since simulations are just mathematical models of reality, validation is an extremely important aspect of their use.
The subject weapon has a plethora of field generated experimental data regarding accuracy and dispersion for several unique gun tubes.
We are submitting a validation effort of our modeling techniques through the attempted reproduction of this data using dedicated models and statistics knowing full well that replication of field generated data is most difficult.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
M1A2 TANK IN DESERT CAMOFLAUGE
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
DESCRIPTION OF THE ANALYSIS MODELSSimulation of Barrel Dynamics (SIMBAD)
A quick running finite element code, which employs beam elements for the gun tube and a variety of options for modeling the projectile, mount and cradle.
Designed to predict the motion of the gun barrel and projectile during the firing phase, ultimately passing the exit conditions of the projectile to the flight prediction model.
Barrel employs three dimensional beam finite element structural representation using an Euler-Bernoulli formulation.
Shot is represented as a two piece flexible structure consisting of a projectile and sabot, both of which employ beam finite element formulation.
The dynamic equations for barrel, sabot and projectile are cast in a standard matrix form.
Since this type of problem is highly non linear, a modified Runge-Kutta time marching integration technique is employed.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
GUN BARREL MODEL IN SIMBAD
209 INCHES LONG
OFFSET BREECH GUN SUPPORT POINTS
(~53 INCH WHEELBASE)
SIMBAD FINITE ELEMENT MODEL: 40 NODES; 41 ELEMENTS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
PROJECTILE MODEL IN SIMBAD
GUN TUBE
FINS SABOT
PENETRATOR
FRONT BORE RIDERREAR BORE RIDER
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
DESCRIPTION OF THE ANALYSIS MODELSBOOM
A six degree of freedom (dof) rigid body aerodynamics code used to predict the external flight path of ordnance projectiles.
The six dof’s are comprised of three body inertial position coordinates as well as three Euler angle body attitudes.The dynamic equations are written with respect to body a frame coordinate system.The total applied force is composed of weight and body aerodynamic force terms (lift, drag, etc).A considerable amount of empirical data (which is projectile dependent) used for lift and drag calculations has been generated at the Army Research Lab Test Center.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
RIGID PROJECTILE MODEL IN BOOM
φ
θψ
IKr
IJr
IIr
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
DESCRIPTION OF THE ANALYSIS MODELSTRANSFER OF DATA FROM SIMBAD TO BOOM
Each of the computer codes are stand-alone employing their own coordinate systems.
An interface routine was developed through a coordinated effort among Benet Labs and the developers of the two codes.
This routine employs several matrix equations to transfer projectile’s exit conditions (i.e. displacement, velocity, etc) from the SIMBAD coordinate system into the coordinate system used by BOOM.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
FUNCTIONAL FIT IS OVER CONSTRAINED(PASSES THROUGH EACH DATA POINT)
DATA POINTS
MEASUREMENT ERROR
FUNCTIONAL FIT IS UNDER CONSTRAINED(MISSES MOST ERROR BARS)
DATA POINTS
MEASUREMENT ERROR
FUNCTIONAL FIT IS APPROPRIATELY CONSTRAINED(PASSES THROUGH ERROR BARS BUT NOT THROUGH EACH POINT)
DATA POINTS
MEASUREMENT ERROR
STATISTICAL METHODS FOR GENERATION OF SIMULATION DATABORE PROFILE FUNCTION
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
ESTIMATION OF THE BORE CENTERLINE PROFILEBore profile centerline is derived from the inspection measurements taken during manufacture. There are usually 23 points (xi , yi) along the gun tube for which measurements are taken.
These measurements are used as the ‘data’ for a least squares polynomial fit (pn) per the following equation:
pn(x) = ao + a1x + a2x2 + a3x3 + ….. + an-1xn-1 + anxn
Several polynomial fits are generated (i.e. n = 2,…,14)
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
ESTIMATION OF THE BORE CENTERLINE PROFILE
The coefficients for each polynomial order is determined by minimizing the residual (defined below) for each fit.
Σ[yi – pn(xi)]2i = 0
22
The change in residual from one order to the next is compared.
To determine which polynomial order yields the appropriate fit an F-test is conducted.
When the improvement from consecutive orders does not change significantly (using a 10% significance level) the lower order polynomial is chosen and the testing is terminated.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
BORE CENTERLINE PROFILE DATA AND POLYNOMIAL FIT FOR TYPICAL GUN TUBE
BORE PROFILE HORIZONTAL DIRECTION
AXIAL LOCATION FROM MUZZLE (mm)0 1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0BORE PROFILE VERTICAL DIRECTION
AXIAL LOCATION FROM MUZZLE (mm)0 1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
STATISTICAL METHODS FOR GENERATION OF SIMULATION DATABALLISTIC PRESSURE AND MUZZLE VELOCITY
Peak pressure and muzzle velocity was recorded for each round in the test.
Each round type and bore profile configuration was fired 3 times on 3 occasions.
This provided the basis for developing a random array of muzzle velocity scale factors applied to the ballistic driving force for each simulated shot.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
STATISTICAL METHODS FOR GENERATION OF SIMULATION DATAPROJECTILE STIFFNESS AND CLEARANCE
The front and rear bore rider diameters have nominal dimensions with tolerance values as do any other engineered part.
A normal distribution of the diameters was assumed with the nominal value set at the midpoint of the diameter range.
The standard deviation of the distribution was set at one-third of the tolerance which would keep nearly all of the random diameter values within the tolerance range.
We had no way of knowing the actual values of these diameters.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
COMPARISON OF TEST DATA TO SIMULATED RESULTS
The simplest method of comparing simulations to test data is in the form of ‘target’ plots indicating the angular offset from the aim point of the data and simulations at the target location.
These ‘target’ plots employ a 2.00 milli-radian square window with the aim point shown as a green cross.
For each gun tube bore profile there are 3 sets of 3 shots each for the test data and a 10 shot simulation employing the statistical variances in the input values previously discussed.
A total of 20 configurations were compared but only a few will be presented and discussed here.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #1: PROFILE
BORE PROFILE HORIZONTAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
0.8
BORE PROFILE VERTICAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
0.8
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #1: LOAD / PROJECTILE DISTRIBUTIONS
1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
ED
RIV
E B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
1 2 3 4 5 6 7 8 9 10PE
RC
ENT
CH
AN
GE
BA
LLIS
TIC
S (%
)-1.0
-0.5
0.0
0.5
1.0
SHOT NUMBER (--)1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
EC
ENTE
RIN
G B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
BALLISTIC LOAD DISTRIBUTION
DISTRIBUTION IN DRIVE BAND DIAMETERS
DISTRIBUTION OF CENTERING BAND DIAMETERS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
RESULTS for TUBE #1: DATA
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
SIMULATIONS
RESULTS for TUBE #1: DATA & SIMULATIONS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #2: PROFILEBORE PROFILE HORIZONTAL DIRECTION
AXIAL LOCATION FROM REAR FACE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
0.8
BORE PROFILE VERTICAL DIRECTION
AXIAL LOCATION FROM REAR FACE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #2: LOAD / PROJECTILE DISTRIBUTIONS
DISTRIBUTION IN DRIVE BAND DIAMETERS
1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
ED
RIV
E B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
BALLISTIC LOAD DISTRIBUTION
1 2 3 4 5 6 7 8 9 10
PER
CEN
T C
HA
NG
EB
ALL
ISTI
CS
(%)
-1.0
-0.5
0.0
0.5
1.0
DISTRIBUTION OF CENTERING BAND DIAMETERS
SHOT NUMBER (--)1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
EC
ENTE
RIN
G B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
RESULTS for TUBE #2: DATA
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
SIMULATIONS
RESULTS for TUBE #2: DATA & SIMULATIONS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #3 PROFILE
BORE PROFILE HORIZONTAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
BORE PROFILE VERTICAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
0.8
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #3 LOAD / PROJECTILE DISTRIBUTIONS
1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
ED
RIV
E B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
1 2 3 4 5 6 7 8 9 10PE
RC
ENT
CH
AN
GE
BA
LLIS
TIC
S (%
)
-1.0
-0.5
0.0
0.5
1.0
SHOT NUMBER (--)1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
EC
ENTE
RIN
G B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
BALLISTIC LOAD DISTRIBUTION
DISTRIBUTION IN DRIVE BAND DIAMETERS
DISTRIBUTION OF CENTERING BAND DIAMETERS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
RESULTS for TUBE #3: DATA
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
1.5
TEST DATA
SIMULATIONS
RESULTS for TUBE #3: DATA & SIMULATIONS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #4 PROFILE
BORE PROFILE HORIZONTAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
0.0
0.2
0.4
0.6
0.8
BORE PROFILE VERTICAL DIRECTION
AXIAL LOCATION FROM REAR of TUBE (mm)
1000 2000 3000 4000 5000
CEN
TER
LIN
E PR
OFI
LE (m
m)
-0.2
0.0
0.2
0.4
0.6
0.8
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILETUBE #4 LOAD / PROJECTILE DISTRIBUTIONS
1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
ED
RIV
E B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
1 2 3 4 5 6 7 8 9 10PE
RC
ENT
CH
AN
GE
BA
LLIS
TIC
S (%
)
-1.0
-0.5
0.0
0.5
1.0
SHOT NUMBER (--)1 2 3 4 5 6 7 8 9 10
DIA
MET
RA
L C
HA
NG
EC
ENTE
RIN
G B
AN
D (m
m)
-0.2
-0.1
0.0
0.1
0.2
SHOT NUMBER (--)
TOLERANCE RANGE
TOLERANCE RANGE
BALLISTIC LOAD DISTRIBUTION
DISTRIBUTION IN DRIVE BAND DIAMETERS
DISTRIBUTION OF CENTERING BAND DIAMETERS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
0.0
0.5
1.0
1.5
2.0
2.5
TEST DATA
RESULTS for TUBE #4: DATA
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
0.0
0.5
1.0
1.5
2.0
2.5
TEST DATA
SIMULATIONS
RESULTS for TUBE #4: DATA & SIMULATIONS
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
SUMMARY OF INDIVIDUAL TUBE RESPONSES
These four cases span the best to the worst in regard to accurately simulating test results.
Reiterating considerable amount of data, which impacts the test is unknown.
Projectile specifications were ‘guessed’ using nominal values and tolerances.
As shown in the simulations, band diameters that are out of tolerance tend to indicate shot impact locations that reside on the outskirts of group distributions.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
STATISTICAL ANALYSIS OF PREDICTIONS AND TEST DATA
The analysis and discussion of these four cases does not allow one to claim the validity of the model.
It would be impossible to predict with a great degree of reliability any one shot, however, trends in shot patterns may offer more representative information.
To this end I suggest that we compare mean impact and dispersion values for the test and simulation groups.
We have nearly 200 test and simulation shots to use in this averaging process.
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
MEAN IMPACT LOCATIONSFOR TEST DATA
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL
IMPA
CT
(mil-
rads
)
0.0
0.5
1.0
1.5
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
MEAN IMPACT LOCATIONS FOR SIMULATED RESULTS
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL
IMPA
CT
(mil-
rads
)
0.0
0.5
1.0
1.5
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
DIFFERENCE IN MEAN VALUES(TEST - SIMULATION)
HORIZONTAL IMPACT (mil-rads)-1.0 -0.5 0.0 0.5 1.0
VER
TIC
AL IM
PAC
T (m
il-ra
ds)
-0.5
0.0
0.5
1.0
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
DISPERSION VALUES FOR TEST RESULTS
HORIZONTAL DISPERSION (mil-rads)0.0 0.1 0.2 0.3 0.4 0.5
VER
TIC
AL
DIS
PER
SIO
N (m
il-ra
ds)
0.0
0.1
0.2
0.3
0.4
0.5
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
DISPERSION VALUESFOR SIMULATED RESULTS
HORIZONTAL DISPERSION (mil-rads)0.0 0.1 0.2 0.3 0.4 0.5
VER
TIC
AL
DIS
PER
SIO
N (m
il-ra
ds)
0.0
0.1
0.2
0.3
0.4
0.5
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ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILECOMPILATION OF RESULTS FOR ALL 20 CASES
DIFFERENCE IN DISPERSION(TEST - SIMULATION)
HORIZONTAL DISPERSION (mil-rads)-0.1 0.0 0.1 0.2 0.3 0.4
VER
TIC
AL D
ISPE
RSI
ON
(mil-
rads
)
-0.1
0.0
0.1
0.2
0.3
0.4
ISO 9001 CertifiedFS15149
ARDECARDECProviding America Advanced Armaments for Peace and War
42
ACCURACY MODELING OF THE 120mm M256 GUN AS A FUNCTION OF BORE CENTERLINE
PROFILE
DISCUSSION AND CONCLUSIONS
An attempt was made to validate coupled simulation routines for predicting projectile impact locations as a function of the bore profile of the gun tube.
Predictions were made for individual shots as well as an averaging method applied to groups of shots.
Mean and dispersion values were compared, the results of which indicated the following:
In 70 percent of the cases the difference between predicted and simulated mean values was equal to or less that 0.50mr
In 60 percent of the cases the difference between predicted and simulated dispersion was less than 0.25mr
Given the level of uncertainty of several parameters we feel that these results are quite good.
ISO 9001 CertifiedFS15149
ARDECARDECProviding America Advanced Armaments for Peace and War
43