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SAD" A285 441
Pitch and Roll Damping Coefficientsof the Australian 81 mm Improved
Mortar Projectile
David A. Pierens
DTICS ELECTE
OCT 1
G
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I FOR PUBLF.IC 1UllA'
Cc.rnr ..w. ot
94-32065
DEPARTMIENT ()I DW- :N,.
DEFENCE SCIEN(CE AND r-(FHN() ()GY ()RG\NISAI ION
Pitch and Roll Damping Coefficients of theAustralian 81mm Improved Mortar Projectile
David A. Pierens
Aeronautical and Maritime Research Laboratory
ABSTRACT
Technical Report
This report presents roll damping coefficients and pitch damping coeffic~entsobtained from dynamic rolling tests and static wind tunnel tests of theAustralian 81mm Improved Mortar Projectile, IMP. An 80% scale model wasused in the dynamic roll tests and a full scale model was used in the static windtunnel tests.
•- /1 For
APPROVED FOR PUBLIC RELEASE , ABco,';iiCcd []
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Published by
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GPO Box 4331Melbourne Victoria 3001 Australia
Telephone: (03) 626 700CFax: (03) 626 7999 0© Commonwealth of Australia 1994AR No. 008-330May 1994
0
APPROVED FOR PUBLIC RELEASE
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CONTENTS
LIST OF FIGURES .................................................................................................... i
LIST OF TABLES ........................................................................................................ ii
NOM ENCLATURE .................................................................................................. iii
FORCE AND M OM ENT AXIS SYSTEM .................................................................... Hi
1. INTRODUCTION ............................................ 1
21 TEST DETAILS ..................................................................................................... 1
2.1 W ind Tunnel ....................................................................................... ........ I
2.2 M odels ......................................................................................................... !
2.3 Experimental Technique ...................................................................................... 1
2.3.1 Roll Damping ............................................................................................... I
2.3.2 Pitch Damping ......................................................................................... 2
3. DISCUSSION OF RESULTS ............................................................................ 2
3.1 Roll Damping ................................................................................................ 2
3.2 Pitch Damping .............................................................................................. 2
4. CONCLUSION .............................................. 3
REFERENCES ...................................................................................................... 4
APPENDIX A DERIVATION OF CIp S
APPENDIX B DETERMINATION OF ROLL BALANCE BEARING FRJCTION
APPENDIX C DERIVATION OF Cm,
DISTRIBUTION LIST
DOCUMENT CONTROL DATA
S
O
0
- - d I" i •l
i4
List of Figures
1. 80% 81rmm mortar model and roll balance
2. Roll balance
3. Roll damping coefficient, C11,. vs Mach no.
4. Pitch damping coefficient, Cm., vs Mach no.
List of TablesI. Roll damping coefficient, C1p
2. Pitch damping coefficient, Cmq
p
Nomenclature
C1 rolling moment coefficient, torque coefficient
C10 static rolling moment coefficient
Ci P roll damping coefficient
Cmq pitch damping coefficient
93 drag force
I rolling moment
L lift force
mn pitching moment
X axial force
Z normal force
0 pitch angle (deg)
Force and Moment Axis System
Xp
D
520.43 mm
202.5 mm
0 90.45 mm ~jI
C.G. location on full scale projectile
il
° S
1. IntroductionThe Australian Army's Engineering Development Establishment (EDE) is working withAustralian Defence Industries Pty Ltd (ADI) to develop and produce a new improved 81ummmortar projectile to replace the M374 High Explosive (HE) round. The Weapon AerodynamicsDiscipline of the Aeronautical Research Laboratory (ARL) was requested by ExplosiveOrdnance Division (EOD) of Materials Research Laboratory (MRL) to determine pitch androll damping data (Cmq and C1 P respectively) for the 81mm mortar from wind tunnel tests. Thedata will be added to existing static aerodynamic data obtained from previous wind tunnel testsof an 80% and 100% scale mortar model (references I and 2), and will be used to model theflight behaviour of the mortar and to establish its stability and range and the effect of launchtransients.
2. Test Details
2.1 Wind Tunnel
The wind tunnel used for these tests was the ARL-Salisbury SI wind tunnel which is a closedcircuit continuous operation tunnel. The working section has dimensions of 380 mm x 360 mmwith slots and has the capability for Mach numbers of 0.35 to 1.0 and 1.4 to 2.8. Tunnel flowconditions are set and recorded using a static pressure port upstream of the model, a pitot tubelocated upstream of the contraction, and a temperature probe in the settling chamber. Themodel was positioned in the working section by a pitch and roll mechanism located beneath theworking section.
2.2 Models
Models tested were an 80% scale metal model aaid a full scale metal model. Both models weredesigned and manufactured at ARL, based on drawings of the full scale Improved MortarProjectile (IMP) supplied by EDE and ADI 80% scale and full scale IIL 18622-022 fuzes andDE 132410018 (extruded, canted metal) fins were attached to the corresponding scale model.
2.3 Experimental Technique
2.3.1 Roll Damping
Roll damping coefficients, Cly were obtained from dynamic wind tunnel tests carried out withan 80% mortar model attached t,, a roll balance as shown in figures 1 and 2. 5
The roll balance is fitted with a !.-kc ','nich consists of an expanding fibrous ring operated bycompressed air working on pistons in the balance shaft. With the brake on, the wind tunnelwas started, and once the desired Mach num her was reached, the brake was released, allowingthe model to accelerate from rest to a constant roll rate. During this time, roll rates andcorresponding times were recorded and saved to disk. Tests were carried out at Msch numbersof 0.5, 0.7, 0.8, 0.9 and 0.95, which encompasses the flight speed range of the 81mm IMPmortar, at pitch angles of 0', 5' and 100
Values of CI were calculated ftom the dynamic rolling data, combined with static rollingmoment daia obtained fior reference 1. A detailed descriftini of the d&riviwon is given inA ppendix A.
IS
2.3.2 Pitch Damping
Pitch damping coefficients were calculated using the technique given in reference 4. This usesstatic aerodynamic lift data foi lifting surfaces and the body acting separately to determine thecontribution of each to the overall pitch damping.
The fin lift characteristics were determined from wind tunnel tests on a ful! scale model. Testswere conducted at Mach numbera of 0.5, 0.7, 0.8, 0.9 and 0.95 and through a pitch angle rangeof-5' to +50, first on the model with fins attached, and then with a plain cylindrical tail piece(no fins) attached. The difference between the "fins on" and the "fins off" lift curve slopes wastaken to be the lift curve slope of the fins alone operating in the body wake. These tests wereconducted as part of a larger test program, and are described in more detail in reference 2.
Appendix C describes the theoretically based derivation of the body lift wontribution, and theuse of the fin and body contributions to calculate the overall pitch damping coefficients.
3. Discussion of Results
3.1 Roll Damping
Values of Ci , derived from the method described in Appendix A, are presented in table I andp'plotted in figure 3.
Mach Roll Damping Coefficient, C1,P
No. CE = 0 a0 = 5° a = 10 ,
0.50 -0.245 -0.242 -0.2560.70 -0.259 -0.256 -0.281
0.60 -0.268 -0.260 -0.302
0.90 -0.268 -0.270 -0.299
0.95 -0.300 -0.314 , -0.347
Table 1: Roll damping coefficient, Clp
Estimates of the static rolling moment, C1o, can be obtained from the dynamic rolling momentdata by extrapolating a least squares straight line fit to die data back to zero roll rate (seefigure A3). The values of C1. so obtained differ from C,,l's report•d in reference I by up to10%. This gives a useful estimate of the uncertainty in using these data to calculate rolldamping, therefore Clp values stated above should be regarding as having uncertainties of the •order of ± 10%.
3.2 Pitch Damping
Values of C N derived from the method described in Appendix C are presented in table 2 andplotted in figure 4. •
2
Mach CNo.
0.50 -32.40.70 -39.7
0.80 -41.4
0.90 -49.3
0.95 -49.4
Table 2: Pitch damping coefficient, CIN
Figure 4 also shows values of C N for an M374 81mm mortar projectile taken fromreference 3. Although this is a different projectile shape, the similarities are sufficient to expectthe values of C to be similar, Comparison of the two sets of data shows that for Machnumbers up to 0.1, reasonable similarity is observed, but differences of practical importanceexist at the higher Mach numbers. The divergence of results above Mach 0.8 may be due tothe unusually large model size, resulting in significant wind tunnel wall interference effects atthe higher Mach numbers. Reference 2 discusses this in more detail. Because of these effects,and the uncertainties inherent in the application of static, data to the estimation of dynamicparameters, the pitch damping results presented here are estimated to have uncertainties of upto ±20%. However, for a fin-stabilised ballistic projectile of this type, this level of uncertaintyis acceptable in terms of predicting the overall flight trajectory.
4. Conclusion
Roll damping coefficients obtained from dynamic wind tunnel tests at various Mach numbersand pitch angles are presented in table I and figure 3. These data are estimated to containunce.tainties of ± 10% due to a lack of low roll rate data, and uncertainties in the measurementof roll bearing friction.
Values for pitch damping coefficient obtained using the theory present-d in Appendix C (asobtained fiom reference 4) and static wind tunnel results, are presented in table 2 and figure 4.These data are estimated to contain uncertainties of up to +20% due to wind tunnel wallinterference and uncertainties inherent in the method. However, from comparison with otherexperiments, it appears that the theory presented in Appendix C produces acceptableapproximations for pitch damping coelficients for configurations and conditions consideredhere.
3
References
1. Walter, S.R., Wind Tunnel Testing of the 81mm Improved Mortar Projectile, ARL-FLIGHT-MECH-TM-430, October 199 1,
2. Pierens, D.A., Aerodytiamic Evaluation of Production Fuzes and Fins for the 81mmImprovedMortar Projectile, AR-008-331 (document in preparation).
3. Rhodes, P., An Aerodynamic and Stability Assessment of the 81mm Mortar Bombfitted with the M734 Fuze, TP 27298, Hunting Engineering Limited, UK, August 1984.
4. ESDU Aerodynamics Sub-series Vol 9a Data Item 90010, Pitching Moment and LiftForce Derivatives Due to Rate of Pitch for Aircraft at Subsonic Speeds, July 1990.
4IS
0
415.3 mm
49.6 mm 1. n
64.9 mmfIJ
Roll Balance
Figure 1: 80% 8 1mm mortar model and roll balance
ModelAttachment Slecve Ten Slots Symm-trically Roll Rate Pickup
Device Arranged Around Periphery (returns ten pules per revolution)
./// Ait-Aclivaledz HBrake4
hecaringss
F"•gure 2. Roll bala~we
1 9 • •
0.0
-0.3-0.4
. -0.3
-0.4
S -
U -0.5 ,-a5
-0.7 '•i- - $
"- -'<P,-- 0a 10*'
"408
"0.9
0.5 0.5os o00 0.65 0.70 0.75 0.30 0.35 0.90 0.9s
Mach No.
Figure 3: Roll damping coefficient, C1 p vs Mach No.
0.0
-0- EDO I.provd Mrt., P-oj•sil.-- ~~-'1- M174 .. oJ'taeproj~dIl0
.10.0
UU
J40.0 -1- ...... .. - 09
-40.0-
A4 _.L .. AA .. L.i..L..L .. LI, L1_1 I. iL1 ELI..i J.. L Il 1, 11 1 .I _I £k 1 1,11I
0@0 0.$5 040 045 070 0 75 0 t0 035 is 00 9
Mah4 No4
Figure 4: Pitch damping coeffi•ic•l, (',. vs Mach No.
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1!
APPENDIX A
DERIVATION OFCp
IS
S
0
0
S
10
Derivation of Cip
Symbols used:
C1 rolling moment coefficient
Cl. static rolling moment coefficient
CIp oll damping coefficient
d reference length (diameter)
p roll rate
V velocity
The data for .oDll rate versus time (see figure AI for an example of the ro;l rates obtained), weredifferentiated to produce values for roll acceleration versus time. From a knowledge of the rollinertia of the model, roll accelerations were then converted to roll torques, to give a set of rolltorques versus roll rate. Bearing friction torque, as calculated in Appendix B, was thensubtracted from the roll torque, producing values for aerodynamic torque versus roll rate. Theaerodynamic torque was non-dimensionalised to obtain rolling moment coefficients, Cl, versusroll rate.
Roll damping coefficient, C1 was calculated using the following equation:
8p d p,) *
Due to the model's rapid acceleration, and the timebase on the Hewlett Packard digital sooscilloscope used to record the data having to be set so as to cater for the high roll ratesexpected, roll rates less than 150 rad/s (- 24 Hz) could not be recorded. Due to the lack of lowroll rate data, it was decided to include zero roll rate data (static rolling moment coefficients)measured in earlier tests anrd reported in reference I. These data did not agree well with simpleextrapolation of the dynamic data (see figure A3), throwing some doubt on the intermediate rollrate data. To get the best estimate of Cl• it was decided to use only the two most reliable Clvalues, ie. Ci from static test data and C1 at the maximum (constant) roll rate Figure A2shows the straight line drawn for Mach 0.95 using only these two extreme values. The gradientof this line is the roll damping coefficient, Cl, for Mach 0.95. Cip values for all other Machnumbers were obtained from the same procedure.
Note that, in figure A2 the magnitude of the bearing friction relative to the aerodynamic torqueis indicated by the height above the roll rate axis at which maximum roll rate occurs. At thissteady state roll rate, bearing friction equals aerodynamic torque. It can be seen that maximumbearing friction is about 5% of maximum aerodynamic torque, and hence moderateuncertainties in the measurement of lxaring friction are not a significant contributor to theoverall uncertainty of the resulL
S
S
0 ----- ----- -I * 0 0 0
O0O: linmu-0a n4memmnmmlnmmi
50 - 0% n
#0 []0s M
a 40 I N30 -- 0- 0 N1
Em0 a0 a
3.,
20 w M-h 0 so
0 M* h 0.70
0 MOah 0.20
f Mdh 0.9010 U Mneh 0.95
LL1J- I I I I 1 1 1 1 1 .LLJLL.EJL LLLL L-L' L -lI J 1 LLLJ_, .LL L
P 5 t0 Is 20 23 30 35 40 45 50 35Timc (s)
Figure A 1: Roll rate vs time (for pitch angle 00)
0.014
• 0)0.000.0 12 h Md0 90
0.010
o - []in o * ed
15)
00
0 so 100 ISO 200 2I0 300 3S0 400 450
RIIR. (re.)
Figure A2: Rolling moment cocfficient vs roll rate (for pitch angle 00)
0
8.012"|4 _ "l 11z:" o dy m•M mV da
•"oi O.l M."
I 4l :
4.004
00004 Q3
0,000
0.002 LI
6.0"M L IL I I I , L5L_ I I L- L
a so too( I ýsa 200 250 300 350 400 450,
Figure A3: Comparison of Cio for Mach 0.95 and pitch angle= 0'
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iS
SL S
APPENDIX B
DETERMINATION OF ROLL BALANCE BEARING FRICTION
I
I
S•, ,". "• •;'•.*•" • • ,:'"• -, • '• • ,,••,,,•, ',, • -• ,•.•t, • -, . , • ,.,.s., .•,.•-.,,•:, - . .-
Determination of Roll Balance Bearing Friction
Tbe model was removed from the balance and replaced with a simple flywheel. Compressedair from an air hose was then used to spin the balance with the flywheel attached. Once thebalance had reached a roll rate slightly greater than the maximum constant spin rate observedduring the wind tunnel tests, the air hose was removed and the balance allowed to come torest. During this time, roll rate data were recorded and saved to disk. A Hewlett Packarddigital oscilloscope was initially set to record the expected high roll rates, and when the rollrate reached the lower end of the timebase range, the .imebase was changed so that the lowerroll rates could be recorded. This procedure was carried out several times and all results werecombined into one file.
The data for roll rate versus time were differentiated to produce values for roll accelerationversus time. From a knowledge of the inertia of the rotating parts, roll accelerations werethen converted to bearing friction torques, to give a set of bearing friction torques versus rollrate. The graph of bearing friction torque versus roll rate is presented in figure BI and hasbeen approximated in further c•Jculations by the two-segmented straight line fit shown there.
This method of measuring bearing friction neglects some parameters (eg. effects of variationsin axial and radial loads). In this use, however, the aerodynamic and gravity loads on thebearings are only a very small fraction of the bearing design loads, and so are assumed tohave a relatively small effect on the bearing friction characteristics. Also, bearing frictiongenerally accounts for only a small part of the calculated roll damping (in this case, less than5%) so that moderate uncertainies in the measurement of the bearing friction are not asignificant contributor to the overall uncertainty of the roll damping measurements.
In a previous use of this technique, test runs were conducted in an evacuated chamber (SIwind tunnel working section) to assess the contribution of aerodynamic damping. In thesetests aerodynamic damping of the flywheel was found to be negligible compared to bearingfriction.
S
0.000-
a for roll rat, < 100 (ad/3- Tne of filt
-0.0002 t 0rque - 0-001t + 4.90-6(ro1! Tate)
-0.0006
S-o~oooa -
for roll rate > 100 rads_-. torque -0.0003 + 2.1e-Orall rate)
.0.0010
ID M
-0.0020 L.LLI I L i Ln I L n i J n I J inL
0 100 200 300 400 50o
Roll Rate (rad!s)
Figure B I: Bearing friction torque of roll damping rig
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o
APPENDIX C
DERIVATION OF C"
p
S
S
o
S
S
Derivation of Cmq
"The following derivation was obtained and mudified from reference 4.
Notition:
ajF experimental lift curve slope of fin
Cq pitch damping coefficient
c reference length
d mortar diameter
i integer involved in summation to replace integral for (Mq)B
ka parameter in calculation of afterbody correction factor (I - ka)
kf correction factor for body fineness
1, body length
1 distance of moment reference point aft of body nose
M Pitching moment about moment reference point
(MI)B body contribution to total pitching moment derivative
(Mq)F fin contribution to total pitching moment derivative
q rate of pitch about moment reference point, positive nose up
Sn planform area of body
Sm cross-sectional area of body that contains maximum body width
Sw reference length (cross-sectional area of mortar at maximum body width)
Ve velocity of mortar relative to air in undisturbed flight
WB local body width
XB longitudinal distance along body axis to general body station, measuredpositive aft of moment reference point
x, longitudinal distance along body axis of 1/4 chord point of aerodynamicmean chord of fin, measured positive aft of raoment reference poiat
S
p density of air
In reference 4 the pitch damping coefficient, Cnl is defined as
Cm- p Ve S"•
This equates to the definition of pitch damping. CMq = (-), which is commonly used in
missile work, where two different reference lengths am used, namely; 0
= d (mismile diameter) for non-dimensionalising the pitching moments-d
and 9 = - (missile radius) for non-dimensionalising the pitch damping coefficient.2
0
Cq-I = ' p V. S. (d 21)p Ve Sw d 2)"
Cmq is calculated as the sum of two contributions, namely body and fin, ie
CM, = (M)B + (Mq)F
Body contribution, (Mq)B is calculated from
(2S) kf (I-k IBo0 2(Mq) = - s-)S (d2/2 W.xB dXB
To perform the integral in the equation above, the body was divided into twenty transversesegments of length 1,/20; these are numbered i = I to 20. from fore Io aft. The local bodywidth wBi and the local moment arm xai are determined at the midpoint of each segment. Theintegral may then be approximated as
B-10 2
Fin contribjhion, (Mq)F is calculated from
(Mq)F alFld2
where alF (in this case) comes from wind tunnel measured data.
Calculated pitch dampirg coefficients at various Mazh numbers are presented in thc tablebelow.
Mach No. (Mq)B (Mq)F Cmq 5
0.5 -5.760 -26.590 -32.3500.7 I-5.926 -33.g08 -39.734
0.8 -6.040 -35.314 -41.3540.9 .6,154 -43.096 -49.250S0.95 1-6.230 -43.136 .- 49.366 -
Table Cl: Pitch damping coefficients
As seen in table Cl, the body contribution is relatively small (-15% of the total), Thereforethe uncertainty in the estimated C,• depends largely on the quality of the tail lift data. Being
experimentally measured, this should be reliable. 5
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PITCH AND ROLL DAMPING INBWxSo• M -r 5CODNF (C) 24COEFFICIENTS OF AUSTRALIAN Fanx1=•D 0M • a•.81mm IMPROVED MORTAR PROJECTILE uL-M Lo).
4DOCUMNT91 ITI'LE ASRC
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Mortar ,ATWoM-SRoll damping 1902Pitch damping 0101Wind tunnel testsIt ANSTIACT
This report presents roll damping coefficients and pitch damping coefficients obtained fromdynamic rolling tests and static wind tunnel tests of the Australian 81mm lmpro)vd MortarIProjectile, IMP. An 80% scale model was used in the dynamic roll tests and a full scale model wasused in the static wind tunnel tests.
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